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Measurements of optical properties of bulk and thin film semiconductors using the PDS technique Elouneg-Jamroz, Miryam 2006

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M E A S U R E M E N T S OF O P T I C A L PROPERTIES OF B U L K A N D T H I N F I L M S E M I C O N D U C T O R S USING T H E PDS T E C H N I Q U E by Miryam Elouneg-Jamroz B . S c , M c G i l l University, 2003. A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in The Faculty of Graduate Studies (Physics) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A November 2006 © Miryam Elouneg-Jamroz, 2006 Abstract i i Abstract Photothermal deflection spectroscopy (PDS) was used to measure the bandgap op-tical parameters and the Urbach energy of semi-insulating (SI) GaAs and a 238nm G a N A s epitaxial thin film in the energy range 800-1 lOOnm. To do so, a P D S ap-paratus was setup using a O. lmW and lOnm bandwidth pump beam obtained with a f/3.8 monochromator and a 150W Tungsten Halogen lamp, a HeNe laser for the probe beam, CCI4 for the deflecting medium and a linear position sensitive detector. The spectra obtained for GaAs and GaNAs were compared with models based on the Rosencwaig-Gersho and the Fernelius theories of I D heat diffusion which consider absorption in respectively one and two sample layers, and also on a model of absorp-tion based on literature results. Preliminary results indicate that more work wil l be needed on the apparatus/models to qualify the validity of the fitted optical param-eters. The P D S apparatus demonstrated an absorbance sensitivity limit of ~ 1 0 - 2 with the samples investigated. Contents i i i Contents Abstract i i Contents i i i List of Tables v List of Figures v i Acknowledgements x i 1 Introduction 1 2 Principles of PDS 3 2.1 Introduction 3 2.2 One-dimensional Heat Diffusion 4 2.2.1 Validity of the One-Dimensional Model 10 2.2.2 Magnitude of the D C temperature . . . . 11 2.3 Probe Beam Deflection 12 2.3.1 Investigating the Effect of x0 and / on the Probe Beam Deflection 15 2.3.2 Probe Beam Size Effects 17 2.4 Sample Surface Temperature Dependence on Optical and Thermal Properties 18 3 Setup and Experiment 21 3.1 Introduction 21 3.2 Sample Setup 21 3.2.1 Deflecting Medium: CC1 4 22 Contents iv 3.2.2 Sample Dimensions, Sample Holder and Cuvette 23 3.3 Probe Beam 25 3.3.1 Probe Beam Path 25 3.3.2 The Knife Edge Method 26 3.3.3 Effect of CC1 4 on the Probe Beam Focus 29 3.4 Pump Excitation Beam 29 3.4.1 Monochromator and Light Source 29 3.4.2 Pump Beam Power Spectrum 30 3.4.3 Bandwidth of Pump Beam 31 3.5 Detection System . .•• 31 4 Experimental Results 37 4.1 Introduction 37 4.2 Semiconductor Absorption at the Bandgap 38 4.3 Modelling the P D S signal 39 4.4 Analysis of P D S results 43 4.4.1 Results for Semi-Insulating GaAs 43 4.4.2 Investigating optical absorption properties of a G a N A s thin film 45 4.5 Discussion 50 5 Improvements to the Experimental Setup 52 6 Conclusions 54 Bibliography 56 Appendices 60 A Comparing Spectra from Rough and Polished Back Surface GaNAs 60 List of Tables v List of Tables 2.1 Thermal properties of some materials of interest. (The data source is (a) from [1], (b) from [2], (c) from [3].) 8 2.2 Parameters describing the P D S experiment on the GaAs substrate. These values were used to generate the time snap-shots of the temper-ature in CCI4 in Figure 2.4 8 2.3 Thermooptical constant ^ for substances commonly used as a deflect-ing medium. (Data source is from [2]) 12 4.1 Values for GaAs optical absorption properties used in modelling the P D S spectra 45 4.2 Values for GaNAs optical absorption properties used in modelling the P D S spectra. The substrate optical properties were fixed and the pa-rameters in this table were fitted to the experimental spectrum. . . . 49 List of Figures v i List of Figures 2.1 The basic P D S setup 4 2.2 Cross-sectional view of the sample also showing the position of the surrounding regions. This geometry is used in the one-dimensional analysis of the heat diffusion 4 2.3 Sketch of the GaAs substrate sample setup 8 2.4 The A C component of the temperature distribution in the CCI4 at the GaAs surface for the conditions described in Table 2.2 with a chopping frequency f=10Hz. The different curves show the temperature profile at different times during one chopper period 9 2.5 Graphs showing the temperature profile at the sample surface in CCI4 for the excitation conditions outlined in Table 2.2 for two different chopping frequencies. As the chopping frequency is increased from (a) 10Hz to (b) 25Hz we notice a decrease in the A C temperature at the sample surface as well as a decrease of the the thermal diffusion length in the deflecting medium 10 2.6 Profile of the D C temperature increase in and around the sample for the excitation conditions outlined in Table 2.2 11 2.7 Schematic of the probe beam bending when it travels through shells of differing refractive index in the I D geometry, (modified from [2]) . . . 13 2.8 Resulting probe beam displacement measured a distance L from the sample 15 List of Figures vii 2.9 Probe beam deflection amplitude and phase measured experimentally and compared with the ID P D S model. Figures (a) and (b) show the deflection dependence on chopping frequency: comparison of the data with the I D model indicates an offset xo — 80/Ltm for these measure-ments. Figures (c) and (d) show the deflection dependence on the offset Xo 16 2.10 Graph (a) shows the temperature profile for the excitation conditions outlined in Section 2.3.1 along with the extent in the x direction of the probe beam with two different diameters, 30/zm and 80/zm centered 80/zm in front of the sample. The deflection of three different parts of the probe beam is shown for beam diameters of (b) 30/xm and (c) 80^um. In the two latter graphs, the solid curve is for the probe center deflection; the dashed curve is the edge travelling closest to the sample; the dash-dot curve is for the edge farthest from the sample 19 2.11 Schematic diagram showing the condition where the thermal diffusion length of the sample fis is much longer than the sample thickness. The P D S signal wi l l strongly depend on the magnitude of the optical skin depth na 20 3.1 Experimental setup for photothermal deflection spectroscopy 22 3.2 Schematic diagram showing the sample holder assembly with the cu-vette. The sample is held onto the glass holder with teflon tape, which doesn't react with CCI4. The circle at the sample surface in the side view shows the out of page propagation of the probe beam, in the pos-itive z direction. In the side view, the positive x direction is to the left, away from the sample surface 24 List of Figures vi i i 3.3 Knife-edge measurements. Figure (a) shows a transverse profile of the gaussian probe beam during knife-edge measurements. Figure (b) shows a schematic diagram of the knife-edge setup. The photodiode is placed close to the focus where the beam cross section is smaller than the active area of the photodiode. (modified from [4]) 26 3.4 Normalized power plotted for a knife-edge measurement of the probe beam cross section near the focus. Values on the x-axis refer to the reading on translation stage transverse to the probe beam direction. From the fit we extract a probe beam radius OJ0 = 66//m 27 3.5 Profile of probe beam radius UJ0 determined with several knife-edge sections around the focus. The x-axis indicates translation stage read-ings. The error bars come from the fit goodness of each knife-edge cross section measurements 28 3.6 Diagram showing the refraction of the probe beam when it enters the cuvette filled with CCI4. The focus position shifts from x to n c c u ^ and the confocal distance also gets stretched by nccu 29 3.7 Power spectrum of the monochromator. The photodiode measurement of the monochromator output spectrum shown in (a) is divided by the photodiode responsivity (obtained from the U D T catalog [5]) for differ-ent photon energies shown in (b) to obtain the acurate monochromator profile shown in (c) 32 3.8 Monochromator output measured with a Fourier Transform spectrom-eter. It shows a FWHM of lOnm. The peak wavelength occurs at lOOlnm, showing a discrepancy of l n m with the lOOOnm that could be read from the monochromator indicator 33 3.9 Total photocurrent generation signal Va + Vb varying with incident probe beam power. Based on this graph, we operated the detector with Va + Vb in the 5V to 8V range in the linear regime safely below the 13V saturation level. 34 List of Figures ix 3.10 The detector photocurrent difference signal 14 — 14 when the detector is moved transverse to the probe beam direction. The probe beam has a round cross section with a gaussian intensity profile and its diameter at the detector is 5mm, same as the width of the detector. The difference signal is directly proportional to the probe beam position around the detector centre. The graph shows a signal per probe deflection ratio T r = 3 . 7 V / m m here. The x-axis indicates readings on the translation stage 35 4.1 This absorption data for semi-insulating GaAs at 294K show a bandgap energy £ ' s =1.427eV with a 9 =8000cm - 1 . The relationship between ab-sorption coefficient and photon energy above the bandgap can be ap-proximated by a straight line with slope A. (Reproduced from M . D . Sturge [6]) 40 4.2 Model of the optical absorption of GaAs used in the treatment of P D S experimental data 41 4.3 Model and experimental results for P D S signal from semi-insulating GaAs. The stars show the experimental data; the solid curve shows the P D S model and the dash dot curve shows the model convoluted with a lOnm bandwidth excitation beam with a peak wavelength shifted by +6.1nm 44 4.4 Graph showing the normalized spectra for the GaAs wafer with and without the GaNAs thin film 47 4.5 Schematic of the sample geometry in the case described by Fernlius' model with a thin film or thin coating on a substrate 48 4.6 Model and experimental results for the P D S signal from a GaNAs 238nm thin film on a semi-insulating GaAs substrate. The model con-volution is done with a lOnm bandwidth exitation pump shifted by +5.7nm towards higher energies 50 List of Figures x A . l A F M images of the back surface of the GaNAs sample wafer before and after it was polished by hand with various size alumina particle pastes. The R M S roughness goes from (a) 652nm before polishing to (b) 9nm after polishing. These images were taken with the help of Micheal Whitwick of the U B C Physics M B E Lab 60 A.2 P D S spectra of GaNAs taken before and after the wafer back surface was polished. In graph (a) of the superposed spectra, the rough back surface sample shows slightly more absorption at the thin film. Fig-ures (b) and (c) show loose fits of the spectra, which yield a bandgap absorption a ^ a N A s of 13800cm - 1 for the sample with the rough back surface and 10200cm - 1 after the back surface was polished 61 Acknowledgements xi Acknowledgements I would like to thank Professor Jeff Young for his supervision, continuous guidance and encouragements. I am grateful to Mario Beaudoin for presenting this project to me; I learned a great deal from it. Thanks to Georg Rieger for his everyday advice and help with the experiment. A n d special thanks to Professor Tom Tiedje for very insightful discussions on the project and for always taking the time to answer my questions. I am lucky to have had the best and the nicest labmates. I 'm talking especially of Murray McCutcheon, Andras Pattantyus, Mohamad Banaee and Haijun Qiao who never hesitated to lend me a hand around the lab. Thanks to Er in Young for collaborating in this project... and thank you for being such a good friend. Thanks to Robson Fletcher...for your incredible support. Finally, special thanks to my family. I dedicate my thesis to them. Chapter 1. Introduction 1 Chapter 1 Introduction Photothermal deflection spectroscopy, or P D S for short, is a discipline in the broader field of photothermal sciences. This field is concerned with deducing thermal and optical properties of materials from the study of heat produced in a sample through light absorption [1]. Indeed, a temperature rise in a sample is directly related to the sample heat capacity and thermal conductivity, and those of the surrounding materials. If those thermodynamic properties are known then measuring the effects of a temperature rise due to light absorption in a sample can reveal its optical properties. In the specific case of P D S , the temperature rise in the sample translates into a temperature rise in the surrounding transparent medium causing a change in its refractive index [7]. This is probed by measuring the deflection of a laser travelling tangent to the sample surface. The strength of the P D S technique lies in the investigation of low absorptions. In this area P D S holds several advantages over transmission spectroscopy, the method most commonly used to measure absorption. A major limitation of transmission is that it cannot distinguish between light absorption and light scattering effects. This is less of a problem in P D S since only the absorbed light produces thermal effects. P D S also exhibits a higher sensitivity and was shown to measure absorbances reliably down to al ~ 10~ 5 as opposed to al ~ 1 0 - 2 commonly demonstrated for transmission techniques [8]. Here a is the absorption coefficient and I is the sample thickness. Moreover, P D S measurements are non-contact and non-destructive to the sample, and the apparatus is low cost and is easily setup with components commonly found in any optics laboratory. P D S is widely used nowadays to study electronic transitions of thin film semicon-ductors below the bandgap [9]. P D S is a particularly suitable method to investigate Chapter 1. Introduction 2 the exponential rise of the bandgap absorption edge or the so called Urbach edge [10][11]. The goal of the present project was to study and understand the P D S technique from a theoretical point of view and to setup and fully characterize a working appa-ratus. The setup was tested by investigating the optical properties of bulk crystalline GaAs and by comparing the results with known values. W i t h the working setup we also investigated the bandgap properties of a thin film of G a N A s that was grown by molecular beam epitaxy. In Chapter 2, we explain the basic principle of the P D S technique. Chapter 2 goes over the theory of the photo-induced heat diffusion in and around the sample and the theory governing the probe laser beam deflection. Chapter 3 goes over how the P D S experiment was built and characterized. Finally Chapter 4 presents P D S spectra for bulk GaAs and for the epitaxial G a N A s thin film along with the model we used to extract optical parameters from the spectra. Chapter 2. Principles of PDS 3 Chapter 2 Principles of PDS 2.1 Introduction The basic principle of P D S is straightforward (see Figure 2.1). A modulated 'pump' beam of light illuminates the front surface of a sample of interest and gets absorbed according to the optical properties of that sample. The absorbed light is either reradiated or converted to heat. The generated heat diffuses throughout the sample and also further flows into the surrounding medium where it creates a heated region above the sample surface. There, temperature gradients give rise to a gradient in the medium's index of refraction. Since the pump beam is modulated, so are the heat flow and the change of index of refraction. W i t h the surrounding medium chosen to be transparent, one can pass a 'probe' laser beam right in front and parallel to the sample surface to measure the gradient of the refractive index, and through modelling, this can be traced back to determine the absolute amount of the pump light absorbed at each incident frequency. This chapter is concerned with explaining the basic principle of P D S in more detail. Section 2.2 describes the theory of the diffusion of heat from the absorbing sample into its surroundings in a one-dimensional geometry. Section 2.3 goes over the theory of the probe beam deflection; and Section 2.4 explores the P D S signal depen-dance on the sample thermal and optical properties in some specific cases relevant to the measurements made in this thesis study. Chapter 2. Principles of PDS 4 probe beam pump beam sample position detector Figure 2.1: The basic P D S setup. pump Figure 2.2: Cross-sectional view of the sample also showing the position of the surrounding regions. T h i s geometry is used i n the one-dimensional analysis of the heat diffusion. 2.2 One-dimensional Heat Diffusion For the understanding and analysis of results from a P D S experiment, the one-dimensional model of heat diffusion [12] is most often used because it provides a good enough approximation to the actual experimental conditions and it is much simpler than a full three-dimensional model [13] [14]. The geometry we use for the analysis is shown in Figure 2.2. Three regions must be taken into account: the backing or sample holder that extends a distance lb behind the sample, the sample of thickness ls and the deflecting medium that extends a distance lg in front of the sample. The deflecting medium can be either a gas or a clear liquid. Both the backing and the deflecting medium are as-sumed to be non-absorbing at the wavelengths where the sample is being investigated. The pump beam incident on the sample is monochromatic and is assumed to be si-nusoidally chopped with angular frequency u (rads/s). Its time-averaged intensity / Chapter 2. Principles of PDS 5 ( W / m ) can be expressed as / = i / 0 ( l + e ^ ) - (2.1) where 7 0 ( W / m 2 ) is the average pump intensity. Note that complex notation is used in this work: it is implied that all the physical values are given by the real part of the complex expressions. A n amount Q ( J /m 3 ) of energy is deposited per unit volume of the sample by the pump beam; assuming that the substrate is homogeneous Q can be expressed as Q(x, t) = ^ar)eaxI0(l + e*"*) for - ls < x < 0, (2.2) where a (1/m) is the optical coefficient of absorption of the sample at some wavelength A and 7/ is a constant between 0 and 1 that characterizes the efficiency of the sample to convert absorbed light of wavelength A to heat in the material. For most solids at room temperature rj—1, so this value wil l be assumed from now on. Note that the value of x in Q and all subsequent equations should have a sign convention consistent with Figure 2.2. One can find out, how the generated heat wi l l distribute and what the temper-ature wil l be in the entire apparatus by solving a heat diffusion equation for the sample, backing, and deflecting medium and by imposing boundary conditions at the interfaces between theses regions. The equations are 0 0 < x < lg, (2.3) -Q(x,t) d2Tg 1 dTg dx2 Pg CH d2Ts 1 dTs dx2 Ps dt d2Tb i m dx2 Pb dt k. -ls<x<0, (2.4) 'S and = 0 -lb-ls<x< -l„ (2.5) -^ slx=o — ^slx=0' Ts\x=_[s — Tb\x=_is, (2-6) ' dx U o ~ s dx l l = 0 ' 3 dx lx=~l° ~ b dx U-(»' 1 ' T9\x=lg = 0, Tb\x=_k^ = 0, (2.8) Chapter 2. Principles of PDS 6 where Ti is the temperature above room temperature in region i and where i is either g, s or b for the deflecting medium, sample or backing respectively; $ ( m 2 s - 1 ) is the thermal diffusivity of material i, defined as where ki ( J / (m s K)) is the thermal conductivity of material i, Pi (kg/m 3 ) is the density, and C, (J/(kg K)) is the heat capacity. The diffusion equations are homogeneous for the backing and deflecting medium because these regions are non-absorbing; in the sample region, the equation has to be solved including the inhomogeneous driving term associated with the deposited heat, Q(x,t). Taking a closer look at the sample heat generation expression, one notices that it can be broken down into a time-independent term and a time-dependent term, respectively ^ctIor)eax and ^alone^e^*. The time independent term gives rise to a constant uniform increase of temperature in the sample and its surroundings. The time dependent term produces a thermal wave with frequency UJ that propagates through the sample and penetrates some distance into the surrounding media. This thermal wave is seen basically as a small A C temperature fluctuation that oscillates at frequency UJ. Combining both the time dependent and independent terms yields a complete solution for the temperature distribution in and around the sample. That is Ti = TitDC + TitAC, (2.9) where i is either b, s or g. The complete set of solutions for the sample and its sur-roundings in the one dimensional geometry described in this chapter are not reported here but can be found in [12] and are usually refered to as the Rosencwaig-Gersho model solutions. The most important solution in the treatment of P D S is the A C temperature in the deflecting medium, that causes the measurable periodic probe beam deflection. This solution is Tg,ac = <(>RG exp(-cr 9 x -I- jut), (2.10) Chapter 2. Principles of PDS 7 where a l 0 r (r - 1)(6 + l)eaJ> - (r + 1)(6 - \)e~a'1' + 2(6 - r)e~al° <f>RG = 2ks{a2 - of) I (g+l)(b+ l)e»''» - {g - l)(b - l)e-"«'« J (2.11) with 6 = kbab/ksas, (2-12) # = kgag/ksas, (2.13) r - ( l - j > / 2 a a . (2.14) Moreover, aj = and = p~l, with m the thermal diffusion length of material i; Oi — (1 + z)a,. In the expression for Tg^c-, <I>RG is the complex amplitude of the temperature at the sample-deflecting medium interface and it is directly proportional to the pump intensity. The extent to which the thermal wave penetrates the deflecting medium is governed by the thermal diffusion length \ig. As fig is proportional to it is expected that the thermal wave wil l penetrate farther into the medium as the chopping frequency is decreased, and vice versa. Table 2.1 presents values for / i , k, p, C and B for different materials of interest, including those used in the present project. A few plots wi l l help explain the temperature behaviour described above. Imagine a semi-insulating GaAs sample 360//m thick mounted on a glass sample holder and immersed in carbon tetrachloride (CC1 4 ). The GaAs sample is illuminated with a pump beam with power O. lmW and cross sectional area 1mm x 1mm (or intensity 5 0 W / m 2 ) chopped at the frequency /=10Hz. For a wavelength where GaAs absorbs strongly such as above the bandgap, a is on the order of 1 x 1 0 4 c m - 1 . Figure 2.3 illus-trates this setup in the familiar one dimensional geometry and Table 2.2 summarizes all the parameters. Figure 2.4 shows the A C temperature distribution due to the diffusion of heat from the GaAs into the CCI4. The A C temperature amplitude A at the sample surface is very small: it oscillates between 0.5mK to -0.5mK in a half-period of the chopped light. The different curves show the temperature profile at a few different times Chapter 2. Principles of PDS 8 Table 2.1: Thermal properties of some materials of interest. (The data source is (a) from [1], (b) from [2], (c) from [3].) Material Density P & Specific Heat C& Conductivity Diffusivity / ? ( x l 0 " 6 f ) Diffusion length /x (mm) 10 Hz 25 Hz A i r 1.16 1007 0.026 22.26 0.842 0.532 Water 1000 4180 0.598 0.143 0.067 0.043 C C 1 4 1600 850 0.103 0.076 0.049 0.031 Rubber 1100 2010 0.13 0.06 0.044 0.028 GaAs 5376 330 55 31 0.993 0.628 Si 2330 712 148 89.21 1.658 1.066 Glass 2210 730 1.4 0.87 0.166 0.105 glass GaAs c c i 4 fc''.-; l:^m — I I I ••• J ——+— -5.36mm -0.36mm 0 5mm Figure 2.3: Sketch of the G a A s substrate sample setup. Table 2.2: Parameters describing the P D S experiment on the G a A s substrate. These values were used to generate the time snap-shots of the temperature in CCI4 in Figure 2.4. parameter value Is 360^/m lb 5mm h 5mm v. 7 ° 50 4 / 10Hz a 1 x l O ^ m - 1 Chapter 2. Principles of PDS 9 Figure 2.4: The AC component of the temperature distribution in the CCI4 at the GaAs surface for the conditions described in Table 2.2 with a chopping frequency f=10Hz. The different curves show the temperature profile at different times during one chopper period. Chapter 2. Principles of PDS 10 0 0.1 0.2 0 0.1 0.2 distance (mm) distance (mm) (a) (b) Figure 2.5: Graphs showing the temperature profile at the sample surface in C C I 4 for the excitation conditions outl ined i n Table 2.2 for two different chopping frequencies. A s the chopping frequency is increased from (a) 10Hz to (b) 25Hz we notice a decrease in the A C temperature at the sample surface as well as a decrease of the the thermal diffusion length i n the deflecting medium. during a half-period. Note that Omk on the plot refers to the D C temperature at the sample surface. The temperature variation in the C C 1 4 only extends ~150^m away from the GaAs surface. Increasing the chopping frequency has the effect of reducing the thermal penetration length and also of decreasing the maximum temperature at the sample surface as can be seen in Figure 2.5. 2.2.1 Validity of the One-Dimensional Model Up to now, it was assumed that there was a net flow of heat only in the x direction. Actually from the point of heat generation in the sample, the heat wave propagates in the x direction by a thermal diffusion length, but it also propagates the same distance in the plane perpendicular to the x direction. If the diameter of the excitation beam is much larger than the thermal diffusion length, i.e. d^> u.s, and its lateral intensity profile is approximately constant, then to a good approximation the ID solution wi l l be valid everywhere in the region in front of the uniform excitation spot. Chapter 2. Principles of PDS 11 position (mm) Figure 2.6: Profile of the D C temperature increase in and around the sample for the excitation conditions outlined in Table 2.2 2 . 2 . 2 Magnitude of the D C temperature Although it is not essential to the P D S analysis, it is interesting to look at a plot of the D C temperature distribution as well again for the conditions outlined in Table 2.2. The plot in Figure 2.6 reveals a uniform D C temperature increase of 0.08°C above room temperature throughout the absorbing GaAs sample, more than 100 times bigger than the A C contribution; this temperature decreases outside the sample to reach zero at the outer edges of the glass backing and CCL> as dictated by the third boundary condition. More specifically, the temperature in the glass backing and CCI4 are proportional to x, a solution of the homogeneous time-independent heat diffusion equation. In this particular case, the D C temperature increase is very slight and the sample setup can be considered to be essentially at room temperature. Note that the pres-Chapter 2. Principles of PDS 12 Table 2.3: Thermoopt ical constant for substances commonly used as a deflecting medium. (Data source is from [2]) Substance % (1(T 6 x K - 1 ) air -0.88 water (20°) -91 C C 1 4 -612 ence of kinks in the temperature at the region boundaries does not contradict the second boundary condition because it is the gradients of heat not the gradients of temperature that must be continuous. 2.3 Probe Beam Deflection The temperature gradient at the sample surface causes a gradient in the refractive index in the deflecting medium. For the small temperature changes encountered here, the temperature dependence of the deflecting medium's refractive index can be well approximated by d/fi n = n0 + —5T, (2.15) al where no is the room temperature value and ^ is called the thermooptical constant. Changing the temperature has a direct effect on the medium density. In most cases a temperature increase causes a decrease in the medium density, which has in turn the effect of decreasing the refractive index, bringing it closer to 1. Thus the thermoop-tical constant is usually negative. Table 2.3 lists the value of ^ for some substances often used as deflecting media in P D S . For a quantitative treatment of the probe beam deflection, Snell's law of refraction can be used in the geometry shown in Figure 2.7 [2]. Once again assume I D heat diffusion so that there is a temperature gradient only in the positive x direction, away from the sample. The probe beam travels in the positive z direction, centered a distance x0 from the sample. Here and for all probe deflection treatment done in Chapter 2. Principles of PDS 13 9+59 * z Figure 2.7: Schematic of the probe beam bending when it travels through shells of differing refractive index in the I D geometry, (modified from [2]) this thesis study we ignore the finite size of the beam; rather, we assume the probe to be an infinitly thin ray. The effect of the finite size of the probe beam is addressed briefly in Section 2.3.2. As it gets deflected perpendicular to the sample surface, the probe beam travels through different temperature regions. These regions can be thought of as very thin sections or shells with slightly different refractive indices. Applying Snell's law at the shell boundary at x0 in Figure 2.7 gives n(xQ) cos 6 = n(x0 + Sx) cos(0 + 59). (2.16) Expanding the refractive index on the right to first order in dx and also expanding the cosine sum gives n(x0)cosO= (n(x0) + -j^-5x^ (cos 9 cos 59 — sin 0 sin 50) (2-17) and considering 69 as small, we have n(xQ) cos 8 — (n(x0) + ~j~$x>) {cos9 — sin959), (2-18) and this can be easily rearranged to obtain dn , .59 — = n(x0) — tan0. dx dx Furthermore, given that tan0 = | j , 66 1 dn(xo)' 8z n(x0) dx (2.19) (2.20) Chapter 2. Principles of PDS, 14 Finally to find the total deflection angle, the last equation needs to be integrated over the probe beam path in the optically heated region: 9 ( 2 2 1 ) The gradient of refractive index is directly proportional to the temperature gra-dient if we use the approximation of Equation 2.15: dn dn dT — = (2.22) dx dT dx v ' dn d{Tg<DC + T9tAC) . . ~ dT dx { 2 - 2 6 ) and ^ can be taken to be at the offset XQ where the probe beam first enters the heated region. This is justified because the probe beam gets deflected only by a small amount when it travels over the sample. So, the probe beam is essentially still at XQ when it leaves the heated region. This is demonstrated in the next section. Also, as was shown with the example of the GaAs sample, the temperature remains close to room temperature in and around the sample, and for this reason n(x) can be assumed to be just the room temperature value no- Clearly Toe creates a constant change in n while TAC provides the time varying part of n. W i t h all that in mind, 9 becomes no dl d(Tg,pc + Tg,Ac) Az, (2.24) dx where Az is the width of the heated region along the probe beam path. As the probe deflections are small, lock-in detection has to be used and consequently only the A C part of the signal is measured. Dropping the time independent contribution from TG,DC and taking the gradient of T9JAC m Equation 2.10 , the amplitude of the time varying deflection angle 9 is 1 dn 9 = ——o-g<pRG exp(-o-gx + jut)Az. (2.25) 77fj al The deflection is measured by looking at the resulting displacement of the probe beam at a position sensitive detector. The probe deflections are small and so the Chapter 2. Principles of PDS 15 probe sample Figure 2.8: Resulting probe beam displacement measured a distance L from the sample. displacement of the probe beam at the detector is just QL, where L is the sample-detector separation. This is illustrated in Figure 2.8. From Equation 2.25 and Figure 2.8 it can be seen that to maximize the measurable deflection one has to maximize Az, L and I0 (which shows up in <ARG)J w i t n a ^ these parameters having a linear effect. The probe should be made to travel as close to the sample as possible because the deflection falls exponentially with the probe-sample distance x0. The choice of chopping frequency is also important but its effect on the probe beam deflection is more complicated as u shows up in both ag and 4>HG-2.3.1 Investigating the Effect of x0 and / on the Probe Beam Deflection So far 6 was expressed in complex form; it can be written as 0 = Dexp\j(ujt-ip)]+c.c. (2.26) What 's measured is D, the amplitude of deflection, and ip the phase lag of the probe deflection with respect to the periodic pump excitation beam. The phase ip can sometimes be used to get optical information on the sample when it is insufficient to only look at D. In an attempt to compare measurements with the I D P D S model, two experiments were carried out. The first experiment consisted in looking at the probe beam deflection and phase when the chopping frequency was increased from 10Hz to 105Hz keeping all other settings fixed. The sample used was GaAs in the Chapter 2. Principles of PDS 16 (c) (d) Figure 2.9: Probe beam deflection amplitude and phase measured experimentally and compared with the ID PDS model. Figures (a) and (b) show the deflection dependence on chopping frequency: comparison of the data with the ID model indicates an offset XQ = 80/xm for these measurements. Figures (c) and (d) show the deflection dependence on the offset XQ. conditions outlined in Section 2.2 with the exception that a HeNe laser was used as the pump beam with a power of 3.5mW on a 1mm diameter round spot (or intensity 4500W/m 2 ) . The heated distance along the probe beam path Az was therefore taken to be 1mm and the sample-detector distance L was 16cm. Figure 2.9 shows clearly that increasing the chopping frequency has the effect of decreasing the deflection amplitude especially at frequencies below 20Hz. The relationship is not exponential. Comparing the data with the I D model of deflection provides a way to find out the probe-sample distance rr0- In this experiment it was found to be 80/zm. At 10Hz Chapter 2. Principles of PDS 17 the deflection is measured to be 14//m at the detector site, and it drops to almost zero by 100Hz. At 10Hz this also means that the probe deflects by less than 0.1/^m in the heated region over the sample. This is very small in comparison to the actual beam diameter of a few tens of micrometers, and therefore it validates the assumption that the probe beam remains essentially at x0 all along the heated region. The choice of £o=80/Lim also makes the phase model agree with experimental results with only a small discrepancy. In the second experiment, the sample was moved away from the sample starting at the initial position found to be XQ = 80/xm through to 280/xm keeping f=10Hz. The results are shown in Figure 2.9. As expected, the deflection decreases exponentially as the probe intercepts the heated region further and further away from the sample. Both the deflection amplitude and the phase agree with the I D model fairly well. 2.3.2 Probe Beam Size Effects The minimum x0 distance is limited by the probe waist diameter at the sample. The waist diameter can typically be made to be a few tens of micrometers. Some parts of the probe beam travel closer to the sample than others and each part intercepts a different temperature gradient. As a result the deflection of the entire probe beam is not uniform. Figure 2.10 shows the deflection of three different parts of the probe beam for two probe beam diameter sizes, 30/im and 80/xm. The probe in each case is centered a distance 80^m from the sample. The parts of the probe beam closest and farthest away from the sample have different deflection amplitudes. Furthermore, the deflections of the different parts of the probe are phase shifted with respect to one another. For the 30/mi probe case, it is clear that averaging the deflections over the gaussian intensity profile of the beam would amount to something close to the center deflection. This clearly would not be the case for the 80/am probe or any larger beam size. This probe beam 'defocusing' is what is measured in Thermal Lensing (TL) , another photothermal spectroscopy technique [2]. We expect that this probe beam size defocusing doesn't prevent us from measuring the periodic deflection with Chapter 2. Principles of PDS 18 a lock-in detection system. Further probe beam size effects are discussed in reference [15]. 2.4 Sample Surface Temperature Dependence on Optical and Thermal Properties When we perform spectroscopic measurements on a semiconductor, we scan through different optical absorption states. The way the signal changes depends on the ab-sorption coefficent and also on the thermal properties of the sample. In this project we dealt only with semiconducting samples with very large thermal conductivities. A t 11Hz, the chopping frequency we usually used, our samples had a thermal diffu-sion length fis much longer than their thickness. That is to say, our samples were thermally thin. Figure 2.11 illustrates this condition schematically. The optical skin depth 1/ct is indicated by pa. The surface temperature and therefore the P D S signal wil l be directly proportional to a when fia is much longer than the sample thickness ls. That is because in this situation the fraction of light absorbed is approximately ctls and the heat generated is uniform throughout the sample. In the case where pa is much shorter than ls, the heat is generated very close to the sample surface but the A C temperature wil l be homogeneous throughout the sample because of the long thermal diffusion length. A t that point, any increase in a wil l not induce an increase of the sample surface A C temperature. In this regime the sample tempera-ture is saturated. So we expect that the signal starts to saturate when /j,a becomes comparable to the sample thickness, or when als ~ 1. The thinner the sample, the larger the a that can be probed with P D S before it enters the saturated regime. It is important to note that for thermally thin samples, the magnitude of the sample surface temperature wil l depend on the thermal properties of the backing or sample holder. To maximze the temperature in the sample, the backing should be chosen to be a poor heat conductor. Chapter 2. Principles of PDS 19 (a) 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 time (s) time (s) (b) (c) Figure 2.10: G r a p h (a) shows the temperature profile for the excitation conditions outlined in Section 2.3.1 along wi th the extent in the x direction of the probe beam wi th two different diameters, 30/zm and 80/xm centered 80/xm in front of the sample. The deflection of three different parts of the probe beam is shown for beam diameters of (b) 30/xm and (c) 80/xm. In the two latter graphs, the solid curve is for the probe center deflection; the dashed curve is the edge travelling closest to the sample; the dash-dot curve is for the edge farthest from the sample. Chapter 2. Principles of PDS 20 backing sample Ms + • 1 pump i I 1 Figure 2.11: Schematic diagram showing the condition where the thermal diffusion length of the sample fis is much longer than the sample thickness. The PDS signal will strongly depend on the magnitude of the optical skin depth na. Chapter 3. Setup and Experiment 21 Chapter 3 Setup and Experiment 3.1 Introduction Setting up a working P D S experiment represented the largest part of the present project. The experiment was assembled using mostly free space optics on an optical table with vibration isolation and it occupied an area 0 .5mxl .5m. Short posts and post holders were used to reduce vibrations. The complete layout of the experiment is sketched in Figure 3.1. The experiment can be broken down essentially into four parts: the probe beam, the sample setup, the pump beam and the detection system. This chapter discusses the details of how each of these parts was assembled and characterized. Knowledge to build the experiment came mostly from literature and partly from discussions with Jun Shen, a P D S expert working at the NRC-Fue l Cell Division in Vancouver. 3.2 Sample Setup The sample was mounted in a cuvette filled with carbon tetrachloride, CCI4, the deflecting medium we used. The cuvette was clamped on x and z translation stages and on a stage that allowed rotation in the x-z plane. The translation stages were necessary to allow precise positionning of the sample with respect to the probe beam; they were also useful in characterizing the probe beam profile with the knife-edge technique described in Section 3.3.2. Chapter 3. Setup and Experiment 22 HeNe AP1 N D F L" • L1 M \ I 0 AP2 L4 monochromator L3 L2 mechanical chopper L5 sample in cuvette H Lock-in amplifier detector -* z Figure 3.1: Experimental setup for photothermal deflection spectroscopy 3.2.1 Deflecting Medium: C C 1 4 There are several reasons why we chose CC14 as deflecting medium. First it has a very large thermooptical constant ^ (almost 7 times bigger than for water and close to 700 times bigger than for air). Furthermore, CC14 is a poor conductor so it helps create a large temperature gradient at the sample surface. Both of these characteristics contribute to a large probe beam deflection. In addition to having good deflecting properties, CCU is virtully non absorbing at all wavelengths from the visible to the far IR [2]. Therefore, it didn't absorb the probe or the pump beams, and being a clear liquid it also allowed us to see the sample when it was placed in the cuvette. During the course of our experiement CCI4 was not found to react with either the sample or the glass sample holder. It was always poured in the cuvette through an inorganic membrane filter to eliminate all suspended particles and impurities that could scatter the probe beam and introduce noise in the P D S signal. It is important to note that CCI4 is a dangerous chemial that can cause serious Chapter 3. Setup and Experiment 23 health problems. It is classified as a suspected carcinogen and reproductive toxin; the ingestion and inhalation of CCI4 are harmful and may be fatal. Long-term exposure to this chemical can lead to kidney and liver damage. The permitted exposure limit ( P E L ) is lOppm for 8 hours. It should always be handled in a fumehood and wearing appropriate protective gear including a lab coat, goggles and nitrile gloves. The M S D S for CCI4 should be studied carefully before it can be handled safely. 3.2.2 Sample Dimensions, Sample Holder and Cuvette A quartz cuvette (282 QS 1000 Hellma Cell) 12mm tall and with a 6mm x 6mm square base was used to hold the sample and the clear liquid. According to the specifications, this type of cuvette transmits a constant 87% of incident light in the spectral range 250nm to 2000nm. Losses are due to reflection only (absorption is negligible). The refractive index is n c u v e t t e — 1.458. The sample holder that went inside the cuvette was prepared in the U B C Chem-istry Glass Blowing Shop. It consisted in two cylindrical glass rods connected with a tapered middle part that fitted perfectly in the tapered circular opening of the cuvette to ensure a good seal. The glass part that was dipped in the CCI4 had a flat carved groove to hold the sample. This is illustrated in Figure 3.2. Samples were cleaved from larger pieces and were 0.36mm to 0.5mm thick, 1.5mm to 2mm wide along the probe beam, and approximately 10mm high. They were held onto the glass sample holder with teflon tape. The sample had to be positioned onto the P D S setup such that its front surface was perfectly parallel to the probe beam. The high index of refraction of CCI4 made it difficult to determine by eye the tilt angle of the sample inside the cuvette with respect to the probe position. To get the sample roughly parallel to the probe, we shone the HeNe laser from mirror M 2 (with M 3 removed; see Section 3.3.1) so that it would arrive at the sample at an angle approximately perpendicular to the probe beam; then the sample holder was turned inside the cuvette until the sample front surface reflected the HeNe beam straight back. Following that, with the working Chapter 3. Setup and Experiment 24 teflon tape sample glass sample holder \ 7 [o | > pump front view side view Figure 3.2: Schematic diagram showing the sample holder assembly with the cuvette. The sample is held onto the glass holder with teflon tape, which doesn't react with CCI4. The circle at the sample surface in the side view shows the out of page propagation of the probe beam, in the positive z direction. In the side view, the positive x direction is to the left, away from the sample surface. Chapter 3. Setup and Experiment 25 experiment, we brought small adjustments to the sample tilt with the rotation stage until the P D S deflection signal was maximized. 3.3 Probe Beam 3.3.1 Probe Beam Path The path of the probe beam was setup first before all the other components of the experiment were added. A 3.5mW HeNe plasma laser served as the source for the probe beam in the experiment. Its wavelength of 633nm was in the optimum sensi-tivity range of the detector. A small fraction of the laser beam was split off with a microscope slide (MS) to become the probe beam. The main (unreflected) beam was used as a high power, fixed wavelength pump beam to test the P D S experiment and it was also used for the sample allignment (see Section 3.2.2). Reflections from the front and back surfaces of the microscope slide created two parallel travelling beams. A n aperture (API ) with a hole opening diameter of about 0.5mm was used to select one of the beams. The aperture diffracted the beam, which made the beam diameter diverge to about 5mm as measured 1.5m away. The choice of beam diameter at the focus represented a compromise between a small beam focus radius LUQ which was desirable to approach the beam close to the sample, and a long confocal distance z0 (defined as the distance on either side of the focus where the UJQ increases by y/2) so that the beam would remain in focus over the entire width of the sample. Equation 3.1 was used to approximate u>o for a given focal length lens and aperture size and Equation 3.2 gave z0: uo = 1 .22A/ n u m (3.1) and zo = —^—, (3.2) where A is the probe beam wavelength, fnum the f-number of the lens used to focus the beam and n is the index of refraction of the medium where the beam is travelling. Chapter 3. Setup and Experiment 26 razor blade knife-edge sections photodiode X Xo (a) (b) Figure 3.3: Knife-edge measurements. Figure (a) shows a transverse profile of the gaussian probe beam during knife-edge measurements. Figure (b) shows a schematic diagram of the knife-edge setup. The photodiode is placed close to the focus where the beam cross section is smaller than the active area of the photodiode. (modified from [4]) Relying on these equations we chose to focus the probe beam with the 100mm focal length lens L I with a beam diameter at the lens of 3.5mm determined with aperture A P 2 in order to obtain OJ0 = 22/xm and z0 = 2.25mm in air. The exact profile of the beam at the focus was measured using the knife-edge technique described in the next section. The detector was placed about 15cm away from the sample where the beam expanded back to 5mm, the lateral size of the detector. 3.3.2 The Knife Edge Method The knife-edge technique [4], which allows the accurate characterization of gaussian laser beams, was used in this experiment to map the spatial profile of the probe beam around the focus. Figure 3.3 shows the setup for the knife-edge measurements. A razor blade attached to a translation stage was moved by increments of 20/zm to eclipse the transverse profile of the beam. Every time the blade was shifted, the transmitted power was measured with a photodiode. Then, a plot of the normalized power Pn, just like the one shown in Figure 3.4, was fitted with Equation 3.3 to obtain the beam radius OJ0: Chapter 3. Setup and Experiment 27 0.8 | 0.6 TD <D N E 0.4 o c 0.2 • knife-edge data fit with Eq. 3.3 \ • • \ 0.25 0.3 0.35 0.4 0.45 0.5 0.55 position of blade (mm) Figure 3.4: Normal ized power plotted for a knife-edge measurement of the probe beam cross section near the focus. Values on the x-axis refer to the reading on translation stage transverse to the probe beam direction. F rom the fit we extract a probe beam radius UIQ = 6 6 / L t m . n y ' 1 + exp[ - (a 0 + mt + 0 2 * 2 + a 3 t 3 ) ] ' v ' where t — ^(x — xo), x$ is the position of the beam center and ao=-6.71x 1 0 - 3 , <2i=-1.55, a2—-5.13xl0~'2, a3= - 5 . 4 9 x l 0 - 2 . The value for x0 was also extracted from the fit but it was not useful otherwise in conducting the P D S experiment. The profile of the probe beam waist at the focus shown in Figure 3.5 was created by repeating the knife-edge measurements for different positions along the beam. In the particular measurement of Figure 3.5, the minimum beam diameter was 29.4/im (u0—l4:.7pm), a little bit less than the target value. Chapter 3. Setup and Experiment 28 5 10 distance along probe beam (mm) Figure 3.5: Profile of probe beam radius Wo determined with several knife-edge sections around the focus. The x-axis indicates translation stage readings. The error bars come from the fit goodness of each knife-edge cross section measurements. Chapter 3. Setup and Experiment 29 Figure 3.6: Diagram showing the refraction of the probe beam when it enters the cuvette filled with CCI4. The focus position shifts from x to nccu% and the confocal distance also gets stretched by " e c u • 3.3.3 Effect of CC1 4 on the Probe Beam Focus Inside the cuvette and the CCI4 the probe focus plane shifts relative to its position de-termined in air because the probe beam undergoes refraction. This effect, illustrated in Figure 3.6, had to be taken into account when positioning the sample. If the cu-vette is positioned such that the probe focus determined in air lies a distance z' inside the cuvette, then the focus plane in CCI4 wil l be shifted to a distance nccuz' • I n our case we considered both CCI4 and the cuvette walls as just one medium because they share the same refractive index n=1.46. The outside width of the cuvette was 12mm and therefore we chose nz' = 6mm or z' = 4.1mm so that the focus would lie in the middle of the cuvette where the sample was mounted. This treatment remains valid for the case where z' is within the cuvette wall. Note that in the cuvette, the beam waist remains unchanged and the confocal length z0 determined in air gets stretched to nzo- These results were derived using paraxial ray optics on a focused gaussian beam and the exact derivation can be found in [2]. 3.4 Pump Excitation Beam 3.4.1 Monochromator and Light Source The pump beam was generated from an incandescent light bulb passing through a monochromator. We used an f/3.8 monochromator (Jarrell Ash Monospec 27) and Chapter 3. Setup and Experiment 30 focal length f m o n o — 275mm with a 600 lines/mm ruled grating. For the light source we chose a 150W Tungsten Halogen high radiance light bulb ( G T E Sylvania FCS) with a filament densely packed over an area 5mmx 3mm and powered with a D C source at 150W. For all measurements the output wavelength was selected manually by turning a knob on the monochromator and by reading the wavelength on an indicator that was precise to 0.5nm. To bring light into the monochromator, we followed the optical arrangement outlined in the O R I E L catalog [16] with all the settings chosen to maximize the monochromator output power. The light bulb filament was placed at the focus of lens L2 with f 2=125mm. The emerging collimated light was then focused by L3 with f 3=100mm onto the entrance slit of the monochromator. The combination of L2 and L3 created a demagnified image of the filament with magnification factor m=f 3/f2 or m=0.8. The monochromator had a rectangular entrance slit 12mm high and the width was set to 2.5mm; the exit slit was 3mm wide. The monochromator output light was collimated with the 100mm focal length lens L4 and focused on the sam-ple with the 40mm focus lens L5. The positions of L4, L5 and mirror M 3 were all simoultaneously adjusted to obtain the highest intensity light spot at the sample and the maximum resulting P D S signal. A t the sample, the spot size was approximately 2mm x 2mm. We used an RG610 Newport colour bandpass filter to remove the 2nd order diffracted visible light from the monochromator output in the range 800nm to llOOnm where the P D S measurements were performed. 3.4.2 Pump Beam Power Spectrum We investigated the monochromator power spectrum by using a U D T silicon photo-diode. Light was focused on the photodiode the same way it was done for the sample and a spectrum of the photodiode output voltage was gathered. This spectrum was then divided by the photodiode responsivity versus A curve that was obtained from the U D T catalog [5]. This yielded the monochromator power profile in arbitrary Chapter 3. Setup and Experiment 31 units shown in Figure 3.7, which was used in the data analysis to normalize the P D S spectra. W i t h a power meter we determined that the monochromator outputted 0 .07mW±0.01mW at a wavelength of 700nm. 3.4.3 Bandwidth of Pump Beam We analysed the monochromator output with a B O M E M Fourier Transform spec-trometer in order to determine the exact bandwidth. From Figure 3.8 the bandwidth, which we took to be the full width at half maximum (FWHM), was lOnm; again, the entrance slit was 2.5mm wide and the exit slit was 3mm wide. Additionally we observed that the peak wavelength was sometimes shifted with respect to the wave-length on the monochromator indicator. This shift that we characterize by S was never more than plus or minus 3nm away from the monochromator indicator value. In Figure 3.8, 5 =+ lnm. 3.5 Detection System We used a linear position sensitive detector ( U D T 1L5SD) to measure the probe beam deflection. It is a silicon p-n junction based detector with an active area 5mm x 1mm that relies on photocurrent creation from absorption of the probe beam laser to determine its position. The laser beam spot was 5mm in diameter and covered the entire detector area, but since it had a gaussian intensity profile the detector was able to distinguish the beam centroid position based on the different photocurrents collected at the two extremities along the 5mm direction. Conversion to voltages Va and Vb of these signals was done with a pre-amplifier biased with ± 1 5 V D C . The pre-amplifier circuit was assembled during the course of this project by Mario Beaudoin and Mike Feaver in the U B C department of Physics and Astronomy. We investigated the detector behavior with respect to the probe beam intensity by observing the total photocurrent generation signal Va + Vb with a multimeter. The probe beam was attenuated with neutral density (ND) filters (indicated by N D F in Figure 3.1) to obtain different intensities. From the results shown in Figure 3.9 we can Chapter 3. Setup and Experiment 32 CD „ CO o T3 O O 2 O x: •••••••• 1.2 1.4 1.6 1.8 photon energy (eV) (a) 1.2 1.4 1.6 photon energy (eV) (b) 1.4 1.5 1.6 photon energy (eV) 1.7 1.8 (c) Figure 3.7: Power spectrum of the monochromator. The photodiode measurement of the monochro-mator output spectrum shown in (a) is divided by the photodiode responsivity (obtained from the U D T catalog [5]) for different photon energies shown in (b) to obtain the acurate monochromator profile shown in (c). Chapter 3. Setup and Experiment 33 Figure 3.8: Monochromator output measured with a Fourier Transform spectrometer. It shows a FWHM of lOnm. The peak wavelength occurs at lOOlnm, showing a discrepancy of lnm with the lOOOnm that could be read from the monochromator indicator. Chapter 3. Setup and Experiment 34 > 8 > + 0.02 power (mW) Figure 3.9: Total photocurrent generation signal Va + Vf, varying with incident probe beam power. Based on this graph, we operated the detector with Va + V), in the 5V to 8V range in the linear regime safely below the 13V saturation level. see that the total photocurrent signal varies linearly with incident probe intensity until it saturates at 13V. When performing the P D S measurements, the probe intensity was adjusted with N D filters such that 14 + 14 would read a value between 5V and 8V, an interval in the linear range safely below saturation. W i t h a multimeter we measured Va — Vb, the photocurrent difference signal, when the detector was moved with a translation stage laterally (in the x direction) with respect to the probe to verify the linearity of the response with probe position. In Figure 3.10, the x-axis is the position read on the translation stage. The difference signal is directly proportional the the probe position for a 2mm range around the middle of the detector with a displacement signal or 'detector transduction factor' T r =3 .7V/mm. This factor was used for example in Section 2.3.1 to convert the P D S Chapter 3. Setup and Experiment 35 > i T =3.7 mV/mm (Va+Vb=6.4V) 7 8 9 position (mm) 10 11 Figure 3.10: The detector photocurrent difference signal Va — Vb when the detector is moved trans-verse to the probe beam direction. The probe beam has a round cross section wi th a gaussian intensity profile and its diameter at the detector is 5mm, same as the wid th of the detector. The difference signal is directly proport ional to the probe beam posit ion around the detector centre. The graph shows a signal per probe deflection ratio T r = 3 . 7 V / m m here. The x-axis indicates readings on the translation stage. voltage signals into probe beam deflections in micrometers. Note that Tr depends on the Va + Vb setting. In Figure 3.10, as the probe approaches the detector edges, the intensity striking the active area drops, which accounts for the curled shape of the signal at the top and bottom of the graph. The detector position was adjusted before every P D S measurement to get Va — Vb — 0 to make sure that the detector worked in its linear range. A lock-in amplifier (Stanford Research Systems SR830) was used to measure the periodic P D S deflections from the Va — Vb detector output. The mechanical chopper (Stanford Research Systems SR540) was placed at the monochromator exit to modu-Chapter 3. Setup and Experiment 36 late the pump beam provided the lock-in reference signal. The chopper frequency was set around l l H z ± 0 . 1 H z . This modulation frequency represented a trade-off between a high frequency that reduces the 1 / f noise and a low frequency, which increases the thermal diffusion length and as a consequence the signal amplitude as was demon-strated in Section 2.3.1. From the lock-in amplifier we could read the rms amplitude of the P D S signal and the phase difference between the P D S and the chopper signals. We used an integration constant between 3s and 10s. The lock-in voltage noise was O. lmV peak to peak, which corresponds to a 40nm peak to peak deflection of the probe beam. This exceeds the reported resolution limit of the detector of better than 5nm. Using a longer integration constant (up to 30s) could not remedy this excess noise effect. The experimenter would instead make a mental average over a minute or so of the lock-in signal for every P D S data point and this would reduce the apparent noise in the data to 0.04mV peak to peak. Stray light on the detector as well as probe beam power and pointing instability might contribute to the noise. Chapter 4. Experimental Results 37 Chapter 4 Experimental Results 4.1 Introduction The optical properties at the bandgap of many samples have been investigated using the P D S apparatus built during this project. These samples fall into two categories: bulk wafer samples including semi-insulating GaAs and InP:Fe, and GaAs epitaxial thin films doped with various dilute amounts of either nitrogen or bismuth. Some of these results were presented in a poster session at the 2006 International Symposium on Compound Semiconductors [17] that was held in Vancouver. In this chapter, we present the two sets of measurements that exhibited the least amount of scatter in the data and that best portray the ability of the P D S apparatus. These particular results are also chosen because in combination, they help give a thorough description of the method we developed to analyse P D S data for both wafer and thin film samples. The first measurements we present are for a bulk wafer of semi-insulating GaAs. The second measurements are for a thin film of nitrogen (N) doped GaAs grown epitaxially on a semi-insulating GaAs wafer. This sample was grown in the U B C Physics M B E Lab by Er in C. Young. For these samples, spectra were gathered in the wavelength range 800nm to HOOnm (or 1.15eV to 1.55eV), always scanning from lower energies to higher energies. The step size used for the scans varied from 2nm (3.06meV) for wavelengths around the bandgap to resolve the absorption edge, to lOnm (15.3meV) for wavelengths far away from the bandgap. The one-dimensional model of P D S presented in Chapter 2 in conjunction with models of semiconductor optical bandgap properties provided a means to fit the experimental spectra. Section 4.2 presents the model for semiconductor bandgap absorption used in this Chapter 4. Experimental Results 38 project. Section 4.3 explains the details of how the fits were generated using the Rosencwaig-Gersho P D S model along with the experimental settings. In the first part of Section 4.4 we present the results obtained from the bare semi-insulating GaAs wafer. In the second part of the section we show how the optical properties of the G a N A s thin film can similarly be investigated by using the Fernelius model [18], essentially an extension of the Rosencwaig-Gersho model. The Fernelius model, which solves the thermal diffusion equation for an extra region in the sample structure, can be used to investigate the effect on the P D S signal of a two layer sample such as an absorbing thin film on an absorbing substrate. 4.2 Semiconductor Absorption at the Bandgap The optical absorption of semiconductors such as the samples investigated in this project can be broken down into three distinct parts: absorption in the subgap region, near the bandgap and above the bandgap. Defects and impurities in the crystal lattice create states within the bandgap region below the absorption edge. Both M . D . Sturge [6] and S. R. Johnson et al. [19] observed that the absorption in this region is weakly energy dependent and Sturge noticed additionally that subgap absorption below the level of 4 c m - 1 varies significantly from sample to sample. For the purpose of building the absorption model, the subgap absorption was assumed to be just a constant at all frequencies called cto- The value ao was adjusted to make the model reproduce the experimental data as closely as possible. Near the bandgap, the absorption follows an exponential shape commonly referred to as the Urbach edge. It is believed to be due to structural and thermal disorder of the semiconductor lattice that gives rise to states right below the bandedge [20] [21]. Below the bandgap then, the absorption can be described by: where hv is the photon energy, ag is the absorption at the bandgap EG, and EQ is the for hu < E, (4.1) Chapter 4. Experimental Results 39 Urbach parameter, which characterizes the width of the exponential edge. The model of semiconductor absorption above the bandgap is not based on specific theory but rather on previous measurements conducted on semi-insulating GaAs at 294K by Sturge. According to Sturge's results, the exciton peak commonly found near the bandedge for low temperatures cannot be resolved at 294K and with that, Sturge's values for absorption above the bandgap clearly can be approximated by a straight line as can be seen from the data reproduced from Sturge's paper in Figure 4.1. Therefore we get ah„ ~ ag +Ag(hv - Eg), for his > Eg, (4.2) where Ag is the proportionality constant equal to 56300cm - 1 / eV. From Figure 4.1 we also get the absorption at the bandgap a s = 8 0 0 0 c m - 1 which occurs at Eg—lA27eV. The absorption is assumed to be linear for all energies above the bandgap although it is only shown to be so for a range 0.07eV above Eg. The shape of the semiconductor optical absorption as described so far is illustrated in Figure 4.2. 4.3 Modelling the PDS signal As was explained in Chapter 2, the magnitude of the probe beam deflection occuring at the surface of the heated sample wil l depend on, among other factors, the opti-cal absorption properties of the sample. When all other experimental settings are kept constant, it is possible to investigate the dependance of the P D S signal on the absorption coefficient by using the P D S deflection equation such that D{hv) = —^•\ag^ahv)e-'r'X0\AzL. (4.3) no at In the experiment we only measure the magnitude of deflection and so here we remove the time dependent term and we take the absolute value of the complex term. To compare these simulations with the experimental spectra, the modelled spectra were first of all normalized to the calculated saturated deflection level Dsat, which occurs where ctls ^> 1 (ls is the sample thickness): D.M = (4.4) Chapter 4. Experimental Results 40 Figure 4.1: This absorption data for semi-insulating GaAs at 294K show a bandgap energy S g=1.427eV with a g =8000cm _ 1 . The relationship between absorption coefficient and photon en-ergy above the bandgap can be approximated by a straight line with slope A. (Reproduced from M . D. Sturge [6]) Chapter 4. Experimental Results 41 Figure 4.2: Model of the optical absorption of GaAs used in the treatment of PDS experimental data. Chapter 4. Experimental Results 42 Doing that makes it unnecessary to find exact values for the sample-detector distance L, the sample-probe distance XQ, the heated distance along the probe beam path Az, the exact pump intensity and the detector transduction factor. A l l these parameters are independant of absorption coefficient and therefore only contribute constant scale factors to the amplitude of the P D S spectra. Among all the experimental parameters, the normalized deflection spectra end up depending only on the chopping frequency and the sample thickness, so those exact values were used in Equation 4.3. A constraint is that the surface dimensions of the sample and the cross section of the pump excitation have to exceed a few thermal diffusion lengths of the sample for the one-dimensional model to remain valid at the chosen chopping frequency. In this project we used sample dimensions and a pump spot size corresponding to approximately 1.5 to 2 thermal diffusion lengths. Since the monochromator output has a bandwidth of approximately lOnm, the finite bandwidth of the excitation source also had to be accounted for in modelling the P D S signal for comparison with experiment. This was done by convolving the 'ideal model' P D S signal with and excitation beam having a gaussian shape in energy and characterized by a full width at half maximum FWHM and a peak wavelength shift 8 (see Section 3.4.3). The value of FWHM was always taken to be lOnm whereas 5 was adjusted while fitting the P D S spectra. Details on the choices of S are given in the following sections. Equation 4.5 shows the convolution formula: 1 f ° ° -(hv-hv'+S)2 DTv{hv) = - / Dn(hv')e n d(hu'), (4.5) J —oo where FWHM T — . and N = TxfK. (4.6) Both the modelled and experimental normalized spectra were plotted on the same graph and absorption model parameters and the experimental parameter 5 could be adjusted until the model fit the data suitably. Chapter 4. Experimental Results 43 4.4 Analysis of PDS results 4.4.1 Results for Semi-Insulating GaAs Measurements were performed on a semi-insulating GaAs sample that was cleaved from a larger wafer. It had a polished front surface, the surface exposed to the pump beam, and a rough back surface. The sample thickness was 363/im; it had a lateral dimension Az along the probe beam path of about 1.5mm, so it was roughly 1.5 thermal diffusion lengths long with the chopping frequency chosen to be 11.4Hz. The measurements were taken with an excitation pump of lOnm bandwidth (15.3meV). The raw spectrum, consisting of deflection voltages read on the lock-in amplifier, was divided through by the pump beam power spectrum. The resulting spectrum was then normalized. Figure 4.3 shows the experimental spectrum along with the model used to fit it. To plot the model we fixed the bandgap parameters £ , ^ ? a A s = 1 . 4 2 7 e V , Q,Ga/i s = 8ooOcm- 1 and i 4 ° O i 4 * = 5 6 3 0 0 c m - 1 / e V as was found from Sturge's data in F ig-ure 4.1. The subgap absorption ao was determined by averaging the low energy 'back-ground' points in the energy range 1.21eV to 1.34eV. The Urbach parameter EQaAs and the pump excitation systematic shift S were chosen according to the method of least squares fitting; that is, by minimizing X 2 J the sum of the squared deviation of the data from the model weighted by the data error bar. The data error bars were on average 0.02 normalized units. The error bars for E$aAs and 6 are extracted from the X2 analysis [22] and are equal to (|§f r - ) ^ 2 and Q ^ f ) ^ respectively. The values of the parameters used to fit the spectrum are summarized in Table 4.4.1. Due to the large thickness of the GaAs sample, the P D S signal was already sat-urating at a ~ 3 0 c m - 1 corresponding roughly to 0.6 normalized units on the graph, far below the absorption value at the bandgap of 8000cm - 1 . The value for subgap absorption ao is determined to be 4 .7cm _ 1 , only slightly larger than other reported values that range from 1 to 4 c m - 1 at 1.3eV [19] [6]. From the data it appears that the subgap absorption remains almost constant for all energies below the bandedge. The effect of the excitation bandwidth and shift 8 is evident when we compare the model curves with and without the convolution. The convolution accounts for Chapter 4. Experimental Results 44 (0 -*—« 'c u T3 0) N "TO E L . o c "ro c tn CO Q D_ 0.8 0.6 0.4 0.2 * data for GaAs model model with convolution 1.3 1.35 1.4 photon energy (eV) 1.45 Figure 4.3: Model and experimental results for PDS signal from semi-insulating GaAs. The stars show the experimental data; the solid curve shows the PDS model and the dash dot curve shows the model convoluted with a lOnm bandwidth excitation beam with a peak wavelength shifted by +6.1nm. Chapter 4. Experimental Results 45 Table 4.1: Values for GaAs optical absorption properties used in modelling the PDS spectra. Parameter Value How it was obtained EGaAs 1 427 e V M . D . Sturge [294K] aGaAs 8 0 0 0 c m - i M . D. Sturge AGaAs 563oo cm-VeV M . D. Sturge aGaAS 4 7 _|. o.2 c m - 1 Average of data from 1.21 to 1.34eV E$aAs 8.69±0.05 meV x2 fittinS 8 +6 .1±0 .2 nm x2 fitting the rounding of the sharper spectral feature at the top of the absorption edge right before saturation. The value of (5=+6.1nm that we extract from the fit is larger than the maximum shift of +3nm that we encountered when taking spectrometer readings of the bandwidth. It is possible but unlikely that the pump excitation shift accounts alone for the fitted value of S. Around room temperature, the E^aAs decreases by 0.4meV/°iv" and so if the temperature at which the measurements were done was just a few degrees above or below 294K, then we should have expected a value for E^aAs different from 1.427eV found from Sturge's data. The exact temperature at the time of the measurements is not known. When we use a different value of a A s in the model, the fitted 5 changes as well 1 . Our value of EQaAs—8.69meV is comparable to values reported in the literature, which range between 5.9meV and 9meV [23] [6] [21] [24]. 4.4.2 Investigating optical absorption properties of a GaNAs thin film For the next sample we chose to investigate a thin film of G a N x A s i _ x with x=0.00559 grown on semi-insulating GaAs by molecular beam epitaxy. Its thickness was 238nm as determined by X-ray diffraction and the substrate was again 363^tm thick. In the dilute G a N x A s i _ x alloys, the incorporation of even a small concentration of nitrogen For example, when we use a/ls=1.424eV we obtain .5=4-7.8 nm. Chapter 4. Experimental Results 46 (N) tends to significantly reduce the bandgap energy from that of pure GaAs [25] (that effect is refered to as a large bandgap bowing). These thin films are of importance in the fabrication of long-wavelength semiconductor lasers on GaAs substrates [26]. The P D S spectrum for the thin film sample is shown in Figure 4.4. It looks almost identical to the GaAs spectrum drawn on the same graph except that it shows an extra hump where the thin film absorbs. As expected, the spectrum shows the absorption of the thin film occuring below the substrate bandedge. The sample is so thin that its P D S spectrum doesn't saturate and so it makes the structure of the absorption above the bandgap visible. A t all wavelengths both the substrate and the thin film absorb, so to extract information specific to the thin film we had to resort to a model taking into account two absorbing layers for an accurate analysis. That model was developped by Nils C. Fernelius. Just like in the Rosencwaig-Gersho model, it treats heat flow in one dimension, but it takes into account two absorbing regions, the thin film or thin coating and the substrate as depicted in Figure 4.5. The complete solution for the heat distribution in and around the absorbing samples can be found elsewhere [18]. The resulting probe beam deflection in the Fernelius model is expressed here: DFer(ashl/, achv) = L ^ \ a g M a 1 w i a ^ e - ^ ' ^ A z L , (4.7) where h is the thickness of the thin film, ctshv and ctchv refer to the substrate and thin film absorption coefficients respectively, and <j>Fer is the complex amplitude of the A C temperature at the thin film-deflecting medium interface: 0 F e r | ( l - b)e-°>l> [(1 - c ) ( l + | ) e ^ + (1 + c ) ( l - 9-)e-°°h] - ( 1 + b)e~?'1' [(1.+ c ) ( l + | ) e a e f c , + (1 - c ) ( l - ^)e~ach] j = 2Eh(rs - b)e-a'^ls + (1 4- 6)(1 - ra)e"1' - (1 - 6)(1 + ra)e-"'1' +Z[2(1 - 6)(1 + r c ) e ( - f f ^ - a ^ - 2(1 + 6)(1 - r c ) e { a ' 1 ' - ^ - ( 1 - 6)(1 - c ) ( l - ^ e ( - ' . ' . + " « f c ) - ( l _ 6)(i + c)(l + ^ e ( - ^ ' - - ^ ) + ( l + 6)(l + c ) ( l - ^ ) e ( ^ + f f ^ + ( l + ^ (4.8) Chapter 4. Experimental Results 47 -*—» 'c Z3 T3 CD N "(0 E o "(6 c D) CO CO Q 0.8 0.6 0.4h 0.2r 0 O GaAs * GaAs + GaNAs thin film 9 $ °. • * ® ***** #* *0 *o O Q O Q O O O 9 9 O co coo 0 0 ° 1.2 1.25 1.3 1.35 1.4 photon energy (eV) 1.45 1.5 Figure 4.4: Graph showing the normalized spectra for the GaAs wafer with and without the GaNAs thin film. where and E Z ashJ0 e x p ( - c 4 » ahJo 2 M ( o L ) 2 - ^ ) ' (4.9) (4.10) c — kco~c/kscst r s = ahv/as> rc — OL^Jzcj osks (4.11) (4.12) (4.13) The subscript c refers to a thin film parameter; the variables fcj, aiy b and g are defined in Section 2.2. To model the P D S spectrum in this case, we assumed that the GaNAs thin film had the same absorption shape as defined in Section 4.2. Moreover, since Chapter 4. Experimental Results 48 backing substrate thin film | :•>: .fO,;t j; p J .,„*.{ i deflecting { * medium i pump -«b •'s - < ) 1 1 •g X Figure 4.5: Schematic of the sample geometry in the case described by Fernlius' model with a thin film or thin coating on a substrate. the thin film is essentially GaAs with only a small concentration of N , its thermal parameters were assumed to be identical to GaAs. The chopping frequency was 11.4Hz and the lateral dimension Az was again about 1.5mm. To fit the model to the experimental data we used optical parameters for both the thin film and the GaAs substrate. First, the subgap absorption ct0 was obtained just like before by averaging the 'background' points in the energy range 1.16eV to 1.24eV. For the GaAs substrate optical parameters we again fixed the values of ctGaAs, E G a A s and AGaAs to the ones shown in Table 4.4.1. We treated EoaAs, 5 and the thin film parameters EfaNAs, afaNAs, AfaNAs and Eg*1**8 here as variables that we adjusted to find a least square fit. The error bars for these variables were found by analysing X2 just like it was done in Section 4.4.1. From Figure 4.6, the model fit seems to reproduce the data very well. The fit parameters for are listed in Table 4.2. A discussion of the parameter values extracted from the model is necessary though. First of all we want to point out that we don't obtain the same fit values for the substrate parameters as were found with the measurements of only GaAs. One should expect these values to remain unchanged in both spectra. The value of ao=3.5cm _ 1 is lower than the value of 4 . 7 c m - 1 found for GaAs. The spectrum's best fit indicates a value of 5 and EoaAs, both slightly lower than for the bare substrate measurements. For the bandgap absorption, we thought that the dilute GaNAs would absorb around 8000cm - 1 just like for GaAs, but instead we obtain a value almost twice as big: 15200cm" 1. We obtain a value £ ^ o J V i 4 i = 8 . 1 ± 1 . 3 m e V ; this is based on only two Chapter 4. Experimental Results 49 Table 4.2: Values for GaNAs optical absorption properties used in modelling the PDS spectra. The substrate optical properties were fixed and the parameters in this table were fitted to the experimental spectrum. Parameter Value j^GaAs nGaAs 9 j^GaAs GaAs a. EGaAs 1.427 eV 8000 c m - 1 56300 cm-VeV 3.5± 0.2 c m - 1 7.71±0.06 meV +5 .7±0 .2 nm How it was obtained M . D . Sturge [294K] M . D. Sturge M . D. Sturge Average of data from 1.16 to 1.24eV X2 fitting X2 fitting £gGaNAs GaNAs a 9 j^GaNAs EGaNAs 1.294±0.001 eV 15200±400 c m " 1 X2 fitting X2 fitting 48600±7500 cm^/eV x2 fitting. 8.1±1.3 meV X 2 fitting Chapter 4. Experimental Results 50 JO | 0.8 T3 CD N l o . 6 i— o c CO o)0.4 CO CO Q 0_ 0.2 * data for GaNAs model with convolution 1.25 1.3 1.35 1.4 photon energy (eV) 1.45 Figure 4.6: M o d e l and experimental results for the P D S signal from a G a N A s 238nm th in film on a semi-insulating G a A s substrate. The model convolution is done wi th a lOnm bandwidth exitat ion pump shifted by +5.7nm towards higher energies. data points on the Urbach edge of the thin film, which explains the large error bar. The position of the optical bandgap E ^ a J V j 4 s = 1 . 2 9 4 ± 0 . 0 0 1 e V agrees with the value of 1.293eV measured using a different technique [25]. 4.5 Discussion The results of this chapter clearly show that the P D S technique is suitable for measur-ing spectra of both bulk semiconductor samples and thin films. Although the models we are using appear to fit the spectra well, the quality of the optical information we extract from them is uncertain. The rather large value of the 8 energy shift of the pump excitation beam of around +6nm remains unaccounted for. This could be due Chapter 4. Experimental Results 51 to a misalignment of the pump beam image with the probe beam path at the sample. This forces us to question the accuracy of the values we obtain for E$aAs and EfaNAs. Furthermore the absorption at the bandgap for the thin film a A r A s = 1 5 2 0 0 c m _ 1 is almost twice as large as the value we expected. The model assumes that the pump light does only one pass through the sample. If there were in fact multiple incoherent reflections of the pump beam inside the sample then the P D S signal would be larger. This effect could be enhanced by scattering of the pump light on the rough back surface of the wafer. To investigate this contribution, we measured the spectrum of GaNAs before and after polishing the wafer back surface. The results presented in Appendix A seem to indicate that the scattering of the pump beam on the rough back surface could explain in part the apparently unusual value of a^aNAs. Finally, we can deduce the sensitivity of our apparatus by looking at the noise level at the thin film bandgap on Figure 4.6. If the bandgap absorption a ^ a J V V U = 1 5 2 0 0 c m - 1 corresponds to 0.26 normalized units above the ao subgap absorption, then the noise level at the thin film bandgap of ~0.02 normalized units corresponds to 1130cm - 1 . Given that the film thickness /i=238nm thick then we have a sensitivity ah=2.7x 1 0 - 2 . Chapter 5. Improvements to the Experimental Setup 52 Chapter 5 Improvements to the Experimental Setup The first version of the P D S experiment built during this project allowed us to reach measurement sensitivities in optical absorptance of ~ 2 x 1 0 - 2 . In this chapter we point out key aspects of the experiment that could be improved and suggest some modifications that should help improve the sensitivity of the experiment. P D S -obtained absorbances of 1 0 - 5 in thin films have been reported in the literature [8]. If those experiments were performed with GaAs backings, the absorptance detection limit would be 6 times larger (i.e. worst) because the thermal diffusion length is 6 times longer in GaAs than in glass for any given chopping frequency. The first improvement would be to reduce the noise in the detector output by dividing the difference photocurrent signal by the total photocurrent signal, or j ^ a ~ | ^ using an auxiliary input of the lock-in amplifier. This common mode rejection scheme would reduce the noise arising from the probe beam power fluctuations or scattering of the probe on dust particles in the air. It may be possible to further optimize the probe beam spot size at the sample. Opting for a probe waist radius of 40>m say instead of 22/rni would increase the confocal length, which would allow us to use wider samples and increase the probe-sample interaction length. If we used a bigger pump beam spot size along with a wider sample then I D heat diffusion conditions would be better met than in the present setup. A suggestion to achieve a probe waist radius of 40pm would be to use a 150mm focal length lens with a beam diameter at the lens of 3mm. This f-number combination would also increase the sample-detector separation! The improvement level of this modification would depend strongly though on the minimum achievable Chapter 5. Improvements to the Experimental Setup 53 probe-sample distance. In the present setup the total pump beam power was limited to O.lmW. This could be improved by using a higher throughput monochromator with an output bandwidth of lOnm, or ideally smaller. The monochromator output should be focused at the sample so as to maximize the pump intensity along the probe beam path. This could be done with a combination of two cylindrical lenses to shape the monochromator output. If we still wish to use the I D models to model the P D S spectra then it would be important to keep the pump spot at the sample large enough with an intensity as uniform as possible to keep the I D approximation valid. Furthermore, it would be also important to determine how the focused spot of the pump beam actually overlaps with the probe beam path at the sample surface. Reducing the chopper frequency by still making sure that the mechanical noise remains low wil l further increase the P D S signal. The reflectivity of the sample-deflecting medium interface should in principle be taken into account because it governs the amount of the pump beam that penetrates the sample. In the case of thin films grown by M B E on GaAs, an idea would be to thin down or completely remove the GaAs substrate and place the thin films on a backing that's more thermally insulating, like glass for example, to help increase the amplitude of the A C temperature inside the sample and at the sample-deflecting medium interface. Finally, it is interesting to know that in the general case where a semiconduct-ing thin film starts absorbing at energies above the bandgap of the substrate where the deflection amplitude signal is saturated, it is still possible to extract absorption information about the thin film by analysing the phase signal [27]. In the present experiment, the phase spectrum was recorded but not analysed. Chapter 6. Conclusions 54 Chapter 6 Conclusions During the course of this project we have acquired a good understanding of the basic principles of the P D S technique. W i t h this knowledge we have assembled and fully characterized a working P D S apparatus. The results we obtained for the P D S signal as a function of chopping frequency and probe-sample separation with a fixed wavelength pump beam could be fairly well replicated by using the Rosencwaig-Gersho model of I D heat diffusion; this indicates that this model provides at least a good approximation when the experimental conditions resemble those outlined in Section 2.3.1. We were successful in measuring P D S spectra of bulk semi-insulating GaAs and of a 238nm G a N A s epitaxial thin film. The model we developped for the absorption around the bandgap for GaAs and GaNAs represents a first step towards a more accurate model of this type of P D S spectra. The results obtained from the models are still inconclusive. The fit results could be reasonably considered only if we were to use wider samples along with a larger and more uniform pump beam spot in order to better fulfill the I D heat diffusion condition assumed by our model. The effect of multiple reflections from rough back surfaces in these high refractive index substrates should be analyzed further. W i t h the present P D S apparatus we have reached sensitivities comparable to transmission spectroscopy, i.e. aZ=10 - 2 . It should be possible by applying the im-provements of Chapter 5 to reach sensitivities closer to what other research groups have typically reported ~ al—10~4. If this level is reached, it would allow us to mea-sure the absorption in 200nm thin films down to 50cm"""1. It may very well be that this level of sensitivity would reveal not only the shape of the Urbach edge of thin films but also subgap states such as arising from nitrogen clustering in the epitaxial Chapter 6. Conclusions 55 G a N A s thin films or bismuth clusterings in other G a B i A s thin films grown in the U B C physics M B E lab. Bibliography 56 Bibliography [1] D. P. Almond and P. M . Patel. Photothermal Science and Techniques. Chapman and Hal l , London, 1996. [2] Stephen E . Bialkowski. Photothermal Spectroscopy Methods for Chemical Anal-ysis. John Wiley and Sons, New York, 1996. [3] John S. Blakemore. Gallium Arsenide. American Institute of Physics, New York, 1987. [4] Luciano Bachmann, Denise Mar ia Zezell, and Edison Puig Maldonado. Determi-nation of beam width and quality for pulsed lasers using the knife-edge method. Instrumentation Science and Technology, 31(l):47-52, 2003. [5] Inc. U D T Sensors. Optoelectronic Components Catalog. U D T Sensors, Inc., Hawthorne. [6] M . D. Sturge. Optical absorption of Gall ium Arsenide between 0.6 and 2.75 ev. Physical Review, 127(3):768-773, 1962. [7] A . C. Boccara, D . Fournier, and J . Badoz. Thermo-optical spectroscopy: "De-tection by the mirage effect". Appl. Phys. Lett, 36(2):130-132, 1980. [8] J . I. Pankove. Semiconductors and Semimetals vol. 21 part B. Academic Press, Orlando, 1984. [9] C. Wetzel, V . Petrova-Koch, F . Koch, and D. Grutzmacher. Photothermal de-flection spectroscopy of InGaAs/InP quantum wells. Semicond. Sci. Technol, 5:702-706, 1990. Bibliography 57 [10] K . Tanaka and T. Gotoh. Photothermal deflection spectroscopy of chalcogenide glasses. J. Appl. Phys., 91(1):125-128, 2002. [11] K . Chew, Rush, S. F . Yoon, J . Ahn , Q. Zhang, V . Ligatchev, E . J . Teo, T. Os-ipowicz, and F . Watt. Gap state distribution in amorphous hydrogenated silicon carbide films deduced from photothermal deflection spectroscopy. J. Appl. Phys., 91(7):4319-4325, 2002. [12] Yoh-Han Pao. Optoacoustic Spectroscopy and Detection. Academic Press, New York, 1977. [13] W . B . Jackson, N . M . Amer, A . C. Boccara, and D. Fournier. Photothermal deflection spectroscopy and detection. Applied Optics, 20(8): 1333-1344, 1981. [14] L . C. Aamodt and J . C. Murphy. Photothermal measurements using a localized excitation source. J. Appl. Phys., 52(8):4903-4914, 1981. [15] E . Legal Lasalle, F . Lepoutre, and J . P. Roger. Probe beam size effects in photothermal deflection experiments. J. Appl. Phys., 64( l ) : l -5 , 1988. [16] Oriel Corporation. Oriel Catalog Vol. 2. Oriel Corporation, U S A , 1994. [17] Miryam Elouneg-Jamroz, P. Pitach, E . C. Young, D. Beaton, Nikolaj Zangen-berg, M . Beaudoin, T. Tiedje, and J . F . Young. Optical band gap and Urbach edge of G a N x A s i _ x investigated with P D S . International Symposium on Com-pound Semiconductors-Poster Session, 2006. [18] Nils C. Fernelius. Extension of the Rosencwaig-Gersho photoacoustic spec-troscopy theory to include effects of a sample coating. J. Appl. Phys., 51(1):650-654, 1980. [19] Shane R. Johnson. Optical Bandgap Thermometry in Molecular Beam Epitaxy. P h D thesis, University of Brit ish Columbia, 1995. [20] C. W . Greeff and H. R. Glyde. Anomalous Urbach tail in GaAs. Physical Review B, 51(3):1778-1783, 1995. Bibliography 58 [21] S. R. Johnson and T. Tiedje. Temperature dependence of the Urbach edge in GaAs. J. Appl. Phys., 78(9):5609-5613, 1995. [22] Louis Lyons. A practicle guide to Data Analysis for Physical Science Students. Cambridge University Press, Cambridge, 1991. [23] M . Beaudoin, A . J . G . DeVries, S. R. Johnson, H . Laman, and T. Tiedje. Optical absorption edge of semi-insulating GaAs and InP at high temperatures. Appl. Phys. Lett, 70(26):3540-3542,: 1997. ' v " " [24] M . K . Weilmeier, K . M . Colbrow, T. Tiedje, T. Van Buuren, and L i X u . A new optical temperature measurement technique for semiconductor substrates in molecular beam epitaxy. C. J. Phys., 69:422-426, 1991. [25] U . Tisch, E . Finkman, and J . Salzman. The anomalous bandgap bowing of G a A s N . Appl. Phys. Lett, 81(3):463-465, 2002. [26] I. Suemune, K . Uesugi, and W . Walukiewicz. Role of nitrogen in the reduced temperature dependence of band-gap energy in GaNAs . Appl. Phys. Lett, 77(19):650-654, 2000. [27] N . Yacoubi, B . Girault, and Jean Fesquet. Determination of absorption co-efficients and themal conductivity of G a A l A s / G a A s heterostructures using a photothermal method. Applied Optics, 25(24):4622-4625, 1986. [28] T. Tiedje, B . Abeles, J . M . Cebulka, and J . Pelz. Photoconductivity enhancement by light trapping in rough amorphous silicon. Appl. Phys. Lett., 42(8):712-714, 1983. Appendix A. Comparing Spectra from Rough and Polished Back Surface GaNAs 59 Appendix A Comparing Spectra from Rough and Polished Back Surface GaNAs To test the effect on the P D S signal of the scattering of the pump beam on the sample rough back surface, we conducted the following experiment. We measured a spectrum of the same GaNAs thin film investigated in Section 4.4.2 with the original rough back surface. Then, the back surface was polished and the spectrum was measured again. The P D S experimental conditions were the same here as the ones used for the measurements of Section 4.4.2 except that the pump beam bandwidth was 5nm. The polishing was done mechanically by hand using 0.3/im to 5/zm alumina particles suspension pastes. Figure A . l shows A F M images of the wafer back surface before and after polishing. These images were taken with the help of Michael Whitwick of the U B C Physics M B E Lab. Our polishing technique reduced the R M S roughness from 652nm to 9nm. The spectra of GaNAs with the rough and polished back surfaces are shown in Figure A.2 . These spectra are more noisy than the ones presented in Chapter 4. The excess of noise could be due to a misalignment of the sample with the probe beam focus. Also we didn't average the P D S signal over a minute for each data point like it was described in Section 3.5; instead, we used a 30 seconds integration constant on the lock-in amplifier, longer than the maximum of a 10 seconds integration constant that we used for the measurements in Section 4.4.2. We clearly observe a higher P D S signal at the thin film bandgap in the sample before it is polished. From a loose fit on the spectra we obtain a bandgap absorption o t g l a N A s = 13800cm - 1 for the original rough sample and a G a N A s = 10200cm - 1 after it is polished. Note the thin film bandgap absorption we obtain here for the original sample is slightly different from aGaNAs _ 15200 ± 400cm _ 1 that we obtained the first time we measured this sample Appendix A. Comparing Spectra from Rough and Polished Back Surface GaNAs 60 (a) (b) Figure A . l : A F M images of the back surface of the GaNAs sample wafer before and after it was polished by hand with various size alumina particle pastes. The RMS roughness goes from (a) 652nm before polishing to (b) 9nm after polishing. These images were taken with the help of Micheal Whitwick of the U B C Physics M B E Lab. (see Section 4.4.2); but considering that the latest measurments are much noisier, it is reasonable to think that both values of a G a N A s for the original rough sample agree within error. The results seem to indicate that the back surface roughness does tend to increase the absorption we measure. The value of a G a N A s = 10200cm - 1 is still higher than the value of 8000cm - 1 for GaAs, which we roughly expected to obtain for the dilute G a N A s thin film. This discrepancy could be due to the polished sample being still a little bit rough. Also, we don't know exactly how the increased absorption in the substrate due to back surface roughness affects the values we obtain for the thin film optical parameters from the model fits. Enhancement of light absorption in a thin film sample due to trapping of light caused by scattering on a substrate rough back surface was observed in a similar experiment, described in reference [28]. Appendix A. Comparing Spectra from Rough and Polished Back Surface GaNAs 61 'c T3 CD N "TO E o c 0.8 0.6 ca &0.4 CO CO Q Q_ 0.2 1 1 a rough i i i i c » a • • polished • • m 9 9 e • o e rx> n 8 8 8 * i i i i 1.2 1.25 1.3 1.35 1.4 photon energy (eV) 1.45 1.5 (a) 1.3 1.4 photon energy (eV) (b) 1.5 1.3 1.4 photon energy (eV) (c) Figure A . 2 : P D S spectra of G a N A s taken before and after the wafer back surface was polished. In graph (a) of the superposed spectra, the rough back surface sample shows slightly more absorption at the th in fi lm. Figures (b) and (c) show loose fits of the spectra, which yie ld a bandgap absorption aGaNAs Q £ 1 3 8 0 0 c m - 1 for the sample wi th the rough back surface and 1 0 2 0 0 c m - 1 after the back surface was polished. 

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