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Ultrafast switching of CO₂ laser pulses by optically-induced plasma reflection in semiconductors Elezzabi, Abdulhakem Y. 1995

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ULTRAFAST SWITCHING OF CO2 LASER PULSES BY OPTICALLY-INDUCEDPLASMA REFLECTION IN SEMICONDUCTORSByABDULHAKEM Y. ELEZZABIB. Sc.(Hon.), (Physics), Brock University, 1987M. Sc., (Physics), University of British Columbia, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJuly 1995© ABDULHAKEM Y. ELEZZABI, 1995In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis br scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)__________________________________Department of_______________________The University of British ColumbiaVancouver, CanadaDate j J’?f5DE.6 (2/88)AbstractUltrafast mid-infrared laser pulse generation using optical semiconductor switching isinvestigated experimentally for application to subpicosecond CO2 laser pulse generationat 10.6 Ilm. Time-resolved infrared measurements, which are based on cross-correlationand reflection-reflection correlation techniques, are used to determine the duration ofthe reflected infrared pulses from a GaAs infrared reflection switch. These time-resolvedmeasurements together with time-integrated measurements are used to derive a modeldescribing the behaviour of the GaAs infrared reflection switch. it is found that diffusionand two-body recombination whose rate is taken to be density-dependent, can accuratelydescribe the ultrafast infrared reflectivity switching process in GaAs. We have also investigated some novel semiconductor materials with ultrafast recombination lifetimes forultrafast semiconductor switching application. A molecular beam epitaxy low temperature grown GaAs (LT-GaAs) and radiation damaged GaAs (RD-GaAs) are successfullyused to switch out ultrashort CO2 laser pulses. Application of the time-resolved cross-correlation technique to nonequilibrium carrier lifetime measurements in highly excitedLT-GaAs, RD-GaAs, and Ino.85Ga1As/GaAs relaxed superlattice structure are foundto be in good agreement with other reported techniques. As an application to semiconductor probing, ultrafast infrared transmission experiments are conducted to determinethe absorption of infrared pulses in Si of various dopings after free carriers have beengenerated by absorption of a subpicosecond laser pulse of above band gap photon energy. By fitting the experimental data to a theoretical model, the free-carrier absorptioncross-sections and the momentum relaxation times are calculated.11Table of ContentsAbstract iiList of Figures viiiAcknowledgments xvii1 Introduction 11.1 Present Investigation. . 21.2 Thesis Organization 32 Semiconductor Switching and Ultrashort Laser Pulses at 10.6 1um 62.1 Introduction 62.2 Ultrashort Pulse Generation Using a CO2 Laser 62.2.1 Mode Locking of a CO2 Laser . 72.2.2 Optical Free Induction Decay (OFID) 92.2.3 Ultrashort Mid-Infrared Pulse Generation with Free Electron Lasers 112.2.4 Ultrashort Mid-Infrared Pulse Generation with Nonlinear FrequencyMixing 132.3 Optical Semiconductor Switching 152.3.1 The Semiconductor Switch 152.4 Ultrafast Optical Excitation 232.4.1 The Dielectric Function 242.4.2 Free-Carrier and Intervalence Band Absorptions 261113 Theory: Infrared Reflection from a Semiconductor Plasma3.1 Introduction ....,.,.,...3.2 Propagation of an Obliquely Incident Electromagnetic Wave in an Inhomogerieous Dielectric Medium3.2.1 The S-Polarized Electric Field Case3.2.2 The P-Polarized Electric Field Case3.3 Numerical Approach to the Solution: P-Polarization Case3.4 Reflection of 10.6 ,um Radiation from a Thin Film Plasma3.5 Temporal Variations of the Plasma Density3.5.1 Electron-Hole Plasma Recombination3.5.2 Diffusion and Time-Dependent Density Profile of the Free Carriers3.6 Simulation of the Reflectivity Pulses from GaAs4.4 Synchronization of the Hybrid CO2 Laser and the Femtosecond Laser System 934.5 Infrared Pulse Detection and Timing System 954.5.1 The Cu:Ge Infrared Detector 9528282831343744535356594 Laser Systems, Optical Setups, and Experimental Procedures 744.1 liltroduction . 744.2 The Femtosecond Laser System4.2.1 The Femtosecond Laser Pulse Generation System4.2.2 The Femtosecond Laser Pulse Amplifying System4.2.3 The Subpicosecond Dye Laser Pulse Amplifier . .4.3 The CO2 Laser Oscillators4.3.1 The CW CO2 Laser Oscillator4.3.2 The High Pressure TEA CO2 Laser Oscillator . .4.3.3 The Hybrid CO2 Laser75•75767777778090iv4.5.2 Electronic Amplifier.4.5.3 Experimental Data Collection System4.6 Hall Conductivity Measurements in Si4.7 Autocorrelation Pulse Width Measurements4.8 Optical Semiconductor Switch Setup4.9 Time Integrated Infrared Reflectivity Setup4.10 10.6 tm Pulse Width Measurement Techniques4.10.1 Reflection-Reflection Correlation Procedure and Optical4.10.2 Cross-Correlation Procedure and Optical Setup4.11 Infrared Pulse-Frequency Measurement Technique4.11.1 The Image Disector4.11.2 Optical Setup and Alignment of the Image Disector4.11.3 Calibration of the Image Disector Optical System5 Experimental Investigation of Infrared Reflection from GaAs 12496979999105107108109111115116116118Setup5.1 Introduction5.2 The Si Transmission Cut-Off Optical Switch .5.2.1 Theoretical Considerations5.2.2 Transmission Cut-off Results at 10.6 jim5.2.3 Discussion of the Transmission Results5.3 Ultrafast 10.6 jim Reflectivity Pulses from a GaAs Switch5.3.1 Time-Integrated Infrared Reflectivity5.3.2 Reflection-Reflection Correlation Measurements5.3.3 Cross- Correlation Measurements5.3.4 Discussion of the Time-Resolved Results5.3.5 Modeling of Free-Carrier Density and Reflectivity124125127132136143143147153155161v5.4 Frequency Spectrum Measurements 1666 Ultrafast Semiconductors for 10.6 Itm Optical Switching 1716.1 Introduction 1716.2 The Need for Semiconductors with Ultrashort Carrier Lifetimes 1716.3 Ultrafast Recombination Semiconductors 1736.4 Using Low-Temperature Grown GaAs for Ultrafast Pulse Generation . 1756.4.1 MBE Growth of LT-GaAs Layers 1766.4.2 Subpicosecond 10.6 m Pulse Generation from LT-GaAs as a Reflection Switch 1786.5 Using Radiation Damaged GaAs for Ultrafast Pulse Generation 1796.5.1 RD-GaAs Samples’ Preparations and Characterizations 1836.5.2 Subpicosecond 10.6 um Pulse Generation from RD-GaAs as a Reflection Switch 1856.6 Using Ino.s5Gao.iAs/GaAs GaAs for Ultrafast Pulse Generation 1906.6.1 MBE Growth of Ino.s5Ga015As/GaAs Relaxed Superlattice . . . 1906.6.2 Ultrafast 10.6 m Pulse Generation from In085Ga0isAs/GaAs asa Reflection Switch 1916.7 Conclusion of the Chapter 1937 Conclusions and Suggestions for Further Work 1987.1 Introduction 1987.2 Summary and Conclusions 1987.3 Suggestions for Further Work 2017.3.1 Ultrashort 10.6 um Laser Pulse Generation by Beam Deflection . 2027.3.2 Back Surface Infrared Reflectivity Measurements 206viBibliography 208Appendices 227A Design Circuits of the Synchronization Unit 227B The Fast Photodetector Amplifier Circuit and Performance 234C Circuit Design of the Pulse Integration Module 237D The Autocorrelator Design and Optical Components 249D.1 Calibration of the Autocorrelator 252viiList of Figures2.1 Principle of OFID short pulse generation. (a) In the time domain, (b) inthe frequency domain 122.2 Typical schematic configurations of optical semiconductor switching operating in a (a) reflection mode, (b) reflection-transmission mode. I =infrared beam (pulse), C = control pulse, S = reflection switch, S2 =transmission switch, R1 and R2 are the infrared reflected pulses, T1 is thetransmitted infrared beam (pulse) and T2 is the transmitted pulse. . . 173.1 An incoming wave whose electric field, E1, is normal to the plane of incidence (S-polarization) 333.2 An incoming wave whose electric field, E1, is parallel to the plane of incidence (P-polarization) 363.3 10.6 tm laser radiation magnetic and electric field amplitude compollentsB (curve a), E (curve b), and (curve c) as a function of = -yz inGaAs. The initial carrier density is n = 5n. Solid curves represent thereal parts and dashed curves represent the imaginary parts 413.4 Brewster angle reflectivity for 10.6 tm laser radiation as function of anexponentially decaying plasma density profile of (a) GaAs and (b) CdTe.The inset figure shows an enlarged plot of the reflectivity for 0 ri/ne1.0 43viii3.5 Phase angle change as a function of plasma density. The solid lines are calculated from the differential equation model. Dashed lines are calculatedfrom the thin film plasma model 453.6 Geometry of the vacuum-plasma-semiconductor interfaces for the thin filmplasma model 483.7 Geometry of multiple reflections from vacuum-plasma and plasma -. semiconductor interfaces 503.8 Brewster angle reflectivity for C02-laser radiation as a function of freecarrier surface density of GaAs for (a) a uniform film thickness-y’ and(b) for an exponentially decaying density profile. The inset figure showsan enlarged plot of the reflectivity for 0 n/nc 1 523.9 The variation due to diffusion of carrier density, n(z, t)/n0 as a function oflongitudinal position and time. The curves are plotted in increasing timesteps of 500 fs. The top curve is calculated at t= 0 ps, and the botttomcurve is calculated at t= 4.5 Ps 603.10 Reflected 10.6 ttm pulses as a function of time for initial plasma densityof (a) n = 0.7flc, (b) n = 0.9nc, and (c) n = 6nc. The solid lines arecalculated from the differential equation model and the dashed lines arecalculated from the thin film plasma model 643.11 Reflected 10.6 m pulses as a function of time for initial plasma density of(a) n = 1.2flc and (b) n = 1.3n. The solid lines are calculated from thedifferential equation model and the dashed lines are calculated from thethin film plasma model 653.12 Phase change in degrees of the reflected 10.6 um pulses as a function oftime for initial plasma density of (a) n = 0.7nc and (b) n = 0.9n. Theplots are calculated from the differential equation model 67ix3,13 Phase change in degrees of the reflected 10.6 im pulses as a function oftime for initial plasma density of (a) n = l.2n and (b) n = 1.3n. Theplots are calculated from the differential equation model 683.14 Phase change in degrees of the reflected 10.6 ,um pulses as a function oftime for initial plasma density of n = 6n. The plot is calculated from thedifferential equation model 693.15 Illustration of the plasma profile used to estimate a constant plasma depthand density from a plasma density profile at a given time after the onsetof laser illumiation 703.16 (a) Normalized surface plasma density at z=0 as a function of time. (b)Effective thickness of the plasma film as a function of time 714.1 The layout of the femtosecond laser pulse generating system 784.2 An illustration of the 40 W CW CO2 laser. R = 0.4 Ml and FIV = 25 kV 814.3 The TEA CO2 laser using an automatically preionized, doublesided, LCinversion circuit. Electrical conductors (aluminum and copper) are shownshaded. The preionizer rod design is also shown below 824.4 (a) The CO2 laser LC inversion circuit and the preionizers connections.P.R.= preionization rod, S.G.= spark gap, and L.D.= laser discharge. (b)The equivalent circuit with C = 64.8 nF, L = 420 nH, R = 1.05 1, C= 64.8 nF, and Le = 6.8 nH 844.5 (a) Main electrode voltage without the glow discharge, VM’, and with theglow discharge, VM. (b) Preionizer/inversion current without the glowdischarge, Ip’, and with the glow discharge, Ip; the main electrode current,89x4.6 (a) The CO2 laser pulse shape at 10.6 ,um, with an energy of 800 mJ. (b)Longitudinal mode beating during the laser oscillation 914.7 The hybrid CO2 laser system arrangement 934.8 (a) Single longitudinal and transverse mode from the hybrid CO2 laser.(b) Same hybrid laser with the CW laser turned off 944.9 A layout of the synchronization between the hybrid CO2 laser and thefemtosecond laser pulse generating system 954.10 The Cu:Ge infrared detector bias/output circuit 964.11 Integrated output from the dual channel pulse integration module as afunction of the input pulse voltage amplitude. The solid circles denotechannel 1 and the empty circles denote channel 2 994.12 The autocorrelator. B.S.= beam splitter, PMT= photomultiplier, andKDP= second harmonic generation crystal (Potassium Dihydrogen Phosphate) 1024.13 Typical autocorrelation traces from the dye laser system. (a) Cavity lengthis optimum resulting in a pulse width = 370 fs. (b) Cavity length istoo short resulting in a pulse width = 500 fs; note the side peaks in theautocorrelation trace. (c) Cavity length is too long resulting in a pulsewidth = 830 fs. The time scale in (a) and (c) is 10 iis/div, whereas in (b)it is 20 Rs/div 1044.14 (a) Autocorrelation signal of an amplified, 1 mJ, 616 nm dye pulse showinga pulse duration of 490 fs. (b) Same conditions but with the injected pulsefrom figure 4.13(b) 1064.15 The experimental arrangement for a GaAs optical semiconductor switch. 107xi4.16 Typical experimental configurations used to measure the infrared pulse duration: (a) Reflection-reflection correlation experimental setup. (b) Cross-correlation experimental setup. B.S.= beam splitter, B.D.= beam dump,E.M.= energy meter, P.E.= power meter, R= reflection switch (GaAs),M= temporary mirror, F= filter (GaAs wafer), D= Cu:Ge infrared detector, and T= transmission switch (Si) 1124.17 Optical arrangement used to eliminate the rear reflection resulting fromthe first GaAs reflection switch 1154.18 Experimental optical setup for the reflected pulses spectrum measurement.T1= temporary mirror, and G= grating 1194.19 A typical oscilloscope trace of the output of the image disector showingten channels 1204.20 Samples arrangement 1204.21 Calibration curve of the spectrometer reading against the CO2 laser wavelength 1214.22 Image disector calibration curve. The error bars are the standard deviationof signals for 10 consecutive shots separated by 13.3 us 1235.1 Transmission signal temporal recovery of the P-type Si transmission cut-offswitch 1305.2 Calculated relative transmission for 10.6 1um radiation through a photoexcited Si wafer as a function of normalized free-carrier surface densityn0/nfor four values of of c [a= 0.1 (uppermost), 0.2, 0.3, and 0.5 (lowest)]. . 133xli5.3 Infrared pulse intensity hr detected for two different Si wafers at zerophotoexcitation as a function of visible laser pulse intensity incident onGaAs reflection switch. The solid line is a linear regression fitted to thedata points (empty circles) up to < 34, and the dashed line is a linearregression through the solid circles 1355.4 Relative transmission coefficient for an infrared laser pulse through basically intrinsic Si (p-type concentration of l.6x 10’ cm3) as a function offree-carrier surface density generated by photoexcitation. The full curve isthe best fitting theoretical prediction to the data points at a = 0.2. Thetheoretical curve for a = 0.5 is also shown (dashed) 1375.5 Relative transmission coefficient for an infrared laser pulse through basically intrinsic Si (p-type concentration of 2.6x 10’ cm3) as a function offree-carrier surface density generated by photoexcitation. The full curve isthe best fitting theoretical prediction to the data points at a = 0.2. Thetheoretical curve for a = 0.5 is also shown (dashed) 1385.6 Relative transmission coefficient as in figure 5.4 for n-type Si concentrationof 4.9x 10’s cm3). The full curve is the best fitting theoretical predictionto the data points at a = 0.5. The theoretical curve for a = 0.2 is alsoshown (dashed) 1395.7 Relative transmission coefficient as in figure 5.4 for n-type Si concentrationof 6x10’5 cm3). The full curve is the best fitting theoretical predictionto the data points at a = 0.5. The theoretical curve for a = 0.2 is alsoshown (dashed) 1405.8 Calculated transmission of p-type Si as a function of time 144xlii5.9 Typical ultrafast reflected infrared pulses (left) and their correspondingexcitation visible pulses (right). The bottom photograph is presented toillustrate the reproducibility of the experimental signals 1465.10 Experimental results of the normalized time integrated reflectivity as afunction the normalized free-carrier density 1485.11 Reflection-reflection correlation signal for an excitation fluence corresponding to 7Fh/n= 3. . 1505.12 Reflection-reflection correlation signal for an excitation fluence corresponding to 7Fh/n= 5 1515.13 Reflection-reflection correlation signal for an excitation fluence corresponding to ‘yFh/n= 7 1525.14 Cross-correlation signal as a function of time for -yFh/n= 0.7 (solid), 2.0(empty) 1565.15 Cross-correlation signal as a function of time for 7Fh/n= 3.0 (empty),15.0 (solid) 1575.16 Reflectivity pulses as a function of time for-yF2i,,/n= 3 (solid), 15 (dash-dot), and 2 (dash) 1585.17 (a) Normalized density as a function of the longitudinal position and fortimes t/r= 0.5 (short dash), 1.0 (solid), 27.00 (long dash) and 125.00(dot-dash). The initial normalized plasma density 7Fh/n= 10. (b) Theinsert indicates the normalized surface plasma density as a function ofnormalized time 1645.18 Model calculations as a function of normalized time of: the normalizedinfrared pulses for 7Fh/n— 10 (upper solid line) and 2 (lower solid line),normalized cross-correlation signal for 7Fh/n— 10 (dash-dot), and normalized reflection-reflection correlation signal for ‘-yFh/n= 10 (dash). . 167xiv5.19 Model calculations for time integrated reflectivity (reflected pulse energy)as a function of the normalized carrier density. The vertical axis scaleunits are arbitrary 1685.20 Wavelength shift of a reflected infrared pulse with an initial excitationfluence of 7Fh/n= 7 1706.1 (a) Schematic diagram representing the LT-GaAs growth layer. (b) Scanning electron micrograph of the LT-GaAs layer 1806.2 (a) A cross-correlation transmission signal between the JR pulse and thevisible pulse creating the transmission temporal gate. The solid line is themodel calculations. (b) The infrared pulse as obtained from differentiatingthe cross-correlation curve 1816.3 Variations of the reflected JR pulse energy as a function of the e-h plasmadensity. The LT-GaAs layer thickness is ‘—i 2 1um 1826.4 Real and Imaginary parts of the dielectric function of undamaged GaAssample (solid) and the ion damaged (dashed). For the damaged GaAs, theion dose level is lxlO’6 cm2 1876.5 Cross-correlation measurements for the reflected infrared laser pulses foran ion damage dose of (a) lxlO’2cm,(b) lx cm2 and (c) lx 1016cm2. Note that in all plots, the cross-correlation signal is plotted inarbitrary units which differ for each diagram 1886.6 Measured 10.6 1um infrared laser pulse widths as a function of the 11+ iondose in GaAs 1896.7 A schematic diagram of the Ino.85Ga .,5As/GaAs relaxed superlattice. . 1946.8 Cross-correlation infrared reflectivity signal as a function of time delay. 1956.9 Differential of the cross-correlation, I, curve as a function of time 196xv7.1 Schematics of the all-optical beam deflector used for ultrashort pulse generation 2057.2 Schematics of the backside infrared reflection experiment 207B.1 The amplifier circuit 235B.2 Photodetector amplifier gain as a function of the input frequency 235B.3 (a) Input signal to the amplifier. (b) Amplified output signal from theamplifier 236D.1 Low pass filter and amplifier circuit used for the autocorrelation pulsemeasurements 251xviAcknowledgmentsI wish to especially thank my supervisor, Prof. Jochen Meyer, for providing me withthe opportunity to work with him and for creating an intellectually stimulating researchenvironment. His constant guidance and encouragement are most appreciated.I deeply thank and appreciate my parents, Youssef Elezzabi and Amna Quaia, and therest of my family, for allowing me the opportunity to pursue my post-secondary studiesin Canada, and for their continuous moral support.Special thanks goes to Lara Cleven whose encouragement and help made the experimental setbacks insignificant.It is also a pleasure to acknowledge Hubert Houtman for a great deal of assistance,guidance, and endless hours of stimulating discussion, which have had a strong positiveimpact on my research.Thanks to my colleague Michael Hughes for his help in operating the experiments, hisassistance in setting up the laser systems, and his valuable discussions. His help accelerated my progress.Thanks to Shane Johnson for growing the semiconductor structures.Prof. Irving Ozier deserves thanks for his thorough reading of the thesis and suggestionsfor the manuscript corrections.Also, I wish to express appreciation to Prof. Thomas Tiedje for the use of the MBEmachine and his useful experimental assistance.Thanks to my fellow colleagues: Ross McKenna, Steven Leffler, Dr. Peter Zhu, Dr. SamirAouadi, Dr. Michel Laberge, and Dr. James Booth. Their presence made the work moresatisfying and pleasant.xviiMy special thanks are extended to the following persons for the unequalled technicalsupport:Philip Akers, Jacobus Bosma, Ole Christiansen, Domenic Di Tomaso, Tom Felton, JamesGislason, Stan Knotek, Heinrich Manfred, Beat Meyer, Joseph O’Connor, Mary AnnPotts, Brian Smith, Douglas Wong, and especially to Alan Cheuck for providing greatservice arid ensuring that the equipment worked and that supplies were available.Thanks are also due to the staff of the U.B.C. Physics Department: Bridget Hamilton,Lore Hoffmarin, and Kim Spears for superb administrative help.The financial assistance of the Libyan Ministry of Higher Education, and the NaturalSciences and Engineering Research Council is appreciated.xviiiChapter 1IntroductionSince the first demonstration of optical semiconductor switching by Alcock et al. in 1976[43], the technique has gained wide interest to its potential application iii generating femtosecond laser pulses at 10.6 ,um. Despite the rapid advances in ultrafast laser technologyin the last decade, the focus of femtosecond laser research is directed towards visible, nearinfrared, and ultraviolet wavelengths. In comparison to other laser wavelengths, minimalresearch has been devoted to ultrashort pulse generation schemes at 10.6 tm. Ultrashortcoherent mid-infrared laser pulses are of interest for the investigation of fundamental processes occurring on short-time scales which cannot be studied with the current ultrafastlasers. Ultrafast CO2 laser pulses operating in the mid-infrared range are of valuableinterest to many research fields. Femtosecond/picosecond 10.6 um laser pulses have awide range of application to semiconductor physics, plasma physics, and chemistry.In semiconductor and solid state physics, ultrashort 10.6 m lasers provide an important tool for exploring several fundamental processes involving carrier dynamics, such asintraband transitions, interband transitions in low band gap materials, intervalence bandabsorption of free holes, free-carrier absorption, intersubband transitions in quantumwells, momentum relaxation times, carrier lifetimes, carrier energy relaxation rates, anddiffusion coefficients. Many of the experimental conclusions can be gained by time resolved measurements of transmission and reflectivity changes induced by nonequilibriumcarrier distributions. The knowledge of these processes aids in the development of newand faster semiconductor and optoelectronic devices. Moreover, ultrashort mid-infrared1Chapter 1. Introduction 2pulses are essential for testing high-speed mid-infrared devices such as detectors andmodulators. In the field of photochemistry, femtosecond 10.6 jtm infrared laser pulsesare of great interest for application to infrared spectroscopy of molecules. The advancesin ultrashort pulses have permitted the investigation of the vibrational-rotational modesin polyatomic molecules, study of fast chemical reaction rates and dynamics, chemicalkinetics and energy transfer in liquids, multiphoton excitation, multiphoton ionization,infrared absorption, and local charge distribution of organic molecules. A 10.6 m ferntosecond laser pulse provides an important tool for application to ultrafast nonlinearprocesses in laser-plasma interactions.1.1 Present InvestigationThe primary objective of this thesis work is to perform a complete experimental study offemtosecond CO2 laser pulse generation operating at 10.6 tm as a part of the developmentof a subpicosecond terawatt table top laser system. To achieve this goal we would liketo employ optical semiconductor switching techniques to generate these pulses. Clearly,before developing such a laser system, there are several studies that must be performed.Specifically, the main issues addressed in this work are:1. The feasibility of generating femtosecond laser pulses at 10.6 m using a singleoptical semiconductor switch, including the switching dynamics of the optical semiconductor switching mechanism to determine the limits on the shortest pulse thatcan be generated.2. The study of the temporal behaviour of the reflected infrared pulses as a functionof injected carrier density.Chapter 1. Introduction 33. Investigation of the role of carrier diffusion and recombination on the speed of theoptical infrared switch.4. To explore some novel semiconductor materials for their use in mid-infrared ferntosecond pulse generation.5. To investigate the use of infrared probing for the measurement of carrier lifetimes.6. To measure the free-carrier absorption cross-sections and momentum relaxationtimes in semiconductors.7. To develop accurate methods for measuring mid-infrared laser pulse temporal shapes,and to explore their limitations and sensitivities.8. To develop simple models that describe the infrared reflection/transmission semiconductor switching process.1.2 Thesis OrganizationThis thesis is divided into seven chapters discussing the details of the experimental andtheoretical work. Four appendices are devoted to the aspects of some technical designsof the experimental equipment. The thesis is organized as follows: the standard methods used in the generating of laser pulses in the mid-infrared range, and especially at10.6 m, are briefly discussed in Chapter 2. A qualitative overview is presented for eachexperimental technique evaluating its general features, advantages, and limitations. Anintroduction of the physical process of optical infrared semiconductor switching and theprinciples behind the generation scheme are also presented in this chapter. The generalformalism describing the dielectric function of a semiconductor along with some important absorption processes at 10.6 m are also introduced in Chapter 2.Chapter 1. Introduction 4In Chapter 3 a model describing the illfrared optical semiconductor switching processis presented. The model is based on the reflection of the infrared radiation from a thinplasma layer with the carrier dynamics determined by ambipolar diffusion. The wavepropagation equation is solved numerically for some experimental semiconductor plasmaconditions, and the time evolution of the plasma is governed by ambipolar diffusion. Fromthe numerical simulations, femtosecond/picosecond pulse generation conditions and characteristics are obtained. The calculations presented in this chapter provide the necessarybackground on the subject of infrared semiconductor switching.A brief description of the experimental equipment that are used during the investigation, the optical setups, and the experimental conditions are presented in Chapter 4.Part of this experimental work is dedicated to the installation, maintenance, and characterizations of the commercial laser system. Thus, a brief review of the major laser systemcomponents is outlined. The details of the construction and the design of the high-powerCO2 laser are also reviewed in this chapter. The electronic and optical instrumentationsthat are constructed and developed for specific experimental purposes are also brieflydiscussed in this chapter. Moreover, the specific techniques and the optical setups fortime-resolved and frequency-resolved measurements used to perform the experiments areoutlined in detail.The time-resolved and time-integrated experimental results on optical semiconductorswitching using GaAs are presented in Chapter 5. Interpretations of the experimentaldata and some estimates of the importance of the physical mechanisms governing the timeevolution of the switch reflectivity are discussed. Based on the experimental observations,a simple model describing the switching process in GaAs is developed to predict theswitching behaviour. The results for free-carrier absorption cross-section and momentumrelaxation times in both doped and intrinsic Si transmission cut-off switches are presentedin the same chapter. A complete model describing the infrared transmission through SiChapter 1. Introduction 5is developed and compared with the experimental results.The growth procedures, sample preparations, and the experimental results of novelultrafast recombination semiconductors are discussed in detail in Chapter 6. Here, theresults of infrared probing of the temporal carrier lifetimes of several semiconductors arepresented. Ultrashort 10.6 pm pulses generated using ultrafast recombination semiconductors are also discussed.Finally, in Chapter 7, we briefly summarize the results of the thesis, with specialemphasis on the major original thesis contributions. A concluding remark on the natureof the free-carriers’ recombination mechanism in GaAs is made. Moreover, suggestionsfor an interesting ultrashort pulse generation scheme and a novel optical arrangementfor semiconductors probing are presented. Also, a numerical estimate on the limit ofgenerated pulse duration is discussed in this chapter.Chapter 2Semiconductor Switching and Ultrashort Laser Pulses at 10.6 tIm2.1 IntroductionThis chapter is intended as an overview of the basic physics and technology dealing withthe generation of ultrashort laser pulses in the mid-infrared region. Since our objectiveis to produce subpicosecond pulses at the CO2 laser wavelength, the review is directedtowards mid-infrared pulses generated at a wavelength of 10.6 sum.The first section of this chapter introduces the essential issues and constraints associated with the generation of ultrashort laser pulses at 10.6 m. The second sectionpresents brief overviews of some standard techniques employed for ultrashort 10.6 mpulse generation such as: mode locking, optical free induction decay, nonlinear frequencymixing, and free electron lasers. In the third section, we introduce optical semiconductor switching, and discuss the basic physical principles behind the generation scheme.Finally, in section four, we present some relevant processes which occur during ultrafastoptical excitation of the semiconductor switch and introduce the semiconductor switchdielectric function.2.2 Ultrashort Pulse Generation Using a CO2 LaserBefore proceeding with the techniques of iiltrashort pulse generation, one should highlightthe basic physical principles that govern the generation of ultrashort laser pulses at 10.6m.6Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 um 7The gain spectrum of the CO2 laser consists of several discrete vibrational-rotationallines. In order to produce subpicosecond laser pulses directly from the laser medium,the gain spectrum must be wide enough to amplify these pulses, The gain spectrumof the CO2 laser can be enhanced to support the generation of ultrashort laser pulsessimply by increasing the operating laser gas pressure [1]. The overlap of the adjacent rotational lines of the CO2 molecules modulates and widens the gain spectrum and helps tominimize pulse distortion. However, high pressure operation decreases the gain risetimeand lifetime due to the increased collisional excitations/de-excitations of the laser levels[2]—[4]. In other words, due to high gas pressure, the excited CO2 molecules relax faster(inversely proportional to the pressure). In addition, the limited gain lifetime restrictsthe duration of the generated pulse by limiting the effective number of pulse round tripsin the laser cavity. That is, if the generated pulse is to be made short enough, a highernumber of cavity round trips is required to take advantage of the wide gain spectrum. Itwas pointed out by Houtman and Meyer [5] that the gain duration for a 10 atmosphereCO2 laser is only 750 us at FWHM (full width at half maximum) and hence, activemode lockers cannot produce pulses shorter than 800 ps. These two facts reduce theeffectiveness of ultrashort pulse generation by mode locking [5, 6].2.2.1 Mode Locking of a CO2 LaserDue to the limited gain bandwidth of a TEA (transverse electric atmospheric) CO2 laser,the long 100-200 ns pulses from a so-called hybrid CO2 laser (a combination of aCW laser and a TEA laser sharing the same laser resonator) can be shortened by modelocking of multiatmosphere transversely excited lasers. Passive and active mode lockingtechniques are commonly used to shorten the duration of a laser pulse.Passive mode locking relies on absorption saturation to generate amplitude modulation by providing an intensity-dependent loss in the laser cavity. That is, the transmissionChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 im 8of a saturable absorber follows the shape of the radiation laser pulse; the peak of thelaser pulse experiences a lower loss than the wings, consequently, the peak of the pulse isamplified, thus resulting in the pulse compression. The technique is especially successfulin generating ultrashort pulses of less than 1 ns [7]—[13] at 10.6 tm. The minimum pulseduration that is achievable with a fast saturable absorber is limited by the absorber’srecovery time and the CO2 laser gain line width. Laser pulses of a duration between 1to 5 ns have been generated using SF6 as a fast saturable absorber [7, 8]. Shorter pulsesof duration between 80 to 500 Ps were obtained by using P-type Ge as a bleachableabsorber [9]—[13]. The CO2 laser pulses generated with passive mode locking techniquesare limited in their pulse duration to ‘ 80 ps.Active mode locking utilizes the beating of the laser oscillation with an externaloscillator frequency [14]. The gain or loss of the laser cavity is periodically modulatedat the oscillator’s frequency (amplitude modulation or frequency modulation) [14]. Acomplete review of the subject of active mode locking is presented in reference [15].Actively mode locked multiatmosphere CO2 lasers [5, 11] [16]—[19], result in longer pulsedurations (‘-.-‘ 1 ns) than the passive mode locking technique. Pulses as short as 500ps (detector limited) have been generated by Houtman et al. [16] with a novel square-wave mode locking and cavity dumping of a 10 atmosphere CO2 laser system. Thispulse generation system produced the shortest pulse ever generated using an active modelocking scheme. In general, the technique can be used to produce pulses as short as 200ps [15, 16]; however, the amount of extracted power is limited to low damage thresholdof the pockels cell crystal.The short gain lifetime and the lack of a wide gain bandwidth necessary to support thegeneration of picosecond or femtosecond pulses makes the generation of pulses shorterthan 500 Ps very challenging by the standard mode locking techniques similar to theones applied to solid state lasers [14]. For these reasons, alternative nonconventionalChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 um 9ways to produce ultrashort mid-infrared laser pulses have been developed: includingoptical free induction decay, free electron lasers, nonlinear frequency mixing and opticalsemiconductor switching.2.2.2 Optical Free Induction Decay (OFID)OFID is originally proposed and demonstrated by Yablonovitch and Coldhar [20] as amethod for generating high power picosecond pulses at 10.6 hum. The central componentsof the system are: a single mode high-power CO2 laser, a plasma shutter, and a hot CO2absorption cell. The principle behind OFID is simple: first the frequency spectrum ofthe CO2 laser pulse has to be widened and then the original central frequency is filteredout. In such pulse generating systems, an optical transmission switch turns off a longsingle mode CO2 laser pulse in a time of approximately a few picoseconds. As a resultof this ultrafast pulse truncation, frequency sidebands are generated around the centralfrequency of the CO2 laser line. The central component frequency can be rejected byusing a narrow resonance absorption filter such as hot CO2 gas. A hot CO2 gas onlyallows the sidebands of the frequency spectrum to be transmitted, hence, producing anultrashort pulse. An alternative time-domain explanation of the OFID process is toconsider a CO2 cell which is heated to ‘- 450 °C to increase the absorption of the 10.6m radiation. If the hot cell is long enough, then a complete attenuation of the CO2laser beam is possible. Under a steady state one can view the absorption process as adestructive interference between the CO2 laser radiation electric field and the inducedelectric-dipole radiation from the hot CO2 gas. The polarization induced electric field isalways coherent with the input electric field but with the opposite phase. Now, whenthe CO2 electric field is suddenly turned off by the plasma shutter in a time durationwhich is much faster than the relaxation time of the CO2 molecules, then the fields are nolonger canceled by destructive interference and the excited CO2 hot molecules continueChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 m 10to radiate in phase with each other (but still out of phase with the applied electric field).That is, turning off the input signal quickly results in the generation of an ultrashort pulsewhose width is limited by the relaxation time (due to dephasing and energy decay) of thedipole radiation. Figure 2.1 illustrates the OFID principle both in time and frequencydomains.The CO2 laser pulse duration can by approximated by the following empirical formula[21]:Tp(pS) o.67() + 10 (2.1)where Td, -ye, and £ are the dephasing time of the resonant absorber, absorption coefficientof the resonant absorber, and its length, respectively.Several OFID experiments employing various shutters [20]—[30] demonstrated the feasibility of this technique in the generation of ultrashort picosecond pulses of a durationadjustable between 33 and 200 ps. The pulse duration is found to be strongly dependenton the CO2 gas pressure which is related to the relaxation time, Td, through the relation[24]:Td(ns) = 42 (2.2)PJ9/300where P and 9 are the CO2 gas pressure in torr and its temperature in degrees Kelvin,respectively. The relaxation time of the CO2 molecules limits the width of the generatedpulses to 30 ps. Other techniques must be employed to reduce to pulse duration below30 Ps.Scherrer and Kneubiihl [25] proposed a new picosecond 10 tm CO2 laser based systemwith far-infrared laser gases (CH3F, D2O, and NH3) as spectral line filters. This OFIDsystem has advantages over the hot CO2 based OFID setup: it can be operated atconsiderably lower gas pressure and at room temperature; in addition, the frequency ofthe pulse can be selected very precisely by proper choice of the gas. However, to date,Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 ,um 11the authors did not present any measurements on their pulse durations using these gases.The OFID pulse is short when the dip in the frequency spectrum is wide [21]; therefore,a major concern, which is usually ignored in the literature and by groups performingOFID experiments, is the background level of the generated pulses. Since the generatedpulses lack the central frequency component in their frequency spectrum, the generatedpulses are in fact not as short as they are claimed to be. With simple mathematicalanalysis it can easily be shown that if one takes a Fourier transform of the OFID pulsefrequency spectrum, the results when mapped into time domain show a short spike of theorder of 30 ps riding on a significantly longer pedestal. The amount of energy containedin the background can be as high as that contained in the ultrafast peak. The pulsedurations are usually determined from autocorrelation measurements which, in all of thereported experiments [20]—[30], are performed above a certain background level.Moreover, in OFID experiments, there are always pulse transients following the initialfast spike lasting for ‘-.i 100 ps. These pulses contain 25% of the energy of the centralpeak [22]. Clearly, it is undesirable to have this type of background or post pulses forconducting time-resolved picosecond experiments.We should emphasize that OFID pulse generation cannot be performed with CW(continuous wave) CO2 lasers. The generation scheme requires a high-power CO2 laserwhich limits the repetition rate of the pulse train to that of the high-power laser.2.2.3 Ultrashort Mid-Infrared Pulse Generation with Free Electron LasersA free electron laser is a device which consists of a linear accelerator (an electron gun,a pulse compression section, and traveling-wave acceleration stage), an electron transport system, an undulator magnet array and an optical resonator cavity [31]. Injectedelectrons exhibit periodic oscillations in the undulator magnetic field (made from a series of magnets of alternating polarities) and lose energy through synchrotron radiation.Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 umHybrid CO2Laser Plasma Shutter OFID Filter70 MHz 100 GHz 70 MHzFigure 2J: Principle of OFID short pulse generation. (a) In the time domain, (b) in thef10Ons(a)(b).i_10 PS—3OO PSfrequency domain.Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 um 13A resonance condition can be achieved through the interaction of the electrons withthe electromagnetic field and the undulator magnetic field which causes the electrons toform bunches in a scale comparable to the optical wavelength. This resonance conditionprovides photon emission coherence and optical gain.Free electron lasers generate a wide band laser spectrum. Recently, free electronlasers have been used to generate ultrashort infrared pulses covering wide ranges ofwavelengths and durations [32]—[36]. The micropulse widths are measured to be between3 - 12 ps with peak powers up to 10 MW at a peak wavelength of 8 m. These pulses areemitted in macropulses of a duration of “-‘ 10 ts at a repetition rate of ‘-‘-‘ 6-50 Hz [35].Glotin et al. [32] pointed out that the limiting factor in reducing the pulse width is theamount of detuning of the cavity length. In their experiment, they managed to producedsubpicosecond pulses as short as 200 fs at 8.5 ,um by simply dephasing the RF field by300 relative to the electron bunches in the accelerator stage. However, the second orderautocorrelation traces presented in the publication [32] show a short 200 fs spike on topof a long - 1 Ps pulse. We believe that because of the nature of the autocorrelationmeasurements, a small noise signal in the pulse trace can show the same effect. Clearly,a time-resolved cross correlation experiment (see section 4.10.2) should definitely providethe exact pulse duration.Since the electron bunches must be accelerated up to ‘ 50 MeV, short pulse generation with free electron lasers is a very complicated, expensive, cumbersome process, andcannot used as a table top ultrashort infrared system.2.2.4 Ultrashort Mid-Infrared Pulse Generation with Nonlinear FrequencyMixingRecently, remarkable progress has been made in the generation and the tunability ofultrafast mid-infrared pulses by using nonlinear difference frequency mixing [37]—[42].Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 1am 14There are several techniques of frequency mixing: to produce a pulse at a wavelengthAir= 10.6 jim, two ultrashort near infrared pulses are needed. For example, if a 1.064tm pulse from an Nd:YAG laser and a 1.183 1um pulse from a dye laser are directedsimultaneously into a nonlinear mixing crystal (GaSe) one can produce coherent photonsat 10.6 jim. A variation on this method consists of amplifying pulses from a femtosecondlaser oscillator and using these pulses to generate a broadband continuum, a selectedfrequency range from the continuum spectrum is in turn mixed with the laser oscillatorfrequency to produce ultrashort mid-infrared pulses [42].Dahinten et al. [40] generated 1 Ps mid-infrared pulses via difference frequency mixingof a mode locked Nd:glass laser 2 Ps pulses at ). = 1.053 1um and tunable traveling-wavedye laser pulses (dye heptamethine pyrylium: 5: 1.16 ,um -1.4 m and dye A 9860: 1.10im-l.6 sum) in AgGaS2 and GaSe crystals. The resulting output covers a broadbandmid-infrared spectrum between 4 m and 18 m with photon conversion efficiency ashigh as 2%. For wavelengths above 10 m, GaSe is used as a mixing crystal. The peakenergy of the 1 Ps 10.6 m pulses is measured to be of the order of a 0.2 iJ.Becker et al. [39] generated mid-infrared pulses by frequency mixing two colourfemtosecond mode locked Ti:sapphire laser pulse in a AgGaS2 crystal. The Ti:sapphirepulses can be tuned from (760 nm to 790 nm) and (820 nm to 865 nm) and the generatedinfrared pulses can be tuned between 7 um to 12 m with a constant pulse duration of310 fs over the whole tuning range.The generated pulse duration is only limited by the duration of the shortest of the seedpulses, and by group velocity dispersion in the nonlinear mixing crystals. On time scalesless than or equal to 1 picosecond, the pulse broadening effect is found to be directlyproportional to thickness of the nonlinear mixing crystal [38]. Seifert et al. [38] pointedout that frequency conversion in a AgGaS2 crystal with laser pulse wavelengths below 1m restricts the duration of the mid-infrared pulse to the lower limit of approximatelyChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 tim 15300 fs. They attributed this lower limit to the group velocity dispersion of the laserpulses iii the nonlinear mixing crystal. They demonstrated that by mixing regenerativelyamplified Ti:Sapphire (740 nm to 850 nm) pulses with 1 tim to 2.5 tim pulses generatedfrom an optical parametric generator/amplifier system, pulse durations of 160 fs (50nJ, 1 kHz) are produced with wide tunability range between 3.3 tim to 10 tim [38].Iii view of the above progress on difference frequency mixing, this method is verypromising for the generation of femtosecond pulses at 10.6 tim. However, in terms ofconversion efficiency, semiconductor switching may have an advantage over nonlinearfrequency mixing. It should be noted that since the frequency mixing process is highlynonlinear, one requires high-power infrared pulses for the mixing process.2.3 Optical Semiconductor SwitchingApplication of optical semiconductor switching technique for the purpose of generatingsubpicosecond 10.6 tim laser pulses from a CO2 laser is discussed below.2.3.1 The Semiconductor SwitchOptical semicoilductor switching of 10.6 tim CO2 laser radiation [43]—[60] offers an alternative and a much simpler method for the generation of ultrashort laser pulses than thepreviously discussed methods. It is based on the principle of modulating and enhancingthe reflection and transmission characteristics of a semiconductor by optically controllingthe free-carrier density. This technique is often used outside the infrared laser cavity totemporally gate an ultrashort pulse from a long 10.6 tim pulse or a continuous beam bysimply reflecting the infrared radiation from an optically injected semiconductor carriers. The process requires three simple components: an ultrafast visible laser pulse, aCO2 laser (pulsed or CW), and an optically-flat undoped semiconductor wafer that isChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 pm 16transparent to the 10.6 pm radiation or the infrared radiation to be switched out. Pioneering experiments by Jamison and Nurmikko [45] and by Alcock et al. [47] have shownthat photoinjection of a high carrier density ( l0’) in semiconductors modifies thereflectivity of the material to 10.6 pm. These experiments serve as the basis for opticalsemiconductor switching. The method has been demonstrated to provide a very powerfuland currently the only sub-100 fs pulse generation method in the mid- and far-infraredpart of the spectrum [55]. Its low power operation makes it very attractive compared tothe previous methods.The basic principle of optical semiconductor switching technique is illustrated in figure2.2 and is described as follows: a semi-insulating semiconductor is transparent to mid(far)-infrared laser radiation in the absence of free carriers. Semiconductor reflectivity toinfrared radiation is determined by the number density of free carriers (semiconductorplasma). The minimum electron-hole density needed to achieve a full reflection is knownas the critical carrier density, n, and it can be determined from the following expressionin c.g.s. units,4ire2 (2.3)where m*, w, Eb, and e are the effective carrier mass, the infrared radiation frequency invacuum, the static dielectric constant and the electron charge, respectively. For moderate photoinjection carrier density 1020 such critical density corresponds to a plasmafrequency, w, in the mid- or far-infrared regions. It should be noted that in deriving theabove expression for, the plasma absorption effects are ignored.The critical density at the CO2 laser wavelength is calculated to be i0’ cm3.For a specific operating infrared wavelength, )jr one selects an appropriate direct bandgap semiconductor which is transparent to the infrared radiation. This requires thatthe band gap energy of the semiconductor switch, E9, be higher than the energy of theChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 m 17(b)TFigure 2.2: Typical schematic configurations of optical semiconductor switching operating in a (a) reflection mode, (b) reflection-transmission mode. I = infrared beam (pulse),C = control pulse, S1 = reflection switch, S2 = transmission switch, R1 and R2 arethe infrared reflected pulses, T1 is the transmitted infrared beam (pulse) and T2 is thetransmitted pulse.CRIS(a)T2YS2CIRiSi T14Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 m 18infrared photon (117 meV for a CO2 laser photons). In order to obtaill a high sigilalto background ratio, the CO2 laser radiation is polarized in the plane of incidence (Ppolarized) and the semiconductor wafer is set at Brewster’s angle with respect to theinfrared radiation beam. With this optical arrangement, the 10.6 m laser radiation istransmitted through the switch and none of the radiation is reflected, thus reducing thebackground reflected signal to the zero level. This state is known as the off-state of thesemiconductor switch. In order for the infrared transparent switch to become reflectiveto the infrared radiation, one must increase the free-carrier density in the switch. Thiscan be accomplished by illuminating the semiconductor switch with an intense opticallaser pulse (control pulse) with photon energy exceeding the forbidden band gap energyof the semiconductor. The control pulse is used to photoexcite the electrons from thevalence band to the conduction band of the semiconductor switch by means of interbandabsorption. These carriers are confined in a thin layer of a thickness approximatelyequal to the absorption skin depth of the control pulse radiation. If a large enoughcarrier density, > n, is generated, then the semiconductor’s surface appears metallic tothe infrared radiation and effectively a very fast transient infrared reflecting “mirror” ismade at the semiconductor’s surface. That is, the photoexcited carriers cause a change inboth the refractive index and the extinction coefficient, resulting in infrared beam (pulse)being reflected at Brewster’s angle with the same divergence as the source infrared beam(pulse). The reflection efficiency of the infrared semiconductor switch at 10.6 im rangesbetween 40% to 80% depending on the density of the photoexcited carriers.For subpicosecond infrared pulse generation, the turn-on speed of the infrared reflectivity is determined by the photoinjection carrier generation rate, which in turn isdetermined by the pulse width of the excitation control laser pulse. liltrafast switchingcan be easily accomplished by photoinjecting the carriers with a subpicosecond visibleChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 itm 19laser pulse. The infrared semiconductor switch remains reflective as long as the photoexcited carrier density is above the critical density; hence, an ultrafast risetime infraredpulse is generated. The temporal termination (decay) of the reflected infrared pulse isdetermined by various carrier dynamics such as recombination and diffusion. It is shownlater in this work that by proper choice of the semiconductor material and the carrierdensity, the decay time of the reflectivity pulse can by dramatically reduced to a sub-picosecond time scale. The ultrafast temporal variation of the optical reflectivity andtransmission due to the semiconductor plasma can be used as a powerful diagnostic toolto probe the transient plasma dynamics on the picosecond or femtosecond time scale.Optical semiconductor switching has been widely used as an active switching element,placed outside the laser cavity, to temporally gate the already generated long pulses orCW far-infrared laser beams. Conventional mode locking, Q-switching of far-infraredlasers with electrooptic crystals is an extremely inefficient process; therefore, for fastoptical modulation at these wavelengths, optical semiconductor switching provides analternative. Ultrashort pulses at 119 um using H2O [58] and CH3O [52] lasers, andat 100-1000 um from a free electron laser [56] have been produced with this scheme;however, no attempt has been made to produce pulses in the far-infared region withpicosecond duration. Semiconductor switching has been applied to some novel cavitydumping techniques, where the semiconductor switch is placed at Brewster’s angle insidethe laser cavity, of optically pumped molecular gas far-infrared lasers such as: CH3Oat 119 um [59], NH3 at 90.8, 148, 292 im and CH3F at 231 um and 496 iim [57]. Theadvantage of using semiconductor switching is that output power is increased since thecirculating pulse can be coupled out of the laser cavity very efficiently.An interesting and effective method of producing ultrashort pulses is using a combination of two infrared semiconductor switches in series [55] (as shown in figure 2.2(b)).The first one is usually a GaAs or a CdTe wafer operating in the reflection mode toChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 m 20generate ultrafast risetime pulses, and the second switch is also set at Brewster’s angle;however, it is operating in a transmission mode. Silicon is usually used as a transmissionswitch due to its large free-carrier absorption cross-section and high reflectivity at 10.6im [55].The operation of the reflection-transmission combination switching method is as follows: the infrared reflected pulse, after being generated by the reflection switch, is directed onto the silicon transmission switch. Silicon transmits the infrared radiation; however, when it is irradiated with a delayed laser pulse (relative to the reflection switch)above band gap radiation, it results in the production of free carriers in a layer 3im thick. Due to the induced infrared reflection and free-carrier/intervalerice band absorption, the transmission property of silicon to the 10.6 1um pulse is altered from fulltransmission to zero in a short time that is required to reach the critical carrier densityand remains unrecovered for a long time (a few nanoseconds). The duration of the infrared pulses is determined by the time interval between the turn-on and turn-off times ofthe reflection and transmission switches, respectively. By proper adjustment of the relative delay of the excitation control pulses between the two switches, one can only allowthe fast rising edge of the infrared reflected pulse to pass through the transmission switch,thus, the transmitted infrared pulse width consists of the ultrafast rising edge from thereflection switch pulse and the ultrafast falling edge from the transmission switch. Figure2.2(b) illustrates a typical schematics of the reflection-transmission switching operation.Rolland and Corkum [55] used amplified 70 fs (620 nm) pulses from a colliding-pulse modelocked dye laser to control the switching operation. They demonstrated this techniquefor the generation of CO2 laser pulses at 9.5 im with duration as short as 130 fs. Thesepulses correspond to only - 4 optical cycles and are the shortest pulses ever generated atthe CO2 laser wavelength. With this method, it is possible to produce infrared pulses ofChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 m 21durations shorter than the excitation control pulse duration by simply reducing the duration of the excitation control pulse. Recently, table-top high-power, sub-30 fs pulses havebeen routinely produced in research laboratories; with the application of these pulses tosemiconductor switching, it is possible to reduce the infrared pulse duration even furtherto less than one infrared oscillation cycle of the CO2 laser. It seems that the limit of thegenerated pulse duration is mainly restricted by the risetime of the control pulse duration required to produce the critical plasma density in the transmission switch. Clearly,the drawback in using two semiconductor switching elements compared to one switchingelement lies in the fact that a high degree to synchronization between the two switchesmust be maintained very accurately by the optical setup. It is extremely advantageous interms of practicality and simplicity to use a single optical infrared semiconductor switchto generate subpicosecond 10.6 im laser pulses. This alternative possibility is part ofthis thesis investigation; therefore, in order to design such a device more effectively, anunderstanding of the physical properties of the photoexcited carriers is essential.To sum up, the advantages of using optical semiconductor switching compared toother ultrashort pulse generation schemes are:1. To perform the infrared switching, the technique requires oniy one ultrashort pulsewith a photon energy greater than the band gap energy of the semiconductor. Thismakes it simple and inexpensive to implement;2. A high reflection efficiency of 40% for a 1 ps pulse duration at 10.6 tm can beobtained;3. An ultrahigh pulse contrast ratio (signal/background) of the order of iO:i (for onereflective switch) can be achieved, and it can be increased to 106:1 by using tworeflective switches in series;Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 tm 224. The duration of the generated infrared pulses are oniy limited by the source controlpulse duration and the type of the semiconductor switching material;5. The power of the switched infrared pulses is only limited by the input power of thesource infrared laser;6. It offers the possibility of the generation of sub-30 fs infrared laser pulses at 10.6,um, and at other infrared wavelengths;7. No critical phase/wavelength matching conditions, nonlinear crystal temperaturecontrol, and group velocity dispersion are required for the switching process;8. It provides inherent synchronization between the optical control pulse and the reflected infrared pulse which is very useful for pump-probe type experiments;9. It can be applied to infrared laser beams or pulses of low power;10. The switched pulse duration can by varied over a wide range;11. The repetition rate of the reflected pulses is limited by the repetition rate of thecontrol laser;12. A high optical-damage power density of ‘s-’ 1 GW/cm2;13. The reflected and transmitted pulses basically map the temporal evolution of thesemiconductor plasma; therefore, the shapes of these pulses provide information onthe carrier dynamics in the semiconductor switch.A complete understanding of the processes involved in optical semiconductor switching requires the knowledge of the semiconductor plasma properties, the behaviour of theoptically generated carriers under ultrafast optical excitation, the dielectric function ofthe semiconductor, the propagation of the infrared radiation in a semiconductor plasma,Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 m 23and finally the absorption processes such as free-carrier and intervalence band absorptionthat may limit (enhance) the speed of the reflection (transmission) switch.2.4 Ultrafast Optical ExcitationThe dynamics of ultrashort laser pulse interaction with a semiconductor are very complex.In the following paragraphs we present the basic carrier dynamics and a sequence of thetime events in order to help in the understanding of infrared switching operation. Acomprehensive review on the subject is presented in references [61]—[74].When a semiconductor is excited by an ultrafast laser pulse whose photon energy isabove the band gap energy of the semiconductor, then electrons (e) and holes (h) areplaced into energy states that are defined by the band structure of the semiconductormaterial and the power spectrum of the absorbed light pulse. The free carriers can gainexcess kinetic energy from the difference between the excitation photon energy and theband gap energy of the semiconductor. Ill ultrafast optical excitation of GaAs with a 616nm laser pulse, a narrow band of states can be excited creating nonthermal free-carrierdistribution for a very short time which is comparable to the excitation pulse width. Theelectrons are initially injected to the I’ valley with excess energies. The electrons areexcited with three distinct energy values of: 0.5 eV (from the heavy hole band), 0.43 eV(from the light hole band), and 0.15 eV (from the split-off band). Approximately 84%of the electrons are injected from the heavy/light hole valence bands with equal strengthand the rest are injected from the split-off valence band. Optical excitation results inan instanteous production of extremely hot nonequilibrium electron and hole distributions. Carrier-carrier (e-e, and h-h) elastic collisions, due to Coulomb forces, is the initialinternal relaxation process which the electrons and holes immediately undertake afterexcitation. These scattering events take place in a time scale of the order of 10 fs,Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 um 24Clearly, since the effective mass of the electrons is smaller than that of the holes, theinitial temperature of the electrons is higher than the hole’s temperature. Energy canbe transferred from the hot electrons to the relatively cold holes through e-h scattering.The e-h collisions eventually drive the plasma towards a thermalized distribution (characterized by a common carrier temperature) within ‘-‘ 200 fs after excitation. The freecarriers are in thermal equilibrium among each other but not at equilibrium with thelattice which is still at room temperature. Cooling of the hot carriers occurs primarilythrough inelastic collisions between the hot carriers and phonons on a time scale of 2ps. The overall effect of relaxation is to reduce the carrier temperature and increase thelattice temperature. Carrier recombination takes place ‘—‘ 100 PS later after excitation.2.4.1 The Dielectric FunctionThe electrical and optical characteristics of a semiconductor are closely related to thedielectric properties of the material; therefore, it is essential to have an understanding of the dielectric function of the semiconductor switch so that one can predict itsswitching behaviour. Infrared reflection properties of the semiconductor switch can becharactretized by a complex index of refraction or in general by the complex dielectricfunction, (w)=1) +i2(w), where and e2 are the real and imaginary parts of thefrequency-dependent dielectric function. In general, i and 2 can be obtained from quantum mechanical calculations [75]—[79], which require a detailed knowledge of the bandstructure, and free-carrier distribution.A widely accepted model for the derivation of the dielectric function is based onDrude treatment of a free electron-hole gas [80]. The free carriers are described in termsof collective harmonic oscillations with a single frequency similar to ionized carriers ina gaseous plasma. In a semiconductor, when the optical frequency of the radiation ismuch less than the interband transition frequency between the valence and conductionChapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 urn 25band, the Drude model provides an excellent description of the dielectric function of theoptically excited carriers.A simple way of obtaining the dielectric function is to consider an isotropic one-dimensional, non-interacting classical free electron gas of density, n. The long wavelengthdielectric response function, E(w), of free electron gas can be modeled microscopically interms of the equation of motion of a free electron in a perturbing external electric field:d2 dm* + v_) 5r —eE. (2.4)Here i’ is the collision frequency, which describes the damping of the electron motion dueto phonons, impurities, and carrier-carrier scattering, etc., and it is inversely related tothe momentum relaxation time of the carriers; r is the spatial displacement; and m* isthe effective mass of the free carrier. By taking into account the polarization due to freecharges, P = —ne3r, the displacement vector D, and r from the solution to equation2.4, one obtains the Drude dielectric functioll of the form:/ w2 /f(w)=(1—--(1+i--1 ). (2.5)\ w2\ J JHere, w is the plasma frequency w = (47rne/€bm*)h/,and b is the background dielectric constant of the material. In arriving at the above expression, a rapid thermalizationof the excess electron and hole energies is assumed; therefore, the effective mass can beconsidered to be a time-independent quantity. Moreover, other mechanisms such as bandgap renormalization by hot carriers, semiconductor lattice heating, and intervaleilce bandabsorption are ignored.The temporal and spatial dependence of the dielectric function can be explicitly included through a time and spatially varying electron-hole plasma density, n(z, t); hence,equation 2.5 can be generalized to have the following form:= b ( - ::t) (i + (2.6)Chapter 2. Semiconductor Switching and Ultrashort Laser Pulses at 10.6 1um 26Here, n is defined by equation 2.3. Since the photoexcitation process of the e-h plasmaoccurs through the absorption of the above band gap radiation by the semiconductorsurface, the amount of radiation penetrating the surface decays exponentially with increasing depth through the bulk semiconductor. Consequently, the e-h plasma densityspatial profile follows the spatial profile of the absorbed radiation. One can write suchprofile as:n(z, 0) =n0e_Sfz (2.7)where n0 is the density of the e-h plasma at the surface immediately after excitation, and-y is the absorption length of the above band gap radiation.In writing equation 2.6 we have assumed a local response of the dielectric function;that is, the dielectric function at any point z depends on the values of the fields at thatpoint. This is equivalent to assuming that the dielectric function fluctuations are largecompared to the electron mean free path.At high excitation levels, the plasma frequency, c, will exceed the infrared probefrequency, . In such a situation, the refractive index becomes imaginary, leading tostrong reflection in the infrared range. Experimentally, Siegal et al. [81, 82] have shownthat under ultrafast high intensity laser excitations, the dielectric function of GaAs canbe described be equation 2.5 up to an excitation energy fluence of 1 kJ/m2. This energyfluence is the damage threshold energy fluellce of GaAs. Our experiments are performedat much lower energy fluences and hence Drude’s dielectric function is an adequate description of the optical properties of the optical semiconductor switch.2.4.2 Free-Carrier and Intervalence Band AbsorptionsOptical excitation of a semiconductor switch induces a change in the imaginary part ofthe dielectric function through optical intraband transitions. It is experimentally shownChapter 2, Semiconductor Switching and Ultrashort Laser Pulses at 10.6 m 27in section 5.2 that absorption processes at 10.6 m influence the operating speed of thesemiconductor switch.Directly after electrons (holes) have been injected with an ultrashort laser pulse in theconduction (valence) band and once the thermalization has occurred, the carriers occupyenergy states in the conduction/valence bands up to an energy level determined by theexcess laser photon energy. Consequently, two intraband infrared absorption processesoccur: free-carrier absorption and intervalence band absorption. Both absorption coefficients are proportional to the photoexcited carrier density and, therefore, may effect theswitching speed and efficiency at higher excitation levels.Free-carrier absorption is a three-particle interaction process. When the 10.6 imradiation passes through the semiconductor plasma, an infrared photon can excite a freecarrier to a virtual state in k-space, and since the absorption mechanism of the 10.6 imphotons requires the conservation of wavevectors, the electrons (holes) interact with thelattice through the emission or absorption of phonons in order to settle in a final statein the conduction (valence) band ( similar to indirect absorption in semiconductors).On the other hand, intervalence band absorption occurs between light and heavy holevalence bands. Holes are excited from the heavy hole band to the light hole band by theabsorption of 10.6 im photons. Intervalence band absorption has been shown to be lesseffective in comparison to free-carrier absorption [83].Chapter 3Theory: Infrared Reflection from a Semiconductor Plasma3.1 IntroductionThe basic theoretical background for optical semiconductor switching and some numericalsimulations are presented in this chapter. The basis of the numerical modelling has beenpresented in our previous publications [84, 85]. The general approach to ultrafast infraredoptical semiconductor switching can be divided into two problems. One is dealing with areflection of infrared radiation from a plasma, and the other is dealing with the temporalbehaviour of the reflecting plasma after optical excitation. Combining these two effects,one should be able to obtain a complete description of the physical situation. In thischapter, the general features of electromagnetic wave propagation in a semiconductorplasma are reviewed. In order to estimate the fastest process controlling the infraredswitching speed, the physical processes governing the temporal decay of the opticallygenerated semiconductor plasma are discussed. The rest of the chapter is devoted to theanalyses of the numerical simulations.3.2 Propagation of an Obliquely Incident Electromagnetic Wave in an Inhomogeneous Dielectric MediumIn this section of the thesis the specific problem of electromagnetic wave propagationat an oblique angle in an inhomogeneous plasma is discussed. A theoretical discussionis given of the specific problem of the reflection of a probing 10.6 um electromagnetic28Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 29wave from a semiconductor plasma. In our situation, we are interested in the reflectionof 10.6 tim radiation from a thin plasma layer where the layer thickness is basically theabsorption length of the excitation visible radiation (‘- 220 nm). The plasma thickness ismuch thinner than the infrared wavelength. Moreover, presence of plasma spatial inhomogeneity requires a generalization of the standard theory dealing with plasma reflection[86, 87, 88]. Therefore, our problem reduces to a reflection of an electromagnetic wavefrom an iiihomogeneous medium whose dielectric function depends on position.The analysis is presented for both electric field polarizations, S (where the electricfield is normal to the plane of incidence) and P (where the electric field is parallel tothe plane of incidence). Our method involves deriving an expression for the electric andmagnetic field components. We will also discuss the difficulties associated with obtainingan analytical solution for the P-polarized case at the point where the dielectric functionvanishes.Here, we use the free electron gas model to describe the optical response of the semiconductor plasma to the incident radiation. This implies that we neglect the contributionof free-carrier absorption, intervalence band transitions, and intraband transitions. Eventhough this model is simple and very crude, it can be used successfully to give a fairlygood description of the reflectivity at 10.6 tim.We start by considering Maxwell’s equations for electromagnetic waves in a dielectricmedium in Gaussian units:47r 1ODVxH=—J+——— (3.1)VxE=— (3.2)V.B = 0 (3.3)where H and E are the magnetic and the electric field vectors, respectively, and D, J areChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 30the electric displacement and the current density. For an isotropic plasma, we can defineJ = crE, D = bE, and B = tH. Here, for a semiconductor plasma we have assumed themagnetic permeability, i, to be equal to unity; b is the background dielectric constant.By taking the curl of equation 3.2 and substituting equation 3.1, we obtain the followingexpression:VxVxE=—--(J$) (3.4)It should be pointed out that in the following derivations we make use of the fact thatthe time variation of the dielectric function is negligible during the oscillation of the waveand hence may be regarded as being constant. Moreover, we also assume that there is noabsorption of the radiation, such that the amplitudes of the electric and magnetic fieldsdo not change during the oscillation of the wave. In general, we can assume that theform of D and J are harmonic functions of time and are written as:D(r,t) EbE(r)e (3.5)J(r, t) = a(r)E(r)et. (3.6)Therefore equation 3.4 can be expressed as:V x V x E = (‘)2(D— iJ). (3.7)By introducing the following identityV x V x E = -V2E + V(V.E) (3.8)and the following expressions for D and JD =€bE, J = uE, (3.9)the above equation (3.7) can be written as:V2E— V(V.E) + ()2c(r)E = 0 (3.10)Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 31where we have defined the dielectric function as €(r) = — (i4iro(r)/w). Equation 3.10describes the electromagnetic wave electric field components in a semiconductor plasmawhich has an effective dielectric function defined by (r) [86, 89]. It should be notedthat in deriving equation 3.7 we assume that the local temporal variation of u(r) is slowcompared to the period of oscillation of the electric field.As it will be pointed out later in sections 3.1.1 and 3.1.2, this differential equationwill be solved exactly for the S-polarized electric field components for a specific dielectricfunction profile. However, for the P-polarized electromagnetic wave case, this equationreduces to two coupled differential equations [86]. An alternative approach to the Ppolarization case is to consider the differential equation for the magnetic field.Next, we need to derive the differential equation that describes the components ofthe magnetic field propagating in the plasma. From equations 3.1, 3.5, and 3.6, and bytaking the curl of the expression, we can writeV x V x B = (V(r) x E + (r)(V x E)) (3.11)Using the following identityV x V x B = —V2B + V(V.B) (3.12)and equation 3.11, we can write the equation for the magnetic field as:V2B + ——VE(r) x (V x B) + ()2(r)B = 0 (3.13)The above equation describes the magnetic field components strength of the probingelectromagnetic wave [86, 89].3.2.1 The S-Polarized Electric Field CaseWe proceed in this section with the physics of propagation of S-polarized radiation (whenthe electric field of the wave is perpendicular to the plane of incidence) in a semiconductorChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 32plasma. The typical geometry of the problem is shown in figure 3.1, where the subscriptsi, r, and t denote incident, reflected, and transmitted electric or magnetic fields, respectively. A uniform electromagnetic plane wave is propagating in free space along thepositive z direction. This wave has a frequency and is incident on a semiconductorplasma from the vacuum side at an arbitrary angle O with respect to the surface normalof the semiconductor. As mentioned before, the solution to the reflected electric field inthe S-polarized case can be obtained by solving the differential equation for the electricfield. In this case we treat the situation as a one dimensional problem and hence we cantreat the dielectric function c(r) as having only a z component dependence. As shownin figure 3.1, let the plane of incidence be defined by the xz plane, where the z axis isperpendicular to the face of the semiconductor (and hence the plasma layer). The wavevector, k, then lies in the plane of incidence (xz) such that k k(sin O, 0, cos O). Weare interested in the y-component of the electric field. Hence we can write this componentas [86]:= (3.14)With this choice of the plane of incidence, the y-component of equation 3.10 can bewritten as [86]:8 + + (W)2E=0. (3.15)By using equations 3.14 and 3.15 we can derive the following equation:82E(z)+ k (E(z) — srn2 o) E(z) = 0 (3.16)which describes the electric field component strength of interest. It should be pointed outthat there is no general solution to the above equation and each functional dependence ofE(z) requires a special approach to the specific problem [86], [89]—[94]. In order to solve thedifferential equation (3.16), one has to assume a form for the dielectric function. Here, weChapter 3. TheorY Infrared Re&cti0fl from a SemiC0fldt0r plasma 33yQ) E Zci4‘7‘—4Er Ei.4.4 ‘FFigure 3.1: An icomiUg wave whose electric field, E, is normal to the plane of incidence(Spo1ariZat0Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 34consider the exponentially decaying dielectric function presented in section 2.4.1, whichis expressed by the formula:(z) (1_fl+?))(3.17)and equation 3.16 can be written in the form:02E(z)+ (a - k (j e)E(z) =0 (3.18)where a = k( — sin2 O). The simple transformation of [91, 94]X = Ib ‘ (3.19)v n(1+)can be applied to equation 3.18. This reduces equation 3.18 to a familiar form:X28+ + (X2 -2)E(X) =0 (3.20)where we have defined = —i2\//’y. The above equation is the familiar Bessel equation.J1(X) is the Bessel function of imaginary order i and complex argument X. The generalsolution to this equation has the formE(x) =C1J_(X) +C2J(X). (3.21)By using the boundary condition (i.e. as z —* ), only the transmitted wave exists insidethe plasma, and we can conclude that C2=0 [91, 94].3.2.2 The P-Polarized Electric Field CaseLet us consider the problem of the solution to equation 3.13 with the same form of thedielectric function (equation 3.17). As shown in figure 3.2, in the case of a P-polarizedelectric field, we take the wave vector k to lie in the xz plane of incidence and the electricfield components E = (Es, 0, Es); hence the magnetic field has only one component inChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 35the y-direction. The magnetic field can be written as B = (0, B, 0). With this choiceof the magnetic field, the differential equation can be reduced to the form:O2B Ô2B 1 O(z)aB“j’ 2B—2 2 +( ) — (• )ôx az (z) öz 9z cIn order to further simplify the above equation, let us represent the incident wave to bea plane wave with its propagation vector lying in the xz plane:Br,, = b(z)e’. (3.23)By substituting equation 3.23 into 3.22, we get___- + k ((z) - sin2 o) b(z) =0. (3.24)Equation 3.24 is known as the Maxwell-Helmholtz wave equation [86, 89, 90, 95J. Thecorresponding electric field components can be determined from Maxwell’s relationships:= ic (3.25)w(z) özand= —ic (3.26)w€z) axThis situation is different from the S-polarization case. In this problem, we need toconsider the dielectric function given by equation 3.17. Upoll examining the differential equation for the magnetic field, it is clear that the second term in equation 3.24approaches infinity as the dielectric function approaches zero.That is, the dielectric function changes sign as the plasma density exceeds the critical density. The dielectric function of the plasma approaches zero where equation 3.24approaches a singularity. As a result, all of the field components B, ET and E approach infinity as the point of singularity is approached. Several authors have discussedin great detail the exact nature of this type of singularity [86, 95, 96]; they have shownChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 36yBL ZC)Q)xBr B&kFigure 3.2: An incoming wave whose electric field, E1, is parallel to the plane of incidence(P-polarization).Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 37that in the neighbourhood of the near zero point of the dielectric function, the electricfield component E approaches infinity as E(z)’ and the other component E approachesinfinity logarithmically. For P-polarized electromagnetic waves, there exists a longitudinal component of the electric field along the density gradient. Under these conditions,this component of the electric field resonantly excites high amplitude oscillations at thecritical density of the CO2 probe radiation with an oscillating frequency of w=,, wherew,, is the plasma frequency. These large amplitude oscillations can influence the motionof the electrons and may result in anharmonic oscillations of the electron plasma. Thetransfer of electromagnetic to electrostatic energy and its subsequent dissipation is knownas resonance absorption [89, 90, 97]. The process is also responsible for higher harmonicgeneration from the probe frequency [98, 99].It should be pointed out that if the angle of incidence O is set equal to zero, themagnetic field structures can be described in the same manner as in the case for theelectric fields in the S-polarization situation where no plasma oscillations are excitedat the critical density. We made several attempts to solve equation 3.24 analytically;however, we were not successful in deriving an analytical solution. To our kilowledge,when all the features are simultaneously present (such as spatially and time varyingdielectric function and the introduction of free-carrier absorption), the general problemhas no analytical solution. At best, one may be able to obtain a numerical solution to theproblem. An extensive body of literature has been devoted to the study of this problem[84]—[86],[95, 96].3.3 Numerical Approach to the Solution: P-Polarization CaseAs we mentioned previously, an analytical solutioll of equation 3.24 proved to be impossible. The next step is to adopt a numerical method for the solution of the differentialChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 38equation. There are several problems associated with any numerical technique whendealing with singularities of the differential equation. Obviously, numerical integrationnear the point where the dielectric function approaches zero leads to an abrupt growthof the electric field E. An infinitesimally small change around the singular point canresult numerically in an unphysical value for the electric field.Another difficulty is associated with the lack of proper boundary conditions at thesurface of the semiconductor (at z=O). These boundary conditions for b(z = 0) and(öb(z)/öz)=o are required in order to initiate the numerical integration procedure forthe second order differential equation for b(z). In fact, we are primarily solving thedifferential equation in order to obtaill the boundary condition values at the vacuum-semiconductor interface. These problems make our numerical approach much more involved than standard numerical solutions.In order to remove the singularity from the differential equation for the magneticfield, one has to evaluate the magnitude of the imaginary part of the dielectric function.Effectively, the magnitude of the v/w term determines the rate at which the criticaldensity is approached. It is clear that if this ratio is >> 1, the large amplitude oscillationsdriven by the longitudinal component of the electric field will be strongly damped dueto absorption, and the numerical solution to the differential equation does not resultin unphysical electric fields. However, in a plasma the damping is often very smallsince the imaginary part of f(z) is small. One must bear in mind that given the reportedexperimental results on the collision frequency v, one has to consider a more realistic ratioin order to obtain physical solutions. In our numerical calculations we take v/w=l02[85].A simple technique for obtaining a boundary condition value is to examine the differential equation far away from the plasma and far into the bulk of the semiconductor.This is similar to the method used in reference [100]. Here, one expects the solution forChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 39the magnetic field to take the form of a simple plane wave. Therefore, one is requiredto obtain a solution for b(z) at a distance where z >> -y’. At a large distance, z, thedifferential equation reduces to the following equation:+ — sin2 O)b(z) = 0, (3.27)which we can easily show to have a solution of the form of a simple plane wave [84]:b(z) Ae_j/_smn29i+p) (3.28)where A and p, are the amplitude and the phase of the magnetic field plane wave,respectively. Ideally, this solution is valid as z —+ oo. In doing numerical calculationsthis limiting condition (z —+ oo) cannot be satisfied; therefore, before performing thenumerical calculation one must examine the range of z that can satisfy the conditionabove. We found that by using a value of yz=l0, the difference between our calculationsand the ideal condition is only i0 which is adequate for our application.The simulations are performed with the following parameters:1. The calculations do not take into account the time evolution of the semiconductorplasma density. This will be treated later on in section 3.6.2. The excitation laser pulse wavelength is 616 nm which corresponds to absorptioncoefficients, -y, of 4.5x10 cm1 [101, 102] for GaAs and 2.56x104 cm’ for CdTe[102].3. The wavelength of the probe radiation is taken to be that of the CO2 laser operatingat 10.6 tim.4. The background dielectric constant. b, is taken to be 10.89 for GaAs and 7.29 forCdTe [103].Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 405. The angle of incidence of the infrared radiation is set at Brewster’s angle for thebulk materials at 10.6 ,um (OB=72° and 700 for GaAs and CdTe, respectively).In general, the magnetic field is a complex function. We transformed equation 3.24 intotwo coupled second-order differential equations for the real and the imaginary part ofb(z). Both equations are solved in parallel using a modified fourth order Riinge-Kuttamethod. The details of the technique are outlined in detail in references [84, 85, 104, 105].The numerical integration is performed in a reverse fashion where we have defined a finalinterval zj and performed the integration backward to the initial value at z=0 with anintegration step of —az. In trying to manoeuver the integration near the points aroundthe critical density, the integration step size is reduced by a factor of 10 in order to obtainhigher accuracy [106]; moreover, the value of the calculated magnetic field is monitoredto check for signs of an abrupt growth. If this occurs, the integration step is furtherreduced by a factor of 10 and the calculations are repeated again around the region nearthe critical density. It should be pointed out that the exact value of the electric fieldcomponent E cannot be obtained at the critical density, but only in the neighbourhoodnear the position of critical density.The calculations for the fields are performed at several initial plasma densities rangingfrom 10n, to zero [84]. The values of b(z), E2, and (z)E amplitudes are calculated asfunctions of normalized distance, = 7z, and the results for GaAs are presented infigure 3.3 for an initial plasma density equal to 5n for both of the real and imaginarycomponents. From figure 3.3(a) and 3.3(c) as the critical density is approached, themagnitudes of b(z) and€E vary smoothly. For n/n=5, this critical density is reachedwhen =l.61. In the f(z)E case, both (z) and Ob(z)/öx approach the =1.61 point atthe same rate, and thus their product has a finite value.It is interesting to note that at (e)=, both of the Er and E curves resembleChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 41Figure 3.3: 10.6 um laser radiation magnetic and electric field amplitude componentsB (curve a), E (curve b), and (curve c) as a function of ç = z in GaAs. Theinitial carrier density is n= 5n. Solid curves represent the real parts and dashed curvesrepresent the imaginary parts.>%xN1-30.20-015-0.501.40.6-0.2—IllIIIw-—-,:s” (c):I I I I0 1 2345Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 42step discontinuities reminiscent of a phase transition as the GaAs changes from being asemiconductor to a “metal” for the 10.6 4um radiation.Once the values of the electromagnetic field amplitudes are obtained as functionsof the initial plasma densities, one needs to calculate the reflectivity of 10.6 ,um radiation from the plasma layer. The tangential component of the electric field and theperpendicular component of the displacement field have to be continuous across thevacuum-semiconductor plasma interface. The reflectivity can be obtained by matchingthe tangential electric field component, E, and the displacement field, cE, at =0.Hence we obtain the following relation for the amplitude reflectivity [107]:E sin 00 + 5E cos 00= (3.29)sin 0—cos 00where c is the dielectric function at the surface of the semiconductor evaluated at =0.The intensity reflectivity, R, and its corresponding phase, 4, are calculated from thefollowing relationsR=r 2 = tan’ (?T:) (3.30)where Re(r) and Im(r) are the real and the imaginary parts of the amplitude reflectivity,r, respectively.Figure 3.4 shows the results of such calculations of the intensity reflectivity for GaAsand CdTe as a function of initial normalized plasma density (n/ne). Both curves showoverall similar behaviour. In the density range 0n/n 0.9 the intensity reflectivityis calculated to be 0.7%; however, in the density range at near the critical density, theintensity reflectivity can be as high as 100%. It should be noted that figure 3.4 showsthe intensity reflectivity maximum value to be only 40%. More elaborate calculationsnear the critical density show that in fact this value is ‘—‘ 100%. Of importance to theultrafast reflection switch scheme is the sharp resonance-like peak occurring at n/n=1.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 431Q02_______I0.8 0.01-0.6 0.00 -___,“ (b)012345n/ncFigure 3.4: Brewster angle reflectivity for 10.6 im laser radiation as function of anexponentially decaying plasma density profile of (a) GaAs and (b) CdTe. The insetfigure shows an enlarged plot of the reflectivity for 0 ri/ne 1.0.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 44For a small change in the plasma density from (n/ne) to 0.9 (ri/ne), the reflectivitydrops to approximately zero. The magnitude of the reflectivity peak is determined bythe magnitude of the complex part of the dielectric function. When the plasma density,ri/n 1.2, the intensity reflectivity increases monotonically with increasing density toa maximum value of 100%. The higher reflectivity from CdTe semiconductor plasmacompared to the one from GaAs is due to the reflection from a thicker plasma layer.This is to be expected since the wavelength of the infrared radiation (10.6 tim) is muchlonger than the plasma layer thickness and one expects the infrared radiation to penetratethrough the plasma layer.Figure 3.5 shows the phase angle change of the reflectivity as a function of the normalized plasma density. The curve shows that at the critical density the reflectivity suffers aphase change of ir. This curve has proven to be very useful in interpreting the temporalshape of the reflectivity pulses.With our complicated numerical simulations, it not clear how to explain the structuresobserved in figures 3.3 and 3.4, and one has to resort to a much simpler analytical modelin order to confirm that the peak in the reflectivity is not just an artifact of the numericalprocedure.3.4 Reflection of 10.6 tIm Radiation from a Thin Film PlasmaIn this section we discuss a much simpler model which describes the reflection of 10.6 ttmradiation from a thin plasma layer. The analyses are based on the Fresnel equation forP-polarized electromagnetic radiation [108]. The plasma layer is assumed to be isotropic,homogeneous, and lossless.We consider the reflections from two semi-infinite plane-parallel regions: one containsthe semiconductor plasma and the second involves the bulk semiconductor material.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 45rJ)Figure 3.5: Phase angle change as a function of plasma density. The solid lines arecalculated from the differential equation model. Dashed lines are calculated from thethin film plasma model.90450-45-90- EEE—01Iii 1111123456fl/fl78910Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 46Since we know that the plasma initial spatial distribution is most likely to have anexponential profile, we can consider the plasma film thickness, 6, to be equal to the absorption length of the visible radiation,-y’. In this thin film layer, the plasma densityis assumed to be constant throughout the entire film thickness. The second film layercontains the bulk semiconductor material and extends to infinity. We also assume thatthe boundary between the two films is sharp. The geometry of the problem is shown infigure 3.6. With the above assumptions in mind, the dielectric function of the switch canbe written as [85]:I cb(1)(z) =if z>6.In order to obtain an expression for the reflectivity at each interface, we have to utilizethe usual boundary conditions derived from Maxwell’s equations, that the tangential,Es,, and the normal, E(z)E, components are continuous through the vacuum-plasmathin film and through the plasma thin film-bulk semiconductor interfaces [107]—[109]. Asillustrated in figure 3.6, the 10.6 m radiation is incident on the vacuum-plasma thinfilm interface at an angle 00, and is transmitted through the interface at an angle Oirelative to the normal to the surface. By matching the boundary conditions, we obtainthe following expressions for the amplitude reflectivity at the first interfacecos 0— \/Eb(1— ri/ne) cos 00r12 =___________. (3.31)cos 0 + b(1 — n/ne) C05For the second interface, the radiation is transmitted at an angle 02 into the semiconductor bulk. By matching the boundary conditions at the second interface, we obtain thefollowing expression for the amplitude reflectivity [84]:— /(1—n/n)cos02ftcos0i—, (3.32)— n/ne) cos02 + Jcos0iChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 47where we have used the fact that the refractive index of vacuum is equal to unity.Under an incident angle equal to Brewster’s angle, we have the conditions that sin 0 =+ tb), and cos00 l//l + b at the surface. Also, by using Snell’s law,siriO0 = /eb(l — ri/n)sinOi = /sin02, (3.33)we obtain the following relation for cos 01:coso1 = 1— (3.34)V + l)(l — n/nc)and for cos 02:cos02=b (3.35)Hence, the amplitude reflectivity, r12, can be expressed as:- (l - n/ne) (n/ne) - (l- n/ne)— (3.36)- n/ne) - (n/ne) + (l - n/ne)and we can show that the amplitude reflectivity,r23 = —r12. (3.37)Multiple reflections and illterferences between the two interfaces have to be taken intoaccount in the calculations for an effective amplitude reflectivity, r. Let us denote theincident electric field on the vacuum-plasma interface and the reflected electric field byE and Er, respectively. Let the reflection amplitudes be defiled in terms of the directionof propagation of the incident electric field as defined in figure 3.7. That is, we use thesubscript notation of + (refers to the left of the interface) and — (refers to the right of theinterface). The other subscript notation, 1 and 2, denote the first and second interfaces,respectively. We can define [110]= —rl_ = r12, (3.38)Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 48—1Plasma Bulk Semiconductor7Figure 3.6: Geometry of the vacuum-plasma-semiconductor interfaces for the thin filmplasma model.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 49r2+ = —r2_ = r23, (3.39)— =t1_ + r = 1. (3.40)Here, the first subscript denoted the interface. Then the amplitude reflectivity dueto multiple reflections from both surface can be written as:Er= ri+ +r2+tj+ti_e + r+ri_1i+ti_e4+ r+r_ti+ti_e61+ ... (3.41)where the phase shift, due to propagation through the plasma film, is given by: 43 =cos 01. At Brewster’s angle propagation, we obtain the following equation:43 = k7’b/(1 + Eb)Eb(1 — n/ne) — (n/ne) (3.42)which describes the phase change due to the propagation through the plasma layer. Here,k is the wave vector in vacuum. Summing up the infinite series for r and using equations3.37-3.40, we arrive with the followillg relation for the effective amplitude reflectivity[108, 110, 111]—2i/3r12 r23e3.431 +1223We have calculated the above equation for various initial plasma densities in the range0 n/nc 10 for the GaAs switch. The result of the intensity reflectivity from the plasmathin film model is presented in figure 3.8(a) for the density range 0 n/ne 2.5 and iscompared to the previous reflectivity calculations from solving the Maxwell-Helmholtzequation (figure 3.8(b)). It is clear that there is very good agreement between the twocurves and the reflectivity peak at fl/flc=1 is not an artifact of our numerical integration.The result for the calculated reflectivity phase shift is shown in figure 3.5; they also showa fair agreement with more elaborate calculations.Since both systems show the same relative reflectivity variations, indicating (a) if wehave a better understanding of the functional dependence of R(n) for the plasma thin film,Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 50r+rtI÷tEr1 r1_ r2+t1_ t2+r2t+-E2Et 2+l_ 1+ t+ \rEti+E.+Figure 3.7: Geometry of multiple reflections from vacuum-plasma and plasma- semiconductor interfaces.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 51we should be able to explain the results from our complicated numerical simulations, and(b) that the reflectivity variation depends predominately on the surface plasma densityrather than the function n(z) in the bulk of the semiconductor [84, 85].The calculation also indicates that a better modelling of the thin film plasma, forexample, dividing the plasma layer into smaller multilayers and calculating the reflectivity of each one, adding them with the proper phase shift, should provide a betterapproximation of the physical situation [111].It is simple to explain the features in figure 3.8 for the plasma thin film model [84].The electron density increases from zero, the reflectivity R, reaches a small maximumvalue of‘P’.’ 0.5% at a plasma density near (n/us) = (eb—l)/(eb + 1) (labelled (I) in infigure 3.8(a)). At this value of the density, the intensity reflectivity from the first interfacer12 2 is minimum. At (n/ne) = (b — 1)/cb the refractive index, /f(z = 0) is unity andthe vacuum-plasma interface disappears. Hence, the plasma layer is illuminated directlyat the Brewster angle, and as a result the reflectivity here is zero. This explains the firstminimum in the reflectivity curve (labelled (II) in figure 3.8(a)) After passing throughthe point of frustrated internal reflection at (n/ne) = cb/(Eb + 1) complete reflectivity isreached once (n/ne) 1 (labelled (III) in figure 3.8(a)). This is the region where thereflectivity shows a resonance-like peak. As the plasma density increases, (n/ne) > 1, theamplitude reflectivities, r12 and r23, are both complex in this region and for simplicity,we can writer12 = (3.44)where_______________________2[(n/n)- 1]fb[(fl/fl) -11+ (n/ne)tanC=. (3.45)— i]2 b[(fl/fl)—1]—(n/ne)Then the intensity reflectivity can be expressed as:(l_a)2R1— 2acos2 + a2 (3.46)Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 520.8>> 06.4=C-)00rr0.202 2.5n/ncFigure 3.8: Brewster angle reflectivity for C02-laser radiation as a function of free carriersurface density of GaAs for (a) a uniform film thickness ‘y’’ and (b) for an exponentiallydecaying density profile. The inset figure shows an enlarged plot of the reflectivity for0< n/ne 1.0 0.5 1 1.5Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 53Here, a = exp(2i/3) is a real function which rapidly decreases with increasing (n/ne).Now, as increases its value from zero at (n/n)=1 towards = (K/2), R decreasestowards a second minimum (labelled (IV) in figure 3.8(a)). Thereafter, the reflectivityincreases monotonically with (n/ne) and asymptotically approaches 1.Clearly, with our simple model we have managed to understand the structures involvedin the reflectivity curve. It also shows that the intensity reflectivity is a function of thephase shift, (F, suffered by the incident radiation and the thickness of the plasma layer.3.5 Temporal Variations of the Plasma DensityThe temporal variation of the plasma density can manifest itself in the temporal behaviour of infrared reflectivity through the time evolution of the dielectric function.In this section we briefly review of the processes that are responsible for the decay ofthe plasma density. Investigation of the recombination and diffusion processes allows us toselectively assess the relative importance of the mechanisms determining the e-h plasmadecay. Ultimately, we are interested in an ultrafast plasma decay process occurring onthe subpicosecond time scale.3.5.1 Electron-Hole Plasma RecombinationWhen a semiconductor equilibrium state is perturbed by an optical excitation pulse, thebalance of the equilibrium carriers is disturbed. If the excitation pulse is removed, theexcess photogenerated carriers will return to the equilibrium state through recombinations.Excess electrons and holes can recombine with each other through several recombination mechanisms: radiative, Auger, multiphonon recombination, capture at impuritysites (which can be either radiative or nonradiative process), and surface recombinationChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 54[112]. These processes determine the lifetime of optically generated excess carriers. Ingeneral, the selection of the recombination process depends on several factors, such as thee-h plasma density, carrier temperature, band structure of the semiconductor material,lattice temperature, impurity concentration, and the semiconductor surface condition.The fundamental theoretical and experimental aspects of recombination processes arediscussed in great detail in references [112]—[117].Two-body recombination is a radiative recombination process. In direct gap semiconductors, an electron in the conduction band can recombine with a hole in the valenceband, resulting in an emission of a photon [118]. The decay rate of the plasma dependson the densities of electrons and holes according to the following relation [119]9n(t)= —B0n2 (3.47)where B0 is the two-body recombination coefficient. For GaAs the two-body recombination coefficient for optically injected carriers is measured to be (3.40±1.17)x10”cm3 s [101]. Clearly, two-body recombination remains insignificant even at the highestcarrier density obtained in our experiments.The Auger recombination process is usually the most dominant recombination processin intrinsic bulk semiconductors at high carrier concentrations and high carrier temperatures. It is a three-carrier process where a conduction band electron and a hole in thevalence band recombine, and the associated excess recombination energy is transferredto a third carrier as kinetic energy. This energy is then thermalized with the rest of thecarriers. The presence of a third carrier is necessary in order to conserve energy and momentum. It should be pointed out that the Auger recombination process does not changethe total energy of the plasma e-h distribution; however, since the number of carriers hasdecreased, the total energy of the carriers is divided among fewer carriers. This results ina significant increase in the individual carrier’s temperature and a decrease in the carrierChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 55density.Since Auger recombination is a three-body interaction, its recombination rate isstrongly dependent on the plasma density. The recombination rate increases with thethird power of the injected carrier density. The decay rate of the plasma density due toAuger recombination can be written as:= Ta (3.48)where Fa is the Auger coefficient.Theoretical calculations and experimental measurements of Auger coefficient havebeen made for a GaAs [101, 120, 121]. Mclean et al. [101] have investigated the Augerrecombination rate in optically excited carriers, and they measured an Auger coefficientof (7±4) x 10—31 cm6/s. Evidently, the Auger recombination decay rate is a slow processcompared to the time scale of interest.In the case of a semiconductor sample of finite size, surface recombination can influence the temporal behaviour of the plasma density through the introduction of surfacestates. These states basically are discrete energy levels in the forbidden energy gap introduced by the discontinuity in the lattice. Since the photoinjected plasma is generatednear the surface, where these levels exist, the surface states can act as recombination centres. The surface recombination velocity is determined by the surface conditions [122].The rate of surface recombination is different from that of the bulk and is defined by asurface recombination velocity, S, asS = (3.49)where, 0ec is the carrier capture cross section (‘—‘ 10—15 cm2), vh is the free carrierthermal velocity (‘—i iO cm/s), and Nstr is the surface trap density ( 1014 cm2). Therecombination time due to surface states is of the order of ‘—i 20 ns.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 56Multiphonon recombination is a recombination process by which an electron and ahole recombine with a cascade emission of several phonons in place of a photon. Thismechanism is very inefficient considering the large number of phonoiis required to makeup the energy of a single photon [123].By examining the above recombination rates, it is evident that their contribution tothe reflectivity occurs in time scales longer than 500 Ps (for n 6n). Therefore, onehas to search for an alternative ultrafast carrier density decay mechanism.3.5.2 Diffusion and Time-Dependent Density Profile of the Free CarriersDiffusion of free carriers can result in a dramatic decrease in the plasma density. Here,we will examine the time evolution of the carrier density on a subpicosecond time scale.Directly after optical excitation, high density nonequilibrium electrons and holes arephotogenerated in the semiconductor switch. The behaviour of the plasma depends primarily upon the processes of diffusion and surface recombination. The spatial distribution of the optically generated plasma through the semiconductor will be inhomogeneous,thus the temporal dependence of the carrier diffusion should be considered as a factor inreducing the e-h plasma density.Diffusion is characterized in terms of a diffusion coefficient, D, which describes thenumber of free carriers passing through a unit area per unit time in the density gradient.In the case of a laser produced e-h plasma, the diffusion of both carriers is describedby an ambipolar diffusion coefficient. Because any separation of charge would createan electric field between the electrons and holes, the two carriers must diffuse at thesame rate. It is often difficult to experimentally isolate the effects of diffusion on theplasma density. To our knowledge, there is no experiment designed to directly measurethe diffusion coefficient of nonequilibrium semiconductor plasma for time scale less than500 fs. Hence, one has to rely on model calculations for D. We will assume that theChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 57electrons and holes are in thermal equilibrium with the lattice. The plasma, althoughinhomogeneous in its spatial distribution, is assumed to have a uniform temperature. Acrude approximation to our problem is to consider a nondegenerate plasma distributionwhere the diffusion coefficient is defined byD= (D€+Dh) (3.50)where De and Dh are the diffusion coefficients for electrons and holes, respectively. Amore general scenario would be to include the density and temperature dependence of thediffusion coefficient. The carrier’s diffusion coefficient is known to increase with the carriertemperature and decrease with lattice temperature; moreover, the diffusion coefficient isalso shown to have a strong dependence on the carrier density above .1019 cm3 wherecarrier degeneracy is reached. Several authors have considered this dependence to explainthe observed experimental results [124]—[130]. The dependence of D on density can becalculated using the Boltzmann transport theory in the relaxation time approximation[126]. A rigorous analysis of the diffusion coefficient has been performed by Young andvan Driel [124] where they have included many-body effects in the plasma. Here, we usedthe ambipolar diffusion coefficient value of 20 cm2/s [131, 132].The temporal and spatial distributions of the plasma density in a semiconductorswitch are described by the diffusion equation in one dimensional form:an(z,t)= D,t) +G(z,t). (3.51)Here, z is the spatial coordinate perpendicular to the semiconductor switch surface,n(z, t) is the number of photogenerated electron-hole pairs, and term G(z, t) is the generation rate of the plasma. No provision was made for the radial plasma concentrationdependence introduced by the gaussian beam profile. This is justified by the value of theeffective diffusion length, LD, relative to the beam size, given the time scale of interest.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 58Equation 3.50 is an approximation of the situation where the diffusion coefficient dependson the density, temperature of the plasma, and the position. In our experiment, we areinterested in a plasma density around 1 x 1019 cm3 before the onset of the plasmadegeneracy [130], thus, we are justified in our assumption. In our calculations, the semiconductor is illuminated with an ultrashort (< 100 fs) laser pulse having a photon energygreater than the band gap of the semiconductor. Hence, the rate of generation of theplasma is considered to be a delta function excitation in time; therefore, we can ignorethe generatioll term. This is justified because the duration of the actual excitation pulseis much shorter than the characteristic times of the physical processes which occur afterthe plasma is generated. We can write the initial condition for the above equation asn(z,0) =n0e2. (3.52)Equation 3.51 will be solved subject to a boulldary condition at the surface of the semiconductor, which can mathematically be represented by setting the carrier flux at thesurface equal to the rate of surface recombination:(anzt)= n(0,t), (3.53)where S is the density independent surface recombination velocity. With the aboveconditions, this linear partial differential diffusion equation can be solved analytically,and we obtain the following solution—O I y(yDt-z) (27Dt — zn(z,t)—— e erfc21+7)t + ZeY(YDt+z)erfc (2-yDt + z7Dt—z \. 2/— 2S__eSt+Derfc (2St + z j (3 54-yD-S 2/)JChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 59Similar solutions are reported before [122, 132, 133] The above equation reduces to theinitial condition (equation.3.52) at t =0.Using typical values for GaAs for 7=4.5 x io cm1, an ambipolar diffusion coefficient D=20 cm2/s and a surface recombination velocity S=lx iO cm/s [131, 132], wecalculated the temporal evolution of the plasma density n(z. t). The calculations areperformed in 500 fs time steps. The result in figure 3.9 displays the normalized densityof the plasma with respect to the normalized penetration depth e=7z at various timesafter delta function excitation pulse. Figure 3.9 indicates that (n/n0)has decreased from1 to 0.85 within the first 500 fs. This ultrafast initial decay will be the subject of furtherstudy later in this chapter. As time evolves, the density decay rate is much slower and thedensity profile is no longer an exponentially decreasing function with respect to depth,but more likely to resemble a gaussian profile. At longer times ( 80 ps), the plasmacontinues to diffuse until it is nearly uniform across the depth of the semiconductor.By then one has to include the effects of the recombination processes. We have foundthat the result in figure 3.9 is fairly insensitive to the actual value of S indicating thatthe initial variation of n0 is limited by ambipolar diffusion from the surface and into thebulk.3.6 Simulation of the Reflectivity Pulses from GaAsIn the previous sections we have performed time-independent calculations for the reflectivity as a function of the initial excitation plasma density. in general, if we combinethose calculations with a process which describes the time evolution of the plasma density,we should have a better understanding of the temporal response of the semiconductorswitch. From the data displayed in figures 3.4, 3.8 and 3.9, it is easy to see how theinfrared reflectivity changes as a function of time after a flash (100 fs) illumination withChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 600C1.10.90.70.50.30.2 0.4 0.6 0.8Figure 3.9: The variation due to diffu0 of carrier density, n(z, t)/n0 as a function oflongitudinal position and time. The curves are plotted in increasing time steps of 500 fs.The top curve is calculated at t= 0 Ps, and the botttom curve is calculated at t= 4.5 Ps.0 1Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 61above band gap radiation. For the proposed reflection switch scheme it is necessary totailor the exciting laser pulse intensity so that the critical density is produced. This mayinvolve intensity discrimination techniques depending on the laser system used. The surface density then has only to decrease to reach (n/ne)=(ci, — 1)/ci, 0.9 in order forthe reflectivity to decrease to zero.In order to gain an insight into the pulse shapes and durations, we compare our calculations to the calculations performed with the simpler plasma thin film model. We cantreat the time dependent dielectric function as [85]I cb(1) ifz<(t)c(z,t) =if z>5(t)where 5(t) is the thickness of the plasma film at time t, and (t = 0)=z’y’. Since thismodel avoids the problems resulting from the singularity of c(z, t) we are able to calculatethe reflectivity at the critical density. The change in the infrared reflectivity is related tothe changes in the excess-carrier density, and the generation of ultrashort pulses makesuse of the initial rapid decay of the electron density. We can account for the rapid dropin the reflectivity by using a simple physical argument [85]. The reflectivity of the switchis ‘- 100% whenever (n/n)=1, and the plasma generated by the femtosecond visibleexcitation pulse is contained in a thin layer of thickness of the order of the absorptionlength of the radiation, y’=2.22x10 cm. Assume that the photogenerateci plasma isuniform in the transverse direction, and suppose that the transverse cross sectional areaof the plasma is A, and that the total number of electrons generated at t=0 is N. Thenthe plasma density is given by the simple relation:(t=O)= A7-’ (3.55)Next, the plasma diffuses into the bulk with a diffusion coefficient D= 20 cm2/s, suchChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 62that in 500 fs the effective diffusion length LD=3.162 x106 cm. Effectively, all theelectrons move into the bulk of the semiconductor by LD. The electrons at the edgeof the plasma thin film will diffuse by LD and the effective plasma thickness becomes(7’+LD). Note that there is no generation of new electrons after the optical excitationis over, and we still have the N electrons in the same effective cross sectional area A( here we have ignored the transverse diffusion of the carriers since the excitation laserspot size on the semiconductor surface is much larger than LD). The new plasma densityat 500 fs is thell given byN(t=5OOfs)= A(7-1 + LD) (3.56)and the ratio of the two densities(ttO) = 1 (3 57fl(t=50018) 1 + 7LDThis ratio is 0.875. That is, the density t= has decreased by i--’ 12% in only 500fs. As previously mentioned, the reflectivity (see figure 3.8) around the peak drops from100% to almost zero when the plasma density in reduced from n = n by only 10% andthis could happen in about 500 fs; therefore, it should be possible to generate ultrashortpulses if the semiconductor is excited to generate plasma density near the critical density.The temporal behaviour of the semiconductor plasma is very complicated. Withthe density profiles of equation 3.54, the differential equation 3.24 becomes even morecumbersome to solve numerically. We have performed the calculation using the MaxwellHelmholtz differential equation with a time dependent dielectric function (z, t).With the plasma density profiles given by equation 3.54, the calculations are repeated for b(x, z, t), E(x, z, t), E(x, z, t) and R(n, t) using a fourth-order Runge-Kuttamethod. The b(x, z, t) field amplitude is assumed not to change rapidly during one oscillation period of the electromagnetic wave. The computer code was modified to includeChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 63the temporal dependence of the plasma density; hence, we were able to calculate the reflectivity R(t) as a function of time for each plasma density profile. That is, for each timeinterval the plasma density profile takes a different gaussian shape and the differentialequation is solved for that specific form.Here, we performed the calculations using GaAs as the semiconductor with sometypical values D= 20 cm2/s, S= iO cm/s and the rest of the parameters are the same asthe ones used for the time independent calculations [85]. The reflected infrared pulses areshown in figures 3.10 to 3.11 for some representative values of the initial plasma densityprofile. These values are chosen to cover a wide span of the reflectivity curve in figures3.10 and 3.11. The regions between the solid lines in the figures indicate the times wherethe electron density in the differential equation approaches the critical density. Thereflectivity is calculated in a small region around the singular point.For (n/n)= 1.2, the FWHM is 200 fs and the reflected pulse increases slowly toreach a maximum value of 0.96 and then decreases slowly to zero in about 1 ps. As thesingular point is approached, the reflectivity approaches unity, and because the change inthe plasma density with time is slow, the dielectric function remains approximately zerofor that period of time. Later, the reflectivity decays back to zero. The fast rise and falltimes of the reflected signals indicate that the semiconductor switch can remain reflectivewith R 1 in the region where (z, t) approaches zero, thus , resulting in reflected pulsesof near rectangular pulse shapes. The initial part ( 100 fs) of the reflected pulse isapproximately zero; as a result, during the pumping by the visible wavelength controlpulse, none of the 10.6 um radiation is reflected. At (n/n)= 1.3, the calculated FWHMis 350 fs. By adjusting the excitation laser fluence so that the initial plasma densityis 0.9n, longer pulses in the picosecond range can be obtained. For example, whenthe initial densities are 0.74n and 0.9n, the reflected pulse widths are 60 and 65 ps,respectively. These pulse intensities are two orders of magnitude lower than the onesChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 640.02-________(a)0.01-000-10 150 310-20 250 5200—o 150 300Time (psec)Figure 3.10: Reflected 10.6 m pulses as a function of time for initial plasma density of(a) n = 0.7n, (b) n= O.9n, and (c) n = 6n. The solid lines are calculated from thedifferential equation model and the dashed lines are calculated from the thin film plasmamodel.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 65_0 0.5 1± 0.50 1.25 2.5Time (psec)Figure 3.11: Reflected 10.6 ,um pulses as a function of time for initial plasma densityof (a) r. 1.2n and (b) ii = 1.3ri. The solid lines are calculated from the differentialequation model and the dashed lines are calculated from the thin film plasma model.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 66calculated near the critical density.We have also calculated the phase shift experienced by the reflected infrared pulsesfor (n/n)= 0.74, 0.9, 1.2, 1.3, and 6. The results are presented iii figures 3.12 to 3.14.The dashed lines in in figure 3.13 curves illustrate the points where the plasma densityhas reached the critical density, and one has to extrapolate around them. By examiningfigure 3.13, we realize that the reflected pulses suffer a phase change of ‘-.‘ir at the timeof the peak of the reflection.For comparison, we have also performed the calculations for the thin film plasmamodel using rectangular variations of the plasma density with depth. As time progresses,the thin film plasma is expanding into the bulk; and to incorporate the time dependencein this film model, we calculate the 1/e point of the density profile at the surface givenby equation 3.54 and we note the corresponding time. These are used to simulate theexpanding step-like film illustrated in figure 3.15. The results are displayed in figure3.16(a). The figure shows that after the first ‘ 20 ps the plasma film thickness remainsalmost constant. From that, we calculated the corresponding effective thickness of thefilm, (t), as a function of time during the first 300 Ps.The results are shown in figure 3.16(b); here the plasma is treated as a step-like filmwhose thickness increases with time. Multiple simulations are performed for the initialnormalized electron densities of 0.74, 0.9, 1.2 1.3, and 6. The results are displayed infigures 3.10 to 3.11 and are found to be iii good agreement with the above numericalcalculations. The rise and the fall times of the reflected pulses are much slower than theones calculated previously. This is to be expected from such a model, since the changein the plasma density with time is much smoother. At the point where (z, t) =0, thereflectivity reaches unity which is in agreement with what is expected from the solutionof the differential equation.We can write the reflectivity as a function of three variables: the phase shift, filmChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 679030—30—900 3009030—30—900Figure 3.12: Phase change in degrees of the reflected 10.6 m pulses as a function of timefor initial plasma density of (a) n = 0.7n and (b) n = O.9n. The plots are calculatedfrom the differential equation model.60 120 180 240100 200 300 400 500PicosecondChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 68- I0 0 0 0 0 0 0(a)Q)30C,)cI—Io000000—90 I0.0 0.2 0.4 0.6 0.8 1.090 I I I(b)oooooo000000)30C,)‘C0I 030 I 0I 00I 000000—900.0 0.5 1.0 1.5 2.0 2.5PicosecondFigure 3.13: Phase change in degrees of the reflected 10.6 um pulses as a function of timefor initial plasma density of (a) n = 1.2ri and (b) n = 1.3n. The plots are calculatedfrom the differential equation model.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 6990 I • If::: 00 60 120 180 240 300PicosecondFigure 3.14: Phase change in degrees of the reflected 10.6 ,um pulses as a function oftime for initial plasma density of n = 6n. The plot is calculated from the differentialequation model.n(z=O)/n...ciit-c-CDCDCl)——.soCD q)—.CD+C—.CD Cl)÷,CD0Ci)Cl) CDPC Cl) p t.C,)CD CD II.. ciiChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 711—____________1.0 (a)0.9N¶0.807osecod¶0.5I Icr2 ‘1i2—•.1z• ,,—40-0 100 200 300 400 500Time (psec)Figure 3.16: (a) Normalized surface plasma density at z=O as a function of time. (b)Effective thickness of the plasma film as a function of time.Chapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 72thickness and electron density. Therefore, the dynamical behaviour of the switch can bewritten as the total derivative of the reflectivity with respect to time.dR dRdn dRd dRdS (3.58)Note that at all times we have (dn/dt)< 0. This means that if the semiconductor isilluminated by a laser fluence sufficient to produce a large enough initial plasma density,i.e. (n/ne) = 6, then a competition between the derivatives of the phase, the density, andthe thickness of the plasma film, with respect to time determines the temporal evolutionof the reflected infrared pulses. By examining figure 3.4 and figure 3.5, the first twoterms (dR/dri)(dn/dt) and (dR/d)(d/dt) are both negative, whereas the last term(dR/dJ)(d6/dt) is positive. The rate of change of the reflectivity depends on whether thesum of the three terms is positive or negative. Initially, the reflectivity changes at a slowrate because the rate of change of the first two terms is slow in the first 10 ps, and the rateof change of the reflectivity is dominated by the change in the thickness of the plasmafilm, thus making (dR/dt) positive. When the reflectivity approaches 0.65, it begins todecrease slowly since the last term no longer dominates the sign of (dR/dt). For the next140 ps the reflectivity decreases until the plasma density decays to 1.26n. At the pointwhere (n/n)=l.26, the contributions of all three terms are positive, and the reflectivityincreases slowly from 0.5 to 0.91 in about 33 ps. When R approaches unity, the electrondensity approaches the point near the critical density. As soon as (n/ne) < 1, we havea different region of reflectivity, where the contribution of the phase to the reflectivityis zero in this region. For the plasma density in the range 0.9 (n/ne) 1, the term(dR/dS)(dS/dt) > 0 and (dR/dn)(dn/dt) < 0. Because of the fast decay of the electrondensity compared to the increase in R due to increasing plasma thickness, the reflectivitydecays very quickly from unity to zero level (at (n/ne) =0.9). For the plasma densityrange 0 (n/ne) < 0.9, the term (dR/dn)(dn/dt) reverses sign and becomes positive butChapter 3. Theory: Infrared Reflection from a Semiconductor Plasma 73the term (dR/d6)(d/dt) > 0 and the reflectivity increases until it reaches a minimumvalue at the point where (dR/dn) 0 (at (n/ne) 0.74). The reflected signal thendecreases slowly because (dR/dn) (dn/dt) switches sign and becomes negative, whereas(dR/d)(dS/dt) > 0 and the reflectivity becomes zero at (n/ne) =0.From the above analysis, we can draw the following conclusions. Femtosecond andpicosecond pulses of variable durations can be generated depending on the initial valueof (n/ne). For a control pulse of the order of 100 fs, one needs to adjust the energyfluence of the laser pulse such that the number density of the photoinjected electrons isin the range 1 .2n—l .3n in order to obtain ultrafast infrared reflection. It seems thatthe temporal response of the switch is limited only by the control pulse duration and theambipolar diffusion coefficient of the semiconductor.The next task is to perform the experiment at different excitation energy fluences onGaAs. Whether our conclusions from the calculation are correct depend on the assumptions we have made in deriving the model.Chapter 4Laser Systems, Optical Setups, and Experimental Procedures4.1 IntroductionIn this chapter, the laser systems, the experimental apparatus, and the techniques usedduring the course of this work are discussed. A brief overview of the femtosecond laserpulse generating/amplifying system is presented with special emphasis on the system performance and characteristics. All the CO2 lasers used in this work have been designed andbuilt in this laboratory and considerable time and effort is spent in characterizing theirperformance as well as their operating conditions. Moreover, the construction details ofthese high-power CO2 lasers are discussed. Further details of the fast electrical dischargeexcitation circuits and on the lasers’ designs and construction are published in our reviewpaper on the subject [134]. In this chapter, we also discuss the design of a home-madeautocorrelator constructed to measure the duration of the pump laser system. A briefoverview on the detection units, some custom electronic modules that are used for datacollection and laser synchronization are discussed in this chapter. Detailed schematicsof the electronic circuits are presented in Appendices A to C. Finally, the experimentalsetups for time-integrated reflectivity, reflection-reflection correlation, cross-correlationtechniques, and frequency spectrum measurements are presented and discussed in detail.74Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 754.2 The Femtosecond Laser SystemThe high power laser pulse excitation system used to operate the optical semiconductorswitch is described in this section. Much of the time during the course of the experimentalwork was spent installing, maintaining, fixing, and optimizing the performance of the lasersystem. The layout of the laser system is illustrated in figure 4.1. A brief description ofthe characteristics of each component is presented below.4.2.1 The Femtosecond Laser Pulse Generation SystemThe ultrafast laser pulse generating system is a commercial laser system consisting of anNd:YAG (Nd3+ doped Yttrium Aluminum Garnet), a pulse compression stage, and a dyelaser.The Nd:YAG LaserThe Nd:YAG laser is a Spectra Physics Model 3800 mode locked laser. The laser is drivenby an acousto-optic mode locker, placed inside the laser cavity near the output mirror,operating at a resonance frequency of 41.0245 MHz and producing a single longitudinaland transverse mode, quasi-continuous pulse train at a wavelength of 1.064 gum. Theoutput pulse train repetition rate is 82.049 MHz with a single pulse duration of 70 ps.The average output power from the laser is between 13 to 14 W.The Pulse CompressorThe Spectra Physics Model 3695 Optical Pulse Compressor utilizes a fibre-grating optical arrangement to shorten the 70 ps (1.064 gum) pulse duration from the mode lockedNd:YAG laser to ‘- 4—5 ps. The 1.064 gum pulse is frequency doubled to 0.532 gum using asecond harmonic generation crystal. With frequency doubling, the duration of the 0.532Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 76m pulse is reduced even further to 3 ps. The maximum output that can be obtainedfrom the pulse compressor is 1.1 W at 0.532 m.The Dye LaserA Spectra Physics Model 3500 Ultrashort Pulse Dye laser is utilized in the final stageof the femtosecond pulse generation system. The dye laser uses Rhodamine 6G dye as again medium which is synchronously pumped by 850—900 mW, 0.532 um (3 ps) outputfrom the pulse compressor. The laser produces 83—250 mW average power with a tuningrange between 575 to 635 nm. The output pulse train (82 MHz) consists of individual500 fs pulses with 1—3 nJ/pulse.4.2.2 The Femtosecond Laser Pulse Amplifying SystemThe nanojoule femtosecond laser pulses are amplified to a higher energy with a subpicosecond laser pulse amplifying system consisting of a three stage dye amplifier pumpedby a Nd:YAG regenerative amplifier.The Nd:YAG Regenerative AmplifierA Continuum Nd:YAG Regenerative Amplifier Model RGA6O is used to pump a subpicosecond laser dye amplifier. A dielectric beam splitter is used to split off ‘— 5% from theNd:YAG laser mode locked train and is injected into the regenerative amplifier. Singlepulses are selected from the train and are amplified to produce 200 mJ, 70 Ps, 1.064 tmlaser pulses at a maximum repetition rate of 10 Hz. The output is frequency doubledin a second harmonic generation crystal to produce 100 mJ at 0.532 im in a singletransverse mode.Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 774.2.3 The Subpicosecond Dye Laser Pulse AmplifierThe femtosecond dye laser pulse is amplified in a Continuum Picosecond Amplifier ModelPTA6O consisting of three Rhodamine 640 dye cells. The dye laser pulse amplifier ispumped synchronously with 25 mJ from the frequency doubled output from the Nd:YAGregenerative amplifier. The injected nanojoule 616 nm dye laser pulses are amplified toa maximum energy of ‘-‘ 1 mJ at 10 Hz with a minimum of pulse broadening.4.3 The CO2 Laser OscillatorsIn this section we give a brief introduction to the continuous wave (CW) CO2 and pulsedlasers used in our experiments. The CO2 lasers have been designed, built, and upgradedin our laboratory, and hence, a considerable amount of time and effort is devoted todetermine their optimum operating conditions and design configuration. Our goal is toconstruct high-power single longitudinal and transverse mode CO2 lasers to carry outthe optical semiconductor switching experiments. The simplicity of the devices’ designsand constructions make them attractive and inexpensive laboratory instruments.4.3.1 The CW CO2 Laser OscillatorDuring the course of our experimental work with the CW CO2 laser, the laser design wasfrequently modified and upgraded to suit our purpose. The original CO2 laser deliveredonly 1.5 W at 10.6 ,um. Clearly, this laser power was not enough to be useful in ourexperiments. Another larger laser has been designed to produce ‘-S- 10 W, and severalexperiments were performed using this laser; however, the detected signals are weak andit was decided to further upgrade it to a higher power (> 30 W).The CW CO2 laser consists of two independent sections. The simple schematic ofthe laser is illustrated in figure 4.2. Both sections use a DC glow discharge to achieveChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 78.AutocorrelatorPulse CompressorAmplifier1 mJ, 490 fsFigure 4.1: The layout of the femtosecond laser pulse generating system.Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 79laser inversion in the CO2 molecules. The two ends of the laser sections are maintainedat a high voltage of 25 kV and are separated by a ground cathode at the centre of thedischarge. Each section consists of a pyrex tube 103 cm in length and 12 mm in diameter,and can be operated independently. The effective laser cavity length is 3 m (end-to-end)with one end being terminated by a 0.64 cm thick, 5.08 cm diameter KC1 Brewster’s anglewindow to ensure a single polarization beam output, and the other end of the laser tubeis terminated by the resonator cavity mirror. Two cold-water (— 14 °C) lucite-jackettubes (6.4 cm in diameter) are used to cool the discharge plasma.In order to have a stable glow discharge between the laser brass electrodes, the negative dynamic resistance (after the CO2 gas breaks down) must be suppressed. This isdone by connecting a series of ballast resistors in series with the high voltage DC powersupply. Both anodes are connected to the power supply via four 0.1 MQ resistors witha total resistance in each arm of 0.4 Mf. The cathode is connected directly to ground.This arrangement ensures that both sections can break down evenly and more reliably.The laser cavity design consists of a concave, 8 m radius of curvature, gold-coatedmirror which is mounted inside the discharge volume and an output coupler consisting ofan uncoated plane-parallel Ce window of 5 mm thickness and 2.54 cm diameter. As in anyetalon, both the front and the back contribute to the reflection. The refractive index ofCe at 10.6 urn is 4.2; hence at normal incidence, the contribution of the surface reflectionis only 36%; however, interference between the two faces can result in reflectivitybetween 0—80% depending on the free spectral range of the Ge etalon.The CO2 can lase on several vibrational-rotational lines simultaneously between 8.7urn to 11.8 urn. These laser transitions are highly competitive, and as a result the beatingof the longitudinal mode causes fluctuations in the laser power output. The Ce flat canbe used as a tunable Fabry-Perot etalon to suppress the oscillation on all lines but the onewhich matches the free spectral range of the Ce etalon. The free spectral range can beChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 80tuned by adjusting the temperature of the Ge fiat. A feed-back temperature electroniccontrol system is used to actively stabilize the resollator cavity. The temperature ofthe output coupler is fixed at 30.15°C at which the laser lases at 10.6 gum and exhibitsexcellent stability. Due to the large length to diameter ratio of the discharge, the laser isforced to operate on a single transverse mode, TEM00 with a beam spot size of 1.5 mm.The discharge current determines the rate of pumping of the CO2 molecules and thusdetermines the output power. In this laser, the maximum pumping current is 40 mA(20 mA for each section). The laser is operated with a gas mixture of He:C02:N with amixture ratio of 84:8:8 and a total gas pressure of 15 torr. During the electrical dischargethe CO2 molecules dissociate and; therefore, the replacement of the gain medium isrequired. The laser gas mixture is flowed through the discharge region, where it isinjected from both anodes and exited through the cathode.With the above operating conditions, the output laser power is measured to be40 W. It seems that the limiting factor in determining the output power of the laser isthe flow rate of the CO2 gas. Improvements on the gas flow system should increase theoutput power. It is clear that the CW CO2 laser does not require synchronization with thefemtosecond laser/amplifier system; therefore, it is used to perform all the time-resolvedexperiments.4.3.2 The High Pressure TEA CO2 Laser OscillatorTEA CO2 Laser Body and CircuitHere we present a design for a TEA discharge CO2 laser which is used to perform some optical semiconductor switching experiments, especially for measuring the frequency spectrum of the reflected infrared pulses. An illustration of a cross section of the laser bodyand its electrical circuit components is shown in figure 4.3. The laser is designed toChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 818 m mirrorHVWater inKC1flatFigure 4.2: An illustration of the 40 W CW CO2 laser. R = 0.4 M1 and HV = 25 kV.operate at high gas pressures in the range between 1 to 7 atmospheres and to be usedas part of a more elaborate CO2 laser system known as a “hybrid laser” arrangement.Most of the electrical, laser energy, and pulse duration measurements discussed in thissection are performed with the discharge laser operating at 1 atmosphere with a lasinggas composition of (C02:NHe) and a mixture ratio of (15:15:70). The laser electrodesare made from aluminum plates with an electrode separation of 9.5 mm. The electrodesare designed to be flat over a 9.5x350 mm2 area, with rounded corners similar to thedesign in reference [135]. The radius of curvature of these rounded corners is 6.3 mm.The gas glow discharge is observed to be uniform over the (9.5x9.5x350) mm3 volumeas indicated by photographing the discharge region.The high pressure electrical discharge is automatically preionized using a double sidedLC inversion circuit which is first described in reference [136]. This circuit is one of themost efficient ways to excite high pressure CO2 gas discharge lasers [134]. Efficient operation of a high pressure gas discharge laser depends strongly on both the low inductancein L.RCO2 out Ge flat1UWater outRHVChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 82•Pick-upCoils.J Plexiglass10 ChamberFigure 4.3: The TEA CO2 laser using an automatically preionized, doublesided, LCinversion circuit. Electrical conductors (aluminum and copper) are shown shaded. Thepreionizer rod design is also shown below./Aluminum IPlatesCapacitorsI I I I I I I I I2468cm scaleChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 83of the driving circuit and the density distribution of the initial electrons produced by thepreionization process. The schematics of the circuit design is presented in figure 4.4. Theprinciple operation of the LC inversion is as follows: the capacitors are charged in paralleland no voltage appears across the laser electrodes; then, when the spark gap switch istriggered and hence closed, the voltage across the top capacitor banks discharges throughthe preionizer rods [135],[137J—[140].Due to the high inductance of the resistors and the preionizer rods, the current continues to flow and the top capacitor bank polarity reverses direction. The voltage across thelaser electrode, at this time, becomes double the charging voltage of the capacitors. Thelaser gas breaks down as soon as the electrode voltage reaches the pressure-dependentbreakdown voltage of the gas mixture.The switching of the discharge is made possible by a low inductance spark gap whichis pressurized with dry air to 50 Psi to withstand a charging voltage of 22 kV.The spark gap is triggered by a triggering pin connected through a krytron (EG&G)high voltage (10 kV) triggering unit through a 6:1 step-up transformer. Twenty-fourdiscrete BaTiO3 doorknob capacitors (Murata Corp. no. DHS6OZ5V272Z-40, 2.7 nF, 40kV ceramic capacitors) are mounted symmetrically, six in each quadrant, between bothsides of the discharge chamber as shown in figure 4.3. This arrangement gives an ultralowinductance configuration. As shown in figure 4.3, the body of the laser is machined out ofa single lucite block, with one additional plate of lucite (surrounding the upper electrode)glued into it using cyanoacrylate, “Krazy glue”.Preionization of the main discharge is provided by two arrays of U.V. sparks. Eachpreionizer rod is constructed as described in references [138, 139], with the centre conductor (a length of Belden no. 8868 high voltage wire) passing through the outer conductorof the 20 cm length of a home-made 50 f coaxial cable, and then all the way throughthe glass tubing to the last stainless steel preionizer electrode. The edges of the stainlessChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 84(b)I.Figure 4.4: (a) The CO2 laser LC inversion circuit and the preionizers connections. P.R.=preionization rod, S.G.= spark gap, and L.D.= laser discharge. (b) The equivalent circuitwith C = 64.8 nF, Lp = 420 nH, Rp = 1.05 1, C = 64.8 nF, and Le = 6.8 nH.C4C4EquivalentChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 85steel tubes are cut at 300 to the axis of the tube. A drop of cyanoacrylate glue is usedat each end of the Belden wire to seal the wire against its insulation, and this glue isalso used to seal the insulation against the first stainless steel preionizer electrode, asshown in figure 4.3. The end of the preionizer is sealed against the lucite laser chamberwith an 0-ring fitting. The other preionizer electrodes are attached to a 5 mm (outsidediameter) pyrex tube using the same glue. We used 15 preionizer spark gaps of 400 tmeach, at 2.5 cm interval along each preionizer rod. We found that the breakdown ofthe two preionizer rods is very reliable if the total length of U.V. sparks, 15x(400 tim),is less than the main electrode spacing of 9.5 mm. In order to minimize the electricaljitter to less than +3 ns, we made use of the “capacitive coupling” to the return lead, sothese sparks actually form sequentially [141]—[143], rather than all at once; the processrequires about 20 ns [142, 143] to form a so-called “running spark” or “sliding spark”,and it is only after all the sparks have formed that the inversion and preionizer current,Ii,,, starts to climb significantly [141]. The preionizer rods are mounted along the sidesof the main discharge and parallel to the laser electrodes at distance of 14 mm, sothat unwanted sparks between them are avoided and uniform preioriization of the maindischarge is obtained.Electrical Current and Voltage Measurements of the Laser DischargeThe discharge current risetime is directly related to the rate of energy deposition. In thislaser discharge, the electric current changes very quickly which induces a time-varyingmagnetic field. By taking advantage of this, very accurate transient current measurements can be performed. The current pulse is measured using twin, subnanosecondrisetime, 10-turn pick-up coils [144] installed between the capacitors, within the fastdischarge main loop, on opposite sides of the chamber, as indicated in figure 4.3. Thetwo coils therefore give equal and opposite signals which, when subtracted by a 1 GHzChapter 4, Laser Systems, Optical Setups, and Experimental Procedures 86oscilloscope (Tektronix 7104 with two 7A29 plug-in units), give the low-noise voltagesignal Vc, proportional to the rate change of the main current,VC=AM, (4.1)where AM is a constant. The current noise is substantially eliminated by “common-moderejection.” The two signal lines are first carefully adjusted to have identical delay times,to within ±50 ps. The delay is measured using an oscilloscope and a coaxial spark gap[137]—[139] cable discharge circuit [137]—[139], [145, 146]. The discharge circuit provides1000 V electrical pulses having a risetime of 300 Ps.Measuring the discharge breakdown voltage gives an insight into the amount of electrical excitation energy that is being delivered during the laser operation. In measuringthe transient discharge high voltage, it is convenient to use a high voltage divider. Thevoltage, VM, on the main electrodes is measured using twin, resistor divider, high-voltageprobes of iO x attenuation (each consisting of 15 two-watt carbon resistors soldered together in series with a terminated 50 cable), one for each electrode. The risetime ofeach probe is measured to be 10 ns. Again, the signals are subtracted by the 1 GHzoscilloscope, giving a low-noise signal representing the voltage, VM, across the discharge;the noise, again, is thereby substantially eliminated by “common-mode rejection.” Thevoltage, VM, across the main electrodes is measured in this way, for an initial chargingvoltage of V0 = 22 kV, and is shown in figure 4.5(a). The main current, IM, starts at t= 300 ns, with a jitter of < ±2 ns, relative to the primary/preionizer current, Ip. Thecurrent, Ip, starts with a jitter <±3 us, relative to the time of firing the spark gap.As observed previously for CO2 lasers [138, 139, 141],[147]—[149], the main current, JM,essentially stops with a finite voltage of VM = 13 kV remaining on the main electrodes.This occurs, presumably, since there is no longer enough voltage to maintain a discharge.However, since the spark gap (and preionizer) current, Ip, are still supplying a chargeChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 87to the main ioop, we observe small current oscillations immediately following the largeinitial pulse, as shown in figure 4.5(b). This initial current pulse contains at least 90% ofthe energy of the entire curreilt pulse, IM. The current pulse FWHM is measured to be40 ns, which is fairly close to the critically damped value of 25.6 us, given by equations(5) and (16) in reference [134].During these current oscillations following the large initial pulse, the voltage, VL,induced in the measurement loop of area, AL, is by Faraday’s law,r fdB’\ Ii0AN dIMVL= JAL—--) .ds —--) ——, (4.2)where A and I are the cross sectional area of the aild the length of the current sheet,respectively. VL has a 2 kV amplitude. Since dIM/di is 0 at certain times t (maximaand minima of ‘M in figure 4.5(b) ), one can compute the discharge resistance at thesetimes from the following equation:r(t) = VM(t) (4.3)‘M(t1)which has strong oscillations also, and this function r(t) is sketched in figure 4.5(a). Thevoltage which would have been on the electrodes during this time had the main dischargenot occurred is shown by the dotted line, VM’, in figure 4.5(a). We measured this voltagesignal by firing the laser with higher pressure in the chamber so that only the primarycircuit fired without a main discharge. Since VM’ = 36 kV at the end of the strong currentpulse, the charge which flowed in the main discharge up to that time is approximatelyLQ = Ce(36.0 — 13.0)kV = 370 JLCoulomb, (4.4)while the electrical energy delivered is approximatelyAE = Ce(36.O2— 13.o2)kv 9.1J, (4.5)Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 88corresponding to a deposition of 280 J11atm.The derivative signal of the equation for dIM/dt, and also one for the preionizer(primary) loop, dlp/dt, are each integrated to give the current pulse shapes. In order tocalculate the inductance of the discharge, the main discharge loop area is measured tohave an area of A = 38.4 +0.1 cm2. A second integration is required for ‘M to give thecharge which flowed through the discharge and, when equated with the change in thecapacitor charge given by equation 4.4, we are able to find the absolute current pulse, ‘M,as shown in figure 4.5 (b). The preionizer/inversion current Ip, is also shown in figure4.5(b) and is scaled by solving the differential equation for an underdamped oscillator[1341, using the same algorithm as mentioned in reference [134], now with parameters C= 32.4 nF, L 420 nH and Rp = 1.05 which are the primary loop parameters foundin the same way as described in reference [135] This algorithm also gave the energy Edeposited into the preionizers iii the first 300 ns preceding the main discharge, as E =4.4 J.Energy and Pulse Output of the TEA CO2 LaserThe laser optical cavity consists of two KC1 windows mounted on 0-rings at Brewster’sangle, a 5 m radius of curvature gold-coated full reflector, and a Ge flat, 80% reflectoras an output coupler. The CO2 laser pulse is measured using a Labimex P005 HgCdTeroom-temperature detector and is shown in figure 4.6.The shape of the infrared pulse from the free running electrically pumped CO2 laserdepends on several laser parameters, such as: the duration of the pumping electricalpulse, the energy delivered by the excitation circuit, the operating gas pressure, andthe ratio of the composition gases. The output pulse duration of the above TEA CO2discharge laser is usually of the order of 400 ns. The overall temporal pulse shape consistsof an initial spike (50 ns long) and a long decay tail (‘- 0.5 us long). The initial peakChapter 4. Laser Systems, Optical Setups, and Experimental Procedures>a,cs(0)04LJCa,(b)—589ioTime [ps]Figure 4.5: (a) Main electrode voltage without the glow discharge, VM’, and with theglow discharge, VM. (b) Preionizer/inversion current without the glow discharge, Ip’, andwith the glow discharge, Ip; the main electrode current, IM.2015110c-)CcsV.,U)05Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 90is known as the gain switched peak which is due to the short time required to build upenough gain compared to cavity round trip time. That is, the gain in the CO2 lasercan be turned on quickly by the pumping circuit so that population inversion above thethreshold value is established before the onset of any noise build up of laser oscillations.The origin of the long tail is due to the gain recovery by collisional energy transferfrom the vibrationally excited N2 buffer molecules to the vibrational states of the CO2molecules. This long pulse is usually known as “the nitrogen tail.” The output usuallyconsists of a superposition of several competing longitudinal modes, as shown in figure4.6(b).The laser pulse energy is measured to be 800 mJ (multimode) using a GenTec energymeter (ED 200). The laser energy output is found to be stable to +2%. The specificoutput energy is 25 J11, which is among the highest values reported for TEA CO2 lasers.The overall efficiency is 5.1%, and the pulse to pulse energy reliability is 100%. Theoutput beam is uniform over the 9.5 mm x 9.5 mm area as indicated by Polaroid film burnspots. However, after about ten shots, one of the new intercavity salt windows exhibitedsevere damage due to the high-power laser pulse, which has not, to our knowledge, beenreported previously for TEA CO2 lasers of only 35 cm discharge length. Because of thisdamage problem, we are not able to make a detailed study of the laser output at higherpressures using the configuration described above. With weaker mixtures, in a hybridlaser coilfiguration, operation should be possible up to about 7 atmospheres.4.3.3 The Hybrid CO2 LaserFor ultrashort pulse generation the switching task is made much easier if the CO2 laserpulse incident on the optical semiconductor switch is made as long as possible with amaximum amount of energy. When the CO2 laser pulse is > 50 us, one may consider thetemporal change of the pulse intensity to be insignificant during the switching time ofChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 91Figure 4.6: (a) The CO2 laser pulse shape at 10.6 ,um, with an energy of 800 rnJ. (b)Longitudinal mode beating during the laser oscillation.Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 92a few picoseconds or iess. In addition, a long CO2 laser pulse reduces the constraint onthe accuracy of the timing and jitter between the control visible pulse and the CO2 laserpulse. Clearly, with long CO2 laser pulses, the experimental situation resembles that ofCW CO2 laser switching.For our application, the temporal power modulation due to longitudinal mode beatingof the above TEA CO2 laser is highly undesirable and single mode operation is required.A combined arrangement of a single longitudinal mode CW CO2 (narrow gain) laser,with a TEA CO2 laser sharing the same resonator cavity, provides a single longitudinaland transverse mode with high power output of the order of 50 kW. This CO2 laserarrangement is known as a “hybrid laser”. A typical hybrid configuration is illustratedin figure 4.7. In this laser arrangement, only one section of the CW CO2 laser delivering6 W is used to lock the longitudinal mode of the TEA CO2 laser. The cavity resonatoris the same as the one used in the CW CO2 laser with a total effective resonator cavitylength of 2.9 m. The high pressure section is operated at 1 atmosphere with a lasinggas mixture of C02:NHe of 6:6:88 at a repetition rate between 1 to 2 Hz. The lasermaximum output energy is measured to be ‘—i 25 mJ.The low-pressure CW laser section with a frequency bandwidth narrower than thelongitudinal mode spacing of the optical resonator provides the initial 10.6 m laserphotons and laser gain at only one particular laser mode. Figure 4.8(a) shows the singlemode pulse output from the CO2 hybrid laser with the CW CO2 laser turned on. Thepulse shape differs from that of figure 4.6, which can be explained as follows: the CWlaser gain is above the lasing threshold of the TEA CO2 laser, thus the laser pulse does notevolve from noise as in the case of a free running TEA laser; this results in the opticalpulse occurring at an earlier time than in the free running TEA laser. Moreover, thetime required to build up enough gain needed for the gain switched pulse is dramaticallyreduced. Consequently, the output pulse shows a single mode pulse with a risetirne ofChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 93CW Section TE LaserElFigure 4.7: The hybrid CO2 laser system arrangement.220 ns and a long decay tail of --‘ L5 ,us long. This temporal width of this pulse is idealfor performing optical semiconductor switching experiments.4.4 Synchronization of the Hybrid CO2 Laser and the Femtosecond LaserSystemIt is crucial that accurate synchronization be maintained between the hybrid CO2 laserand the femtosecond pulses from the dye amplifier. This has proved to be an extremelydifficult problem for the following reasons: the whole femtosecond laser system is internally synchronized with respect to the Nd:YAG mode locker’s frequency of 41.0245 MHz.Moreover, the combined delay in the krytron circuit, spark gap, the LC inversion circuit,and the CO2 laser gain build-up time amounts to ‘ 1.5 s which is long compared to themode locker’s clock of 24 ns. That is, the CO2 laser must be triggered about 1.5 its beforethe laser amplifier output to allow for perfect pulse synchronization at the optical semiconductor switch. An electronic timing system that does not disturb the performance ofHV(thapter 4. Laser Systems, Optical Setups, and Experimental Procedures 94Figure 4.8: (a) Single longitudinal and transverse mode from the hybrid CO2 laser. (b)Same hybrid laser with the CW laser turned off.the ferntosecond laser system is the most important priority in our design.An adjustable electronic synchronization unit was designed and built through theUBC Physics Department Electronics Shop to perform the task. The details of thecircuit design are presented in Appendix A. The unit has dual channel TTL output unitswhich can be adjusted independently over the delay range between 0 to 3 ps relativeto the Nd:YAG RGA6O output pulse. For proper operation of the timing unit, thecommercial laser system triggering input was modified with no observable change in thesystem performance. The RF from the mode locker was diverted from its input to theNd:YAG RGA6O amplifier unit, and was directed into the synchronization unit. Thesynchronization unit circuit locks on the 41.0245 MHz clock from the mode locker andtriggers a TTL output signal. The 5 VTTL signal is amplified to 30 V and is usedto trigger the CO2 laser krytron unit that triggers the laser discharge spark gap. Afterthe onset of the channel delay (‘-..‘ 1.1 s) the timing unit triggers the RGA6O timingcircuit to begin optical pulse injection. Figure 4.9 shows a layout of the lasers’ timingChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 95Figure 4.9: A layout of the synchronization between the hybrid CO2 laser and the ferntosecond laser pulse generating system.arrangements. With this timing unit, the overall pulse jitter is ±10 ns, which we believeoriginates from the krytron unit and the spark gap.4.5 Infrared Pulse Detection and Timing System4.5.1 The Cu:Ge Infrared DetectorThe detection of ultrashort CO2 laser pulses is quite difficult because conventional infrared detectors with time constants of 100 Ps are too slow. Since the pulse width ofthe reflected infrared pulses is much less than the response time of an infrared detector,the output amplitude depends on the response time of the detector. In this case, thedetector integrates the input optical pulse, thus acting as a very sensitive energy meter.Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 96220 pFDetector ToInput Oscilloscope180VBiasFigure 4.10: The Cu:Ge infrared detector bias/output circuit.A Cu:Ge infrared detector (Santa Barbara Research Center) is utilized to detect the infrared reflected pulses. The detector has a spectral response over the range between 2 ,umto 30 tm with a risetime of-‘. 0.5 ns. In preparation for the experimental measurements,the detector’s dewar is pumped to 1O torr, then filled with liquid nitrogen and leftto cool for about 1 hour. After that, the liquid nitrogen is disposed and the dewar isfilled with liquid helium to cool it to 4.2 K°. When in use, the detector is biased at 160V with the circuit arrangement displayed in figure 4.10. The detector can be operatedfor a period of six hours on a single liquid helium fill.4.5.2 Electronic AmplifierWhen conducting experiments with the CW CO2 laser, at detector output signals ofthe order of 1 mV, the detector’s signals cannot be measured by the oscilloscope, thus,the signals are electronically amplified in a GHz amplifier connected directly on top ofthe Cu:Ge infrared detector. The amplifier is impedance matched to the 50 ! output10iHVChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 97impedance of the infrared detector. The electronic amplifier was designed and builtthrough the UBC Physics Department Electronics Shop. A complete electronic circuit ispresented in appendix B. The amplifier gain is measured to be 34 dB with a noise levelof —88 dB. The amplifier shows excellent range of linearity with no pulse distortion. Theamplifier is shielded in an RF Faraday cage to minimize the RF noise from the lasers.4.5.3 Experimental Data Collection SystemThe experimeiltal data of the reflected infrared and the visible excitation pulses aredisplayed on a Tektronix 7104 oscilloscope with a 50 l plug-in (7A19) unit. The effectivebandwidth of this oscilloscope is 1 GHz. Initially, we performed some of the experimentsby measuring the reflected signals directly from the oscilloscope traces. Both infraredand visible signals are recorded simultaneously using a video camera for each laser shot.This technique proved to be inexpensive (compared to using Polaroid film) and allowsreal-time analyses of the data; however, it is very time consuming since all the analysisis done manually. Therefore, we have developed a computer controlled electronic datacollection system to perform this task.In the time resolved measurements, we are interested in the amplitude of the reflectedpulses (or energy) as a function of the time delay. Thus, the maximum amplitude levelof an integrated infrared pulse is proportional to the energy contained in the pulse itself.It is evident that the electronic system must have certain characteristics, such as: (1) theability to perform the integration process on a time scale of ‘-‘. 1 ns with a linear integration curve independent of the duration of the pulse; (2) it can be synchronized with thecommercial femtosecond laser system; (3) it must be compatible with the Cu:Ge detector/amplifier arrangement; (4) it must have a low signal to noise ratio with a maximuminput signal sensitivity of ‘—‘ 20 mV in 50 f; (5) it should allow a real-time oscilloscopeChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 98observation if desired. Clearly, our experimental constraints cannot be met by inexpensive commercial sample-hold electronic systems, and a custom-made design had to bedeveloped. A pulse integration module (PIM), which satisfies the above properties, wasdesigned and built through the UBC Physics Department Electrollics Shop. Completeelectronic circuit designs are presented in appendix C.The PIM channels are triggered from the “Sync-out” signal from the output of theNd:YAG regenerative amplifier which arrives 30 ns earlier than the output of the 70 ps0.532 tm optical pulse. The electronic data capture system consists of dual channelintegration modules, one for the infrared pulse and the other for the excitation pulse.Each integration channel has an integration window of 5 ns in width; therefore, thesignals are timed very accurately to within 250 ps using a built-in variable delay circuit, sothat the pulses fall inside their respective integration window. The signal synchronizationcan be performed by monitoring the signal and the integration window, through theanalog output of the device, on the oscilloscope while varying the delays. Both signalsare captured and integrated simultaneously. The device was tested for proper bandwidthand linearity before its use in the experiments. Figure 4.11 shows the linearity from bothchannels using simulated 1 ns input pulses. The linearity of the device is ‘- +8%, whichis sufficient for our experimental purposes.The integral values from the infrared pulse and its corresponding visible excitationpulse are digitized and stored directly on a personal computer for further analysis. Theattractive features of this device make it an indispensable laboratory instrument forpulse-probe type experiments.Chapter 4. Laser Systems, Optical Setups, arid Experimental Procedures 993210543C21023 4 5 6101 102 103Input (mV)Figure 4.11: Integrated output from the dual channel pulse integration module as afunction of the input pulse voltage amplitude. The solid circles denote channel 1 and theempty circles denote channel 2.4.6 Hall Conductivity Measurements in SiThe Van der Pauw method [150, 151] is used to measure the conductivity, minority carrierconcentration, and the type of the carriers in several Si wafers. The measurements areperformed in a high magnetic field of 0.4 T produced by a 3.8 A power supply.4.7 Autocorrelation Pulse Width MeasurementsIn this experiment, we are working with ultrashort excitation pulses; therefore, the characterization and the ability to control the duration of the control excitation pulses fromthe dye laser (amplifier) are extremely important. The duration of the excitation pulsedetermines the temporal response of the optical semiconductor switch. The pulse duration of the laser system is very sensitive to the daily alignment and the operatingconditions of the Nd:YAG laser; therefore, pulse width measurements must be performedChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 100before the start of any experiment. The manufacturer’s specification on the dye laserpulse is < 500 fs. However, since we replaced several components in the laser system:laser mode locker and laser cavity in the Nd:YAG laser, and the optical fiber in the pulsecompressor stage, the optimum parameters, including the pulse width, of the laser systemmust be finely tuned.When working with ultrafast optical pulses of a few picoseconds or less, there is noconvenient direct method of observing the duration of the laser pulses with conventionalphotodetector/oscilloscope having an adequate bandwidth. The correlation techniques[152]—[l60] using nonlinear optical processes in suitable crystals are the most popularand cost effective experimental methods to measure femtosecond pulse durations. Wehave constructed an autocorrelator based on a non-collinear beam Michelson type interferometer which permits the performance of background free pulse width autocorrelationmeasurements. The layout of the autocorrelator is illusrated in figure 4.12. The 82 MHzpulse train from the dye laser is equally split by a beam splitter; half of the pulse trainis incident on fYI4 and M5. A linear time delay, r, is repetitively produced in one armof the Michelson interferometer. This time delay is achieved by using a pair of parallelmirrors (M4 and M5) mounted on a plate which is rotating at a constant frequency, fr.When the shaft is rotated by an angle, Or, this beam traverses a different path and isreflected back by M2 parallel to the its original direction. The second half is reflected bythe retroreflector mirrors (M6 and M7) and is slightly displaced. The two pulses can beoverlapped in time at the KDP second harmonic crystal (SH) by mechanically changingone of the optical path lengths by a small amount (a 400 fs pulse duration is only 130um long).The parallel mirror assembly [152] leads to an increase (or decrease) of the optical pathlength for the optical pulse. Thus the transmitted pulse train is delayed (or advanced)about a reference position (zero delay). With a small angle approximation, the timeChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 101delay varies linearly with the angle rotation. The two pulses are focused by a 3 cmfocal length plano-convex lens on a KDP, SH generating crystal. The maximum U.V.output is obtained when the two pulses are coincident in time, and the SH decreasesas one pulse is delayed with respect to the other. This technique measures the secondorder autocorrelation function of an intensity pulse, I(t), which is given by the followingexpressionG2( ) — <I(t)I(t+r)> (46)T—were < > indicates the average over a sufficiently long interval of time. The true pulseshape is shown to be a double exponential and is related to the autocorrelation signalwidth by [160]AT = 2.421Ar, (4.7)where Ar, and Ar are the FWHM pulse widths of G2(r) and I(t), respectively. Thedetails of the design of the autocorrelator and the optical components are presented inAppendix D. The autocorrelator is found to have excellent stability and pulse reproducibility. Its characteristics are comparable with the commercially available autocorrelators. The autocorrelator can be modified so that it can be used to measure both thedye laser pulse train at 82 MHz and the amplified dye laser output pulses at 10 Hz.The femtosecond dye laser system is optimized to produce the shortest pulses possible. Figure 4.13 shows a typical autocorrelation trace from the dye laser pulses beforeamplification. Assuming a double exponential pulse shape [160], the shortest pulse widthobtained from our dye laser system is 370 fs at 616 nm. Detuning the dye laser cavitylength by less than 1 tm results in various pulse durations. In the case of the dye resonator cavity being longer than the optimum length, the resulting pulse is wide. Onthe other hand, when the dye resonator cavity is tuned to be shorter than its optimumlength, a double-pulse shape results. These pulses are shown in figure 4.13 (b,c). Clearly,Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 102PMTKDPM3M2Figure 4.12: The autocorrelator. B.S.= beam splitter, PMT= photomultiplier, andKDP= second harmonic generation crysta’ (Potassium Dihydrogen Phosphate).M1M7B.S.M4Laser Beam InputChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 103the pulse duration is very sensitive to the optical alignment and cavity detuning lengthof the dye laser; therefore, the duration of the dye pulse is always monitored during theexperiments and before injecting the laser pulse into the dye amplifier.The autocorrelation method described above is a scanning quasi-CW technique, whichlooks at signals that are repeating every 12 ns (82 MHz). What is observed on theoscilloscope is a sample average over thousands of pulses. However, the situation ismore complicated when dealing with laser pulses with a low repetition rate such as theones from the dye amplifier. One can interchange the role of the arms of the Michelsoninterferometer, so that the rotating arm of the interferometer is used as a referencearm and the reference arm is used as a scanning one. Measurement of the amplifiedpulse duration is done manually by fixing the rotating mirrors at a certain position andscanning the delay of the retroreflecing mirrors (M7 and M6). This interferometer armis moved through the overlap region, thus obtaining a slow scan of the autocorrelationsignal. The autocorrelation trace is recorded as a function of the relative time delay. Wehave performed several experiments to measure the duration of the amplified pulse as afunction of the input dye laser pulse; figure 4.14 shows a measured amplified dye pulseduration of 490 fs (assuming double exponential pulse shape). Each point in the graphis averaged over 15 shots and the standard error is indicated. This pulse is obtained byinjecting the dye amplifier with a 370 fs pulse for the dye laser system. The increase inthe duration of the pulse width is a result of group velocity dispersion in the dye amplifierdye-cells and the optical components. With proper pulse compression techniques, it ispossible to restore the pulse duration to its original width. Our results indicate that thelimiting factor in the dye amplifier output pulse duration is the duration of the injecteddye laser pulse. It is evident that by injecting the amplifier with a pulse similar to the onein figure 4.13 (b), this results in an amplified pulse of almost the same shape as shown infigure 4.14 (b), thus care must be taken during the experiment to avoid obtaining suchChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 104Figure 4.13: Typical autocorrelation traces from the dye laser system. (a) Cavity lengthis optimum resulting in a pulse width = 370 fs. (b) Cavity length is too short resultingin a pulse width = 500 fs; note the side peaks in the autocorrelation trace. (c) Cavitylength is too long resulting in a pulse width = 830 fs. The time scale in (a) and (c) is 10ps/div, whereas in (b) it is 20 jts/div.Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 105pulse shapes.4.8 Optical Semiconductor Switch SetupThe experimental layout for the optical switch is illustrated in figure 4.15. The singlecrystal semiconductor samples used in experiments are undoped GaAs (Crystal Specialties, Intl.) with a resistivity of -‘ 108 l cm. The GaAs samples are cleaved to 2x1.5 cm2from a 2.54 cm (diameter) wafer, as shown in figure 4.15. The sample thickness is 450tim. polished on both surfaces, and it is mounted on a rotary-xy translation stage.The infrared beam is focused by a 20 cm focal length KC1 lens to an elliptical spot ofan area 1.2 mm2 on the GaAs wafer. The semiconductor wafer is set at Brewster’s angleof 72° to obtain a high contrast ratio relative to background infrared reflection. Thisis necessary to detect small changes in the transient reflectivity. The accurate settingof Brewster’s angle is achieved by rotating the GaAs crystal until a minimum reflectionis obtained from the front surface. Due to the finite divergence of the infrared beamin the focal region and due to the thickness of the wafer, it is not possible to obtainzero reflection from both surfaces simultaneously. Therefore, the wafer is adjusted forzero reflection with respect to the wafer’s front surface only. A high contrast signal tobackground ratio of i0:i ratio is obtained during the experiment.The visible excitation pulse is split into two identical pulses by a 50:50 beam splitter(as shown in figure 4.16). One pulse is directed towards the GaAs reflection switch, andthe second pulse is passed through a variable delay line (which is used for pulse widthmeasurements). The accuracy of the temporal delay is ±40 fs. Sharply focusing thehigh energy visible pulse on the switch is undesirable. If the excitation pulse spot size issmaller than the CO2 beam spot size, then this results in the reflection of only a smallportion of the infrared beam. Thus, infrared pulses of low energy and high divergenceChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 1066 1.1 (a)i..—.3..—Ci)Cl) 1•.0• . ——2.5 —1.5 —0.5 0.5 1.5 2.56 I I I5 (b). .L.•; :•PicosecondFigure 4.14: (a) Autocorrelation signal of an amplified, 1 mJ, 616 nm dye pulse showinga pulse duration of 490 fs. (b) Same conditions but with the injected pulse from figure4.13(b).Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 107Figure 4.15: The experimental arrangement for a GaAs optical semiconductor switch.are produced. In order to ensure good reflected beam quality, the visible excitation pulseis reduced to a spot size of 3 mm2 in area and is superimposed on the infrared laserspot. The angular spread between the infrared beam and the visible pulse is kept to aminimum angle of ‘-. 50 so that the reflected infrared pulses do not suffer from wave frontdistortion as the control pulse wave front sweeps across the switch. Approximately 2%of the excitation pulse is picked up from the surface reflection from the focusing lens andis used to monitor the visible pulse excitation energy. The detection is performed with afast photodiode (Hamamatsu-R1193U.03) having a risetime of 500 Ps.4.9 Time Integrated Infrared Reflectivity SetupIn order to reach low excitation levels, the intensity of the visible control pulse is graduallyreduced by passing it through a sequence of variable stacks of calibrated neutral densityfilters (Kodak Wratten Gelatin). The linearity of the calibration is checked with a stable490 fs, 618 nmPulseCO2 Laserf=20 cmTo PowerMeterReflectedPulseGaAsTo EnergyMeter50Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 108HeNe laser, and the calibration factors are found to be about ±5% from their nominalvalues. A new calibration curve is deduced and used throughout our experimental work.In this experiment, the natural shot-to-shot fluctuations in the amplified visible laserpulse allow us to access a continuous range of excitation energies which provides anoverlap range between the different neutral density filters. During the course of theexperiments, great care is taken to ensure that placing the neutral density filters in frontof the visible excitation pulse does not disturb the alignment of the infrared and thevisible laser spots. The duration of the 370 fs dye oscillator laser pulse is measured afterpassing through the filters with no change in its duration.4.10 10.6 um Pulse Width Measurement TechniquesMeasurement of the reflected infrared 10.6 1um laser pulse durations cannot be performeddirectly with photodiodes. The fastest photodiode operating at 10.6 pm has a risetimeof 100 Ps with a fall time of ‘—‘ 1 ns. Clearly this is not sufficient to resolve thesubpicosecond reflected pulses. We are interested in measuring the temporal shape ofthe reflected infrared pulses with an expected pulse duration of 50 ps; but since thepeak power of the reflected pulse is low, it is impossible to use conventional secondharmonic autocorrelation techniques or conventional measurements through frequencyupconversion mixing with the control visible pulse. Moreover, the low repetition rate ofthe pulses creates an additional difficulty.It is evident that the measurement of the pulse duration has to be performed bysome indirect manner. Indirect methods using nonconventional correlation techniquescan overcome the limitations imposed by the measuring system. In the following section we briefly review the principles underlying two independent schemes for measuringthe reflected pulse durations: reflectioll-reflection correlation and cross-correlation. TheChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 109principle of these methods is to transform the temporal pulse duration information intospatial information which is clearly easier to analyse. These correlation techniques arecapable of determining the infrared pulse duration with subpicosecond time resolutionand can be applied to other ultrashort infrared laser pulses at different wavelengths.Since the duration of the visible excitation pulse is well-characterized (490 fs), in bothcorrelation techniques, one uses the visible excitation optical pulse (control pulse) as ameasuring scale to determine the infrared pulse duration.4.10.1 Reflection-Reflection Correlation Procedure and Optical SetupThe reflection-reflection correlation infrared pulse measuring method is similar to theautocorrelation technique in the sense that the reflected infrared pulse is convoluted withan identical copy of itself as a function of time. In this type of experiment, we requirethe use of a second identical GaAs infrared reflection switch which is optically-triggeredsynchronously with the first GaAs reflection switch. Due to the nature of the reflection-reflection correlation technique, certain assumptions have to be made about the pulseshape. The reflection-reflection correlation measurements can produce ambiguous signals,and any sharp temporal features associated with the pulse are washed out through thecorrelation process. However, this type of experiment is necessary to obtain an estimateof the overall pulse width.The measured reflection-reflection correlation signal, A(r), is proportional to:A(r) j I(t)I(t + r)dt (4.8)where, 1(t), is the infrared reflection pulse produced by the first switch, and I(t + r)is the reflection from the second optical semiconductor switch at a delay time, r. Thesecond GaAs switch reflectivity is delayed by time r relative to the first GaAs switch.The delay time, r, must be long enough to encompass the infrared pulse width from theChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 110first GaAs switch. The product signal is largest when the two peaks of the infrared pulseand the control pulses of the second switch overlap at the second switch (r=0). Theproduct signal is smallest when those two signals are separated by T which is longer thanthe infrared pulse width. Concentrating initially on the expression for A(r) in equation4.8, it is clear that 1(t) cannot be recovered from equation 4.8 without some additionalinformation. The shape of A(r) is always symmetrical about r=0, even if the initialpulse is asymmetrical.The schematics of the whole experimental measuring system is in figure 4.16(a). Bothreflection switches are taken from the same semiconductor wafer. Here, a second GaAsreflection switch is set at Brewster’s angle with respect to the reflected infrared pulsefrom the first GaAs switch. Since reflection-reflection correlation type experiments aresensitive to the alignment of both switches and the background infrared reflection, theangle setting is accurately adjusted for the first GaAs switch, then the semiconductoris removed and a small mirror (gold-coated Si wafer of the same thickness as the GaAswafer) is mounted in its place. The full CO2 laser beam is reflected and is used to align thesecoild semiconductor switch exactly at Brewster’s angle. The experimental coilditionson both GaAs switches are made to be almost identical.The infrared pulse is focused on the second GaAs switch with a 15 cm focal lengthKC1 lens, and its visible excitation pulse is delayed and focused to an approximatelyidentical spot size to that of the first GaAs switch. However, the angle between theinfrared pulse and the visible excitation pulse on the second GaAs switch is limited byour optical setup and is measured to be 8°. A removable mirror is placed in the opticalpath of the collection system to provide a reference signal corresponding to the infraredreflection from the first GaAs reflection switch. With this optical arrangement, we are notable to entirely eliminate the back surface reflection from the first GaAs switch, and thereflection-reflection experiments are performed with the presence of a small backgroundChapter 4, Laser Systems, Optical Setups, and Experimental Procedures 111infrared reflection. The stray visible pulse light reflection coming onto the detector iseliminated by placing a GaAs wafer at Brewster’s angle at the entrance to the detector.The exact time delay range is initially set by accurately measuring the optical pathsthat the infrared and the visible pulses take to within ±3 mm. Then the delay line isscanned over this distance range, and at the same time the infrared reflection from thesecond switch is monitored on the oscilloscope until a maximum reflection is obtained(this defines the overlap of the reflection pulses from the two switches). The delay lineis then moved forward and backward to measure the wings of the pulse by 30 — 60 ps.4.10.2 Cross- Correlation Procedure and Optical SetupWe are interested in measuring the exact temporal shapes of the reflected infrared pulses.Therefore, we present a simple method to perform this task: the time-resolved cross-correlation experiment is basically a method of convolving the infrared reflected pulsewith an ultrafast transmission function.The cross-correlation method does not directly provide the pulse width but the pulsedifferential with respect to time. Also, it is superior to autocorrelation schemes in preserving the details of the pulse shape and providing an indication of the background level.The technique relies on the e-h plasma generation in a semiconductor which serves as afast temporal transmission gate. The semiconductor must have a large absorption depthfor the visible radiation, a long recombination lifetime compared to the measured pulsewidth, and a small free-carrier absorption cross-section for the infrared wavelength. Wehave experimented with two semiconductors, germanium and silicon, as possible candidates for infrared transmission cut-off switches; however, since the plasma layer in Ge isapproximately 180 nm thick, the 10.6 um radiation is able to penetrate and leak throughthe plasma layer. Thus, the experiments performed with Ge are done above a backgroundlevel and are not discussed in this work. On the other hand, Si provided an excellentChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 112FLCO2 LaserFigure 4.16: Typical experimental configurations used to measure the infrared pulseduration: (a) Reflection-reflection correlation experimental setup. (b) Cross-correlationexperimental setup. B.S.= beam splitter, B.D.= beam dump, E.M.= energy meter,P.E.= power meter, R= reflection switch (GaAs), M= temporary mirror, F= filter (GaAswafer), D= Cu:Ce infrared detector, and T= transmission switch (Si).Dye Laser B.S.PulseDelay(a) FE.M.P.M.MLE(b) TChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 113contrast ratio; therefore, it is used throughout this work. It will be shown in chapter 5that silicon is an ideal semiconductor for this type of experiment.The cross-correlation experiments are performed in the following manner: the probevisible pulse is directed towards a transmission cut-off switch to optically excite thesemiconductor, and thus creates a plasma density greater than the critical density5 x iO’ cm3) in the absorption skin depth of silicon. The thickness of the plasma layeris 3 1um. When the visible excitation pulse arrives at the Si transmission cut-offswitch earlier than the infrared pulse, the infrared pulse is both reflected and absorbedby the free carriers. As the visible pulse is delayed, part of the infrared pulse from thereflection switch propagates through the Si switch. The part of the pulse which arrivesafter the critical plasma density is created suffers from large reflection and absorption.By scanning the relative delay between the infrared pulse and the visible probe pulse, theinfrared pulse is temporally gated and integrated by the detector as a function of time,and a transmission step whose risetime is the cross-correlation between the infrared andthe visible pulse is obtained. The time integral of the pulse is obtained as a functionof the relative delay. The measured integrated pulse shape, 1jr, is calculated from thefollowing expression:j R(t)T(t + r)dt (4.9)where R(t) is the reflectivity of the optical semiconductor reflection GaAs switch andT(t + T) is the transmission of the cut-off Si switch at a time delay, r.The experimental optical arrangement of the cross-correlation experiment is illustrated in figure 4.16(b). The transmission cut-off switch is made of a 50 tm thick pdoped (1.56x10’6 cm3) Si wafer (optically polished on both surfaces) cut to a size oflxi cm2. The surface reflection of the Si sample is measured to be 35% at 10.6 1um, andresistivity of the sample is measured to be 1.41 l cm. The sample is mounted behind aChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 114small hole of ‘- 0.5 mm diameter and is placed normal to the incoming infrared pulse.The excitation pulse (visible) is made to cover the pinhole; therefore, the cut-off switchis uniformly illuminated. Furthermore, with the introduction of the pinhole, the uncertainty involving the overlap of the pump and probe pulse is eliminated. The angle ofillumination of the Si cut-off switch is kept to a minimum of - 9° relative to the infraredpulse. This is limited only by the geometry of the optical setup.In this type of experiment, one must eliminate the reflection from the rear of thesemiconductor GaAs reflection switch. Therefore, the stray reflection is eliminated withthe optical collection system, as shown in figure 4.17. With the aid of the HeNe laserbeam we are able to trace the exact path of the reflected infrared pulse, and we measurethe separation between the position of the reflected pulse and the reflection resulting fromthe rear surface to be -‘ 7 mm. An adjustable iris is placed between the two collimatinglenses at a distance of 18 cm away from the focus to obstruct the stray reflection. Withthis simple arrangement we are able to obtain a signal to background ratio of i:i0. Insome experiments an optically polished Ge flat is used as an infrared filter to ensure thatno visible radiation leaks through to the infrared detector.The correct time delay range is initially set by accurately measuring to within 3mm, the optical paths between the infrared and the visible pulses. Then the delay line isscanned over this distance range, and at the same time the infrared signal transmissionis monitored on the oscilloscope until the infrared transmission is completely cut-off (thisdefines the zero delay time). The delay line is then moved forward (for earlier arrivalof the visible pulse relative to the infrared pulse) by 5—10 Ps to provide a long zerotransmission base-line in order to resolve the initial risetime of the pulse.Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 115Iris Si Pinhole IR PulseIR CW ReflectionFigure 4.17: Optical arrangement used to eliminate the rear reflection resulting from thefirst GaAs reflection switch.4.11 Infrared Pulse-Frequency Measurement TechniqueMeasurement of the frequency spectrum of the reflected infrared pulses should providea complementary and independent method to both reflection-reflection correlation andcross-correlation techniques. However, there is a difficulty associated with the detectionof the infrared spectrum, mainly the lack of a fast sensitive charged coupled deviceoperating at 10.6 m. Although pyroelectric arrays can serve this purpose, they lack thesensitivity and the temporal response at 10.6 tm. In fact, we have used unsuccessfullysuch a device to record the frequency spectrum. Thus we investigate the use of animage disector optical setup, combined with an infrared spectrometer, to measure thefrequency spectrum of the infrared pulse on a single shot basis. The apparatus permitsthe measurement of the spectrum with a very high detectivity by using only a singleinfrared detector.“I,To DetectorChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 1164.11.1 The Image DisectorThe image disector has been used widely in our laboratory to measure the frequencyspectrum from scattered light in laser-plasma interaction experiments. It is based onthe principle that the individual frequencies making up the pulse spectrum are mappedonto time delayed signals (in contrast to correlation experiments where the temporalinformation is mapped into spatial distribution). To explain further, an ultrashort opticalinfrared pulse at 10.6 tim, with a duration less than the response time of the detector,has a frequency spectrum whose width in frequency is inversely proportional to thepulse duration. The spectrum of the infrared pulse is spatially dispersed by passingthe pulse through a spectrometer, and if the frequency spatial dispersion is made wideenough, then by circulating the optical pulse through a special optical mirror arrangement(image disector), one can allow only successive parts of the frequency spectrum to exitthe optical arrangement for each transient reflection the infrared pulse takes through theoptical system. Consequently, one can use a single fast infrared detector to obtain a pulsetrain (channels) that maps out the full pulse frequency spectrum. Clearly, the temporaldelay for the pulse inside the optical system must be longer than the response time ofthe infrared detector. By proper choice of spatial dispersion of the spectrum, one canobtain the desired frequency resolution per channel of the optical setup.4.11.2 Optical Setup and Alignment of the Image DisectorThe optical arrangement of the image disector and the optical collection system is illustrated in figure 4.18. The image disector itself consists of three concave gold-coatedmirrors, M1, M2 and M3, all of the same focal length of 50 cm. Both M2 and M3 are 5.08cm in diameter and are separated form M3 by a distance of 1 m. The M1 mirror is squareedged (7 cmxi cm) with the flat sides cut to a sharp edge of 100 to allow the part of theChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 117infrared image spectrum to exit the multi-pass optical arrangement. Since the techniquerequires a few reflections on each pass, the optical qualities and the reflectivities of themirrors, M1, M2, and M3 must be high: A/10 and ‘ 99%, respectively.The reflected infrared pulse is collimated with two NaC1 lenses (f.l.= 15 cm) to form a1:1 telescope arrangement. The infrared pulse is directed toward the spectrometer whereit is focused on a 380 im entrance spectrometer slit with a NaC1 (f.l.= 15 cm) lens.Upon exiting the spectrometer, the infrared pulse image spectrum is focused at a pointdirectly over the front surface of M1 of the image disector by a 45 cm focal length (7.62cm diameter) concave mirror. With this focusing mirror, the image of the exit slit ofthe spectrometer is made to fully cover M2. Mirror M2 produces series of images of thespectrum progressing down and towards the right edge of M1, while mirror M3 producesimages of the spectrum progressing down and to the left edge of M1. On successivereflections, a small part of the spectrum is sliced off and allowed to exit the disector.This in turn represents the first channel of a spectrum. The rest of the spectrum imageis reflected back again through the optical arrangement, successively displaced verticallyfrom one another and to the right near the mirror’s M1 edge, and progressively sliced off(later in time) as the spectrum of the pulse is scanned by the spectrometer. By properalignment of the mirrors, as much as 10 channels can be obtained. The resolution of theimage disector depends on the spatial spacing between the channels. Figure 4.19 showsa typical ten channel output spectrum from the image disector system. The outputchannels of the image disector are collected with a 77 cm focal length mirror (7.62 cmin diameter), a 50 cm focal length NaCl lens (12.7 cm in diameter) and a 10 cm focallength NaCl lens to focus the channels on a single Cu:Ge infrared detector.Several temporary mirrors are placed in the pulse path to bypass the image disectorand the spectrometer. This proved to be very useful before the start of the experimentwhen the visible control pulse spot and the infrared beam spot are aligned. Once aChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 118reflected pulse in detected by the Cu:Ge detector, these mirrors are removed and spectrumis measured.4.11.3 Calibration of the Image Disector Optical SystemIn order to simplify the alignment procedure of the optical system, we placed a goldcoated Si wafer, a Si wafer, and the GaAs optical switch on the same sample holder.The sample holder is mounted on a fine linear translation stage, so that each sampleor the mirror can be placed at the focus of the CO2 laser beam without disturbing thealignment of the optical system. Figure 4.20 illustrates the wafers’ arrangements. Thegold-coated mirror is used to reflect the CO2 laser beam so that the laser beam can beused for the purpose of aligning both the spectrometer and the image disector.The spectrometer used in this experiment requires a precise calibration against aknown wavelength. Initially, a HeNe laser =0.6328 m) is used to calibrate all the 17orders from the grating against the dial reading on the spectrometer; however, over thislong calibration range, the dial reading is nonlinear with the wavelength reading. For asmall dial range, the dial linearity is found to be excellent. Therefore, the spectrometercalibration is performed with the aid of CW CO2 laser lines combined with the 0.6328 tmHeNe laser line (over a small wavelength range). To obtain different lines from the CO2laser, the Ge etalon output coupler temperature is adjusted so that the laser is made tolase at three different lines: 10.611 tm, 10.632 m, and 10.591 ,um. The lasing wavelengthis checked with another calibrated infrared spectrometer (Optical Engineering). Twoother calibration wavelengths of 10.125 um and 10.758 pm are obtained from the 16thand the l7 orders of the HeNe laser line. Figure 4.21 shows a complete plot of thecalibration of the dial reading as a function of a wavelength. A linear fit through thedata points gives a calibration value of 10 A per one dial reading.Since each channel of the spectrum goes through a different number of reflectionsChapter 4. Laser Systems, Optical Setups, and Experimental Procedures0L19cmFigure 4.18: Experimental optical setup for the reflected pulses spectrum measurement.T= temporary mirror, and G= grating.IR Pulse f 15 cmf=77 cm To DetectorSpectrometer f=50 cmM2 M3Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 120Figure 4.19: A typical oscilloscope trace of the output of the image disector showing tenchannels.d ItSi Au Mirror GaAsTranslation AxisIRFigure 4.20: Samples arrangementChapter 4. Laser Systems, Optical Setups, and Experimental Procedures 121.128002600240022002000180010.0 10.2 10.4 10.6 10.8Wavelength (micrometers)11.0Figure 4.21: Calibration curve of the spectrometer reading against the CO2 laser wave-length.Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 122inside the image disector, it is expected that the reflectivity of the image disector opticsvaries for each one. A simple method to calibrate the reflectivity of each channel is to usea long 10.6 tm laser pulse. A Si wafer is used as an optical semiconductor switch (in placeof GaAs) to generate - 1 ns pulses at 10.6 1um. These pulses have a narrow spectrum(narrower than the ones generated from the GaAs) which can fit in one channel. Then thespectrometer output spectrum is scanned across a 160 m exit slit so that the maximumof each channel is displayed on the oscilloscope. A total of six channels are obtained withrelative normalized reflectivity, as shown in figure 422, The spectrum of the reflectedinfrared pulse from the GaAs optical switch is deconvoluted with the calibration curve infigure 4.22. The spacing between the channels is obtained directly from the dial reading.The alignment and the calibration of the image disector is adjusted before the start ofeach experiment.Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures 1231.2 I I •—Ct.cr 0.8N.—Ct$1.4O 0.2z0.00 2 4 6 8Channel NumberFigure 4.22: Image disector calibration curve. The error bars are the standard deviationof signals for 10 consecutive shots separated by 13.3 ns.Chapter 5Experimental Investigation of Infrared Reflection from GaAs5.1 IntroductionThis chapter describes the experimental results and methods used to generate and tomeasure ultrafast infrared optical pulses at 10.6 tim, The infrared reflection experimentsare mainly performed on GaAs semiconductor plasmas. The major experimental workand results in this chapter have been presented in our current publications [161, 162]. Inorder to have a clear understanding of the optical semiconductor switching process(es),we have performed four types of experiments followed by theoretical modelling of theswitching process. We start the chapter by examining in detail the optical and temporal response of a Si transmission cut-off switch by performing infrared transmissionexperiments. This type of experiment is undoubtly crucial in determining the temporalresolution of the time resolved measurements. Moreover, we present some theoretical considerations of the dielectric constant as a function of the optically generated free-carrierconcentration and its spatial distribution and calculate the transmission of an infraredpulse through such a distribution as a function of the carrier density at the surface of theilluminated Si-wafer. The results of the experimental work and the analysis of the resultsbased on model predictions are also presented. Next, we present the experimental workdealing with the variations of the infrared reflectivity with the photogenerated plasmadensity. This experiment is used to examine the proper e-h density operation region ofthe reflection switch. Details of time resolved experiments used to measure the durations124Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 125and temporal shapes of the 10.6 jim reflectivity pulses are determined by two independent methods: cross-correlation and reflection-reflection correlation measurements. Thelimits and advantages of the two methods are presented and the results are discussed ingreat detail. A modifed infrared reflection model is also presented to account for the observed time resolved experimental data. Finally, the experimental results of the infraredreflected pulses frequency spectrums are outlined at the end of this chapter.5.2 The Si Transmission Cut-Off Optical SwitchBefore proceeding with the time resolved cross-correlation measurements, one needs tocharacterize the speed of the optical switching elements. We have developed a novelmethod for measuring the infrared pulse durations and temporal shapes. This cross-correlation technique is reviewed in section 4.10.2. Clearly, its temporal sensitivity andresolution is determined by the choice of the active optical switching element. The choiceof a proper semiconductor switching element is limited by the magnitudes of both free-carrier and intervalence band absorption, and the lifetime of the optically generatedcarriers. As we will show later in this section, the magnitude of the first two absorptionprocesses determine the speed of the initial transmission cut-off of the switch from fulltransmission (T= 1) to zero level (T= 0), whereas the lifetime of the carriers determinesthe temporal persistance of the off-state of the optical transmission switch. It is evidentthat for an ideal situation one needs to minimize the initial infrared transmission temporalcut-off so that it is less than the optical excitation pulse by reducing the effects due to thefree-carrier absorption process. On the other hand, the carrier lifetime (due to Auger andtwo-body recombinations) must be optimized to be longer than the measured infraredpulse. Ideally, the transmission switching element behaves as a temporal step function.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 126The knowledge of free-carrier absorption cross-sections is especially useful in understanding the behavior of other types of high power optical-optical semiconductor switches.Optical-optical reflection and transmissioll cut-off switches [55] have been used extensively for short pulse generation schemes. Ill such applications, one relies on both thedegree of free-carrier absorption and the level of reflection of infrared radiation to operate the Si cut-off switch in the THz range. Rolland and Corkum [55] have used Sias a transmission cut-off switch where they managed to gate high-power 130 fs pulsesat 10.6 pm. The authors calculated the transmission of the switch as a function of theoptically generated carriers; however, they did not provide the necessary experimentalwork to optimize the switch, such as an investigation of the type of doping needed forfaster operations.In our current work, we were interested in using this switch to perform time-resolvedcross-correlation measurements. In order to model the performance of the switch, detailedknowledge of the dielectric constant c= Er + cj, in particular its imagmary component,j, arising from free carrier and possibly intervalence band absorption, is important. We,for example, are especially interested in the response time of a Si transmission switchfor 10.6 pm radiation after irradiation with 0.49 Ps, 616 nm laser pulse, in which casethe magnitude of,critically affects the switching speed [161]. The main question to beinvestigated is: can the switch transmission be turned off on a time scale less than theexcitation visible pulse?In general the absorption cross-section for such photoexcited free carrier Si-plasmas isinferred from measurements on both p- and n-doped samples in which the infrared wavelength and magnitude of the reflectivity minimum is determined as a function of carrierconcentration [163]. However, it is not at all clear whether this inference is justified considering that both electrons and holes are photogenerated with significant energies abovethe band minima leading to highly elevated carrier and lattice temperatures. It wouldChapter 5. Experimental Investigation of Infrared Reflection from GaAs 127therefore be desirable to conduct measurements of the relevant parameters directly onphotoexcited free carriers. Here, we present the results on infrared pulse transmissionexperiments which permit such measurements. The results show that at 10.6 ,um, in contrast to intervalence band absorption, free-carrier absorption dominates the absorptionprocess [163]. From these experiments, the momentum relaxation times can be determined. Also, the experiments reveal the interesting fact that these relaxation times areshorter by a factor of 0.4 if the carriers are generated in n-type as compared to p-typeSi.5.2.1 Theoretical ConsiderationsThe model treatment of the physical processes involved is very simple. Here, severalassumptions are introduced to simplify the physical situation. We begin by treating theoptically generated plasma in Si as being an inhomogeneous plasma which is subjected to10.6 im radiation. It is appropriate to treat the situation as a one dimensional problem.This is justified because the diameter of the excitation area on the Si surface is muchlarger than the absorption skin depth of the visible radiation. Moreover, the spatial profile of the plasma in the transverse direction is assumed to be uniform. The model treatsthe absorption of the 10.6 ,tim radiation to be proportional to the free-carrier concentration; this situation is similar to free-carrier absorption in highly doped semiconductors[164]. Since interband transitions are not allowed at this wavelength, the response of themedium to the applied electromagnetic field can be characterized by the Drude theory forthe frequency-dependent dielectric function. The Drude model of free carriers has beenvery successful in describing the optical properties of semiconductors after quantum corrections for intervalence band absorption have been made [164]. Combining the effects ofelectrons and holes [163] and transferring averages over the carrier energy distributionsto that over the carrier relaxation times [165], we write the real and imaginary parts ofChapter 5. Experimental Investigation of Infrared Reflection from GaAs 128the dielectric constant as:/ 4irne2 w2<r0> ‘\I (5.1)\ fbrn*w1+w< o>)and/4irrie2 w<r0> A= b I + crVbn) . (5.2)\mw1+<r0> \/7t )Here b= 11.8 is the background dielectric constant for the bulk Si and 0vb is theintervalence band absorption cross-section. For carrier densities less than 1020 cm3, thecarriers effective masses may be taken to have their low-density values [166] (m* =m’+mj’, with m= 0.26m and m = 0.38m) [163], <T0 > is the mean momentumrelaxation time for the optical process, and ub the intervalence (heavy to light hole)band absorption cross-section. The electrons and holes are assumed to have the samerelaxation time which is taken to be independent of the energy of the carriers. Also thedependence of the dielectric function on the lattice temperature is ignored in this model.We now define a critical density n:bm*w2 (1 + W2 <To >2)nc = (5.3)4Te2 w2 <r0 >2and write for the complex dielectric constant:= b (i_ L(i - ia)). (5.4)Here a combines the effect of both free-carrier and intervalence band absorption: a =afc + a with aj = 1/(w < T >), where afc and ab are the first and second termsof equation 5.2, respectively. The only free parameter in this model is the free-carrierabsorption cross-section which is due to a combination of both electrons and holes and isconsidered to be constant over the range of the plasma e-h density used in this experiment.In the experiments to be described later the free carriers are produced by absorptionof photons in a 490 fs, 616 nm laser pulse; the generation rate is taken to be a deltaChapter 5. Experimental Investigation of Infrared Reflection from GaAs 129function in time as compared to the experimental time scale. This pulse generates adensity distribution in a direction perpendicular to the illuminated Si-wafer surface atz= 0 of the form:ri(z) = (55)The absorption depth, at an excitation wavelength of 616 nm is measured tobe 3 m [167]. Due to this large depth, ambipolar diffusion has very little effect onthe density profile over time scales of interest in the present experiment (<50 ps) andwe neglect it in our calculations [168]—[170]. At these time scales both Auger and two-body recombination can also be neglected. Auger coefficients of Si are measured to be9.9x1032cm6s1for p-type, 2.8x103’cm6s1for n-type, and 4x103’cm6s1for highlyexcited Si [171]. Therefore, by using a maximum plasma density of 7x10’9 cm3,we canobtain recombination times of 2 x s for p-type, 7.3 x 10’° s for n-type, and 5.1 x 10_lUs for the highly excited Si, respectively. All three are several orders of magnitudes largerthan the experimental time scale. Two-body recombination time is measured by usduring the experiment and is found to be of the order of 2x108 s. Figure 5.1 shows thetransmission cut-off for a CW laser beam at 10.6 im just after excitation with the 0.49ps pulse. The photograph shows a sharp initial drop in the transmission followed by atransmission-recovery tail lasting for 35 ns.We now proceed to calculate the transmission of a normally incident pulse of belowbandgap photon energy (wavelength A) through the photoexcited Si-wafer. We normalizethe density as 1 = n/ne and write (v) = b[1 — ii(1 — ia)]. The amplitude reflectivityand transmission from a discontinuity in the dielectric function from to 2 are givenby:56Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 1:30Figure 5.1: Transmission signal temporal recovery of the P-type Si transrnissioii cut-offswitch.andt=1—r. (5.7)At the Si wafer surface we then have:=— (.8)andt0=1—r (5.9)where u0 = n0/n. The plasma layer is modeled by a finely layered medium where theelectric field is constant in each region. We consider a small density step of At’ at adensity t’q inside the wafer with a reflectivity of:Tq= (t’q—At’)(5.10)+(t’q — Av)We now approximate the exponential density profile v0et’ by one consisting of a largenumber m of density steps At’ = zí0/m. Propagating from one step to the next the waveChapter 5. Experimental Investigation of Infrared Reflection from GaAs 131suffers a phase change of:A/3q= (5.11)The transmission of light not reflected from the e-h plasma is then:rn--i= t0 [J (1 — rq)e’”. (5.12)q=OIf m is chosen to be large enough (in our case m > 50), then the magnitude of the rqis much smaller than one. With this choice of large m, one can ignore the higher orderterms in equation 5.12, and equation 5.12 can be approximated as:t0(1 — pi)e (5.13)withrn—ipi = rq (5.14)q=Oandrn—i> A/3q. (5.15)q0Light reflected from the density profile (reflectivity P2) is reflected from the wafersurface at a potentially large reflectivity —r0 and propagates again through the carrierdistribution:rn-i / 1P2 = rqexp (2iA/3) . (5.16)q=O \ j0 /For this part of the incident radiation the transmission coefficient is:t2 = —r0tp2(1—p)ei. (5.17)Subsequent reflections from the profile can be neglected if a > 0.02. The total transmission coefficient is then t = t1 + t2. Thus the intensity transmission coefficient T canbe calculated:Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 132T = I t0(1 — pi)(l — rop2)et 2. (5.18)The described calculation can be simply performed using common math-software ona PC. The transmission T is calculated as a function of surface free-carrier density v,for various values of a. For comparison with experiments it is convenient to normalizethe transmission to that for v= 0 (bulk) and display the results as a function of log(v0). Figure 5.2 shows resulting curves for the calculated values of a = 0.1, 0.2, 0.3,and 0.5. The transmission curves are normalized to the transmission coefficient at zerophotoexcitation, T0.5.2.2 Transmission Cut-off Results at 10.6 sum,The infrared transmission results are measured with the optical setup described in Chapter 4 for the cross-correlation setup. The details of the experimental procedure andsample preparations are also outlined in section 4.10.2.In the first part of each experimental series for a given Si sample, we recorded thetransmitted infrared energy as a function of visible laser light energy, while the pumppulse blocked off the Si-wafer. These proved to be necessary in order to obtain accuratemeasurements of the photoexcited plasma densities. The results, shown in figure 5.3for two Si samples indicate the variation of the infrared pulse energy as a function ofcontrol pulse energy incident on the GaAs reflection switch. The straight lines throughthe data points are linear regression curves and serve as reference values for the analysisof each experiment. Figure 5.3 shows that a certain control minimum pulse energy, I, isnecessary to generate a measurable infrared signal. Above this intercept the energy of theinfrared signal increases linearly with the control pulse energy over the range used in thepresent experiments. As it will be discussed later in section 5.3.1, the intercept energyChapter 5. Experimental Investigation of Infrared Reflection from GaAs 1331.00.80.6C0.40.20.0—2.0Figure 5.2: Calculated relative transmission for 10.6 ,um radiation through a photoexcitedSi wafer as a function of normalized free-carrier surface density n0/n for four values ofof a {cr= 0.1 (uppermost), 0.2, 0.3, and 0.5 (lowest)].—1.5 —1.0 —0.5 0.0 0.5log(no/ne)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 134corresponds to that necessary to generate the critical free-carrier density of 1019 cm3 atthe surface of the GaAs switch, as can be expected from theoretical considerations [84].Since this energy, I, is the same for each experimental series and is independent of theoptical condition of the investigated Si wafer, its determination can serve to calibratethe individual experiments with respect to one another. In the second part of eachexperimental series, the transmitted infrared pulse energy is recorded at pump pulseenergies varying over several orders of magnitude. The pump intensity, Ii,, in arbitraryunits is calculated by multiplying the monitored visible laser energy with the transmissioncoefficient of the neutral density filter stack placed in the pump beam.The relative transmission T/TO is determined by dividing the monitored infraredenergy by the reference value at the same visible laser energy as measured iii part oneof the series. The resulting data are averaged over at least 15 points with a standarddeviation of the order of 10% in pump intensity bins of I,± 5%. In order to comparethe results with the theory of the previous section the average values of T/TO are plottedas a function of log(I). The photoexcited free-carrier density at the surface of the Siwafer is proportional to and log(I) equals log(z0) plus a constant. Therefore curvesof the form shown in Figure 5.2 can be fitted to the data and the best fitting value ofa can be determined. Figures 5.4, to 5.7 show the results for the four investigated Sisamples. The fitted theoretical curves determine a to + 25%. For the basically intrinsic(p-type) sample of figure 5.4 and the p-type sample of figure 5.5 curves with a = 0.2provide the best fit, while for both n-doped samples (figures 5.6 and 5.7) a value of a= 0.5 is determined. Using the calibration procedure of equating the intercept energyI of the reference curves described in the previous paragraph, we can also compare thepump energies‘pC required to generate the critical free-carrier surface density [log(t’0) =0]. By performing this cross calibration, we find that‘PC for the samples with a = 0.5 is(1.7±0.5) times larger than that for samples with a = 0.2. This indicates a relationshipChapter 5. Experimental Investigation of Infrared Reflection from GaAs 1354030d20ce1000 50Figure 5.3: Infrared pulse intensity hr detected for two different Si wafers at zero photoexcitation as a function of visible laser pulse intensity incident on GaAs reflectionswitch. The solid line is a linear regression fitted to the data points (empty circles) upto I 34, and the dashed line is a linear regression through the solid circles.10 20 30 40Ivs (arb.u.)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 136between the critical densities of the form:n(n — type) = (1.7 + 0.5) >< flc(p — type). (5.19)5.2.3 Discussion of the Transmission ResultsComparison of the experimental points and the theoretical curves in figures 5.4 to 5.7indicates that for a given value of a the model developed in section 5.2.1 provides a gooddescription of the transmission of an infrared light pulse through crystalline Si in whichfree carriers have been generated by absorption of above band gap radiation.Thus the imaginary part of the dielectric constant can be accurately determined bythe technique described in the previous section. As pointed out in section 5.2.1, a is potentially composed of two components: one (aj) arising from free-carrier absorption andthe other (ab) from intervalence band absorption. At the laser probe wavelength of 10.6jim, the contribution of intervalence band absorption to the dielectric function is insignificant compared to free-carrier absorption contribution [163, 164], and the intervalenceband absorption term can be ignored.Changing a does not alter n. On the other hand n is related to afc. According tothe considerations of section 5.2.1 this relationship (see equation 5.3) is of the form:= ebmW(a + 1). (5.20)The experimental results show the critical plasma density depends on the magnitudeof the free-carrier absorption term (or the carrier type). Thus if the absorption is predominantly determined by free-carrier absorption, one can calculate the absorption crosssection for each a:a = (5.21)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 1371.00.80.6C0.40.20.0—1.5Figure 5.4: Relative transmission coefficient for an infrared laser pulse through basicallyintrinsic Si (p-type concentration of 1.6x 1014 cm3) as a function of free-carrier surfacedensity generated by photoexcitation. The full curve is the best fitting theoretical prediction to the data points at a = 0.2. The theoretical curve for a 0.5 is also shown(dashed).—1.0—0.5 0.0 0.51og(n0/n)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 1381.00.80.6C0.40.20.0—1.2 0.6Figure 5.5: Relative transmission coefficient for an infrared laser pulse through basicallyintrinsic Si (p-type concentration of 2.6x i0’ cm3) as a function of free-carrier surfacedensity generated by photoexcitation. The full curve is the best fitting theoretical prediction to the data points at c = 0.2. The theoretical curve for a = 0.5 is also shown(dashed).—0.6 0.0iog( no/ne)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 1391.21.00.8CH0.40.20.0—2.0 0.5Figure 5.6: Relative transmission coefficient as in figure 5.4 for n-type Si concentrationof 4.9x1O5 cm3). The full curve is the best fitting theoretical prediction to the datapoints at a = 0.5. The theoretical curve for = 0.2 is also shown (dashed).—1.5 —1.0 —0.5 0.0log(n/ne)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 1401.00.80.6HH040.20.0—1.6—1.4—1.2—1.0—0.8—0.6—0.4—0.2 0.0 0.2log(no/nc)Figure 5.7: Relative transmission coefficient as in figure 5.4 for n-type Si concentration of6x10’5 cm3). The full curve is the best fitting theoretical prediction to the data pointsat a = 0.5. The theoretical curve for a = 0.2 is also shown (dashed).Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 141For the p-type samples we obtain cry, = 1.1 x 1016 cm2 arid for the n-type ones= 2.3x10’6 cm2. These cross sections are the result of phonon scattering of bothhot electrons in the conduction band and hot holes in the valence band, in contrastto cross sections determined from absorption measurements of doped samples withoutphotoexcited free carriers. For p-doped Si, in which case the absorption arises due tohole relaxation in the valence band, a value of crh = 1.3 x 10_16 cm2 has been reported[172] whilst for the case of absorption due to electron relaxation in the conduction bandin n-doped Si, a value of o. = 3.2x10’6 cm2 has been measured [163]. The differencebetween 0h and °e is understandable due to the different types of carriers involved inthe absorption process. However, in our experiments the carriers are photogeneratedby the pump pulse, hence the number of the photoexcited electrons and holes are equaland one should measure a combined free-carrier absorption cross-section due to the holesand electrons. The dopant concentrations are very small compared to the photoexcitedcarrier concentration and therefore should have an insignificant contribution to the absorption process. However, we have found that the absorption process depends on thetype of dopant. Presently, it is not clear to us what the effects of the dopants are on theabsorption mechanism. The measurement of a also permits an estimate of the averagemomentum relaxation time < r0 >. Taking the frequency for CO2 laser radiation in a= 1/(w < r0 >), we find < r0 >= 26.5 fs for p-type and < r0 >= 10.6 fs for n-typesamples. It is evident from these results that p-type silicon has higher < T0 > thann-type. This is in contrast to the experimental results presented in reference [163] fordoped silicon. Considering the very low doping concentrations as compared to the criticaldensity 1.8 x 10’s cm3) of the investigated samples, again this significant differenceof < r0 > between p- and n-doped Si is rather interesting.To sum up, we have measured the free-carrier absorption of 10.6 im radiation in Si ofvarious dopings in which free carriers have been generated by absorption of photons withChapter 5. Experimental Investigation of Infrared Reflection from GaAs 142above band gap energy. By fitting experimental measurements to theoretical predictionsfor the absorption of an infrared pulse propagating through a photoexcited e-h plasma,the absorption cross-sections and the momentum relaxation times are calculated. We findthat in contrast to p-doped material, n-doping has a significant effect on the absorptionprocess, increasing the momentum relaxation rate and thus the absorption cross-sectionand the critical density.We would like to point out that because the free-carrier absorption cross-section islower in p-type Si than in n-type Si, it is desirable to use p- rather than n-type Si for high-contrast optical semiconductor switching. That is, because the slope of the transmissioncurve turn-off for p-type Si as a function of the incident energy fluence (or the plasmadensity) is much steeper than that of n-type Si, then for a given finite excitation pulseduration, a full switch transmission turn-off can occur at much lower plasma density.Such a condition can be satisfied during the risetime of the 490 fs excitation pulse. Inorder to gain an insight on the speed of the transmission cut-off switch, we have toconsider how the photoinjected plasma density evolves over time. The time evolution ofthe initially generated e-h plasma corresponds to the expression:n(t) = n0 (i — exp(_[t/rp]2)) (5.22)where n0 is the initially generated plasma density, and r, is the optical excitation pulsewidth. In the following calculations n0 is set to the experimental value of 6n. Here,we assume that the critical density is reached at the peak of the excitation pulse. Fromequations 5.18 and 5.22, we can calculate the transmission cut-off time of the Si switch.The results of the calculations for p-type Si are presented in figure 5.8. It is clear fromthe figure that the termination of the transmission occurs in a time of approximately0.49r. In our experiment this corresponds to 240 fs which is fast enough to be used toperform time-resolved cross-correlation experiments on the reflected pulses from a GaAsChapter 5. Experimental Investigation of Infrared Reflection from GaAs 143switch.5.3 Ultrafast 10.6 ttm Reflectivity Pulses from a GaAs SwitchIn this section we report on the results of ultrafast pulse generation from GaAs semiconductor plasma. In Chapter 3, we outlined the basic underlying theory. We have shownthat, in accordance with a simple diffusion model which describes the temporal behaviourof the switching process, it should be possible to produce picosecond or shorter pulses at10.6 m. The pulse width was predicted to be a strong function of the excitation energyfluence,Of interest are the variation of the reflected pulse energy with the amount of theexcitation energy fluence and the variations of the pulse width with the level of theexcitation.5.3.1 Time-Integrated Infrared ReflectivityWe have performed a series of experiments to investigate the behaviour of the time-integrated infrared intensity as a function of the visible pulse excitation energy fluenceincident on the GaAs switch. This allows us to determine the visible irradiation levelrequired to induce a measurable infrared reflection change in the GaAs switch. Thistype of experiment is also essential to perform because the time-integrated reflectivityshould provide an initial check on the validity of the infrared reflectivity model proposedin Chapter 3. That is, time-resolved measurements are usually difficult to interpret.However, by integrating the infrared reflectivity pulses calculated for various initial e-hplasma densities, one should be able to fit the calculations to the experimental data.The basic experimental setup and procedures are outlined in section 4.9. Because ofthe sensitivity of the model to the photoinjected carrier density, to carry out this studyChapter 5. Experimental Investigation of Infrared Reflection from GaAs 1441. .‘ I I IO.800.60.4•0.20.0 I0.0 0.1 0.2 0.3 0.4PicosecondFigure 5.8: Calculated transmission of p-type Si as a function of time.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 145we must first determine the initial e-h photoexcited carrier density. Figure 5.9 shows aphotograph of the observed time-integrated reflectivity pulse measured simultaneouslywith its corresponding visible excitation pulse. The integrated temporal profiles of thesepulses correspond to the time-integrated reflectivity and the excitation energy.A typical result of the experimental data is presented in figure 5.10. The figure showsthe data point for each single shot, and the scatter of the data points is indicative ofthe experimental uncertainty. The horizontal scale of the figure is calibrated (from theexcitation energy recorded directly by the detector) in terms of the plasma density. Weshould point out that this conversion is meaningful only for a well-characterized laserbeam profile.One way to estimate the carrier density is by knowing that the maximum possibleexcitation energy is 0.2 mJ, which is deposited into a 0.5 mmx3 mm spot on the wafer atan incidence angle of 80°. This allows the calculation the maximum energy fluence. Byusing the Fresnel reflectivity equation for S-polarized light, the above angle of incidence,a refractive index of 3.4 and an absorption coefficient of-y= 4.5x10 cm1 at A= 616nm, it can be shown that 20% of this fiuience is absorbed by the wafer and thus generatesfree carriers. The product of this absorbed fluence, Fh,,and the assumed quantumefficiency of unity gives the maximum possible free-carrier density, om, at the wafersurface, which would result in the absence of any recombination or diffusion mechanismsacting during the time scale of the generating pulse. This value is calculated to beom 2 x 1020 cm3. This method for obtaining the plasma density can provide a goodestimate only for high excitation levels 2n). A better estimate of the plasma densityaround the critical density and over a wider density range can be obtained from a simpleexperimental procedure. By plotting the measured time-integrated reflectivity signal asa function of ‘low’ visible excitation energy, we obtain a linear relationship. The leastsquare fitted line through these points intercepts the excitation energy horizontal axisChapter 5. Experimental Investigation of Infrared Reflection from GaAs 146Figure 5.9: Typical ultrafast reflected infrared pulses (left) and their corresponding excitation visible pulses (right). The bottom photograph is presented to illustrate thereproducibility of the experimental signals.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 147at n. We have used the latter method throughout our experimeutal analysis to obtainmore accurate values for the carrier density.We normalized the maximum excitation energy to the n, value and plotted in figure5.10 the reflected infrared energy as a function of -yFh in terms of the critical density n.The data in figure 5.10 show that over the density range of 1.5 7Fph/flc<_5 the reflectedinfrared energy increases linearly with the excitation energy. For excitation energieswith 7Fh/fl>6 the reflected infrared energy starts to saturate and remains effectivelyconstant for 7Fh/n>8. Integration of the calculated reflectivity pulses from the modelpresented in Chapter 3 shows that the experimental data do not agree with the modelpredictions. Our calculations show that an increase of an initial plasma density fromr’/n= 1 to n/n= 6 results in an integrated reflectivity pulse n-i 180 times larger thanthe one calculated at the critical density. This is just a representation of the width of thereflectivity pulse. However, the experimental results (see figure 5.10) indicate that theintegrated reflectivity is only n-i 13 times its value at the critical density. Moreover, theobserved saturation of the time-integrated signal cannot be obtained with such model.Contrary to our observations, the calculated time-integrated signal increases stronglywith initial plasma density. Obviously, the saturation of the signal is a clear indicationthat the reflectivity pulse widths remain almost unchanged when the GaAs switch isoperated in the region 7Fh/n > 6. The temporal behaviour of the reflectivity pulsescannot be explained by diffusion model; a mechanism which is more significant at highplasma densities must be included in the calculations to account for these observations.5.3.2 Reflection-Reflection Correlation MeasurementsHere, we report the first experimental results on time-resolved ultrafast reflection fromoptically induced transient plasmas. As mentioned previously in the discussion of thereflection-reflection correlation technique (section 4.10.1), this type of experiment is notChapter 5. Experimental Investigation of Infrared Reflection from GaAs 1481001 I -____00090- 0GDOO00 08000000070 060 0d 5000C 40• 3020Ji10-00 2 4 6 8 10 121416 1820yFph/nFigure 5.10: Experimental results of the normalized time integrated reflectivity as afunction the normalized free-carrier density.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 149sensitive to the infrared pulse shape; however, one should be able to obtain an overallpulse duration, which may help to explain the observed time-integrated reflection saturation at high excitation fluences. That is, if the infrared reflected pulse duration doesnot change with the level of photoinjected carriers, then this can be easily detected fromthe measurements of the full widths at half maximum of the durations of the reflection-reflection correlation signals.Several experiments are performed at various levels of optical exciation. Typicalresults from the reflection-reflection correlation measurements are presented in figures5.11, 5.12, and 5.13 for-yFh/nc= 3, 5, and 7, respectively. Here, the correlation signalis normalized to a reference reflection obtained when the excitation pulse on the secondswitch is blocked-off and the transmission through it is detected. The data points areaveraged over at least 10 shots, and the error bars are an indication of the standard errorof the experiment.The time delay t= 0 in the figures corresponds to the peak overlap between thereflected infrared pulse from the first GaAs switch and the peak of the visible excitationpulse at the second GaAs switch. The measured correlation signal represents the widthof the dominant temporal features in the infrared pulse. The reason for the asymmetry ofthe reflection-reflection measurements is attributed to an experimental error in the delayline scan. For long time scans greater than 20 ps, the critical alignment of the infraredand the visible spots changes slightly. The asymmetry gives us information about theuncertainty of the measurements. This uncertainty is estimated to be + 3 Ps.Even though the graphs correspond to different excitation energy fluences, all ofthe figures show the effective correlation width to be 17 Ps at half of the full widthhalf maximum. The experiments indicate that the infrared pulse width seems to beindependent of the plasma density above Evidently, this effect supports the resultsobtained from the time-integrated reflectivity experiments. The reflectivity pulse widthsChapter 5. Experimental Investigation of Infrared Reflection from GaAs 1500.30 I •CZ 0.240.18oC)0.12Q)0.060.00—60 —30 0 30 60Delay (ps)Figure 5.11: Reflection-reflection correlation signal for an excitation fluence corresponding to-yFh/n= 3.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 1510.20C.Z 0.16c:5C(-)0.080.040.00—60 0 60Delay (ps)Figure 5.12: Reflection-reflection correlation signal for an excitation fluence corresponding to 7Fh/rIc= 5.—30 30Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 152Z 0.24030 I I ‘I0.120.180U0.06a)0.00 I—50 —25 0 25 50Delay (ps)Figure 5.13: Reflection-reflection correlation signal for an excitation fluence corresponding to 7Fh/n= 7.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 153do not scale with the calculated pulse widths as indicated by the diffusion model.Unfortunately, with our limited infrared laser power and detection sensitivity, experiments at 7Fh/ri < 2 are not possible, since the level of the reflected signal to thebackground noise is high enough to wash out the reflection-reflection correlation signal.With our reflection-reflection correlation technique it is not easy to arrive at an exactpulse shape by these measurements alone. Of importance to our analysis is the time thatthe plasma density takes to reach the critical density. This will be discussed in the nextsection.5.3.3 Cross- Correlation MeasurementsIn order to understand the nature of the disagreement between the diffusion based infrared reflectivity model and the experimental results, one needs to know the exact shapeof the reflected infrared pulses, so that the time evolution of the plasma density can beinferred from the temporal shapes of the reflectivity signals. It has been shown before[84, 85] that the infrared reflectivity of a photoexcited GaAs wafer shows some significant variation with surface free-carrier density n0. It has a minimum when n0/n equals( — 1)/€: E is the dielectric constant of the bulk GaAs. At n0 = n the reflectivityhas a sharp maximum. Just above n it has a minimum and from then on increasesmonotonically with n0. The magnitude of the features at n0/n= ( — 1)/c and 1 depend on the magnitude of the free-carrier absorption. It is therefore expected that thereflected infrared pulse will show some significant temporal variation as n0 decays fromits maximum initial value. As shown in section 4.10.2, these measurements display“jr=f R(t’)dt’ and its slope therefore determines the magnitude of the reflectivity.We performed several time-resolved cross correlation measurements over a wide rangeof pump intensities which we relate to 7Fh/n of figure 5.10. Throughout the experimental work, we selected a fixed excitation energy range and we studied the reflected infraredChapter 5. Experimental Investigation of Infrared Reflection from GaAs 154energy as a function of the time delay between the infrared and the optical excitationpulses. Since the detection sensitivity depends on details of the optical alignment and islikely to change from day to day, the experiments were performed in the following way.Before realignment and laser retuning became necessary, it was possible to conduct twoexperimental sequences. By placing two different sets of neutral density filters into thepump beam, the two experimental sequences covered two different ranges of 7Fh/rI ofwhich the first one was chosen to fall into the linear part of figure 5.10. At the start,at the end, and at various times during each experimental sequence, the control beamoperating the Si cut-off switch wa.s blocked-off and the measured infrared energy was displayed as a function of the monitored energy to derive reference signals. A least squarefitted line was placed through the reference data points of the first sequence. Setting theline intercept of the pump energy axis equal to 7Fh/n= 1 normalizes the pump energy.We have found that it is necessary to perform the ‘reference’ experiment at the beginningand at the end of the temporal scan.At each optical delay line setting, which determines the cut-off time, the average ofat least 30 infrared energy signals measured for the same pump energy was determinedand normalized to the reference infrared signal for the equivalent 7Fh/n. Due to theimportance of this type of experiment, we have performed over 40 experiments coveringa wide range of experimental conditions. The basic features of the experimental setupare discussed and outlined in section 4.10.2. The optical and data collection systemsare constantly improved throughout this work. Figures 5.14 and 5.15 show the resultsfrom two experimental days for four values of ‘yFh/n (0.7 and 2 in figure 5.14, 3 and 15in figure 5.15) which are representative of all experiments performed. They display thenormalized infrared energy ‘norm, as function of cut-off delay time. Obviously towardsthe end of the reflected infrared pulse ‘norm has to approach the value of 1. The detectedinfrared signals for figure 5.14 are quite small and as a result the standard error perChapter 5. Experimental Investigation of Infrared Reflection from GaAs 155point is of the order of 20%. The best fitting curves through the points have a constantslope indicating basically a constant reflectivity after photoexcitation over the periodexamined in the experiments. After 50-ps, Inorm is still less than 0.2 which indicates thatthe reflected infrared pulses have a duration of several 100 ps. For the experiments offigure 5.15 the situation is quite different. The standard error per point during the first40-ps is 4% increasing to 7% at times later than 60 Ps. At the end of the examinedperiod of 100 ps, the slope, and thus the reflectivity, has decreased to zero within themeasurable accuracy. Fitting curves through each of the two sets of data points andmeasuring their slope as a function of time results in normalized infrared reflectivitypulses of the form shown in figure 5.16. The most prominent features of these pulses arethe unresolved large transient maximum of <0.8 ps duration at the time of the pumppulse and the minimum observed 28 Ps later which we identify as the reflectivity minimumat n0/n= ( — 1)/c.Also remarkable is that the normalized infrared pulses for the two energy fluencesdiffering by a factor of five, up to t= 34 ps, are basically identical. However, since thereference signals at 7Fh/n= 15 are three times larger than those at 7Fh/n= 3 theactual reflected intensity for both pulses differs by a factor of three.5.3.4 Discussion of the Time-Resolved ResultsTo describe the experimental results, we will consider two processes (diffusion and recombination) which determine the time evolution of the plasma density. Our previouscalculations show that the effects of surface recombination on the time evolution of theplasma density is unimportant [84, 85] and hence is ignored in the following calculations.Carrier diffusion is known to increase with carrier temperature and decrease with latticetemperature; moreover, the diffusion coefficient is also shown to have a strong dependence on the carrier density above a certain value where carrier degeneracy is reachedChapter 5. Experimental Investigation of Infrared Reflection from GaAs 1562 — I I I I I I I I I l’tIIIlII![ I000o0000.1 0000000000. 0000000000000 00000000.00 10 20 30 40 50time (ps)Figure 5.14: Cross-correlation signal as a function of time for 7Fh/n= 0.7 (solid), 2.0(empty).Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 1571. • I I I III•I I. Q 0 0• • 0 008 ••• 0•••• 000.6 •Q000•o.4..;0.40.00 10 20 30 40 50 60 70 80 90 100time (ps)Figure 5.15: Cross-correlation signal as a function of time for 7Fh/n= 3.0 (empty), 15.0(solid).Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 1585 I I40 10 20 30 40 50 60 70 80 90 100time (ps)Figure 5.16: Reflectivity pulses as a function of time for ‘yFh/n= 3 (solid), 15 (dash-dot),and 2 (dash).Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 159[173]. The experimental results show that once the initial carrier density surpasses 5n,the integrated reflectivity saturates with increasing excitation fluence. This cannot beexplained by diffusion of the free carriers alone, In fact, using various models for calculating the diffusion coefficient [173] in the reflectivity calculations show that the effect ofthe diffusion coefficient on the decay of the surface density from Om to n, is negligible.The time that it takes the reflectivity to reach a minimum determines the time neededfor the density of the photoexcited carriers to reach the critical density. This time ismeasured to be 28 ps; by then the photoexcited carriers have cooled to the latticetemperature and thus temperature effects on the diffusion coefficient are insignificant.Our calculations show that diffusion is important for carrier densities below the criticaldensity. Hence, the simplest approach of treating the diffusion coefficient as temperatureand density independent is adequate in the following analysis.One would expect that the decay of the free-carrier surface density, n0, during thefirst hundreds of picoseconds after photoexcitation, is dominated by diffusion, while therecombination processes catch up in nanosecond time scales. In order to study theevolution ofn0(t) due to diffusion one has to solve the diffusioll equation. However, sucha solution shows [84, 85] that the free-carrier density as a function of distance from thesurface, z, quickly resembles that of a gaussian distribution. Since a gaussian profile is asolution to the diffusion equation, we can assume for the present that the density, n(z, t)is given by,n(z,t) =n0(t)exp{—(7(t)z)2} (5.23)withn0(t)/-y(t)= constant. From equation 5.23 and the diffusion equation (3.54), weobtain a differential equation describing the time evolution of plasma density:= —2D-y3. (5.24)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 160Then taking0(0)=yFh and setting -y(t = 0)=-y, we find for n0(t),7Fhn0(t)= V’1 +4y2Dt5.25)The time, t, it takes forn0(t) to decrease to the critical density can then be calculated.For the given values of-y and D this is:= 6.17{(7Fh/n)2— 1}ps. (5.26)The main contribution to the total reflected energy, ‘jr, pulses of figure 5.10 for7Fph/fl> 3 is generated during this time. One can estimate for these pulses,j R(t)dt < R > t. (5.27)The average reflectivity < R > increases also, but not rapidly with 7Fh/n. At thevery least, one would expect in the presence of diffusion only, that the pulse, Ii,., of figure5.10 like t, increases with the square of the fluence. Figure 5.10 shows that this is not thecase, instead I initially increases linearly with 7Fh and then quickly saturates. Figure5.16 indicates that t, also saturates at “-‘ 25 ps. In the case of carrier diffusion, one wouldhave expected for ‘yFh/ri= 15 a time t, of the order of one nanosecond.In order to show that normal Auger recombination at the given rate cannot explainthe observed saturation, we examined a hypothetical situation in which only this processdetermines the decrease ofn0(t). The time t is given by the solution to equation 3.48:= 14{1— (n/-yFh)2}ns. (5.28)In order for this time (due to Auger recombination) to be comparable to t, due todiffusion only, it requires -yFh/nc.--’ 48. Therefore, if only diffusion and normal Augerrecombination determinen0(t), the Ii,. of figure 5.10 should increase with (7Fh/n)2overthe range shown and would only be expected to saturate at twice the maximum valueChapter 5. Experimental Investigation of Infrared Reflection from GaAs 161attained in this experiment. Also t should oniy saturate at ns-time scales. Clearly, anadditional, much more rapid recombination process governs the dynamics of high densityphotoexcited free carriers. This mechanism should be responsible for the saturation ofthe time-integrated reflectivity signal and for the observed t being density independent.That is, a recombination process whose recombination rate depends on the photoexcitedplasma density should be considered in the analysis.We can model our experimental results if we assume a decay process of the same formas Auger recombinatioll at a rate of 1= 1.9x 1028 cm6/s. This could, for example, bea two-body recombination process for which the decay rate is nearly a linear function offree-carrier density.5.3.5 Modeling of Free-Carrier Density and ReflectivityIn order to model the free-carrier density development one needs to know the excitationpulse shape. For mathematical convenience, we assume that this pulse has the form:P(t) = 2yFpexp{_(t/rp)2}. (5.29)For r= 0.49 ps this pulse has the same width as our laser pulse. In term of normalizeddensities v = (n/ne) and f = (7Fh/n), we write the time evolution of the normalizedplasma density as:9v t= 2f—-exp{—-yz — (t/r)2}+ D—- — tw3. (5.30)Here ic = Fn, and for I’ we take the rate from the previous section. The first term onthe right hand side results from the e-h generation rate, the second term arises from thediffusion of the carriers, and the last term describes the recombination process. In orderto perform numerical integrations we simplify the diffusion term. If the distribution hasa gaussian shape of the form v =0exp{—[z/d(t)]2},where v0 is the surface density, thenChapter 5. Experimental Investigation of Infrared Reflection from GaAs 162the diffusion term simplifies to:= {2[z/d(t)] - 1}v(t,z) (5.31)9z d(t)withd(t)= /(t) (5.32)Here N(t)(= j° v(z)dz) is the total normalized number of free carriers. We approximatethe diffusion term by this form and now can numerically integrate the differential equationat each position z with the initial condition v(0, z)= 0. After each time step we integrateover the profile to determine d(t). In performing the calculations one has to take intoaccount that the density varies most rapidly near the surface and at early times. Wechose a dimensionless length coordinate x = exp(—7z) and divided the interval 0x1into 100 equal steps. The time intervals progressed with step number p asi0—p3.Figure 5.17(a) shows the resulting density profiles at various times for -yFh/n= 10,and figure 5.17(b) indicates the temporal variation of the surface density for the samecase. Profiles for all values of 7Fh/n 3 are quite similar and reach ,= 1 at the sametime. The only difference exists in an increase of the sharp initial surface density featureand an increase of the width of the density profile as the photon flux is increased.Next we proceed to calculate the reflectivity for infrared radiation incident withBrewster’s angle if v= 0. We use the Drude model for the dielectric constant {c(v) =— i’(1— ic)]} and introduce=/{1—v0(t)[1— ia(t)]} (5.33)andX = Eb{1 -v0(t)[1 - ia(t)]} -v0(t)[1-ia(t)]. (5.34)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 163Then the amplitude reflectivity from the surface is given by [84, 85]:r0(t) = X (535)Here we assumed that the imaginary part of the dielectric function, (t), is a functionof time. It arises from the free-carrier absorption and is a function of free-carrier temperature. In order to include the contribution to the reflectivity arising from the densityprofile inside the wafer, we make the use of density steps introduced previously. Similarto the previous approximation made for calculating the transmission cut-off, the plasmalayer is treated as a multilayered structure of variable density. Each layer is consideredto have a homogeneous density profile. Taking the density at step number m as 1m weintroduce:am = 1— 11m(t)[1 — ia(t)] (5.36)andbm(t) = {1- Ym(t)[1 - ia(t)]}- Vm(t)[1 - i(t)}. (5.37)In terms of these functions the reflectivity of the density step from m— 1 to m isgiven by:— am(t)bm_i(t)— am_i(t)bm(t)rm —am(t)bm_i(t) + am_i(t)bm(t)The transmission through the density step in the incident direction is (1— rm) and it is(1 + rm) for propagation in the opposite direction.In order to find the contribution from the whole profile we also have to consider thephase change, /3m due to the propagation through the different optical paths of individuallayers. Writing for a length /Zm of a plasma layer m:I b/3m = ko/.Zmf bm_i(t) (5.39)one finds for a density profile reflectivity:m mp(t) = exp(2ii3) fl[i— r?_1(t)}ri(t). (5.40)m 1=1 1=1Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 1640 20 40 60 80 100 120I N1 N-V— -—— VLVF-.—0 I I -o i 2 3 4Figure 5.17: (a) Normalized density as a function of the longitudinal position and fortimes t/r= 0.5 (short dash), 1.0 (solid), 27.00 (long dash) and 125.00 (dot-dash). Theinitial normalized plasma density 7Fh/n= 10. (b) The insert indicates the normalizedsurface plasma density as a function of normalized time.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 165The total reflectivity from the plasma layer is due to the individual reflectivities fromeach homogeneous layer and is given by:r(t) = r0 + p(t) (5.41)1 +r0(t)p(t)Before we can calculate the intensity reflectivity r(t) 12 we have to assume a functionfor the absorption term, a(t). Based on the experimental results for initial carrier densities > n, we always measure a distinct reflectivity minimum which approaches zero aftera time of the order of 28 ps. For this minimum reflectivity to exist, we require the imaginary part of the dielectric function to be much smaller than 1 (i.e. small free-carrier andintervalence band absorption). We can describe phenomenologically the time evolutionof the free-carrier and intervalence band absorptions by a single absorption coefficientc(t). The coefficient can be written as:a(t) = 0.001 + f{1 — exp[—(t/8r)2]}exp[ (t/10r)]. (5.42)The carrier absorption coefficient and thus the imaginary component of the dielectricconstant is a function of the free-carrier temperature. The magnitude of the absorptionis enhanced at higher carrier temperature. In this case, one has to consider the rateof cooling of the hot carrier distribution at a high initial carrier density which in turnshould reflect the rate of decay of free-carrier absorption. The cooling rate is taken to be(10T)’, which is slightly larger than the value of “ 1 ps from the measurements presented in reference [174]. Moreover, we also have to assume that it takes a finite time afterphotoexcitation for the free-carrier absorption to reach a maximum value, which is proportional to the absorbed photon flux. The constant term in the expression in equation5.42 arises from the absorption at room temperature. Figure 5.18 shows the reflectivitypulses for f= 10 and 2 respectively. Also shown are, for f= 10, the integrated reflectivity simulating the reflectivity cross-correlation and the reflectivity-reflectivity correlationChapter 5. Experimental Investigation of Infrared Reflection from GaAs 166measurements. Comparison with the experimental results of figures 5.13, 5.15, 5.16 tofigure 5.18, and figure 5.10 to 5.19 , indicates that the model provides a good representation of the experimental situation. Note that the time scale in figure 5.19 is normalizedto the excitation pulse width ri,. It also shows that the situations in which the maximumfree-carrier density is below critical (f < 2.5) one obtains very long, nearly constant,low-intensity, reflected infrared pulses. In figure 5.19 the total integrated reflectivity isshown as a function of f = Fh/n. The calculations are performed by integrating thereflectivity curves for various initial plasma densities. The final integration time is takento be 200 ps. Comparison with figure 5.10 again indicates the good agreement betweenthe model and the experiment.Clearly, by invoking an additional two-body recombination mechanism whose recombination rate is taken to be a function of the carrier density, we are able to obtain a goodagreement between the experimental results and the proposed model calculations. So farwe have no explanation as to the exact nature of the recombination mechanism.We believe that this phenomenological model is essentially correct; however, moreexperimental and theoretical study is required to completely determine the exact natureof the recombination process.5.4 Frequency Spectrum MeasurementsMeasurements of the frequency bandwidths, /f of the reflected infrared pulses can provide complementary information on the duration of the pulses, We have performedthis type of experiment for the following reason: since the infrared reflection occurs froma time-dependent plasma layer, one expects the infrared pulse to have a frequency chirp.The overall pulse duration can be obtained by only one single shot measurement.However, the exact pulse width-bandwidth product for an arbitrary pulse shape dependsChapter 5. Experimental Investigation of Infrared Reflection from GaAs 167f—(I I, II II0.8__//0.6\I /0.E:Jr—.--0 20 40 60 80 100 120t/-rFigure 5.18: Model calculations as a function of normalized time of: the normalizedinfrared pulses for 7Fh/ri= 10 (upper solid line) and 2 (lower solid line ), normalizedcross-correlation signal for -yFh/n= 10 (dash-dot), and normalized reflection-reflectioncorrelation signal for 7Fh/n= 10 (dash).Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 16840_____30201000 5 10 15 207Fph/ncFigure 5.19: Model calculations for time integrated reflectivity (reflected pulse energy)as a function of the normalized carrier density. The vertical axis scale units are arbitrary.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 169on several factors: the exact shape of the pulse (gaussian, square, exponential, etc.),how and are defined (rms, FWHM, 1/e, etc.), and the amount of chirp or otheramplitude or phase substructure within the pulse. From the previous time-resolved cross-correlation measurements, we find that the reflected infrared pulse shapes show verycomplicated structures. The main question in these cases is how to define the pulsewidths. Our approach to this problem is to analyze the pulse widths measured by thereflection-reflection correlation experiments. This correlation experimental results showsthat the overall shapes of the reflected pulses can be approximated by gaussian pulseswith a pulse width-bandwidth product LS.r14f 0.44.The experimental setup and the procedures for the frequency spectrum measurementsare outlined in section 4.11. We have performed several experiments to measure thefrequency spectrum. Due to the low sensitivity of the optical system, we are not able tomeasure the frequency spectrum for different values of excitation energy fluences. Thus,the experiments are only performed for high excitation levels (7Fh/n > 6). Figure 5.20shows a typical wavelength shift spectrum for an optical pulse with an initial excitationfluence-/Fh/n= 7. Each data point in the figure is averaged over 10 points and thestandard error of the measurements is shown as error bars. The figure shows asymmetrywhere the spectrum shifts more towards the longer wavelength. From the FWHM (87A) of the wavelegth spectrum curve, we can calculate a pulse width of 18 ps. Thiscalculated pulse width is in very good agreement with the direct measurements of thecorrelation profile of figure 5.13.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs 17020 I I I I I I I I16H‘ 124.—250 —150 —50 50 150 250Wavelength Shift (A)Figure 5.20: Wavelength shift of a reflected infrared pulse with an initial excitationfluence of 7Fh/fl 7.Chapter 6Ultrafast Semiconductors for 10.6 1um Optical Switching6.1 IntroductionThis chapter deals with the experimental study of semiconductor materials having ultra-short recombinatiori carrier lifetimes for possible application to optical infrared semiconductor switching. The major body of the experimental work is presented in our currentpublications [175]—[177]. Details of experimental measurements from three types of semiconductors: low-temperature grown GaAs, radiation damaged GaAs, and In0g5Ga15As/GaAs relaxed superlattice structures are presented as possible candidates for ultrashortpulse generation. Molecular beam epitaxy growth procedures for some structures andsample preparations are also discussed. Where appropriate, the time-resolved cross-correlation results for the carrier lifetimes are compared with the photoconductivitymeasurement values reported in the literature.6.2 The Need for Semiconductors with Ultrashort Carrier LifetimesIn chapter 5 we discussed the experimental infrared 10.6 jim reflection from intrinsicGaAs. Evidently, the pulses generated from such a reflection switch are too long forour practical use. Most of the generated pulses have long reflectivity tails which last forseveral picoseconds, and in order to get rid of this long reflection, alternative materials andtechniques must be used to produce ultrashort reflectivity pulses. Since we are interestedin the generation of a laser pulse with a duration of 1 ps using only one switching171Chapter 6. Ultrafast Semiconductors for 10.6 um Optical Switching 172element, we have investigated other modified GaAs based semiconductor switches toserve this purpose. In principle, the GaAs semiconductor is altered to have its carrierlifetime, Tr, shorter than the radiative lifetime and the diffusion time. The nonradiativerecombination centre density and capture cross section must be large enough such thatthe temporal evolution of the plasma is solely determined by the carrier recombinationand the plasma density can be reduced below the critical density in a time scale Tr.Now, if the semiconductor materials with ultrashort recombination lifetimes (of the orderof a picosecond) are used in place of the GaAs switch, then it is possible, due to ultrafastcarrier nonradiative recombination, to generate ultrashort infrared pulses limited only bythe lifetimes of the semiconductor materials. When the semiconductor carrier lifetimeis longer than the excitation optical laser pulse, then the generation rate of the e-hplasma can be considered to be instantaneous. That is, in time resolved cross-correlationexperiments this shows as a fast risetime of the cross-correlation signal [1 75]—[1 77]. Thedecay rate of the electron hole plasma should follow the simple relation,n(t) fl0Ct/Tr, (6.1)which in turn determines the decay rate of the reflectivity pulses. Therefore, in principle,this method is more attractive than just using intrinsic GaAs since the reflected infraredpulse duration does not depend on the amount of the excitation energy fluence. Moreover,the choice of the infrared pulse duration can be easily adjusted to the required value byproper selection of the carrier lifetime [176]. Finally, it should be pointed out thatusing time-resolved infrared reflectivity measurements provides an alternative methodfor measuring Tr for semiconductor materials [l75]—[177}.Chapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 1736.3 Ultrafast Recombination SemiconductorsIn this section we give a brief and largely qualitative account of the techniques used toreduce semiconductor carrier lifetimes. Comprehensive reviews on the subject can befound in references [178]—[182]. Our main task is to search for optimal semiconductormaterials with a minimum free-carrier absorption and a minimum carrier lifetime to guarantee that a high reflectivity and an ultrashort decay time are exhibited simultaneously.Different experimental approaches and techniques have been used to enhance the speedof response of semiconductor materials. Most of the work is directed towards the designand the fabrication of ultrawide bandwidth optoelectronic devices [178]—[180].The techniques rely on the introduction of sufficient deep level states in the crystallinesemiconductor material. Deep levels in semiconductors are basically energy levels closeto the middle of the energy band gap. These levels can be created by impurities or bycrystal defects (vacancies and interstitials)and dislocations. Photoexcited carriers can becaptured at these sites and possibly recombine with their opposite kind. The recombination process can be either a single recombination event or a multi-level recombinationevent. In the latter, the photoexcited carriers are captured for a short time and thenreleased to be captured by another deep level and so on. Depending on the nature of therecombination level, both types of carriers (electrons and holes) can be captured withcapture cross-sections c.e and and 0ch, for electrons and holes, respectively.At high dopant concentrations, carrier recombination occurs through lattice defectsgenerated by the dopant. This causes an increase in the density of the recombinationcentres. Free carriers excited in the conduction and valence bands of these materials arerapidly trapped at deep defect levels. The carrier lifetime of GaAs can be reduced from afew nanoseconds to 70 ps by the introduction of Cr [183]—[185], whereas by doping theGaAs with Er (5 xl O’ cm3)the carrier lifetime is reduced to 1 ps [186]. ExperimentalChapter 6. Ultrafast Semiconductors for 10.6 ,um Optical Switching 174observations have shown that for a doping range of 1016_1019 cm3 the carrier lifetimedecreases with increasing dopant concentration [1861. Doping InP with Fe reduces thecarrier lifetime to 100-1000 ps depending on the impurity concentration [187]—[190].Even though these semiconductors have short lifetimes, the lifetimes for Cr:GaAsand Fe:GaAs are not fast enough to provide significant improvement in our optical semiconductor infrared switching system. For Er:GaAs, due to heavy Er doping, there issignificant background reflection that reduces the contrast ratio of the reflected pulserelative to the background reflection.Picosecond and subpicosecond carrier lifetimes can also be achieved in usual polycrystalline and amorphous semiconductors where the naturally occurring large defectsat the grain boundaries act as effective carrier trapping and recombination centres. Forpolycrystalline materials, for example, Si, Ge, and CdTe carrier lifetimes are measuredto be 2—50 ps [191], 50 Ps [192] and 4 Ps [193], respectively, and for amorphous materialscarrier lifetimes are measured to be 5-20 ps for a:Si [1941. These semiconductors haveultrashort recombination times and clearly can be used as optical infrared semiconductor switches; however, the main problem associated with such semiconductors is thatthe carrier reflectivity is dramatically reduced due to increased elastic scattering. Thatis, the increase in the carrier scattering results in low infrared reflection efficiencies dueto increased free-carrier absorption in the semiconductors. Consequently, a compromisebetween the reflection efficiency and the speed of the switch must be reached. For thesereasons, no attempt has been made to study the infrared reflection from these materials.The details of the theory dealing with recombination through a single level recombination centre is discussed by Schockley, Read and Hall (SRH) [195, 196]. The carrierlifetime can be related to the trap density, N through the following simple relationTr = (6.2)NtJc_e h <Vth >Chapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 175where < v > is the mean thermal velocity of the carrier. In this case, the trap density and therefore the free-carrier lifetime are inversely related. In light of the aboveequation, it is clear that one needs to increase the defect and dislocation density in thesemiconductors.Next, we examine three types of semiconductors with ultrashort recombination carrierlifetimes. We investigate low-temperature grown GaAs (LT-GaAs), radiation damagedGaAs (RD-GaAs), and InGaAs/GaAs relaxed superlattice.6.4 Using Low-Temperature Grown GaAs for Ultrafast Pulse GenerationA novel and interesting approach to shorten carrier lifetime is the use of low-temperatureMolecular Beam Epitaxy (MBE) grown GaAs (LT-GaAs). This semiconductor exhibitsa unique set of properties such as high carrier mobility(‘—i1O cm2/V s), ultrashortcarrier lifetime (0.4-60 ps depending on the growth temperature), high resistivity (‘--‘1O l cm) and high quantum efficiency. The combination of the above properties attracted wide interest in low-temperature grown semiconductors for the development ofwide bandwidth optoelectronic devices such as photoconductors and photoconductiveswitches [197]—[216]. Here, by using a GaAs layer grown by molecular beam epitaxy(MBE) at a low substrate temperature (LT-GaAs) as an optical semiconductor switch,we demonstrated the generation of ultra.short infrared pulses at 10.6 jim [175].Two important parameters which determine the optical and electrical characteristicsof epitaxial growth of GaAs layers on GaAs substrates are: the substrate temperaturewhich must be maintained at ‘- 600°C, and the As/Ga beam-equivalent-pressure ratio.Lowering the substrate temperature to-‘- 200°— 300° C causes a highly nonstoichiometricgrowth where excess arsenic (of approximately ‘ 1%) is incorporated into the GaAsepitaxial layer [200, 203, 205, 208, 214, 215]. Post growth annealing of the substrateChapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 176causes the excess arsenic precipitates to form nanometer-size arsenic clusters [197] andthe resistivity increases by several orders of magnitude from 10 cm to iO flcm [203, 214, 215]. It is these arsenic clusters that are of great interest since theydeplete any photoexcited free carriers from the surrounding GaAs material. Ultrafastcarrier recombination is attributed to the efficient recombination centres due to excessAs clusters. Unannealed samples are found to have a variety of defects such as: neutraland ionized arsenic antisites ([A5Ga]°’ 1020 cm3, [A5Ga]’ 5x 1018 cm3) which mayact as deep donors, arsenic interstatials (As) Ga vacancies (VGa”-’ 1018 cm3) and Gaantisites (GaA3’—’ 5x 1018 cm3). These last two defects may act as acceptors [198]—[201],[204, 217]. After annealing the defect concentration is reduced about an order ofmagnitude with no effect on the carrier lifetime. Either both types of carriers are trappedat midgap defect bands and then recombine; or the midgap donor or acceptor deep levelscapture carriers which then recombine. Several authors reported on the growth/annealtemperature dependence of the carrier lifetime [203],[205]—[207],[214] and have shownthat the degree of excess As is greater for lower substrate temperatures.6.4.1 MBE Growth of LT-GaAs LayersIn this section the LT-GaAs growth procedure is outlined. The properties of LT-GaAscritically depend on the growth and the annealing conditions during the epitaxial growth,any small fluctuations in any of the growth parameters can significantly alter the carrierlifetime of the sample.The incorporation of high density recombination centres is achieved using a nonconventional MBE growth technique. High densities of excess As are incorporated into aGaAs active layer using a low substrate growth temperature with a moderate As2 overpressure.The LT-GaAs samples are grown by S. R. Johnson in the U.B.C. Physics Department.Chapter 6. Ultrafast Semiconductors for 10.6 ,um Optical Switching 177The LT-GaAs epi-layer is grown on a semi-insulating GaAs substrate using a vacuumgenerator V80H MBE system. The substrate and the holder are treated in a U.V. generated ozone atmosphere (for 4 mm) to remove any residual organics from the surfaceof the wafer. After the ozone treatment, the holder and the GaAs wafer are placed intothe MBE growth chamber where the oxide is thermally desorbed under an As2 flux.The oxide is desorbed by ramping the substrate temperature at a rate of 5°C/mm from500°C to about 10°C above the oxide desorption temperature of -- 600°C. This processroughens the surface of the substrate. The increase in the surface roughness and hencethe oxide desorption are monitored using laser light scattering [2181. The substrate issmoothed by growing a 2 zm thick (1 tim/hr) GaAs buffer layer at a temperature of600°C. Next, a 100 nm thick GaAs temperature-transition layer is grown on the bufferlayer. During the growth of this layer, the temperature of the substrate is lowered from600°C to 320°C in 6 mm. Following this, a 200 nm thick layer of LT-GaAs is grown at320°C with a As2 to Ga flux ratio of 3:1. After the growth of the LT-GaAs layer, thesample is heated inside the growth chamber by raising the substrate temperature from320° C to 550° C (in 3 mm) and annealed for 6 mm at 550° C under an As2 flux. Alllayers are grown nominally undoped. From the reported value in the literature, underthese growth conditions, the arsenic precipitate density is estimated to be approximately3x10’T cm3 with an average cluster size of’- 2—5 urn [197, 219]. It has been shown thatLT-GaAs maintains its crystalline structure [197, 199]; therefore, no attempt is madeto characterize the degree of crystallinity of the layer. The surface morphology of theLT-GaAs shows a smooth surface with no diffuse reflection at 10.6 gum. We should pointout that during the growth process the substrate temperature is measured using diffusereflectance spectroscopy (DRS) [220]. This optical temperature measurement techniquehas ±1°C sensitivity. Figure 6.1 shows a schematic diagram of the LT-GaAs structureand a scanning electron micrograph of the LT-GaAs layer.Chapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 1786.4.2 Subpicosecond 10.6 urn Pulse Generation from LT-GaAs as a Reflection SwitchWe used a cross-correlation method outlined in section 4.10.2. to measure the temporalJR pulse shape. Figure 6.2(a) displays a typical integrated infrared pulse energy as afunction of the relative delay. The experiment is performed at a fixed excitation energyfluence which corresponds to a plasma density of ‘—‘ 5x10’9 cm3. The time origin inthe figure represents the relative arrival time of the visible pulse prior to the arrival ofthe infrared pulse to signify the zero base line of the transmission. By differentiating thetransmission step curve in figure 6.2(a), we can obtain the pulse width. The measuredcharacteristic feature of the curve shows an initial rapid increase in transmission. Therise time of the transmission cross-correlation is a clear indication that the pulse widthis about 1 + 0.2 Ps [175] with a long decaying tail. This kind of decay is expected sincethe visible pulse is mainly absorbed in the LT-GaAs 200 nm thick layer; hence, most ofthe e-h plasma is generated there. We attribute the short pulse to the fast recombinationtimes in the material, whereas the long tail is due to the GaAs buffer and the substratelayers. Once the carriers are generated in the LT-GaAs layer they will recombine in about0.5 ps, and the carriers which are generated in the buffer layer will persist for a longertime. Thus the infrared reflectivity decay time depends on the diffusion of the carriersthrough the buffer layer. The reflectivity tail can be reduced by making the LT-GaAslayer much larger than the absorption skin depth of the optical pulse. The energy of theJR pulse is estimated to be 10 pJ limited primarily by the source CO2 laser power.The cross-correlation measurements can be compared with calculations based on asimple model in which the free carriers are generated in the LT-GaAs film by the absorption of a 0.49 Ps FWHM semi-gaussian visible pulse. The majority of the generatedcarriers recombine exponentially with a lifetime of 0.5 ps while ten percent are allowed toChapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 179diffuse into the buffer layer with a diffusion coefficient of 20 cm2/s. The cross-correlationsignal and its differential are evaluated based on a technique described in section 4.10.2.The good agreement with the experiment indicates a free-carrier lifetime of 0.5 Ps whichagrees with the reported carrier lifetime based on the presence of a high density of Asprecipitates in this material. That is, if one considers equation 6.2 with the followingparameters [203]: N= 3x10’7 cm3, u=2.83x10’3cm2, and < Vj >=2.5x107cm/s (300 K), we calculate a carrier lifetime of 0.5 Ps. Our measured carrier lifetime is thesame as the one measured by other techniques [203].We examined the reflected infrared energy for different levels of visible laser excitation.Figure 6.3 illustrates the variation of the reflected infrared pulse energy as a function ofthe plasma density (or energy fluence) generated in a 2 m thick LT-GaAs switch. Incontrast to the GaAs measurements (figure 5.10), the experimental results show a linearrelation and no indication of saturation at high excitation levels. The linear behaviourfor LT-GaAs is consistent with what is expected if one assumes that the existence of therecombination centres in the sample, and that the width of the reflected pulses do notvary with the amount of the excitation energy fluence.In practice, the switching element is shown to be very reliable and simple to operate.Our experimental results show that LT-GaAs, grown under the conditions specified above,is ideally suited for optical semiconductor switching of 10.6 tm radiation.6.5 Using Radiation Damaged GaAs for Ultrafast Pulse GenerationWe have explored another potential semiconductor material for ultrashort infrared pulsegeneration. Radiation damaged semiconductors are known to have ultrashort carrierChapter 6. Ultrafast Semiconductors for 10.6 ,um Optical Switching(a)180Figure 6.1: (a) Schematic diagram representing the LT-GaAs growth layer. (b) Scanningelectron micrograph of the LT-GaAs layer./LT—GaAs (200 nm)GaAs/LI—GaAs TransUon Layer (100 nm)MBE—GaAs (1 m)GaAs SubstrateChapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 1811.’l I I I I I I I I 1.u1,l212 (a)z.—1.0 1.00.8 0.8c10.6 0.6 >0.4 (b) -0.40.2-0.2 SC_) 0 . 0 — I I I 0 . o0 2 4 6 8 10 12 14 16 18 20Delay (ps)Figure 6.2: (a) A cross-correlation transmission signal between the IR pulse and thevisible pulse creating the transmission temporal gate. The solid line is the model calculations. (b) The infrared pulse as obtained from differentiating the cross-correlationcurve.Chapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 18250 I I •z40 o0biJC).00C) 100 2 4 6 8 10 12 14 16 18 20Carrier Density (1019 cm3)Figure 6.3: Variations of the reflected JR pulse energy as a function of the e-h plasmadensity. The LT-GaAs layer thickness is ‘— 2 m.Chapter 6. Ultrafast Semiconductors for 10.6 im Optical Switching 183lifetimes ranging from - 100 fs to 10 Ps [221]—[230]. Our purpose in using ion bombardment is to take advantage of the resulting damage as a means of introducing a predetermined defect density into the crystalline semiconductor [231]—[235]. The reductionof the free-carrier lifetime is a direct result of the defects introduced by the irradiatingion beam. The carrier lifetime of the radiation damaged semiconductor depends on several factors such as: the energy of the radiation beam, type of semiconductor, type ofimpurities, and the material temperature. When a GaAs substrate is irradiated withhigh energy particles two processes occur: the atoms in the host lattice are displacedinto interstitial sites producing a vacancy pulse interstitial (what is known as Frenkelpairs VGaGai and VAS-AS). Both Va and VAs are effective electron and hole traps,respectively [233, 234], and the interstitial sites Ga: and As behave as donors [182]. Inaddition, nanometer-size defect clusters are also formed due to impurities implant. Thesedefects and vacancies act as ultrafast efficient traps and recombination centres. Radiation damaging GaAs with a proton beam produces various trap levels with energies 0.11,0.31, and 0.71 eV for electrons and energies of 0.06, 0.44, and 0.57 eV for holes withcapture cross sections of 1.3x10’ cm2 for electrons and 2.3x10’ cm2 for holes[235]. Earlier work on radiation damaged GaAs (RD-GaAs) [224, 225] has shown thatthe carrier lifetime is reduced to 500 fs by irradiating the semiconductor with a 180 keVproton beam at a dose of 1.37x10’5cm2. The irradiated GaAs shows no sign of loss ofcrystalline structure [224, 225]; however, above that dosage, the observed carrier lifetimeis found to reach a lower limit of 500 fs.6.5.1 RD-GaAs Samples’ Preparations and CharacterizationsThe infrared reflection switches are made from a 450 m thick semi-insulating (‘10 Qcm) GaAs (100) wafer. The wafer is optically polished on both surfaces and is cleavedinto three pieces each irradiated with a different H ion dose. The ion damaging isChapter 6. Ultrafast Semiconductors for 10.6 um Optical Switching 184performed at Dr. N. Jaeger’s Ion Implant Laboratory in the U.B.C. Electrical EngineeringDepartment. The samples are bombarded with a 180 keV H+ ion beam to produceeffective doses of 1 xlO’2, 1 x1014, and 1 xlO’6 cm2. During the implantation process,the samples are mounted on an aluminum block in order to reduce sample damage dueto ion beam heating. The ion beam current density is 1,5x104 A/cm2 incident at anangle of 70 to the surface normal and is scanned uniformly over the samples. For thesesamples the thickness of the damaged layers is larger than the penetration depth of thedye laser excitation pulse (-- 0.2 zm), thus the carriers are generated only in the radiationdamaged layer and diffusion of the carriers outside the damaged layer is of no effect.Heavy ion bombardment of the GaAs wafer may result in a permanent change in thecrystalline structure of the semiconductor. Early work showed that bombardment witha high H+ ion dose > 1.37x105 cm2 on crystalline GaAs transforms it into an amorphous material [224, 225]. In order to characterize accurately the structure of the iondamaged layer, several ellipsometric measurements were performed on the highly radiation damaged samples and compared to the measured dielectric function of undamagedGaAs. The ellipsometric measurements were performed by Dr. R. Parsons’ group inthe U.B.C. Physics Department. Figure 6.4 shows the resultant dielectric function forthe radiation damaged GaAs with an ion dose of 1 x 1016 cm2. It is clear that there isno significant change in the form of the dielectric function except the disappearance ofthe peaks around 3 eV. This and the overall small deviations of the dielectric functionare attributed to the surface roughness. The result suggests that the RD-GaAs samplesmaintain their crystalline structures even at an ion dose level of 1 x 1016 cm2.Chapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 1856.5.2 Subpicosecond 10.6 1um Pulse Generation from RD-GaAs as a Reflection SwitchThe experimental arrangement and the procedure used to generate and to measure thepulse widths are similar to the ones presented in section 4.10.2 except for the replacementsof the LT-GaAs switch with RD-GaAs switches.We have used a cross-correlation method again to time resolve the reflected infraredlaser pulse shapes. In performing the experiments, all the switches are irradiated withenough excitation energy fluence to produce electron-hole plasma density of ‘-‘ 2 x 1019cm3. Figure 6.5 shows some of the typically measured cross-correlation signals from thethree RD-GaAs switches. Each data point in the plots is averaged over at least 60 singleshots and the error bar is an indication of the standard error in the measurements. Thesecurves represent the temporal integral of the reflected infrared pulses. The differentialsof these curves with respect to time provides an accurate representation of the temporalshape of the reflected infrared pulses. The risetimes of these pulses is governed by therisetime of the excitation pulse (490 fs). The measured pulse width is found to be astrong function of the ion dosage on the switch. At an H+ ion dose of 1 x 1012 cm2the reflected infrared pulse is measured to be 15+1.5 ps. By increasing the irradiationion level to 1 xlO’4 cm2 the reflected infrared pulse width is reduced to 2.4+0.3 Ps.An additional increase in the dosage level to 1 xlO’6 cm2 further reduces the reflectedinfrared pulse to 600±200 fs. By taking our detectivity for these pulses, we estimatethe reflected energy of the infrared pulses to be 5 pJ. This corresponds to a peakreflectivity of 50%. The results for the lx 1016 cm2 RD-GaAs switch reflection pulsewidth is comparable with the visible excitation pulse width of 490 fs. Therefore, underour experimental conditions, the reflected infrared pulse width is mainly determined bythe lifetime of the semiconductor switch and the width of the visible excitation pulse. InChapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 186light of the above experimental results, to produce and measure pulse widths of shorterduration the visible excitation pulse must be compressed.In order to explain the observed ultrafast carrier recombination times, we can approximate the carrier lifetime by equation 6.2. If one assumes that N is directly proportionalto the H ion dose and that the reflectivity pulse width represents the carrier lifetime,then a log—log plot of the ion dose as a function of infrared reflected pulse width shouldresult in a linear curve with a slope of —1. Figure 6.6 represents a plot of the measured reflected infrared pulse width as a function of the H+ ion dose. The curve showsthe predicted linear relationship between the reflected infrared laser pulse and the iondose. However, the calculated experimental slope is —0.4 which differs from the predictedslope of —1. One possible explanation is that the density of the recombination centres isnot directly proportional to the ion dose. This is similar to what has been observed iiierbium-doped GaAs [186]. The other possibility is that the defect density is lower thanthe density of the optically generated carriers which may result in the saturation of thetraps and the recombination centres due to excess free carriers.From figure 6.6 we can calculate the relationship between the ion dose, Q, and thereflected infrared pulse width, r, in picoseconds to be:= 106Q°4 (6.3)With the above relation, one can simply tailor the infrared pulse width to the requiredduration by simply adjusting the amount of damage on the switch. In fact, by adjustingthe dosage across the surface of the wafer, a multi-speed switch can be easily constructedon a single wafer.CC.)C.)—10Energy (eV)Figure 6.4: Real and Imaginary parts of the dielectric function of undamaged GaAssample (solid) and the ion damaged (dashed). For the damaged GaAs, the ion dose levelis 1 xlO’6 cm2.Chapter 6. Ultrafast Semiconductors for 10.6 1um Optical Switching 1872520151050—51.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0Chapter 6. Ultrafast Semiconductors for 10.6 im Optical Switching 1881.0I0.8 (a)0.60.40.2I I0 10 20 30 40 50C2 5 I I I20(b)rr) °•Ci)0 0.0 ——— I I0 4 8 12 161.5 I(c)1.0.a0.500 2 4 6 8Delay (ps)Figure 6.5: Cross-correlation measurements for the reflected infrared laser pulses for anion damage dose of (a) lxlO’2cm,(b) ixiO’4 cm2 and (c) 1x1O’6 cm2. Note thatin all plots, the cross-correlation signal is plotted in arbitrary units which differ for eachdiagram.Chapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 189I 11111 I I 111111 I Illilif I I 11111 I I I IIIII I I IIICl)Cl)J I I i I I iii I I iii I I I i iii I I IIIJI1011 1012 10’s 1014 10 1016 1017Ion Dose (cm2)Figure 6.6: Measured 10.6 ,im infrared laser pulse widths as a function of the H iondose in GaAs.Chapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 1906.6 Using Ino.85Ga .i5As/GaAs GaAs for Ultrafast Pulse GenerationIn this section, we investigate a novel and alternative semiconductor structure for application to infrared semiconductor switching. The growth of lattice mismatched semiconductor layers by MBE above the critical layer thickness results in the formation ofdefects and dislocations. Clearly, in the fabrication of electronic devices, it is undesirable to introduce dislocations where the ultimate performance, efficiency, and lifetimeof the devices are mainly limited by the dislocations introduced during epitaxial growth[236]—[239]. However, increasing the recombination centre density during the epitaxial growth enhances the speed of the material. Dislocations at the interfaces betweenlattice mismatched semiconductors such as InGaAs and GaAs, can serve as ultrafastnon-radiative recombination centres. The growth sequence of InGai_As/GaAs can bedivided into the following stages: (a) initial growth where InGai_As is grown under coherent strain where only a finite amount of lattice mismatch is accommodated by strain;(b) intermediate growth when the InGai_rAs layer thickness reaches the critical layerthickness (which depends on the strained alloy indium concentration) and dislocationsare generated at the interface; and (c) the final growth phase when the thickness of theInGaAs layer is increased far beyond the thickness of the critical layer, a relaxation of thestructure takes place and as a result some of the lattice mismatch is accommodated bymisfit dislocations. Continual growth above this point results in an island-type growthstructure [239, 240].6.6.1 MBE Growth of Ino.85Ga1As/GaAs Relaxed SuperlatticeThe samples are grown by S. R. Johnson in the U.B.C. Physics Department. The layersare grown on a semi-insulating (100) GaAs substrate using the Vacuum Generators V8OHmolecular beam epitaxy (MBE) machine. The substrate preparation procedure is similarChapter 6. Ultrafast Semiconductors for 10.6 ,um Optical Switching 191to the one discussed previously in section 6.4.1. The layer thicknesses of the superlatticeare as follows: the first three layers consist of 210 A of GaAs on 84 A ofIn085Ga1As,the next three layers consist of 210 A of GaAs on 126 A ofIn0•85Ga15As, and the lastfour layers consist of 210 A of GaAs on 84 A ofIn0•85Ga15As. These layers are grownat a substrate temperature of 500 °C. The substrate is annealed at 630 °C for 3 mm. Aschematic diagram of the structure is presented in figure 6.7The lattice mismatch between the In085Ga1As layer and the GaAs layer is 6%.The layers of the InGaAs/GaAs superlattice are relaxed as they are much thicker thanthe critical layer thickness which is oniy a few monolayers (‘-. 20 A) [239, 241]. Thesurface roughness of the grown structure is greater than the surface roughness of thelattice matched buffer layer. However, this roughness is not large enough to cause diffusereflection at 10.6 1um. The sample showed a smooth and featureless surface when observedwith a scanning electron microscope.In order to enhance the effects of non-radiative recombination at the defects, severalsteps are taken to ensure maximum recombination efficiency: alternating layers of InGaAsand GaAs are chosen so that the total number of interface boundaries and, hence, the totalnumber of the dislocations is maximized. The total thickness of the relaxed superlatticeis chosen to be about the same as the absorption skin depth of the visible excitation pulse,such that the majority of the carriers are optically generated throughout the superlatticestructure. At this high In concentration, the layer grows as islands [239, 240, 242, 243].6.6.2 Ultrafast 10.6 tm Pulse Generation from In0g5Ga0isAs/GaAs as a Reflection SwitchWe have used a cross-correlation technique to measure the carrier lifetime in the superlattice structure. The details of the experimental set up and the measurement procedureare similar to previous ones except for the replacement of the LT-GaAs or RD-GaAsChapter 6. Ultrafast Semiconductors for 10.6 um Optical Switching 192with the Ino.g5Gao.isAs/GaAs relaxed superlattice structure. The ultrafast change of the10.6 im reflection is monitored as a function of time delay between the visible excitationpulse used to turn on the Si switch and the infrared pulse. The excitation energy fluencethroughout the experiment is kept constant and is estimated to be 0.4 mJ/cm2 Withknowledge of the pulse energy, spot size, and the absorption skin depth, we can estimatethe maximum generated electron-hole (e-h) plasma density per pulse to be 5 x 1019 cm3.The cross-correlation reflectivity curve represents the temporal behaviour of the optically generated plasma inside the relaxed superlattice structure. The risetime is governedby the generation rate of the e-h plasma created by the 490 fs excitation laser pulse. Initially, the optically induced plasma remains confined to the absorption skin depth layerof 220 nm. As time evolves, the defects/dislocations at the interfaces and throughout therest of the relaxed superlattice will act as ultrafast non-radiative recombination centresfor the plasma as it diffuses throughout the layers. Figure 6.8 illustrates a typical cross-correlation curve, where the reflectivity is plotted versus the time delay following theplasma excitation for the initial 10-ps following excitation. The cross-correlation curveresembles the integral of a double exponential reflectivity function. When the differentialof the reflectivity cross-correlation curve is plotted on a logarithmic scale, as shown infigure 6.9, it is clear that there are linear regions representing two intrinsic recombinatioritimes. The initial ultrafast decay is measured to be 2.6 ± 0.3 ps, and the slow decay is10.0 ± 0.3 ps. The 2.6 ps exponential decay time represents the effective recombinationlifetime of the carriers at the dislocations and defects. The origin of the long 10 Ps decay tail may be due to space charge regions near dislocations which produce potentialbarriers and wells for non-equilibrium holes and electrons. These barriers/wells occurin regions around dislocations, where strain is maximized. Once the plasma is created,all the electrons/holes occupy different states high/low in the conduction/valence bands.Chapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching 193While most of the carriers recombine rapidly at recombination centres, a significant number with low energy get trapped by the barriers/wells and therefore have a much longerrecombination time. These trapped carriers recombine through Auger recombination. Asa result, one expects a long infrared reflectivity tail indicating the presence of these carriers. The structure’s carrier lifetime is comparable to that of RD-GaAs ( with a dose of ‘-2x1012 cm2) and LT-GaAs semiconductors (grown at 300 °C). It should be noted thatthis structure can be utilized as an ultrafast optical-optical infrared reflectivity switch[177]. Here, we managed to generate ultrashort 10.6 m laser pulses of 10 Ps duration.After this experiment was completed and the results were submitted for publication[177], two papers appeared in the literature which discuss carrier lifetime in similarstructures [237, 244]. Pelouch and Schlie [244] measured a rapid absorption recoverysignal of the order of ‘—‘ 10 Ps fl a Ino,65Ga .3As/GaAs structure. They attribute theultrafast absorption recovery to recombination at misfit dislocations. On the other hand,the results of the recently published work by Hugi et al. [237] showed two lifetime scalesfor similar structures mainly Ps for electrons and 10 Ps for holes. They attribute the 3ps lifetime to trapping at substitutional oxygen on arsenic site °As (with correspondingdensity and capture cross-section of 8x10’6 cm3 and 1.9x10’3 cm2, respectively) andthe 10 Ps lifetime due to large densities of misfits and threading dislocations due to latticemismatch.6.7 Conclusion of the ChapterIn conclusion, we have demonstrated the feasibility of generating ultrashort pulses at 10.6m using LT—GaAs, RD-GaAs, and Ino.s5Gao.isAs/GaAs relaxed superlattice as singleswitching elements. The pulse duration ranges from 600 fs to 15 Ps depending on theactive switching elements. Furthermore, with the optimization of the growth parametersChapter 6. Ultrafast Semiconductors for 10.6 tm Optical Switching 194I84AT-I84ATI84AT84ATI126 ATI126 ATI126 AT 1!’$j £*i2OAr84ArT 4$;210’n r>’84ATj K[%4 219i. iIttr84At GaAs Bufferlayer on Semi-insulatingGaAs SubstrateFigure 6.7: A Schematic diagram of the Inos5Ga .iAs/GaAs relaxed superlattice.3lOnmChapter 6. Ultrafast Semiconductors for 10.6 um Optical Switching 1952.0 I I I I I I I I•1 I1.61.J.C’‘J.CC.)I 0.4C12C f.. I I I012345678910Delay (ps)Figure 6.8: Cross-correlation infrared reflectivity signal as a function of time delay.Chapter 6. Ultrafast Semiconductors for 10.6 tm Optical Switching 196IIC2.0 I • I • I • I • I1.51.00.500000 102 3 4 5Delay (ps)6 7 8Figure 6.9: Differential of the cross-correlation, I, curve as a function of time.Chapter 6. Ultrafast Semiconductors for 10.6 ,um Optical Switching 197of LT-GaAS, and the use of RD-InP pulses as short as 100 fs at 10.6 m can be easilyproduced. Obviously this requires reducing the pumping pulse width to 100 fs.The sensitivity of this technique to low-density photogerierated plasmas (compared tousing the visible beam as an optical probe) and the deep penetration depth of the probelaser beam make it ideal for studying carrier dynamics of buried interfaces where electrically injected carriers are generated deep within the structure. This is clearly demonstrated in the measurement of the non-equilibrium carrier lifetime in Ino.s5Gao.iAs/GaAsrelaxed superlattice [177].It should be emphasized that the experiment described above provides an exampleof the utilization of this switch at 10.6 m; however, the frequency of the reflected pulseis determined by the infrared laser radiation source. By replacing the CO2 laser withanother infrared laser (A 1 nm), it is possible to generate ultrashort pulses at thesewavelengths. It is interesting to note that the generation of optical pulses in the far-infrared range, with a pulse duration of less than one optical cycle, can be achieved withthis method.Finally, we should point out that in conducting the previous experiments, the carriersare initially injected with excess energy high in the conduction band. The contributionof intraband carrier relaxation and intervalley scattering may play a role in determiningthe duration of the reflectivity pulses. Clearly, it is preferable to photoexcite the carrierswith photon energy just above the band gap such that the effects of these processes areminimized.Chapter 7Conclusions and Suggestions for Further Work7.1 IntroductionThis chapter summarizes the major experimental results of this dissertation, followed bysome useful suggestions for future experimental work on ultrashort pulse generation andsemiconductor probing.7.2 Summary and ConclusionsIn this thesis, we first described the principles and the theory behind optical semiconductor switching and the possibility of generating subpicosecond infrared pulses at 10.6jtm. A numerical simulation of the switching process was presented to aid in the understanding of the infrared single-switching process. The original model, which is based onthe carrier diffusion from the surface of the switch into the bulk, shows the feasibilityof producing picosecond and femtosecond laser pulses. The pulse duration is found todepend on the initial injected carrier density.The measurement techniques used during the course of the experiments are time - integrated infrared reflectivity measurements, time-integrated infrared transmission measurements, time-resolved reflection-reflection correlation measurements, and time - resolvedcross-correlation measurements. The information obtained from these experiments isused to determine the speed and the optimum operation of the optical semiconductor198Chapter 7. Conclusions and Suggestions for Further Work 199switches. Even though the initial original-model calculations provide a reasonable description of some of the observed infrared reflectivity experimental results, the modeldoes not fully describe the observed time-resolved reflectivity pulses from GaAs. This isconfirmed by performing detailed experimental investigations of the basic characteristicsand the temporal evolution of the photogenerated plasma in a GaAs infrared reflectionswitch. The information obtained from the original model and an enormous number ofexperiments on GaAs are used to develop a better model that accounts for the overalltemporal and integrated behaviour of the infrared reflectivity pulses. By introducing anadditional two-body recombination mechanism, whose rate is a function of the carrierdensity, we are able to obtain good agreement between the proposed model calculationsand the experimental results. Experimentally, at carrier densities-10n, the two-bodyrecombination time is found to be 0.5 ps. It is clear that this ultrashort recombination time cannot be explained in terms of Auger or density independent two-body recombination processes. A possible recombination mechanism might be a nonradiativeplasmon-assisted recombination with a recombination rate F= 1.9 x 10—28 cm6/s. Thisrecombination mechanism is more efficient at high plasma density. As the plasma densityand plasma frequency increase, the electrons at the bottom of the conduction band recombine with the holes high in the valence band. The recombination mechanism resultsin the emission of plasmons. To our knowledge, there is no experimental observation ofplasmon-assisted recombination in GaAs, and one cannot conclude that from performingreflectivity measurements alone. Clearly, other experiments are required to verify thisrecombination mechanism.In addition to the transient 10.6 zm reflectivity from the GaAs switch, the absorptionof infrared radiation in Si of various doping is investigated after free carriers are generated by absorption of a subpicosecond laser pulse of above band gap photon energy. Atheoretical model is presented which predicts the transmission coefficient for an infraredChapter 7. Conclusions and Suggestions for Further Work 200laser pulse through a photogenerated e-h plasma in Si of various surface free-carrier densities. By fitting the experimental data to the theoretical predictions, the imaginarycomponent of the dielectric function is accurately determined. From the results, the free-carrier absorption cross-sections at 10.6 ,im and the relaxation times are calculated. Themomentum relaxation time in n-doped Si is measured to be 10.6 fs, whereas for p-dopedand intrinsic Si it is found to be 26.5 fs. These measurements are used to determinethe speed of the infrared transmission cut-off switch. Application of the transmissioncut-off switch to the time-resolved cross-correlation method showed that it is possible tomeasure the duration and the shape of infrared pulses with a resolution limited only bythe duration of the excitation laser pulse.Clearly, for ultrashort pulse generation, the type of semiconductor material used forthe switching process is crucial. The duration of the 10.6 im laser pulses generatedfrom a single GaAs optical semiconductor switch are 20—30 Ps long. These pulsesare two orders of magnitude longer than what we expected to produce. We have foundthat to operate a single switch with a subpicosecond speed, the optically induced carrierlifetime must be reduced. Thus, several techniques were explored during the course ofthe experimental work to reduce the carrier lifetime. Ultrafast recombination centresare introduced during the semiconductor material growth procedure, by irradiation ofthe semiconductor material with an ion beam, and by the creation of defects in latticemismatched semiconductors.By using a 200 nm low-temperature molecular beam epitaxy grown GaAs layer grownat a low temperature of 320 °C on a GaAs substrate, we demonstrated the generationof 1 picosecond infrared pulses at 10.6 ftm. The presence of many As precipitates inthis material act as fast recombination centres, giving the optically generated carrier alifetime of 0.5 ps. Furthermore, ultrafast infrared pulses at 10.6 tm as short as 600 fs areproduced by using radiation damaged GaAs with a 180 KeV H dose of lx 1016 cm2Chapter 7. Conclusions and Suggestions for Further Work 201as an optical-optical switch. It was found that the generated infrared reflectivity pulsewidths are proportional to the H dose to the power —0.4. This allowed precise controlover the generated pulse duration. We believe pulses as short as 100 fs can be relativelyeasily achieved by the use of radiation damaged InP as an optical semiconductor switch.We have also investigated the recombination lifetime of nonequilibrium carriers in ahighly excited Ino.s5GaoiAs/GaAs relaxed superlattice structure by studying the time-resolved infrared reflectivity at 10.6 gum. Lattice mismatch between Ino85Ga015As andGaAs layers gives rise to misfit dislocations which act as ultrafast recombination centreswhich result in a dramatic decrease of the carrier lifetime. We demonstrated that thiscarrier lifetime is 2.6 ps. Laser pulses as short as 10 ps were produced using this structure.This thesis demonstrates the feasibility of generating femtosecond laser pulses usingonly a single optical semiconductor switch. The lasers, the electronic equipment, and theoptical diagnostic systems built as part of this thesis work are still in use and many moreinteresting experiments are planned using this ultrashort pulse laser system. Currently,a unique high-energy 1 J, 500 fs CO2 laser system, based on this work, is beingdeveloped. The low power optically switched 10.6 m laser pulses will be amplified ina 15 atmosphere CO2 laser amplifier module for the purpose of studying laser-plasmainteractions.7.3 Suggestions for Further WorkDuring the course of the experimental work, several alternative techniques concernedwith the generation of ultrashort laser pulses were frequently discussed in our laboratory.Here, we present an experimental proposal for producing such pulses and an alternatemethod for probing semiconductors.Chapter 7. Conclusions and Suggestions for Further Work 2027.3.1 Ultrashort 10.6 Aum Laser Pulse Generation by Beam DeflectionHere, we propose a simple technique for producing an ultrashort laser pulse in a widerange of wavelengths. The proposed technique is based on ultrafast beam deflection usingthe transient optical Kerr effect in highly nonlinear materials [245]—[252] . The principleof ultrafast all-optical laser beam (pulse) deflection is discussed by several authors forapplication to all-optical modulation [248], all-optical subpicosecond streak camera [250],ultrafast pulse duration measurement [249], and femtosecond laser pulse generation [250,251]. The analysis presented in this section is similar to those of references [248]—[252].The optical arrangement of the ultrafast optical Kerr deflector is illustrated in figure7.1, and it consists of the following components: a CW CO2 laser, an intense ultrashortpump pulse of a duration of 500 fs, a nonlinear material such as CS2, a small entranceslit, a focusing lens, and a small pinhole. The basic operation of the ultrashort pulsegeneration scheme is simple: the nonlinear optical material is placed behind a smallentrance slit of width d0, then the CO2 laser beam is directed perpendicular onto theaperture and is focused by a small focal length lens on the edge of a pin hole of widthW. The intense ‘-. 1 mJ, 616 nm, 490 fs laser pulse is directed on the entrance slit atan angle with respect to the CO2 beam, so that it excites a prism-shaped volume inthe CS2 cell, as shown in figure 7.1. The CO2 laser beam passes through an opticallyinduced temporal prism which is created by the intense pump beam due to the opticalKerr effect. The nonlinear refractive index, is time dependent and it is equal ton2Is(i), where n2 is the nonlinear refractive index coefficient, and I3(t) is the visiblepump pulse intensity. As the 10.6 m beam propagates through the medium of lengthL, the temporal Kerr prism causes spatial phase modulation that results in the infraredbeam deflection. Clearly, the deflection angle, Od(t), is a function of time; therefore,for ultrafast deflection operation, it is appropriate to use materials with an ultrafastChapter 7. Conclusions and Suggestions for Further Work 203nonlinear response. If the infrared deflected beam is made to scan a small pinhole placedat a distance S away from the nonlinear medium, the transit time of the deflected beamthrough the opening, W, can be of the order of a picosecond or less. Thus, an ultrashortpulse is produced by ultrafast transmission through the pinhole.As an illustrative example, we present some simple approximate calculations to determine the minimum pulse width that can be produced at 10.6 tim. The numerical valuesthat are used in the calculations are based on the lasers, material, and components whichare available in our laboratory. More comprehensive calculations should be performed toproperly characterize the speed of the device in detail.In the far field approximation where S >> L and d0, the time, TD, needed for thedeflected infrared beam to scan a small pinhole is related to the deflection angle Oj by_W dO-1TD— --(--) . (7.1)With the aid of figure 7.1 and by using Snell’s law for light refraction, we obtain theexpression(n0 +n1)L =n0[LcosOd +d0siriOdj (7.2)where n0 is the linear refractive index. By using a small deflection angle approximation,Od and COSOd 1, the expression reduces toO(t)d= nt)L (7.3)An important parameter that must be considered is the diffraction of the deflected beam.The diffraction angle determines the number of the resolvable spots (resolution of thedeflector), N, and thus the minimum aperture width of the pinhole. For a gaussianbeam, the far field diffraction angle, O, is given byAOf = , (7.4)7rw0Chapter 7. Conclusions and Suggestions for Further Work 204where w0 is the beam waist. Using equations 7.3 and 7.4, the number of resolvable spotsisN3 = 0d = w0n1L (75)The minimum aperture size is limited by the diffraction spot of the infrared beam. Forminimum separation of two observable spots, the minimum pin hole width is given by(7.6)7tW0The rate of change of the deflection angle with time is proportional to the rate ofchange in the nonlinear refractive index, ni. Therefore it is highly desirable to use anonlinear material with an ultrafast response time, Tr. For an ultrafast excitation pulse,the expression dOd/dt can be approximated by its instantaneous response to the pulse:dOd — dn1 L n1L7 7dt — dt doTrdoBy combining equations 7.1, 7.6 and 7.7, one obtains an expression for the minimumpulse width that can be obtained from such a deflector\d0TrTD,mjn = (7.8)lrwonrjl LIt is possible to produce intense pulses with our ultrashort laser system (1 mJ in490 fs pulse) of the order of 50 GW/cm2.Using this intensity and n2= 1.5xl01 (esu)for CS2, we obtain a value for ni=6.3x103 By substituting some realistic numericalvalues: Tr 2 ps [251], d0 w0, L = 23 mm (i.e. cv= 85°), and )= 10.6 m, we calculatea minimum pulse width of 46 fs with N3= 43. This pulse is approximately 1.5 opticalcycles of the CO2 laser radiation. The potential for this technique to generate evenshorter pulses is possible by simply using a faster nonlinear medium.Chapter 7. Conclusions and Suggestions for Further Work 205__________________4—_______________________10.6___ ___________[.meFigure 7.1: Schematics of the all-optical beam deflector used for ultrashort pulse generation.Chapter 7. Conclusions and Suggestions for Further Work 2067.3.2 Back Surface Infrared Reflectivity MeasurementsAn interesting experiment that can be performed is a measurement of the backside infrared reflection from GaAs as illustrated in figure 7.2. The experimental arrangement isthe same as that used for front surface probing of GaAs, except that the optical excitationpulse is made incident on the GaAs from the backside and the infrared probe is incidenton the front surface. As a result, the e-h plasma density gradient is created in the opposite direction from the usual infrared switch operation. The 10.6 jim radiation interactswith an e-h plasma which is exponentially increasing with depth. Clearly, the reflectionproperties (efficiency, pulse shape, and duration) of the backside illuminated switch aredifferent from the standard operation. Unlike time-resolved front side probing, wherethe infrared beam is reflected off a thin overdense plasma layer, for backside reflectionthe probing infrared radiation propagates through a thicker plasma layer with its criticaldensity layer propagating into the bulk. Thus, one expects to observe a stronger phasemodulation across the reflected pulse. We performed with success a pilot experimentto see whether we could observe this effect. However, no further attempt was made totime-resolve the duration of the reflected pulses. The detector-limited pulse shapes arefound to be very sensitive to the angle of the excitation beam relative to the sample. Itis not clear why this is the case. Unfortunately, due to time constraints, no further workwas done to characterize the observations. 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Sci, Instrum., 62, 600 (1991).Appendix A,5YcoDesign Circuits of the Synchronization UnitThis appendix outlines the electronic circuit diagrams of the synchronization unitused to synchronize the hybrid CO2 laser with the femtosecond laser pulse system.Diagram A.1:UBC PHYSICS — ELECTRONICS LABI4/Z/ I V ITItLCPOWER SUPPLY227UBCPHYSICS—ELECTRONICSLABOATt94/5/JI.4E110,61ItL(40MHzBUFFERI—II-iI..... I.40110*4(7OOnVp—p)>114-14L5 IT40L01oOUT(IVp—p)Appendix A. Design Circuits of The Synchronization UnitDiagram A.3:CLKI+5V+5V22994/5/3LJBC PHYSICS — ELECTRONICS LABJscci or 9TItLTRIGGER CIRCUITTRIG 047C7345V5319?49C20Appendix A. Design Circuits of The Synchronization Unit 230Diagram A.4:;Lz10-_!__: .____-_____ _ _TTTT‘ri’ ‘ 1i’4.’Appendix A. Design Circuits of The Synchronization Unit 231Diagram A.5:,-U)*A;;.;v:__d I_______: :2‘5rrrrrrfl1Fr—— —.I_ORsf2.._I’j[.1C 3 0I—U,> -C z m0 0 a I.,a,C)-o-C (I, C) U) m m C, -l 0 C-)U)I > a,—.I—.rMINPUTni JI.04W+24WC4OUTPUTSneNobI2PinUicvophoneCannOtto,-J4I SC4 26NoteI:UIOptionalNote2:R6—2k43(900nS)Note3:63,C3NotInelotlodUBCPHYSICS—ELECTRONICSLABDAlI,94/5/16ISACET,ITII‘Ott,30VPulseAmplifierC3Appendix BThe Fast Photodetector Amplifier Circuit and PerformanceIn this appendix we present a complete electronic circuit design of a fast photodetector amplifier which was discussed in Chapter 4. The amplifier electronic circuitis shown in figure B.l. The amplifier’s output as a function of pulse frequency ispresented in figure B.2.In order to check the pulse width distortion and measure the gain of the amplifier,a 1 ns (337 nm) pulse from a nitrogen laser is attenuated to the signal level of thatfrom Cu:Ge. The signal is detected with a fast detector (Hamamatsu-R1193U.03)and displayed on the 1 GHz bandwidth oscilloscope. The amplifier does not causeany pulse distortion, as shown in figure B.3. The measured gain at 1 GHz is 34 dB.234Appendix B. The Fast Photodetector Amplifier Circuit and Performance 2351.1 Siohj,i .2 50ohl Li 50h, FEEOTROUGH_______________________ ____________________rrrrn—mm mm5 J6 J7 I J6 J9 Jsii JI2 JS’ +]14 Tu i 0ip i 00p 00p 1 00p 0UI cat cat cat, 21 330 270Ri —r22R310 I2ouru001 cOOL - 2UL uOtUL041CLII jA1_.uOOicatcat cot catFigure B.1: The amplifier circuit.lL;I:. J lllil• 111(111’ III •I0 0 00 039 0000— 37 035 00.133°3142 345 2 345101 102 10Frequency (MHz)Figure B.2: Photodetector amplifier gain as a function of the input frequency.Appendix B. The Fast Photodetector Amplifier Circuit and Performance 236Figure B.3: (a) Input signal to the amplifier. (b) Amplified output signal from the amplifier.Appendix CSW4—C5W.-CSW4—85W4—45W4—2SW4—15W3—8SW3—45W3—2$W3—lSW2—Cswl—cSW2—8SW2—4SW2—2SW2—lswi—eWI—’SWI—2Owl—IbELAY 00/DELAYThI/DELAYTh2,OELAY:osbELAY 04/OELAYO5,DELAY:oebELAY 07N0—GND/DELAY 08/OELAYThO/DELAYI0/DELAYII/DELA’C12/DELAYI3/DELAY14/DELAYISENDONOCircuit Design of the Pulse Integration ModuleIn this appendix, we present the circuit diagrams for the pulse integration module(PIM) which was discussed in Chapter 4.Diagram C.1:NOl.UBC PHYSICS — ELECTRONICS LABDTC 8J/I0/20 Icct I or IDELAY PROGRAMMING MODULE237i.UBCPHYSICS—ELECTRONICSLABDAT(-O7—IInIGATEDINTEGRATORMODULEWod.Got.—Integrator—SamplikHoId.07AA°MPULSEINPUT+/—2VpeakZERORESTOREINTEGRATOR1:4attnINTEGRATOROUTPUT(tOOpSec)C,ZEROAOJ.INTEGRATOROUTPUT(JosampIngADC)>PJ—IA00C’ I*71.P—INA<P3-teeDELAYEDTRIGGERGATE6nS.cGATEPULSE*01.74HCTOO500nS.cDELAY7411CTOOSf012UBCPHYSICS—ELECTRONICSLA1tC•2—O7—17INTGATEDINTEGRATORMODULEGot.Puls.G•nirotort’3Appendix C. Circuit Design of The Pulse Integration ModuleDiagram C.4:--t:-Th-t:240-JC.,z0C.,-JwC,,C-,C,,>-=3-C.,w-Jz00I-;I— az(J0w aii-. a.C)4 JHt r-i-t-I-(-t: F-IHt F—•1______—a_r4jJ4TLI>Pl-IOAUBCPHYSICS—ELECTRONICSLABo*tc93/9/IIsnIor3IIrL(LASERTRIGGERDELAY— cjq ‘-iC)I: ciTRIGGERMONIIORPt-IA<€—ii—CSL_LCII_LC2OJ_4_L1i_cs_LC5i_Cli_Cl.JCSi_Cl?i_Cl0i_Cl.C2Pt-ISP1—hA!I%;IoIoIotoIoIoI.iI.itotolPt—ha<4—jPI—flAPl—2OPt—IAPt—liPt—es<P1-SILASERTRIGGERINPUT/ADCTRIGGER00074ACTO1A7UCt0ZAppendix C. Circuit Design of The Pulse Integration Module 242Diagram C.6:-J(I,C.)o,aU:w-J C,wI I(4(4 u)- .=a..,InC.)iiwC,a Zo — e’i .n . Ino 0 0 0 0 0 0 0)- )- )- ,- ,.. - ). )-4 4 4 4 4 4 4 4_J _a I j I J ..I II.J W I.J W W I.* W W 0 00 0 0 0 0 0 0 0 ZZ‘% •% .- .-. •1 %. •••. CC,).. )- )- )- >. >. ).. >_j _I _j_I _I J_l Jw w w w w W W I a aa a a a a a a a zz% % % —-. •% %_ — ,ø-IU,C.,z0IC.)w-awU,C-)U,0.C-)Appendix C. Circuii Design of The Pulse Integration Module 243Diagram C.7:C,’L.all-p.‘C-Jww(3C,I-.U,‘C-aINPUT2UBCPHYSICS—ELECTRONICSLABDAft,9—O9—O8II€u,1@i2TITLI,ANALOGOUTPUTMODULEaqC) t1 1. 0 CbUTOANALOGOUTPUTANALOGINPUT+ITCIATE—ANALOGINPUT—ANALOGOUTPUT/ADCTRIGGERPt-nA<Pt—il.<Pi—I2A<(4.._......—C91CSIC14I.C16Is,.! CIIC201C21‘1-I.P1-17*<--TTt”]_UITwTwTT]_Ut1U1pI7.<P1-52*<‘c:;to..I_citP1-321<TTwT°’T°’T°1TUI TwIUIQEI7411C4311UBCPHYSICS—ELECTRONICSLABIliCt93—09—08Isicci2oc2IltLC,ANALOGOUTPUTMODULEH I7OuS.c7111+02•5Sic14OCT20•52/ADCTRGC€RP1—HAP1—118Pt—hA<ctI-Iaq(),sy600HzXUITRATE74HCO874HC108A.1114z7411CT123ONLEDUBCPHYSICS—ELECTRONICSLABOATC93/9/2Ior3TI1LtDUALSERIAl.ADCMODULEAppendix C. Circuit Design of The Pulse Integration Module-JU,z00-I0U.)00Diagram C.11:riI2j24700U0IaUID0•1C.IN+ I + I— —,. za. N a. a. > a.z C.U (3 (3 (3o + 0 0 0_I_J_I +_I4 4 4 4z z z z4 4 4 4(Na.z-jcn.z0C.)--aw -U,C.)U,>-..1Appendix C. Circuit Design of The Pulse Integration Module 248Diagram C.12:0aU,0 000 0 0 0 00 0000000 Z 0Z a a a a a a aId-J002U00..-Hii-:!----:!----—U.-1E-‘[I“Iaz‘-4I,,a144II II W _c;.a-I-ThAppendix DThe Autocorrelator Design and Optical ComponentsThe main component in the design of the autocorrelator is the second harmonicgeneration crystal (SHG). The nonlinear crystal used in the current setup is a 0.5mm thick Potassium Dihydrogen Phosphate (KDP) crystal with a 10 mm aperture.The angular adjustment of the crystal is very crucial in obtaining a SR signal; therefore, the crystal is mounted on a fine-rotational-tilt stage which provides excellentcontrol over the crystal alignment. The crystal is oriented to obtain a maximumSH signal which emerges from the crystal along the bisector of the two converginginput light beams.In order to produce a SH signal from the 616 nm laser pulses, the two pulses mustbe simultaneously present at the crystal with a phase matching angle of 59.26° fromthe optical axis. The crystal is cut at an angle of 58.6° which is slightly less thanthe phase matching angle. The small angle difference of 0.7° eliminates the backreflection into the laser cavity.The thickness of the crystal limits the temporal resolution of the autocorrelator.This can limit the minimum pulse that can be measured with this device. Thecrystal length determines the bandwidth of the SHG signal, and it should be shorterthan the coherence length of the frequency components of the light pulse in orderto avoid dispersion. For a given KDP crystal length, ALcry, one can calculate thebandwidth resolution, AVcr,, of the autocorrelator from the following relation [253]VcryALcry = 0.3122(nm — cm) (D.1)From our experimental parameters, the temporal resolution of the autocorrelator249Appendix D. The Autocorrelator Design and Optical Components 250is calculated to be 90 fs times the pulse shape factor. For a double exponentialpulse shape the autocorrelator resolution, due to the crystal thickness only, is --‘ 40fs. The overall resolution is ‘ 60 fs. This temporal resolution is adequate for ourexperimental purposes.The KDP crystal is transparent to both fundamental (616 nm) and SH (308 urn)signals; therefore, for proper SH detection, the fundamental signal must be filteredout. In the autocorrelator design, a piece of 3x5x5 cm3 Corning (G 57-54-1) U.V.glass filter is used. The filter is inserted directly in front of the photornultiplierhousing.Since the SH signal is in the U.V. range, for the detection of such signal one requiresa photomultiplier which is sensitive to this wavelength. In the autocorrelator design,we used a Hamarnatsu photomultiplier with a U.V. input window and a risetime of2.5 us. The photornultiplier is biased to a voltage of 600 V. Due to the operatingsensitivity of the photornultiplier, it is placed in a light-tight cylindrical housingwith the SR signal entering through a 3 mm diameter pinhole.A low pass filter/amplifier is used to filter out the high frequency components inthe autocorrelation trace and to amplify the autocorrelation signal. The circuitdesign for the filter/amplifier is presented in figure D.1. The output signal from theelectronic amplifier/filter arrangement is used to drive the vertical axis of a highimpedence oscilloscope, where the signal amplitude corresponds to points on theautocorrelation trace. All the mirrors used in the autocorrelator are front surfacealuminum coated silica: M1—M5 are 2.5 cm in diameter and 6.5 mm in thickness.The retrorefiector mirrors M6 and M7 have a dimension of 12.5x 12.5x6 mm3.The 50:50 beam splitter used in the autocorrelator is 6.35 cm in diameter. Thefocussing lens is a plano convex type with a focal length of 3 cm and a diameter of12 mm. This lens is mounted on a homemade fine-translation stage to adjust thefocus on the SH crystal. The rotation of the mirrors is done with a torque motorAppendix D. The Autocorrelator Design and Optical Components3 Pir, 4icrophonePower Corrnectior,s5 Pole Low Pose Bessel Fifter 500kHz TowO.8050—2C15-dE--Io,F357C16D8l1C?7-‘Hdo°g V251Figure D.1: Low pass filter and amplifier circuit used for the autocorrelation pulse mea0=50=4243 1k62+5VJr Ic, IC21 LI L3 LO‘H40O5F I (— —HF—lO,F 1SF357 357CO C1207511 0261? L—iCO C13CND>— r,020>22 J_. I ‘c!7 ‘::C22 H040055V T’ T°’ L2 5v — L610 F 1SF ‘v’ L4 I0F \1--7surements.Appendix D. The A utocorrelator Design and Optical Components 252which rotates at a constant reliable frequency of 25 Hz. This motor provided analmost vibrational-free scanning mechanism. The control box of the autocorrelatorhas the functions of: relative delay scan adjustment between the trigger pulse andthe autocorrelation scan, and signal gain adjustment. Triggering of the oscilloscopefrom the autocorrelator is performed using an optical interrupter placed under therotating mirrors. The delay of the trigger signal can be adjusted between 0.5 to 10ms relative to the beginning of the scan.D.1 Calibration of the AutocorrelatorIt is clear that one is required to calibrate the time scale on the oscilloscope screenfrom the relative scanning time to the real time. The calibration of the horizontalscale is done manually. Here, one uses the optical pulse itself to calibrate the timescale. If the two arms of the interferometer are equal, both laser pulses overlap onlyat one point in time. When the retroreflector is scanned while the rotating arm isspinning, the dye pulses overlap at different points in time, resulting in the SHsignal peak being shifted as a function of the retroreflector scan. One can use thisto obtain a calibration factor for the autocorrelator from the following relationTscaie —20t(ps/ms) (D.2)where Xd is the distance in mm travelled by the retroreflector arm, Sd is the peakshift in ms of the SH signal, and t is the time scale. The factor of 2 accounts forthe actual distance travelled by the pulse. Experimentally, the calibration factor ismeasured to be 81.33 ps/ms. Theoretical calculation of the calibration factor fromreference [134] givesTscaie = 4frDr (D.3)where c is the speed of light, Dr (= 7.62 cm) is the distance between the tworotating mirrors, and fr (= 25 Hz) is the rotational frequency, giving a calibrationAppendix D. The Autocorrelator Design and Optical Components 253factor of 79.79 ps/ms which is in good agreement with the above measured value.

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