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Electrical and structural characterization of GaAs and Al Ga₋ As gr Xu, Li 1991

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ELECTRICAL AND STRUCTURAL CHARACTERIZATION OF GaAs AND AI xGai. xAs GROWN BY M B E by Li Xu B.Sc, Shandong University, Shandong, China, 1982 M.Sc, Beijing University of Posts and Telecommunications, Beijing, China, 1984 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1991 ©Li Xu, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of p/*y<i^f The University of British Columbia Vancouver, Canada Date O*. /?H DE-6 (2/88) Abstract The electrical and structural properties of GaAs and A l x G a i - x A s grown by molecular beam epitaxy have been studied, including cross section morphology, aluminum mole fraction, and electrical transport properties. The film cross section has been investigated by selective etching, and microscopy. The selectively etched samples were examined with an alpha step instrument, a scanning electron microscope, and a scanning tunneling microscope which is a new approach. The aluminium mole fraction of A l x Gai . x As in grown layers have been measured with x-ray diffraction. A Rigaku x-ray diffractometer designed for powders was extended to single crystals. A new way of calculating the Al mole fraction from the x-ray diffraction spectrum was developed. The electrical transport properties including carrier concentration, Hall coefficients, resistivity and Hall mobility have been measured and calculated from 4 K to 300 K by means of the ii Van der Pauw method. Sample patterning was found to be necessary for accurate and reproducible measurements. A variety of samples was measured, including doped and undoped GaAs films. The two-band theory was used to interpret the measurement results. The temperature dependence of electron concentration in the conduction band was fit with an exponential function. From the fit, we obtained the activation energy of the impurity. The residual impurity in the MBE system was found to be mainly silicon. iii Table of Contents Abstract i i Table of Contents iv Table of Figures v i Acknowledgements v i i i 1 Introduction 1 1.1 Overview 1 1.2 Outline of the Thesis 5 2 Microscopy 7 2.1 Selective Etching 7 2.1.1 Introduction 7 2.1.2 Etching Experiments and Results 8 2.2 Results of Scanning Electron Microscopy (SEM) and Scanning Tunneling Microscopy (STM) 14 3 X-Ray Diffractometry 2 0 3.1 Background and Calculations 20 3.2 X-Ray Measurement of Al Mole Fraction in Al x Gai- x As . . 2 6 3.3 Resolution Improvement 3 0 3.4 Calculation and Comparison 3 9 iv 4 Electrical Transport Properties 4 4 4.1 Sample Preparation 4 5 4.1.1 Patterning 45 4.1.2 Ohmic Contacts 4 8 Thermal Diffraction 49 Vacuum Evaporation 5 4 4.2 Measurement and Analysis 5 5 4.2.1 Electrical Transport Measurement Apparatus 5 5 4.2.2 Calculations 5 8 4.2.3 Results and Discussion 61 5 Conclusions 7 9 References 8 1 v List of Figures 2.1 Step height measurement of GaAs sample etched by H 2 0 2 : N H 4 O H : H 2 0 (1:1:5 by volume) 10 2.2 Step height measurement of Alo.5Gao.5As sample etched by H 2 0 2 : N H 4 O H : H 2 0 (1:1:5 by volume) 11 2.3 Step height measurement of Alo.5Gao.5As sample etched by K 3 Fe(CN) 6 : K O H : H 2 0 (1:1.5:62.5 by weight) 13 2.4 SEM picture of sample no.35 16 2.5 SEM picture of sample no.37 17 2.6 Scanning tunneling microscope picture of sample no.37 . . . . 18 3.1 Lattice matching of AlGaAs and GaAs 21 3.2 X-ray spectrum of Al x Gai- x As/GaAs sample no.30 2 3 3.3 High resolution x-ray spectrum for peak {400} 24 3.4a Rigaku x-ray diffractometer used for single crystals 2 7 3.4b Schematic representation of a double crystal x-ray diffractometer 27 3.5 Effect of sample thickness on diffraction curves 3 3 3.6 Double-crystal x-ray diffraction spectrum of sample no.30 . . 3 8 3.7 Comparison of the formulas relating the A l fraction to the v i angular separation 4 3 4.1 Sample patterning 4 6 4.2a Electrode of the spark erosion machine 4 8 4.2b Mask for sand blasting 4 8 4.3 Thermal diffusion apparatus for making electrical contacts 5 0 4.4 Contact resistance 5 2 4.5 Sample probe 5 5 4.6 Experimental setup for Van der Pauw measurement 5 6 4.7 Diode calibration curve 5 7 4.8 Resistivity vs temperature, sample no.32 6 2 4.9 Hall coefficients vs temperature, sample no.32 6 3 4.10 Calculated conduction band electron concentration vs temperature, sample no.32 6 4 4.11 Hall mobility vs temperature, sample no.32 6 5 4.12 Temperature dependence of the electron Hall mobility for four n-type GaAs samples 66 4.13 Resistivity vs temperature, sample no. 13 6 7 4.14 Hall coefficients vs temperature, sample no. 13 6 8 4.15 Calculated conduction band electron concentration vs temperature, sample no.13 6 9 4.16 Hall mobility vs temperature, sample no.13 7 0 vii Acknowledgements I would like to gratefully acknowledge my supervisors, Dr. Thomas Tiedje whom I have worked with and Dr. Richard Johnson, for their constant constructive advise and kindly support during the thesis work. I also wish to thank Hiroshi Kato, Douglas Bonn, lqbal Athwal, Jim Mackenzie, Christian Lavoie, Yuan Gao and Brad Robinson for their assistance in the sample preparation and measurements. viii CHAPTER 1. INTRODUCTION 1 Chapter 1 Introduction 1.1 Overview T h e m o l e c u l a r b e a m e p i t a x y ( M B E ) t e c h n i q u e i s c a p a b l e o f p r o d u c i n g c o m p o u n d s e m i c o n d u c t o r m a t e r i a l s w i t h h i g h p u r i t y , a c c u r a t e c o m p o s i t i o n , p r e c i s e t h i c k n e s s , a w i d e r a n g e o f d o p a n t l e v e l s , a n d h i g h q u a l i t y c r y s t a l s t r u c t u r e s . T h e a b o v e p r o p e r t i e s a r e v e r y i m p o r t a n t f o r o p t o - e l e c t o n i c a n d e l e c t r o n i c d e v i c e s , s u c h a s n o n l i n e a r o p t i c a l d e v i c e s [ 1 . 1 , 1.2], s u p e r l a t t i c e s [1 . 3 ] , q u a n t u m w e l l l a s e r s [ 1 . 4 , 1.5], d e t e c t o r s [ 1 . 6 ] , m o d u l a t o r s [1.7, 1.8], a m p l i f i e r s [1 .9 ] , a n d t r a n s i s t o r s [ 1 . 1 0 ] . C h a r a c t e r i z a t i o n o f t h e t h i c k n e s s , c r y s t a l l i n e s t r u c t u r e , c o m -p o s i t i o n , a n d e l e c t r i c a l t r a n s p o r t p r o p e r t i e s o f t h e M B E - g r o w n m a t e r i a l s a r e e s s e n t i a l b o t h f o r t h e g r o w t h o f m a t e r i a l s a n d f a b r i c a t i o n o f d e v i c e s . CHAPTER 1. INTRODUCTION 2 The growth rate depends on a number of parameters. It can be determined by the MBE beam flux intensities [1.11], by the intensity oscillation of RHEED diffraction [1.12], or by the intensity oscillation of the reflected light of a He-Ne laser beam impinging onto the wafer through a viewport on the MBE chamber [1.13]. These methods work accurately provided that some relevant parameters are known accurately. They all need to be calibrated by thickness measurements after growth. One direct approach for thickness measurements after growth is to selectively etch the grown wafers and do thickness measurement under scanning electron microscope (SEM) or scanning tunneling microscope (STM). Other topographic properties can also be investigated with SEM and STM, such as the evenness of interfaces and uniformity of layer thicknesses. In our VG V80H MBE system, GaAs and Al xGai- xAs ( 0 < x < 1 ) are the grown materials, doped by Be (for p-type) and Si ( for n-type). Gallium arsenide was first created by Goldschmidt in 1920s [1.14], and has a zincblende crystal structure. This structure has a face-centered cubic (fee) translational symmetry, with a basis of one GaAs molecule, one atom at 000 and the other at 4 4 4 " of the fee unit cube. The cube contains four such GaAs molecules in a volume a3, where a is the lattice constant of GaAs. The nearest-neighbor bond Via length is For stoichiometric GaAs at 300 K, the lattice constant a = 5.65 A, and the unit cube volume is a3 = 1.8067 xlO" 2 3 cm3. The g atomic density is ~ = 4.4379x1022 cm"3, and the crystal density is a 5.3174 g/cm3 at 300 K. For photons with energy just below the CHAPTER 1. INTRODUCTION 3 intrinsic absorption edge of GaAs, the refractive index of GaAs is n = 3.3, which results in a reflectance R = 0.29. The effective mass of electrons at the conduction band edge is 0.063 m e , while the effective mass of heavy holes is 0.50 m 0 , and that of light holes is 0.076 m 0 at 300 K. The rms thermal speeds of heavy holes, light holes and 300 K, the mobility of electrons is about 8000 cm 2/Vs which is much higher than the corresponding value for silicon which is 1900 c m 2 / V s . The high mobility and the ability to emit light are very attractive properties of GaAs for device applications. Most of the applications of GaAs would not be possible without A l x G a i - x A s as a mate. A l x G a i - x A s has the same structures as GaAs except that some of the Ga sites are occupied by A l atoms. Its lattice constant is very close to that of GaAs. The lattice constant of AlAs is 0.14% larger than that of GaAs at 300 K. A l x G a i - x A s also has a wider energy band gap and a lower refractive index than GaAs. In addition, both the energy band gap and refractive index of A l x G a i . x A s are changeable by adjusting the aluminium content x. When GaAs and A l x G a i . x A s are grown over one another, a heterojunction is formed. Combination of the heterojunctions of different height and distances results in double heterostructures, quantum wells, and superlattices and graded bandgap/refractive index materials. The combination is a special field called band gap engineering. Obviously, one important parameter is the aluminium content in A l x G a i - x A s . conduction electrons are all of the order cm/sec. At CHAPTER 1. INTRODUCTION 4 There are several techniques to measure the Al mole fraction in A l x G a i - x A s , which use: photoluminescence [1.14], MBE flux intensities [1.11], nuclear resonant reaction analysis [1.15], x-ray diffraction [1.11, 1.14, 1.15], secondary ion mass spectroscopy, Auger electron spectroscopy, opto-electronic effect [1.16], and other techniques. X-ray diffraction is a non-destructive, accurate and convenient technique. However, there is a slight problem remaining to be solved, that is, how to calculate the Al mole fraction in A l x G a i -x As from the x-ray spectrum of the A l x G a i - x A s / G a A s sample. Empirical formulas for the calculation of Al mole fraction have been reported [1.11, 3.2]. But due to differences in details of their experiments, these two formulas are different. Their difference increases linearly from zero as x increases, and reaches 14% at x=l. Another aspect of characterization concerns the electrical transport properties including resistivity, Hall coefficient, carrier concentration and Hall mobility. In a polar crystal containing dissimilar atoms like GaAs, the carrier scattering processes are complex. The scattering processes and the impurity bands have strong effects on all the electrical transport properties. In 1958, L. J. van der Pauw introduced a good method to measure the electrical resistivity and the Hall effect of flat samples of arbitrary shape. So far, this is still a standard method to measure these properties. In order to apply this method to MBE-grown materials, epitaxial layers have to be grown on semi-insulating substrates. In order to get stable and accurate results, samples have to be properly patterned and well alloyed for the electrical contacts. CHAPTER I. INTRODUCTION 1 1.2 Outline of the thesis The following chapters are nearly independent since the characterization is done for totally different properties of the MBE-grown materials. Chapter 2 describes the experiments to investigate the topography of the cleaved ends of the samples by means of selective etching and microscopy techniques. One good etchant which etches GaAs selectively and another one which etches A l x G a i - x A s were chosen among a number of etchants in order to achieve good selectivity and a smooth etched surface. The etch depth was measured with a Tencor Alpha Step 200 profilometer. The cleaved and selectively etched ends were investigated with an optical microscope, a scanning electron microscope, and a scanning tunneling microscope. Chapter 3 discusses x-ray diffractometry. The Al mole fraction in Al x Gai . x As was measured by this technique. The powder x-ray machine (Rigaku Rotating Anode Machine), was successfully used to measure Al mole fraction with reasonable accuracy (±2%). How the resolution could be improved is discussed. A new mathematical formula is derived to determine the Al mole fraction from the x-ray spectrum. Chapter 4 discusses the measurements of electrical properties. Sample patterning was found to be important for the measurements. Hall mobilities differed by a factor of 2 depending on whether or not the samples were patterned. A mask with a special pattern and a fine sand blaster were used to CHAPTER 1. INTRODUCTION 6 prepare the samples. Electrical properties were measured from 4 K to 300 K with the Van der Pauw method. A variety of samples was measured, including doped and undoped GaAs films. The two-band model was used to interpret the electrical transport results. The temperature dependence of the electron concentration in the conduction band was fit with an exponential function. From this fit, we obtained the activation energy of the impurity. We conclude that the residual impurity in the MBE system is mainly silicon. The results of mobility measurement are compared with other work reported in the literature. Finally, in Chapter 5, the results of this study are summarized. CHAPTER 2. MICROSCOPY 1 Chapter 2 Microscopy 2.1 Selective Etching 2 . 1 . 1 Introduction The goal of the selective etching is to measure the thickness of the M B E layers, and to study other structural properties of the M B E layers, such as the evenness of the interfaces, and the layer uniformity. The selective etchants etch GaAs and AlGaAs at different rates. No etchant has been found that is perfectly selective for GaAs or A l x G a i . x A s . Only in the case of x = 1, according to Eli Yablonovitch [2.1], hydrofluoric acid [2.2] etches AlAs much faster than GaAs, with selectivity greater than 10 7 . For unknown reasons we were unable to reproduce this result in our lab using the same ethants, either concentrated or diluted. CHAPTER 2. MICROSCOPY 2.2.2 Etching Experiments and Results The selectivity of a given etchant is defined as a ratio of two etching rates, i.e. For our purposes mentioned above, not only good selectivity but also a smooth etched surface is needed. More than ten existing selective etchants for GaAs and Al x Gai . x As have been tried. The best etchant to etch GaAs relative to Al x Gai. x As was found to be Its etching rate for Alo .5Gao.5As is about 20 A/sec. The selectivity for x=0.5 is greater than 10. The selectivity was measured in the following way: • spin Shipley SI400 photoresist on the sample at a speed of 4000 rpm; • bake the photoresist at 70 °C for 20 min; • expose the photoresist with a mask of parallel stripes; • develop the exposed parts of photoresist; • bake the photoresist again at 150 °C for 30 min; • etch the masked sample by wet chemical etching; • use Tencor Alpha Step 200 instrument to measure the etched step selectivity = faster etching rate for material 1 slower etching rate for material 2' H 2 0 2 : N H 4 O H : H 2 0 (1:1:5 by volume). height. CHAPTER 2. MICROSCOPY 9 Results of the step measurements with the same etchant H2O2 : N H 4 O H : H 2 0 (1:1:5 by volume) are shown in Fig. 2.1 and Fig. 2.2. The sample used in Fig. 2.1 was GaAs, and the one used in Fig. 2.2 was A l o . 5 G a o . 5 A s . In Fig. 2.2 no etch steps are observable which indicates that the etchant H 2 O 2 : N H 4 O H : H2O (1:1:5 by volume) almost does not etch A l o . 5 G a o . 5 A s . By comparison of the etched depth, we determined the selectivity (>10). The selectivity is greater as the value of x in Al x Gai . x As increases. While the sample is being etched by H2O2 : N H 4 O H : H2O, the etchant induces many bubbles on the surface of the sample. The bubbles have a bad effect on the etching uniformity. When a bubble stays on the surface of the sample, it prevents fresh etchant from coming to the place where it stays, therefore, leaving an under-etched circular pattern beneath it. In an attempt to remove the bubbles, the container with the etchant and the sample was moved into a ultra-sonic wave sink. However the ultra-sonic waves were not sufficient to move the bubbles. Stirring did not work either. Finally, another simple method was found, i.e., to blow the bubbles and sample, during the period of etching, using a glass tube attached to a rubber bulb, sucking some etchant and blowing it out towards the sample. The best etchant for preferentially etching A l x G a i - x A s with respect to GaAs was found to be K 3Fe(CN) 6 : KOH : H 2 0 ( 1 : 1.5 : 62.5 by weight). The etching rate for x = 0.5 is about 15 A/sec, and the selectivity is 12 3 08 si. M 0 4 at X 0 0 1/ - 0 . 4 T O TTiT Urtl Scanning range (um) Fig. 2.1. Step height measurement done with Alpha Step 200 Tencor Instrument. Sample: GaAs. Etchant: H 2 0 2 : N H 4 O H : H 2 0 (1:1:5 by volume). OA - 0 . 2 -0 4 TT "TiTTT U l i l Scanning range ( u m ) Fig. 2.2. Step height measurement done with Alpha Step 200 Tencor Instrument. Sample: Alo.5Gao.5As. Etchant: H 2 0 2 : N H 4 O H : H 2 0 (1:1:5 by volume). CHAPTER 2. MICROSCOPY 12 about 5. The selectively of this etchant for AlAs relative to GaAs was quite obvious under an optical microscope. This etchant provides very smooth etched surfaces as shown in Fig. 2.3, and is quite stable. Once it has been prepared, the etchant can be repeatedly used for many weeks without apparent loss of its etching ability. While for GaAs, the etchant H2O2 : N H 4 O H : H2O is not very stable. When GaAs samples are being etched, in addition to lots of bubbles around the sample as a product of the chemical reaction, the etching function is gone about one hour later after the preparation of the solution because the ammonia evaporates. The following are the selective etchants which have been used [2.4, 2.5, 2.6]: - for GaAs • H 2 0 2 : H 2 0 ( pH=7 ) • I 2 : KI ( 0.1 : 0.3 mol/liter, pH=9.4 ) • H 2 0 2 : N H 4 O H ( 19 :1 by volume ) • H 2 0 2 : N H 4 O H : H 2 0 ( 1 : 1 : 5 by volume ) • KI 3 : KI : H 2 0 ( 1.7 : 1.8 : 50 by weight, pH > 3 ) • K 3Fe(CN) 6 : K4Fe(CN)6 : H 2 0 ( 3.8 : 4.1 : 50 by weight, pH>9 ) - for AlGaAs • HF : H 2 0 ( 1:1 by volume ) • K4Fe(CN) 6 : KOH : H 2 0 ( 1.5 : 2 :15 by weight ) • K 3 Fe(CN) 6 : KOH : H 2 0 ( 1 : 1.5 :12.5 by weight) • K 3 Fe(CN) 6 : KOH : H 2 0 ( 1 : 1.5 : 62.5 by weight) • K I 3 : KI : H 2 0 ( 1.7 :1.8 : 50 by weight, pH >3 ) Scanning range (|im) Fig. 2.3. Step height measurement done with Alpha Step 200 Tencor Instrument. Sample: Alo.5Gao.5As. Etchant: K 3 Fe(CN) 6 : K O H : H 2 0 ( 1 : 1.5 : 62.5 by weight ). CHAPTER 2. MICROSCOPY 14 • K 3Fe(CN) 6 : K4Fe(CN)6 : H 2 0 ( 3.8 : 4.1 : 50 by weight, pH<9 ) Some etchants are good for both GaAs and AlGaAs if their pH values are adjusted, for example, K3Fe(CN)6 : K4Fe(CN)6: H 2 0 [2.4]. 2.2 Results of Scanning Electron Microscopy (SEM) and Scanning Tunneling Microscopy (STM) Two differnet SEM's (Hitachi S-570 and Hitachi S-2300) were used to image the samples. To measure the layer thickness and morphology of the interfaces, samples were cleaved along (110) planes, and selectively etched by one of the two etchants mentioned above. Then, they were held vertically with a specially designed holder in the SEM sample chamber. The chamber was evacuated to 10"5 torr. Typical scanning conditions are: working distance 5 mm, aperture no.4, accelerating voltage 20 KV, and magnification 20 to 40 K. The best resolution was achieved with the smallest aperture, the minimum astigmatism (which was eliminated by adjusting the position of the aperture), and a short working distance between the object lens and the sample. The SEM, without calibration, gives an uncertainty of about 30% for dimension measurement. In order to obtain an accurate measurement, calibration of the system was done with a standard crystal under the same scanning conditions right after the sample measurement. Fig. 2.4 shows an SEM picture of MBE sample no.35. CHAPTER 2. MICROSCOPY 15 The layers from bottom to top are GaAs substrate, AlAs marker, GaAs of 0.515 u.m, second AlAs marker, and GaAs of 3.44 jim. The first AlAs layer is not flat because of the uneven surface of the substrate. The second AlAs layer is much flater than the first one. This is a result of surface migration of Ga and As 2 during epitaxial growth. Fig. 2.5 is an SEM picture of MBE sample no. 37 which consists of five groups of multi-quantum wells. All of the quantum wells have the same depth in energy since the Al content in all of the AlGaAs layers was made the same. The evenness of the layers is fairly good due to the smoothing effect of the buffer layer beneath them. For a high contrast sample the resolution of the SEM system is 50 A which is adequate for the layers in the bottom group, but not sufficient for the rest of the quantum well layers. Therefore, a scanning tunneling microscope (STM) was used [3.3]. Scanning tunneling microscopy is a technique which is capable of viewing a conducting or semiconducting material with atomic resolution. The experiment using STM for GaAs/Al x Gai- x A s cross section analysis is still in progress in our Lab. Samples were cleaved and viewed on the (100) surfaces, the same way as was done for the SEM samples. Because STM does not work well for rough surfaces, it is critical to selectively etch the sample only a little. Fig. 2.6 is a measured STM picture of sample no. 37. It does not show the topographic structure that we hoped to see. The spheres in the picture might be oxide, since they do not have regular cystalline CHAPTER 2. MICROSCOPY x l 5 k 8 9 7 0 2 0 k V 2^m Fig. 2.4. SEM picture of sample no.35. CHAPTER 2. MICROSCOPY 12 x4@k 1886 2 0 k V 1 — - . - . — • "~ Fig. 2.5. S E M picture of sample no.37 which contains five groups of multi-layers or multi-quantum wells. From bottom to top, group (1) consists of 120 A GaAs + 200 A Alo. 6Gao. 4As, 7 pairs; (2) 60 A GaAs + 100 A Alo .6Gao.4As, 7 pairs; (3) 40 A GaAs + 70 A A l 0 . 6 Ga 0 . 4 A s , 8 pairs; (4) 20 A GaAs + 30 A A l 0 . 6 Ga 0 . 4 A s , 15 pairs; and (5) 10 A GaAs + 20 A Al0.eGa0.4As, 30 pairs. CHAPTER 2. MICROSCOPY Fig. 2.6. Scanning tunneling microscope picture of the cross section of sample no.37. Scanning ranges: x - 150 A, y - 110 A, and z - 20 A. structures as could be revealed in such small scales, nor could be cleaned off easily as dust. The scanning ranges are: x ~ 150 A, y ~ 110 A, and z ~ 20 A. In order to get a picture of the cross section without oxidation, it will be necessary to place the STM into a UHV chamber. CHAPTER 3. X-RAY DIFFRACTOMETRY 20 Chapter 3 X - Ray Diffractometry 3.1 Background and calculations A l x G a i . x A s has the same cubic zincblende crystal structure as GaAs, but it has a larger lattice constant [3.1] a(x) = 5.6533 + 0.0078x A , ( 3.1 ) than that of GaAs ( a = 5.6533 A ) for any value of x within the range of 0 < x < 1. Experiments have shown that when Al x Gai- x As is grown on the GaAs substrate, it tends to perfectly match the lattice constant of GaAs [3.1]. Therefore, the cubic lattice cell of A l x Gai_ x As is squeezed horizontally and expanded vertically as shown in Fig. 3.1. A crystal of the zincblende structure has {400} family planes, where [400} corresponds to Miller indices h=4, k=0, and 1=0. For GaAs, each plane in the {400} family is either occupied only by Ga atoms or only by As atoms. Ga planes alternate with As planes. The distance CHAPTER 3 X-RAY DIFFRACTOMETRY 21 '//A '///, '//A •V/A '//A •V/A 'ft*. - • / / / , 'ft*. '//A '//A '//A (a) •*/// '/// ••//A '//A '//A '//A '//A '/// / / / / . < • / / / / / / / ///*< / / / / '//A '///, '//A //// '//A //// '•/A A/A/ ////'/AA //// /A// //// VA// '/// 'A/A '//A '//A '//A / / / • '//A / / / / / / / / ///> / / / / '//A '//A '/// '/// //// '//A //// '//A / / / / ' / / / //// '//A / / / / / / / / / / / / '//A '//A '//A / / / / / / / / / / / / / / / / '//A '//A '//A '//A / / / / ' / / / / / / / ///> / / / / / / / / / / / / '//A '//A '//A '//A '//A / / / / ///> / / / / / / / / / / / / / / / / / / / / / / / / '/// '//A '/// '//A '//A '//A '//A '/// / / / / ' / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / ' / / / ' / / / ' / / / ' / / / ' / / / ' / / / ' / / / ////'//A / / / / / / / / ///> ///> / / / • / / / / ///> '//A '//A '//A '//A '//A '//A '//A ///• '//A ///>'/// / / / / ' / / / / / / / ' / / / / / / / / / / / / / / / '/// '/// '//A //// '//A //// '//A / / / / ' / / / //// '//A ///<* '//A ///> '//A ////'//A ///> ///> / / / / / / / / ///> / / / / ///> ///> ///> ///> / / / / / / / / / / / / / / / / / / / / / / / / ///> ///> / / / / ///> / / / / ///> ///> ///> AlGaAs GaAs Fig. 3.1. Lattice matching of AlGaAs and GaAs. (a) AlGaAs grown on GaAs substrate, (b) detailed picture to show the deformation of AlGaAs. CHAPTER 3 X-RAY DIFFRACTOMETRY 22 between the adjacent planes is one fourth of the lattice constant. When Ga atoms are partially replaced by Al atoms with a mole fraction x, we get Al x Gai . x As which still keeps the cubic zincblende structure. If A l x G a i - x A s is grown on a GaAs substrate and the sample is measured by x-ray diffraction, the x-ray spectrum would contain two {400} peaks as shown in Fig. 3.2 and Fig. 3.3. One peak corresponds to GaAs, and the other corresponds to Al x Gai . x As. X-ray diffraction peaks are the result of constructive interference of x-ray beams reflected from a set of lattice planes at the Bragg angle Al x Gai - x As has a larger d, thus a smaller 0B. SO , the peak on the left corresponds to A l x G a i . x A s . By the angular separation of the two peaks, and a proper method of calculation, the Al mole fraction can be obtained. But what is the proper calculation? So far in the literature, there is no consistent mathematical formula for use. Xiong et al reported a relationship [3.2]: with an error of 3%, based on x-ray diffraction and nuclear resonant reaction analysis (NRRA). B = arc sin — . (3.2) 69(degree) = 0.109x . (3.3) While, Bassignana et al. reported another formula [1.11]: 80(degree) = 0.0958x . (3.4) Z03062.RAW 10 20 30. 40. 50. 60. 20 (degree) 70 80. Fig. 3.2. X-ray spectrum of Al xGai. xAs/GaAs sample no.30. The left peak corresponds to (200) planes, the right one (400) planes. to Z03105.RAW o o o o T c 3 O u </> c GAAS#30. 4, 18 /4 /91 . 20KVX20MA, NEW SLITS, LX GaAs, K a i + AIo .86Gao.14As, K«2 Alo .86Gao. i4As , K a l GaAs, K«2 -1— 1 —1— 1 1 1 1 1 1 j — • — 1 — « — 1 — • — 1 — • — 1 — » — j — • 1 • 1 ' I 1 l 65 .5 66.0 66 .5 67 28 (degree) 1 a SO O Fig. 3.3. High resolution x-ray spectrum for peak {400) CHAPTER 3. X-RAY DIFFRACTOMETRY 25 with an error of 2% at lower x, and 3% at higher x. Equation (3.4) was obtained from both experiments and calculations. In the experiments, Bassignana used AlAs as an internal standard for the x-ray diffraction and the method of thickness analysis to extimate x in A l x G a i - x A s . In the calculations, he assumed a constant Poisson's ratio. The results of Xiong and Bassignana both show a linear relationship between the angular separation and the Al content, which is not exactly true since in fact the Poisson's ratio is not a constant for Al x Gai- x As although the non linear factor is very small [3.1]. The reason for the difference between Eq.(3.3) and Eq.(3.4) might be due to the usage of different samples and other experimental details. AlAs was used as an internal standard for calibration by both authors. The AlAs layer, 1 to 3 |xm thick, used by Xiong was grown directly on a GaAs substrate. While the AlAs layers, 0.5 to 1.5 jim thick, used by Bassignana were grown on A l x G a i . x A s (x=0.25 to 0.5), and the A l x Gai . x As was again grown on a series of other epitaxial layers. Different techniques were also used to calibrate their x-ray diffractometers. Xiong employed the nuclear resonant reaction analysis. Bassignana used the scanning electron microscopy to estimate Al content x from the thickness of Al x Gai - x As layers, and calculations with the assumption of a constant Poisson's ratio. The two formulas (3.3) and (3.4), at x = 1, differ by 14%. In this thesis, a result which is in between the above two results has been derived theoretically. The detailed calculation will be given in section 3.4. CHAPTER 3. X-RAY DIFFRACTOMETRY 26 3.2 X - Ray Measurement of Al Mole Fraction in AlxGai-xA s Fig. 3.2 and Fig. 3.3 are the 9/20 x-ray rocking curves for sample no. 30 grown by our V G V80H MBE system. There are two sharp and high peaks in Fig. 3.2. The left is a {200} reflection, and the right is a {400} reflection. The spectra were obtained from the computerized Rigaku Rotating Anode X-Ray Diffractometer which is designed for measurement of powders and polycrystalline thin films (Fig. 3.4a). The machine uses 4 slits to collimate the x-ray beam. One is between the source and the sample holder, and two are between the sample holder and the detector. The fourth one is in front of the detector. Between the 3rd and 4th slits, there is a bent graphite crystal monochromator which is set to reflect the k„ component, remove the continuum background radiation from the source and x-ray fluorescence from the sample, and focus the divergent radiation diffracted from the sample. All components after the sample holder are fixed on a moveable goniometer. During operation, both the sample holder and the goniometer rotate. The goniometer rotates at a speed two times greater than the sample holder. This is so-called 0/20 scanning. The resolution of this Rigaku diffractometer in terms of the width of the diffraction peaks is 40 s 0 .025° = 90 arc sec. The resolution is limited by the poor quality of the x-ray beam impinging on the sample, i.e., the beam divergence and spectral width of the x-ray source. This will be discussed in more CHAPTER 3. Y-RAY DIFFRACTOMETRY 22 Fig. 3.4a. Use of Rigaku x-ray diffractometer for single crystal measurement. high quality GaAs(fixed) detector x-ray source AX, AG * sample e Fig. 3.4b. Schematic representation of the double-crystal x-ray diffractometer. CHAPTER 3. X-RAY DIFFRACTOMETRY 28 detail in the next section. One advantage of the Rigaku diffracto-meter is that besides 8/26 scanning, the sample holder or the goniometer can rotate independently with the other fixed at a desired angle. The smallest angular step that the sample holder and the goniometer can rotate is 0.002° (7.2"). Using these special functions, one can measure single crystals by carefully aligning the source, holder and goniometer. Results showed that the machine could be used to measure the Al content with satisfactory accuracy. There are several ways of doing the alignment by computer. The,, most effective procedure was found to be the following: 1° 1° • Choose a set of narrow slits: slit 1, — ; slit 2, — ; slit 3, 0.15; and slit 1° 4, 0.15 (Fig. 3.4a), where — , 0.15 are the labels on the slits. Choose the smallest scanning interval 0.002° as well; • Use a piece of double-side sticky tape to mount the sample gently on a glass plate; • Scan 9/20 at a speed of 2°/min from 29 = 60 to 70 degrees to find the {400} peak which could be of low intensity at the moment; • Position the goniometer to 28, the angular position of the peak; • Scan 0 only to find the angle corresponding to the highest intensity; • Position the sample holder at the new 6 found in the last step, and scan 28 only to find a new angle for the peak intensity. Normally, CHAPTER 3. X-RAY DIFFRACTOMETRY 22 the peak intensity increases after each scan; • Repeat the last three steps until no further improvement can be made. Now, denote the angular position of the sample holder as <Ph, and that of the goniometer Wg', and • Reset the initial angle of the sample holder to a new initial angle q> e n e w = 6 o + [ ( P h - y ] . (3.5) where 6 0 is the originally set initial angle. Note that other common steps and how to use the computer to control the operation of the system are omitted in this thesis for simplicity. Usually, one needs only to repeat the procedure a few times in order to optimize the alignment. 6 n e w is normally of the order of 0.1 degrees. Fig. 3.3 is a spectrum scanned in the vicinity of the {400} peak. In this detailed spectrum, three peaks are observed. The x-ray source material is copper. When bombarded by high energy electrons, the atoms of copper are excited to upper energy levels. When the excited atoms have radiative transitions back to the ground state, the so-called K shell, K group x-ray is emitted, which include K a i , K a2, Kp, and so on. The wavelengths of Kai (1.540598 A), K«2 (1.544418 A), and Kp (1.392249 A) are very close, especially for K a i , K a2 which correspond to the energy transitions from ls ! 2p 6 to ls 22p 5 (j=l/2), and l s^p 6 to ls 22p 5 (j=3/2). It is impossible to elimi-CHAPTER 3. X-RAY DIFFRACTOMETRY 3_Q nate K a 2 by employing narrow slits in the x-ray system designed for powders when a low quality crystal is to be measured. Therefore, the x-ray beam used for the measurements includes both K a i and K a 2 . The intensity of K a 2 is one half of that of Kai. The peak on the left in Fig. 3.3 corresponds to Al x Gai- x As, K a i . The one on the right corresponds to GaAs, K a 2 . And the middle one is a mixture of Al x Gai-xAs, K a 2 a n d GaAs, K a i , but mainly GaAs, K a i . The Al mole fraction x=0.85 which was calculated according to Eq.(3.29) in section 3.4. The lineshape of the peaks has a Gaussian distribution [3.2], The angular separation between any two peaks is equal to the separation between the two central lines of the peaks. Although the Rigaku system does not have a very high resolution for single crystals, its resolution, after proper arrangement, is sufficient to measure the Al content mole fraction with an uncertainty of 2%. Higher resolution x-ray measurements are needed in order to measure the Al content more accurately, and to measure other structural properties such as dislocation density and the thickness of the grown layers [1.11]. 3 . 3 Resolution Improvement As shown in Fig. 3.4a, an x-ray source has a certain divergence angle A0, and contains several wavelengths Xi, X2 X n , each with a natural line width AXi, AX2,..., AXn [3.4, 3.5]. For copper CHAPTER 3. X-RAY DIFFRACTOMETRY i i K a i , the natural line width is 2.11 eV [3.6]. The corresponding width in wavelength is AX= \'2* Ae(eV) nm = 4.0xl0-4 A. (3.6) ez(eV) where e = hc/X, = 8048 eV, for X = 1.54 A. It is clear that the spectral width and angular divergence will limit the resolution of the x-ray measurement. If the crystalline structure of the measured sample is of high quality and is sufficiently thick, the wavelength in the diffracted beam will be regularly distributed according to Bragg diffraction equation such that a beam of a longer wavelength will have a larger reflection angle, and beams of wavelengths which do not satisfy the Bragg angles are not reflected. This feature of the Bragg scattered radiation can be used to obtain better resolution in the following way. One high-quality crystal is placed right after the source to re-arrange the raw x-ray beams by diffraction, and the sample to be measured is placed behind that crystal. This setup is the so-called double crystal x-ray diffractometer (Fig. 3.4b). Its resolution depends on the quality of the first crystal and can be much better than that of a single crystal x-ray diffractometer. Quantitatively, the resolution of the single crystal x-ray system can be represented by the angular width of the reflected beam 6A 5d 86 = tan0B (— + —) + A9 i t + A0 d e f + A 0 c o m p . (3.7) A d CHAPTER 3. X-RAY DIFFRACTOMETRY 11 where 6B = Bragg angle, A6u = angular width induced by the finite thickness of the grown layer in the sample with presence of the x-ray beam divergence, A6def = angular width induced by defects in the sample, A6 c o m p = angular width induced by the compositional imho-mogeneity, — is due to 8X, the spectral width of the x-ray line width, A. 6d — is due to inhomogeneous strain, d For a pure and thick GaAs sample, the last three terms in Eq.(3.6) including A8i t as explained in the following, are negligible. In this case This can be derived from the Bragg equation, 2dsin0B = A. If we assume that other broadening mechanisms of line width do not exist, and consider only the finite thickness of the measured sample, we show below that A8it= . (3.9) 2t COS0B where d = the distance between the adjacent lattice planes, 8X 8d 59 = tan6 B (3.8) m = the number of all lattice planes in the grown layer, t = md, the thickness of the grown layer (see Fig. 3.5a). CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 21 Fig. 3.5b and c. Effect of sample thickness on diffraction curves. Equation 3.9 can be proved readily. As shown in Fig. 3.5a, the rays A, D, M which make exactly the Bragg angle 8B interfere constructively. Reflected rays A' and D' differ in phase by one wavelength, while reflected rays A' and M ' differ in phase by mL Considering incident rays that make Bragg angles only slightly different from 8 B , we find that destructive interference is not complete. Ray B, for example, makes a slightly larger angle 8 i , such that ray L ' is (m+l)A out of phase with B \ In the midway of the crystal, there is a plane scattering a ray which is (m+l)X/2 out of phase with B'. These rays are destructive. They cancel one another, and so do other rays from similar pairs of planes throughout the crystal, the net effect being that rays scattered by the top half of the crystal cancel those scattered by the bottom half. The intensity of the beam diffracted at the angle 61 is therefore zero. Similarly, the path difference of ray C and N' at reflection angle 82 is (m-l)X. The intensity at 82 is zero. The diffracted intensity in ranges of ( 8 2 , 8 3 ) and ( 8 B , 8 I ) is not zero, but has a value intermediate between zero and the maximum intensity at 8B - The spectrum will then appear as shown in Fig. 3.5b in contrast to Fig. 3.5c which illustrates the hypothetical case of diffraction occuring only at the exact Bragg angle. The width of the peak W, can be taken as half the difference between 81 and 82, that is W = | ( e 2 - 8 i ) . The Bragg equations for rays at 81 and 82 are CHAPTER 3. X-RAY DIFFRACTOMETRY 11 2(md) sinSi = (m+l)X. 2(md) sin02 = (m-l)X. (3.10) (3.11) By subtracting (3.11) from (3.10), one gets md ( s in0i- sin92 ) = X. i.e. 2md cos sm 01-02^ = X. (3.12) For (400) peaks of GaAs and AlGaAs, 0 i and 02 are very close to 0B. Therefore, approximately 01 + 0 2 = 2 0 B . and sin f01-0 2N l '01-02^ Then, Eq.(3.12) becomes 2md cos0 B '01-02"! = X. Thus W = 2md COS0B = A 0 i t . (3.13) This is what we have in Eq.(3.9). A more exact treatment gives a slightly different result 0.9X A G i t 2md COS0B' (3.14) CHAPTER 3. X-RAY D1FFRACT0METRY which is known as the Scherrer formula [3.7]. 3_£ One way to get better resolution is to monochromatize and collimate better the x-rays impinging on the sample. Alternatively one can increase the resolution by means of the double crystal diffraction technique. In this technique a high-quality thick GaAs crystal is placed between the x-ray source and the sample as shown in Fig. 3.4b. The high-quality crystal is positioned at the Bragg angle with respect to the source which contains a range of wavelengths and beam divergence. Ideally the high-quality GaAs crystal has no compositional inhomo-geneity. It can also be considered as infinitively thick, and nearly free of defects. Therefore, A8j t, A0def and A0Comp vanish. If surface strain is released by etching, the term 8d — is also negligible. Then, Eq.(3.7) becomes d 8A 80 = taneB—. (3.15) A. This is a direct result of the Bragg condition with absence of strain. Due to the very critical Bragg condition, each wavelength of the source will only reflect at a particular angle on the first crystal. Thus the reflected beam from the first crystal has a precise relationship between the angle of the reflected ray and its wavelength. By symmetry, any x-ray photon which satisfies the Bragg condition at the first crystal will also satisfy the Bragg condition on the second crystal, if the two crystals are aligned parallel to each other. If the second crystal ( the sample ) is rotated slightly, then its Bragg reflec-CHAPTER 3. X-RAY DIFFRACTOMETRY 3_Z tion peak can bemeasured. Since the raw x-ray contains K«i and K a 2 in every direction within the divergence angle, and usually the difference of their Bragg angles (<0.11° if copper is the x-ray source) is smaller than the divergence angle of the x-ray source beam, both K a i and K a 2 satisfy the Bragg conditions and are simultaneously reflected by the first high-quality crystal. Because of the different Bragg angles, K a i and K a 2 beams are spatially separated at the measured sample. Since the detector has a 4.5 mm wide detection window and has no slit in front of it, K a i and K a 2 are simultaneously detected. Thus the peaks of K a i and K a 2 overlap in the spectrum. If the sample is slightly curved, which may be caused by substrate unevenness, non-uniform epitaxial growth, or inhomo-geneous strain induced by sample mounting, the peaks of K a i and K a 2 will separate slightly and the widths of the x-ray peaks will increase. To prevent the increase of the width, one can eliminate K a 2 by positioning narrow slits between the two crystals. If without these narrow slits, and if the sample is curved to some extent, K a i and K a 2 will not be detected at the same time. This phenomenon might be utilized as a means of measuring curvature. Fig. 3.6 is the result of a double-cystal x-ray diffraction measurement for the same sample shown in Fig. 3.2 and Fig. 3.3. This measurement was done at McMaster University by B. Robinson. By extending the same idea and placing two or four high-quality crystals between the source and the sample, one can achieve even better resolution [3.8]. Once a good spectrum has been obtained, the CHAPTER .?. X-RAY DIFFRACTOMETRY 11 COMXTitt joooc :oooo, — ? +- GaAs *- 28 sec 1SCOO . IOC00 . Alo .85Gao.15AS sooo. * / 230 s e c / 1^1 » . 1 \ / 1 <t—305 sec_». • -*oo -200 0 2M »eo sec. AXU 1 Fig. 3.6. Double-crystal x-ray diffraction spectrum of sample no.30. The measurement was done by Brad Robinson at McMaster University. CHAPTER 3. X-RAY D1FFRACTOMETRY 3_9_ next question is how to calculate the Al content from the angular separation of the Al x Gai- x As and GaAs {400} peaks. 3.4 Calculation and Comparison From strain and stress relations, the strains of Al x Gai . x As can be expressed as [3.11] 2y £ z z = - — £ y y , (3.16) 1-y Aa f z - Aa f £ z z = — r t — • ( 3 - 1 7 ) Aa f v - Aa f £ y y = Tt , (3.18) where y = 0.31 + O.Olx, is Poisson's ratio [3.1], af= af(x) = 5.6533 + 0.0078x (A), lattice constant of Al x Gai- x As film, Aaf= a f- as, afz = deformed af in vertical direction, a s = lattice constant of the GaAs substrate, afy = deformed af in horizontal direction, Aa f z= afz- a f | and Aafy - Sf-aty, as indicated in Fig. 3.1b. The deformed lattice structure of Al x Gai . x As belongs to the tetragonal crystal system. The distance between two adjacent planes are [3.9, 3.10] CHAPTER 3. X-RAY DIFFRACTOMETRY 40 d = ^aFZJ a f y 2 J (3.19) where (h,k,l) are Miller indices. Before deformation, a f y= a fe = af, so d = 1^/2 h 2 + k 2 + l 2 (3.20) After deformation, afy and afZ are different from af. But still afy » afz « af. (3.21) Differentiating Eq.(3.19) with respect to afy and a f Z , and using the approximation in Eq.(3.21), one gets 5 d = ( h 2 + k 2 + 12)3/2 t h 2 5 a * + ( k 2 + 1 2 ) 5 a * J ( 3 - 2 2 > Combining Eq.(3.20) and Eq.(3.22), and denoting 8afz as Aa f y , and 6a fy as Aa f y, one finds 5d 1 d h 2 + k2 + 12 , A a f 2 „ A a f y h 2 — + ( k 2 + l 2 ) — ^ af af (3.23) For {400} planes 5_d d Aa f z af (3.24) From eqs. (3.18) to (3.24), Aa: Aa fz fy (1 + Y^i a - Y Aaf A a ty 21 _ A + Y " | A a f 1 - Y = 11 - Y j A a f y ' (3.25) CHAPTER 3. X-RAY DIFFRACTOMETRY ±1 Aaf since experiments have shown that, in general, » 1, i.e., the misfit of GaAs and A l x G a i - x A s in horizontal direction is negligible compare to the difference of af and as [3.11]. Thus Aa f z = 1 + ^ Aa f . (3.26) From the Bragg equation, 8d 80 d tan0j (3.27) Combining Eq.(3.1), Eq.(3.4), Eq.(26) and Eq.(3.27), and taking 0B in Eq.(3.27) as the Bragg angle for GaAs {400} planes, we find g e r . , 0.29 ( 1.31 + O.Olx ) x  ( egree ; ( 5 5 5 3 3 + o.0078x ) ( 0.69 - O.Olx )' ( 3 , 2 8 ) where the wavelength of copper Kai has been used. Approximately, Eq.(3.28) can be written as 88( degree ) = 0.0976 ( 1 + 0.022x ) x. (3.29) Comparison of our result and the results in the literature is shown in Fig. 3.7. The calculated one falls in between the results of Xiong's [3.2], 80( degree ) = 0.109x, (3.30) and Bassignana's [1.11], 80( degree ) = 0.0958x. (3.31) CHAPTER 3. X-RAY DIFFRACTOMETRY 42 It is also shown in Fig. 3.7 that the approximation of Eq.(3.29) is very good. The relation between the angular separation 89 and the Al content x, was linear by Xiong and Bassignana. But, according to Eq.(3.29), it is not exactly linear. The linearity of Eq.(3.31) results from the constant Poisson's ratio as Bassignana assumed. The linearity of Eq.(3.30) might due to the experimental errors which make it difficult to resolve the small non-linear factor 2.15x10"4 in Eq.(3.29). The results of Xiong's and Bassignana's differ by 14% at x=l. Equation (3.29) is closer to that of Bassignana's, especially when x is small. CHAPTER 3. X-RAY DIFFRACTOMETRY 41 Fig. 3.7. Comparison of the formulas relating the Al mole fraction to the angular separation. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 44 Chapter 4 Electrical Transport Properties Unlike the measurement of Al content for which there are a number of widely accepted techniques, there is a quite unique and standard technique to measure electrical transport properties of semiconductors: the Van der Pauw method [4.1]. The electrical transport properties measured with this method include resistivity and Hall coefficient from which carrier concentration and Hall mobility are derived. Another method to measure electrical property is the four-probe method. Only one electrical property, the resistivity, can be measured with this method. Although the Van der Pauw method has been used by many people for more than 30 years, experimental details are difficult to find in the literature. Accordingly we developed every detail from the beginning including the experimental setup, and the sample preparation in order to increase the accuracy and reproducibility of the measurements. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 4.1 Sample Preparation Al 4.1.1 Patterning In order to measure electrical transport properties of MBE-grown films, semi-insulating substrates (resistivity =107 Q-cm) have to be used. In the beginning, square samples (Fig. 4.1a) were used for electrical transport property measurements. The measurement results were not reproducible, especially the Hall voltages. Samples were then patterned with a diamond cutter in a clover leaf pattern as shown in Fig. 4.1b. As the cut lines were made longer, i.e. closer to the center, the Hall voltages under the same measurement conditions became larger. Samples with the pattern shown in Fig. 4.1c had the largest values of Hall voltages and the best reproducibility as well. The mobilities for the same wafer with the pattern of Fig. 4.1a and that of Fig. 4.1c were found to differ by a factor of two. This result shows that it is important to pattern the sample, so that the electrical contacts are in contact with the perimeter of the sample. In Van der Pauw's theory, the electrical contacts are assumed to be at the perimeter or circumference of the sample, and are sufficiently small. If one of the four point contacts is moved towards the center of the sample, it would result in measurement errors in the resistivity and Hall voltage which, in turn, would result in a relative error in the Hall mobility of [4.1] AuH 2d lb TtD CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 16 indium semi-insulating substrate sand blasted areas Fig. 4.1. Sample patterning, (a) square sample not patterned, (b) sample with a clover pattern, and (c) best patterned sample. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 47 where D = the diameter of a circular sample, d = the distance of a contact away from the circumference, of the circle, L l H = Hall mobility of the sample. The negative sign on the right-hand side of Eq.(4.1) indicates that the shift of the contact towards the center of the sample would cause an error such that the reading value of the Hall mobility is smaller than its real value. In the case shown in Fig 4.1a, all four contacts were away from the edge. Each of them will contribute a relative error given in Eq.(4.1), so that the total relative error is four times of the value in Eq.(4.1), ^ = - M (4 2) The final pattern (Fig. 4.1c) satisfies the condition of the Van der Pauw method that the contacts are at the circumference of the sample. Another condition of the Van der Pauw method, as mentioned above, is that the contacts be sufficiently small. For the pattern of Fig. 4.1c, with a finite width w of the arms, the relative error in the mobility is [4.1] 4 r k = _ 8 w ( 4 3 ) Therefore, the arms were made as narrow as possible to minimize the errors. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 48 The patterning was done with specialized tools. First, a brass bar was machined with a structure shown in Fig. 4.2a. This bar was then used as an electrode in our AGIE spark erosion machine. A square piece of stainless steel plate was eroded with the electrode. We thus get a mask with the negative pattern of that of the bar as shown in Fig. 4.2b. The MBE-grown wafer was cleaved into a square of about 6x6 m m 2 which is slightly larger than the mask. Then the sample was covered by the mask oriented at 45 degrees as shown in Fig. 4.2b Finally, the masked sample was sand blasted down to 0.1 ~ 0.2 mm with an Al sand blaster. Sand blasting took about 10 seconds. Fig. 4.2a. Electrode of the spark erosion machine. sample position V p mask window Fig.4.2b Mask for sand blast-ing. The dashed square corresponds to the position of the sample. 4.1.2 Ohmic Contacts CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 4 J ) In order to measure the carrier electrical transport properties, ohmic contacts were made on four spots of the MBE grown wafers as shown in Fig. 4.1. Two methods were employed in making ohmic contacts: thermal diffusion between In and GaAs, and vacuum evaporation of Au-Ge. Thermal Diffusion Indium is often used to make ohmic contacts on GaAs [4.2]. Fig. 4.3 is the apparatus used for the contact diffusion. A patterned sample was first put onto the stage inside the diffusion chamber. Four indium spheres about 0.5 mm in diameter were flattened in order to prevent them from rolling around on the sample, and then they were positioned one in each corner. A thermocouple was placed onto another piece of wafer which was the same size as the patterned one. Purified N 2 gas was bubbled through a HCl solution (36.5 - 38%) and thus carried HCl into the diffusion chamber. HCl etches the oxide off the GaAs and the indium metal. For the oxide on the indium metal, the reaction was 6HC1 + ln 2 0 3 = 2InCl3 + 3H 20 . ( 4 . 4 ) This allowed indium to have a direct contact with GaAs. The alloy formed between GaAs and In as a result of the diffusion is believed to be In xGai- xAs [2.5], with some of the Ga atoms being replaced by In atoms. A suitable annealing temperature was found to be 200 °C CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 50 CHAPTER 4 ELECTRICAL TRANSPORT PROPERTIES 11 For conducting films, either p or n type, it is good to heat up as fast as possible to 200 °C and cool down right away when the tem-perature reaches 200 °C, but cool down slowly to room temperature in about 20 minutes. None of these parameters are critical. For undoped films, it is better to keep the temperature at 200 °C for 2 minutes. For conducting films with a carrier concentration of 5 x 10 1 7 cm- 3, the resistance between the two indium contacts was less than 0.2 Q. For undoped GaAs, the resistance was several KQ. The MBE-grown materials, no matter whether they are intentionally doped or not, they are much more conductive than the semi-insulating substrates. The contact resistance of a thin layer R c can be calculated as follows: with the help of a Gaussian closed surface inside the layer as shown in Fig. 4.4a, the current density can be calculated as (Fig. 4.4) J = oE = I (4.5) 27ttr' where r I applied current, radius of the closed cylinder, t thickness of the film, E electric field, and o conductivity. With reference to Fig. 4.4b the electric field at point (x,o) is CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES U E = 2nat 1 + 1 d /2 - x d /2 + x (4.6) Applied current, I F i g . 4.4a. l a y e r . T h e G a u s s i a n c l o s e d s u r f a c e , the c y l i n d e r , i n a g r o w n y A Fig. 4.4b. Two contacts with a separation d on a thin film of thickness t. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 5_3_ The potential difference between the two contacts is given by d/2-a V = - fEdx = — ± — i n — (4.7) -d/f+a 7t a t a where d is the separation of the two contacts, and a is the radius of the contacts as indicated in Fig. 4.4. The sheet resistance is then obtained as V 1 d-a Rs = - = ln (4.8) 8 I rcot a For rectangular samples with length 1 and width w, the measured resistance between two contacts is R = 2RC+ — R s (4.9) w From Eq.(4.9), the contact resistance is found to be 1 lp d-a R c = 2 ( R - ^ l n — > <4'10> where l/o = p(resistivity) was used. In the case of undoped sample MBE no.31, with carrier concentration n = 5 x l O 1 5 cm*3, R = 7 KQ, d = 4 mm, a = 0.5 mm, t = 2.4 |im, 1 ~ d, w = 2 mm, and p = 0.2 Q c m , R c =2.5kQ. The contact resistance produces local heating at the contacts, which causes instability of the measurement in the square samples with electrodes as shown in Fig. 4.1a. With the sample pattern shown in Fig. 4.1c, the local heating is less serious since the heated CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES contacts are not part of the circular area being measured. 5_4 Vacuum Evaporation Samples were cleaned with trichloroethylene, acetone and ethanol in the ultrasonic chamber for 10 minutes individually. After being dried, they were put into the evaporation chamber with an aluminum holder and a metal mask. Au-Ge(88:12) was used as the evaporation source. The main working conditions of the evaporation are • pressure: 10"5 torr, • filament current: 125 A, • evaporation rate: 0.5 A/sec. Typical thickness of the deposited Au-Ge film was 2400 A. After the deposition, annealing was done with the same apparatus shown in Fig. 4.3, in a N 2 gas environment. The contacts were annealed at 450 °C, for 2 minutes. According to Eq.(4.10), the resulting contact resistance for the n-type doped sample no.13, with n = 8xl0 1 7 cm'3, p = 3xl0"3n-cm at room temperature was calculated to be R c ~ 8 fl. The contacts made by indium diffusion have more than 10 CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 11 times larger resistance than contacts made by vacuum evaporation. Vacuum evaporation makes better contacts, but the process is more complex and time consuming. 4.2 Measurement and Analysis 4.2.1 Electrical Transport Measurement Apparatus Fig. 4.6 shows the Van der Pauw measurement system. Fig. 4.5 shows the sample probe which fits inside a long cylindrical stainless steel heater coil brass spring contacts sample x e s s ? — -T diode temperature sensor Fig. 4.5. Sample probe vacuum chamber. The samples were electrically contacted by four movable pressure c^tacts made of thin metal foils. A cryogenic diode temperature sensor was mounted close to the sample. The diode was calibrated with a standard platinum resistance thermo-Transfer Line Liquid He or Liquid N Vacuum Pump Switch Board Magnetic Coil Current Source /v. Sample Current Source Voltmeter Computer Temperature Controller Temperature Monitor P *o >> CO o 3 O *o O J 50 to Fig. 4.6. Experimental setup for Van der Pauw measurement. 1. cryogenic dewar; 2. magnetic coil. ON CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES -12 meter between 4 K and room temperature. Fig. 4.7 is the result of the calibration. Next to the sample and the sensor there is a heater coil which is driven by a temperature controller. The sample holder shown in Fig. 4.5 is made of copper which is then covered by a cylindrical copper tube. The rest of the long probe is Q I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 0 50 100 150 200 250 300 350 Temperature (K) Fig. 4.7. Temperature calibration of the cryogenic diode sensor. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 18 made of thin wall stainless steel tube. The vacuum chamber wall consists of stainless steel tubing with a copper cap at one end. At the other end, the tubing is attached to a brass support plate which acts as the cover for the vacuum chamber. The long vacuum cylinder was evacuated by a mechanical pump. Electrical transport properties were measured at temperatures ranging from 4K to 300 K. For measurements below 77 K, liquid nitrogen was used prior to liquid helium to cool down the cryogenic dewar to save liquid helium which is much more expensive and has a much lower latent heat of vaporization than nitrogen. A temperature controller was built to control the temperature of the sample. A PC computer was used in some cases to acquire the measurement data through IEEE 488 interfaces and to do numerical calculations. The program was written in Quick Basic. 4.2.2 Calculations The resistivity of the sample is given by [4.1] RAB.CD + RBC.DA (4.13) ln2 2 where R AB.CD _ R BC.DA — CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 5_9 V C D and V D A are measured voltages across C,D and D,A. IA B and IBc are applied currents across A,B and B,C (Fig. 4.1). Finally, f is a correction factor for the asymmetry of the four contacts and the sample, with a value between 0 and 1. The factor f can be calculated numerically from the following equation [4.1]: cosh HnlRAB.CD-RBC.DA>j = I e ( l n 2 ) / f < ( 4 i l 4 ) I K - A B . C D + K B C . D A J & If the the four contacts and the sample are exactly symmetric, the correction factor is equal to 1. The Hall coefficient is given by R H - l ' V » ( B ) - V „ ( 0 ) I D -I A C where t = thickness of the grown layer, B = the applied magnetic induction, VBD(B) = corresponds to the voltage V B D with magnetic field, and VBD(O) = corresponds to the voltage V B D with B = 0. For doped semiconductor materials, carriers exist not only in the conduction band and the valance band, but also in the impurity bands. For n-type semiconductors, electrons are found in the conduction band and the donor band. The measured electrical transport properties are a combined effect of electrons in both the conduction band and the donor band. One theory dealing with doped semiconductors is called the two-band model [4.3, 4.4, 4.5]. According to the two-band model, the resistivity is given by [4.6]: CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 6_j0 P= 7 , (4.16) en cn c+enDnD where n c = electron concentration in the conduction band, u.c = electron mobility in the conduction band, n D = electron concentration in the donor band, u.D = electron mobility in the donor band. The Hall coefficient is defined as [4.6] r , n c u / + n n uV e (ncnc + n D u D ) 2 where the Hall factor [4.7] 3 ^ ( 2r + I" )! r H = — — (4.18) 4((r + | ) , J For acoustic deformation potential scattering, for example, r = -1/2 [4.7], and rH = 1.18. For ionized impurity potential scattering, r = 3/2, and r H= 1.93. By definition, we have the combined Hall mobility u. = = - — . (4.19) p e n c n c +n D n D Normally the mobility u.c is much greater than the mobility u.D at any temperature. At high temperatures, electrons mainly stay in the conduction band, nc > nD, and n c u . c 2 » n D | i D 2 , therefore CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 6J, 1 P = , e n c j i c R « enc' At very low temperatures, because of the finite activation energy of shallow dopants, n c decreases indefinitely with decreasing tempera-ture. Finally, a temperature is reached at which n c n c 2 « n D n D 2 . (4.20) Then, 1 enDuD R h enD' A computer program was written to calculate the electrical properties from the measurement data. 4.2.3 Results and Discussion The measured resistivities and Hall coefficients are shown in Figs. 4.8 and 4.9, and the derived carrier concentrations and Hall CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES _6_2 2.5 + - » • 1—( > 1.5 0.5 0 • 1 1 11 I I I 1" 1 1 1 1 I I I . 1 1 1 1 MBE RI . . . ._ FN#32 --- • -• -• ' 1 1 1 1 1 1 1 1 • • t i l l • • • i i i • • i i . . . i i 50 100 150 200 Temperature (K) 250 300 Fig. 4.8. Resistivity vs temperature, sample no. 32. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 11 4.0 1 0V U 3.5 1 0V CO 3.0 1 0s S 2.5 1 0 3 o *4—I _ c3 < a 1.5 1 1.0 1 ov l i l l • *. l i l l I I I I I i I I | J | I I I I | 1 ample 1 1 i i i i 4o.32 : • • -• • -• • -• • -l i l l i i i i • • I I I I • • . . . . • • . . . . • • —I—1 1 1 " 50 100 150 200 250 300 Temperature (K) Fig. 4.9. Hall coefficients vs temperature, sample no.32. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES Fig. 4.10. Calculated conduction band electron concentration vs temperature (solid line). Data points (•) are derived from l/(eRH). The data points at low temperatures show the existance of conduc-tion in the donor band. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES Al 2.0 10 C/5 B X 1.0 10' o ffi 3 5.0 1 0 D 1T™|—|— • • " 1 11 "I'—| • • 1 1 1 1 —I—1—1—1— — i — r - T — i — • • • • -• • .+ • • • 1 1 1 1 _.J. I I 1 • I I I I 1 1 1 1 vTBERU , . . , N#32 " 0 50 100 150 200 250 300 Temperature (K) Fig. 4.11. Hall mobility vs temperature, sample no.32. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 6_£ T—I I I I 1111 1 1 I 1 1 l I IIII TEMPERATURE T (K) Fig. 4.12. Temperature dependence of the electron Hall mobility for four n-type GaAs samples. A, B, C after Stillman [4.15], and D made in UBC. The estimated donor densities are (A) 5 x lO 1 3 cm 3 , (B) 101S cm"3, (C) 5 x l O 1 5 cm'3, and (D) 5.5 x l O 1 5 cm 3 . The compensation ratios are: 0.3 to 0.4 for A, B, C, and 0.5 for D. Contributions from three major scattering processes are shown. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES Fig. 4.13. Resistivity vs temperature, sample no.13. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES Fig. 4.14. Hall coefficients vs temperature, sample no.13. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES Fig. 4.15. Calculated conduction band electron concentration vs temperature (solid curve). Data points (•) are derived from l/(eRH). The data points at low temperatures show the presence of conduction in the donor band. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES IQ Fig. 4.16. Hall mobility vs temperature, sample no. 13. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 21 mobilities are shown in Figs. 4.10 and 4.11 for an undoped GaAs sample. This sample, no.32, was grown on a semi-insulating GaAs substrate. The growth conditions are • substrate temperature: 600 °C, • Ga cell temperature: 1040 °C, • As cell temperature: 350 °C, • vacuum pressure: 1.4xl0"8 mbar, • growth rate: 103 A/min, • layer thickness: 2.88 u.m. The substrate temperature during growth was measured with a unique optical method as described in Ref. [4.8]. The thickness was found with the techniques of the selective etching and SEM as mentioned in Chapter 2 of this thesis. -For a doped sample, the corresponding properties are given in Figs. 4.12 to 4.16. This sample was also grown on a semi-insulating GaAs substrate and doped by silicon, with growth conditions listed in the following: • substrate temperature: 580-600 °C, • Ga cell temperature: 1067 °C, • As cell temperature: 392 °C, • Si cell teamperature: 1100 °C, • vacuum pressure: 1.1 xlO' 8 mbar, • growth rate: 213 A/min, • layer thickness: 4260.A. CHAPTER 4, ELECTRICAL TRANSPORT PROPERTIES 7_2 The transport properties are governed by the carriers in different bands and by a combination of several scattering processes, including neutral impurity scattering, ionized impurity scattering, longitudinal acoustic deformation potential scattering, piezoelectric scattering, polar optical phonon scattering and dislocation scattering. The main scattering processes for MBE-grown GaAs materials are polar optical phopnon scattering, longitudinal acoustic deformation potential scattering and ionized impurity scattering. The first two are dominant at high temperatures, while the last one dominates at low temperatures. The polar optical phonon scattering is due to the interaction of carriers with the optical mode of lattice vibration in a polar semiconductor. The mobility due to this scattering at low temperatures T « © is given by [4.7] M = - V - ^ e e / T (4.21) 2m* a co0 where q = electron charge, m* = effective mass of a carrier, a = polar constant, co0 = optical phonon angular frequency, and 0 = Debye temperature. At high temperatures, T > 0 [4.7] 2 m * a a > 0 3 y n® CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 7_3_ In the intermediate range of temperatures ( T ~ 0 ), numerical methods have to be applied [4.7]. The longitudinal acoustic deformation potential scattering is due to the interaction of carriers with the acoustic mode of lattice vi-bration. The longitudinal acoustic wave in a semiconductor causes the periodic change of distance between atoms, and in turn the periodic change of the bandgap along the propagation direction of the wave. To carriers, the change is equivalent to an additional potential. In equilibrium the energy of carriers is approximately kT, so that they occupy a narrow range in k-space. These carriers are called thermal carriers with a mobility [4.7] V 3 m * 5 / 2 k 3 / 2 £ a c 2 - T (4.23) where C{ = pco^q, , the average longitudinal elastic constant, co, = angular frequency of the longitudinal phonon, q, = wave number of the longitudinal phonon, l a c k T m 2 , 1/2 acoustic deformation potential constant, l a c = mean free path of carrier for acoustic phonon scattering, k = Boltzmann constant, and "ft = Planck constant / 2TT. Ionized impurities, either donors or acceptors, also scatter electrons and holes. The mobility limited by ionized impurity scattering is given by [4.7] CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 14 = 2 7 / 2 (47ce ) 2 (kT) 3 / 2 3 / 2 * TI 3 / 2 Z 2 e3 m ^ ^ N ^ l n C l + p 2 ) - (32/(l + p2)] ~ T ' ( 4 ' 2 4 ) where Z = ionic charge of an ionized impurity atom in units of e, Ni = concentration of ionized impurity, e = dielectric constant, n = carrier concentration, P = Brooks and Herring's factor, which is given by 2 k T " \ J 6 m e / n P £ • (4-25) The mobilities mentioned above are each due to one certain scattering process. Let's denote them as {M^ }. The overall mobility that the carriers encounter is a combination of these {M-j}, and is evaluated according to Matthiessen's rule as a simple inverse sum [4.9]: — = ! , — , (4.26) where Z. is a sum over i, the individual scattering process, M-H = the overall Hall mobility, h= the component drift mobility due to certain scattering process, and r H = the corresponding Hall factor. Obviously, the combined mobility is smaller than the mobility due to one scattering process as shown in Fig. 4.14. CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 15 The resistivity in Fig. 4.8 remains nearly constant from room temperature to 50 K due to the balance between the increase of the mobility as a result of the weaker lattice scattering and the decrease of carrier concentration. Below 50 K, there is a sharp increase which is caused by a reduction in carrier density due to the freeze-out of carriers. The Hall coefficients of sample no.32 is plotted in Fig. 4.9. At high temperatures R H = - rH/(en c), and at very low temperatures R H = - r H / (en D ) . At intermediate range of temperatures, electrons transfer exponentially from the conduction band to the donor band with decreasing temperature. At the maximum point of RH, ncu.c=nDu.D, which is derived from Eq. 4.17. Although, it was not intentionally doped, sample no.32 still has an electron concentration of order 1015 c m 3 (Fig.4.9). This was caused by the residual or background impurity that existed in the MBE growth chamber by the time the sample was grown. The doping was n-type which was measured by heating one end of the sample, and measuring the heat induced voltage across the sample, or by the sign of Hall voltage. If the electrical potential is higher at the hot end, the sample is n-type. The doping type was also confirmed by measuring the sign of Hall voltage. The electron concentration in the conduction band at high temperatures is n c=^~. While n c at low temperatures is obtained by the exponential extrapolation from n c at high temperatures according to the theoretical formula [3.9]: CHAPTER 4 ELECTRICAL TRANSPORT PROPERTIES f N c ( N „ - N d)V / 2 I 2 J ' exp -( AE C 2kT (4.27) where N = By fitting the electron concentration data in Fig. 4.10, we found that the activation energy for sample no.32 is AE C = 6.0 ± 0.5 meV. Similarly, for the Si-doped sample no.13, it is found that AE C = 5 ± 1 meV. According to Ref.[4.10], GaAs does have five n-type shallow impurity elements with activation energies in agreement with 6.0 ± 0.5 meV. The shallow impurities and their corresponding activation energies are: Si, 5.8 meV; Ge, 6 meV; S, 6 meV; Se, 5.9 meV; and Te, 30 meV. Since the sample is measured as n-type, and silicon is the only n-type dopant we have been used in our MBE system, the residual or background impurity in the MBE chamber is most likely silicon. For MBE systems, the main residual impurities of n-type were reported to be silicon [4.11], sulphur [4.11], and lead [4.12], and p-type, carbon [4.13] and manganese [4.14]. Although oxygen could be one of the residual n-type impurities, its binding energy in GaAs is too large (400 meV) to be ionized at room temperature. Sample no.32 contains both n and p type residual impurities since the compensa-C H A P T E R 4, ELECTRICAL TRANSPORT PROPERTIES 11 tion ratio is 0.5 which was obtained by comparing our data to the data of Rode [4.15]. The compensation ratio is defined as the ratio of acceptor impurity concentration over donor impurity concentration, i.e., Na/Nd. The Hall mobility (Fig. 4.10) increases from 7,000 cm2/Vs at 300 K to 19,000 cm2/Vs at 70 K because of the weaker polar optical phonon scattering and longitudinal acoustic phonon deformation potential scattering [4.15]. At temperatures lower than 65 K , because of the domination of the ionized impurity scattering, and the switchover from the conduction band conduction to the donor band conduction, the Hall mobility decreases rapidly below 65 K . A comparison of the mobility of our sample with Stillman's data is shown in Fig. 4.12. Curves A, B, and C are after G. E. Stillman [4.15]. Curve D is our sample no.32. The electron concentrations of curve A, B, C and D are 5 x l 0 1 3 , 1015, 5 x l 0 1 5 , and 5.5xl0 1 5 cm"3. The compensation ratios N a / N d are 0.3 to 0.4 for curves A, B, and C, and 0.5 for curve D. Our result curve D is consistent with the results of Stillman. Comparing the electrical transport properties of Si-doped sample no.13 (Figs. 4.13 to 4.16) with those of the undoped sample no. 32, we find that all six curves (Figs. 4.8 to 4.11, and Figs. 4.13 to 4.16) have an extreme point at some temperature. As the dopant level increases, these extreme points shift towards higher temperature, which indicates stronger ionized impurity scattering because of the higher impurity concentration. Comparing the curves in Figs. 4.8 to 4.11 with the curves in Figs. 4.13 to 4.16, one can see CHAPTER 4. ELECTRICAL TRANSPORT PROPERTIES 7JS that the electrical properties of the undoped sample change more with respect to temperature than those of the doped sample. From the resistivities of these two samples, it is clear that the doped sample is much more conductive than the undoped one although the undoped one has a higher mobility. CHAPTER 5. CONCLUSION 12. Chapter 5 Conclusion A variety of electrical and structural characterization tools have been used to study the properties of GaAs and A l x G a i . x A s epitaxial films grown by molecular beam epitaxy. The topographic properties of cleaved ends of grown layers were investigated by means of selective etching and microscopic techniques including scanning electron microscopy (SEM) and scanning tunneling microscopy (STM). The etchant H202:NH40H:H20 (1:1:5 by volume) was used to selectively etch GaAs, and K3Fe(CN)6: KOH:H20 ( 1:1.5:62.5 by weight ) to selectively etch Al x Gai- x As. Al mole fraction in A l x G a i - x A s was measured by x-ray diffractometry. An x-ray machine designed for powders was used to measure Al mole fraction in single crystal Al x Gai- x As with sufficient accuracy. The resolution of x-ray diffractometry was discussed. Al mole fraction was calculated with a newly derived formula. This for-CHAPTER 5. CONCLUSION 8_0 mula falls in between two other results available in the literature. Electrical transport properties of GaAs were measured by the Van der Pauw method. | Sample patterning was found to be very important to achieve accurate and reproducible measurement results. The Hall mobilities measured on the same sample with or without the proper pattern differ by a factor of two. A variety of samples were investigated, including the Si-doped n-type, Be-doped p-type, and undoped samples. The two-band theory was used to interpret the electrical transport results. The temperature dependence of the electron concentration in the conduction band was fit with an exponential function. From this fit, we obtained the activation energy of the impurity. We conclude that the residual impurity is silicon. The undoped GaAs material that we have measured has a residual Si donor impurity concentration of 5x l0 1 5 cirr 3 at room temperature. The highest Hall electron mobility is 19,000 cm2/Vs at 70 K. REFERENCE &1 References [1.1] P. Boucaud, F. H. Julien, D. D. Yang, and J-M Lourtioz; Detailed Analysis of Second-Harmonic Generation Near 10.6 nm in GaAslAlGaAs Asymmetric Quantum Wells. Appl. Phys. Lett. 57, 215 (1990). [1.2] D. J. Leopold, and M. M. Leopold; Tunneling - Induced Optical Nonlinearities in Asymmetric Alo.3Gao.7AslGaAs Double-Quantum-Well Structures. Phys. Rev. B42, 11147 (1990). [1.3] Marcos H. Degani; Stark Ladders in Strongly Coupled GaAs-AlAs Superlattices. Appl. Phys. Lett. 59, 57 (1991). [1.4] Y. J. Yang, T. G. Dziura, R. Fernandez, S. C. Wang, G. Du, and S. Wang; Low-Threshold Operation of a GaAs Single Quantum Well Mushroom Structure Surface-Emitting Laser. Appl. Phys. Lett. 58, 1780 (1991). [1.5] T. Sogawa, and Y. Arakawa; Wavelength Switching of Picosecond Pulse (< Wps ) in a Quantum Well Laser and Its All-Optical Logic Gating Operations. Appl. Phys. Lett. 58, REFERENCE 82 1709 (1991). [1.6] G. Hasnain, B. F. Levine, D. L. Sivco, and A. Y. Cho; Mid-Infrared Detectors in the 3-5 jum Band using Bound to Continuum State Absorption in InGaAs/InAlAs Multiquantum Well Structures. Appl. Phys. Lett. 56, 770 (1990). [1.7] Doyeol Ahn; Enhancement of the Stark Effect in Coupled Quantum Wells for Optical Switching Devices. IEEE J. Quantum Electron., 25, 2260 (1989). [1.8] R. W. Wickman, A. L. Moretti, K. A. Stair, and T. E. Bird; Electric Field-Induced Optical Waveguide Intensity Modulators Using GaAslAlxGai.xAs Quantum Wells. Appl. Phys. Lett. 58, 690 (1991). [1.9] J. M. Wiesenfeld, G. Raybon, U. Koren, G. Eisenstein, and C. A. Burrus; Gain Spectra and Gain Compression of Strained-Layer Multiple Quantum Well Optical Amplifiers. Appl. Phys. Lett. 58, 219 (1991). [1.10] N . Chand, P. R. Berger, and N . K. Dutta; Substantial Improve-ment by Substrate Mis orientation in dc Performance of Alo.5Gao.5As/GaAs/Alo.5Gao.5As Double-Heterojunction NpN Bipolar Transistors Grown by Molecular Beam Epitaxy. Appl. Phys. Lett. 59, 186 (1991). [1.11] I. C. Bassignana, and C. C. Tan; Determination of Epitaxic-Layer Composition and Thickness by Double-Crystal X-ray Diffraction. J. Appl. Cryst. 22, 269 (1990). [1.12] J. H. Neave, B. A. Joyce, P. J. Dobson, and N. Norton; Dynamics of Film Growth of GaAs by MBE from RHEED Observations. Appl. Phys. A31, 1 (1983). [1.13] C. Lavoie, T. Tiedje, J. Mackenzie, K. Colbow, T. Van Buuren, and Li Xu; Diffuse optical reflectivity measurements on GaAs during MBE processing. The First Graduate Student Conference on Opto-electronics, June 24-26, 1991, Hamilton, Ontario, Canada. [1.14] R. Dingle, R. A. Logon, and J. R. Arthur; Gallium Arsenide and Related Compounds, 1976. Inst. Phys. Conf. Ser. 33a, 210 (1977). [2.1] Eli Yablonovitch, T. Gmitter, J. P. Harbison, and R. Bhat; Extreme Selectivity in the Lift-off of Epitaxial GaAs Films. Appl. Phys. Lett. 51, 2222 (1987). [2.2] M. Konagai, M. Sugimoto, and K. Takahashi; High Efficiency GaAs Thin Film Solar Cells by Peeled Film Technology. J. Cryst. Growth 45, 277 (1978). [2.3] X.-S. Wang, J. L. Goldberg, N. C. Bartelt, T. L. Einstein, and E. D. Williams; Phys. Rev. Lett. 65, 2430 (1990). [2.4] R. P. Tijburg and T. van Dongen; Selective Etching of III-V REFERENCE 84 Compounds with Redox Systems. J. Electrochem. Soc: Solid-State Science and Technology, 123, 689 (1976). [2.5] S. D. Mukherjee, and D. W. Woodard; Etching and Surface Preparation of GaAs for Device Fabrication, in: Gallium Arsenide, ed. M. J. Howes and D. V. Morgan, J. Wiley&Sons, (1985). [2.6] K. Sangwal; Etching of Crystals, Theory, Experiment, and Application, ed. S. Amelinckx-J. Nihoul, North-Holland Physics Publishing, (1987). [3.1] Sadao Adachi; GaAs, AlAs, and AlxGai.xAs Material Parameters for Use in Research and Device Applications. J. Appl. Phys. 58, R1-R29 (1985). [3.2] Fulin Xiong, T. A. Tombrello, H. Z. Chen, H. Morkoc, and A. Yariv; Direct Determination of Al content in Molecular-Beam Epitaxially Grown AlxGai.xAs ( 0 <x < 1 ) by Nuclear Resonant Reaction Analysis and X-Ray Rocking Curve Techniques. J. Vac. Sci. Technol. B6, 758 (1988). [3.3] B. D. Cullity; X - Ray Diffraction, Addison-Wesley, (1956). [3.4] S. I. Salem, and D. L. Lee; At. Data Nucl. Data Tables, 18, 233 (1976). [3.5] V. M. Pessa; Data for Graphical Resolution of Two Over-REFERENCE 8_5 lapping X-Ray Emission Lines. Natural Width of kai,2 of the Elements Z=10 to 92. X-Ray Spectrometry, 2, 169 (1973). [3.6] M. O. Kause, and J. H. Oliver; Natural Widths of Atomic K and Levels, K X-Ray Lines and Several KLL Auger Lines. J. Phys. Chem. Ref. Data, 8, 329 (1979). [3.7] J. M. Vandenberg, R. A. Hamm, M. B. Panish, and H. Temkin; High-Resolution X-Ray Diffraction Studies of InGaAs(P)/InP Superlattices Grown by Gas-Source Molecular-Beam Epitaxy. J. Appl. Phys. 62, 1278 (1987). [3.8] K. Ishida, J. Matsui, T. Kamejima, and I. Sakuma; X-Ray Study of AlxGai.xAs Epitaxial Layers. Phys. Stat. Sol. (a) 31, 255 (1975). [3.9] N. W. Ashcroft, and N. D. Mermin; Solid State Physics, Saunders College, (1976). [3.10] R. A. Smith; Wave Mechanics of Crystalline Solids, 1969. [4.1] L. J. van der Pauw; A Method of Measuring Specific Resistivity and Hall Effect of Discs of Arbitary Shape. Philips Research Reports, 13, R334 (1958). [4.2] J. Lowen, and R. H. Rediker; Gallium - Arsenide Diffused Diodes. J. Electrochem. Soc. 107, 26 (1960). [4.3] D. L. Mitchell; Hall Conductivity and Lorentz Force Law for Two-Band Semiconductors. Phys. Rev. B 33, 4021 (1986). [4.4] R. M. Dickstein, S. L. Titcomb, and R. L. Anderson; Carrier Concentration Model for n-Type silicon at Low Temperatures. J. Appl. Phys. 66, 2437 (1989). [4.5] T. Saso and T. Kasuya; Theory of Resistance and Hall Maxima in Sb-Doped Ge in the Metallic Range. J. Phys. Soc. Japan 49, 383 (1980) Suppl. [4.6] C. S. Hung, and J. R. Gliessman; Resistivity and Hall Effect of Germanium at Low Temperatures. Phys. Rev. 96, 1226 (1954). [4.7] Seeger; Semiconductor Physics. Springer-Verlag/Wien, (1973). [4.8] M.K.Weilmeier, K.M.Colbow, T.Tiedje, T.Van Burren, Li Xu; A new optical temperature measurement technique for semiconductor substrates in molecular beam epitaxy. Can. J. Phys. 69, 422(1991). [4.9] D.L. Rode, and S. Knight; Electron Transport in GaAs. Phys. Rev. B3, 2534 (1971). [4.10] S. M. Sze; Physics of Semiconductor Devices, 2nd Edition, John wiley & Sons, Inc., (1981). [4.11] M. Ilegems; Properties of III-V Layers, in: The Technology and Physics of Molecular Beam Epitaxy, ed. E.H.C.Parker, Plenum Press, New York, (1985). REFERENCE 8JZ [4.12] T. S. Low, G. E. Stillman, and C. M. Wlofe; Identification of Residual Donor Impurities in Gallium Arsenide. Inst. Phys. Conf. Ser. 63, 143 (1981). [4.13] M. Ilegems, and R. Dingle; Acceptor Incorporation in GaAs Grown by Beam Epitaxy. Inst. Phys. Conf. Ser. 24, 1 (1974). [4.14] M. Ileges, R. Dingle, and L. W. Rupp.Jr.; Optical and Electrical Properties of Mn-doped GaAs Grown by Molecular-Beam Epitaxy. J. Appl. Phys. 46, 3059 (1975). [4.15] G. E. Stillman, C. M. Wolfe, and J. O. Kimmock; Hall Coefficient Factor for Polar Mode Scattering in n-type GaAs. J. Phys. Chem. Solids 31, 1199 (1970). 


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