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Ultrafast switching of CO₂ laser pulses by optically-induced plasma reflection in semiconductors Elezzabi, Abdulhakem Y. 1995-12-31

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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 presentingthis thesis inpartial fulfilmentof the requirementsfor an advanceddegree at theUniversity of BritishColumbia, Iagree thatthe Library shallmake itfreely availablefor reference andstudy. I furtheragree thatpermission forextensivecopying ofthis thesisbr scholarly purposesmay be grantedby the headof mydepartment orby his orher representatives.It is understoodthat copyingorpublication ofthis thesis forfinancial gainshall not beallowed withoutmy writtenpermission.(Signature)__________________________________Departmentof_______________________The Universityof British ColumbiaVancouver,CanadaDatejJ’?f5DE.6 (2/88)AbstractUltrafast mid-infrared laser pulse generation using optical semiconductorswitching isinvestigated experimentally for application to subpicosecondCO2 laser pulse generationat 10.6Ilm.Time-resolved infrared measurements, which are basedon cross-correlationand reflection-reflection correlation techniques, areused to determine the duration ofthe reflected infrared pulses from a GaAs infrared reflectionswitch. These time-resolvedmeasurements together with time-integrated measurementsare used to derive a modeldescribing the behaviour of the GaAs infrared reflectionswitch. it is found that diffusionand two-body recombination whose rate is takento be density-dependent, can accuratelydescribe the ultrafast infrared reflectivity switchingprocess in GaAs. We have alsoinvestigated some novel semiconductor materialswith ultrafast recombination lifetimesforultrafast semiconductor switching application.A molecular beam epitaxy low temperature grown GaAs (LT-GaAs) and radiationdamaged GaAs (RD-GaAs) aresuccessfullyused to switch out ultrashort CO2 laserpulses. Application of the time-resolvedcross-correlation technique to nonequilibriumcarrier lifetime measurements inhighly excitedLT-GaAs, RD-GaAs, and Ino.85Gao.15As/GaAsrelaxed superlattice structure arefoundto be in good agreement with other reported techniques.As an application to semiconductor probing, ultrafast infraredtransmission experiments are conductedto determinethe absorption of infrared pulsesin Si of various dopings after free carriershave beengenerated by absorption of a subpicosecondlaser pulse of above bandgap photon energy. By fitting the experimental data to a theoreticalmodel, the free-carrier absorptioncross-sections and the momentum relaxationtimes are calculated.11Table of ContentsAbstractiiList of FiguresviiiAcknowledgmentsxvii1 Introduction11.1 Present Investigation. . 21.2 Thesis Organization32 Semiconductor Switching and Ultrashort LaserPulses at 10.6 1um 62.1 Introduction62.2 Ultrashort Pulse Generation Using aCO2 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 ElectronLasers 112.2.4 Ultrashort Mid-Infrared Pulse Generation with NonlinearFrequencyMixing132.3 Optical Semiconductor Switching152.3.1 The Semiconductor Switch152.4 Ultrafast Optical Excitation232.4.1 The Dielectric Function242.4.2 Free-Carrier and Intervalence BandAbsorptions261113 Theory: Infrared Reflection from a SemiconductorPlasma3.1 Introduction ....,.,.,...3.2 Propagation of an Obliquely Incident ElectromagneticWave in an Inhomogerieous Dielectric Medium3.2.1 The S-Polarized Electric FieldCase3.2.2 The P-Polarized Electric FieldCase3.3 Numerical Approach to the Solution: P-PolarizationCase3.4 Reflection of 10.6 ,um Radiationfrom a Thin Film Plasma3.5 Temporal Variations of the Plasma Density3.5.1 Electron-Hole Plasma Recombination3.5.2 Diffusion and Time-Dependent DensityProfile of the Free Carriers3.6 Simulation of the Reflectivity Pulsesfrom GaAs4.4 Synchronization ofthe Hybrid CO2 Laser and theFemtosecond Laser System934.5 Infrared Pulse Detectionand Timing System954.5.1 The Cu:Ge Infrared Detector9528282831343744535356594 Laser Systems, Optical Setups,and Experimental Procedures744.1 liltroduction .744.2 The Femtosecond Laser System4.2.1 The Femtosecond Laser PulseGeneration System4.2.2 The Femtosecond Laser PulseAmplifying System4.2.3 The Subpicosecond DyeLaser Pulse Amplifier . .4.3 The CO2 Laser Oscillators4.3.1 The CW CO2 Laser Oscillator4.3.2 The High Pressure TEACO2 Laser Oscillator . .4.3.3 The Hybrid CO2 Laser75•75767777778090iv4.5.2 Electronic Amplifier.4.5.3 Experimental Data Collection System4.6 Hall Conductivity Measurementsin Si4.7 Autocorrelation Pulse Width Measurements4.8 Optical Semiconductor Switch Setup4.9 Time Integrated Infrared ReflectivitySetup4.10 10.6 tm Pulse Width MeasurementTechniques4.10.1 Reflection-Reflection CorrelationProcedure and Optical4.10.2 Cross-Correlation Procedure and OpticalSetup4.11 Infrared Pulse-Frequency MeasurementTechnique4.11.1 The Image Disector4.11.2 Optical Setup and Alignmentof the Image Disector4.11.3 Calibration of the Image DisectorOptical System5 Experimental Investigation of InfraredReflection from GaAs12496979999105107108109111115116116118Setup5.1 Introduction5.2 The Si Transmission Cut-OffOptical Switch .5.2.1 Theoretical Considerations5.2.2 Transmission Cut-off Resultsat 10.6 jim5.2.3 Discussion of the TransmissionResults5.3 Ultrafast 10.6 jim Reflectivity Pulsesfrom a GaAs Switch5.3.1 Time-Integrated Infrared Reflectivity5.3.2 Reflection-Reflection CorrelationMeasurements5.3.3 Cross- Correlation Measurements5.3.4 Discussion of the Time-ResolvedResults5.3.5 Modeling of Free-Carrier Density andReflectivity124125127132136143143147153155161v5.4 Frequency Spectrum Measurements1666 Ultrafast Semiconductors for 10.6ItmOptical Switching1716.1 Introduction1716.2 The Need for Semiconductors with UltrashortCarrier Lifetimes 1716.3 Ultrafast Recombination Semiconductors1736.4 Using Low-Temperature Grown GaAs for UltrafastPulse Generation . 1756.4.1 MBE Growth of LT-GaAs Layers1766.4.2 Subpicosecond 10.6 m PulseGeneration from LT-GaAs as aReflection Switch1786.5 Using Radiation Damaged GaAsfor Ultrafast Pulse Generation1796.5.1 RD-GaAs Samples’ Preparationsand Characterizations1836.5.2 Subpicosecond 10.6 um PulseGeneration from RD-GaAs asa Reflection Switch1856.6 Using Ino.s5Gao.iAs/GaAs GaAsfor Ultrafast Pulse Generation1906.6.1 MBE Growth ofIno.s5Ga0.15As/GaAsRelaxed Superlattice . . .1906.6.2 Ultrafast 10.6 m Pulse Generationfrom In085Ga0isAs/GaAs asa Reflection Switch1916.7 Conclusion of the Chapter1937 Conclusions and Suggestions forFurther Work1987.1 Introduction1987.2 Summary and Conclusions1987.3 Suggestions for Further Work2017.3.1 Ultrashort 10.6 umLaser Pulse Generation byBeam Deflection .2027.3.2 Back Surface InfraredReflectivity Measurements206viBibliography208Appendices227A Design Circuits of the SynchronizationUnit227B The Fast Photodetector AmplifierCircuit and Performance234C Circuit Design of the Pulse IntegrationModule237D The Autocorrelator Design andOptical Components249D.1 Calibration of the Autocorrelator252viiList of Figures2.1 Principle of OFID short pulse generation.(a) In the time domain, (b) inthe frequency domain122.2 Typical schematic configurationsof optical semiconductor switchingoperating 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, T1is thetransmitted infrared beam(pulse) and T2 is the transmittedpulse. . . 173.1 An incoming wave whose electric field,E1, is normal to the plane of incidence (S-polarization)333.2 An incoming wave whose electricfield, E1, is parallel to theplane of incidence (P-polarization)363.3 10.6 tm laser radiation magneticand electric field amplitudecompollentsB (curve a),E (curve b), and (curve c) as a functionof = -yz inGaAs. The initial carrier densityis n =5n. Solid curves represent thereal parts and dashed curvesrepresent the imaginary parts413.4 Brewster angle reflectivityfor 10.6 tm laser radiation asfunction of anexponentially decaying plasmadensity profile of (a) GaAsand (b) CdTe.The inset figure showsan enlarged plot of the reflectivityfor 0ri/ne1.043viii3.5 Phase angle change as a function of plasma density.The solid lines are calculated from the differential equationmodel. Dashed lines are calculatedfrom the thin film plasma model453.6 Geometry of the vacuum-plasma-semiconductor interfacesfor the thin filmplasma model483.7 Geometry of multiple reflections from vacuum-plasmaand plasma -. semiconductor interfaces503.8 Brewster angle reflectivity for C02-laser radiationas a function of freecarrier surface density of GaAs for (a)a uniform film thickness-y’and(b) for an exponentially decaying densityprofile. The inset figureshowsan enlarged plot of the reflectivityfor0n/nc 1 523.9 The variation due to diffusion ofcarrier density, n(z, t)/n0 as afunction oflongitudinal position and time.The curves are plotted in increasingtimesteps of 500 fs. The top curveis calculated at t= 0 ps, andthe botttomcurve is calculated att= 4.5 Ps603.10 Reflected 10.6 ttm pulses as a functionof time for initial plasma densityof (a) n= 0.7flc, (b) n = 0.9nc, and (c) n =6nc. The solid lines arecalculated from the differentialequation model andthe dashed lines arecalculated from the thin filmplasma model643.11 Reflected 10.6 m pulsesas a function of time for initialplasma density of(a) n= 1.2flc and (b) n = 1.3n. The solid lines are calculatedfrom thedifferential equation modeland the dashed lines arecalculated from thethin film plasma model653.12 Phase change in degreesof the reflected 10.6 umpulses as a function oftime for initial plasma densityof (a) n= 0.7nc and (b) n = 0.9n. Theplots are calculated from thedifferential equation model67ix3,13 Phase change in degrees of the reflected10.6 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 differentialequation model683.14 Phase change in degrees of the reflected10.6 ,um pulses as a function oftime for initial plasma density ofn = 6n. The plot is calculated fromthedifferential equation model693.15 Illustration of the plasma profileused to estimate a constant plasma depthand density from a plasma density profileat a given time after the onsetof laser illumiation703.16 (a) Normalized surface plasma densityat z=0 as a function of time.(b)Effective thickness of the plasmafilm as a function of time714.1 The layout of the femtosecondlaser pulse generating system784.2 An illustration of the 40W CW CO2 laser. R = 0.4 Ml andFIV = 25 kV 814.3 The TEA CO2 laserusing an automatically preionized,doublesided, LCinversion circuit. Electrical conductors(aluminum and copper)are shownshaded. The preionizer rod designis also shown below824.4 (a) The CO2 laser LCinversion circuit and the preionizersconnections.P.R.= preionization rod, S.G.=spark gap, and L.D.= laser discharge.(b)The equivalent circuit withC = 64.8 nF, L = 420 nH,R = 1.05 1, C= 64.8 nF, andLe = 6.8 nH844.5 (a) Main electrode voltagewithout the glow discharge,VM’, and with theglow discharge,VM. (b) Preionizer/inversion current without theglowdischarge, Ip’, and withthe glow discharge,Ip; the main electrode current,89x4.6 (a) The CO2 laser pulse shape at 10.6 ,um, with anenergy of 800 mJ. (b)Longitudinal mode beating during thelaser oscillation 914.7 The hybrid CO2 laser system arrangement934.8 (a) Single longitudinal and transverse modefrom the hybrid CO2 laser.(b) Same hybrid laser with the CW laser turnedoff 944.9 A layout of the synchronization between thehybrid CO2 laser and thefemtosecond laser pulse generating system954.10 The Cu:Ge infrared detector bias/output circuit964.11 Integrated output from the dual channelpulse integration module as afunction of the input pulse voltage amplitude.The solid circles denotechannel 1 and the empty circles denotechannel 2994.12 The autocorrelator. B.S.= beam splitter,PMT= photomultiplier, andKDP= second harmonic generationcrystal (Potassium Dihydrogen Phosphate)1024.13 Typical autocorrelation traces fromthe 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 lengthis too long resulting in a pulsewidth = 830 fs. The time scale in(a) and (c) is 10 iis/div, whereasin (b)it is 20Rs/div 1044.14 (a) Autocorrelation signal of an amplified,1 mJ, 616 nm dye pulse showinga pulse duration of 490 fs. (b) Same conditionsbut with the injected pulsefrom figure 4.13(b)1064.15 The experimental arrangement fora GaAs optical semiconductorswitch. 107xi4.16 Typical experimental configurations used tomeasure the infrared pulse duration: (a) Reflection-reflection correlation experimentalsetup. (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 therear reflection resulting fromthe first GaAs reflection switch1154.18 Experimental optical setup for the reflectedpulses spectrum measurement.T1= temporary mirror, and G= grating1194.19 A typical oscilloscope trace of theoutput of the image disector showingten channels1204.20 Samples arrangement1204.21 Calibration curve of the spectrometerreading against the CO2 laser wavelength1214.22 Image disector calibration curve. Theerror bars are the standard deviationof signals for 10 consecutiveshots separated by 13.3 us1235.1 Transmission signal temporal recoveryof the P-type Si transmissioncut-offswitch1305.2 Calculated relative transmissionfor 10.6 1um radiation througha photoexcited Si wafer as a functionof normalized free-carriersurface densityn0/nfor four values of of c [a=0.1 (uppermost), 0.2, 0.3,and 0.5 (lowest)]. .133xli5.3 Infrared pulse intensityhrdetected for two different Si wafersat zerophotoexcitation as a function of visible laser pulseintensity incident onGaAs reflection switch. The solid lineis a linear regression fitted to thedata points (empty circles) up to <34, and the dashed line is a linearregression through the solid circles1355.4 Relative transmission coefficient foran infrared laser pulse through basically intrinsic Si (p-type concentrationof l.6x 10’ cm3)as a function offree-carrier surface density generated by photoexcitation.The full curve isthe best fitting theoretical predictionto the data points at a = 0.2. Thetheoretical curve for a= 0.5 is also shown (dashed)1375.5 Relative transmission coefficient for an infraredlaser pulse through basically intrinsic Si (p-type concentrationof 2.6x 10’ cm3)as a functionoffree-carrier surface density generatedby photoexcitation. The full curve isthe best fitting theoretical predictionto the data points at a = 0.2. Thetheoretical curve for a = 0.5 is also shown(dashed)1385.6 Relative transmission coefficient as in figure5.4 for n-type Si concentrationof 4.9x 10’s cm3). The full curve is the bestfitting theoretical predictionto the data points at a = 0.5. The theoreticalcurve for a = 0.2 is alsoshown (dashed)1395.7 Relative transmission coefficientas in figure 5.4 for n-type Si concentrationof 6x10’5 cm3). The full curve is thebest fitting theoreticalpredictionto the data points at a =0.5. The theoretical curve for a= 0.2 is alsoshown (dashed)1405.8 Calculated transmission of p-typeSi as a function of time144xlii5.9 Typical ultrafast reflected infrared pulses (left) and their correspondingexcitation visible pulses (right). The bottom photographis presented toillustrate the reproducibility of the experimentalsignals 1465.10 Experimental results of the normalized time integratedreflectivity as afunction the normalized free-carrier density1485.11 Reflection-reflection correlation signal for an excitationfluence corresponding to 7Fh/n= 3. .1505.12 Reflection-reflection correlation signalfor an excitation fluence corresponding to 7Fh/n= 51515.13 Reflection-reflection correlation signalfor an excitation fluence corresponding to ‘yFh/n= 71525.14 Cross-correlation signal as a functionof time for -yFh/n= 0.7 (solid), 2.0(empty)1565.15 Cross-correlation signal asa function of time for7Fh/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 functionof 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 normalizedplasma density7Fh/n= 10. (b) Theinsert indicates the normalizedsurface plasma density as a functionofnormalized time1645.18 Model calculations as a functionof normalized time of: thenormalizedinfrared pulses for7Fh/n— 10 (upper solid line) and 2 (lower solid line),normalized cross-correlation signalfor 7Fh/n— 10 (dash-dot), andnormalized reflection-reflection correlationsignal for ‘-yFh/n= 10(dash). . 167xiv5.19 Model calculations for time integrated reflectivity (reflectedpulse energy)as a function of the normalized carrier density.The vertical axis scaleunits are arbitrary1685.20 Wavelength shift of a reflected infrared pulse withan initial excitationfluence of7Fh/n= 7 1706.1 (a) Schematic diagram representing the LT-GaAsgrowth layer. (b) Scanning electron micrograph of the LT-GaAslayer 1806.2 (a) A cross-correlation transmission signalbetween the JR pulse and thevisible pulse creating the transmission temporalgate. The solid line is themodel calculations. (b) The infraredpulse as obtained from differentiatingthe cross-correlation curve1816.3 Variations of the reflected JR pulse energyas a function of the e-h plasmadensity. The LT-GaAs layer thicknessis ‘—i 2 1um1826.4 Real and Imaginary parts of the dielectricfunction of undamaged GaAssample (solid) and the ion damaged (dashed).For the damaged GaAs, theion dose level is lxlO’6cm21876.5 Cross-correlation measurements for the reflectedinfrared laser pulses foran ion damage dose of (a) lxlO’2cm,(b) lx cm2 and (c) lx1016cm2. Note that in all plots,the cross-correlation signal is plottedinarbitrary units which differ for eachdiagram1886.6 Measured 10.6 1um infrared laser pulse widthsas a function of the11+iondose in GaAs1896.7 A schematic diagram of theIno.85Gao.,5As/GaAsrelaxed superlattice. .1946.8 Cross-correlation infrared reflectivity signalas a function of time delay.1956.9 Differential of the cross-correlation,I, curve as a function of time196xv7.1 Schematics of the all-optical beam deflector used forultrashort pulse generation2057.2 Schematics of the backside infrared reflectionexperiment 207B.1 The amplifier circuit235B.2 Photodetector amplifier gain as a functionof the input frequency 235B.3 (a) Input signal to the amplifier. (b) Amplifiedoutput signal from theamplifier236D.1 Low pass filter and amplifier circuit used forthe autocorrelation pulsemeasurements251xviAcknowledgmentsI wish to especially thankmy supervisor, Prof. Jochen Meyer, for providingme withthe opportunity to work withhim and for creating an intellectually stimulatingresearchenvironment. His constant guidanceand encouragement are most appreciated.I deeply thank and appreciate myparents, Youssef Elezzabi and Amna Quaia, andtherest of my family, for allowing me the opportunityto pursue my post-secondary studiesin Canada, and for their continuous moralsupport.Special thanks goes to Lara Cleven whose encouragementand help made the experimental setbacks insignificant.It is also a pleasure to acknowledge Hubert Houtmanfor 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 Hughesfor 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 semiconductorstructures.Prof. Irving Ozier deserves thanks for his thoroughreading of the thesis and suggestionsfor the manuscript corrections.Also, I wish to express appreciation to Prof. Thomas Tiedjefor 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 presencemade the work moresatisfying and pleasant.xviiMy special thanks are extended to the followingpersons for the unequalled technicalsupport:Philip Akers, Jacobus Bosma, Ole Christiansen,Domenic Di Tomaso, Tom Felton,JamesGislason, Stan Knotek, Heinrich Manfred, BeatMeyer, Joseph O’Connor, Mary AnnPotts, Brian Smith, Douglas Wong, and especiallyto Alan Cheuck for providing greatservice arid ensuring that the equipmentworked and that supplies were available.Thanks are also due to the staff of theU.B.C. Physics Department: Bridget Hamilton,Lore Hoffmarin, and Kim Spears forsuperb administrative help.The financial assistance of the LibyanMinistry of Higher Education, andthe NaturalSciences and Engineering Research Councilis appreciated.xviiiChapter 1IntroductionSince the first demonstration of optical semiconductorswitching by Alcock et 1976[43], the technique has gained wide interestto its potential application iii generatingfemtosecond laser pulses at 10.6 ,um. Despitethe rapid advances in ultrafast lasertechnologyin the last decade, the focus of femtosecondlaser research is directed towardsvisible, nearinfrared, and ultraviolet wavelengths.In comparison to other laser wavelengths,minimalresearch has been devoted to ultrashortpulse generation schemes at 10.6tm. Ultrashortcoherent mid-infrared laser pulses areof interest for the investigationof fundamental processes occurring on short-timescales which cannot be studiedwith the current ultrafastlasers. Ultrafast CO2 laser pulses operatingin the mid-infrared rangeare of valuableinterest to many research fields.Femtosecond/picosecond10.6 um laser pulses have awide range of application tosemiconductor physics, plasmaphysics, and chemistry.In semiconductor and solid state physics,ultrashort 10.6 m lasersprovide an important tool for exploring severalfundamental processes involvingcarrier dynamics,such asintraband transitions, interbandtransitions in low band gap materials,intervalence bandabsorption of free holes, free-carrierabsorption, intersubbandtransitions in quantumwells, momentum relaxationtimes, carrier lifetimes,carrier energy relaxationrates, anddiffusion coefficients. Manyof the experimental conclusionscan be gained by time resolved measurementsof transmission and reflectivitychanges induced by nonequilibriumcarrier distributions. The knowledgeof these processes aidsin the development of newand faster semiconductor andoptoelectronic devices.Moreover, ultrashortmid-infrared1Chapter 1. Introduction2pulses are essential for testing high-speed mid-infrared devicessuch as detectors andmodulators. In the field of photochemistry, femtosecond10.6 jtm infrared laser pulsesare of great interest for applicationto infrared spectroscopy of molecules. The advancesin ultrashort pulses have permitted the investigationof the vibrational-rotational modesin polyatomic molecules, study of fast chemicalreaction rates and dynamics, chemicalkinetics and energy transfer in liquids,multiphoton excitation, multiphoton ionization,infrared absorption, and local charge distributionof organic molecules. A 10.6 mferntosecond laser pulse provides an importanttool for application to ultrafast nonlinearprocesses in laser-plasma interactions.1.1 Present InvestigationThe primary objective of this thesis workis to perform a complete experimentalstudy offemtosecond CO2 laser pulse generationoperating at 10.6 tm as a partof the developmentof a subpicosecond terawatt tabletop laser system. To achievethis goal we would liketo employ optical semiconductorswitching techniques to generatethese pulses. Clearly,before developing such a laser system,there are several studiesthat must be performed.Specifically, the main issues addressedin this work are:1. The feasibility of generatingfemtosecond laser pulses at10.6musing a singleoptical semiconductor switch, includingthe switching dynamics ofthe optical semiconductor switching mechanismto determine the limits on theshortest pulse thatcan be generated.2. The study of the temporalbehaviour of the reflected infraredpulses as a functionof injected carrier density.Chapter 1. Introduction33. Investigation of the role of carrier diffusion and recombinationon the speed of theoptical infrared switch.4. To explore some novel semiconductormaterials for their use in mid-infraredferntosecond pulse generation.5. To investigate the use of infrared probingfor the measurement of carrier lifetimes.6. To measure the free-carrier absorption cross-sectionsand momentum relaxationtimes in semiconductors.7. To develop accurate methods for measuringmid-infrared laser pulse temporalshapes,and to explore their limitations andsensitivities.8. To develop simple models that describethe infrared reflection/transmissionsemiconductor switching process.1.2 Thesis OrganizationThis thesis is divided into sevenchapters discussing thedetails of the experimentalandtheoretical work. Fourappendices are devoted tothe aspects of some technicaldesignsof the experimental equipment.The thesis is organized asfollows: the standardmethods used in the generatingof laser pulses in the mid-infraredrange, and especially at10.6 m, are briefly discussedin Chapter 2. A qualitative overviewis presented for eachexperimental techniqueevaluating its general features,advantages, and limitations.Anintroduction of the physicalprocess of optical infraredsemiconductor switchingand theprinciples behindthe generation schemeare also presented in thischapter. The generalformalism describing thedielectric functionof a semiconductor along withsome important absorption processesat 10.6mare also introducedin Chapter 2.Chapter 1. Introduction4In Chapter 3 a model describing the illfrared optical semiconductor switchingprocessis presented. The model is based on the reflection of theinfrared radiation from a thinplasma layer with the carrier dynamics determined byambipolar diffusion. The wavepropagation equation is solved numericallyfor some experimental semiconductor plasmaconditions, and the time evolution of the plasma is governedby ambipolar diffusion. Fromthe numerical simulations, femtosecond/picosecondpulse generation conditions and characteristics are obtained. The calculations presentedin this chapter provide the necessarybackground on the subject of infrared semiconductorswitching.A brief description of the experimental equipment thatare used during the investigation, the optical setups, and the experimentalconditions are presented in Chapter4.Part of this experimental work is dedicated to theinstallation, maintenance, andcharacterizations of the commercial laser system.Thus, a brief review of the major lasersystemcomponents is outlined. The detailsof the construction and the design of the high-powerCO2 laser are also reviewed in this chapter. The electronicand optical instrumentationsthat are constructed and developed forspecific experimental purposes are alsobrieflydiscussed in this chapter. Moreover, thespecific techniques and the opticalsetups fortime-resolved and frequency-resolvedmeasurements used to perform theexperiments areoutlined in detail.The time-resolved and time-integratedexperimental results on opticalsemiconductorswitching using GaAs are presentedin Chapter 5. Interpretations of the experimentaldata and some estimates of the importanceof the physical mechanisms governingthe timeevolution of the switch reflectivityare discussed. Based on the experimentalobservations,a simple model describing the switchingprocess in GaAs is developedto predict theswitching behaviour. The resultsfor free-carrier absorption cross-sectionand momentumrelaxation times in both doped and intrinsicSi transmission cut-off switchesare presentedin the same chapter. A complete modeldescribing the infrared transmissionthrough SiChapter 1. Introduction5is developed and compared with the experimentalresults.The growth procedures, sample preparations,and the experimental results of novelultrafast recombination semiconductorsare discussed in detail in Chapter6. Here, theresults of infrared probing of the temporalcarrier lifetimes of several semiconductorsarepresented. Ultrashort 10.6 pm pulsesgenerated using ultrafast recombinationsemiconductors are also discussed.Finally, in Chapter 7, we briefly summarizethe results of the thesis, withspecialemphasis on the major original thesis contributions.A concluding remark on the natureof the free-carriers’ recombination mechanismin GaAs is made. Moreover, suggestionsfor an interesting ultrashort pulse generationscheme and a novel optical arrangementfor semiconductors probing are presented.Also, a numerical estimate onthe limit ofgenerated pulse duration is discussedin this chapter.Chapter 2Semiconductor Switchingand Ultrashort Laser Pulses at10.6tIm2.1 IntroductionThis chapter is intended as an overviewof the basic physics and technologydealing withthe generation of ultrashort laserpulses in the mid-infraredregion. Since our objectiveis to produce subpicosecondpulses at the CO2 laser wavelength,the review is directedtowards mid-infrared pulsesgenerated at a wavelengthof 10.6 sum.The first section of this chapterintroduces the essentialissues and constraints associated with the generationof ultrashort laser pulses at10.6 m. The second sectionpresents brief overviews ofsome standard techniquesemployed for ultrashort10.6 mpulse generation such as: modelocking, optical free inductiondecay, nonlinear frequencymixing, and free electronlasers. In the third section,we introduce opticalsemiconductor switching, and discussthe basic physical principlesbehind the generationscheme.Finally, in section four, wepresent some relevant processeswhich occur duringultrafastoptical excitation ofthe semiconductor switchand introduce the semiconductorswitchdielectric function.2.2 Ultrashort PulseGeneration Usinga CO2 LaserBefore proceeding with thetechniques of iiltrashortpulse generation, oneshould highlightthe basic physical principlesthat govern the generationof ultrashort laser pulsesat 10.6m.6Chapter 2. Semiconductor Switching and UltrashortLaser Pulses at 10.6 um7The gain spectrum of the CO2 laser consists ofseveral discrete vibrational-rotationallines. In order to produce subpicosecondlaser pulses directly from thelaser medium,the gain spectrum must be wide enoughto amplify these pulses, The gain spectrumof the CO2 laser can be enhanced tosupport the generation of ultrashortlaser pulsessimply by increasing the operating lasergas pressure [1]. The overlapof the adjacent rotational lines of the CO2 molecules modulatesand widens the gain spectrum andhelps tominimize pulse distortion. However,high pressure operation decreases the gainrisetimeand lifetime due to the increased collisionalexcitations/de-excitations ofthe laser levels[2]—[4]. In other words, due to highgas pressure, the excited CO2 moleculesrelax faster(inversely proportional to the pressure).In addition, the limited gain lifetimerestrictsthe duration of the generatedpulse by limiting the effectivenumber of pulse round tripsin the laser cavity. That is, if the generatedpulse is to be made short enough,a highernumber of cavity round trips is requiredto take advantage of the widegain spectrum. Itwas pointed out by Houtmanand Meyer [5] that the gain durationfor a 10 atmosphereCO2 laser is only 750 us at FWHM(full width at half maximum)and hence, activemode lockers cannot produce pulsesshorter than 800 ps. Thesetwo facts reduce theeffectiveness of ultrashort pulse generationby mode locking [5, 6].2.2.1 Mode Locking of a CO2LaserDue to the limited gain bandwidthof a TEA (transverse electricatmospheric) CO2 laser,the long 100-200 ns pulsesfrom a so-called hybridCO2 laser (a combination ofaCW laser and a TEA laser sharingthe same laser resonator) canbe shortened by modelocking of multiatmosphere transverselyexcited lasers. Passiveand active mode lockingtechniques are commonly usedto shorten the durationof a laser pulse.Passive mode locking relieson absorption saturation to generateamplitude modulation by providingan intensity-dependent loss in thelaser cavity. That is, thetransmissionChapter 2. Semiconductor Switching and UltrashortLaser Pulses at 10.6 im8of a saturable absorber follows the shape of theradiation laser pulse; the peakof thelaser pulse experiences a lower loss thanthe wings, consequently, the peak of thepulse 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 minimumpulseduration that is achievable with a fastsaturable absorber is limited bythe absorber’srecovery time and the CO2 laser gain linewidth. Laser pulses of a durationbetween 1to 5 ns have been generated usingSF6 as a fast saturable absorber[7, 8]. Shorter pulsesof duration between 80 to 500Ps were obtained by using P-typeGe as a bleachableabsorber [9]—[13]. TheCO2 laser pulses generated with passive modelocking techniquesare limited in their pulse durationto ‘ 80 ps.Active mode locking utilizes thebeating of the laser oscillationwith an externaloscillator frequency [14]. Thegain or loss of the laser cavityis periodically modulatedat the oscillator’s frequency (amplitudemodulation or frequencymodulation) [14]. Acomplete review of the subjectof active mode locking is presentedin reference [15].Actively mode locked multiatmosphereCO2 lasers [5, 11] [16]—[19], resultin longer pulsedurations(‘-.-‘1 ns) than the passive mode lockingtechnique. Pulses asshort as 500ps (detector limited) have beengenerated by Houtman etal. [16] with a novel square-wave mode locking and cavitydumping of a 10 atmosphereCO2 laser system. Thispulse generation systemproduced the shortest pulse evergenerated usingan active modelocking scheme. In general,the technique can be usedto produce pulses as shortas 200ps [15, 16]; however, the amountof extracted power is limitedto low damage thresholdof the pockels cell crystal.The short gain lifetime and thelack of a wide gain bandwidthnecessary to supportthegeneration of picosecondor femtosecond pulses makesthe generation of pulsesshorterthan 500 Ps very challengingby the standard modelocking techniques similarto theones applied to solidstate lasers [14]. For thesereasons, alternative nonconventionalChapter 2. Semiconductor Switchingand Ultrashort Laser Pulses at10.6 um 9ways to produce ultrashort mid-infraredlaser pulses have been developed:includingoptical free induction decay, free electronlasers, nonlinear frequencymixing and opticalsemiconductor switching.2.2.2 Optical Free InductionDecay (OFID)OFID is originally proposedand demonstrated by Yablonovitchand Coldhar [20] as amethod for generating high power picosecondpulses at 10.6 hum. The centralcomponentsof the system are: a single mode high-powerCO2 laser, a plasma shutter, anda hot CO2absorption cell. Theprinciple behind OFID is simple:first the frequency spectrumofthe CO2 laser pulse has to be widenedand then the original centralfrequency is filteredout. In such pulse generatingsystems, an optical transmissionswitch turns off a longsingle mode CO2 laser pulsein a time of approximatelya few picoseconds.As a resultof this ultrafast pulse truncation,frequency sidebands aregenerated around the centralfrequency of the CO2 laser line.The central componentfrequency can be rejectedbyusing a narrow resonance absorptionfilter such as hotCO2 gas. A hotCO2 gas onlyallows the sidebandsof the frequency spectrumto be transmitted, hence,producing anultrashort pulse. An alternativetime-domain explanationof the OFID processis toconsider a CO2 cell whichis heated to‘-450 °C to increase the absorptionof the 10.6m radiation. If the hot cellis long enough, then a completeattenuation of theCO2laser beam is possible.Under a steady stateone can view the absorptionprocess as adestructive interferencebetween theCO2 laser radiation electricfield and the inducedelectric-dipole radiationfrom the hot CO2 gas. Thepolarization induced electricfield isalways coherent with theinput electric field butwith the opposite phase.Now, whenthe CO2 electric field issuddenly turned off bythe plasma shutter ina time durationwhich is much fasterthan the relaxation timeof the CO2 molecules,then the fields arenolonger canceled by destructiveinterference and the excitedCO2 hot molecules continueChapter 2. Semiconductor Switching and UltrashortLaser Pulses at 10.6 m 10to radiate in phase with each other (but still outof phase with the applied electric field).That is, turning off the input signal quicklyresults in the generation of an ultrashort pulsewhose width is limited by the relaxationtime (due to dephasing and energy decay)of thedipole radiation. Figure 2.1 illustratesthe OFID principle both in time and frequencydomains.The CO2 laser pulse duration can by approximatedby the following empirical formula[21]:Tp(pS) o.67()+10 (2.1)whereTd, -ye, and £ are the dephasing time of the resonant absorber, absorptioncoefficientof the resonant absorber, andits length, respectively.Several OFID experiments employing variousshutters [20]—[30] demonstrated thefeasibility of this technique in the generationof ultrashort picosecond pulses ofa durationadjustable between 33 and 200ps. The pulse duration is foundto be strongly dependenton the CO2 gas pressure whichis related to the relaxation time,Td, through the relation[24]:Td(ns)= 42(2.2)PJ9/300where P and 9 are theCO2 gas pressure in torr and its temperaturein degrees Kelvin,respectively. The relaxation timeof the CO2 molecules limits thewidth of the generatedpulses to 30 ps. Other techniquesmust be employed to reduceto pulse duration below30 Ps.Scherrer and Kneubiihl [25] proposeda new picosecond 10 tmCO2 laser based systemwith far-infrared laser gases(CH3F, D2O, and NH3) as spectralline filters. This OFIDsystem has advantages over thehot CO2 based OFID setup:it can be operated atconsiderably lower gas pressureand at room temperature; inaddition, the frequency ofthe pulse can be selectedvery precisely by proper choiceof the gas. However,to date,Chapter 2. Semiconductor Switching and UltrashortLaser Pulses at 10.6 ,um 11the authors did not present any measurementson their pulse durations using these gases.The OFID pulse is short when the dip inthe frequency spectrum is wide [21]; therefore,a major concern, which is usually ignored in theliterature and by groups performingOFID experiments, is the background levelof the generated pulses. Since thegeneratedpulses lack the central frequency component intheir frequency spectrum, the generatedpulses are in fact not as short as they are claimedto be. With simple mathematicalanalysis it can easily be shown that ifone takes a Fourier transform of the OFIDpulsefrequency spectrum, the results when mappedinto time domain show a short spike oftheorder of 30 ps riding on a significantly longer pedestal.The amount of energy containedin the background can be as highas that contained in the ultrafast peak.The pulsedurations are usually determined fromautocorrelation measurements which,in all of thereported experiments [20]—[30], are performedabove a certain background level.Moreover, in OFID experiments, thereare always pulse transients followingthe initialfast spike lasting for‘-.i100 ps. These pulses contain25% of the energy of the centralpeak [22]. Clearly, it is undesirableto have this type of background orpost pulses forconducting time-resolved picosecond experiments.We should emphasize that OFIDpulse generation cannot be performedwith CW(continuous wave) CO2 lasers. Thegeneration scheme requiresa high-power CO2 laserwhich limits the repetitionrate of the pulse train to that of thehigh-power laser.2.2.3 Ultrashort Mid-InfraredPulse Generation withFree Electron LasersA free electron laseris a device which consists of a linearaccelerator (an electron gun,a pulse compression section, andtraveling-wave accelerationstage), an electron transport system, an undulatormagnet array and an opticalresonator cavity [31]. Injectedelectrons exhibit periodicoscillations in the undulatormagnetic field (made froma series of magnets of alternatingpolarities) and lose energy throughsynchrotron radiation.Chapter 2. SemiconductorSwitching and Ultrashort Laser Pulses at10.6 umHybrid CO2Laser PlasmaShutter OFIDFilter70 MHz100 GHz 70MHzFigure 2J: Principleof OFID shortpulse generation.(a) In the timedomain, (b) in thef10Ons(a)(b).i_10 PS—3OO PSfrequency domain.Chapter 2. SemiconductorSwitching and Ultrashort Laser Pulses at10.6 um 13A resonance condition can be achieved throughthe interaction of the electrons withthe electromagnetic field and the undulatormagnetic field which causesthe electrons toform bunches in a scale comparableto the optical wavelength. This resonanceconditionprovides photon emission coherenceand optical gain.Free electron lasers generatea wide band laser spectrum. Recently,free electronlasers have been used to generateultrashort infrared pulses coveringwide ranges ofwavelengths and durations [32]—[36].The micropulse widths are measuredto be between3 - 12 ps with peak powers up to 10MW at a peak wavelength of8 m. These pulses areemitted in macropulses ofa duration of “-‘ 10 ts at arepetition rate of ‘-‘-‘ 6-50 Hz[35].Glotin et al. [32] pointedout that the limiting factorin reducing the pulse widthis theamount of detuning of thecavity length. In their experiment,they managed to producedsubpicosecond pulsesas short as 200 fs at 8.5 ,umby simply dephasing the RFfield by300relative to the electron bunchesin the accelerator stage. However,the second orderautocorrelation traces presentedin the publication [32] showa short 200 fs spike on topof a long - 1 Ps pulse. We believethat because of the natureof the autocorrelationmeasurements, a small noisesignal in the pulse trace canshow the same effect.Clearly,a time-resolved cross correlationexperiment (see section 4.10.2)should definitely providethe exact pulse duration.Since the electron bunches mustbe accelerated up to‘ 50 MeV, short pulse generation with free electron lasersis a very complicated, expensive,cumbersome process,andcannot used as a tabletop ultrashort infrared system.2.2.4 UltrashortMid-Infrared Pulse Generationwith NonlinearFrequencyMixingRecently, remarkable progresshas been made inthe generation andthe tunability ofultrafast mid-infrared pulsesby using nonlinear differencefrequency mixing [37]—[42].Chapter 2. Semiconductor Switching and Ultrashort LaserPulses 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, ifa 1.064tm pulse from an Nd:YAG laser and a 1.183 1umpulse 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 amplifyingpulses from a femtosecondlaser oscillator and using these pulses to generatea broadband continuum, a selectedfrequency range from the continuum spectrum isin turn mixed with the laser oscillatorfrequency to produce ultrashort mid-infraredpulses [42].Dahinten et al. [40] generated1 Ps mid-infrared pulses via difference frequencymixingof a mode locked Nd:glass laser 2 Ps pulsesat ). = 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.6sum) in AgGaS2 and GaSe crystals. Theresulting output covers a broadbandmid-infrared spectrum between 4mand 18 m with photon conversionefficiency ashigh as 2%. For wavelengths above 10m, GaSe is used as a mixing crystal.The peakenergy of the 1 Ps 10.6 m pulses is measuredto be of the order of a 0.2 iJ.Becker et al. [39] generated mid-infraredpulses by frequency mixing two colourfemtosecond mode locked Ti:sapphirelaser pulse in a AgGaS2 crystal.The Ti:sapphirepulses can be tuned from(760 nm to 790 nm) and (820 nm to865 nm) and the generatedinfrared pulses can be tuned between7 um to 12 m with a constant pulse durationof310 fs over the whole tuning range.The generated pulse duration is only limitedby the duration of the shortestof the seedpulses, and by group velocity dispersionin the nonlinear mixing crystals.On time scalesless than or equal to 1 picosecond,the pulse broadening effectis found to be directlyproportional to thickness of thenonlinear mixing crystal[38]. Seifert et al. [38] pointedout that frequency conversionin a AgGaS2crystal with laserpulse wavelengths below 1m restricts the duration ofthe mid-infrared pulse to thelower limit of approximatelyChapter 2. Semiconductor Switchingand Ultrashort Laser Pulses at 10.6tim 15300 fs. They attributed this lower limit to the groupvelocity dispersion of the laserpulses iii the nonlinear mixing crystal.They demonstrated that by mixing regenerativelyamplified Ti:Sapphire (740 nm to850 nm) pulses with 1timto 2.5timpulses generatedfrom an optical parametric generator/amplifiersystem, pulse durations of160 fs (50nJ, 1 kHz) are produced with wide tunabilityrange between 3.3timto 10tim [38].Iii view of the above progress on differencefrequency mixing, this methodis verypromising for the generation offemtosecond pulses at 10.6tim.However, in terms ofconversion efficiency, semiconductorswitching may have an advantageover nonlinearfrequency mixing. It should benoted that since the frequency mixingprocess is highlynonlinear, one requires high-powerinfrared pulses for the mixing process.2.3 Optical Semiconductor SwitchingApplication of optical semiconductorswitching technique for the purposeof generatingsubpicosecond 10.6timlaser pulses from a CO2 laser is discussedbelow.2.3.1 The SemiconductorSwitchOptical semicoilductor switchingof 10.6timCO2 laser radiation [43]—[60] offersan alternative and a much simpler methodfor the generation of ultrashortlaser pulses than thepreviously discussed methods.It is based on the principle of modulatingand enhancingthe reflection and transmission characteristicsof a semiconductor by opticallycontrollingthe free-carrier density. This techniqueis often used outside the infraredlaser cavity totemporally gate an ultrashortpulse from a long 10.6timpulse or a continuous beambysimply reflecting the infrared radiationfrom an optically injectedsemiconductor carriers. The process requires threesimple components: anultrafast visible laser pulse,aCO2 laser (pulsed or CW), and an optically-flatundoped semiconductorwafer that isChapter 2. Semiconductor Switching andUltrashort Laser Pulses at 10.6pm 16transparent to the 10.6 pm radiationor the infrared radiation to be switchedout. Pioneering experiments by Jamison and Nurmikko[45] and by Alcock et al. [47] haveshownthat photoinjection of a high carrier density(l0’) in semiconductors modifies thereflectivity of the material to 10.6pm. These experiments serveas the basis for opticalsemiconductor switching. Themethod has been demonstrated toprovide a very powerfuland currently the only sub-100 fs pulse generationmethod in the mid- and far-infraredpart of the spectrum [55]. Its low poweroperation makes it very attractivecompared tothe previous methods.The basic principle of optical semiconductorswitching technique isillustrated in figure2.2 and is described as follows:a semi-insulating semiconductoris transparent to mid(far)-infrared laser radiation inthe absence of free carriers. Semiconductorreflectivity toinfrared radiation is determinedby the number densityof free carriers (semiconductorplasma). The minimum electron-holedensity needed to achievea full reflection is knownas the critical carrier density,n, and it can be determined from the followingexpressionin c.g.s. units,4ire2(2.3)wherem*,w, Eb, and e are the effective carrier mass,the infrared radiation frequencyinvacuum, the static dielectric constantand the electron charge, respectively.For moderate photoinjection carrier density 1020such critical density correspondsto a plasmafrequency, w, in the mid- or far-infraredregions. It should be notedthat in deriving theabove expression for, theplasma absorption effectsare ignored.The critical densityat the CO2 laser wavelength iscalculated to bei0’ cm3.For a specific operating infraredwavelength,)jrone selects an appropriatedirect bandgap semiconductor whichis transparent to the infraredradiation. This requiresthatthe band gap energy of the semiconductorswitch, E9, be higher thanthe energy of theChapter 2. Semiconductor Switching andUltrashort Laser Pulses at10.6 m 17(b)TFigure 2.2: Typical schematicconfigurations of opticalsemiconductor switchingoperating in a (a) reflectionmode, (b) reflection-transmissionmode. I = infraredbeam (pulse),C = control pulse,S1 = reflection switch,S2 = transmission switch,R1 and R2 arethe infrared reflectedpulses, T1 is the transmittedinfrared beam(pulse) and T2 isthetransmitted pulse.CRIS(a)T2YS2CIRiSiT14Chapter 2. Semiconductor Switching andUltrashort Laser Pulses at 10.6 m18infrared photon (117 meV for aCO2 laser photons). In order to obtaill a high sigilalto background ratio, the CO2 laser radiationis polarized in the plane of incidence (Ppolarized) and the semiconductor waferis set at Brewster’s angle with respectto theinfrared radiation beam. With this opticalarrangement, the 10.6mlaser radiation istransmitted through the switch and noneof the radiation is reflected, thus reducingthebackground reflected signal to the zerolevel. This state is known as the off-stateof thesemiconductor switch. In order for theinfrared transparent switch tobecome reflectiveto the infrared radiation, one must increasethe free-carrier density in the switch. Thiscan be accomplished by illuminatingthe semiconductor switch with an intenseopticallaser pulse (control pulse) withphoton energy exceeding the forbiddenband gap energyof the semiconductor. The control pulseis used to photoexcite theelectrons from thevalence band to the conductionband of the semiconductor switchby means of interbandabsorption. These carriers are confinedin a thin layer of a thickness approximatelyequal to the absorption skin depthof the control pulse radiation. If alarge enoughcarrier density, > n, is generated,then the semiconductor’s surface appearsmetallic tothe infrared radiation and effectivelya very fast transient infrared reflecting“mirror” ismade at the semiconductor’s surface. Thatis, the photoexcited carrierscause a change inboth the refractive index andthe extinction coefficient, resultingin infrared beam (pulse)being reflected at Brewster’sangle with the same divergenceas the source infrared beam(pulse). The reflection efficiency ofthe infrared semiconductor switchat 10.6 im rangesbetween 40% to 80% depending onthe density of the photoexcited carriers.For subpicosecond infraredpulse generation, the turn-onspeed of the infraredreflectivity is determined bythe photoinjection carrier generationrate, which in turnisdetermined by the pulsewidth of the excitation controllaser pulse. liltrafast switchingcan be easily accomplishedby photoinjecting the carriers witha subpicosecond visibleChapter 2. Semiconductor Switching and Ultrashort LaserPulses at 10.6itm 19laser pulse. The infrared semiconductor switch remains reflectiveas 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 suchas recombination and diffusion. It is shownlater in this work that by proper choiceof the semiconductor material and the carrierdensity, the decay time of the reflectivity pulsecan by dramatically reduced to a sub-picosecond time scale. The ultrafast temporalvariation of the optical reflectivityandtransmission due to the semiconductorplasma can be used as a powerful diagnostic toolto probe the transient plasma dynamicson the picosecond or femtosecond timescale.Optical semiconductor switching has been widelyused as an active switching element,placed outside the laser cavity, to temporally gatethe already generated long pulses orCW far-infrared laser beams. Conventional modelocking, Q-switching of far-infraredlasers with electrooptic crystals isan extremely inefficient process; therefore,for fastoptical modulation at these wavelengths,optical semiconductor switchingprovides analternative. Ultrashort pulses at119 um using H2O [58] and CH3OH[52] lasers, andat 100-1000 um from a free electronlaser [56] have been producedwith this scheme;however, no attempt has beenmade to produce pulses in the far-infaredregion withpicosecond duration. Semiconductorswitching has been appliedto some novel cavitydumping techniques, where the semiconductorswitch is placed atBrewster’s angle insidethe laser cavity, of optically pumpedmolecular gas far-infrared laserssuch as: CH3OHat 119 um [59], NH3 at 90.8, 148,292 im and CH3F at 231 um and496iim [57]. Theadvantage of using semiconductorswitching is that output poweris increased since thecirculating pulse can be coupled outof the laser cavity very efficiently.An interesting and effective methodof producing ultrashortpulses is using a combination of two infrared semiconductorswitches in series[55] (as shown in figure 2.2(b)).The first one is usually a GaAs ora CdTe wafer operating in the reflectionmode toChapter 2. Semiconductor Switching andUltrashort Laser Pulses at 10.6 m20generate ultrafast risetime pulses, and thesecond switch is also set at Brewster’sangle;however, it is operating in a transmissionmode. Silicon is usually used as a transmissionswitch due to its large free-carrier absorptioncross-section and high reflectivityat 10.6im [55].The operation of the reflection-transmission combinationswitching method is as follows: the infrared reflected pulse,after being generated by the reflectionswitch, is directed onto the silicon transmission switch.Silicon transmits the infrared radiation; however, when it is irradiated with a delayedlaser pulse (relative to the reflectionswitch)above band gap radiation, it resultsin the production of free carriersin a layer 3im thick. Due to the induced infraredreflection and free-carrier/intervalericeband absorption, the transmission propertyof silicon to the 10.6 1um pulseis altered from fulltransmission to zero in a shorttime that is required to reachthe critical carrier densityand remains unrecovered for a longtime (a few nanoseconds).The duration of the infrared pulses is determined bythe time interval between theturn-on and turn-off times ofthe reflection and transmissionswitches, respectively. By properadjustment of the relative delay of the excitationcontrol pulses between the twoswitches, one can only allowthe fast rising edge of the infraredreflected pulse to pass throughthe transmission switch,thus, the transmitted infraredpulse width consists of the ultrafastrising edge from thereflection switch pulse and theultrafast falling edge from thetransmission switch. Figure2.2(b) illustrates a typical schematicsof the reflection-transmissionswitching operation.Rolland and Corkum[55] used amplified 70 fs (620 nm) pulsesfrom a colliding-pulsemodelocked dye laser to control theswitching operation. They demonstratedthis techniquefor the generation of CO2laser pulses at 9.5 im withduration as short as130 fs. Thesepulses correspond to only - 4 opticalcycles and are the shortest pulsesever generated atthe CO2 laser wavelength. Withthis method, it is possible toproduce infrared pulsesofChapter 2. Semiconductor Switchingand Ultrashort Laser Pulses at10.6 m 21durations shorter than the excitationcontrol pulse duration by simplyreducing the duration of the excitation control pulse.Recently, table-top high-power, sub-30fs pulses havebeen routinely produced in researchlaboratories; with the applicationof these pulses tosemiconductor switching,it is possible to reduce the infraredpulse duration even furtherto less than one infrared oscillationcycle of the CO2 laser. It seems thatthe limit of thegenerated pulse durationis mainly restricted by the risetimeof the control pulse duration required to produce the criticalplasma density in the transmissionswitch. Clearly,the drawback in using two semiconductorswitching elements comparedto one switchingelement lies in the factthat a high degree to synchronizationbetween the two switchesmust be maintained very accuratelyby the optical setup.It is extremely advantageousinterms of practicality andsimplicity to use a single opticalinfrared semiconductorswitchto generate subpicosecond10.6 im laser pulses. This alternativepossibility is part ofthis thesis investigation; therefore,in order to design such adevice more effectively,anunderstanding of the physical propertiesof the photoexcited carriersis essential.To sum up, the advantagesof using optical semiconductorswitching comparedtoother ultrashort pulse generationschemes are:1. To perform the infrared switching,the technique requiresoniy one ultrashort pulsewith a photon energygreater than the band gapenergy of the semiconductor.Thismakes it simple andinexpensive to implement;2. A high reflection efficiencyof 40% for a 1 ps pulseduration at 10.6 tmcan beobtained;3. An ultrahigh pulse contrast ratio(signal/background) ofthe order of iO:i (foronereflective switch) canbe achieved, and itcan be increased to106:1by using tworeflective switches inseries;Chapter 2. Semiconductor Switching andUltrashort Laser Pulses at 10.6 tm224. The duration of the generated infraredpulses are oniy limited by the source controlpulse duration and the type of the semiconductorswitching material;5. The power of the switched infrared pulses isonly limited by the input powerof thesource infrared laser;6. It offers the possibility of the generationof sub-30 fs infrared laser pulsesat 10.6,um, and at other infrared wavelengths;7. No critical phase/wavelength matching conditions,nonlinear crystal temperaturecontrol, and group velocity dispersionare required for the switchingprocess;8. It provides inherent synchronization betweenthe optical control pulse andthe reflected infrared pulse whichis very useful for pump-probe typeexperiments;9. It can be applied to infrared laser beamsor pulses of low power;10. The switched pulse durationcan by varied over a wide range;11. The repetition rate of the reflectedpulses is limited by the repetitionrate of thecontrol laser;12. A high optical-damage powerdensity of ‘s-’ 1 GW/cm2;13. The reflected and transmittedpulses basically map the temporalevolution of thesemiconductor plasma;therefore, the shapesof these pulses provide informationonthe carrier dynamics in the semiconductorswitch.A complete understanding ofthe processes involved inoptical semiconductorswitching requires the knowledgeof the semiconductor plasmaproperties, the behaviourof theoptically generated carriersunder ultrafast opticalexcitation, the dielectricfunction ofthe semiconductor, thepropagation of the infraredradiation in a semiconductorplasma,Chapter 2. Semiconductor Switching andUltrashort Laser Pulses at 10.6 m23and finally the absorption processes suchas free-carrier and intervalence band absorptionthat may limit (enhance) the speedof the reflection (transmission) switch.2.4 Ultrafast Optical ExcitationThe dynamics of ultrashort laser pulse interactionwith a semiconductor are very complex.In the following paragraphs we presentthe basic carrier dynamics anda sequence of thetime events in order to help inthe understanding of infrared switchingoperation. Acomprehensive reviewon the subject is presented in references[61]—[74].When a semiconductor is excitedby an ultrafast laser pulse whosephoton energy isabove the band gap energyof the semiconductor, then electrons(e) and holes (h) areplaced into energy states thatare defined by the band structureof the semiconductormaterial and the power spectrumof the absorbed light pulse.The free carriers can gainexcess kinetic energy fromthe difference between the excitationphoton energy and theband gap energy of the semiconductor.Ill ultrafast optical excitationof GaAs with a 616nm laser pulse, a narrowband of states can be excited creatingnonthermal free-carrierdistribution for a very shorttime which is comparable tothe excitation pulsewidth. Theelectrons are initially injectedto the I’ valley with excessenergies. The electronsareexcited with three distinctenergy values of:0.5 eV (from the heavy holeband), 0.43 eV(from the light hole band),and 0.15 eV (from the split-offband). Approximately84%of the electrons are injectedfrom the heavy/light holevalence bands with equalstrengthand the rest are injected fromthe split-off valence band.Optical excitation resultsinan instanteous productionof extremely hot nonequilibriumelectron and holedistributions. Carrier-carrier (e-e, andh-h) elastic collisions, dueto Coulomb forces, is the initialinternal relaxation processwhich the electrons and holesimmediately undertakeafterexcitation. These scatteringevents take placein a time scale of the orderof 10 fs,Chapter 2. Semiconductor Switching andUltrashort Laser Pulses at 10.6 um24Clearly, since the effective massof the electrons is smaller than that of the holes,theinitial temperature of the electronsis higher than the hole’s temperature.Energy canbe transferred from the hot electrons tothe relatively cold holes throughe-h scattering.The e-h collisions eventually drive theplasma towards a thermalized distribution(characterized by a common carriertemperature) within ‘-‘200 fs after excitation. The freecarriers are in thermal equilibriumamong each other but notat equilibrium with thelattice which is still at room temperature.Cooling of the hot carriers occursprimarilythrough inelastic collisions betweenthe hot carriers and phonons ona time scale of 2ps. The overall effect of relaxationis to reduce the carrier temperatureand increase thelattice temperature. Carrier recombinationtakes place ‘—‘ 100 PS laterafter excitation.2.4.1 The Dielectric FunctionThe electrical and optical characteristicsof a semiconductor areclosely related to thedielectric properties of the material;therefore, it is essentialto have an understanding of the dielectric function ofthe semiconductor switchso that one can predictitsswitching behaviour. Infraredreflection properties ofthe semiconductor switchcan becharactretized by a complexindex of refraction or in generalby the complex dielectricfunction, (w)=1(w)+i2(w), where and e2are the real and imaginaryparts of thefrequency-dependent dielectric function.In general,iand2can be obtained from quantum mechanical calculations[75]—[79], which require adetailed knowledge of thebandstructure, and free-carrierdistribution.A widely accepted model for thederivation of the dielectricfunction is basedonDrude treatment of a freeelectron-hole gas [80]. Thefree carriers are describedin termsof collective harmonic oscillationswith a single frequencysimilar to ionized carriersina gaseous plasma. In a semiconductor,when the optical frequencyof the radiation ismuch less than the interbandtransition frequency betweenthe valence and conductionChapter 2. Semiconductor Switching and UltrashortLaser Pulses at 10.6urn 25band, the Drude model provides an excellent descriptionof the dielectric function of theoptically excited carriers.A simple way of obtaining the dielectric functionis to consider an isotropic one-dimensional, non-interacting classicalfree electron gas of density, n.The long wavelengthdielectric response function, E(w), offree electron gas can be modeled microscopicallyinterms of the equation of motionof a free electron in a perturbing externalelectric field:d2 dm*+v_) 5r —eE.(2.4)Herei’is the collision frequency, whichdescribes the damping of the electronmotion dueto phonons, impurities, and carrier-carrierscattering, etc., and itis inversely related tothe momentum relaxation timeof the carriers; r is the spatial displacement;andm*isthe effective mass of the free carrier.By taking into account the polarizationdue to freecharges, P = —ne3r, the displacementvector D, and r fromthe solution to equation2.4, one obtains the Drude dielectric functiollof the form:/w2/f(w)=(1—--(1+i--1). (2.5)\w2\ JJHere, w is the plasma frequencyw= (47rne/€bm*)h/,andbis the background dielectric constant of the material. In arrivingat the above expression,a rapid thermalizationof the excess electron and holeenergies is assumed; therefore,the effective mass can beconsidered to be a time-independentquantity. Moreover, othermechanisms such as bandgap renormalization by hot carriers,semiconductor lattice heating,and intervaleilce bandabsorption are ignored.The temporal and spatial dependenceof the dielectric function canbe explicitly included through a timeand spatially varying electron-holeplasma density, n(z, t);hence,equation 2.5 can be generalizedto have the following form:= b(- ::t) (i+(2.6)Chapter 2. Semiconductor Switching and Ultrashort LaserPulses at 10.6 1um 26Here, n is defined by equation 2.3. Sincethe photoexcitation process of the e-h plasmaoccurs through the absorption of the above bandgap radiation by the semiconductorsurface, the amount of radiation penetrating thesurface decays exponentially with increasing depth through the bulk semiconductor.Consequently, the e-h plasma densityspatial profile follows the spatial profileof the absorbed radiation. One can writesuchprofile as:n(z, 0)=n0e_Sfz(2.7)where n0 is the density of the e-h plasmaat the surface immediately after excitation,and-y is the absorption length of the above band gap radiation.In writing equation 2.6 we have assumeda local response of the dielectric function;that is, the dielectric function at any pointz depends on the values of the fieldsat thatpoint. This is equivalent to assuming thatthe dielectric function fluctuations arelargecompared to the electron mean freepath.At high excitation levels, the plasma frequency,c, will exceed the infrared probefrequency, . In such a situation, the refractiveindex becomes imaginary, leadingtostrong reflection in the infrared range. Experimentally,Siegal et al. [81, 82] have shownthat under ultrafast high intensity laserexcitations, the dielectric functionof GaAs canbe described be equation 2.5up to an excitation energy fluence of1 kJ/m2.This energyfluence is the damage thresholdenergy fluellce of GaAs. Our experimentsare performedat much lower energy fluencesand hence Drude’s dielectric functionis an adequate description of the optical propertiesof the optical semiconductor switch.2.4.2 Free-Carrier andIntervalence Band AbsorptionsOptical excitation of asemiconductor switch induces achange in the imaginarypart ofthe dielectric function throughoptical intraband transitions.It is experimentally shownChapter 2, Semiconductor Switching and UltrashortLaser Pulses at 10.6 m 27in section 5.2 that absorption processes at 10.6minfluence the operating speed of thesemiconductor switch.Directly after electrons (holes) havebeen injected with an ultrashort laser pulse in theconduction (valence) band and once the thermalizationhas occurred, the carriers occupyenergy states in the conduction/valencebands up to an energy level determinedby theexcess laser photon energy. Consequently,two intraband infrared absorption processesoccur: free-carrier absorption andintervalence band absorption. Both absorptioncoefficients are proportional to the photoexcitedcarrier density and, therefore, mayeffect theswitching speed and efficiency at higherexcitation levels.Free-carrier absorption is a three-particleinteraction process. When the10.6 imradiation passes through the semiconductorplasma, an infrared photon canexcite a freecarrier to a virtual state in k-space,and since the absorption mechanismof the 10.6 imphotons requires the conservationof wavevectors, the electrons (holes)interact with thelattice through the emissionor absorption of phonons in orderto settle in a final statein the conduction (valence) band(similar to indirect absorptionin semiconductors).On the other hand, intervalence band absorptionoccurs between lightand heavy holevalence bands. Holes are excitedfrom the heavy hole band to thelight hole band by theabsorption of 10.6 im photons. Intervalenceband absorption has been shownto be lesseffective in comparisonto free-carrier absorption[83].Chapter 3Theory: Infrared Reflection froma Semiconductor Plasma3.1 IntroductionThe basic theoretical background for opticalsemiconductor switching and some numericalsimulations are presented in this chapter.The basis of the numerical modellinghas beenpresented in our previous publications[84, 85]. The general approach to ultrafast infraredoptical semiconductor switchingcan be divided into two problems. Oneis dealing with areflection of infrared radiation from a plasma,and the other is dealing with thetemporalbehaviour of the reflecting plasma afteroptical excitation. Combiningthese two effects,one should be able to obtain a complete descriptionof the physical situation. In thischapter, the general features of electromagneticwave propagation in a semiconductorplasma are reviewed. In orderto estimate the fastest process controllingthe infraredswitching speed, the physical processesgoverning the temporal decayof the opticallygenerated semiconductor plasma are discussed.The rest of the chapter is devotedto theanalyses of the numerical simulations.3.2 Propagation of an ObliquelyIncident Electromagnetic Wavein an Inhomogeneous DielectricMediumIn this section of the thesis the specificproblem of electromagnetic wavepropagationat an oblique angle in an inhomogeneousplasma is discussed.A theoretical discussionis given of the specific problemof the reflection of a probing10.6 um electromagnetic28Chapter 3. Theory: Infrared Reflection from a SemiconductorPlasma 29wave from a semiconductor plasma. In our situation,we are interested in the reflectionof 10.6timradiation from a thin plasma layer where the layerthickness is basically theabsorption length of the excitation visible radiation(‘-220 nm). The plasma thicknessismuch thinner than the infrared wavelength. Moreover, presenceof plasma spatial inhomogeneity requires a generalization of the standardtheory dealing with plasma reflection[86, 87, 88]. Therefore, our problem reduces to a reflection ofan electromagnetic wavefrom an iiihomogeneous medium whose dielectricfunction depends on position.The analysis is presented for both electric fieldpolarizations, S (where the electricfield is normal to the plane of incidence) andP (where the electric field is paralleltothe plane of incidence). Our method involvesderiving an expression for the electricandmagnetic field components. We willalso discuss the difficulties associated withobtainingan analytical solution for the P-polarized caseat the point where the dielectric functionvanishes.Here, we use the free electron gas modelto describe the optical response ofthe semiconductor plasma to the incidentradiation. This implies that we neglectthe contributionof free-carrier absorption, intervalence bandtransitions, and intraband transitions.Eventhough this model is simple and very crude,it can be used successfully to givea fairlygood description of the reflectivity at10.6tim.We start by considering Maxwell’s equationsfor electromagnetic waves in adielectricmedium in Gaussian units:47r 1ODVxH=—J+——— (3.1)VxE=—(3.2)V.B = 0(3.3)where H and E are the magneticand the electric field vectors, respectively,and D, J areChapter 3. Theory: Infrared Reflection from a SemiconductorPlasma 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;bis the background dielectric constant.By taking the curl of equation 3.2 and substitutingequation 3.1, we obtain the followingexpression:VxVxE=—--(J$)(3.4)It should be pointed out that in the followingderivations we make use of the fact thatthe time variation of the dielectric functionis negligible during the oscillation ofthe waveand hence may be regarded as being constant.Moreover, we also assumethat there is noabsorption of the radiation, such thatthe amplitudes of the electricand magnetic fieldsdo not change during the oscillationof the wave. In general, wecan assume that theform of D and J are harmonic functionsof 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 expressedas: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 expressionsfor 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 Reflectionfrom a Semiconductor Plasma31where we have defined the dielectricfunction as €(r)=— (i4iro(r)/w). Equation 3.10describes the electromagnetic waveelectric field components ina semiconductor plasmawhich has an effective dielectric functiondefined by (r) [86,89]. It should be notedthat in deriving equation 3.7 weassume that the local temporal variationof u(r) is slowcompared to the period of oscillationof the electric field.As it will be pointed out later in sections3.1.1 and 3.1.2, this differentialequationwill be solved exactly for theS-polarized electric field componentsfor a specific dielectricfunction profile. However, forthe P-polarized electromagneticwave case, this equationreduces to two coupled differentialequations [86]. An alternativeapproach to the Ppolarization case is to consider thedifferential equation for themagnetic field.Next, we need to derivethe differential equation thatdescribes the componentsofthe magnetic field propagatingin the plasma. From equations3.1, 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 writethe equation for themagnetic field as:V2B+——VE(r) x (V x B)+()2(r)B= 0 (3.13)The above equation describesthe magnetic field componentsstrength of the probingelectromagnetic wave[86, 89].3.2.1 The S-PolarizedElectric Field CaseWe proceed in this sectionwith the physics of propagationof S-polarized radiation(whenthe electric field of the waveis perpendicular to theplane of incidence) ina semiconductorChapter 3. Theory: Infrared Reflection from aSemiconductor Plasma 32plasma. The typical geometry of the problemis shown in figure 3.1, wherethe subscriptsi, r, and t denote incident, reflected, andtransmitted electric or magnetic fields,respectively. A uniform electromagneticplane wave is propagating in freespace along thepositive z direction. This wave hasa frequency and is incidenton a semiconductorplasma from the vacuum side at anarbitrary angle O with respect to thesurface normalof the semiconductor. As mentioned before,the solution to the reflected electricfield inthe S-polarized case can be obtained by solvingthe differential equation for the electricfield. In this case we treat the situation asa one dimensional problem and hencewe cantreat the dielectric function c(r) ashaving only a z component dependence.As shownin figure 3.1, let the plane of incidencebe defined by the xz plane, wherethe z axis isperpendicular to the faceof the semiconductor (and hence theplasma layer). The wavevector, k, then lies in the planeof incidence (xz) such thatk k(sin O, 0, cosO). Weare interested in the y-componentof the electric field. Hencewe can write this componentas [86]:=(3.14)With this choice of the planeof incidence, the y-componentof equation 3.10 can bewritten as [86]:8 ++ (W)2E=0.(3.15)By using equations 3.14 and 3.15we can derive the followingequation:82E(z)+k (E(z) — srn2 o) E(z)= 0 (3.16)which describes the electricfield component strength of interest.It should be pointedoutthat there is no general solutionto the above equationand each functional dependenceofE(z) requires a special approachto the specific problem[86], [89]—[94]. In order to solvethedifferential equation(3.16), one has to assume a formfor the dielectric function.Here, weChapter3.TheorY Infrared Re&cti0fl fromaSemiC0fldt0rplasma33yQ)E Zci4‘7‘—4Er Ei.4.4‘FFigure 3.1:AnicomiUgwave whose electricfield,E, isnormalto the plane of incidence(Spo1ariZat0Chapter 3. Theory: Infrared Reflection from a SemiconductorPlasma 34consider the exponentially decaying dielectric functionpresented in section 2.4.1, whichis expressed by the formula:(z) (1_fl+?))(3.17)and equation 3.16 can be written in theform:02E(z)+ (a - k(je)E(z) =0 (3.18)where a = k( — sin2 O). The simpletransformation of [91, 94]X =Ib‘(3.19)vn(1+)can be applied to equation 3.18. Thisreduces equation 3.18 to a familiarform:X28+ + (X2 -2)E(X)=0 (3.20)where we have defined = —i2\//’y.The above equation is the familiarBessel equation.J1(X) is the Bessel function of imaginaryorder i and complex argumentX. The generalsolution to this equation has theformE(x) =C1J_(X)+C2J(X). (3.21)By using the boundary condition(i.e. as z —*),only the transmitted wave existsinsidethe plasma, and we canconclude that C2=0 [91, 94].3.2.2 The P-Polarized Electric FieldCaseLet us consider the problem of thesolution to equation 3.13 with thesame form of thedielectric function (equation3.17). As shown in figure 3.2,in the case of a P-polarizedelectric field, we take the wave vectork to lie in the xz plane of incidenceand the electricfield components E = (Es, 0,Es); hence the magnetic field has only one componentinChapter 3. Theory: Infrared Reflection froma Semiconductor Plasma35the y-direction. The magnetic field can be writtenas B = (0, B, 0). With this choiceof the magnetic field, the differential equationcan be reduced to the form:O2B Ô2B 1 O(z)aB“j’ 2B —2 2 +( ) — (• )ôx az (z) öz 9zcIn order to further simplify the above equation,let us represent the incident wave tobea plane wave with its propagation vectorlying in the xz plane:Br,, = b(z)e’.(3.23)By substituting equation 3.23 into3.22, we get___-+ k ((z) - sin2 o) b(z)=0. (3.24)Equation 3.24 is knownas the Maxwell-Helmholtz waveequation [86, 89, 90,95J. Thecorresponding electric field componentscan be determined from Maxwell’srelationships:= ic(3.25)w(z) özand= —ic(3.26)w€z) axThis situation is different from theS-polarization case. In this problem,we need toconsider the dielectric functiongiven by equation3.17. Upoll examining thedifferential equation for the magneticfield, it is clear that the secondterm in equation3.24approaches infinity asthe dielectric function approacheszero.That is, the dielectric functionchanges sign as the plasmadensity exceeds the critical density. The dielectricfunction of the plasma approacheszero where equation3.24approaches a singularity.As a result, all of thefield components B,ET and E approach infinity as the pointof singularity is approached.Several authors havediscussedin great detail the exactnature of this type ofsingularity [86, 95,96]; they have shownChapter3. Theory: Infrared Reflection from aSemiconductor Plasma36yBLZC)Q)xBrB&kFigure 3.2:An incomingwave whose electricfield, E1,is parallelto the planeof incidence(P-polarization).Chapter 3. Theory: Infrared Reflection froma Semiconductor Plasma 37that in the neighbourhood of the near zero point ofthe dielectric function, the electricfield componentE approaches infinity as E(z)’ and the other componentE approachesinfinity logarithmically. For P-polarizedelectromagnetic waves, there exists a longitudinal component of the electric field alongthe density gradient. Under these conditions,this component of the electric field resonantly exciteshigh amplitude oscillations at thecritical density of the CO2 probe radiation withan oscillating frequency of w=,, wherew,, is the plasma frequency. These large amplitudeoscillations can influence the motionof the electrons and may result in anharmonicoscillations of the electron plasma.Thetransfer of electromagnetic toelectrostatic energy and its subsequentdissipation is knownas resonance absorption [89, 90,97]. The process is also responsible for higherharmonicgeneration from the probe frequency[98, 99].It should be pointed out thatif the angle of incidence O is setequal to zero, themagnetic field structures canbe described in the same manneras in the case fortheelectric fields in the S-polarizationsituation where no plasmaoscillations are excitedat the critical density. We madeseveral attempts to solve equation3.24 analytically;however, we were not successfulin deriving an analytical solution.To our kilowledge,when all the features are simultaneouslypresent (such as spatiallyand time varyingdielectric function and the introductionof free-carrier absorption), thegeneral problemhas no analytical solution. At best, onemay be able to obtain a numericalsolution to theproblem. An extensive bodyof literature has been devotedto the study of thisproblem[84]—[86],[95, 96].3.3 Numerical Approachto the Solution: P-PolarizationCaseAs we mentioned previously,an analytical solutioll ofequation 3.24 proved tobe impossible. The next step is toadopt a numerical methodfor the solution of the differentialChapter 3. Theory: Infrared Reflection from aSemiconductor Plasma38equation. There are several problemsassociated with any numerical techniquewhendealing with singularities of the differential equation.Obviously, numerical integrationnear the point where the dielectric function approacheszero leads to an abrupt growthof the electric fieldE. An infinitesimally small change around the singular pointcanresult numerically in an unphysical valuefor the electric field.Another difficulty is associated with thelack of proper boundary conditionsat thesurface of the semiconductor (atz=O). These boundary conditions for b(z= 0) and(öb(z)/öz)=o are required in order to initiate the numerical integrationprocedure forthe second order differential equationfor b(z). In fact, we are primarilysolving thedifferential equation in order toobtaill the boundary condition valuesat the vacuum-semiconductor interface. Theseproblems make our numerical approachmuch more involved than standard numericalsolutions.In order to remove the singularityfrom the differential equationfor the magneticfield, one has to evaluate the magnitudeof the imaginary part of the dielectricfunction.Effectively, the magnitude of thev/w term determines the rateat which the criticaldensity is approached. It is clear that ifthis ratio is>> 1, the large amplitude oscillationsdriven by the longitudinal componentof the electric field will be stronglydamped dueto absorption, and the numerical solutionto the differential equation doesnot resultin unphysical electric fields. However,in a plasma the damping is oftenvery smallsince the imaginary part of f(z)is small. One must bearin mind that given the reportedexperimental results onthe collision frequencyv,one has to consider amore realistic ratioin order to obtain physical solutions.In our numerical calculationswe takev/w=l02[85].A simple technique for obtaining a boundarycondition value is to examinethe differential equation far awayfrom the plasma and far intothe bulk of the semiconductor.This is similar to the methodused in reference [100]. Here, oneexpects the solution forChapter 3. Theory: Infrared Reflection from a SemiconductorPlasma 39the magnetic field to take the form of a simpleplane wave. Therefore, one is requiredto obtain a solution for b(z) at a distance wherez>> -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 solutionof the form of a simple plane wave[84]:b(z)Ae_j/_smn29i+p)(3.28)where A andp, are the amplitude and the phase of the magnetic field plane wave,respectively. Ideally, this solution is validas z —+ oo. In doing numerical calculationsthis limiting condition (z —+ oo) cannotbe satisfied; therefore, before performingthenumerical calculation one must examinethe range of z that can satisfythe conditionabove. We found that by using a valueof yz=l0, the difference betweenour calculationsand the ideal condition is onlyi0 which is adequate for our application.The simulations are performed with thefollowing parameters:1. The calculations do not take intoaccount the time evolution of thesemiconductorplasma density. This will be treatedlater on in section3.6.2. The excitation laser pulse wavelengthis 616 nm which corresponds toabsorptioncoefficients,-y, of 4.5x104cm1 [101, 102] for GaAs and 2.56x104cm’ for CdTe[102].3. The wavelength of the probe radiationis taken to be that of theCO2 laser operatingat 10.6 tim.4. The background dielectric constant.b,is taken to be 10.89 for GaAsand 7.29 forCdTe [103].Chapter 3. Theory: Infrared Reflection from aSemiconductor Plasma 405. The angle of incidence of the infrared radiationis set at Brewster’s angle for thebulk materials at 10.6 ,um(OB=72°and700for GaAs and CdTe, respectively).In general, the magnetic field is a complex function.We transformed equation 3.24intotwo coupled second-order differentialequations for the real and the imaginarypart ofb(z). Both equations are solved in parallelusing a modified fourth order Riinge-Kuttamethod. The details of the technique are outlinedin detail in references[84, 85, 104, 105].The numerical integration is performedin a reverse fashion where we have defineda finalinterval zj and performed the integrationbackward to the initial value atz=0 with anintegration step of —az. In trying tomanoeuver the integration nearthe points aroundthe critical density, the integration step sizeis reduced by a factor of 10in order to obtainhigher accuracy [106]; moreover, the valueof the calculated magnetic fieldis monitoredto check for signs of an abrupt growth.If this occurs, the integration stepis furtherreduced by a factor of 10 and thecalculations are repeated againaround the region nearthe critical density. It shouldbe pointed out that the exact valueof the electric fieldcomponentE cannot be obtained at the critical density, but onlyin the neighbourhoodnear the position of critical density.The calculations for the fields are performedat several initial plasma densitiesrangingfrom 10n, to zero [84]. The valuesof b(z), E2, and(z)E amplitudes are calculated asfunctions of normalized distance,= 7z, and the results forGaAs are presented infigure 3.3 for an initial plasmadensity equal to5nfor both of the real andimaginarycomponents. From figure3.3(a) and 3.3(c) as the criticaldensity is approached,themagnitudes of b(z) and€E vary smoothly. Forn/n=5, this critical density is reachedwhen =l.61. In thef(z)E case, both (z) and Ob(z)/öx approach the=1.61 point atthe same rate, and thus theirproduct has a finite value.It is interesting to notethat at(e)=,both of theEr and E curves resembleChapter 3. Theory: Infrared Reflectionfrom a Semiconductor Plasma41Figure 3.3: 10.6 um laserradiation magneticand electric fieldamplitude componentsB (curve a),E (curve b), and (curve c)as a function ofç = z in GaAs. Theinitial carrier density isn= 5n.Solid curves representthe real parts anddashed curvesrepresent the imaginaryparts.>%xN1-30.20-015-0.501.40.6-0.2—IllIIIw-—-,:s”(c):I I II0 1 2345Chapter 3. Theory: Infrared Reflectionfrom a Semiconductor Plasma42step discontinuities reminiscent ofa phase transition as the GaAs changes from beingasemiconductor to a “metal” forthe 10.6 4um radiation.Once the values of the electromagneticfield amplitudes are obtained as functionsof the initial plasma densities, one needsto calculate the reflectivity of10.6 ,um radiation from the plasma layer. The tangentialcomponent of the electric fieldand theperpendicular component of the displacementfield have to be continuous acrossthevacuum-semiconductor plasma interface.The reflectivity can be obtainedby matchingthe tangential electric field component,E, and the displacement field,cE, at =0.Hence we obtain the following relationfor the amplitude reflectivity[107]:E sin 00 + 5E cos 00=(3.29)sin 0— cos 00where c is the dielectric function atthe surface of the semiconductorevaluated at =0.The intensity reflectivity, R, and its correspondingphase, 4, are calculatedfrom thefollowing relationsR=r2= tan’ (?T:)(3.30)where Re(r) and Im(r) are thereal and the imaginary parts of theamplitude reflectivity,r, respectively.Figure 3.4 shows the resultsof such calculations of the intensityreflectivity for GaAsand CdTe as a function of initialnormalized plasma density(n/ne). Both curves showoverall similar behaviour. In thedensity range0n/n 0.9 the intensity reflectivityis calculated to be 0.7%; however,in the density range at near thecritical density, theintensity reflectivity canbe as high as 100%. It shouldbe noted that figure 3.4showsthe intensity reflectivity maximumvalue to be only40%. More elaborate calculationsnear the critical density showthat in fact this valueis ‘—‘ 100%. Of importanceto theultrafast reflection switch schemeis the sharp resonance-likepeak occurring atn/n=1.Chapter 3. Theory: Infrared Reflection froma Semiconductor Plasma 431Q02_______I0.80.01-0.60.00-_______,“ (b)012345n/ncFigure 3.4: Brewsterangle reflectivityfor 10.6 im laserradiation asfunction ofanexponentially decayingplasma densityprofile of (a) GaAsand (b) CdTe.The insetfigure shows anenlarged plotof the reflectivityfor 0 ri/ne 1.0.Chapter 3. Theory: Infrared Reflection from aSemiconductor Plasma 44For a small change in the plasma densityfrom (n/ne) to 0.9(ri/ne), the reflectivitydrops to approximately zero. The magnitudeof the reflectivity peak is determined bythe magnitude of the complex part ofthe dielectric function. When the plasma density,ri/n 1.2, the intensity reflectivity increases monotonically with increasingdensity toa maximum value of 100%. The higher reflectivityfrom CdTe semiconductor plasmacompared to the one from GaAs isdue to the reflection from a thicker plasmalayer.This is to be expected since the wavelengthof the infrared radiation (10.6 tim) ismuchlonger than the plasma layer thicknessand one expects the infrared radiationto penetratethrough the plasma layer.Figure 3.5 shows the phase angle changeof the reflectivity as a functionof the normalized plasma density. The curve showsthat at the critical density thereflectivity suffers aphase change of ir. This curvehas proven to be very useful ininterpreting the temporalshape of the reflectivity pulses.With our complicated numericalsimulations, it not clear how to explainthe structuresobserved in figures 3.3and 3.4, and one has to resort toa much simpler analyticalmodelin order to confirm that the peakin the reflectivity is not just an artifactof the numericalprocedure.3.4 Reflection of 10.6tImRadiation from a Thin FilmPlasmaIn this section we discuss a muchsimpler model which describesthe reflection of10.6ttmradiation from a thin plasma layer.The analyses are basedon the Fresnel equationforP-polarized electromagneticradiation [108]. The plasmalayer is assumed to be isotropic,homogeneous, and lossless.We consider the reflectionsfrom two semi-infinite plane-parallelregions: one containsthe semiconductor plasmaand the second involvesthe bulk semiconductormaterial.Chapter3. Theory: InfraredReflection froma SemiconductorPlasma45rJ)Figure 3.5:Phase anglechangeas a functionof plasma density.The solidlines arecalculatedfrom thedifferentialequationmodel. Dashedlines arecalculatedfrom thethin film plasmamodel.90450-45-90-EEE—01Iii1111123456fl/fl78910Chapter 3. Theory: Infrared Reflection froma Semiconductor Plasma46Since we know that the plasma initial spatialdistribution is most likely to haveanexponential profile, we can consider theplasma film thickness, 6, to be equalto the absorption length of the visible radiation,-y’. In this thin film layer, the plasma densityis assumed to be constant throughout the entirefilm thickness. The second filmlayercontains the bulk semiconductor materialand extends to infinity. We alsoassume thatthe boundary between the two films issharp. The geometry of the problemis shown infigure 3.6. With the above assumptionsin mind, the dielectric function of theswitch canbe written as [85]:Icb(1)(z) =if z>6.In order to obtain an expression forthe reflectivity at each interface, wehave to utilizethe usual boundary conditionsderived from Maxwell’sequations, that the tangential,Es,, and the normal,E(z)E, components are continuous through the vacuum-plasmathin film and through the plasmathin film-bulk semiconductorinterfaces [107]—[109].Asillustrated in figure 3.6, the 10.6m radiation is incident onthe vacuum-plasmathinfilm interface at an angle00, and is transmitted through the interface atan angleOirelative to the normal to the surface.By matching the boundary conditions,we obtainthe following expressionsfor the amplitude reflectivity atthe first interfacecos 0 —\/Eb(1 — ri/ne) cos 00r12 =___________. (3.31)cos0 + b(1 — n/ne) C05For the second interface, the radiationis transmitted at an angle02 into the semiconductor bulk. By matching the boundaryconditions at the second interface,we obtain thefollowing expression for theamplitude reflectivity[84]:— /(1—n/n)cos02—ftcos0i—, (3.32)— n/ne) cos02+ Jcos0iChapter 3. Theory: Infrared Reflectionfrom a Semiconductor Plasma47where we have used the fact that the refractiveindex of vacuum is equal to unity.Under an incident angle equal to Brewster’sangle, we have the conditions thatsin 0 =+tb),and cos00 l//l+ bat the surface. Also, by usingSnell’s law,siriO0= /eb(l — ri/n)sinOi = /sin02, (3.33)we obtain the following relation forcos 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 amplitudereflectivity,r23 = —r12.(3.37)Multiple reflections and illterferencesbetween the two interfaceshave to be taken intoaccount in the calculationsfor an effective amplitude reflectivity,r. Let us denote theincident electric fieldon the vacuum-plasma interfaceand the reflected electric fieldbyE andEr, respectively. Let the reflection amplitudes be defiledin terms of the directionof propagation of the incidentelectric field as definedin figure 3.7. That is, we usethesubscript notation of+(refers to the left of the interface)and — (refers to theright of theinterface). The other subscriptnotation, 1 and 2, denotethe first and secondinterfaces,respectively. We candefine [110]= —rl_ = r12,(3.38)Chapter 3. Theory:Infrared Reflection from aSemiconductor Plasma48—1PlasmaBulk Semiconductor7Figure 3.6: Geometryof the vacuum-plasma-semiconductorinterfaces forthe thin filmplasma model.Chapter 3. Theory: Infrared Reflection from aSemiconductor Plasma 49r2+= —r2_ = r23,(3.39)— =t1_+r = 1.(3.40)Here, the first subscript denoted the interface.Then the amplitude reflectivitydueto multiple reflections from both surface can bewritten 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 propagationthrough the plasma film, is givenby: 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 dueto the propagation through the plasmalayer. Here,k is the wave vector in vacuum. Summing up the infinite seriesfor r and using equations3.37-3.40, we arrive with the followillgrelation for the effectiveamplitude reflectivity[108, 110, 111]—2i/3r12 r23e3.431+1223We have calculated the above equationfor various initial plasma densitiesin the range0 n/nc 10 for the GaAs switch. The result of the intensity reflectivityfrom the plasmathin film model is presented infigure 3.8(a) for the density range0 n/ne 2.5 and iscompared to the previous reflectivitycalculations from solving theMaxwell-Helmholtzequation (figure 3.8(b)).It is clear that there is very goodagreement between the twocurves and the reflectivity peakat fl/flc=1 is not an artifact of ournumerical integration.The result for the calculated reflectivityphase shift is shown in figure3.5; they also showa fair agreement withmore elaborate calculations.Since both systems show the samerelative reflectivity variations,indicating (a) if wehave a better understandingof the functional dependenceof R(n) for the plasma thinfilm,Chapter 3. Theory:Infrared Reflection from aSemiconductor Plasma50r+rtI÷tEr1r1_r2+t1_ t2+r2t+ -E2Et2+l_ 1+ t+ \rEti+E.+Figure 3.7: Geometryof multiple reflectionsfrom vacuum-plasmaand plasma- semiconductor interfaces.Chapter 3. Theory: Infrared Reflection from aSemiconductor Plasma 51we should be able to explain the resultsfrom our complicated numerical simulations,and(b) that the reflectivity variation dependspredominately on the surface plasmadensityrather than the function n(z) in thebulk of the semiconductor[84, 85].The calculation also indicates thata better modelling of the thinfilm plasma, forexample, dividing the plasma layerinto smaller multilayers and calculatingthe reflectivity of each one, adding them withthe proper phase shift, should providea betterapproximation of the physicalsituation [111].It is simple to explain the featuresin figure 3.8 for the plasma thinfilm model [84].The electron density increases from zero,the reflectivity R, reaches asmall maximumvalue of ‘P’.’ 0.5% at a plasma densitynear (n/us)= (eb—l)/(eb+1) (labelled (I) in infigure 3.8(a)). At this value ofthe density, the intensity reflectivityfrom the first interfacer12 2 is minimum. At(n/ne)= (b — 1)/cbthe refractive index, /f(z= 0) is unity andthe vacuum-plasma interface disappears.Hence, the plasma layer is illuminateddirectlyat the Brewster angle, and asa result the reflectivity here is zero.This explains the firstminimum in the reflectivity curve(labelled (II) in figure3.8(a)) After passing throughthe point of frustrated internal reflectionat(n/ne) = cb/(Eb +1) complete reflectivityisreached once(n/ne) 1 (labelled (III) in figure 3.8(a)). Thisis the region where thereflectivity shows a resonance-likepeak. As the plasma densityincreases,(n/ne)> 1, theamplitude reflectivities, r12and r23, are both complexin 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]2b[(fl/fl)—1]—(n/ne)Then the intensity reflectivitycan be expressed as:(l_a)2R1— 2acos2+a2(3.46)Chapter3. Theory:Infrared Reflectionfrom a SemiconductorPlasma520.8>>06.4=C-)00rr0.202 2.5n/ncFigure 3.8:Brewsterangle reflectivityfor C02-laserradiation asa functionof free carriersurface densityof GaAs for(a) a uniformfilm thickness‘y’’and (b)for an exponentiallydecaying densityprofile.The insetfigure showsan enlargedplot of thereflectivityfor0< n/ne1.0 0.5 11.5Chapter 3. Theory: Infrared Reflectionfrom a Semiconductor Plasma53Here, a = exp(2i/3) is a real function whichrapidly decreases with increasing(n/ne).Now, as increases its value fromzero 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 managedto understand the structures involvedin the reflectivity curve. It also showsthat the intensity reflectivityis a function of thephase shift, (F, suffered by the incident radiationand the thickness of the plasma layer.3.5 Temporal Variations of thePlasma DensityThe temporal variation of the plasmadensity can manifest itself inthe temporal behaviour of infrared reflectivity throughthe time evolution of the dielectricfunction.In this section we briefly review ofthe processes that are responsiblefor the decay ofthe plasma density. Investigation ofthe recombination and diffusionprocesses allows us toselectively assess the relativeimportance of the mechanismsdetermining the e-h plasmadecay. Ultimately, we are interestedin an ultrafast plasma decayprocess occurring onthe subpicosecond time scale.3.5.1 Electron-Hole PlasmaRecombinationWhen a semiconductor equilibriumstate is perturbed by anoptical excitation pulse,thebalance of the equilibrium carriersis disturbed. If the excitationpulse is removed,theexcess photogenerated carrierswill return to the equilibriumstate through recombinations.Excess electrons andholes can recombine with eachother through severalrecombination mechanisms: radiative,Auger, multiphonon recombination,capture at impuritysites (which can be eitherradiative or nonradiative process),and surface recombinationChapter 3. Theory: Infrared Reflection from aSemiconductor Plasma 54[112]. These processes determine the lifetimeof optically generated excess carriers.Ingeneral, the selection of the recombinationprocess depends on several factors,such as thee-h plasma density, carrier temperature, band structureof the semiconductor material,lattice temperature, impurityconcentration, and the semiconductor surfacecondition.The fundamental theoretical and experimentalaspects of recombination processesarediscussed in great detail in references [112]—[117].Two-body recombination is a radiativerecombination process. In directgap semiconductors, an electron in the conductionband can recombine with a holein the valenceband, resulting in an emission ofa photon [118]. The decay rate ofthe plasma dependson the densities of electrons and holesaccording to the following relation[119]9n(t)= —B0n2(3.47)where B0 is the two-body recombinationcoefficient. For GaAs the two-bodyrecombination coefficient for optically injectedcarriers is measured to be(3.40±1.17)x10”cm3s [101]. Clearly, two-body recombinationremains insignificant even atthe highestcarrier density obtained in ourexperiments.The Auger recombination processis usually the most dominantrecombination processin intrinsic bulk semiconductorsat high carrier concentrationsand high carrier temperatures. It is a three-carrier processwhere a conduction bandelectron and a hole in thevalence band recombine, andthe associated excess recombinationenergy is transferredto a third carrier as kinetic energy.This energy is then thermalizedwith the rest of thecarriers. The presence of a thirdcarrier is necessary in order toconserve energy andmomentum. It should be pointed outthat the Auger recombination processdoes not changethe total energy of the plasmae-h distribution; however, sincethe number of carriershasdecreased, the total energy of thecarriers is divided amongfewer carriers. This resultsina significant increase in the individualcarrier’s temperature anda decrease in the carrierChapter 3. Theory: Infrared Reflection from a SemiconductorPlasma 55density.Since Auger recombination is a three-bodyinteraction, its recombination rate isstrongly dependent on the plasma density. Therecombination rate increases with thethird power of the injected carrier density. Thedecay rate of the plasma density due toAuger recombination can be written as:= Ta (3.48)whereFais the Auger coefficient.Theoretical calculations and experimentalmeasurements of Auger coefficienthavebeen made for a GaAs [101, 120, 121].Mclean et al. [101] have investigatedthe Augerrecombination rate in optically excitedcarriers, and they measuredan Auger coefficientof (7±4) x10—31cm6/s. Evidently, the Auger recombinationdecay rate is a slow processcompared to the time scale of interest.In the case of a semiconductor sample offinite size, surface recombinationcan influence the temporal behaviour ofthe plasma density through the introductionof surfacestates. These states basicallyare discrete energy levels in the forbiddenenergy gap introduced by the discontinuity inthe lattice. Since the photoinjectedplasma is generatednear the surface, where these levels exist,the surface states can act as recombinationcentres. The surface recombination velocityis determined by the surface conditions[122].The rate of surface recombination is differentfrom that of the bulk andis defined by asurface recombination velocity,S, asS =(3.49)where,0ecis the carrier capturecross section(‘—‘10—15 cm2),vh is the free carrierthermal velocity(‘—iiO cm/s), andNstr is the surface trap density(1014cm2). Therecombination time due to surfacestates is of the order of ‘—i 20ns.Chapter 3. Theory: Infrared Reflection froma Semiconductor Plasma56Multiphonon recombinationis a recombination process by whichan electron and ahole recombine with a cascade emissionof several phonons in place ofa photon. Thismechanism is very inefficient consideringthe large number of phonoiisrequired to makeup the energy of a single photon[123].By examining the above recombinationrates, it is evident that their contributiontothe reflectivity occurs in time scaleslonger than 500 Ps (forn6n). Therefore, onehas to search for an alternative ultrafastcarrier density decay mechanism.3.5.2 Diffusion and Time-DependentDensity Profile of the FreeCarriersDiffusion of free carriers can resultin a dramatic decreasein the plasma density. Here,we will examine the timeevolution of the carrier densityon a subpicosecond time scale.Directly after optical excitation,high density nonequilibrium electronsand holes arephotogenerated in the semiconductorswitch. The behaviour ofthe plasma depends primarily upon the processes ofdiffusion and surface recombination.The spatial distribution of the optically generated plasmathrough the semiconductorwill be inhomogeneous,thus the temporal dependenceof the carrier diffusion shouldbe considered as a factorinreducing the e-h plasma density.Diffusion is characterizedin terms of a diffusion coefficient,D, which describes thenumber of free carriers passingthrough a unit area perunit time in the density gradient.In the case of a laser producede-h plasma, the diffusionof both carriers is describedby an ambipolar diffusion coefficient.Because any separationof charge would createan electric field between theelectrons and holes,the two carriers mustdiffuse at thesame rate. It is often difficultto experimentallyisolate the effects ofdiffusion on theplasma density. To our knowledge,there is no experiment designedto directly measurethe diffusion coefficient ofnonequilibrium semiconductorplasma for time scaleless than500 fs. Hence, one has torely on model calculationsfor D. We will assumethat theChapter 3. Theory: Infrared Reflection from a SemiconductorPlasma 57electrons and holes are in thermal equilibrium withthe lattice. The plasma, althoughinhomogeneous in its spatial distribution,is assumed to have a uniform temperature.Acrude approximation to our problem is to considera nondegenerate plasma distributionwhere the diffusion coefficient is definedbyD= (D€+Dh)(3.50)whereDe and Dh are the diffusion coefficients for electrons and holes, respectively.Amore general scenario would beto include the density and temperaturedependence of thediffusion coefficient. The carrier’s diffusioncoefficient is known to increasewith the carriertemperature and decrease withlattice temperature; moreover,the diffusion coefficient isalso shown to have a strong dependenceon the carrier density above.1019cm3 wherecarrier degeneracy is reached.Several authors have consideredthis dependence to explainthe observed experimental results[124]—[130]. The dependence ofD on density can becalculated using the Boltzmann transporttheory in the relaxation timeapproximation[126]. A rigorous analysis of the diffusioncoefficient has been performedby Young andvan Driel [124] where they haveincluded many-body effects inthe plasma. Here, we usedthe ambipolar diffusion coefficientvalue of 20 cm2/s [131,132].The temporal and spatial distributionsof the plasma density in a semiconductorswitch are described by thediffusion equation in one dimensionalform:an(z,t)= D,t)+G(z,t). (3.51)Here, z is the spatial coordinateperpendicular to the semiconductorswitch surface,n(z, t) is the number of photogeneratedelectron-hole pairs, andterm G(z, t) is the generation rate of the plasma. Noprovision was made for theradial plasma concentrationdependence introducedby the gaussian beam profile.This is justified by the valueof theeffective diffusion length,LD, relative to the beam size, given the timescale of interest.Chapter 3. Theory: Infrared Reflection from aSemiconductor Plasma58Equation 3.50 is an approximation of thesituation where the diffusion coefficient dependson the density, temperature of the plasma, andthe position. In our experiment, weareinterested in a plasma density around1 x1019cm3 before the onset of the plasmadegeneracy [130], thus, we are justifiedin 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 oftheplasma is considered to be a delta functionexcitation in time; therefore, wecan ignorethe generatioll term. This is justified becausethe duration of the actual excitationpulseis much shorter than the characteristictimes of the physical processeswhich occur afterthe plasma is generated. We can writethe initial condition for the aboveequation asn(z,0) =n0e2.(3.52)Equation 3.51 will be solved subjectto a boulldary conditionat the surface of the semiconductor, which can mathematicallybe represented by setting thecarrier flux at thesurface equal to the rate of surfacerecombination:(anzt)= n(0,t),(3.53)where S is the density independentsurface recombination velocity.With the aboveconditions, this linear partialdifferential diffusion equationcan be solved analytically,and we obtain the following solution—OIy(yDt-z)(27Dt — zn(z,t) — — e erfc21+7)t+ZeY(YDt+z)erfc(2-yDt+ z7Dt—z\. 2/— 2S__eSt+Derfc (2St+zj(354-yD-S2/)JChapter 3. Theory: Infrared Reflection from a SemiconductorPlasma 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 xio cm1,an ambipolar diffusion coefficient D=20 cm2/s and a surface recombinationvelocity S=lx iO cm/s [131,132], wecalculated the temporal evolution ofthe plasma density n(z. t). The calculationsareperformed in 500 fs time steps.The result in figure 3.9 displays the normalizeddensityof the plasma with respect to the normalizedpenetration depthe=7zat various timesafter delta function excitation pulse. Figure3.9 indicates that (n/n0)has decreased from1 to 0.85 within the first 500 fs. This ultrafastinitial decay will be the subject offurtherstudy later in this chapter. As time evolves,the density decay rate is much slowerand thedensity profile is no longer an exponentiallydecreasing function with respectto depth,but more likely to resemblea gaussian profile. At longer times(80 ps), the plasmacontinues to diffuse until it is nearlyuniform across the depth of thesemiconductor.By then one has to include the effectsof the recombination processes.We have foundthat the result in figure 3.9 is fairly insensitiveto the actual value of S indicatingthatthe initial variation of n0 is limitedby ambipolar diffusion from thesurface and into thebulk.3.6 Simulation ofthe Reflectivity Pulses fromGaAsIn the previous sections we haveperformed time-independentcalculations for the reflectivity as a functionof the initial excitationplasma density. in general, ifwe combinethose calculations with a processwhich describes thetime evolution of the plasmadensity,we should have a better understandingof the temporal responseof the semiconductorswitch. From the datadisplayed in figures 3.4,3.8 and 3.9, it is easy tosee how theinfrared reflectivity changesas a function of timeafter a flash (100 fs) illuminationwithChapter 3. Theory:Infrared Reflectionfrom aSemiconductor Plasma600C1. 0.40.6 0.8Figure 3.9: Thevariation dueto diffu0of carrierdensity,n(z, t)/n0 asa functionoflongitudinal positionand time.The curvesare plottedinincreasing timesteps of500 fs.The top curveiscalculated at t=0 Ps, andthebotttom curveis calculatedat t= 4.5Ps.01Chapter 3. Theory: Infrared Reflectionfrom a Semiconductor Plasma61above band gap radiation.For the proposed reflection switchscheme it is necessary totailor the exciting laser pulse intensity sothat the critical density is produced.This mayinvolve intensity discrimination techniquesdepending on the laser systemused. The surface density then has only to decreaseto reach(n/ne)=(ci, — 1)/ci, 0.9 in order forthe reflectivity to decrease to zero.In order to gain an insight intothe pulse shapes and durations, wecompare our calculations to the calculations performedwith the simpler plasma thinfilm model. We cantreat the time dependent dielectricfunction as [85]Icb(1) ifz<(t)c(z,t) =if z>5(t)where 5(t) is the thicknessof the plasma film at timet, and (t = 0)=z’y’. Since thismodel avoids the problems resultingfrom the singularity of c(z, t) weare able to calculatethe reflectivity at the criticaldensity. The change in the infraredreflectivity is related tothe changes in the excess-carrierdensity, and the generationof ultrashort pulses makesuse of the initial rapid decayof the electron density. Wecan account for the rapid dropin the reflectivity by usinga simple physical argument[85]. The reflectivity of theswitchis‘-100% whenever(n/n)=1, and the plasma generated by thefemtosecond visibleexcitation pulse is containedin a thin layer of thickness ofthe order of the absorptionlength of the radiation,y’=2.22x10 cm. Assumethat the photogenerateciplasma isuniform in the transversedirection, and suppose thatthe transverse crosssectional areaof the plasma is A, and thatthe total number of electronsgenerated at t=0 isN. Thenthe plasma density is givenby the simple relation:(t=O)= A7-’(3.55)Next, the plasma diffusesinto the bulk with adiffusion coefficient D=20 cm2/s, suchChapter 3. Theory: Infrared Reflection from a SemiconductorPlasma 62that in 500 fs the effective diffusion lengthLD=3.162 x106 cm. Effectively, all theelectrons move into the bulk of the semiconductorby LD. The electrons at the edgeof the plasma thin film will diffuse byLD and the effective plasma thickness becomes(7’+LD). Note that there is no generation of new electrons after the opticalexcitationis over, and we still have the N electronsin the same effective cross sectional areaA(here we have ignored the transversediffusion of the carriers since the excitationlaserspot size on the semiconductor surface is muchlarger thanLD). 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(357fl(t=50018)1+ 7LDThis ratio is 0.875. That is, the densityt=has decreased by i--’ 12% in only500fs. As previously mentioned, thereflectivity (see figure3.8) around the peak drops from100% to almost zero when the plasma densityin reduced from n =nby only 10% andthis could happen in about 500fs; therefore, it should be possibleto generate ultrashortpulses if the semiconductor is excitedto generate plasma density near the criticaldensity.The temporal behaviour ofthe semiconductor plasma is verycomplicated. Withthe density profiles of equation3.54, the differential equation3.24 becomes even morecumbersome to solve numerically.We have performed the calculation usingthe MaxwellHelmholtz differential equation witha time dependent dielectric function(z, t).With the plasma density profilesgiven by equation 3.54, thecalculations are repeated for b(x, z, t),E(x, z, t), E(x, z, t) and R(n, t) using a fourth-orderRunge-Kuttamethod. The b(x, z, t) fieldamplitude is assumed not to changerapidly during one oscillation period of the electromagneticwave. The computer code wasmodified to includeChapter 3. Theory: Infrared Reflection froma Semiconductor Plasma63the temporal dependence of the plasma density;hence, we were able to calculate thereflectivity R(t) as a function of timefor each plasma density profile. Thatis, for each timeinterval the plasma density profiletakes a different gaussian shape andthe differentialequation is solved for that specificform.Here, we performed the calculationsusing GaAs as the semiconductorwith sometypical values D= 20 cm2/s,S= iO cm/s and the rest of the parametersare the same asthe ones used for the time independentcalculations [85]. The reflected infraredpulses areshown in figures 3.10 to 3.11for some representative values of theinitial plasma densityprofile. These values are chosen tocover a wide span of the reflectivitycurve in figures3.10 and 3.11. The regions betweenthe solid lines in the figures indicatethe times wherethe electron density in the differentialequation approaches thecritical density. Thereflectivity is calculated ina small region around the singularpoint.For (n/n)= 1.2, the FWHM is200 fs and the reflected pulse increasesslowly toreach a maximum value of 0.96 andthen decreases slowlyto zero in about 1 ps. As thesingular point is approached,the reflectivity approachesunity, and because the changeinthe plasma density with timeis slow, the dielectric functionremains approximatelyzerofor that period of time. Later,the reflectivity decays backto zero. The fast rise and falltimes of the reflected signals indicatethat the semiconductor switchcan remain reflectivewith R 1 in the region where(z, t) approaches zero, thus, resulting in reflectedpulsesof near rectangular pulseshapes. The initial part(100 fs) of the reflected pulseisapproximately zero; as a result,during the pumping bythe visible wavelength controlpulse, none of the 10.6 um radiationis reflected. At(n/n)= 1.3, the calculated FWHMis 350 fs. By adjusting theexcitation laser fluence sothat the initial plasma densityis0.9n, longer pulses in the picosecond rangecan be obtained. Forexample, whenthe initial densitiesare0.74n and 0.9n, the reflected pulse widthsare 60 and 65 ps,respectively. These pulseintensities are two ordersof magnitude lowerthan the onesChapter 3.Theory: InfraredReflection froma Semiconductor Plasma640.02 -________(a)0.01 -000-10150310-20 2505200—o 150 300Time (psec)Figure 3.10:Reflected10.6 m pulsesas a functionof time forinitial plasmadensity of(a) n =0.7n, (b) n= O.9n, and (c) n= 6n. The solid lines are calculatedfrom thedifferential equationmodel andthe dashedlines are calculatedfrom the thin filmplasmamodel.Chapter3. Theory: InfraredReflection from aSemiconductor Plasma65_0 0.5 1± 0.50 1.252.5Time (psec)Figure 3.11: Reflected10.6 ,um pulses as a functionof time for initial plasma densityof (a) r.1.2n and (b) ii = 1.3ri. The solid lines are calculatedfrom the differentialequation model and the dashed linesare calculated from thethin film plasma model.Chapter 3. Theory: Infrared Reflectionfrom a Semiconductor Plasma66calculated near the critical density.We have also calculated the phaseshift experienced by the reflected infraredpulsesfor (n/n)= 0.74, 0.9, 1.2, 1.3, and6. The results are presented iii figures3.12 to 3.14.The dashed lines in in figure 3.13 curvesillustrate the points wherethe plasma densityhas reached the critical density,and one has to extrapolate aroundthem. By examiningfigure 3.13, we realize that thereflected pulses suffer a phase changeof ‘-.‘ir at the timeof the peak of the reflection.For comparison, we have also performedthe calculations for thethin film plasmamodel using rectangular variationsof the plasma density with depth.As time progresses,the thin film plasma is expanding intothe bulk; and to incorporate thetime dependencein this film model, we calculatethe 1/e point of the density profileat the surface givenby equation 3.54 and we notethe corresponding time. Theseare used to simulate theexpanding step-like film illustratedin figure 3.15. The resultsare displayed in figure3.16(a). The figure shows that afterthe first ‘ 20 ps the plasmafilm thickness remainsalmost constant. From that,we calculated the correspondingeffective thickness of thefilm, (t), as a function of timeduring the first300 Ps.The results are shown infigure 3.16(b); here the plasma istreated as a step-like filmwhose thickness increaseswith time. Multiple simulationsare performed for theinitialnormalized electron densitiesof 0.74, 0.9, 1.2 1.3, and6. The results are displayed infigures 3.10 to 3.11 andare found to be iii goodagreement with the abovenumericalcalculations. The riseand the fall times of thereflected pulses are muchslower than theones calculated previously.This is to be expectedfrom such a model, sincethe changein the plasma density withtime is much smoother.At the point where (z,t) =0, thereflectivity reaches unity whichis in agreement with whatis expected from thesolutionof the differential equation.We can write the reflectivityas a function of three variables:the phase shift, filmChapter 3. Theory:Infrared Reflectionfrom a SemiconductorPlasma679030—30—9003009030—30—900Figure 3.12:Phase changein degreesof the reflected10.6 m pulsesas a functionof timefor initialplasma densityof (a) n= 0.7n and(b) n= O.9n. The plotsare calculatedfrom the differentialequationmodel.60 120180 240100200300 400500PicosecondChapter 3. Theory:Infrared Reflection froma Semiconductor Plasma68-I0 0 00 000(a)Q)30C,)cI—Io000000—90I0.0 0.20.4,)‘C0I030I0I00I000000—900. 2.5PicosecondFigure 3.13: Phasechange indegrees of thereflected10.6 um pulsesas a functionof timefor initial plasma densityof (a) n= 1.2ri and (b) n= 1.3n. The plots arecalculatedfrom the differentialequationmodel.Chapter3. Theory: Infrared Reflection from a SemiconductorPlasma 6990I •If:::00 60120180 240300PicosecondFigure 3.14:Phase changein degreesof the reflected10.6 ,um pulsesas a functionoftime for initialplasma densityof n =6n. The plot is calculatedfrom thedifferentialequation model.n(z=O)/n...ciit-c- CDCDCl) ——.so CDq)—.CD+C—.CD Cl)÷,CD0Ci)Cl) CDP C Cl)p t.C,)CD CDII. . ciiChapter 3. Theory:Infrared Reflection from aSemiconductor Plasma711—____________1.0(a)0.9N¶0.807osecod¶0.5______IIcr2 ‘1i2—•.1z• ,,—40-0 100200300 400500Time(psec)Figure 3.16: (a)Normalizedsurface plasmadensityat z=O as afunctionof time. (b)Effective thicknessof the plasmafilm as a functionof time.Chapter 3. Theory: Infrared Reflectionfrom a Semiconductor Plasma72thickness and electron density. Therefore,the dynamical behaviour of the switchcan bewritten as the total derivativeof the reflectivity with respectto time.dR dRdn dRd dRdS(3.58)Note that at all times we have(dn/dt)< 0. This means that ifthe semiconductor isilluminated by a laser fluence sufficientto produce a large enoughinitial plasma density,i.e.(n/ne)= 6, then a competition between the derivativesof the phase, the density, andthe thickness of the plasmafilm, with respect to time determinesthe temporal evolutionof the reflected infraredpulses. By examining figure3.4 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. Therate of change of the reflectivitydepends on whether thesum of the three terms is positiveor negative. Initially, the reflectivitychanges at a slowrate because the rate of change ofthe first two terms is slow inthe first 10 ps, and the rateof change of the reflectivityis dominated by the changein the thickness of the plasmafilm, thus making (dR/dt) positive.When the reflectivity approaches0.65, it begins todecrease slowly since the lastterm no longer dominates thesign of (dR/dt). For thenext140 ps the reflectivity decreasesuntil the plasma density decaysto1.26n. At the pointwhere(n/n)=l.26, the contributions of all three terms arepositive, and the reflectivityincreases slowly from0.5 to 0.91 in about 33 ps. WhenR approaches unity, the electrondensity approaches thepoint near the criticaldensity. As soon as(n/ne)< 1, we havea different region of reflectivity,where the contributionof the phase to the reflectivityis zero in this region. Forthe plasma density in the range0.9(n/ne)1, the term(dR/dS)(dS/dt) > 0 and(dR/dn)(dn/dt)< 0. Because of the fast decay ofthe electrondensity compared to the increasein R due to increasing plasmathickness, the reflectivitydecays very quicklyfrom unity to zero level(at (n/ne) =0.9). For theplasma densityrange 0(n/ne) < 0.9, the term (dR/dn)(dn/dt) reversessign and becomespositive butChapter 3. Theory: Infrared Reflectionfrom a Semiconductor Plasma73the 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 signalthendecreases slowly because (dR/dn)(dn/dt) switches sign and becomesnegative, whereas(dR/d)(dS/dt) > 0 and the reflectivitybecomes zero at(n/ne) =0.From the above analysis, wecan draw the following conclusions.Femtosecond andpicosecond pulses of variabledurations can be generated dependingon the initial valueof (n/ne). For a control pulse of theorder of 100 fs, one needs to adjustthe energyfluence of the laser pulse suchthat the number density of thephotoinjected electrons isin the range 1.2n—l.3nin order to obtain ultrafastinfrared reflection. It seemsthatthe temporal response of the switchis limited only by the control pulseduration and theambipolar diffusion coefficientof the semiconductor.The next task is to performthe experiment at different excitationenergy fluences onGaAs. Whether our conclusionsfrom the calculation are correctdepend on the assumptions we have made in derivingthe model.Chapter 4Laser Systems, Optical Setups,and Experimental Procedures4.1 IntroductionIn this chapter, the laser systems, the experimentalapparatus, and the techniquesusedduring the course of this workare discussed. A brief overviewof the femtosecond laserpulse generating/amplifying systemis presented with special emphasison the system performance and characteristics.All the CO2 lasers used in this work havebeen designed andbuilt in this laboratory and considerabletime and effort is spentin characterizing theirperformance as well as their operatingconditions. Moreover, the constructiondetails ofthese high-power CO2 lasers arediscussed. Further detailsof the fast electrical dischargeexcitation circuits and on the lasers’designs and constructionare published in our reviewpaper on the subject [134]. In thischapter, we also discussthe design of a home-madeautocorrelator constructedto measure the duration of thepump laser system.A briefoverview on the detection units,some custom electronic modulesthat are used for datacollection and laser synchronizationare discussed in this chapter.Detailed schematicsof the electronic circuits are presentedin Appendices A to C. Finally,the experimentalsetups for time-integrated reflectivity,reflection-reflection correlation,cross-correlationtechniques, and frequency spectrummeasurements are presentedand discussed in detail.74Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures754.2 The Femtosecond Laser SystemThe high power laser pulse excitation system usedto operate the optical semiconductorswitch is described in this section. Much of the timeduring the course of the experimentalwork was spent installing, maintaining, fixing, andoptimizing the performance of the lasersystem. The layout of the laser system is illustratedin figure 4.1. A brief description ofthe characteristics of each component is presentedbelow.4.2.1 The Femtosecond Laser Pulse GenerationSystemThe ultrafast laser pulse generating systemis a commercial laser system consistingof anNd:YAG(Nd3+doped Yttrium Aluminum Garnet), a pulsecompression stage, and a dyelaser.The Nd:YAG LaserThe Nd:YAG laser is a Spectra PhysicsModel 3800 mode locked laser. The laseris drivenby an acousto-optic mode locker, placedinside the laser cavity near the outputmirror,operating at a resonance frequencyof 41.0245 MHz and producing a singlelongitudinaland transverse mode, quasi-continuouspulse train at a wavelength of1.064 gum. Theoutput pulse train repetition rate is 82.049MHz with a single pulse durationof 70 ps.The average output power from the laseris between 13 to 14 W.The Pulse CompressorThe Spectra Physics Model3695 Optical Pulse Compressor utilizesa fibre-grating optical arrangement to shortenthe 70 ps (1.064 gum) pulse durationfrom the mode lockedNd:YAG laser to ‘- 4—5 ps. The 1.064gum pulse is frequency doubledto 0.532 gum usingasecond harmonic generationcrystal. With frequency doubling,the duration of the 0.532Chapter 4. Laser Systems, Optical Setups, andExperimental Procedures76m pulse is reduced even further to3 ps. The maximum output that can be obtainedfrom the pulse compressor is 1.1W at 0.532 m.The Dye LaserA Spectra Physics Model 3500 UltrashortPulse Dye laser is utilized in thefinal stageof the femtosecond pulse generation system.The dye laser uses Rhodamine6G dye as again medium which is synchronously pumpedby 850—900 mW, 0.532 um(3 ps) outputfrom the pulse compressor. Thelaser produces 83—250mW average power with a tuningrange between 575 to 635 nm. The outputpulse train (82 MHz) consistsof individual500 fs pulses with 1—3 nJ/pulse.4.2.2 The Femtosecond LaserPulse Amplifying SystemThe nanojoule femtosecond laserpulses are amplified to ahigher energy with a subpicosecond laser pulse amplifyingsystem consisting of a threestage dye amplifier pumpedby a Nd:YAG regenerative amplifier.The Nd:YAG RegenerativeAmplifierA Continuum Nd:YAG RegenerativeAmplifier Model RGA6Ois used to pump a subpicosecond laser dye amplifier.A dielectric beam splitteris used to split off‘— 5% from theNd:YAG laser mode locked trainand is injected into theregenerative amplifier. Singlepulses are selected fromthe train and are amplifiedto produce 200 mJ,70 Ps, 1.064 tmlaser pulses at a maximumrepetition rate of 10 Hz. Theoutput is frequencydoubledin a second harmonic generationcrystal to produce100 mJ at 0.532 im ina singletransverse mode.Chapter 4. Laser Systems, Optical Setups,and Experimental Procedures774.2.3 The SubpicosecondDye Laser Pulse AmplifierThe femtosecond dye laser pulse is amplifiedin a Continuum Picosecond AmplifierModelPTA6O consisting of three Rhodamine640 dye cells. The dye laser pulseamplifier ispumped synchronously with25 mJ from the frequency doubledoutput from the Nd:YAGregenerative amplifier. The injectednanojoule 616 nm dye laserpulses are amplified toa maximum energy of ‘-‘ 1mJ at 10 Hz with a minimum of pulse broadening.4.3 The CO2 Laser OscillatorsIn this section we give a brief introductionto the continuous wave (CW)CO2 and pulsedlasers used in our experiments. TheCO2 lasers have been designed, built,and upgradedin our laboratory, and hence, a considerableamount of time and effortis devoted todetermine their optimum operatingconditions and design configuration.Our goal is toconstruct high-power single longitudinaland transverse mode CO2 lasersto carry outthe optical semiconductor switchingexperiments. The simplicityof the devices’ designsand constructions make them attractiveand inexpensive laboratory instruments.4.3.1 The CW CO2 Laser OscillatorDuring the course of our experimentalwork with theCW CO2 laser, the laser designwasfrequently modified and upgradedto suit our purpose. The originalCO2 laser deliveredonly 1.5 W at 10.6 ,um. Clearly,this laser power was notenough to be usefulin ourexperiments. Another largerlaser has been designedto produce ‘-S- 10 W,and severalexperiments were performedusing this laser; however,the detected signalsare weak andit was decided to further upgradeit to a higher power (>30 W).The CW CO2 laser consistsof two independent sections.The simple schematicofthe laser is illustratedin figure 4.2. Both sectionsuse a DC glow dischargeto achieveChapter 4. LaserSystems, Optical Setups,and Experimental Procedures78.AutocorrelatorPulse CompressorAmplifier1 mJ, 490 fsFigure 4.1: Thelayout of thefemtosecond laserpulse generatingsystem.Chapter 4. Laser Systems,Optical Setups, and ExperimentalProcedures79laser inversion in the CO2 molecules.The two ends of the laser sectionsare maintainedat a high voltage of 25kV and are separated bya ground cathode at the centreof thedischarge. Each section consistsof a pyrex tube 103 cmin length and 12 mm in diameter,and can be operated independently.The effective laser cavitylength is 3 m (end-to-end)with one end being terminatedby a 0.64 cm thick,5.08 cm diameter KC1 Brewster’sanglewindow to ensurea single polarization beam output,and the other end of the lasertubeis terminated by the resonatorcavity mirror. Two cold-water(—14 °C) lucite-jackettubes (6.4 cm in diameter)are used to cool thedischarge plasma.In order to have a stable glowdischarge betweenthe laser brass electrodes,the negative dynamic resistance(after the CO2 gas breaksdown) must be suppressed.This isdone by connecting aseries of ballast resistorsin series with the high voltageDC powersupply. Both anodesare connected to the powersupply via four 0.1MQ resistors witha total resistance in eacharm of 0.4 Mf. The cathodeis connected directly to ground.This arrangement ensuresthat both sectionscan break down evenly andmore reliably.The laser cavity designconsists of a concave,8 m radius of curvature,gold-coatedmirror which is mountedinside the discharge volumeand an output couplerconsisting ofan uncoated plane-parallelCe window of 5 mm thicknessand 2.54 cm diameter.As in anyetalon, both thefront and the backcontribute to the reflection.The refractive indexofCe at 10.6urnis 4.2; hence at normalincidence, the contributionof the surface reflectionis only 36%; however,interference betweenthe two faces canresult in reflectivitybetween0—80% depending on the free spectralrange of the Ge etalon.The CO2 can laseon several vibrational-rotationallines simultaneouslybetween 8.7urnto 11.8urn.These laser transitionsare highly competitive,and as a result thebeatingof the longitudinalmode causes fluctuationsin the laser power output.The Ce flatcanbe used as a tunableFabry-Perot etalonto suppress the oscillationon all lines but theonewhich matches the freespectral rangeof the Ce etalon. Thefree spectral range canbeChapter 4. Laser Systems, OpticalSetups, and Experimental Procedures80tuned by adjusting the temperatureof the Ge fiat. A feed-back temperatureelectroniccontrol system is usedto actively stabilize the resollatorcavity. The temperatureofthe output coupler is fixed at30.15°C at which the laser lases at10.6 gum and exhibitsexcellent stability. Due to the large lengthto diameter ratio of the discharge,the laser isforced to operate on a single transversemode, TEM00,with a beam spotsize of 1.5 mm.The discharge current determinesthe rate of pumping of theCO2 molecules and thusdetermines the output power.In this laser, the maximumpumping current is 40 mA(20 mA for each section). Thelaser is operated with agas mixture of He:C02:N withamixture ratio of 84:8:8and a total gas pressure of15 torr. During the electricaldischargethe CO2 molecules dissociateand; therefore, the replacementof the gain mediumisrequired. The lasergas mixture is flowed throughthe discharge region, whereit isinjected from both anodesand exited through thecathode.With the above operating conditions,the output laser poweris measured to be40 W. It seems that the limitingfactor in determining theoutput power ofthe laser isthe flow rate of the CO2gas. Improvements onthe gas flow system shouldincrease theoutput power. It is clearthat the CWCO2 laser does not require synchronizationwith thefemtosecond laser/amplifiersystem; therefore, itis used to perform all thetime-resolvedexperiments.4.3.2 The High PressureTEA CO2 Laser OscillatorTEA CO2 Laser Bodyand CircuitHere we present a designfor a TEA dischargeCO2 laser which is used to performsome optical semiconductor switchingexperiments, especiallyfor measuring thefrequency spectrum of the reflected infraredpulses. An illustration ofa cross section of the laserbodyand its electrical circuitcomponents is shownin figure 4.3. The laseris designed toChapter4. LaserSystems, OpticalSetups, and ExperimentalProcedures818 m mirrorHVWaterinKC1flatFigure 4.2:An illustrationof the 40W CW CO2laser.R = 0.4 M1and HV= 25 kV.operateat high gaspressuresin the rangebetween1 to 7 atmospheresand to beusedas partof a moreelaborateCO2 lasersystem knownas a “hybridlaser” arrangement.Most ofthe electrical,laser energy,and pulsedurationmeasurementsdiscussedin thissection areperformedwith the dischargelaser operatingat 1 atmospherewith a lasinggas compositionof (C02:N:He)and a mixtureratio of (15:15:70).The laserelectrodesare madefrom aluminumplates withan electrodeseparationof 9.5 mm.The electrodesare designedto be flat overa 9.5x350mm2 area,with roundedcorners similarto thedesign in reference[135]. Theradius ofcurvatureof these roundedcorners is6.3 mm.The gasglow dischargeis observedto be uniformover the(9.5x9.5x350)mm3 volumeas indicatedby photographingthe dischargeregion.The high pressureelectricaldischargeis automaticallypreionizedusing a doublesidedLC inversioncircuit whichis first describedin reference[136]. Thiscircuit isone of themost efficientways toexcitehigh pressureCO2 gas dischargelasers [134].Efficientoperation ofa high pressuregas dischargelaser dependsstronglyon boththe low inductanceinL.RCO2 outGe flat1UWateroutRHVChapter4. Laser Systems, OpticalSetups, and ExperimentalProcedures82•Pick-upCoils.JPlexiglass10ChamberFigure 4.3:The TEACO2 laser usingan automaticallypreionized,doublesided,LCinversioncircuit. Electricalconductors(aluminumand copper)are shown shaded.Thepreionizer roddesign is also shownbelow./AluminumIPlatesCapacitorsI I I II I I I I2468cm scaleChapter 4. Laser Systems,Optical Setups,and Experimental Procedures83of the driving circuitand the density distributionof the initial electronsproduced by thepreionization process.The schematics ofthe circuit designis presented in figure4.4. Theprinciple operationof the LC inversionis as follows: thecapacitors arecharged in paralleland no voltage appearsacross the laserelectrodes; then,when the sparkgap switch istriggered and henceclosed, the voltageacross the topcapacitor banks dischargesthroughthe preionizerrods [135],[137J—[140].Due to the high inductanceof the resistors andthe preionizer rods,the current continues to flow and thetop capacitor bankpolarity reversesdirection. The voltageacross thelaser electrode,at this time, becomesdouble thecharging voltageof the capacitors.Thelaser gas breaks downas soon as theelectrode voltagereaches the pressure-dependentbreakdown voltageof the gas mixture.The switching ofthe dischargeis made possibleby a low inductancespark gap whichis pressurizedwith dry air to50 Psi to withstanda charging voltageof 22 kV.The spark gapis triggered bya triggering pin connectedthrough a krytron(EG&G)high voltage (10kV) triggering unitthrough a 6:1step-up transformer.Twenty-fourdiscrete BaTiO3doorknob capacitors(MurataCorp. no. DHS6OZ5V272Z-40,2.7 nF, 40kV ceramic capacitors)are mountedsymmetrically,six in each quadrant,between bothsides of the dischargechamber as shownin figure 4.3.This arrangementgives an ultralowinductance configuration.As shown infigure 4.3, thebody of the laseris machined outofa single lucite block,with one additionalplate of lucite(surroundingthe upper electrode)glued into it usingcyanoacrylate,“Krazy glue”.Preionizationof the main dischargeis provided by twoarrays of U.V.sparks. Eachpreionizer rodis constructed asdescribed inreferences [138,139], with thecentre conductor (a lengthof Belden no.8868 high voltagewire) passingthrough the outerconductorof the 20 cm lengthof a home-made50 f coaxial cable,and then all theway throughthe glass tubingto the last stainlesssteel preionizerelectrode. Theedges of thestainlessChapter4. LaserSystems,OpticalSetups,and ExperimentalProcedures84(b)I.Figure4.4: (a)TheCO2laserLC inversioncircuitand thepreionizersconnections.P.R.=preionizationrod,S.G.=sparkgap,and L.D.=laserdischarge.(b) TheequivalentcircuitwithC = 64.8nF,Lp =420 nH,Rp =1.051, C= 64.8nF,andLe = 6.8nH.C4C4EquivalentChapter 4. Laser Systems, OpticalSetups, and Experimental Procedures85steel tubes are cut at300to the axis of the tube.A drop of cyanoacrylate glue isusedat each end of the Belden wireto seal the wire against its insulation,and this glue isalso used to seal the insulationagainst the first stainless steelpreionizer electrode,asshown in figure 4.3. The endof the preionizer is sealedagainst the lucite laser chamberwith an 0-ring fitting. Theother preionizer electrodes areattached to a5 mm (outsidediameter) pyrex tube using thesame glue. We used 15 preionizerspark gaps of 400 tmeach, at 2.5 cm intervalalong each preionizer rod.We found that the breakdownofthe two preionizer rodsis very reliable if the total lengthof U.V. sparks, 15x(400tim),is less than the main electrodespacing of9.5 mm. In order to minimize the electricaljitter to less than+3 ns, we made use of the “capacitivecoupling” to the return lead,sothese sparks actually formsequentially [141]—[143],rather than all at once;the processrequires about 20 ns [142,143] to form a so-called“running spark” or “slidingspark”,and it is only after all thesparks have formed thatthe inversion and preionizercurrent,Ii,,, starts to climb significantly[141]. The preionizer rodsare mounted alongthe sidesof the main discharge andparallel to the laser electrodesat distance of 14 mm,sothat unwanted sparks betweenthem are avoided and uniformpreioriization of themaindischarge is obtained.Electrical Current andVoltage Measurementsof the Laser DischargeThe discharge current risetimeis directly related to therate of energy deposition.In thislaser discharge, the electriccurrent changes veryquickly which inducesa time-varyingmagnetic field. Bytaking advantage of this,very accurate transientcurrent measurements can be performed.The current pulse ismeasured using twin,subnanosecondrisetime, 10-turn pick-upcoils [144] installed betweenthe capacitors,within the fastdischarge main loop,on opposite sides ofthe chamber, as indicatedin figure 4.3.Thetwo coils thereforegive equal and oppositesignals which, when subtractedby a 1 GHzChapter 4, LaserSystems, OpticalSetups, and ExperimentalProcedures86oscilloscope (Tektronix7104 with two7A29 plug-in units),give the low-noisevoltagesignalVc, proportional to the ratechange of the maincurrent,VC=AM,(4.1)whereAM is a constant. The currentnoise is substantiallyeliminated by “common-moderejection.” Thetwo signal linesare first carefullyadjusted tohave identical delaytimes,to within±50 ps. The delayis measured usingan oscilloscopeand a coaxialspark gap[137]—[139] cabledischarge circuit[137]—[139], [145,146]. The dischargecircuit provides1000 V electricalpulses havinga risetime of300 Ps.Measuring the dischargebreakdown voltagegives an insightinto the amountof electrical excitationenergy thatis being deliveredduring the laseroperation. Inmeasuringthe transientdischarge highvoltage, itis convenient touse a high voltagedivider. Thevoltage,VM, on the main electrodesis measured usingtwin, resistor divider,high-voltageprobes ofiO x attenuation (eachconsisting of15 two-wattcarbon resistorssoldered together in serieswith a terminated50 cable), one foreach electrode.The risetime ofeach probeis measuredto be 10 ns. Again,the signals aresubtractedby the 1 GHzoscilloscope, givinga low-noise signalrepresentingthe voltage,VM, across the discharge;the noise, again,is thereby substantiallyeliminated by“common-moderejection.” Thevoltage,VM, across the main electrodesis measuredin this way,for an initialchargingvoltage ofV0 = 22 kV, andis shown in figure4.5(a). Themain current,IM,starts att= 300 ns, witha jitter of< ±2 ns, relativeto the primary/preionizercurrent,Ip. Thecurrent,Ip, starts with ajitter <±3us, relative tothe time of firingthe sparkgap.As observed previouslyfor CO2 lasers[138, 139, 141],[147]—[149],the main current,JM,essentiallystops with afinite voltageofVM = 13 kV remainingon the mainelectrodes.This occurs,presumably,since thereis no longerenough voltageto maintain adischarge.However, sincethe spark gap(and preionizer)current,Ip, are still supplyinga chargeChapter 4. Laser Systems, OpticalSetups, and ExperimentalProcedures87to the main ioop, we observesmall current oscillations immediatelyfollowing the largeinitial pulse, as shown in figure4.5(b). This initial currentpulse contains at least90% ofthe energy of the entire curreiltpulse,IM.The current pulse FWHMis measured to be40 ns, which is fairly close tothe critically damped valueof 25.6 us, given by equations(5) and (16) in reference [134].During these current oscillationsfollowing the largeinitial pulse, the voltage,VL,induced in the measurementloop of area,AL, is by Faraday’s law,rfdB’\Ii0AN dIMVL= JAL—--).ds—--)——,(4.2)where A and I are thecross sectional areaof the aild the length ofthe current sheet,respectively.VLhas a 2 kV amplitude.SincedIM/di is 0 at certain times t (maximaand minima of‘Min figure 4.5(b)),one can compute the dischargeresistance at thesetimes from the followingequation:r(t)= VM(t)(4.3)‘M(t1)which has strong oscillationsalso, and this function r(t)is sketched in figure4.5(a). Thevoltage which wouldhave been on the electrodesduring this time hadthe main dischargenot occurred is shown bythe dotted line,VM’, in figure 4.5(a). We measured this voltagesignal by firing thelaser with higher pressurein the chamber sothat only the primarycircuit fired withouta main discharge. SinceVM’ = 36 kV at the end of the strong currentpulse, the chargewhich flowed in the maindischarge up to that timeis approximatelyLQ = Ce(36.0 — 13.0)kV = 370JLCoulomb,(4.4)while the electricalenergy deliveredis approximatelyAE= Ce(36.O2— 13.o2)kv 9.1J,(4.5)Chapter 4. LaserSystems, OpticalSetups, and ExperimentalProcedures88corresponding toa depositionof 280 J11atm.The derivativesignal of the equationfordIM/dt, and also one forthe preionizer(primary) loop,dlp/dt, are eachintegrated togive the currentpulse shapes.In order tocalculate theinductance ofthe discharge, themain discharge looparea is measuredtohave an areaof A = 38.4+0.1 cm2. A secondintegrationis required for‘Mto give thecharge which flowedthrough thedischarge and, whenequated withthe change inthecapacitor chargegiven by equation4.4, we are ableto find the absolutecurrent pulse,‘M,as shown infigure 4.5 (b).The preionizer/inversioncurrentIp, is also shown in figure4.5(b) andis scaled by solvingthe differentialequation foran underdampedoscillator[1341,using the samealgorithm asmentioned in reference[134], now withparametersC= 32.4 nF, L420 nH andRp = 1.05 whichare the primaryloop parametersfoundin the same wayas describedin reference[135] This algorithmalso gave theenergy Edeposited intothe preionizersiii the first300 ns preceding themain discharge,as E =4.4 J.Energy andPulse Outputof the TEACO2 LaserThe laser opticalcavity consistsof two KC1windowsmounted on 0-ringsat Brewster’sangle, a 5 m radiusof curvature gold-coatedfull reflector,and a Ge flat,80% reflectoras an outputcoupler. TheCO2 laser pulseis measuredusing a LabimexP005 HgCdTeroom-temperaturedetector andis shown infigure 4.6.The shape ofthe infrared pulsefrom the freerunning electricallypumpedCO2 laserdepends on severallaser parameters,such as:the durationof the pumpingelectricalpulse, the energydelivered bythe excitationcircuit, theoperating gaspressure, andthe ratio of thecompositiongases. The outputpulse durationof the aboveTEA CO2discharge laseris usuallyof the order of400 ns. The overalltemporal pulseshape consistsof an initialspike (50ns long) anda long decaytail(‘-0.5 us long). Theinitial peakChapter 4.LaserSystems, Optical Setups,and ExperimentalProcedures>a,cs(0)04LJCa,(b)—589ioTime [ps]Figure 4.5: (a) Mainelectrode voltage withoutthe glow discharge,VM’, and with theglow discharge,VM. (b) Preionizer/inversion currentwithout the glow discharge,Ip’, andwith the glow discharge,Ip; the main electrode current,IM.2015110c-)CcsV.,U)05Chapter 4. Laser Systems, Optical Setups, and ExperimentalProcedures 90is known as the gain switched peak which is dueto the short time required to build upenough gain compared to cavity round trip time.That is, the gain in theCO2 lasercan be turned on quickly by the pumping circuitso that population inversion above thethreshold value is established before the onsetof any noise build up of laser oscillations.The origin of the long tail is due to thegain recovery by collisional energy transferfrom the vibrationally excited N2 buffer moleculesto the vibrational states of the CO2molecules. This long pulse is usually knownas “the nitrogen tail.” The output usuallyconsists of a superposition of several competinglongitudinal modes, as shownin figure4.6(b).The laser pulse energy is measured to be800 mJ (multimode) using a GenTec energymeter (ED 200). The laser energy outputis found to be stable to+2%. The specificoutput energy is 25 J11,which is amongthe highest values reported for TEACO2 lasers.The overall efficiency is5.1%, and the pulse to pulse energy reliabilityis 100%. Theoutput beam is uniform over the9.5 mm x 9.5 mm area as indicated by Polaroidfilm burnspots. However, after about tenshots, one of the new intercavity salt windowsexhibitedsevere damage due to the high-powerlaser pulse, which has not, toour knowledge, beenreported previously for TEACO2 lasers of only 35 cm discharge length.Because of thisdamage problem, we are notable to make a detailed study of thelaser output at higherpressures using the configurationdescribed above. With weakermixtures, in a hybridlaser coilfiguration, operationshould be possible up to about7 atmospheres.4.3.3 The Hybrid CO2LaserFor ultrashort pulse generationthe switching task is made mucheasier if the CO2 laserpulse incident on theoptical semiconductor switchis made as long as possiblewith amaximum amount of energy.When the CO2 laser pulseis > 50 us, one mayconsider thetemporal change of the pulseintensity to be insignificantduring the switching timeofChapter 4. Laser Systems, Optical Setups, andExperimental Procedures 91Figure 4.6: (a) TheCO2 laser pulse shape at 10.6 ,um, withan energy of 800 rnJ. (b)Longitudinal mode beatingduring the laser oscillation.Chapter 4. LaserSystems, Optical Setups,and ExperimentalProcedures92a few picosecondsor iess. In addition,a long CO2 laserpulse reduces theconstraint onthe accuracy ofthe timing and jitterbetween the controlvisible pulse andthe CO2 laserpulse. Clearly,with long CO2 laserpulses, the experimentalsituation resemblesthat ofCW CO2 laser switching.For our application,the temporal powermodulation dueto longitudinal modebeatingof the above TEACO2 laser is highly undesirableand single mode operationis required.A combined arrangementof a single longitudinalmode CWCO2 (narrow gain)laser,with a TEACO2 laser sharingthe same resonatorcavity, providesa single longitudinaland transverse modewith high poweroutput of theorder of 50kW. This CO2laserarrangement isknown as a “hybridlaser”. A typicalhybrid configurationis illustratedin figure 4.7. Inthis laser arrangement,only one sectionof the CWCO2 laser delivering6 W is used to lockthe longitudinalmode of the TEACO2 laser. The cavityresonatoris the same as theone used in theCW CO2 laser witha total effectiveresonator cavitylength of 2.9 m.The high pressuresection is operatedat 1 atmospherewith a lasinggas mixture ofC02:N:He of6:6:88 at a repetitionrate between1 to 2 Hz. Thelasermaximum outputenergy is measuredto be ‘—i 25 mJ.The low-pressureCW laser section witha frequency bandwidthnarrower thanthelongitudinal modespacing of theoptical resonatorprovides theinitial 10.6m laserphotons and lasergain at only oneparticular lasermode. Figure4.8(a) showsthe singlemode pulse outputfrom the CO2hybrid laser withthe CWCO2 laser turnedon. Thepulse shape differsfrom thatof figure 4.6, whichcan be explainedas follows:the CWlaser gain is abovethe lasing thresholdof the TEACO2 laser, thusthe laser pulsedoes notevolve from noiseas in the caseof a free runningTEA laser; thisresults in theopticalpulse occurringat an earliertime than in thefree runningTEA laser. Moreover,thetime requiredto build upenough gain neededfor the gain switchedpulse is dramaticallyreduced. Consequently,the outputpulse showsa single mode pulsewith a risetirneofChapter 4. Laser Systems, OpticalSetups, and Experimental Procedures93CW Section TE LaserElFigure 4.7: The hybridCO2 laser system arrangement.220 ns and a long decay tailof --‘ L5 ,us long. This temporalwidth of this pulseis idealfor performing optical semiconductorswitching experiments.4.4 Synchronization ofthe Hybrid CO2 Laserand the FemtosecondLaserSystemIt is crucial that accuratesynchronization be maintainedbetween the hybridCO2 laserand the femtosecond pulsesfrom the dye amplifier.This has proved tobe an extremelydifficult problem for thefollowing reasons: the wholefemtosecond lasersystem is internally synchronized withrespect to the Nd:YAGmode locker’s frequencyof 41.0245 MHz.Moreover, the combineddelay in the krytroncircuit, spark gap,the LC inversion circuit,and the CO2 laser gain build-uptime amountsto ‘ 1.5 s which is longcompared to themode locker’s clock of24 ns. That is, theCO2 laser must be triggeredabout 1.5itsbeforethe laser amplifier output toallow for perfectpulse synchronizationat the optical semiconductor switch. Anelectronic timingsystem that doesnot disturb theperformance ofHV(thapter 4. Laser Systems,Optical Setups, and ExperimentalProcedures94Figure 4.8: (a) Singlelongitudinal and transversemode from the hybridCO2 laser. (b)Same hybrid laser withthe CW laser turnedoff.the ferntosecond laser systemis the most important priorityin our design.An adjustable electronicsynchronization unit wasdesigned and builtthrough theUBC Physics DepartmentElectronics Shop toperform the task.The details of thecircuit design arepresented in AppendixA. The unit has dual channelTTL outputunitswhich can be adjustedindependently overthe delay range between0 to 3 ps relativeto the Nd:YAGRGA6O output pulse. Forproper operationof the timing unit,thecommercial laser systemtriggering input wasmodified withno observable change inthesystem performance.The RF from the modelocker was divertedfrom its input totheNd:YAG RGA6Oamplifier unit, andwas directed intothe synchronizationunit. Thesynchronizationunit circuit lockson the 41.0245MHz clock from themode locker andtriggers a TTLoutput signal. The5 VTTL signal is amplifiedto 30 V andis usedto trigger theCO2 laser krytron unitthat triggers thelaser discharge sparkgap. Afterthe onset of thechannel delay(‘-..‘1.1 s) the timingunit triggersthe RGA6O timingcircuit to begin opticalpulse injection. Figure4.9 shows a layout ofthe lasers’ timingChapter 4.Laser Systems, OpticalSetups, and ExperimentalProcedures95Figure 4.9:A layout of thesynchronizationbetween thehybrid CO2 laserand the ferntosecond laserpulse generatingsystem.arrangements.With this timingunit, the overallpulse jitter is±10 ns, whichwe believeoriginates fromthe krytronunit and thespark gap.4.5 InfraredPulse Detectionand TimingSystem4.5.1 TheCu:Ge InfraredDetectorThe detectionof ultrashortCO2 laser pulsesis quite difficultbecause conventionalinfrared detectorswith timeconstants of100 Ps are too slow.Since thepulse widthofthe reflected infraredpulses ismuch less thanthe responsetime of aninfrared detector,the output amplitudedepends onthe responsetime of thedetector.In this case,thedetector integratesthe inputoptical pulse,thus acting asa very sensitiveenergy meter.Chapter4. LaserSystems, OpticalSetups, andExperimentalProcedures96220 pFDetectorToInputOscilloscope180VBiasFigure 4.10:The Cu:Geinfrareddetector bias/outputcircuit.A Cu:Geinfrareddetector(Santa BarbaraResearchCenter) isutilizedto detectthe infrared reflectedpulses.The detectorhas a spectralresponseover therange between2 ,umto 30 tmwith a risetimeof -‘. 0.5 ns.In preparationfor the experimentalmeasurements,the detector’sdewaris pumpedto 1Otorr, thenfilled withliquid nitrogenand leftto cool forabout1 hour.After that,the liquidnitrogenis disposedand thedewar isfilled withliquid heliumto cool itto 4.2 K°.When inuse, thedetectoris biasedat 160V with thecircuitarrangementdisplayedin figure4.10. Thedetectorcan be operatedfor a periodof six hourson a singleliquid heliumfill.4.5.2ElectronicAmplifierWhen conductingexperimentswith theCW CO2laser,at detectoroutputsignalsofthe orderof 1 mV,the detector’ssignals cannotbe measuredby theoscilloscope,thus,the signalsare electronicallyamplifiedin a GHzamplifierconnecteddirectlyon top ofthe Cu:Geinfrareddetector.The amplifieris impedancematchedto the50 ! output10iHVChapter 4. Laser Systems, Optical Setups, andExperimental Procedures97impedance of the infrared detector.The electronic amplifier was designedand builtthrough the UBC Physics DepartmentElectronics Shop. A complete electroniccircuit ispresented in appendix B. The amplifiergain is measured to be 34 dB witha noise levelof —88 dB. The amplifier shows excellentrange of linearity with no pulse distortion.Theamplifier is shielded in anRF Faraday cage to minimize theRF noise from the lasers.4.5.3 Experimental DataCollection SystemThe experimeiltal data ofthe reflected infrared and the visibleexcitation pulses aredisplayed on a Tektronix 7104 oscilloscopewith a 50 l plug-in (7A19) unit.The effectivebandwidth of this oscilloscopeis 1 GHz. Initially, we performedsome of the experimentsby measuring the reflectedsignals directly from the oscilloscopetraces. Both infraredand visible signals are recorded simultaneouslyusing a video camera for eachlaser shot.This technique proved to beinexpensive (compared tousing Polaroid film)and allowsreal-time analyses ofthe data; however, it is very timeconsuming since all the analysisis done manually. Therefore, wehave developed a computercontrolled electronicdatacollection system to performthis task.In the time resolved measurements,we are interested in theamplitude of the reflectedpulses (or energy) asa function of the time delay.Thus, the maximumamplitude levelof an integrated infrared pulseis proportional to theenergy contained in thepulse itself.It is evident that the electronicsystem must have certaincharacteristics, such as:(1) theability to perform theintegration processon a time scale of ‘-‘. 1 ns witha linear integration curve independentof the duration of thepulse; (2) it can besynchronized with thecommercial femtosecondlaser system;(3) it must be compatible with theCu:Ge detector/amplifier arrangement;(4) it must have a low signalto noise ratio with a maximuminput signal sensitivity of‘—‘ 20 mV in 50 f; (5)it should allow a real-timeoscilloscopeChapter 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 hadto 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 the70 ps0.532 tm optical pulse. The electronic data capture system consists of dualchannelintegration modules, one for the infrared pulse and the other forthe excitation pulse.Each integration channel has an integration window of5 ns in width; therefore, thesignals are timed very accurately to within 250 ps using a built-in variabledelay circuit, sothat the pulses fall inside their respective integration window. Thesignal synchronizationcan be performed by monitoring the signal and the integrationwindow, through theanalog output of the device, on the oscilloscope while varyingthe delays. Both signalsare captured and integrated simultaneously. The device was testedfor proper bandwidthand linearity before its use in the experiments. Figure 4.11 showsthe linearity from bothchannels using simulated 1 ns input pulses. The linearityof the device is ‘- +8%, whichis sufficient for our experimental purposes.The integral values from the infrared pulse andits corresponding visible excitationpulse are digitized and stored directly on a personalcomputer for further analysis. Theattractive features of this device make it an indispensablelaboratory instrumentforpulse-probe type experiments.Chapter 4. LaserSystems, Optical Setups, arid ExperimentalProcedures993210543C21023 4 5 6101102103Input (mV)Figure 4.11:Integrated outputfrom the dual channelpulse integrationmodule asafunction of theinput pulse voltageamplitude. Thesolid circles denotechannel 1 andtheempty circles denotechannel 2.4.6 Hall ConductivityMeasurementsin SiThe Van der Pauwmethod[150, 151] is usedto measure theconductivity,minority carrierconcentration,and the type ofthe carriers in severalSi wafers. Themeasurementsareperformed ina high magneticfield of 0.4 T producedby a 3.8 A powersupply.4.7 AutocorrelationPulse WidthMeasurementsIn this experiment,we areworking with ultrashortexcitationpulses; therefore,the characterizationand the abilityto controlthe durationof the controlexcitationpulses fromthe dye laser(amplifier)are extremelyimportant.The durationof the excitationpulsedetermines thetemporalresponse ofthe opticalsemiconductorswitch. Thepulse duration of thelaser systemis very sensitiveto the dailyalignmentand theoperatingconditions of theNd:YAGlaser; therefore,pulse widthmeasurementsmust 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 beamMichelson type interferometer which permits the performance of background free pulse widthautocorrelationmeasurements. The layout of the autocorrelator is illusrated in figure4.12. 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 inone armof the Michelson interferometer. This time delay is achieved byusing a pair of parallelmirrors (M4 and M5) mounted on a plate which is rotating at aconstant 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 secondhalf is reflected bythe retroreflector mirrors (M6 and M7) and is slightly displaced.The two pulses can beoverlapped in time at the KDP second harmoniccrystal (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] leadsto an increase (or decrease) of the optical pathlength for the optical pulse. Thus thetransmitted pulse train is delayed(or advanced)about a reference position (zero delay). Witha small angle approximation, thetimeChapter 4. Laser Systems, Optical Setups, and Experimental Procedures101delay varies linearly with the angle rotation. The twopulses 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 coincidentin 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 overa sufficiently long interval of time. The truepulseshape is shown to be a double exponentialand is related to the autocorrelation signalwidth by [160]AT = 2.421Ar,(4.7)where Ar, and Ar arethe FWHM pulse widths ofG2(r) and I(t), respectively. Thedetails of the design of the autocorrelatorand the optical components are presentedinAppendix D. The autocorrelatoris found to have excellent stabilityand pulse reproducibility. Its characteristics are comparablewith the commercially availableautocorrelators. The autocorrelatorcan be modified so that it can be usedto measure both thedye laser pulse train at 82 MHz andthe amplified dye laser outputpulses at 10 Hz.The femtosecond dye laser systemis optimized to produce the shortestpulses possible. Figure 4.13 shows a typical autocorrelationtrace from the dye laser pulsesbeforeamplification. Assuminga double exponential pulse shape[160], the shortest pulse widthobtained from our dye lasersystem is 370 fs at 616 nm.Detuning the dye laser cavitylength by less than 1 tm resultsin various pulse durations.In the case of the dye resonator cavity being longer thanthe optimum length, the resultingpulse is wide.Onthe other hand, when the dyeresonator cavity is tuned tobe shorter than its optimumlength, a double-pulse shaperesults. These pulses areshown in figure 4.13 (b,c). Clearly,Chapter 4. LaserSystems, Optical Setups, and ExperimentalProcedures 102PMTKDPM3M2Figure 4.12:The autocorrelator.B.S.= beam splitter,PMT= photomultiplier,andKDP= secondharmonic generationcrysta’ (PotassiumDihydrogen Phosphate).M1M7B.S.M4LaserBeamInputChapter 4. Laser Systems, Optical Setups, and Experimental Procedures103the pulse duration is very sensitive to the optical alignment and cavitydetuning lengthof the dye laser; therefore, the duration of thedye pulse is always monitored during theexperiments and before injecting the laser pulseinto the dye amplifier.The autocorrelation method described above is ascanning quasi-CW technique, whichlooks at signals that are repeating every 12ns (82 MHz). What is observed on theoscilloscope is a sample average over thousandsof pulses. However, the situationismore complicated when dealing with laser pulseswith a low repetition rate such as theones from the dye amplifier. One can interchangethe role of the arms of the Michelsoninterferometer, so that the rotating arm of theinterferometer is used as a referencearm and the reference arm is used as a scanningone. Measurement of the amplifiedpulse duration is done manuallyby fixing the rotating mirrors at a certain positionandscanning the delay of the retroreflecingmirrors (M7 and M6). This interferometerarmis moved through the overlap region,thus obtaining a slow scan of the autocorrelationsignal. The autocorrelation traceis recorded as a function of the relativetime delay. Wehave performed several experimentsto measure the duration of the amplifiedpulse as afunction of the input dye laser pulse;figure 4.14 shows a measured amplifieddye pulseduration of 490 fs (assuming double exponentialpulse shape). Each point inthe graphis averaged over 15 shots and the standarderror is indicated. This pulseis obtained byinjecting the dye amplifier witha 370 fs pulse for the dye laser system.The increase inthe duration of the pulse width is a resultof group velocity dispersion inthe dye amplifierdye-cells and the optical components. Withproper pulse compression techniques,it ispossible to restore the pulse durationto its original width. Our resultsindicate that thelimiting factor in the dye amplifier outputpulse duration is the duration ofthe injecteddye laser pulse. It is evident thatby injecting the amplifier with a pulsesimilar to the onein figure 4.13 (b), this results in an amplifiedpulse of almost the same shape as showninfigure 4.14 (b), thus care must be takenduring the experiment to avoidobtaining suchChapter 4. Laser Systems, Optical Setups,and Experimental Procedures104Figure 4.13: Typicalautocorrelation traces fromthe dye laser system.(a) Cavity lengthis optimum resultingin a pulse width= 370 fs. (b) Cavity length istoo short resultingin a pulse width = 500fs; note the side peaks in theautocorrelation trace.(c) Cavitylength is too long resultingin 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 Procedures105pulse shapes.4.8 Optical Semiconductor Switch SetupThe experimental layout for the optical switch is illustrated infigure 4.15. The singlecrystal semiconductor samples used in experiments are undopedGaAs (Crystal Specialties, Intl.) with a resistivity of-‘ 108l cm. The GaAs samples are cleaved to 2x1.5cm2from a 2.54 cm (diameter) wafer, as shown in figure4.15. The sample thickness is 450tim. polished on both surfaces, and it is mountedon a rotary-xy translation stage.The infrared beam is focused by a 20 cm focal lengthKC1 lens to an elliptical spot ofan area 1.2 mm2 on the GaAs wafer. The semiconductorwafer is set at Brewster’s angleof 72° to obtain a high contrast ratio relativeto background infrared reflection. Thisis necessary to detect small changes inthe transient reflectivity. The accurate settingof Brewster’s angle is achieved by rotating the GaAscrystal until a minimum reflectionis obtained from the front surface. Dueto the finite divergence of the infrared beamin the focal region and due to the thickness ofthe wafer, it is not possible to obtainzero reflection from both surfaces simultaneously.Therefore, the wafer is adjustedforzero reflection with respect to the wafer’sfront surface only. A high contrast signaltobackground ratio of i0:i ratio is obtainedduring the experiment.The visible excitation pulse is split into two identicalpulses by a 50:50 beam splitter(as shown in figure 4.16). One pulse is directedtowards the GaAs reflection switch,andthe second pulse is passed through a variabledelay line (which is used for pulsewidthmeasurements). The accuracy of thetemporal delay is ±40 fs. Sharplyfocusing thehigh energy visible pulse on the switchis undesirable. If the excitationpulse spot size issmaller than the CO2 beam spotsize, then this results in the reflectionof only a smallportion of the infrared beam. Thus,infrared pulses of low energyand high divergenceChapter 4.Laser Systems, OpticalSetups, and ExperimentalProcedures10661.1 (a)i..—.3..—Ci)Cl)1•.0• . ——2.5 —1.5 —0.50.5 1.5 2.56I II5(b). .L.•; :•PicosecondFigure 4.14:(a) Autocorrelationsignal of anamplified, 1mJ, 616 nmdye pulseshowinga pulseduration of490 fs. (b)Same conditionsbut with theinjected pulsefrom figure4.13(b).Chapter 4.Laser Systems,Optical Setups, and ExperimentalProcedures107Figure 4.15:The experimentalarrangementfor a GaAs opticalsemiconductorswitch.are produced.In order toensure goodreflected beamquality, the visibleexcitation pulseis reduced toa spot sizeof 3 mm2in area andis superimposedon the infraredlaserspot. The angularspread betweenthe infraredbeam andthe visible pulseis kept to aminimum angleof‘-. 50so that thereflected infraredpulses donot suffer fromwave frontdistortion asthe controlpulse wavefront sweepsacross theswitch. Approximately2%of the excitationpulse is pickedup from thesurface reflectionfrom the focusinglens andis used to monitorthe visible pulseexcitation energy.The detectionis performedwith afast photodiode(Hamamatsu-R1193U.03)havinga risetime of500 Ps.4.9 TimeIntegratedInfrared ReflectivitySetupIn order to reachlow excitationlevels, theintensity ofthe visiblecontrol pulseis graduallyreducedby passing itthrough asequence ofvariable stacksof calibratedneutral densityfilters (KodakWrattenGelatin). Thelinearity ofthe calibrationis checked witha stable490 fs, 618nmPulseCO2 Laserf=20 cmTo PowerMeterReflectedPulseGaAsTo EnergyMeter50Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures108HeNe 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 visiblelaserpulse allow us to access a continuous range of excitation energieswhich provides anoverlap range between the different neutral density filters. Duringthe course of theexperiments, great care is taken to ensure that placingthe neutral density filters in frontof the visible excitation pulse does not disturb the alignment ofthe infrared and thevisible laser spots. The duration of the370 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 laserpulse durations cannot be performeddirectly with photodiodes. The fastest photodiodeoperating at 10.6 pm has a risetimeof 100 Ps with a fall time of ‘—‘ 1 ns. Clearlythis is not sufficient to resolve thesubpicosecond reflected pulses. We are interestedin measuring the temporal shape ofthe reflected infrared pulses with an expected pulseduration of 50 ps; but since thepeak power of the reflected pulse is low, it isimpossible to use conventional secondharmonic autocorrelation techniques or conventionalmeasurements through frequencyupconversion mixing with the control visible pulse.Moreover, the low repetition rateofthe pulses creates an additional difficulty.It is evident that the measurement of thepulse duration has to be performedbysome indirect manner. Indirect methodsusing nonconventional correlation techniquescan overcome the limitations imposedby the measuring system. Inthe following section we briefly review the principlesunderlying two independent schemesfor measuringthe reflected pulse durations: reflectioll-reflectioncorrelation and cross-correlation.TheChapter 4. Laser Systems, Optical Setups, and ExperimentalProcedures 109principle of these methods is to transform the temporal pulseduration information intospatial information which is clearly easier to analyse. Thesecorrelation techniques arecapable of determining the infrared pulse duration with subpicosecondtime resolutionand can be applied to other ultrashort infrared laser pulsesat different wavelengths.Since the duration of the visible excitation pulseis well-characterized (490 fs), in bothcorrelation techniques, one uses the visible excitationoptical pulse (control pulse) as ameasuring scale to determine the infraredpulse duration.4.10.1 Reflection-Reflection CorrelationProcedure and Optical SetupThe reflection-reflection correlation infraredpulse measuring method is similarto theautocorrelation technique in the sensethat the reflected infrared pulse is convoluted withan identical copy of itself as a functionof time. In this type of experiment,we requirethe use of a second identical GaAsinfrared reflection switch which isoptically-triggeredsynchronously with the first GaAs reflectionswitch. Due to the nature of the reflection-reflection correlation technique, certainassumptions have to be made aboutthe pulseshape. The reflection-reflection correlationmeasurements can produce ambiguoussignals,and any sharp temporal features associatedwith the pulse are washed outthrough thecorrelation process. However, thistype of experiment is necessaryto obtain an estimateof the overall pulse width.The measured reflection-reflectioncorrelation signal, A(r), is proportionalto:A(r)jI(t)I(t+r)dt(4.8)where, 1(t), is the infrared reflectionpulse produced by the first switch,and I(t+r)is the reflection from the second opticalsemiconductor switch at a delay time,r. Thesecond GaAs switch reflectivity is delayedby time r relative to the first GaAsswitch.The delay time, r, must be long enoughto encompass the infrared pulse widthfrom theChapter 4. Laser Systems, Optical Setups, and Experimental Procedures110first GaAs switch. The product signal is largest when the two peaksof the infrared pulseand the control pulses of the second switch overlap at thesecond switch (r=0). Theproduct signal is smallest when those two signals are separated byT which is longer thanthe infrared pulse width. Concentrating initiallyon the expression for A(r) in equation4.8, it is clear that 1(t) cannot be recovered fromequation 4.8 without some additionalinformation. The shape of A(r) is always symmetricalabout r=0, even if the initialpulse is asymmetrical.The schematics of the whole experimental measuring systemis in figure 4.16(a). Bothreflection switches are taken from the same semiconductorwafer. Here, a second GaAsreflection switch is set at Brewster’s angle withrespect to the reflected infrared pulsefrom the first GaAs switch. Since reflection-reflectioncorrelation type experiments aresensitive to the alignment of both switchesand the background infrared reflection, theangle setting is accurately adjusted forthe first GaAs switch, then the semiconductoris removed and a small mirror (gold-coatedSi wafer of the same thickness as theGaAswafer) is mountedin its place. The full CO2 laser beam is reflected andis used to align thesecoild semiconductor switch exactlyat Brewster’s angle. The experimentalcoilditionson both GaAs switches aremade to be almost identical.The infrared pulse is focused on the secondGaAs switch with a 15 cm focallengthKC1 lens, and its visible excitation pulseis delayed and focused to anapproximatelyidentical spot size to thatof the first GaAs switch. However, theangle between theinfrared pulse and the visible excitationpulse on the second GaAs switchis limited byour optical setup and is measuredto be 8°. A removable mirroris placed in the opticalpath of the collection system to providea reference signal correspondingto the infraredreflection from the first GaAsreflection switch. With this opticalarrangement, we are notable to entirely eliminatethe back surface reflection from the firstGaAs switch, and thereflection-reflection experimentsare performed with the presenceof a small backgroundChapter 4, Laser Systems, Optical Setups, andExperimental Procedures 111infrared reflection. The stray visiblepulse light reflection coming onto the detectoriseliminated by placing a GaAs wafer at Brewster’sangle at the entrance to the detector.The exact time delay range is initially setby accurately measuring the optical pathsthat the infrared and the visible pulsestake to within ±3 mm. Then thedelay line isscanned over this distance range, andat the same time the infrared reflectionfrom thesecond switch is monitored onthe oscilloscope until a maximum reflectionis obtained(this defines the overlap of the reflection pulsesfrom the two switches). The delay lineis then moved forward and backward tomeasure the wings of the pulseby 30 — 60 ps.4.10.2 Cross- CorrelationProcedure and Optical SetupWe are interested in measuring the exacttemporal shapes of the reflectedinfrared pulses.Therefore, we presenta simple method to perform this task:the time-resolved cross-correlation experiment is basicallya method of convolving the infraredreflected pulsewith an ultrafast transmissionfunction.The cross-correlation methoddoes not directly provide the pulsewidth but the pulsedifferential with respect totime. Also, it is superiorto autocorrelation schemesin preserving the details of the pulseshape and providing an indicationof the background level.The technique relies on the e-h plasmageneration in a semiconductor whichserves as afast temporal transmission gate.The semiconductor must havea large absorption depthfor the visible radiation, a longrecombination lifetimecompared to the measuredpulsewidth, and a small free-carrierabsorption cross-section forthe infrared wavelength.Wehave experimented withtwo semiconductors, germaniumand silicon, as possiblecandidates for infrared transmissioncut-off switches; however,since the plasma layerin Ge isapproximately 180 nmthick, the 10.6 um radiationis able to penetrate andleak throughthe plasma layer. Thus,the experiments performed withGe are done above abackgroundlevel and are not discussedin this work. Onthe other hand, Si providedan excellentChapter 4.Laser Systems, OpticalSetups, and ExperimentalProcedures112FLCO2 LaserFigure 4.16:Typical experimentalconfigurationsused tomeasurethe infraredpulseduration:(a) Reflection-reflectioncorrelationexperimentalsetup.(b) Cross-correlationexperimentalsetup.B.S.= beamsplitter,B.D.=beam dump,E.M.= energymeter,P.E.= powermeter, R=reflectionswitch(GaAs), M=temporarymirror, F=filter (GaAswafer), D=Cu:Ce infrareddetector,and T=transmissionswitch(Si).Dye LaserB.S.PulseDelay(a)FE.M.P.M.MLE(b) TChapter 4. Laser Systems, Optical Setups, and Experimental Procedures113contrast ratio; therefore, it is used throughoutthis work. It will be shown in chapter5that silicon is an ideal semiconductor for this type of experiment.The cross-correlation experiments are performedin the following manner: the probevisible pulse is directed towards a transmissioncut-off switch to optically excite thesemiconductor, and thus creates a plasmadensity greater than the critical density5 x iO’ cm3)in the absorption skin depth of silicon. The thicknessof the plasma layeris 3 1um. When the visible excitation pulsearrives at the Si transmission cut-offswitch earlier than the infrared pulse,the infrared pulse is both reflected andabsorbedby the free carriers. As the visiblepulse is delayed, part of the infrared pulsefrom thereflection switch propagates throughthe Si switch. The part of thepulse which arrivesafter the critical plasma densityis created suffers from large reflection and absorption.By scanning the relative delay betweenthe infrared pulse and the visible probe pulse,theinfrared pulse is temporally gated andintegrated by the detector as a functionof time,and a transmission step whose risetimeis the cross-correlation between the infraredandthe visible pulse is obtained.The time integral of the pulse is obtainedas a functionof the relative delay. The measuredintegrated pulse shape,1jr,is calculated from thefollowing expression:jR(t)T(t+r)dt(4.9)where R(t) is the reflectivity ofthe optical semiconductor reflectionGaAs switch andT(t+T) is the transmission of the cut-offSi switch at a time delay, r.The experimental optical arrangementof the cross-correlation experimentis illustrated in figure 4.16(b). Thetransmission cut-off switch is madeof a 50 tm thickpdoped (1.56x10’6cm3)Si wafer (optically polished onboth surfaces) cut to asize oflxi cm2. The surface reflectionof the Si sample is measured tobe 35% at 10.6 1um, andresistivity of the sampleis measured to be 1.41l cm. The sample is mounted behindaChapter 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, theuncertainty 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 eliminatedwiththe optical collection system, as shown in figure 4.17. With the aid of the HeNelaserbeam we are able to trace the exact path of the reflected infraredpulse, and we measurethe separation between the position of the reflected pulse and thereflection resulting fromthe rear surface to be -‘ 7 mm. An adjustable iris is placed betweenthe two collimatinglenses at a distance of 18 cm away from the focus to obstructthe stray reflection. Withthis simple arrangement we are able to obtain a signal to backgroundratio of i:i0. Insome experiments an optically polished Ge flat is used as an infraredfilter to ensure thatno visible radiation leaks through to the infrared detector.The correct time delay range is initially set by accurately measuringto 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 infraredsignal transmissionis monitored on the oscilloscope until the infraredtransmission is completely cut-off (thisdefines the zero delay time). The delay lineis then moved forward (for earlier arrivalof the visible pulse relative to the infraredpulse) by 5—10 Ps to provide a long zerotransmission base-line in order to resolvethe initial risetime of the pulse.Chapter 4. LaserSystems, Optical Setups,and Experimental Procedures115IrisSi PinholeIR PulseIR CWReflectionFigure 4.17: Opticalarrangementused to eliminatethe rear reflectionresulting fromthefirst GaAsreflection switch.4.11 InfraredPulse-FrequencyMeasurementTechniqueMeasurementof the frequencyspectrumof the reflectedinfrared pulsesshould providea complementaryand independentmethod toboth reflection-reflectioncorrelationandcross-correlationtechniques. However,there is a difficultyassociatedwith the detectionof the infraredspectrum,mainly thelack of a fastsensitivecharged coupleddeviceoperatingat 10.6 m.Although pyroelectricarrays can servethis purpose,they lack thesensitivityand the temporalresponse at10.6 tm. In fact,we have usedunsuccessfullysuch a deviceto recordthe frequencyspectrum.Thus we investigatethe use ofanimage disectoroptical setup,combinedwith an infraredspectrometer,to measurethefrequencyspectrumof the infraredpulse on asingle shotbasis.The apparatuspermitsthe measurementof the spectrumwith a veryhigh detectivityby using onlya singleinfrareddetector.“I,To DetectorChapter 4. Laser Systems, Optical Setups,and Experimental Procedures1164.11.1 The Image DisectorThe image disector has beenused widely in our laboratory to measurethe frequencyspectrum from scattered light in laser-plasmainteraction experiments. Itis based onthe principle that the individualfrequencies making up the pulse spectrumare mappedonto time delayed signals (in contrastto correlation experiments wherethe temporalinformation is mapped into spatialdistribution). To explain further, anultrashort opticalinfrared pulse at 10.6 tim, witha duration less than the responsetime of the detector,has a frequency spectrum whosewidth in frequency is inverselyproportional to thepulse duration. The spectrumof the infrared pulse is spatiallydispersed by passingthe pulse through a spectrometer,and if the frequency spatial dispersionis made wideenough, then by circulating the opticalpulse through a special opticalmirror arrangement(image disector), one can allowonly successive parts of the frequencyspectrum to exitthe optical arrangementfor each transient reflection theinfrared pulse takes throughtheoptical system. Consequently,one can use a single fastinfrared detector to obtain a pulsetrain (channels) that mapsout the full pulse frequency spectrum.Clearly, the temporaldelay for the pulse insidethe optical system must be longerthan the response timeofthe infrared detector. By properchoice of spatial dispersionof the spectrum, one canobtain the desired frequencyresolution per channel of theoptical setup.4.11.2 Optical Setup andAlignment of the ImageDisectorThe optical arrangementof the image disector andthe optical collectionsystem is illustrated in figure4.18. The image disector itselfconsists of three concavegold-coatedmirrors, M1, M2 andM3,all of the same focal lengthof 50 cm. Both M2 andM3 are 5.08cm in diameter and areseparated form M3 by adistance of 1 m. The M1mirror is squareedged (7 cmxi cm)with the flat sides cut toa sharp edge of100to allow the part oftheChapter 4. Laser Systems, Optical Setups, and ExperimentalProcedures 117infrared image spectrum to exit the multi-pass opticalarrangement. Since the techniquerequires a few reflections on each pass, the optical qualitiesand the reflectivities of themirrors, M1,M2, and M3 must be high: A/10 and‘ 99%, respectively.The reflected infrared pulse is collimated with twoNaC1 lenses (f.l.= 15 cm) to form a1:1 telescope arrangement. The infrared pulseis directed toward the spectrometer whereit is focused on a 380imentrance spectrometer slit with a NaC1(f.l.= 15 cm) lens.Upon exiting the spectrometer, the infrared pulseimage spectrum is focused at a pointdirectly over the front surface of M1 of the imagedisector by a 45 cm focal length(7.62cm diameter) concave mirror. With thisfocusing mirror, the image of the exitslit ofthe spectrometer is madeto fully cover M2. Mirror M2 produces seriesof images of thespectrum progressing down and towardsthe right edge of M1,while mirrorM3 producesimages of the spectrum progressingdown and to the left edge of M1.On successivereflections, a small part of the spectrumis sliced off and allowed to exit the disector.This in turn represents the first channelof a spectrum. The rest of thespectrum imageis reflected back again through the opticalarrangement, successivelydisplaced verticallyfrom one another and to the rightnear the mirror’s M1 edge, and progressivelysliced off(later in time) as the spectrum ofthe 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 thespatial spacing between the channels.Figure 4.19 showsa typical ten channel output spectrumfrom the image disector system.The outputchannels of the image disector arecollected with a 77 cm focallength mirror (7.62 cmin diameter), a50 cm focal length NaCl lens (12.7 cmin diameter) and a 10 cm focallength NaCl lens to focus the channelson a single Cu:Ge infrared detector.Several temporary mirrors areplaced in the pulse path to bypassthe image disectorand the spectrometer. This provedto be very useful before the startof the experimentwhen the visible control pulsespot and the infrared beam spotare aligned. Once aChapter 4. Laser Systems, Optical Setups, and Experimental Procedures118reflected pulse in detected by the Cu:Ge detector,these mirrors are removed and spectrumis measured.4.11.3 Calibration of the Image DisectorOptical SystemIn order to simplify the alignment procedure of the opticalsystem, we placed a goldcoated Si wafer, a Si wafer, and the GaAs opticalswitch on the same sample holder.The sample holder is mounted on a fine linear translationstage, so that each sampleor the mirror can be placed at the focus of theCO2 laser beam without disturbing thealignment of the optical system. Figure4.20 illustrates the wafers’ arrangements.Thegold-coated mirror is used to reflect theCO2 laser beam so that the laser beamcan beused for the purpose of aligning boththe spectrometer and the image disector.The spectrometer used in this experiment requiresa precise calibration against aknown wavelength. Initially, a HeNe laser=0.6328 m) is used to calibrate all the17orders from the grating against the dialreading on the spectrometer; however,over thislong calibration range, the dial reading isnonlinear with the wavelengthreading. For asmall dial range, the dial linearity is foundto be excellent. Therefore, the spectrometercalibration is performed with the aidof CW CO2 laser lines combined with the0.6328 tmHeNe laser line (over a small wavelengthrange). To obtain differentlines from the CO2laser, the Ge etalon outputcoupler temperature is adjusted sothat the laser is made tolase at three different lines: 10.611tm, 10.632 m, and 10.591 ,um. Thelasing wavelengthis checked with another calibratedinfrared spectrometer (OpticalEngineering). Twoother calibration wavelengthsof 10.125 um and 10.758pm are obtained from the16thand the l7 orders of theHeNe laser line. Figure 4.21shows a complete plot ofthecalibration of the dial readingas a function of a wavelength.A linear fit through thedata points gives a calibrationvalue of 10 A per one dial reading.Since each channel of the spectrumgoes through a different numberof reflectionsChapter 4. LaserSystems, Optical Setups, and ExperimentalProcedures0L19cmFigure 4.18: Experimentaloptical setupfor the reflectedpulses spectrummeasurement.T= temporary mirror,and G= grating.IR Pulse f 15 cmf=77cmTo DetectorSpectrometerf=50 cmM2 M3Chapter 4. Laser Systems, Optical Setups, and Experimental Procedures120Figure 4.19: A typical oscilloscopetrace of the output ofthe image disector showingtenchannels.dItSi AuMirrorGaAsTranslationAxisIRFigure 4.20:Samples arrangementChapter 4.Laser Systems,Optical Setups, andExperimental Procedures121.128002600240022002000180010.0 10.210.4 10.610.8Wavelength(micrometers)11.0Figure 4.21:Calibration curveof thespectrometerreadingagainst theCO2 laser wave-length.Chapter 4. Laser Systems, Optical Setups, and ExperimentalProcedures 122inside the image disector, it is expected that thereflectivity of the image disector opticsvaries for each one. A simple method to calibratethe reflectivity of each channel is to usea long 10.6 tm laser pulse. A Si wafer isused as an optical semiconductor switch(in placeof GaAs) to generate - 1 ns pulses at10.6 1um. These pulses have a narrow spectrum(narrower than the ones generated fromthe GaAs) which can fit in one channel.Then thespectrometer output spectrum is scanned across a160 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 shownin figure 422, The spectrum of the reflectedinfrared pulse from the GaAs optical switchis deconvoluted with the calibration curve infigure 4.22. The spacing between the channels is obtaineddirectly from the dial reading.The alignment and the calibrationof the image disector is adjusted beforethe start ofeach experiment.Chapter 4. LaserSystems, Optical Setups,and Experimental Procedures1231.2I I•— 0.8N.—Ct$1.4O0.2z0.002 46 8Channel NumberFigure 4.22: Imagedisectorcalibration curve.The errorbars are thestandard deviationof signalsfor 10 consecutiveshots separatedby 13.3 ns.Chapter 5Experimental Investigation of Infrared Reflection fromGaAs5.1 IntroductionThis chapter describes the experimentalresults and methods used to generateand tomeasure ultrafast infrared optical pulses at10.6 tim, The infrared reflection experimentsare mainly performed on GaAs semiconductorplasmas. The major experimental workand results in this chapter have been presentedin our current publications [161, 162]. Inorder to have a clear understandingof the optical semiconductor switching process(es),we have performed four types ofexperiments followed by theoretical modellingof theswitching process. We start the chapterby examining in detail theoptical and temporal response of a Si transmission cut-off switchby performing infrared transmissionexperiments. This type of experiment isundoubtly crucial in determiningthe temporalresolution of the time resolved measurements.Moreover, we present some theoreticalconsiderations of the dielectric constantas a function of the optically generatedfree-carrierconcentration and its spatial distributionand calculate the transmissionof an infraredpulse through such a distribution asa function of the carrier density at thesurface of theilluminated Si-wafer. The resultsof the experimental work and the analysisof the resultsbased on model predictions are alsopresented. Next, we present the experimentalworkdealing with the variationsof the infrared reflectivity with the photogeneratedplasmadensity. This experimentis used to examine the proper e-h densityoperation region ofthe reflection switch. Details of time resolvedexperiments used to measurethe durations124Chapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 125and temporal shapes of the 10.6 jim reflectivity pulsesare determined by two independent methods: cross-correlation and reflection-reflectioncorrelation measurements. Thelimits and advantages of the two methods are presentedand the results are discussed ingreat detail. A modifed infrared reflection modelis also presented to account for the observed time resolved experimental data. Finally, theexperimental results of the infraredreflected pulses frequency spectrums are outlinedat the end of this chapter.5.2 The Si Transmission Cut-OffOptical SwitchBefore proceeding with the time resolvedcross-correlation measurements,one needs tocharacterize the speed of the opticalswitching elements. We have developeda novelmethod for measuring the infrared pulsedurations and temporal shapes.This cross-correlation technique is reviewed in section4.10.2. Clearly, its temporal sensitivityandresolution is determined by the choiceof the active optical switching element.The choiceof a proper semiconductor switching elementis limited by the magnitudesof both free-carrier and intervalence band absorption,and the lifetime of the optically generatedcarriers. As we will show laterin this section, the magnitude of the firsttwo absorptionprocesses determine the speedof the initial transmission cut-offof the switch from fulltransmission (T= 1) to zero level(T= 0), whereas the lifetime of thecarriers determinesthe temporal persistance of the off-stateof the optical transmission switch.It is evidentthat for an ideal situation one needsto minimize the initial infraredtransmission temporalcut-off so that it is less than theoptical excitation pulse by reducingthe 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 thanthe measured infraredpulse. Ideally, the transmissionswitching element behaves as atemporal step function.Chapter 5. Experimental Investigationof Infrared Reflection from GaAs126The knowledge of free-carrier absorption cross-sectionsis especially useful in understanding the behavior of other types of high power optical-opticalsemiconductor switches.Optical-optical reflection and transmissiollcut-off switches [55] have been used extensively for short pulse generation schemes.Ill such applications, one relies on boththedegree of free-carrier absorption and thelevel of reflection of infrared radiationto operate the Si cut-off switchin the THz range. Rolland and Corkum[55] have used Sias a transmission cut-off switch wherethey managed to gate high-power130 fs pulsesat 10.6 pm. The authors calculated the transmissionof the switch as a function oftheoptically generated carriers; however, theydid not provide the necessary experimentalwork to optimize the switch,such as an investigation of the type ofdoping needed forfaster operations.In our current work, we were interestedin using this switch to perform time-resolvedcross-correlation measurements. In orderto model the performanceof the switch, detailedknowledge of the dielectric constantc= Er+cj, in particular its imagmary component,j, arising from free carrier and possibly intervalenceband absorption, is important.We,for example, are especiallyinterested in the response timeof a Si transmission switchfor 10.6 pm radiation after irradiationwith 0.49 Ps, 616 nm laserpulse, in which casethe magnitude of,critically affects the switching speed[161]. The main question tobeinvestigated is: can the switch transmissionbe turned off on a timescale less than theexcitation visible pulse?In general the absorption cross-sectionfor such photoexcited free carrierSi-plasmas isinferred from measurementson bothp- and n-doped samples in which the infrared wavelength and magnitude ofthe reflectivity minimum is determinedas a function of carrierconcentration [163]. However,it is not at all clear whetherthis inference is justifiedconsidering that both electronsand holes are photogenerated withsignificant energies abovethe band minima leadingto highly elevated carrier andlattice temperatures.It wouldChapter 5. Experimental Investigation of Infrared Reflection from GaAs127therefore be desirable to conduct measurements of the relevantparameters directly onphotoexcited free carriers. Here, we present the results oninfrared pulse transmissionexperiments which permit such measurements. The results showthat at 10.6 ,um, in contrast to intervalence band absorption, free-carrier absorptiondominates the absorptionprocess [163]. From these experiments, the momentum relaxationtimes can be determined. Also, the experiments reveal the interestingfact that these relaxation times areshorter by a factor of 0.4 if the carriers are generatedin n-type as compared to p-typeSi.5.2.1 Theoretical ConsiderationsThe model treatment of the physical processesinvolved is very simple. Here,severalassumptions are introduced to simplifythe physical situation. We begin bytreating theoptically generated plasma in Si as being an inhomogeneousplasma which is subjected to10.6 im radiation. It is appropriate to treat the situationas a one dimensional problem.This is justified because the diameter ofthe excitation area on the Si surfaceis muchlarger than the absorption skin depth of the visibleradiation. Moreover, the spatial profile of the plasma in the transverse directionis assumed to be uniform. The modeltreatsthe absorption of the 10.6 ,tim radiationto be proportional to the free-carrierconcentration; this situation is similar to free-carrier absorptionin highly doped semiconductors[164]. Since interband transitions are notallowed at this wavelength, theresponse of themedium to the applied electromagneticfield can be characterized by the Drudetheory forthe frequency-dependent dielectricfunction. The Drude model of freecarriers has beenvery successful in describingthe optical properties of semiconductorsafter quantum corrections for intervalence bandabsorption have been made [164].Combining the effects ofelectrons and holes [163]and transferring averages over the carrierenergy distributionsto that over the carrier relaxation times[165], we write the real and imaginaryparts ofChapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 128the dielectric constant as:/4irne2 w2<r0>‘\I (5.1)\fbrn*w1+w<ro>)and/4irrie2 w<r0> A= b I + crVbn) . (5.2)\mw1+w<r0> \/7t)Hereb=11.8 is the background dielectric constant for thebulk Si and0vbis theintervalence band absorption cross-section. For carrier densitiesless than1020cm3,thecarriers effective masses may be taken to have theirlow-density values [166](m* =m’+mj’, with m= 0.26m0 and m = 0.38m0)[163], <T0> is the mean momentumrelaxation time for the optical process, andubthe intervalence (heavy to light hole)band absorption cross-section. The electrons andholes are assumed to have the samerelaxation time which is taken to be independentof the energy of the carriers. Also thedependence of the dielectric function onthe lattice temperature is ignored inthis model.We now define a critical densityn: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 ofboth free-carrier and intervalence bandabsorption: a =afc + a with aj = 1/(w < T >), whereafc and ab are the first and second termsof equation 5.2, respectively.The only free parameter in this modelis the free-carrierabsorption cross-section which is dueto a combination of both electrons andholes and isconsidered to be constant over the rangeof the plasma e-h density usedin this experiment.In the experiments to be describedlater the free carriers are producedby absorptionof photons in a 490 fs, 616nm laser pulse; the generation rateis taken to be a deltaChapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 129function in time as compared to the experimentaltime scale. This pulse generates adensity distribution in a direction perpendicularto the illuminated Si-wafer surface atz= 0 of the form:ri(z)=(55)The absorption depth, at an excitation wavelengthof 616 nm is measured tobe 3 m [167]. Due to this large depth,ambipolar diffusion has very little effectonthe density profile over time scales ofinterest 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. Augercoefficients of Si are measured to be9.9x1032cm6s1for p-type, 2.8x103’cm6s1forn-type, and 4x103’cm6s1for highlyexcited Si [171]. Therefore, by using amaximum plasma density of 7x10’9cm3,we canobtain recombination times of 2 xs for p-type, 7.3 x 10’° s for n-type,and 5.1 x10_lUs for the highly excited Si, respectively.All three are several orders of magnitudeslargerthan the experimental time scale.Two-body recombination time is measuredby usduring the experiment and is foundto be of the order of 2x108 s. Figure5.1 shows thetransmission cut-off for a CWlaser beam at 10.6 im just after excitationwith the 0.49ps pulse. The photograph shows a sharpinitial drop in the transmission followedby atransmission-recovery tail lasting for35 ns.We now proceed to calculate thetransmission of a normally incidentpulse of belowbandgap photon energy (wavelengthA) through the photoexcited Si-wafer.We normalizethe density as 1 =n/ne and write (v) =b[1— ii(1 — ia)]. The amplitudereflectivityand transmission from a discontinuityin the dielectric functionfrom to2are givenby:56Chapter 5. Experimental Investigationof Infrared Reflection from GaAs 1:30Figure 5.1: Transmission signal temporalrecovery of the P-typeSi 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 afinely layered medium where theelectric field is constantin each region. We considera small density stepof At’ at adensityt’qinside the wafer witha reflectivity of:Tq= (t’q —At’)(5.10)+(t’q— Av)We now approximate the exponentialdensity profile v0et’ byone consisting of a largenumber m of density stepsAt’ = zí0/m. Propagatingfrom one step to the nextthe waveChapter 5. Experimental Investigationof Infrared Reflection from GaAs131suffers a phase change of:A/3q=(5.11)The transmission of light not reflectedfrom 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 casem > 50), then the magnitude ofthe rqis much smaller than one. With this choiceof large m, one can ignore the higherorderterms in equation 5.12, and equation5.12 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 densityprofile (reflectivityP2)is reflected from the wafersurface at a potentially largereflectivity —r0 and propagatesagain through the carrierdistribution:rn-i/ 1P2 =rqexp (2iA/3). (5.16)q=O\j0/For this part of the incidentradiation the transmission coefficientis:t2 = —r0tp2(1 —p)ei.(5.17)Subsequent reflections fromthe profile can be neglectedif a > 0.02. Thetotal transmission coefficient is then t = t1+t2. Thus the intensitytransmission coefficient Tcanbe calculated:Chapter 5. Experimental Investigation of Infrared Reflection fromGaAs 132T=It0(1— pi)(l— rop2)et2.(5.18)The described calculation can be simply performedusing common math-software ona PC. The transmission T is calculated as a functionof surface free-carrier density v,for various values of a. For comparison with experimentsit 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 calculatedvalues of a = 0.1, 0.2,0.3,and 0.5. The transmission curves are normalizedto the transmission coefficient atzerophotoexcitation, T0.5.2.2 Transmission Cut-off Results at10.6 sum,The infrared transmission results are measuredwith the optical setup describedin Chapter 4 for the cross-correlation setup.The details of the experimental procedureandsample preparations are also outlinedin section 4.10.2.In the first part of each experimental seriesfor a given Si sample, we recordedthetransmitted infrared energyas a function of visible laser lightenergy, while the pumppulse blocked off the Si-wafer. Theseproved to be necessary in orderto obtain accuratemeasurements of the photoexcitedplasma densities. The results,shown in figure 5.3for two Si samples indicate the variationof the infrared pulse energyas a function ofcontrol pulse energy incidenton the GaAs reflection switch. Thestraight lines throughthe data points are linear regressioncurves and serve as referencevalues for the analysisof each experiment. Figure 5.3 shows thata certain control minimum pulseenergy, I, isnecessary to generate a measurableinfrared signal. Above this interceptthe energy of theinfrared signal increases linearlywith the control pulse energy overthe range used in thepresent experiments. As it willbe discussed later in section5.3.1, the intercept energyChapter 5.ExperimentalInvestigation of InfraredReflectionfrom GaAs1331.00.80.6C0.40.20.0—2.0Figure 5.2:Calculatedrelativetransmissionfor 10.6 ,umradiationthrough aphotoexcitedSi wafer asa functionof normalizedfree-carriersurfacedensityn0/nfor fourvalues ofof a {cr=0.1 (uppermost),0.2, 0.3, and0.5 (lowest)].—1.5—1.0— 5. Experimental Investigation of Infrared Reflection from GaAs134corresponds to that necessary to generate the critical free-carrier density of1019cm3 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 andis independent of theoptical condition of the investigated Si wafer, its determinationcan serve to calibratethe individual experiments with respect to one another. Inthe second part of eachexperimental series, the transmitted infrared pulse energy isrecorded at pump pulseenergies varying over several orders of magnitude.The pump intensity, Ii,, in arbitraryunits is calculated by multiplying the monitored visible laserenergy with the transmissioncoefficient of the neutral density filter stack placed inthe pump beam.The relative transmission T/TO is determined by dividingthe monitored infraredenergy by the reference value at the same visiblelaser energy as measured iii part oneof the series. The resulting data are averaged overat least 15 points with a standarddeviation of the order of10% in pump intensity bins of I,±5%. In order to comparethe results with the theory of the previous sectionthe average values of T/TO are plottedas a function of log(I). The photoexcited free-carrierdensity 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 befitted to the data and the best fitting valueofa can be determined. Figures 5.4, to5.7 show the results for the four investigatedSisamples. The fitted theoretical curvesdetermine a to + 25%. For the basicallyintrinsic(p-type) sample of figure 5.4 and the p-typesample of figure 5.5 curves witha = 0.2provide the best fit, while for bothn-doped samples (figures5.6 and 5.7) a value of a= 0.5 is determined. Using the calibration procedureof equating the intercept energyI of the reference curves describedin the previous paragraph, we canalso compare thepump energies‘pCrequired to generate the critical free-carriersurface density [log(t’0)=0]. By performing this cross calibration, wefind that‘PCfor the samples with a= 0.5 is(1.7±0.5) times larger than that for samples witha = 0.2. This indicates a relationshipChapter5. ExperimentalInvestigationof InfraredReflection fromGaAs1354030d20ce100050Figure 5.3: Infraredpulse intensityhrdetected for twodifferent Si wafersat zero photoexcitation asa function ofvisible laserpulse intensityincident onGaAs reflectionswitch. The solidline is a linearregression fittedto the data points(empty circles)upto I 34, andthe dashed lineis a linearregression throughthe solid circles.10 203040Ivs(arb.u.)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs136between 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 curvesin figures 5.4 to 5.7indicates that for a given value of a the model developedin section 5.2.1 provides a gooddescription of the transmission of an infrared light pulse throughcrystalline Si in whichfree carriers have been generated by absorptionof above band gap radiation.Thus the imaginary part of the dielectric constant can be accuratelydetermined 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 absorptionto the dielectric function is insignificant compared to free-carrier absorptioncontribution [163, 164], and the intervalenceband absorption term can be ignored.Changing a does not altern.On the other handn 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 thecritical plasma density depends onthe magnitudeof the free-carrier absorption term(or the carrier type). Thus ifthe absorption is predominantly determined by free-carrierabsorption, one can calculatethe absorption crosssection for each a:a =(5.21)Chapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs1371.00.80.6C0.40.20.0—1.5Figure 5.4: Relativetransmission coefficientfor an infrared laserpulse through basicallyintrinsic Si (p-type concentrationof 1.6x1014cm3)as a functionof free-carrier surfacedensity generated byphotoexcitation.The full curve is thebest fitting theoreticalprediction to the datapoints at a = 0.2.The theoretical curvefor a 0.5 is alsoshown(dashed).—1.0— 5. ExperimentalInvestigation of Infrared Reflection fromGaAs 1381.00.80.6C0.40.20.0—1.20.6Figure 5.5: Relativetransmission coefficientfor an infraredlaser pulsethrough basicallyintrinsic Si (p-typeconcentration of2.6x i0’ cm3)as a function offree-carrier surfacedensity generatedby photoexcitation.The full curveis the best fittingtheoretical prediction to the datapoints at c =0.2. The theoreticalcurve for a= 0.5 is also shown(dashed).—0.60.0iog(no/ne)Chapter5. Experimental Investigationof Infrared Reflection fromGaAs1391.21.00.8CH0.40.20.0—2.00.5Figure 5.6: Relativetransmissioncoefficient asin figure5.4 for n-typeSi concentrationof 4.9x1O5cm3). Thefull curve isthe best fittingtheoreticalpredictionto the datapoints at a= 0.5. The theoreticalcurve for= 0.2 is alsoshown (dashed).—1.5—1.0—0.50.0log(n/ne)Chapter 5. Experimental Investigation of Infrared Reflection from GaAs1401.00.80.6HH040.20.0—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 transmissioncoefficient as in figure 5.4 forn-type Si concentration of6x10’5cm3). The full curveis the best fittingtheoretical prediction tothe data pointsat a = 0.5. The theoreticalcurve for a= 0.2 is also shown (dashed).Chapter 5. Experimental Investigation of InfraredReflection from GaAs 141For the p-type samples we obtain cry, = 1.1 x1016cm2 arid for the n-type ones= 2.3x10’6cm2. These cross sections are theresult of phonon scattering of bothhot electrons in the conduction band and hotholes in the valence band, in contrastto cross sections determined from absorption measurementsof doped samples withoutphotoexcited free carriers. For p-dopedSi, in which case the absorption arisesdue tohole relaxation in the valence band, a valueof crh = 1.3 x10_16cm2 has been reported[172] whilst for the case of absorption dueto electron relaxation in the conductionbandin n-doped Si, a value of o. = 3.2x10’6cm2has been measured [163]. The differencebetween0hand°eis understandable due to the differenttypes of carriers involvedinthe absorption process. However,in our experiments the carriers are photogeneratedby the pump pulse, hence the numberof the photoexcited electrons andholes are equaland one should measure a combined free-carrierabsorption cross-section dueto the holesand electrons. The dopant concentrationsare very small compared to the photoexcitedcarrier concentration and thereforeshould have an insignificant contributionto the absorption process. However, we have foundthat the absorption process dependson thetype of dopant. Presently, it is notclear to us what the effects ofthe dopants are on theabsorption mechanism. The measurementof a also permits an estimateof the averagemomentum relaxation time< r0 >. Taking the frequency forCO2 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 fromthese results that p-type siliconhas higher < T0 > thann-type. This is in contrast tothe experimental results presentedin reference [163] fordoped silicon. Considering the verylow doping concentrations ascompared to the criticaldensity 1.8 x 10’s cm3)of the investigated samples, againthis significant differenceof < r0 > betweenp- and n-doped Si is rather interesting.To sum up, we have measuredthe free-carrier absorption of10.6 im radiation in Si ofvarious dopings in whichfree carriers have been generatedby absorption of photonswithChapter 5. Experimental Investigation of Infrared Reflection from GaAs142above band gap energy. By fitting experimental measurements to theoreticalpredictionsfor the absorption of an infrared pulse propagatingthrough a photoexcited e-h plasma,the absorption cross-sections and the momentum relaxationtimes are calculated. We findthat in contrast to p-doped material, n-doping has a significant effect onthe absorptionprocess, increasing the momentum relaxation rate and thus the absorptioncross-sectionand the critical density.We would like to point out that because the free-carrier absorptioncross-section islower in p-type Si than in n-type Si, it is desirableto 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 theincident energy fluence (or the plasmadensity) is much steeper than that of n-typeSi, then for a given finite excitation pulseduration, a full switch transmission turn-offcan occur at much lower plasma density.Such a condition can be satisfied during the risetimeof the 490 fs excitation pulse. Inorder to gain an insight on the speed of thetransmission cut-off switch, we have toconsider how the photoinjected plasmadensity evolves over time. The time evolutionofthe initially generated e-h plasma corresponds to theexpression: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 calculationsn0 is set to the experimental value of6n. Here,we assume that the critical densityis reached at the peak of the excitationpulse. Fromequations 5.18 and 5.22, we can calculatethe transmission cut-off time ofthe Si switch.The results of the calculationsfor p-type Si are presented in figure5.8. It is clear fromthe figure that the terminationof the transmission occurs in a timeof approximately0.49r. In our experiment this correspondsto 240 fs which is fast enough to beused toperform time-resolved cross-correlationexperiments on the reflected pulsesfrom a GaAsChapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 143switch.5.3 Ultrafast 10.6ttmReflectivity Pulses from a GaAs SwitchIn this section we report on the results of ultrafast pulsegeneration from GaAs semiconductor plasma. In Chapter 3, we outlined thebasic underlying theory. We have shownthat, in accordance with a simple diffusion modelwhich describes the temporal behaviourof the switching process, it should be possible to producepicosecond or shorter pulses at10.6 m. The pulse width was predictedto be a strong function of the excitationenergyfluence,Of interest are the variation of the reflectedpulse energy with the amount of theexcitation energy fluence and the variationsof the pulse width with the level oftheexcitation.5.3.1 Time-Integrated Infrared ReflectivityWe have performed a series of experimentsto investigate the behaviourof the time-integrated infrared intensity asa function of the visible pulse excitationenergy fluenceincident on the GaAs switch.This allows us to determine thevisible irradiation levelrequired to induce a measurableinfrared reflection change in theGaAs switch. Thistype of experiment is also essential toperform because the time-integratedreflectivityshould provide an initial checkon the validity of the infrared reflectivitymodel proposedin Chapter 3. That is, time-resolvedmeasurements are usuallydifficult to interpret.However, by integrating the infraredreflectivity pulses calculatedfor various initial e-hplasma densities, one shouldbe able to fit the calculationsto the experimentaldata.The basic experimental setupand procedures are outlinedin section 4.9. Becauseofthe sensitivity of the model tothe photoinjected carrierdensity, to carry out thisstudyChapter 5. ExperimentalInvestigation of InfraredReflection from GaAs1441. .‘I I IO.800.60.4•0.20.0I0.0 0.10.2 0.30.4PicosecondFigure 5.8:Calculated transmissionof p-typeSi as a functionof time.Chapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 145we must first determine the initial e-h photoexcited carrierdensity. Figure 5.9 shows aphotograph of the observed time-integrated reflectivity pulsemeasured simultaneouslywith its corresponding visible excitation pulse. The integratedtemporal profiles of thesepulses correspond to the time-integrated reflectivity and the excitationenergy.A typical result of the experimental data is presentedin figure 5.10. The figure showsthe data point for each single shot, and the scatterof the data points is indicative ofthe experimental uncertainty. The horizontal scaleof 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 meaningfulonly for a well-characterized laserbeam profile.One way to estimate the carrier density is by knowingthat the maximum possibleexcitation energy is 0.2 mJ, which isdeposited into a 0.5 mmx3 mm spot onthe wafer atan incidence angle of 80°. This allowsthe calculation the maximum energyfluence. Byusing the Fresnel reflectivity equation forS-polarized light, the above angle of incidence,a refractive index of 3.4 and an absorptioncoefficient of-y= 4.5x104 cm1 at A= 616nm, it can be shown that20% of this fiuience is absorbed by the wafer andthus generatesfree carriers. The product of thisabsorbed fluence,Fh,,and the assumed quantumefficiency of unity gives themaximum possible free-carrier density,om,at the wafersurface, which would result in the absenceof any recombination or diffusion mechanismsacting during the time scale ofthe generating pulse. This value is calculatedto beom2 x1020cm3. This method for obtainingthe plasma density can providea goodestimate only for high excitation levels2n). A better estimate of the plasma densityaround the critical density and over a widerdensity range can be obtainedfrom a simpleexperimental procedure. By plottingthe measured time-integrated reflectivitysignal asa function of ‘low’ visible excitationenergy, we obtain a linearrelationship. The leastsquare fitted line through these pointsintercepts the excitationenergy horizontal axisChapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 146Figure 5.9: Typical ultrafastreflected infrared pulses (left) andtheir correspondingexcitation visible pulses(right). The bottom photographis presented to illustrate thereproducibility of theexperimental signals.Chapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 147at n. We have used the latter method throughoutour experimeutal analysis to obtainmore accurate values for the carrier density.We normalized the maximum excitation energyto 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 rangeof 1.5 7Fph/flc<_5 the reflectedinfrared energy increases linearlywith the excitation energy. For excitationenergieswith 7Fh/fl>6 the reflected infraredenergy starts to saturate and remains effectivelyconstant for7Fh/n>8. Integration of the calculated reflectivity pulses fromthe modelpresented in Chapter3 shows that the experimental data do not agreewith the modelpredictions. Our calculationsshow that an increase of an initial plasmadensity fromr’/n= 1 to n/n= 6 results inan integrated reflectivity pulsen-i180 times larger thanthe one calculated at the criticaldensity. This is just a representationof the width of thereflectivity pulse. However,the experimental results (see figure5.10) indicate that theintegrated reflectivity is only n-i13 times its value at the critical density.Moreover, theobserved saturation of thetime-integrated signal cannot beobtained with such model.Contrary to our observations,the calculated time-integratedsignal increases stronglywith initial plasma density. Obviously,the saturation of the signal is aclear indicationthat the reflectivity pulse widthsremain almost unchanged whenthe GaAs switch isoperated in the region7Fh/n > 6. The temporal behaviour of the reflectivitypulsescannot be explained by diffusionmodel; a mechanism whichis more significantat highplasma densities mustbe included in the calculations toaccount for these observations.5.3.2 Reflection-ReflectionCorrelation MeasurementsHere, we report the first experimentalresults on time-resolved ultrafastreflection fromoptically induced transientplasmas. As mentioned previouslyin the discussion of thereflection-reflection correlationtechnique (section 4.10.1), thistype of experiment is notChapter 5.Experimental Investigation ofInfrared Reflection fromGaAs 1481001 I -____00090- 0GDOO0008000000070 0600d5000C40• 3020Ji10-00 24 68 101214161820yFph/nFigure 5.10:Experimentalresults of thenormalized timeintegrated reflectivityas afunction thenormalized free-carrierdensity.Chapter 5. Experimental Investigation of Infrared Reflection from GaAs149sensitive to the infrared pulse shape; however, oneshould be able to obtain an overallpulse duration, which may help to explain the observedtime-integrated reflection saturation at high excitation fluences. That is, if theinfrared reflected pulse duration doesnot change with the level of photoinjected carriers, then thiscan be easily detected fromthe measurements of the full widths at half maximumof the durations of the reflection-reflection correlation signals.Several experiments are performed at variouslevels of optical exciation. Typicalresults from the reflection-reflectioncorrelation measurements are presentedin figures5.11, 5.12, and 5.13 for-yFh/nc= 3, 5, and 7, respectively. Here, the correlation signalis normalized to a reference reflection obtainedwhen the excitation pulse on thesecondswitch is blocked-off and the transmissionthrough it is detected. The data pointsareaveraged over at least 10 shots, andthe error bars are an indication ofthe standard errorof the experiment.The time delay t=0 in the figures corresponds to the peak overlapbetween thereflected infrared pulse from the firstGaAs switch and the peak of the visibleexcitationpulse at the second GaAs switch. The measuredcorrelation signal representsthe widthof the dominant temporal featuresin the infrared pulse. The reason for theasymmetry ofthe reflection-reflection measurementsis attributed to an experimentalerror in the delayline scan. For long time scansgreater than 20 ps, the criticalalignment of the infraredand the visible spots changesslightly. The asymmetry givesus information abouttheuncertainty of the measurements.This uncertainty is estimatedto be + 3 Ps.Even though the graphs correspondto different excitation energyfluences, all ofthe figures show the effectivecorrelation width to be 17Ps at half of the full widthhalf maximum. The experimentsindicate that the infraredpulse width seems tobeindependent of the plasma densityabove Evidently, this effectsupports the resultsobtained from the time-integratedreflectivity experiments. Thereflectivity pulse widthsChapter5. Experimental Investigationof Infrared Reflectionfrom GaAs1500.30I •CZ 0.240.18oC)0.12Q)0.060.00—60—3003060Delay(ps)Figure 5.11:Reflection-reflectioncorrelationsignal foran excitationfluence corresponding to-yFh/n= 3.Chapter 5. ExperimentalInvestigation of Infrared Reflection fromGaAs 1510.20C.Z0.16c:5C(-)—60060Delay (ps)Figure 5.12:Reflection-reflectioncorrelationsignal for an excitationfluence corresponding to7Fh/rIc= 5.—3030Chapter5. ExperimentalInvestigation ofInfrared Reflectionfrom GaAs152Z 0.24030II ‘I0.120.180U0.06a)0.00I—50—2502550Delay (ps)Figure 5.13:Reflection-reflectioncorrelationsignal foran excitationfluencecorresponding to7Fh/n= 7.Chapter 5. Experimental Investigation ofInfrared Reflection from GaAs153do not scale with the calculated pulse widthsas indicated by the diffusion model.Unfortunately, with our limited infraredlaser power and detection sensitivity,experiments at7Fh/ri < 2 are not possible, since the level of the reflected signalto thebackground noise is high enoughto wash out the reflection-reflection correlationsignal.With our reflection-reflection correlationtechnique it is not easy to arrive atan exactpulse shape by these measurements alone.Of importance to our analysisis the time thatthe plasma density takes to reachthe critical density. This will bediscussed in the nextsection.5.3.3 Cross- Correlation MeasurementsIn order to understand the natureof the disagreement between thediffusion based infrared reflectivity model and theexperimental results, one needsto know the exact shapeof the reflected infrared pulses,so that the time evolution of theplasma density canbeinferred from the temporal shapesof the reflectivity signals. Ithas been shown before[84, 85] that the infrared reflectivityof a photoexcited GaAs wafer showssome significant variation with surface free-carrierdensity n0. It has a minimumwhenn0/n equals(— 1)/€: E is the dielectricconstant of the bulkGaAs. At n0=n the reflectivityhas a sharp maximum. Justabove n it has a minimumand from then on increasesmonotonically with n0. Themagnitude of the featuresat n0/n= (— 1)/c and 1 depend on the magnitudeof the free-carrier absorption.It is therefore expected thatthereflected infrared pulse willshow some significant temporalvariation as n0 decays fromits maximum initial value. Asshown in section 4.10.2,these measurements display“jr=fR(t’)dt’ and its slope thereforedetermines the magnitudeof the reflectivity.We performed severaltime-resolved cross correlationmeasurements over a widerangeof pump intensities whichwe relate to7Fh/n of figure 5.10. Throughout the experimental work, we selected afixed excitation energy rangeand we studied the reflectedinfraredChapter 5. Experimental Investigation of InfraredReflection from GaAs 154energy as a function of the time delay between theinfrared and the optical excitationpulses. Since the detection sensitivity depends on detailsof the optical alignment and islikely to change from day to day, the experimentswere performed in the following way.Before realignment and laser retuning became necessary,it was possible to conduct twoexperimental sequences. By placing two differentsets of neutral density filters into thepump beam, the two experimental sequences coveredtwo different ranges of7Fh/rI ofwhich the first one was chosen to fall intothe linear part of figure 5.10. At the start,at the end, and at various times during each experimentalsequence, the control beamoperating the Si cut-off switch wa.s blocked-offand the measured infrared energy wasdisplayed as a function of the monitored energy toderive reference signals. A least squarefitted line was placed through the reference data pointsof the first sequence. Setting theline intercept of the pump energy axis equalto7Fh/n= 1 normalizes the pump energy.We have found that it is necessary to performthe ‘reference’ experiment at the beginningand at the end of the temporal scan.At each optical delay line setting, which determinesthe cut-off time, the average ofat least 30 infrared energy signals measuredfor the same pump energy was determinedand normalized to the reference infraredsignal for the equivalent7Fh/n. Due to theimportance of this type of experiment,we have performed over 40 experimentscoveringa wide range of experimental conditions.The basic features of the experimentalsetupare discussed and outlined in section4.10.2. The optical and data collectionsystemsare constantly improved throughout thiswork. Figures 5.14 and5.15 show the resultsfrom two experimental days for four valuesof ‘yFh/n (0.7 and 2 in figure 5.14,3 and 15in figure 5.15) which are representativeof all experiments performed. Theydisplay thenormalized infrared energy‘norm,as function of cut-off delay time.Obviously towardsthe end of the reflected infrared pulse‘normhas to approach the value of 1. Thedetectedinfrared signals for figure 5.14 arequite small and as a result thestandard error perChapter 5. Experimental Investigationof Infrared Reflection from GaAs155point is of the order of 20%. The best fitting curvesthrough the points have a constantslope indicating basically a constant reflectivityafter photoexcitation over theperiodexamined in the experiments. After 50-ps,Inorm is still less than 0.2 which indicates thatthe reflected infrared pulses have a durationof several 100 ps. For the experimentsoffigure 5.15 the situation is quite different.The standard error per point duringthe first40-ps is 4% increasing to7% at times later than 60 Ps. At the end of theexaminedperiod of 100 ps, the slope, and thus the reflectivity,has decreased to zero within themeasurable accuracy. Fitting curvesthrough each of the two setsof data points andmeasuring their slopeas a function of time results in normalizedinfrared reflectivitypulses of the form shown in figure5.16. The most prominent features ofthese pulses arethe unresolved large transient maximumof <0.8 ps duration at the timeof the pumppulse and the minimum observed28 Ps later which we identifyas the reflectivity minimumat n0/n=(— 1)/c.Also remarkable is that thenormalized infrared pulses forthe two energy fluencesdiffering by a factor of five,up to t= 34 ps, are basicallyidentical. However, sincethereference signals at7Fh/n= 15 are three times larger than those at7Fh/n= 3 theactual reflected intensity for bothpulses differs by a factor ofthree.5.3.4 Discussion of theTime-Resolved ResultsTo describe the experimentalresults, we will consider twoprocesses (diffusionand recombination) which determinethe time evolution of the plasmadensity. Our previouscalculations show that the effectsof surface recombination onthe time evolution oftheplasma density is unimportant[84, 85] and hence is ignored inthe following calculations.Carrier diffusion is knownto increase with carrier temperatureand decrease with latticetemperature; moreover,the diffusion coefficient isalso shown to have astrong dependence on the carrierdensity above a certainvalue where carrierdegeneracy is reachedChapter 5. ExperimentalInvestigation ofInfrared Reflection from GaAs1562— I I I I II I I I l’tIIIlII![I000o0000.10000000000. 000000000000000000000.00 10 2030 4050time (ps)Figure 5.14:Cross-correlationsignal as afunction of timefor7Fh/n= 0.7 (solid),2.0(empty).Chapter 5.Experimental Investigation ofInfrared Reflection fromGaAs1571. •I II III•II. Q00•• 0008 •••0•••• 000.6•Q000•o.4..;0.40.00 10 2030 40 50 6070 8090 100time (ps)Figure 5.15:Cross-correlationsignal as afunction of timefor7Fh/n= 3.0 (empty),15.0(solid).Chapter 5.Experimental Investigationof Infrared Reflectionfrom GaAs1585II40 10 20 3040 50 60 70 8090 100time (ps)Figure 5.16:Reflectivitypulses as a functionof time for‘yFh/n=3 (solid), 15(dash-dot),and 2 (dash).Chapter 5. Experimental Investigation of InfraredReflection from GaAs 159[173]. The experimental results show that oncethe initial carrier density surpasses5n,the integrated reflectivity saturates withincreasing excitation fluence. This cannotbeexplained by diffusion of the free carriersalone, In fact, using various models forcalculating the diffusion coefficient [173]in the reflectivity calculations show that the effectofthe diffusion coefficient on the decay ofthe surface density fromOmto n, is negligible.The time that it takes the reflectivityto reach a minimum determinesthe time neededfor the density of the photoexcited carriersto reach the critical density. This timeismeasured to be 28 ps; by thenthe photoexcited carriers have cooledto the latticetemperature and thus temperature effectson the diffusion coefficient are insignificant.Our calculations show that diffusionis important for carrier densities belowthe criticaldensity. Hence, the simplestapproach of treating the diffusion coefficientas temperatureand density independent is adequatein the following analysis.One would expect that the decay of thefree-carrier surface density,n0, during thefirst hundreds of picoseconds after photoexcitation,is dominated by diffusion, whiletherecombination processes catch upin nanosecond time scales.In order to study theevolution ofn0(t) due to diffusion one hasto solve the diffusioll equation.However, sucha solution shows [84, 85] that the free-carrierdensity as a function ofdistance from thesurface, z, quickly resembles thatof a gaussian distribution. Sincea gaussian profile is asolution to the diffusion equation,we can assume for the presentthat 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 thediffusion equation (3.54),weobtain a differential equationdescribing the time evolutionof plasma density:= —2D-y3.(5.24)Chapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 160Then takingn0(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 criticaldensity 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 reflectedenergy,‘jr,pulses of figure 5.10 for7Fph/fl> 3 is generated during this time. One can estimate for thesepulses,jR(t)dt < R> t. (5.27)The average reflectivity< R > increases also, but not rapidly with7Fh/n. At thevery least, one would expectin the presence of diffusion only,that the pulse,Ii,.,of figure5.10 like t, increases with the squareof the fluence. Figure 5.10 showsthat this is not thecase, instead I initially increaseslinearly with7Fh and then quickly saturates. Figure5.16 indicates that t, also saturatesat “-‘ 25 ps. In the caseof carrier diffusion, one wouldhave expected for ‘yFh/ri=15 a time t, of the order of one nanosecond.In order to show that normal Augerrecombination at the given ratecannot explainthe observed saturation, we examineda hypothetical situationin which only this processdetermines the decrease ofn0(t). The time t is givenby the solution to equation3.48:= 14{1 —(n/-yFh)2}ns. (5.28)In order for this time (dueto Auger recombination)to be comparable to t,due todiffusion only, it requires-yFh/nc.--’ 48. Therefore,if only diffusion andnormal Augerrecombination determinen0(t), the Ii,. of figure5.10 should increase with(7Fh/n)2overthe range shown and wouldonly be expected to saturateat twice the maximumvalueChapter 5. Experimental Investigationof Infrared Reflection from GaAs161attained in this experiment. Also t shouldoniy saturate at ns-time scales.Clearly, anadditional, much more rapid recombinationprocess governs the dynamics ofhigh densityphotoexcited free carriers. Thismechanism should be responsiblefor the saturation ofthe time-integrated reflectivity signal andfor the observed t being densityindependent.That is, a recombination processwhose recombination rate dependson the photoexcitedplasma density should be considered inthe analysis.We can model our experimental resultsif we assume a decay processof the same formas Auger recombinatioll at a rateof 1= 1.9x1028cm6/s. This could, for example,bea two-body recombination process forwhich the decay rate is nearlya linear function offree-carrier density.5.3.5 Modeling of Free-CarrierDensity and ReflectivityIn order to model the free-carrierdensity development one needsto know the excitationpulse shape. For mathematicalconvenience, we assume that thispulse has the form:P(t)=2yFpexp{_(t/rp)2}.(5.29)For r= 0.49 ps this pulse hasthe same width as our laserpulse. In term of normalizeddensities v= (n/ne) andf= (7Fh/n), we write the time evolution of thenormalizedplasma density as:9v t= 2f—-exp{—-yz — (t/r)2}+D—- — tw3.(5.30)Here ic = Fn, and for I’ we takethe rate from the previoussection. The first termonthe right hand side resultsfrom the e-h generationrate, the second termarises from thediffusion of the carriers,and the last term describesthe recombination process.In orderto perform numerical integrationswe simplify the diffusionterm. If the distributionhasa gaussian shape of the formv =0exp{—[z/d(t)]2},wherev0 is the surface density, thenChapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 162the diffusion term simplifies to:={2[z/d(t)]2- 1}v(t,z)(5.31)9z d(t)withd(t)= /(t)(5.32)Here N(t)(= j° v(z)dz) is the total normalizednumber of free carriers. We approximatethe diffusion term by this form andnow can numerically integrate thedifferential equationat each position z with the initial conditionv(0, z)= 0. After each time step weintegrateover the profile to determine d(t).In performing the calculations onehas to take intoaccount that the density variesmost rapidly near the surface andat early times. Wechose a dimensionless length coordinatex = exp(—7z) and dividedthe interval0x1into 100 equal steps. The time intervalsprogressed with step numberp asi0—p3.Figure 5.17(a) shows the resultingdensity profiles at various timesfor -yFh/n= 10,and figure 5.17(b) indicates the temporalvariation of the surface densityfor the samecase. Profiles for all values of7Fh/n3are quite similar and reach,= 1 at the sametime. The only difference exists inan increase of the sharp initialsurface density featureand an increase of the widthof the density profile as the photonflux is increased.Next we proceed to calculatethe reflectivity for infraredradiation incident withBrewster’s angle if v=0. We use the Drude model forthe 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 InfraredReflection from GaAs 163Then the amplitude reflectivity from thesurface is given by [84, 85]:r0(t) =X(535)Here we assumed that the imaginary partof the dielectric function, (t), is a functionof time. It arises from the free-carrierabsorption and is a function offree-carrier temperature. In order to include the contributionto the reflectivity arising from the densityprofile inside the wafer, we make theuse of density steps introduced previously.Similarto the previous approximation made forcalculating the transmissioncut-off, the plasmalayer is treated as a multilayered structureof variable density. Each layeris consideredto have a homogeneous density profile.Taking the density at stepnumber m as1mweintroduce: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 reflectivityof 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 densitystep in the incident directionis (1— rm) and it is(1+ rm)for propagation in the oppositedirection.In order to find the contribution fromthe whole profile we also haveto consider thephase change,/3mdue to the propagation throughthe different optical pathsof individuallayers. Writing for a length/Zm of a plasma layer m:Ib/3m = ko/.Zmf bm_i(t) (5.39)one finds for a density profilereflectivity:m mp(t) = exp(2ii3) fl[i—r?_1(t)}ri(t). (5.40)m1=1 1=1Chapter 5. ExperimentalInvestigation of InfraredReflection from GaAs 1640 2040 6080 100120IN1N-V— - — — VLVF-.—0II-oi 234Figure 5.17: (a)Normalized densityas a function ofthe longitudinalposition and fortimes t/r=0.5 (short dash),1.0 (solid),27.00 (long dash)and 125.00 (dot-dash).Theinitial normalizedplasma density7Fh/n= 10. (b) The insertindicates thenormalizedsurface plasma densityas a function of normalizedtime.Chapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 165The total reflectivity from the plasma layer isdue 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 reflectivityr(t) 12 we have to assume a functionfor the absorption term, a(t). Based onthe experimental results for initial carrier densities > n, we always measure a distinct reflectivityminimum which approaches zero aftera time of the order of 28 ps. For this minimum reflectivityto exist, we require the imaginary part of the dielectric function to be much smallerthan 1 (i.e. small free-carrierandintervalence band absorption). We candescribe phenomenologically the time evolutionof the free-carrier and intervalence band absorptionsby 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 andthus the imaginary componentof the dielectricconstant is a function of the free-carriertemperature. The magnitude of theabsorptionis enhanced at higher carrier temperature. Inthis case, one has to considerthe rateof cooling of the hot carrier distributionat a high initial carrier density whichin turnshould reflect the rate of decay of free-carrierabsorption. The cooling rateis taken to be(10T)’, which is slightly larger thanthe value of “ 1 ps from the measurementspresented in reference [174]. Moreover,we also have to assume that ittakes a finite time afterphotoexcitation for the free-carrierabsorption to reach a maximumvalue, which is proportional to the absorbed photonflux. The constant term in theexpression in equation5.42 arises from the absorption at roomtemperature. Figure 5.18shows the reflectivitypulses forf=10 and 2 respectively. Also shownare, forf=10, the integrated reflectivity simulating the reflectivity cross-correlationand the reflectivity-reflectivity correlationChapter 5. Experimental Investigation of Infrared Reflectionfrom GaAs 166measurements. Comparison with the experimentalresults of figures 5.13, 5.15, 5.16 tofigure 5.18, and figure 5.10 to 5.19 , indicatesthat the model provides a good representation of the experimental situation. Note thatthe time scale in figure 5.19 is normalizedto the excitation pulse width ri,. It also shows thatthe 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 reflectivityisshown as a function off= Fh/n. The calculations are performed by integrating thereflectivity curves for various initial plasmadensities. The final integration timeis takento be 200 ps. Comparison with figure5.10 again indicates the good agreementbetweenthe model and the experiment.Clearly, by invoking an additional two-bodyrecombination mechanism whoserecombination rate is taken to be a function ofthe carrier density, we areable to obtain a goodagreement between the experimentalresults and the proposed modelcalculations. So farwe have no explanationas to the exact nature of the recombinationmechanism.We believe that this phenomenologicalmodel is essentially correct; however,moreexperimental and theoreticalstudy is required to completelydetermine the exact natureof the recombination process.5.4 Frequency Spectrum MeasurementsMeasurements of the frequencybandwidths, /f of the reflectedinfrared pulsescan provide complementary informationon the duration of the pulses,We have performedthis type of experiment for the followingreason: since the infrared reflectionoccurs froma time-dependent plasma layer,one expects the infraredpulse to have a frequencychirp.The overall pulse durationcan be obtained by only onesingle shot measurement.However, the exact pulsewidth-bandwidth productfor an arbitrary pulse shapedependsChapter 5. ExperimentalInvestigation of Infrared Reflectionfrom GaAs 167f —(I I, IIII0.8__//0.6\I/0.E:Jr—.--0 204060 80100120t/-rFigure 5.18:Model calculationsas a functionof normalized timeof: the normalizedinfrared pulses for7Fh/ri= 10 (uppersolid line) and2 (lower solid line),normalizedcross-correlationsignal for -yFh/n=10 (dash-dot),and normalizedreflection-reflectioncorrelation signalfor7Fh/n= 10 (dash).Chapter 5. ExperimentalInvestigation of Infrared Reflectionfrom GaAs 16840_____30201000 51015 207Fph/ncFigure 5.19:Model calculationsfor time integratedreflectivity (reflectedpulse energy)as a functionof the normalizedcarrier density.The verticalaxis scale unitsare arbitrary.Chapter 5. Experimental Investigation of InfraredReflection 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 withinthe pulse. From the previous time-resolvedcross-correlation measurements, we find thatthe reflected infrared pulse shapes showverycomplicated structures. The main questionin these cases is how to define the pulsewidths. Our approach to thisproblem is to analyze the pulse widthsmeasured by thereflection-reflection correlation experiments.This correlation experimentalresults showsthat the overall shapes of the reflectedpulses can be approximated by gaussianpulseswith a pulse width-bandwidthproduct LS.r14f 0.44.The experimental setup and the proceduresfor the frequency spectrum measurementsare outlined in section 4.11. We haveperformed several experimentsto measure thefrequency spectrum. Due to the low sensitivityof the optical system, we are notable tomeasure the frequency spectrum for differentvalues of excitation energy fluences.Thus,the experiments are only performed forhigh excitation levels(7Fh/n > 6). Figure 5.20shows a typical wavelength shift spectrumfor an optical pulse with an initialexcitationfluence-/Fh/n= 7. Each data point in the figure is averaged over10 points and thestandard error of the measurementsis shown as error bars. The figureshows asymmetrywhere the spectrum shiftsmore towards the longer wavelength.From the FWHM(87A) of the wavelegth spectrum curve,we can calculate a pulse widthof 18 ps. Thiscalculated pulse width is in verygood agreement with the directmeasurements of thecorrelation profile of figure 5.13.Chapter5. ExperimentalInvestigation ofInfrared Reflectionfrom GaAs17020I I II II I I16H‘ 124.—250 —150—5050 150250WavelengthShift (A)Figure5.20: Wavelengthshift of areflectedinfrared pulsewith aninitial excitationfluence of7Fh/fl 7.Chapter 6Ultrafast Semiconductors for 10.6 1um OpticalSwitching6.1 IntroductionThis chapter deals with the experimentalstudy of semiconductor materials having ultra-short recombinatiori carrier lifetimes for possible applicationto optical infrared semiconductor switching. The major body of the experimentalwork is presented in our currentpublications [175]—[177]. Details of experimentalmeasurements from three types of semiconductors: low-temperature grown GaAs,radiation damaged GaAs, andIn0g5Ga015As/GaAs relaxed superlattice structures are presentedas possible candidates for ultrashortpulse generation. Molecular beam epitaxygrowth procedures for some structuresandsample preparations are also discussed.Where appropriate, the time-resolvedcross-correlation results for the carrier lifetimes arecompared with the photoconductivitymeasurement values reportedin the literature.6.2 The Need for Semiconductorswith Ultrashort Carrier LifetimesIn chapter 5 we discussed the experimentalinfrared 10.6 jimreflection from intrinsicGaAs. Evidently, the pulses generatedfrom such a reflection switchare too long forour practical use. Most of the generatedpulses have long reflectivity tailswhich last forseveral picoseconds,and in order to get rid of this long reflection,alternative materials andtechniques must be used toproduce ultrashort reflectivity pulses.Since we are interestedin the generation of a laserpulse with a duration of1 ps using only one switching171Chapter 6. Ultrafast Semiconductors for10.6 um Optical Switching 172element, we have investigated othermodified GaAs based semiconductor switchestoserve this purpose. In principle, theGaAs semiconductor is altered to haveits carrierlifetime,Tr, shorter than the radiative lifetime and the diffusion time. Thenonradiativerecombination centre densityand capture cross section must be largeenough such thatthe temporal evolution of the plasma issolely determined by the carrierrecombinationand the plasma density can be reducedbelow the critical density ina time scaleTr.Now, if the semiconductor materials withultrashort recombination lifetimes(of the orderof a picosecond) are used in placeof the GaAs switch, then it is possible,due to ultrafastcarrier nonradiative recombination,to generate ultrashort infraredpulses limited only bythe lifetimes of the semiconductormaterials. When the semiconductorcarrier lifetimeis longer than the excitation opticallaser pulse, then the generationrate of the e-hplasma can be considered to be instantaneous.That is, in time resolved cross-correlationexperiments this shows as a fast risetimeof the cross-correlation signal[1 75]—[1 77]. Thedecay rate of the electron holeplasma should follow the simplerelation,n(t)fl0Ct/Tr,(6.1)which in turn determines thedecay rate of the reflectivitypulses. Therefore, in principle,this method is more attractivethan just using intrinsic GaAssince the reflectedinfraredpulse duration does not dependon the amount of the excitationenergy fluence. Moreover,the choice of the infraredpulse duration can be easilyadjusted to the requiredvalue byproper selection of the carrierlifetime [176]. Finally, itshould be pointed out thatusing time-resolved infraredreflectivity measurements providesan alternative methodfor measuringTr for semiconductor materials [l75]—[177}.Chapter 6. Ultrafast Semiconductors for 10.6m Optical Switching 1736.3 Ultrafast Recombination SemiconductorsIn this section we give a brief and largely qualitativeaccount of the techniques usedtoreduce semiconductor carrier lifetimes.Comprehensive reviews on the subjectcan befound in references [178]—[182]. Our maintask is to search for optimal semiconductormaterials with a minimum free-carrier absorptionand a minimum carrier lifetime toguarantee that a high reflectivity and an ultrashortdecay time are exhibited simultaneously.Different experimental approaches andtechniques have been used toenhance the speedof response of semiconductor materials.Most of the work is directed towards thedesignand the fabrication of ultrawide bandwidthoptoelectronic devices [178]—[180].The techniques rely on the introductionof sufficient deep level states in the crystallinesemiconductor material. Deep levelsin semiconductors are basically energylevels closeto the middle of the energy bandgap. These levels can be created byimpurities or bycrystal defects (vacancies andinterstitials)and dislocations.Photoexcited carriers can becaptured at these sites andpossibly recombine with theiropposite kind. The recombination process can be eithera single recombination eventor a multi-level recombinationevent. In the latter, the photoexcitedcarriers are captured fora short time and thenreleased to be captured by anotherdeep level and so on. Dependingon the nature oftherecombination level, both typesof carriers (electrons and holes)can be captured withcapture cross-sectionsc.eand and0ch,for electrons and holes,respectively.At high dopant concentrations,carrier recombination occursthrough lattice defectsgenerated by the dopant.This causes an increasein the density of therecombinationcentres. Free carriers excitedin the conduction andvalence bands of these materialsarerapidly trapped at deepdefect levels. The carrier lifetimeof GaAs can be reducedfrom afew nanoseconds to70 ps by the introductionof Cr [183]—[185], whereasby doping theGaAs with Er (5 xl O’ cm3)thecarrier lifetime is reducedto 1 ps [186]. ExperimentalChapter 6. Ultrafast Semiconductorsfor 10.6 ,um Optical Switching174observations have shown thatfor a doping range of1016_1019cm3 the carrier lifetimedecreases with increasing dopantconcentration[1861.Doping InP with Fe reducesthecarrier lifetime to 100-1000 psdepending on the impurity concentration[187]—[190].Even though these semiconductorshave short lifetimes, the lifetimesfor Cr:GaAsand Fe:GaAs are not fast enough toprovide significant improvementin our optical semiconductor infrared switchingsystem. For Er:GaAs,due to heavy Er doping, thereissignificant background reflectionthat reduces the contrast ratioof the reflected pulserelative to the backgroundreflection.Picosecond and subpicosecondcarrier lifetimes can alsobe achieved in usual polycrystalline and amorphous semiconductorswhere the naturally occurringlarge defectsat the grain boundaries act aseffective carrier trappingand recombination centres.Forpolycrystalline materials,for example, Si, Ge, and CdTecarrier lifetimes are measuredto be 2—50 ps [191], 50Ps [192] and 4 Ps [193], respectively,and for amorphous materialscarrier lifetimes are measuredto be 5-20 ps for a:Si[1941.These semiconductorshaveultrashort recombinationtimes and clearly canbe used as optical infrared semiconductor switches; however, the mainproblem associated withsuch semiconductors isthatthe carrier reflectivity is dramaticallyreduced due to increasedelastic scattering. Thatis, the increase in the carrierscattering resultsin low infrared reflection efficienciesdueto increased free-carrier absorptionin the semiconductors.Consequently, a compromisebetween the reflection efficiencyand the speed of theswitch must be reached.For thesereasons, no attempt hasbeen made to study theinfrared reflection fromthese materials.The details of the theorydealing with recombinationthrough a single level recombination centre is discussedby Schockley, Readand Hall (SRH) [195,196]. The carrierlifetime can be relatedto the trap density,N through the following simple relationTr =(6.2)NtJc_eh <Vth >Chapter 6. Ultrafast Semiconductors for10.6 m Optical Switching 175where < v > is the mean thermal velocity ofthe carrier. In this case, the trapdensity and therefore the free-carrier lifetime are inverselyrelated. In light of the aboveequation, it is clear that one needsto increase the defect and dislocation densityin thesemiconductors.Next, we examine three types of semiconductorswith ultrashort recombination carrierlifetimes. We investigate low-temperaturegrown GaAs (LT-GaAs), radiationdamagedGaAs (RD-GaAs), and InGaAs/GaAsrelaxed superlattice.6.4 Using Low-Temperature GrownGaAs for Ultrafast Pulse GenerationA novel and interesting approachto shorten carrier lifetime is the useof low-temperatureMolecular Beam Epitaxy (MBE)grown GaAs (LT-GaAs). Thissemiconductor exhibitsa unique set of properties suchas high carrier mobility(‘—i1O cm2/V s), ultrashortcarrier lifetime (0.4-60 ps dependingon the growth temperature),high resistivity(‘--‘1O l cm) and high quantum efficiency.The combination of the aboveproperties attracted wide interest in low-temperaturegrown semiconductors for thedevelopment ofwide bandwidth optoelectronicdevices such as photoconductorsand photoconductiveswitches [197]—[216]. Here, byusing a GaAs layer grown by molecularbeam epitaxy(MBE) at a low substrate temperature(LT-GaAs) as an optical semiconductorswitch,we demonstrated the generationof ultra.short infrared pulses at10.6 jim [175].Two important parameterswhich determine the opticaland electrical characteristicsof epitaxial growth ofGaAs layers on GaAs substratesare: the substrate temperaturewhich must be maintained at‘- 600°C, and the As/Ga beam-equivalent-pressureratio.Lowering the substratetemperature to -‘- 200°—300° C causes a highly nonstoichiometricgrowth where excess arsenic(of approximately ‘1%) is incorporated intothe GaAsepitaxial layer [200, 203,205, 208, 214, 215]. Post growthannealing of thesubstrateChapter 6. Ultrafast Semiconductors for10.6 m Optical Switching176causes the excess arsenic precipitatesto form nanometer-size arsenic clusters[197] andthe resistivity increases by several orders ofmagnitude from 10 cm toiO flcm [203, 214, 215]. It is these arsenic clustersthat are of great interest sincetheydeplete any photoexcited free carriersfrom the surrounding GaAs material.Ultrafastcarrier recombination is attributed to the efficientrecombination centres dueto excessAs clusters. Unannealed samples are found to havea variety of defects such as: neutraland ionized arsenic antisites([A5Ga]°’1020cm3,[A5Ga]’ 5x1018cm3)which mayact as deep donors, arsenic interstatials (As)Ga vacancies(VGa”-’1018cm3) and Gaantisites(GaA3’—’ 5x1018cm3). These last two defectsmay act as acceptors[198]—[201],[204, 217]. After annealing thedefect concentration is reducedabout an order ofmagnitude with no effect on thecarrier lifetime. Either both typesof carriers are trappedat midgap defect bands and then recombine;or the midgap donor or acceptordeep levelscapture carriers which then recombine.Several authors reported on thegrowth/annealtemperature dependenceof the carrier lifetime [203],[205]—[207],[214]and have shownthat the degree of excess As is greaterfor lower substrate temperatures.6.4.1 MBE Growthof LT-GaAs LayersIn this section the LT-GaAs growthprocedure is outlined. The propertiesof LT-GaAscritically depend on the growthand the annealing conditions duringthe epitaxial growth,any small fluctuations in any ofthe growth parameters can significantlyalter the carrierlifetime of the sample.The incorporation of high densityrecombination centres is achievedusing a nonconventional MBE growthtechnique. High densities of excessAs are incorporated intoaGaAs active layer using a low substrategrowth temperature witha moderate As2 overpressure.The LT-GaAs samples are grownby S. R. Johnson in theU.B.C. Physics Department.Chapter 6. Ultrafast Semiconductors for 10.6,um Optical Switching 177The LT-GaAs epi-layer is grown ona semi-insulating GaAs substrate using a vacuumgenerator V80H MBE system. The substrate andthe holder are treated in aU.V. generated ozone atmosphere (for 4 mm) to remove anyresidual organics from the surfaceof the wafer. After the ozone treatment,the holder and the GaAs wafer are placedintothe MBE growth chamber wherethe oxide is thermally desorbed underan As2 flux.The oxide is desorbed by ramping thesubstrate temperature at a rateof 5°C/mm from500°C to about 10°C above the oxide desorptiontemperature of -- 600°C. Thisprocessroughens the surface of the substrate.The increase in the surfaceroughness and hencethe oxide desorption are monitored usinglaser light scattering[2181.The substrate issmoothed by growing a 2zm thick (1 tim/hr) GaAs bufferlayer at a temperature of600°C. Next, a 100 nm thick GaAs temperature-transitionlayer is grown on the bufferlayer. During the growth of thislayer, the temperature of the substrateis lowered from600°C to 320°C in 6 mm. Followingthis, a 200 nm thick layer ofLT-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 growthchamber by raising the substratetemperature from320° C to 550° C (in 3 mm) andannealed for 6 mm at 550° C underan As2 flux. Alllayers are grown nominallyundoped. From the reported valuein the literature, underthese growth conditions, thearsenic precipitate density is estimatedto be approximately3x10’Tcm3 with an average clustersize of’- 2—5 urn [197, 219].It has been shown thatLT-GaAs maintains its crystallinestructure [197, 199]; therefore,no attempt ismadeto characterize the degreeof crystallinity of the layer. Thesurface morphology oftheLT-GaAs shows a smooth surfacewith no diffuse reflection at10.6 gum. We should pointout that during the growthprocess the substrate temperatureis measured using diffusereflectance spectroscopy(DRS) [220]. This optical temperaturemeasurement techniquehas ±1°C sensitivity. Figure6.1 shows a schematic diagramof the LT-GaAs structureand a scanning electronmicrograph of the LT-GaAslayer.Chapter 6. Ultrafast Semiconductors for 10.6m Optical Switching1786.4.2 Subpicosecond 10.6urn Pulse Generation from LT-GaAsas a Reflection SwitchWe used a cross-correlation method outlinedin section 4.10.2. to measure the temporalJR pulse shape. Figure 6.2(a) displaysa typical integrated infrared pulseenergy as afunction of the relative delay.The experiment is performed at a fixedexcitation energyfluence which correspondsto a plasma density of ‘—‘ 5x10’9 cm3.The time origin inthe figure represents the relative arrivaltime of the visible pulse priorto the arrival ofthe infrared pulse to signifythe zero base line of the transmission.By differentiating thetransmission step curve infigure 6.2(a), we can obtain thepulse width. The measuredcharacteristic feature of the curve showsan initial rapid increase in transmission.Therise time of the transmissioncross-correlation is a clear indicationthat the pulse widthis about 1 + 0.2 Ps [175] with along decaying tail. This kind of decayis expected sincethe visible pulse is mainlyabsorbed in the LT-GaAs200 nm thick layer; hence, mostofthe e-h plasma is generatedthere. We attribute the short pulseto the fast recombinationtimes in the material, whereasthe long tail is due to the GaAsbuffer and the substratelayers. Once the carriers are generatedin the LT-GaAs layer they willrecombine in about0.5 ps, and the carriers whichare generated in the buffer layerwill persist for a longertime. Thus the infrared reflectivitydecay time depends on the diffusionof the carriersthrough the buffer layer.The reflectivity tail can be reducedby making the LT-GaAslayer much larger than the absorptionskin depth of the opticalpulse. The energy of theJR pulse is estimated to be 10pJ limited primarily by the sourceCO2 laser power.The cross-correlation measurementscan be compared withcalculations based onasimple model in which the freecarriers are generatedin the LT-GaAsfilm by the absorption of a 0.49 Ps FWHMsemi-gaussian visiblepulse. The majorityof the generatedcarriers recombine exponentiallywith a lifetime of0.5 ps while ten percentare allowed toChapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching179diffuse into the buffer layer with a diffusion coefficientof 20 cm2/s. The cross-correlationsignal and its differential are evaluated based on atechnique described in section 4.10.2.The good agreement with the experiment indicatesa free-carrier lifetime of 0.5 Ps whichagrees with the reported carrier lifetime basedon the presence of a high density of Asprecipitates in this material. That is, if one considers equation6.2 with the followingparameters [203]:N= 3x10’7cm3,u=2.83x10’3cm2,and < Vj >=2.5x107cm/s(300 K), we calculate a carrier lifetime of0.5 Ps. Our measured carrier lifetime is thesame as the one measured by other techniques [203].We examined the reflected infrared energy for differentlevels of visible laser excitation.Figure 6.3 illustrates the variation of the reflectedinfrared pulse energy as a function ofthe plasma density (or energy fluence) generatedin a 2 m thick LT-GaAs switch.Incontrast to the GaAs measurements (figure5.10), the experimental results showa linearrelation and no indication of saturationat high excitation levels. The linearbehaviourfor LT-GaAs is consistent with whatis expected if one assumes that theexistence of therecombination centres in the sample,and that the width of the reflectedpulses do notvary with the amount of the excitation energyfluence.In practice, the switching element is shown tobe very reliable and simple tooperate.Our experimental results show thatLT-GaAs, grown under the conditionsspecified above,is ideally suited for optical semiconductorswitching of 10.6 tm radiation.6.5 Using Radiation DamagedGaAs for Ultrafast Pulse GenerationWe have explored another potentialsemiconductor material for ultrashortinfrared pulsegeneration. Radiation damaged semiconductorsare known to have ultrashortcarrierChapter 6. Ultrafast Semiconductors for 10.6 ,um OpticalSwitching(a)180Figure 6.1: (a) Schematicdiagram representingthe LT-GaAsgrowth layer. (b)Scanningelectron micrographof the LT-GaAslayer./LT—GaAs (200 nm)GaAs/LI—GaAs TransUon Layer (100 nm)MBE—GaAs (1 m)GaAs SubstrateChapter 6. UltrafastSemiconductors for 10.6m Optical Switching 1811.’l I II II II I1.u1,l212(a)z.—>0.4(b) -0.40.2-0.2 SC_)0 . 0—III0 . o0 24 68 10 1214 1618 20Delay (ps)Figure 6.2: (a)A cross-correlationtransmission signalbetween theIR pulse andthevisible pulsecreating the transmissiontemporal gate.The solid lineis the modelcalculations. (b)The infrared pulseas obtained from differentiatingthe cross-correlationcurve.Chapter 6. UltrafastSemiconductors for 10.6m Optical Switching18250II•z40 o0biJC) .00C) 100 2 46 8 1012 14 1618 20CarrierDensity(1019cm3)Figure 6.3: Variationsof the reflectedJR pulse energyas a functionof the e-h plasmadensity. TheLT-GaAs layerthicknessis ‘— 2 m.Chapter 6. Ultrafast Semiconductors for 10.6 im OpticalSwitching 183lifetimes ranging from - 100 fs to 10Ps [221]—[230]. Our purpose in using ion bombardment is to take advantage of the resulting damage asa means of introducing a predetermined defect density into the crystalline semiconductor[231]—[235]. The reductionof the free-carrier lifetime is a direct resultof the defects introduced by the irradiatingion beam. The carrier lifetime of the radiationdamaged semiconductor depends on several factors such as: the energy of the radiation beam,type of semiconductor, type ofimpurities, and the material temperature. Whena GaAs substrate is irradiated withhigh energy particles two processes occur: theatoms in the host lattice are displacedinto interstitial sites producinga vacancy pulse interstitial (what is knownas Frenkelpairs VGaGai andVAS-AS). Both Va and VAs are effective electron and hole traps,respectively [233, 234], and the interstitialsites Ga: and As behave as donors[182]. Inaddition, nanometer-size defect clustersare also formed due to impurities implant.Thesedefects and vacancies act as ultrafastefficient traps and recombination centres.Radiation damaging GaAs with a proton beamproduces various trap levels with energies0.11,0.31, and 0.71 eV for electronsand energies of 0.06, 0.44, and0.57 eV for holes withcapture cross sections of 1.3x10’3cm2for electrons and 2.3x10’3cm2 forholes[235]. Earlier work on radiation damagedGaAs (RD-GaAs) [224, 225]has shown thatthe carrier lifetime is reduced to500 fs by irradiating the semiconductorwith a 180 keVproton beam at a dose of 1.37x10’5cm2.The irradiated GaAs showsno sign of loss ofcrystalline structure [224, 225]; however,above that dosage, the observedcarrier lifetimeis found to reach a lower limit of500 fs.6.5.1 RD-GaAs Samples’ Preparationsand CharacterizationsThe infrared reflection switchesare made from a 450m thick semi-insulating(‘10 Qcm) GaAs (100) wafer. The waferis optically polished on bothsurfaces and is cleavedinto three pieces each irradiatedwith a different Hion dose. The ion damagingisChapter 6. Ultrafast Semiconductorsfor 10.6umOptical Switching184performed at Dr. N. Jaeger’s Ion ImplantLaboratory in the U.B.C. ElectricalEngineeringDepartment. The samples are bombardedwith a 180 keVH+ion beam to produceeffective doses of 1 xlO’2,1 x1014,and1 xlO’6 cm2. During the implantationprocess,the samples are mounted on an aluminumblock in order to reduce sampledamage dueto ion beam heating. The ion beam currentdensity is 1,5x104 A/cm2 incidentat anangle of70to the surface normal and is scanned uniformlyover the samples. For thesesamples the thickness of the damaged layersis larger than the penetration depthof thedye laser excitation pulse(--0.2 zm), thus the carriers are generatedonly in the radiationdamaged layer and diffusion of the carriersoutside the damaged layeris of no effect.Heavy ion bombardment of theGaAs wafer may result in a permanentchange in thecrystalline structure of the semiconductor.Early work showed that bombardmentwitha highH+ion dose > 1.37x1015 cm2on crystalline GaAs transformsit into an amorphous material [224, 225]. Inorder to characterize accuratelythe structure of the iondamaged layer, several ellipsometricmeasurements were performedon the highly radiation damaged samples and comparedto the measured dielectric functionof undamagedGaAs. The ellipsometric measurementswere performed by Dr.R. Parsons’ group inthe U.B.C. Physics Department.Figure 6.4 shows the resultantdielectric function forthe radiation damagedGaAs with an ion dose of 1 x1016cm2.It is clear that thereisno significant change in the form of thedielectric function exceptthe disappearance ofthe peaks around 3 eV. This andthe overall small deviationsof the dielectric functionare attributed to the surface roughness.The result suggests that theRD-GaAs samplesmaintain their crystallinestructures even at an iondose level of 1 x1016cm2.Chapter 6. Ultrafast Semiconductors for 10.6 m OpticalSwitching 1856.5.2 Subpicosecond 10.6 1um Pulse Generation fromRD-GaAs as a Reflection SwitchThe experimental arrangement and the procedureused to generate and to measure thepulse widths are similar to the ones presentedin section 4.10.2 except for the replacementsof the LT-GaAs switch with RD-GaAs switches.We have used a cross-correlation method againto time resolve the reflected infraredlaser pulse shapes. In performing theexperiments, all the switches are irradiatedwithenough excitation energy fluence to produceelectron-hole plasma densityof ‘-‘ 2 x1019cm3.Figure 6.5 shows some of the typically measuredcross-correlation signals fromthethree RD-GaAs switches. Each data point inthe plots is averaged over at least 60 singleshots and the error bar is an indicationof the standard error in the measurements.Thesecurves represent the temporal integral ofthe reflected infrared pulses.The differentialsof these curves with respect to time providesan accurate representation of the temporalshape of the reflected infraredpulses. The risetimes of these pulsesis governed by therisetime of the excitation pulse(490 fs). The measured pulse widthis found to be astrong function of the ion dosageon the switch. At anH+ion dose of 1 x1012cm2the reflected infrared pulse is measuredto be 15+1.5 ps. By increasingthe irradiationion level to 1 xlO’4 cm2 the reflectedinfrared pulse width is reducedto 2.4+0.3 Ps.An additional increase in the dosagelevel to 1 xlO’6 cm2 furtherreduces the reflectedinfrared pulse to 600±200fs. By taking our detectivity forthese pulses, we estimatethe reflected energy ofthe infrared pulses to be5 pJ. This corresponds to a peakreflectivity of 50%. The resultsfor the lx1016cm2 RD-GaAs switchreflection pulsewidth is comparable with thevisible excitation pulse widthof 490 fs. Therefore,underour experimental conditions,the reflected infrared pulse widthis mainly determined bythe lifetime of the semiconductorswitch and the width of thevisible excitation pulse.InChapter 6. Ultrafast Semiconductors for 10.6 m Optical Switching186light of the above experimental results, to produceand measure pulse widths of shorterduration the visible excitation pulse must be compressed.In order to explain the observed ultrafast carrier recombinationtimes, we can approximate the carrier lifetime by equation6.2. If one assumes thatN is directly proportionalto the H ion dose and that the reflectivity pulsewidth represents the carrier lifetime,then a log—log plot of the ion dose asa 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 widthas a function of theH+ion dose. The curve showsthe predicted linear relationship betweenthe reflected infrared laser pulse and theiondose. However, the calculated experimentalslope is —0.4 which differs from the predictedslope of —1. One possible explanation is thatthe density of the recombination centres isnot directly proportional to the ion dose. Thisis similar to what has been observediiierbium-doped GaAs [186]. The other possibilityis that the defect density is lowerthanthe density of the optically generatedcarriers which may result in the saturationof thetraps and the recombination centres due to excessfree carriers.From figure 6.6 we can calculate the relationshipbetween 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 pulsewidth to the requiredduration by simply adjustingthe amount of damage on the switch.In fact, by adjustingthe dosage across the surface of the wafer,a multi-speed switch can be easilyconstructedon a single wafer.CC.)C.)—10Energy (eV)Figure 6.4: Real and Imaginaryparts of the dielectricfunction of undamagedGaAssample (solid) and theion damaged (dashed). For thedamaged GaAs, the iondose levelis 1 xlO’6 cm2.Chapter 6. Ultrafast Semiconductors for 10.6 1um Optical Switching 1872520151050—51.5 2.0 2.5 3.03.5 4.0 4.55.0 5.5 6.0Chapter 6. UltrafastSemiconductors for 10.6 im Optical Switching1881.0I0.8(a) 10 20 30 40 50C2 5I I I20(b)rr)°•Ci)0 0.0 ——— II0 4 8 12161.5I(c)1.0.a0.500 2 4 6 8Delay (ps)Figure 6.5: Cross-correlationmeasurementsfor the reflectedinfrared laser pulsesfor anion damage doseof (a) lxlO’2cm,(b) ixiO’4 cm2and (c) 1x1O’6cm2.Note thatin all plots, thecross-correlationsignal is plottedin arbitraryunits which differfor eachdiagram.Chapter 6. UltrafastSemiconductors for 10.6m Optical Switching189I11111 I I 111111 I IllilifI I11111 I I I IIIII I IIIICl)Cl)JI I i I I iiiI I iii I II i iiiI I IIIJI1011 101210’s1014101016 1017Ion Dose(cm2)Figure 6.6:Measured10.6 ,im infraredlaser pulsewidths asa functionof the H iondose in GaAs.Chapter 6. Ultrafast Semiconductors for 10.6 mOptical Switching 1906.6 UsingIno.85Gao.i5As/GaAs GaAs for UltrafastPulse GenerationIn this section, we investigate a novel and alternative semiconductorstructure for application to infrared semiconductor switching. Thegrowth of lattice mismatched semiconductor layers by MBE above the critical layerthickness results in the formation ofdefects and dislocations. Clearly, in the fabricationof electronic devices, it is undesirable to introduce dislocations where theultimate performance, efficiency, andlifetimeof the devices are mainly limited by thedislocations introduced during epitaxialgrowth[236]—[239]. However, increasing the recombinationcentre density during theepitaxial growth enhances the speed ofthe material. Dislocations at the interfacesbetweenlattice mismatched semiconductors suchas InGaAs and GaAs, can serve as ultrafastnon-radiative recombination centres. Thegrowth sequence ofInGai_As/GaAs can bedivided into the following stages:(a) initial growth whereInGai_As is grown under coherent strain where only a finite amountof lattice mismatch is accommodatedby strain;(b) intermediate growth when theInGai_rAs layer thickness reaches the critical layerthickness (which depends on the strainedalloy indium concentration) anddislocationsare generated at the interface; and(c) the final growth phase when thethickness of theInGaAs layer is increased far beyondthe thickness of the critical layer,a relaxation of thestructure takes place and as a result someof the lattice mismatch is accommodatedbymisfit dislocations. Continual growth abovethis point results in an island-typegrowthstructure [239, 240].6.6.1 MBE Growth ofIno.85Gao.15As/GaAsRelaxed SuperlatticeThe samples are grown byS. R. Johnson in the U.B.C. Physics Department.The layersare grown on a semi-insulating(100) GaAs substrate using theVacuum GeneratorsV8OHmolecular beam epitaxy (MBE)machine. The substrate preparationprocedure is similarChapter 6. Ultrafast Semiconductors for 10.6 ,um Optical Switching191to the one discussed previously in section 6.4.1. The layer thicknessesof the superlatticeare as follows: the first three layers consist of 210 Aof GaAs on 84 A ofIn085Ga015As,the next three layers consist of 210 A of GaAs on126 A ofIn0•85Ga015As, and the lastfour layers consist of 210 A of GaAs on 84 A ofIn0•85Ga015As.These layers are grownat a substrate temperature of 500 °C. The substrateis annealed at 630 °C for 3 mm. Aschematic diagram of the structure is presented infigure 6.7The lattice mismatch between the In085Ga015Aslayer and the GaAs layer is 6%.The layers of the InGaAs/GaAs superlattice arerelaxed as they are much thicker thanthe critical layer thickness which is oniy a fewmonolayers(‘-.20 A) [239, 241]. Thesurface roughness of the grown structureis greater than the surface roughness of thelattice matched buffer layer. However, this roughnessis not large enough to cause diffusereflection at 10.6 1um. The sample showed a smoothand featureless surface when observedwith a scanning electron microscope.In order to enhance the effects of non-radiativerecombination at the defects, severalsteps are taken to ensure maximum recombinationefficiency: alternating layersof InGaAsand GaAs are chosen so that the totalnumber of interface boundaries and,hence, the totalnumber of the dislocations is maximized.The total thickness of the relaxedsuperlatticeis chosen to be about the same as the absorptionskin depth of the visible excitationpulse,such that the majority of the carriersare optically generated throughoutthe superlatticestructure. At this high In concentration,the layer grows as islands [239,240, 242, 243].6.6.2 Ultrafast 10.6 tm Pulse Generationfrom In0g5Ga0isAs/GaAsas a Reflection SwitchWe have used a cross-correlationtechnique to measure the carrierlifetime in the superlattice structure. The details of the experimentalset up and the measurementprocedureare similar to previous onesexcept for the replacementof the LT-GaAs or RD-GaAsChapter 6. Ultrafast Semiconductors for10.6 um Optical Switching 192with theIno.g5Gao.isAs/GaAs relaxed superlattice structure. The ultrafast changeof the10.6 im reflection is monitored as a function oftime delay between the visible excitationpulse used to turn on the Si switch andthe infrared pulse. The excitation energyfluencethroughout the experiment is kept constantand 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 x1019cm3.The cross-correlation reflectivity curverepresents the temporal behaviourof the optically generated plasma inside the relaxed superlatticestructure. The risetime is governedby the generation rate of the e-h plasmacreated by the 490 fs excitation laserpulse. Initially, the optically induced plasmaremains confined to the absorptionskin depth layerof 220 nm. As time evolves, the defects/dislocationsat the interfaces and throughouttherest of the relaxed superlattice will act asultrafast non-radiative recombinationcentresfor the plasma as it diffuses throughoutthe layers. Figure 6.8 illustratesa typical cross-correlation curve, where the reflectivityis plotted versus the time delayfollowing theplasma excitation for the initial10-ps following excitation. Thecross-correlation curveresembles the integral of a double exponentialreflectivity function. Whenthe differentialof the reflectivity cross-correlation curveis plotted on a logarithmic scale,as shown infigure 6.9, it is clear that thereare linear regions representingtwo intrinsic recombinatioritimes. The initial ultrafast decayis measured to be 2.6± 0.3 ps, and the slow decay is10.0 ± 0.3 ps. The 2.6 ps exponentialdecay time represents the effectiverecombinationlifetime of the carriers at the dislocationsand defects. The origin ofthe long 10 Ps decay tail may be due to space chargeregions near dislocationswhich produce potentialbarriers and wells for non-equilibriumholes and electrons. Thesebarriers/wells occurin regions around dislocations,where strain is maximized.Once the plasma iscreated,all the electrons/holes occupydifferent states high/lowin the conduction/valencebands.Chapter 6. Ultrafast Semiconductors for 10.6 mOptical Switching 193While most of the carriers recombine rapidly at recombinationcentres, a significant number with low energy get trapped by the barriers/wellsand therefore have a much longerrecombination time. These trapped carriers recombinethrough Auger recombination. Asa result, one expects a long infrared reflectivitytail indicating the presence of these carriers. The structure’s carrier lifetime is comparableto that of RD-GaAs(with a dose of ‘-2x1012 cm2)and LT-GaAs semiconductors (grownat 300 °C). It should be noted thatthis structure can be utilized as an ultrafast optical-opticalinfrared reflectivity switch[177]. Here, we managed to generate ultrashort10.6 m laser pulses of 10 Ps duration.After this experiment was completed and the resultswere submitted for publication[177], two papers appeared in the literature whichdiscuss carrier lifetime in similarstructures [237, 244]. Pelouch and Schlie[244] measured a rapid absorption recoverysignal of the order of ‘—‘ 10 Ps fla Ino,65Gao.35As/GaAs structure. Theyattribute theultrafast absorption recovery to recombination atmisfit dislocations. On the other hand,the results of the recently publishedwork by Hugi et al. [237] showed twolifetime scalesfor similar structures mainly Ps forelectrons and 10 Ps for holes. Theyattribute the 3ps lifetime to trapping at substitutionaloxygen on arsenic site°As(with correspondingdensity and capture cross-section of 8x10’6cm3 and 1.9x10’3cm2,respectively)andthe 10 Ps lifetime due to large densitiesof misfits and threading dislocationsdue to latticemismatch.6.7 Conclusion of the ChapterIn conclusion, we have demonstratedthe feasibility of generatingultrashort pulses at 10.6m using LT—GaAs, RD-GaAs, andIno.s5Gao.isAs/GaAs relaxedsuperlattice as singleswitching elements. Thepulse duration ranges from600 fs to 15 Ps depending on theactive switching elements. Furthermore,with the optimization ofthe growth parametersChapter 6. Ultrafast Semiconductors for10.6 tm Optical Switching 194I84AT-I84ATI84AT84ATI126 ATI126 ATI126 AT1!’$j£*i2OAr84ArT4$;210’nr>’84ATjK[%4219i.iIttr84At GaAs Bufferlayer onSemi-insulatingGaAs SubstrateFigure 6.7: ASchematic diagram oftheInos5Gao.iAs/GaAsrelaxed superlattice.3lOnmChapter 6. Ultrafast Semiconductors for 10.6 um OpticalSwitching 1952.0I I I I I I I I•1 I1.61.J.C’‘J.CC.)I 0.4C12Cf..I I I012345678910Delay (ps)Figure 6.8: Cross-correlationinfrared reflectivity signalas a function oftime delay.Chapter 6. Ultrafast Semiconductors for 10.6 tm OpticalSwitching 196IIC2.0I • I • I • I• I1.51.00.500000 102 3 4 5Delay (ps)6 7 8Figure 6.9: Differential ofthe cross-correlation,I, curve as a functionof time.Chapter 6. Ultrafast Semiconductors for 10.6 ,umOptical Switching 197of LT-GaAS, and the use of RD-InP pulses as short as100 fs at 10.6 m can be easilyproduced. Obviously this requires reducing the pumping pulsewidth to 100 fs.The sensitivity of this technique to low-densityphotogerierated 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 dynamicsof buried interfaces where electrically injected carriers are generated deep withinthe structure. This is clearly demonstrated in the measurement of the non-equilibriumcarrier lifetime inIno.s5Gao.iAs/GaAsrelaxed superlattice [177].It should be emphasized that the experimentdescribed above provides an exampleof the utilization of this switchat 10.6 m; however, the frequency of thereflected pulseis determined by the infrared laser radiation source.By replacing the CO2 laser withanother infrared laser (A 1 nm), it is possibleto generate ultrashort pulses at thesewavelengths. It is interesting to notethat the generation of optical pulsesin the far-infrared range, with a pulse duration ofless than one optical cycle, can be achievedwiththis method.Finally, we should point out that inconducting the previous experiments,the carriersare initially injected with excessenergy high in the conductionband. The contributionof intraband carrier relaxationand intervalley scattering may playa role in determiningthe duration of the reflectivity pulses.Clearly, it is preferable to photoexcitethe carrierswith photon energy just abovethe band gap such that the effects ofthese processes areminimized.Chapter 7Conclusions and Suggestions forFurther Work7.1 IntroductionThis chapter summarizes the major experimentalresults of this dissertation, followedbysome useful suggestions forfuture experimental work on ultrashort pulsegeneration andsemiconductor probing.7.2 Summary and ConclusionsIn this thesis, we first describedthe principles and the theory behindoptical semiconductor switching and the possibilityof generating subpicosecondinfrared pulses at 10.6jtm. A numerical simulation of theswitching process was presentedto aid in the understanding of the infrared single-switchingprocess. The original model,which is based onthe carrier diffusion from the surfaceof the switch into the bulk,shows the feasibilityof producing picosecond and femtosecondlaser pulses. The pulseduration is found todepend on the initial injectedcarrier density.The measurement techniquesused during the course of theexperiments are time- integrated infrared reflectivitymeasurements, time-integratedinfrared transmissionmeasurements, time-resolved reflection-reflectioncorrelation measurements,and time - resolvedcross-correlation measurements.The information obtainedfrom these experimentsisused to determine the speedand the optimum operationof the optical semiconductor198Chapter 7. Conclusions and Suggestionsfor Further Work199switches. Even though the initial original-modelcalculations provide a reasonabledescription of some of the observed infraredreflectivity experimental results, the modeldoes not fully describe the observed time-resolvedreflectivity pulses from GaAs.This isconfirmed by performing detailed experimental investigationsof the basic characteristicsand the temporal evolution of the photogeneratedplasma in a GaAs infrared reflectionswitch. The information obtained fromthe original model and an enormousnumber ofexperiments on GaAs are used to developa better model that accounts for theoveralltemporal and integrated behaviourof the infrared reflectivity pulses.By introducing anadditional two-body recombination mechanism,whose rate is a function ofthe carrierdensity, we are able to obtain good agreementbetween the proposed model calculationsand the experimental results. Experimentally,at carrier densities- 10n, the two-bodyrecombination time is foundto be 0.5 ps. It is clear thatthis ultrashort recombination time cannot be explainedin terms of Auger or densityindependent two-body recombination processes. A possiblerecombination mechanismmight be a nonradiativeplasmon-assisted recombinationwith a recombination rate F=1.9 x10—28cm6/s. Thisrecombination mechanism ismore efficient at high plasma density.As the plasma densityand plasma frequency increase, the electronsat the bottom of the conductionband recombine with the holes highin the valence band. The recombinationmechanism resultsin the emission of plasmons.To our knowledge, there is noexperimental observation ofplasmon-assisted recombinationin GaAs, and one cannot concludethat from performingreflectivity measurements alone.Clearly, other experimentsare required to verify thisrecombination mechanism.In addition to the transient10.6 zm reflectivity from the GaAsswitch, the absorptionof infrared radiation inSi of various doping is investigatedafter free carriers are generated by absorption of a subpicosecondlaser pulse of above band gapphoton energy. Atheoretical model is presentedwhich predicts the transmissioncoefficient for an infraredChapter 7. Conclusions and Suggestions for FurtherWork 200laser pulse through a photogenerated e-hplasma in Si of various surface free-carrierdensities. By fitting the experimental datato the theoretical predictions, the imaginarycomponent of the dielectric function is accuratelydetermined. From the results, thefree-carrier absorption cross-sectionsat 10.6 ,im and the relaxation times are calculated.Themomentum relaxation time in n-dopedSi is measured to be 10.6 fs, whereas forp-dopedand intrinsic Si it is found to be 26.5 fs.These measurements are usedto determinethe speed of the infrared transmissioncut-off switch. Application of the transmissioncut-off switch to the time-resolved cross-correlationmethod showed that it is possibletomeasure the duration and the shapeof infrared pulses with a resolution limitedonly bythe duration of the excitation laserpulse.Clearly, for ultrashort pulse generation,the type of semiconductor materialused forthe switching process is crucial.The duration of the 10.6 im laser pulsesgeneratedfrom a single GaAs optical semiconductorswitch are 20—30 Ps long. Thesepulsesare two orders of magnitude longerthan what we expected to produce.We have foundthat to operate a single switch witha subpicosecond speed, the opticallyinduced carrierlifetime must be reduced. Thus,several techniques were exploredduring the courseofthe experimental work to reducethe carrier lifetime. Ultrafastrecombination centresare introduced during thesemiconductor material growthprocedure, by irradiation ofthe semiconductor material withan ion beam, and by the creationof defects in latticemismatched semiconductors.By using a 200 nm low-temperaturemolecular beam epitaxy grownGaAs layer grownat a low temperature of 320°C on a GaAs substrate, we demonstratedthe generationof 1 picosecond infrared pulsesat 10.6 ftm. The presenceof many As precipitatesinthis material act as fastrecombination centres, givingthe optically generatedcarrier alifetime of 0.5 ps.Furthermore, ultrafast infraredpulses at 10.6 tm as shortas 600 fs areproduced by using radiation damagedGaAs with a 180 KeVH dose of lx1016cm2Chapter 7. Conclusions and Suggestions for FurtherWork 201as an optical-optical switch. It was found that thegenerated infrared reflectivity pulsewidths are proportional to the H dose to the power—0.4. This allowed precise controlover the generated pulse duration. We believe pulsesas short as 100 fs can be relativelyeasily achieved by the use of radiation damaged InPas an optical semiconductor switch.We have also investigated the recombination lifetimeof nonequilibrium carriers in ahighly excited Ino.s5GaoiAs/GaAs relaxed superlatticestructure by studying the time-resolved infrared reflectivity at 10.6 gum. Latticemismatch between Ino85Ga015As andGaAs layers gives rise to misfit dislocations whichact as ultrafast recombination centreswhich result in a dramatic decrease ofthe carrier lifetime. We demonstratedthat thiscarrier lifetime is 2.6 ps. Laser pulses asshort as 10 ps were produced using this structure.This thesis demonstrates the feasibilityof generating femtosecond laser pulsesusingonly a single optical semiconductor switch.The lasers, the electronic equipment,and theoptical diagnostic systems built as partof this thesis work are still in use andmany moreinteresting experiments are plannedusing this ultrashort pulse laser system.Currently,a unique high-energy 1 J, 500 fsCO2 laser system, based on this work,is beingdeveloped. The low power optically switched10.6 m laser pulses will be amplifiedina 15 atmosphereCO2 laser amplifier module for the purpose of studyinglaser-plasmainteractions.7.3 Suggestions for FurtherWorkDuring the course of the experimentalwork, several alternative techniquesconcernedwith the generation of ultrashortlaser pulses were frequently discussedin our laboratory.Here, we present an experimentalproposal for producing suchpulses and an alternatemethod for probing semiconductors.Chapter 7. Conclusions and Suggestionsfor Further Work 2027.3.1 Ultrashort 10.6AumLaser Pulse Generation by BeamDeflectionHere, we propose a simple technique for producingan ultrashort laser pulse in a widerange of wavelengths. The proposed techniqueis based on ultrafast beam deflectionusingthe transient optical Kerr effect in highlynonlinear materials [245]—[252] .The principleof ultrafast all-optical laser beam (pulse) deflectionis 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 sectionis similar to those of references[248]—[252].The optical arrangement of the ultrafastoptical Kerr deflector is illustratedin figure7.1, and it consists of the following components:a CW CO2 laser, an intense ultrashortpump pulse of a duration of500 fs, a nonlinear material such asCS2,a small entranceslit, a focusing lens, and a smallpinhole. The basic operation ofthe ultrashort pulsegeneration scheme is simple: thenonlinear optical materialis placed behind a smallentrance slit of width d0, then theCO2 laser beam is directed perpendicularonto theaperture and is focused by a smallfocal length lens on the edgeof a pin hole of widthW. The intense‘-.1 mJ, 616 nm, 490 fs laser pulseis directed on the entranceslit atan angle with respect to theCO2 beam, so that it excites a prism-shapedvolume inthe CS2 cell, as shownin figure 7.1. The CO2 laserbeam passes through anopticallyinduced temporal prism whichis created by the intensepump beam due tothe opticalKerr effect. The nonlinear refractiveindex, is time dependentand it is equal ton2Is(i), where n2 is the nonlinear refractive indexcoefficient, andI3(t) is the visiblepump pulse intensity. As the10.6 m beam propagates throughthe medium of lengthL, the temporal Kerr prism causesspatial phase modulation thatresults in the infraredbeam deflection. Clearly, thedeflection angle,Od(t), is a function of time; therefore,for ultrafast deflection operation,it is appropriate to usematerials with an ultrafastChapter 7. Conclusions and Suggestions for FurtherWork 203nonlinear response. If the infrared deflectedbeam is made to scan a small pinhole placedat a distance S away from the nonlinear medium,the transit time of the deflectedbeamthrough the opening, W, can beof the order of a picosecond or less. Thus,an ultrashortpulse is produced by ultrafast transmissionthrough the pinhole.As an illustrative example, we present some simpleapproximate calculations to determine the minimum pulse width that can be producedat 10.6 tim. The numerical valuesthat are used in the calculations are basedon the lasers, material, and componentswhichare available in our laboratory. More comprehensivecalculations should be performedtoproperly characterize the speed ofthe device in detail.In the far field approximation whereS >> L and d0, the time,TD, needed for thedeflected infrared beam to scan a smallpinhole is related to the deflectionangle Oj by_W dO-1TD— --(--). (7.1)With the aid of figure 7.1 and byusing Snell’s law for light refraction,we obtain theexpression(n0+n1)L =n0[LcosOd +d0siriOdj (7.2)where n0 is the linear refractiveindex. By using a small deflectionangle approximation,Odand COSOd 1, the expressionreduces toO(t)d= nt)L(7.3)An important parameter thatmust be considered is the diffractionof the deflected beam.The diffraction angle determinesthe number of the resolvablespots (resolution of thedeflector),N, and thus the minimum aperture widthof the pinhole. For a gaussianbeam, the far field diffractionangle, O, is given byAOf =, (7.4)7rw0Chapter 7. Conclusions and Suggestions for FurtherWork 204where w0 is the beam waist. Using equations7.3 and 7.4, the number of resolvable spotsisN3= 0d= w0n1L(75)The minimum aperture size is limited by the diffractionspot of the infrared beam.Forminimum separation of two observablespots, the minimum pin hole widthis given by(7.6)7tW0The rate of change of the deflection anglewith time is proportional to therate ofchange in the nonlinear refractive index,ni. Therefore it is highly desirable to useanonlinear material with an ultrafast responsetime, Tr. For an ultrafast excitationpulse,the expressiondOd/dt can be approximated by its instantaneous responseto the pulse:dOd — dn1 L n1L7 7dt — dtdoTrdoBy combining equations 7.1, 7.6 and7.7, one obtains an expression for theminimumpulse width that can be obtainedfrom such a deflector\d0TrTD,mjn =(7.8)lrwonrjl LIt is possible to produce intensepulses with our ultrashort lasersystem (1 mJ in490 fs pulse) of the order of50 GW/cm2.Using this intensity andn2= 1.5xl011 (esu)for CS2,we obtain a value forni=6.3x103By substituting some realisticnumericalvalues:Tr 2 ps [251], d0 w0, L = 23 mm (i.e. cv= 85°), and )=10.6m,we calculatea minimum pulse widthof 46 fs with N3= 43. This pulseis approximately1.5 opticalcycles of the CO2 laser radiation.The potential for thistechnique to generate evenshorter pulses is possible bysimply using a faster nonlinearmedium.Chapter 7.Conclusions and Suggestionsfor Further Work205__________________4—_______________________10.6___ _____ ________________[.meFigure 7.1:Schematics of theall-optical beamdeflector used forultrashort pulsegeneration.Chapter 7. Conclusions and Suggestions for Further Work2067.3.2 Back Surface Infrared Reflectivity MeasurementsAn interesting experiment that can be performedis a measurement of the backside infrared reflection from GaAs as illustrated in figure7.2. 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 backsideand the infrared probe is incidenton the front surface. As a result, the e-h plasmadensity 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 increasingwith depth. Clearly, the reflectionproperties (efficiency, pulse shape, and duration) ofthe backside illuminated switch aredifferent from the standard operation.Unlike time-resolved front side probing, wherethe infrared beam is reflectedoff a thin overdense plasma layer, for backsidereflectionthe probing infrared radiation propagatesthrough a thicker plasma layer with itscriticaldensity 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 thiseffect. However, no further attemptwas made totime-resolve the duration of the reflectedpulses. 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Sci, Instrum.,62, 600 (1991).Appendix A,5YcoDesign Circuits of the SynchronizationUnitThis appendix outlines theelectronic circuit diagramsof the synchronization unitused to synchronize the hybridCO2 laser with the femtosecond laserpulse system.Diagram A.1:UBC PHYSICS — ELECTRONICS LABI4/Z/ I V ITItLCPOWER SUPPLY227UBCPHYSICS—ELECTRONICSLABOATt94/5/JI.4E110,61ItL(40MHzBUFFERI—II-i I..... I.40110*4(7OOnVp—p)>114-14L5IT40L01oOUT(IVp—p)Appendix A. DesignCircuits of The SynchronizationUnitDiagram A.3:CLKI+5V+5V22994/5/3LJBC PHYSICS —ELECTRONICS LABJscci or 9TItLTRIGGER CIRCUITTRIG 047C7345V5319?49C20Appendix A. Design Circuits of The SynchronizationUnit 230Diagram A.4:;Lz10-_!__: .____-_______ ___TTTT‘ri’‘1i’4.’Appendix A. DesignCircuits of The SynchronizationUnit 231Diagram A.5:,-U)*A;;.;v:__d I_______: :2‘5rrr rrrfl1Fr—— —.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—. rMINPUTniJI.04W+24WC4OUTPUTSneNobI2PinUicvophoneCannOtto,-J4ISC426NoteI: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 electroniccircuit design of a fast photodetector amplifier which was discussedin Chapter 4. The amplifier electronic circuitis shown in figure B.l. The amplifier’s outputas a function of pulse frequency ispresented in figure B.2.In order to check the pulse width distortion and measurethe gain of the amplifier,a 1 ns (337 nm) pulse from a nitrogenlaser is attenuated to the signal levelof thatfrom Cu:Ge. The signal is detected witha fast detector (Hamamatsu-R1193U.03)and displayed on the 1 GHz bandwidthoscilloscope. The amplifier doesnot causeany pulse distortion, as shown in figureB.3. The measured gain at 1 GHz is34 dB.234Appendix B. The Fast PhotodetectorAmplifier Circuit and Performance 2351.1 Siohj,i .2 50ohlLi 50h, FEEOTROUGH_______________________ ____________________rrrrn—mm mm5J6 J7IJ6 J9JsiiJI2 JS’+]14Tu i 0ip i 00p00p 1 00p 0U_ _Icat cat cat, 21330270Ri —r22R310 I2ouru001 cOOL- 2UL uOtUL041CLIIjA1_.uOOicatcat cot catFigure B.1: The amplifiercircuit.lL;I:.Jlllil• 111(111’ III •I0 000039 0000— 3703500.133°3142 345 2 345101 10210Frequency (MHz)Figure B.2: Photodetector amplifiergain as a function of theinput frequency.Appendix B. The Fast Photodetector AmplifierCircuit and Performance 236Figure B.3: (a) Input signalto the amplifier. (b) Amplified outputsignal 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 ofthe Pulse Integration ModuleIn this appendix, wepresent the circuit diagramsfor the pulse integration module(PIM) which was discussedin 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 Designof The Pulse IntegrationModuleDiagram C.4:--t:-Th-t:240-JC.,z0C.,-JwC,,C-,C,,>-=3-C.,w-Jz00I-;I— az(J0w aii-. a.C)4JHtr-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—flA Pl—2OPt—IA Pt—li Pt—es<P1-SILASERTRIGGERINPUT/ADCTRIGGER00074ACTO1A7UCt0ZAppendix C. CircuitDesign of The Pulse Integration Module 242Diagram C.6:-J(I,C.)o,aU:w-JC,wII(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 aaa a a a a a a a zz% % % — -. •% %_ — ,ø-IU,C.,z0IC.)w-awU,C-)U,0.C-)Appendix C. CircuiiDesign of The Pulse IntegrationModule 243Diagram C.7:C,’L.all-p.‘C-Jww(3C,I-.U,‘C-aINPUT2UBCPHYSICS—ELECTRONICSLABDAft,9—O9—O8II€u,1@i2TITLI,ANALOGOUTPUTMODULEaqC)t11.0 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°1TUITwIUIQE I7411C4311UBCPHYSICS—ELECTRONICSLABIliCt93—09—08Isicci2oc2IltLC,ANALOGOUTPUTMODULEHI7OuS.c7111+02•5Sic14OCT20•52/ADCTRGC€R P1—HAP1—118Pt—hA<ctI-Iaq(),sy600HzXUITRATE74HCO874HC108A.1114z7411CT123ONLEDUBCPHYSICS—ELECTRONICSLABOATC93/9/2Ior3TI1LtDUALSERIAl.ADCMODULEAppendix C. Circuit Designof The Pulse IntegrationModule-JU,z00-I0U.)00Diagram C.11:riI2Ij24700U0IaUID0•1C.IN+ I +I— —,. za.N a. a. > a.z C.U (3 (3(3o+0 00_I _J_I + _I4 44 4z zz z4 44 4(Na.z-jcn.z0C.)--aw -U,C.)U,>-..1Appendix C. CircuitDesign of The Pulse IntegrationModule 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 ofthe autocorrelator is the second harmonicgeneration crystal (SHG). The nonlinear crystalused in the current setup is a0.5mm thick Potassium Dihydrogen Phosphate(KDP) crystal with a 10 mm aperture.The angular adjustment of the crystal is very crucialin obtaining a SR signal; therefore, the crystal is mounted on a fine-rotational-tiltstage which provides excellentcontrol over the crystal alignment. Thecrystal is oriented to obtaina maximumSH signal which emerges from the crystalalong the bisector of the two converginginput light beams.In order to produce a SH signal fromthe 616 nm laser pulses, the two pulses mustbe simultaneously present at the crystalwith a phase matching angle of59.26° fromthe optical axis. The crystal is cut atan angle of 58.6° which is slightlyless thanthe phase matching angle. The small angledifference of 0.7° eliminates thebackreflection into the laser cavity.The thickness of the crystal limits thetemporal resolution of the autocorrelator.This can limit the minimumpulse that can be measured withthis device. Thecrystal length determines the bandwidthof the SHG signal, and it shouldbe shorterthan the coherence length of the frequencycomponents of the lightpulse in orderto avoid dispersion. For a given KDP crystallength,ALcry, one can calculate thebandwidth resolution,AVcr,, of the autocorrelator from the followingrelation [253]VcryALcry = 0.3122(nm — cm)(D.1)From our experimental parameters,the temporal resolution of theautocorrelator249Appendix D. The Autocorrelator Design and Optical Components250is calculated to be 90 fs times the pulse shape factor.For a double exponentialpulse shape the autocorrelator resolution, due tothe crystal thickness only, is --‘ 40fs. The overall resolution is ‘ 60 fs. This temporal resolution is adequatefor ourexperimental purposes.The KDP crystal is transparent to both fundamental (616nm) and SH (308 urn)signals; therefore, for proper SH detection, the fundamentalsignal must be filteredout. In the autocorrelator design, a piece of 3x5x5cm3 Corning (G 57-54-1) filter is used. The filter is inserted directlyin 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 photomultiplierwith a U.V. input window and a risetimeof2.5 us. The photornultiplier is biased to a voltageof 600 V. Due to the operatingsensitivity of the photornultiplier, itis placed in a light-tight cylindrical housingwith the SR signal entering through a3 mm diameter pinhole.A low pass filter/amplifier is used to filter outthe high frequency components inthe autocorrelation trace and to amplifythe autocorrelation signal. The circuitdesign for the filter/amplifier is presentedin figure D.1. The output signal from theelectronic amplifier/filter arrangementis used to drive the vertical axis of ahighimpedence oscilloscope, where thesignal amplitude correspondsto points on theautocorrelation trace. All the mirrorsused in the autocorrelator are frontsurfacealuminum coated silica: M1—M5 are2.5 cm in diameter and 6.5 mmin thickness.The retrorefiector mirrors M6 andM7 have a dimension of 12.5x12.5x6 mm3.The 50:50 beam splitter used in the autocorrelatoris 6.35 cm in diameter.Thefocussing lens is a plano convextype with a focal lengthof 3 cm and a diameter of12 mm. This lens is mountedon a homemade fine-translation stageto adjust thefocus on the SH crystal. The rotationof the mirrors is done with atorque motorAppendix D. The AutocorrelatorDesign 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 amplifiercircuit used for the autocorrelationpulse mea0=50=4243 1k62+5VJrIc,IC21LI L3LO‘H40O5FI (— —HF—lO,F 1SF357 357CO C1207511 0261?L—iCO C13CND>— r,020>22J_.I ‘c!7‘::C22H040055VT’ T°’L25v— L610 F1SF‘v’ L4I0F \1--7surements.Appendix D. The A utocorrelator Design and Optical Components252which rotates at a constant reliable frequency of 25 Hz. This motorprovided analmost vibrational-free scanning mechanism. The controlbox of the autocorrelatorhas the functions of: relative delay scan adjustment between the triggerpulse andthe autocorrelation scan, and signal gain adjustment. Triggeringof the oscilloscopefrom the autocorrelator is performed using an optical interrupterplaced under therotating mirrors. The delay of the trigger signalcan 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 scaleon the oscilloscope screenfrom the relative scanning time to the real time.The calibration of the horizontalscale is done manually. Here, one uses the opticalpulse itself to calibrate the timescale. If the two arms of the interferometer areequal, both laser pulses overlap onlyat one point in time. When the retroreflectoris scanned while the rotating arm isspinning, the dye pulses overlap atdifferent points in time, resulting inthe SHsignal peak being shifted as afunction of the retroreflector scan. Onecan use thisto obtain a calibration factor for the autocorrelatorfrom the following relationTscaie —20t(ps/ms) (D.2)whereXd 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 accountsforthe actual distance travelled by thepulse. Experimentally, the calibrationfactor ismeasured to be 81.33 ps/ms. Theoreticalcalculation of the calibrationfactor fromreference [134] givesTscaie= 4frDr(D.3)where c is the speed of light,Dr(=7.62 cm) is the distance betweenthe tworotating mirrors, andfr(=25 Hz) is the rotational frequency,giving a calibrationAppendix D. The Autocorrelator Designand Optical Components253factor of 79.79 ps/ms which is in goodagreement with the above measured value.


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