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

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E L E C T R I C A L AND STRUCTURAL CHARACTERIZATION OF GaAs AND AI Gai. As GROWN BY M B E x  x  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 copying  agree that permission for extensive  of this thesis for scholarly purposes may be granted  department  or  by  his or  her  representatives.  It  is  by the head of my  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  DE-6 (2/88)  O*.  /?H  Abstract The  electrical  Al Gai- As x  x  and  structural  properties  of  GaAs  and  grown by molecular beam epitaxy have been studied,  including cross  section  morphology, aluminum mole fraction, and  electrical transport properties. The etching,  film  cross  section  and microscopy.  examined  with  an  alpha  has been investigated  The selectively step  etched  instrument,  a  by selective samples  scanning  were  electron  microscope, and a scanning tunneling microscope which is a new approach. The aluminium mole fraction of A l G a i . A s in grown layers x  have  been  measured  with  x-ray  x  diffraction.  A  Rigaku  x-ray  diffractometer designed for powders was extended to single crystals. A  new  way of calculating the A l mole fraction from the x-ray  diffraction spectrum was developed. The  electrical  transport  concentration, Hall coefficients,  properties  resistivity  including  carrier  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. temperature dependence  The  of electron concentration in the conduction  band was fit with an exponential function. the activation energy of the impurity.  The residual impurity in the  MBE system was found to be mainly silicon.  iii  From the fit, we obtained  Table of Contents Abstract  ii  Table  of Contents  iv  Table  of Figures  vi  Acknowledgements 1  2  viii  Introduction  1  1.1  Overview  1  1.2  Outline of the Thesis  5  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)  3  X-Ray  14 20  Diffractometry  3.1  Background and Calculations  20  3.2  X-Ray Measurement of Al Mole Fraction in Al Gai- As . . 2 6  3.3  Resolution Improvement  30  3.4  Calculation and Comparison  39  x  iv  x  4  Electrical Transport Properties  4 4  4.1  Sample Preparation  45  4.1.1 Patterning  45  4.1.2 Ohmic Contacts  48  4.2  5 Thermal Diffraction  49 Vacuum Evaporation  54  Measurement and Analysis  55  4.2.1 Electrical Transport Measurement Apparatus  55  4.2.2 Calculations  58  4.2.3 Results and Discussion  61 7 9  Conclusions  81  References  v  List of Figures 2.1  Step height measurement of GaAs sample etched by H 0 2  2.2  : N H 4 O H : H 0 (1:1:5 by volume) 2  10  Step height measurement of Alo.5Gao.5As sample etched by H 0 2  2.3  2  2  : N H 4 O H : H 0 (1:1:5 by volume) 2  11  Step height measurement of Alo.5Gao.5As sample etched by K F e ( C N ) : K O H : H 0 (1:1.5:62.5 by weight)  13  2.4  S E M picture of sample no.35  16  2.5  S E M 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 A l G a i - A s / G a A s sample no.30  23  3.3  High resolution x-ray spectrum for peak {400}  24  3.4a  Rigaku x-ray diffractometer used for single crystals  27  3.4b  Schematic representation of a double crystal x-ray  3  6  2  x  x  diffractometer  27  3.5  Effect of sample thickness on diffraction curves  33  3.6  Double-crystal x-ray diffraction spectrum of sample no.30 .  3.7  Comparison of the formulas relating the A l fraction to the vi  .38  4.1  angular separation  43  Sample patterning  46  4.2a Electrode of the spark erosion machine  48  4.2b Mask for sand blasting  48  4.3  Thermal diffusion apparatus for making electrical contacts  50  4.4  Contact resistance  52  4.5  Sample probe  55  4.6  Experimental setup for Van der Pauw measurement  56  4.7  Diode calibration curve  57  4.8  Resistivity vs temperature, sample no.32  62  4.9  Hall coefficients vs temperature, sample no.32  63  4.10  Calculated conduction band electron concentration vs  4.11  temperature, sample no.32  64  Hall mobility vs temperature, sample no.32  65  4.12 Temperature dependence of the electron Hall mobility for four n-type GaAs samples  66  Resistivity vs temperature, sample no. 13  67  4.14 Hall coefficients vs temperature, sample no. 13  68  4.13  4.15  Calculated conduction band electron concentration vs temperature, sample no.13  69  4.16 Hall mobility vs temperature, sample no.13  vii  70  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.  1  INTRODUCTION  Chapter 1  Introduction 1.1  Overview The  molecular  producing accurate  beam  compound  epitaxy  ( M B E ) technique  semiconductor  composition,  precise  materials  thickness,  with  a wide  i s capable o f high  range  purity,  o f dopant  levels, a n d high quality crystal structures. The and  above properties  are very  important  f o r opto-electonic  e l e c t r o n i c devices, such as n o n l i n e a r o p t i c a l devices  superlattices  [ 1 . 1 , 1.2],  [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  m o d u l a t o r s [1.7, 1.8],  [1.6],  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 ] .  Characterization o f the thickness, crystalline structure, composition,  and electrical  materials  are essential both  fabrication o f devices.  transport  properties  f o r the growth  o f the M B E - g r o w n o fmaterials  and  CHAPTER 1.  INTRODUCTION  2  The growth rate depends on a number of parameters. be determined  It can  by the M B E 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 M B E chamber [1.13]. methods  work accurately provided that some relevant  are known accurately. measurements  after  measurements  These  parameters  They all need to be calibrated by thickness  growth.  One direct approach for  thickness  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 V G V80H MBE system, GaAs and Al Gai- As ( 0 < x < 1 ) x  x  are the grown materials, doped by Be (for p-type) and Si ( for ntype). 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 cube.  and the other at 4 4 4 " of the fee unit  The cube contains four such GaAs molecules in a volume a , 3  where a is the lattice constant of GaAs. length is  Via  The nearest-neighbor bond  For stoichiometric GaAs at 300 K, the lattice constant  a = 5.65 A , and the unit cube volume is a = 1.8067 xlO" cm . The g atomic density is ~ = 4.4379x10 cm" , and the crystal density is a 5.3174 g/cm at 300 K. For photons with energy just below the 3  22  3  3  23  3  CHAPTER 1. intrinsic  INTRODUCTION  3  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 , while the effective e  mass of heavy holes is 0.50 m , and that of light holes is 0.076 m at 0  300  K.  0  The rms thermal speeds of heavy  holes, light holes and  conduction electrons are all of the order  cm/sec.  At  300 K, the mobility of electrons is about 8000 cm /Vs which is much 2  higher  than  the  corresponding  value  for  silicon  which  is  1900  light  are  very  cm /Vs. 2  The  high  mobility  attractive properties  and the  of GaAs  ability  for device  to  emit  applications.  Most of the  applications of GaAs would not be possible without A l G a i - A s as a x  mate.  A l G a i - A s has the same structures as GaAs except that some x  x  of the Ga sites are occupied by A l atoms. close to that of GaAs.  Its lattice constant is very  The lattice constant of A l A s is 0.14% larger  than that of GaAs at 300 K.  A l G a i - A s also has a wider energy band x  x  gap and a lower refractive index than GaAs.  In addition, both the  energy band gap and refractive index of A l G a i . A s x  by adjusting the aluminium content x.  x  are  the  heterojunctions  of  double  heterostructures,  graded  bandgap/refractive  different quantum index  changeable  When GaAs and A l G a i . A s x  are grown over one another, a heterojunction is formed. of  x  height wells,  materials.  special field called band gap engineering.  Combination  and distances results in and  superlattices  The combination  and is  a  Obviously, one important  parameter is the aluminium content in A l G a i - A s . x  x  x  CHAPTER  1.  INTRODUCTION  4  There are several techniques to measure the A l mole fraction in A l G a i - A s , x  x  intensities  which use:  photoluminescence  [1.14], M B E flux  [1.11], nuclear resonant reaction analysis  [1.15], x-ray  diffraction [1.11, 1.14, 1.15], secondary ion mass spectroscopy, Auger electron  spectroscopy,  techniques.  X-ray  x  As  effect  [1.16],  and  other  diffraction is a non-destructive, accurate and  convenient technique. to be solved, that is,  opto-electronic  However, there is a slight problem remaining how to calculate the Al mole fraction in A l G a i x  from the x-ray spectrum of the A l G a i - A s / G a A s x  sample.  x  Empirical formulas for the calculation of A l mole fraction have been reported [1.11, 3.2]. experiments,  But due to differences  in details of their  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  transport properties including resistivity, concentration  and Hall  dissimilar atoms complex.  mobility.  like GaAs,  the  Hall  the electrical  coefficient,  carrier  In a polar crystal containing carrier  scattering processes are  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.  1.2  INTRODUCTION  1  Outline of the thesis  The  following  chapters  are  nearly  independent  since  the  characterization is done for totally different properties of the M B E grown materials.  Chapter 2 describes the experiments to investigate  the topography of the cleaved ends of the samples by means of selective etching which  etches  and microscopy techniques. GaAs  selectively  One good  etchant  and another one which etches  A l G a i - A s were chosen among a number of etchants in order to x  x  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 A l G a i . A s was measured by this technique.  The  x  powder  x-ray  successfully  machine  used  accuracy (±2%).  x  to  (Rigaku Rotating Anode Machine), was  measure  A l mole  fraction with  reasonable  How the resolution could be improved is  discussed.  A new mathematical formula is derived to determine the A l mole fraction  from  the  x-ray  spectrum.  measurements of electrical properties. to be important for the measurements.  Chapter  4  discusses  Sample patterning  the  was found  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.  6  INTRODUCTION  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. temperature  dependence  of  the  electron  concentration  conduction band was fit with an exponential function. we obtained the activation energy of the impurity.  in  of  mobility  measurement  reported in the literature. study are summarized.  the  From this fit,  We conclude that  the residual impurity in the M B E system is mainly silicon. results  The  are compared with  The  other work  Finally, in Chapter 5, the results of this  CHAPTER  2.  MICROSCOPY  1  Chapter 2  Microscopy 2.1 2.1.1  Selective Etching 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  GaAs or A l G a i . A s . x  Yablonovitch  x  [2.1],  been  found  that is perfectly selective for  Only in the case of x = 1, according to Eli  hydrofluoric acid  [2.2]  etches AlAs much faster  than GaAs, with selectivity greater than 1 0 . 7  For unknown reasons  we were unable to reproduce this result in our lab using the same ethants, either concentrated or diluted.  CHAPTER  2.2.2  MICROSCOPY  2.  Etching Experiments  and  Results  The selectivity of a given etchant is defined as a ratio of two etching rates, i.e. selectivity =  faster etching rate for material 1 slower etching rate for material 2'  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 A l G a i . A s have been tried. x  The best etchant  x  to etch GaAs relative to A l G a i . A s was found to be x  H 0 2  2  x  : N H 4 O H : H 0 (1:1:5 by volume). 2  Its etching rate for Alo.5Gao.5As is about 20 A/sec. x=0.5 is  greater than 10. The selectivity  The selectivity for  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 height.  2.  CHAPTER  MICROSCOPY  9  Results of the step measurements with the same etchant H2O2 : NH4OH  : H 0 (1:1:5 by volume) are shown in Fig. 2.1 and Fig. 2.2. 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 : H 2 O (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). as the value of x in A l G a i . A s increases. x  x  The selectivity is greater While the sample is being  etched by H2O2 : N H 4 O H : H 2 O , the etchant induces many bubbles on the surface of the sample. etching uniformity.  The bubbles have a bad effect on the  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.  the ultra-sonic waves were  not sufficient  Stirring did not work either.  However  to move the bubbles.  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 G a i - A s x  x  with  respect to GaAs was found to be K Fe(CN) : KOH : H 0 ( 1 : 1.5 : 62.5 by weight). 3  6  2  The etching rate for x = 0.5 is about 15 A/sec,  and the selectivity is  3  12  08  si. M  0 4  at  X 00  1/  -0.4  TTiT  TO  Urtl  Scanning range ( u m )  Fig. 2.1. Step height measurement done with Alpha Step 200 Tencor Instrument. Sample: GaAs. Etchant: H 0 : N H 4 O H : H 0 (1:1:5 by volume). 2  2  2  OA  -0.2  -0 4 "TiTTT  TT  Scanning  Fig.  Ulil  range ( u m )  2.2. Step height measurement done with Alpha Step 200 Tencor Instrument.  Sample: Alo.5Gao.5As.  Etchant: H 0 : N H 4 O H : H 0 (1:1:5 by volume). 2  2  2  CHAPTER  2.  about 5.  The selectively of this etchant for AlAs relative to GaAs  was  quite  MICROSCOPY  obvious  12  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 : H 2 O 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 0 : H 0 ( pH=7 ) 2  2  2  • I : KI ( 0.1 : 0.3 mol/liter, pH=9.4 ) 2  • H 0 : NH4OH 2  2  ( 19 :1 by volume )  • H 0 : N H 4 O H : H 0 ( 1 : 1 : 5 by volume ) 2  2  2  • KI : KI : H 0 ( 1.7 : 1.8 : 50 by weight, pH > 3 ) 3  2  • K Fe(CN) : K4Fe(CN) : H 0 ( 3.8 : 4.1 : 50 by weight, pH>9 ) 3  6  6  2  - for AlGaAs • HF : H 0 ( 1:1 by volume ) 2  • K4Fe(CN) : KOH : H 0 ( 1.5 : 2 :15 by weight ) 6  2  • K Fe(CN) : KOH : H 0 ( 1 : 1.5 :12.5 by weight) 3  6  2  • K Fe(CN) : KOH : H 0 ( 1 : 1.5 : 62.5 by weight) 3  6  2  • K I : KI : H 0 ( 1.7 :1.8 : 50 by weight, pH >3 ) 3  2  Scanning range  Fig.  2.3.  Step height measurement done  Sample: Alo.5Gao.5As.  (|im)  with Alpha  Step  200  Tencor Instrument.  Etchant: K F e ( C N ) : K O H : H 0 ( 1 : 1.5 : 62.5 by weight ). 3  6  2  CHAPTER  2.  MICROSCOPY  14  • K Fe(CN) : K4Fe(CN) : H 0 ( 3.8 : 4.1 : 50 by weight, pH<9 ) 3  6  6  2  Some etchants are good for both GaAs and AlGaAs if their pH values are adjusted, for example, K Fe(CN)6 : K4Fe(CN)6: H 0 [2.4]. 3  2  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. morphology  of the interfaces,  To measure the layer thickness and 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. 10"  5  torr.  The chamber was evacuated to  Typical scanning conditions are: working distance 5 mm,  aperture no.4, accelerating voltage 20 K V , 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 A s growth.  2  during epitaxial  Fig. 2.5 is an SEM picture of M B E 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 A l 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 Gai- A s x  cross section analysis is still in progress in our Lab.  x  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  have regular cystalline  might be  oxide,  since  they  do not  CHAPTER  2.  MICROSCOPY  xl5k  Fig. 2.4.  8970  20kV  SEM picture of sample no.35.  2^m  CHAPTER  2.  12  MICROSCOPY  x4@k  1886 —  Fig. 2.5.  20kV .  -.-  —  •  1 "~  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. Gao. As, 7 pairs; (2) 60 A GaAs + 6  4  100 A Alo.6Gao.4As, 7 pairs; (3) 40 A GaAs + 70 A A l . G a . 4 A s , 8 pairs; 0  6  0  (4) 20 A GaAs + 30 A A l . G a . 4 A s , 15 pairs; and (5) 10 A GaAs + 20 A 0  Al0.eGa0.4As, 30 pairs.  6  0  CHAPTER  2.  Fig. 2.6.  Scanning tunneling microscope picture of the cross section of  sample no.37.  MICROSCOPY  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. 110 A, and z ~ 20 A.  The scanning ranges are: x ~ 150 A, y ~  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 G a i . A s has the same cubic zincblende crystal structure as x  x  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 A l G a i - A s is grown x  x  on the GaAs substrate, it tends to perfectly match the lattice constant of GaAs [3.1].  Therefore, the cubic lattice cell of A l G a i _ A s is x  x  squeezed horizontally and expanded vertically as shown in Fig. 3.1. A crystal of the zincblende structure has {400} [400} corresponds  to  Miller  family planes, where  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  (a)  X-RAY  21  DIFFRACTOMETRY  / / / / '/// / / / / '//A ////.<•/// / / / / '//A / / / > '//A / / / / '//A / / / / '/// / / / > '//A '//A ///*< '///, / / / / '//A ///> '//A / / / / '//A / / / > '//A '///, / / / / '//A / / / / '//A / / / • '//A '/// ///> //// '//A // // // // '//A '//A '//A / / / / '//A '/// //// / / / / '//A •V/A / / / / '//A / / / > '//A / / / / '//A '//A //// '//A //// '//A / / / / '//A / / / / '/// ///• '//A //// '//A ////'//A •V/A 'ft*. //// '•/A //// '//A / / / / '//A / / / / ' / / / - • / / / , A/A/ / / / / '//A 'ft*. ////'/AA / / / / '//A / / / / '//A '/// '//A //// /A// 'A/A //// '//A '//A '//A / / / / ' / / / '//A VA// '//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 A l atoms with a mole fraction x,  we get A l G a i . A s which still keeps the cubic zincblende  structure.  If A l G a i - A s  x  x  x  x  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 A l G a i . A s . x  x  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 B  A l G a i - A s has a larger d, thus a smaller 0B. x  x  corresponds  to A l G a i . A s . x  x  (3.2)  = arc sin — .  SO, the peak on the left  By the angular separation of the two  peaks, and a proper method of calculation, the A l 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]: 69(degree) = 0.109x .  (3.3)  with an error of 3%, based on x-ray diffraction and nuclear resonant reaction analysis (NRRA). While, Bassignana et al. reported another formula [1.11]: 80(degree) = 0.0958x .  (3.4)  Z03062.RAW  10  20  40.  30.  50.  60.  70  80.  20 (degree) Fig. 3.2.  X-ray spectrum of Al Gai. As/GaAs x  x  to (200) planes, the right one (400) planes.  sample no.30.  The left peak corresponds to  1 a  Z03105.RAW GAAS#30. 4, 1 8 / 4 / 9 1 . 20KVX20MA, NEW SLITS, LX o o o  GaAs, K a i +  o T  AIo.86Gao.14As, K « 2  c  3 O u  SO  </>  O  c  Alo.86Gao.i4As, K a l  -1—1—1—1  1  1  1  1  65.5  1  GaAs, K « 2  j—•—1—«—1—•—1—•—1—»—j—•  66.0  1  •  1  66.5 28 (degree)  Fig. 3.3.  High resolution x-ray spectrum for peak {400)  '  I  1  l  67  CHAPTER 3.  X-RAY  DIFFRACTOMETRY  25  with an error of 2% at lower x, and 3% at higher x. was  obtained  from  both  experiments  Equation (3.4)  and calculations.  In the  experiments, Bassignana used AlAs as an internal standard for the xray diffraction and the method of thickness analysis to extimate x in Al Gai- As. x  In the calculations, he assumed a constant  x  ratio. The results  of Xiong  relationship between the  Poisson's  and Bassignana both show a linear  angular separation  and the  A l content,  which is not exactly true since in fact the Poisson's ratio is not a constant for A l G a i - A s although the non linear factor is very small x  x  [3.1].  The reason for the difference between Eq.(3.3) and Eq.(3.4)  might  be  due  to  the  experimental details.  usage  of  different  samples  and  other  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 G a i . A s x  x  (x=0.25 to 0.5), and the A l G a i . A s was again grown on a series of x  other  epitaxial  layers.  x  Different  techniques  calibrate their x-ray diffractometers. resonant reaction analysis.  were also used  to  Xiong employed the nuclear  Bassignana used the scanning electron  microscopy to estimate Al content x from the thickness of A l G a i - A s x  x  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. section 3.4.  The detailed calculation will be given in  CHAPTER 3.  3.2  X-RAY  26  DIFFRACTOMETRY  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 M B E system. There are two sharp and high peaks in Fig. 3.2. the right is a {400}  The left is a {200}  reflection, and  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. front of the detector. graphite  crystal  component, source  Between the 3rd and 4th slits, there is a bent  monochromator  remove  and x-ray  The fourth one is in  which  is  set  to reflect  the k„  the continuum background radiation from the 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.  operation, both the sample holder and the goniometer rotate. goniometer holder.  rotates at a speed two times greater than the  This is so-called 0/20 scanning.  During The sample  The resolution of this Rigaku  diffractometer in terms of the width of the diffraction peaks is 40 s 0 . 0 2 5 ° = 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  22  DIFFRACTOMETRY  Fig. 3.4a. Use of Rigaku x-ray diffractometer for single crystal measurement.  high quality GaAs(fixed) detector  x-ray source AX, AG  * e  sample  Fig. 3.4b. Schematic representation of the double-crystal x-ray diffractometer.  CHAPTER  3.  X-RAY  DIFFRACTOMETRY  detail in the next section.  One advantage of the Rigaku diffracto-  meter is that besides 8/26 goniometer  can rotate  desired angle.  28  scanning, the  independently  sample holder or the  with the  other fixed  at a  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 A l 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,  3.  CHAPTER  X-RAY  22  DIFFRACTOMETRY  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  w=6o+[ Ph-y].  (3.5)  (  n e  where 6 is the originally set initial angle. 0  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  new  is normally of the  order of 0.1 degrees. Fig. 3.3 is a spectrum scanned in the vicinity of the peak. ray  {400}  In this detailed spectrum, three peaks are observed. The x-  source material is copper.  electrons, the atoms of When  the  excited  When bombarded by high energy  copper are excited to upper energy levels.  atoms  have radiative transitions  back to  the  ground state, the so-called K shell, K group x-ray is emitted, which include K i , K 2, Kp, and so on. The wavelengths of Kai (1.540598 A), a  a  K«2 (1.544418 A), and Kp (1.392249 A) are very close, especially for K a i , K 2 which correspond to the energy transitions from l s 2 p !  a  ls 2p 2  5  (j=l/2), and l s ^ p to ls 2p 6  2  5  6  to  (j=3/2). It is impossible to elimi-  CHAPTER  nate K  a 2  3.  X-RAY  DIFFRACTOMETRY  3_Q  by employing narrow slits in the x-ray system designed for  powders when a low quality crystal is to be measured. the x-ray beam used for the measurements K  a 2  .  The intensity of K  a 2  x  a 2  includes both K i and a  is one half of that of Kai. The peak on the  left in Fig. 3.3 corresponds to corresponds to GaAs, K  Therefore,  A l G a i - A s , K i . The one on the right x  x  a  . And the middle one is a mixture of A l G a i x  As, K a n d GaAs, K i , but mainly GaAs, K i . The A l mole fraction a2  a  a  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 A l content mole fraction with an uncertainty of 2%. Higher resolution x-ray measurements are needed in order to measure  the  A l 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 As  divergence  shown  Improvement  in Fig. 3.4a,  an x-ray  source  has  a certain  angle A0, and contains several wavelengths Xi, X  each with a natural line width AXi, AX ,..., AXn [3.4, 3.5]. 2  2  X ,  For copper  n  CHAPTER  3.  X-RAY  i i  DIFFRACTOMETRY  K i , the natural line width is 2.11 eV [3.6].  The corresponding width  a  in wavelength is AX=  \' * Ae(eV) nm = 4.0xl0e (eV) 2  A.  4  z  (3.6)  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. of  If the crystalline structure of the measured sample is  high quality and is  diffracted  sufficiently  thick, the wavelength  in the  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. the so-called  double crystal x-ray diffractometer  This setup is  (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  system can be represented  resolution  of  the  single crystal  by the angular width of the  x-ray  reflected  beam 6A 5d 86 = tan0 (— + —) + A9 + A 0 A d B  it  def  + A0  c o m p  .  (3.7)  CHAPTER  3.  X-RAY  11  DIFFRACTOMETRY  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  = angular width induced by the compositional imho-  p  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 as explained in the following, are negligible. t  In this  case 59 = tan6  8X  8d  (3.8)  B  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 A8i =  .  t  (3.9)  2t COS0B where  d = the distance between the adjacent lattice planes, 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  Fig. 3.5b and c.  TRANSPORT  PROPERTIES  Effect of sample thickness on diffraction curves.  21  Equation 3.9 can be proved readily.  As shown in Fig. 3.5a, the rays  A,  the Bragg angle 8 B interfere  D,  M which make exactly  constructively.  Reflected rays A ' and D' differ in phase by one  wavelength, while reflected rays A ' and M ' differ in phase by m L Considering different complete.  incident rays  from  8 B , we  that  find  make Bragg that destructive  angles only interference  slightly is  not  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'. and  These rays are destructive.  They cancel one another,  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 and  (8B,8I)  82  is zero.  The diffracted intensity in ranges of  (82,83)  is not zero, but has a value intermediate between zero  and the maximum intensity at 8 B - 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.  (3.10)  2(md) sin02 = (m-l)X.  (3.11)  By subtracting (3.11) from (3.10), one gets md ( s i n 0 i - 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 0 . 2  '01-02^  f01-0 l N  and  sin  B  2  Then, Eq.(3.12) becomes 2md c o s 0  '01-02"! B  = X.  Thus W =  = A0 . i t  2md COS0B  This is what we have in Eq.(3.9).  (3.13)  A more exact treatment gives a  slightly different result AG  0.9X i t  2md COS0B'  (3.14)  CHAPTER 3.  X-RAY  3_£  D1FFRACT0METRY  which is known as the Scherrer formula [3.7]. 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. compositional  Ideally the high-quality GaAs crystal has no  inhomo-geneity.  It  can  also  infinitively thick, and nearly free of defects. and A0 omp vanish. C  8d — is also negligible. d  be  considered  as  Therefore, A8j , A0d f t  e  If surface strain is released by etching, the term Then, Eq.(3.7) becomes 8A 80 = tane —. A. B  (3.15)  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  tion peak can bemeasured. in  every  3_Z  Since the raw x-ray contains K«i and K  direction within the divergence  angle,  a 2  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 i and K a  a 2  satisfy  the Bragg conditions and are simultaneously  reflected by the first high-quality crystal. Bragg  angles,  K i and K  measured sample.  a  a  2  Because of the different  beams are spatially separated at the  Since the detector has a 4.5 mm wide detection  window and has no slit in front of it, K i and K a  detected.  Thus the peaks of K i and K a  a 2  a 2  are  simultaneously  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 i and K a  a 2  will  slightly and the widths of the x-ray peaks will increase. the increase of the width, one can eliminate K narrow slits between the two crystals.  a  2  To prevent  by positioning  If without these narrow slits,  and if the sample is curved to some extent, K i and K a  detected at the same time.  separate  a 2  will not be  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  <t—305 sec_». ^11  ». -*oo  Fig. 3.6. The  -200  •  0  2M  »eo  sec. AXU 1  Double-crystal x-ray diffraction spectrum of sample no.30.  measurement  University.  1  was  done  by  Brad  Robinson  at McMaster  CHAPTER 3.  X-RAY  D1FFRACTOMETRY  3_9_  next question is how to calculate the A l content from the angular separation of the A l G a i - A s and GaAs {400} peaks. x  3.4  x  Calculation and Comparison From strain and stress relations, the strains of A l G a i . A s can x  x  be expressed as [3.11] 2y  £  z z  =-—  Aa £  z  z  Aa  y y  - Aa  fz  = — r  £yy=  £  1-y  T  (3.16)  f  — •  t  fv  ,  - Aa  (  3  -  1  7  )  f  t  ,  (3.18)  where y = 0.31 + O.Olx, is Poisson's ratio [3.1], a = a (x) = 5.6533 + 0.0078x (A), lattice constant of Al Gai- As film, f  f  x  x  Aa = a - a , f  f  s  afz = deformed af in vertical direction, a = lattice constant of the GaAs substrate, s  afy = deformed a in horizontal direction, f  Aa = a - a and fz  fz  f|  Aafy - Sf-aty, as indicated in Fig. 3.1b. The deformed lattice structure of A l G a i . A s belongs to the x  tetragonal crystal system. are [3.9, 3.10]  x  The distance between two adjacent planes  CHAPTER 3.  X-RAY  40  DIFFRACTOMETRY  d=  ^a J  a  FZ  where (h,k,l) are Miller indices. d=  (3.19)  J  2 fy  Before deformation, a = a = a , so fy  fe  f  ^1/2  h  + k  2  +l  2  (3.20)  2  After deformation, afy and af are different from af. But still Z  (3.21)  afy » af « af. z  Differentiating  Eq.(3.19) with respect to afy and a f , and using the Z  approximation in Eq.(3.21), one gets 5  d  ( 2  =  h  +  k  2 + 12)3/2 t  h  2 5  a  * +(  k  2  +  1 2  ) *J  ( - >  5 a  3  2 2  Combining Eq.(3.20) and Eq.(3.22), and denoting 8a as Aa , and 6a fz  fy  fy  as Aa , one finds fy  5d d  1 h + k2 + 12 2  h  , Aa „ — + ( k + l a f 2  2  2  f  2  Aa ) —^ a f y  (3.23)  f  For {400} planes 5_d d  Aa a  (3.24)  fz  f  From eqs. (3.18) to (3.24), Aafz Aa fy :  (1 + Y^i Aa  a  - Y  21  f  A aty  1  -  _ Y  =  A  +  Y"| A a  11  -  Y j A a  f  f  y  '  (3.25)  CHAPTER  3.  X-RAY  ±1  DIFFRACTOMETRY  Aa  f  since experiments have shown that, in general,  »  1, i.e., the  misfit of GaAs and A l G a i - A s in horizontal direction is negligible x  x  compare to the difference of a and a [3.11]. Thus f  Aa  fz  s  =  1  +  ^ Aa .  (3.26)  f  From the Bragg equation, 8d d  80 tan0j  (3.27)  Combining Eq.(3.1), Eq.(3.4), Eq.(26) and Eq.(3.27), and taking 0 in B  Eq.(3.27) as the Bragg angle for GaAs {400} planes, .  g e r  (  , egree ;  (  we find  0.29 ( 1.31 + O.Olx ) x 55533 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)  80( degree ) = 0.0958x.  (3.31)  and Bassignana's [1.11],  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 A l  content x, was linear by Xiong and Bassignana. But, according to Eq.(3.29), it is not exactly linear. from the constant  Poisson's  The linearity of Eq.(3.31) results  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" in 4  Eq.(3.29). x=l.  The results of Xiong's and Bassignana's differ by 14% at  Equation (3.29) is closer to that of Bassignana's, especially when  x is small.  CHAPTER 3.  X-RAY  Fig. 3.7.  DIFFRACTOMETRY  Comparison of the formulas relating the A l mole  fraction to the angular separation.  41  CHAPTER 4.  ELECTRICAL  TRANSPORT  44  PROPERTIES  Chapter 4  Electrical Transport Properties Unlike the measurement of A l content for which there are a number of widely accepted techniques, there is a quite unique and standard  technique  to  measure  electrical  transport properties  semiconductors: the Van der Pauw method  [4.1].  of  The electrical  transport properties measured with this method include resistivity and  Hall  mobility  coefficient are  from which carrier concentration  derived.  Another  property is the four-probe method.  method  to  measure  and Hall electrical  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  4.1  Sample Preparation  4.1.1  Patterning  PROPERTIES  Al  In order to measure electrical transport properties of M B E grown films, semi-insulating substrates (resistivity =10 to be used. for  7  Q-cm) have  In the beginning, square samples (Fig. 4.1a) were used  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. Pauw's theory, the electrical contacts  In Van der  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] Au lb  H  2d 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.  where  ELECTRICAL  TRANSPORT PROPERTIES  47  D = the diameter of a circular sample, d = the distance of a contact away from the circumference, of the circle, L l = Hall mobility of the sample. H  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), ^ = -  (4 2)  M  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]  4rk _8w =  (  4  3  )  Therefore, the arms were made as narrow as possible to minimize the errors.  CHAPTER 4.  The  ELECTRICAL  patterning  was  with specialized tools. brass bar was  TRANSPORT  48  PROPERTIES  done  First, a  machined with a  structure shown in Fig. 4.2a.  This  bar was then used as an electrode in  our  AGIE  spark  machine.  A  square  stainless  steel  plate  with the electrode.  erosion piece  of  was eroded  We thus get a  Fig. 4.2a. spark  Electrode  erosion  o f the  machine.  mask with the negative pattern of that of the bar as shown in Fig. 4.2b.  The MBE-grown wafer was  sample position  V p  cleaved into a square of about 6x6 mm  which is slightly larger than  2  the  mask.  Then the sample was  covered by the mask oriented at  mask window  45 degrees as shown in Fig. 4.2b Finally,  the masked sample  was  sand blasted down to 0.1 ~ 0.2 mm with an A l sand blaster.  Sand  blasting took about 10 seconds.  4.1.2  Ohmic Contacts  Fig.4.2b Mask for sand blasting.  The  corresponds  dashed to  of the sample.  the  square position  CHAPTER 4.  In  ELECTRICAL  order  to  TRANSPORT PROPERTIES  measure  properties, ohmic contacts  the  carrier  4J)  electrical  transport  were made on four spots of the M B E  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. onto  another piece  patterned one.  of wafer  Purified N  2  A thermocouple was placed  which was  the  same  size as the  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 + l n 0 = 2InCl + 3H 0 . 2  3  3  2  (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 Gai- As [2.5], with some of the Ga atoms being replaced by x  In atoms.  x  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 temperature 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 1 0  17  cm- , the resistance between the two indium contacts was less than 3  0.2 Q. For undoped GaAs, the resistance was several K Q . 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  can be calculated as follows:  c  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 =  where  I  27ttr'  I  applied current,  r  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  (4.5)  CHAPTER 4.  ELECTRICAL E  =  TRANSPORT 1  2nat d / 2 - x  +  Applied current,  F i g . 4.4a. layer.  The  PROPERTIES 1  d/2 + x  U  (4.6)  I  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  =—±— in— 7t a t  -d/f+a  (4.7)  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 R =-= I  1 d-a ln rcot a  8s  (4.8)  For rectangular samples with length 1 and width w, the measured resistance between two contacts is R = 2R + — R w C  (4.9)  s  From Eq.(4.9), the contact resistance is found to be 1 R  c  =  2  lp (  R  - ^  where l/o = p(resistivity) was used.  l  d-a n  —  >  <' > 4  10  In the case of undoped sample  MBE no.31, with carrier concentration n = 5 x l O  15  cm* , R = 7 KQ, d = 3  4 mm, a = 0.5 mm, t = 2.4 |im, 1 ~ d, w = 2 mm, and p = 0.2 Q c m , R =2.5kQ. c  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.  shown in Fig. 4.1c,  With the sample pattern  the local heating is less serious since the heated  CHAPTER 4.  ELECTRICAL  TRANSPORT  5_4  PROPERTIES  contacts are not part of the circular area being measured.  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. evaporation source.  Au-Ge(88:12) was used as the  The main working conditions of the evaporation  are • pressure:  10" torr, 5  • 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  apparatus shown in Fig. 4.3, in a N  2  done with the  gas environment.  were annealed at 450 °C, for 2 minutes.  same  The contacts  According to Eq.(4.10), the  resulting contact resistance for the n-type doped sample no.13, with n = 8xl0  17  cm' , p = 3xl0" n-cm 3  at room temperature was calculated  3  to be R ~ 8 fl. c  The  contacts  made  by  indium diffusion have more than 10  CHAPTER 4.  ELECTRICAL TRANSPORT PROPERTIES  times larger resistance  11  than contacts made by vacuum evaporation.  Vacuum evaporation makes better contacts, but the process is  more  complex and time consuming.  4.2  4.2.1  Measurement and Analysis Electrical  Transport  Fig. 4.6 shows 4.5  shows the  Measurement  Apparatus  the Van der Pauw measurement system.  sample probe which  heater coil  fits inside  spring contacts  Fig.  a long cylindrical  sample  x  T  ess?—-  stainless steel  diode temperature sensor  brass Fig. 4.5.  vacuum chamber.  The  Sample probe  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  Switch Board  Magnetic Coil Current Source  P *o  /v.  Sample Current Source >>  Computer CO  o  Voltmeter  3 O  *o  OJ  50  Vacuum Pump  Temperature Controller  Temperature Monitor  Fig. 4.6. Experimental setup for Van der Pauw measurement. 1. cryogenic dewar; 2. magnetic coil.  to  ON  CHAPTER 4.  ELECTRICAL  TRANSPORT  meter between 4 K and room temperature. the calibration.  -12  PROPERTIES  Fig. 4.7 is the result of  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.  Q  I  I  0  I  I  I  I  50  I  I  The rest of the long probe is  I  I  I  100  I  I  I  I  I  150  I  I  I  I  I  I  I  200  I  I  I  250  I  I  I  I  I  300  I  I  I  I  350  Temperature ( K ) Fig. 4.7.  Temperature calibration of the cryogenic diode sensor.  CHAPTER 4.  ELECTRICAL  TRANSPORT  18  PROPERTIES  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  vaporization than nitrogen.  a much lower  A temperature controller was built to  control the temperature of the sample. some cases to interfaces  A PC computer was used in  acquire the measurement  and to  latent heat of  data through IEEE  do numerical calculations.  488  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  ln2 where  R AB.CD R BC.DA  _  —  2  (4.13)  CHAPTER  V  C D  4.  and V  D A  ELECTRICAL  TRANSPORT PROPERTIES  are measured voltages across C,D and D,A. I  5_9  AB  and I c are B  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 HnlR B.CD-RBC.DA j >  A  I  K-AB.CD  +  K  =  I  BC.DA J  e ( l n 2 ) / f <  ( 4 i l 4 )  &  If the the four contacts and the sample are exactly symmetric, the correction factor is equal to 1. The Hall coefficient is given by RH - l ' V » ( B ) - V „ ( 0 ) I -I A C  D  where  t = thickness of the grown layer, B = the applied magnetic induction,  and  VBD(B)  = corresponds to the voltage  VBD(O)  = corresponds to the voltage  V  B  V D B  with magnetic field,  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  conduction band and the donor band.  are found in the  The measured electrical  transport properties are a combined effect of electrons in both the conduction band and the donor band. semiconductors  is  called  the  One theory dealing with doped  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  P=  7 , en n +en n c  where  6_j0  D  c  (4.16)  D  n = electron concentration in the conduction band, c  u. = electron mobility in the conduction band, c  n  = electron concentration in the donor band,  D  u.  = electron mobility in the donor band.  D  The Hall coefficient is defined as [4.6]  r,  n u/ n uV c  n  +  e (n n + n u ) c  c  D  2  D  where the Hall factor [4.7]  +I " )!  r  3 ^ ( 2r H = — — 4((r | ) , J  (4.18)  +  For acoustic deformation potential scattering, for example, r = -1/2 [4.7], and r = 1.18. H  For ionized impurity potential scattering, r = 3/2,  and r = 1.93. H  By definition, we have the combined Hall mobility u. =  = -— e n n +n n  p  c  c  D  .  (4.19)  D  Normally the mobility u. is much greater than the mobility u. at any c  temperature.  D  At high temperatures,  electrons mainly stay in the  conduction band, n > n , and n u . » n |i , therefore 2  c  D  c  c  2  D  D  CHAPTER 4.  ELECTRICAL  TRANSPORT PROPERTIES  P =  1 en ji c  «  R  6J,  , c  en ' c  At very low temperatures, because of the finite activation energy of shallow dopants, n ture.  c  decreases indefinitely with decreasing tempera-  Finally, a temperature is reached at which n n «n n 2  c  D  c  D  2  .  (4.20)  Then, 1  en u D  R  h  D  en ' D  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.  2.5  ELECTRICAL  • 1 1 11  I I I  TRANSPORT  1 1 11  1"  _6_2  PROPERTIES  1 1 11  I I I .  . . . ._  MBE RIFN#32 1.5  •  -  + - » 1—(  •  -  •  -  >  0.5  •  0 ' 1 1 11 50  •  1 1 1 1  100  150  • t  i  l  l  200  • •  i  •  • i  i  i  250  Temperature (K)  Fig. 4.8.  Resistivity vs temperature, sample no. 32.  i... i  • i  300  CHAPTER 4.  ELECTRICAL  4.0 1 0  V  U  3.5 1 0  V  CO  l i l l  TRANSPORT  PROPERTIES  I I I I  l i l l  I  i  I I ||  •  I I I I |1  i i  i  J1 ample 14o.32  • *. •  3.0 1 0  11  i : -  s  •  -  • S o  2.5 1 0  *4—I  _  3  -  •  • •  c3  a  •  -  <  •  1.5 1  1.0 1 o  v  l i l l  i i i i 50  •  I I I I  100  •  • . . . .  150  Temperature  Fig. 4.9.  200  • • • . . . . —I—1  • 1  250  (K)  Hall coefficients vs temperature, sample no.32.  1 "  300  CHAPTER 4.  Fig. 4.10.  ELECTRICAL  TRANSPORT  PROPERTIES  Calculated conduction band electron concentration vs  temperature (solid line).  Data points (•)  are derived from l/(eR ). H  The data points at low temperatures show the existance of conduction in the donor band.  CHAPTER  4.  ELECTRICAL  2.0 10  TRANSPORT  1T™|—|— •  • •  •  B  -  • •  •  X  o  Al  " 1 11 "I'—| 1 1 1 1—I—1—1—1—— i — r - T — i —  •  C/5  PROPERTIES  1.0 10' •  •  •  •  ffi  3 5.0 1 0  .+  D  •  1 1 1 1_.J. 0  50  IvTBERU N#32 II  1  •  100  III  1 11 1 , . . , 150  200  250  Temperature (K)  Fig. 4.11.  "  Hall mobility vs temperature, sample no.32.  300  CHAPTER 4.  ELECTRICAL  T—I  TRANSPORT  I I I 1111  1  PROPERTIES  1 I  6_£  1  TEMPERATURE  1 l I IIII  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 l O c m , (B) 10 cm" , (C) 5 x l O cm' , and (D) 5.5 x l O cm . 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. 13  3  1 5  3  1 5  3  3  1S  CHAPTER 4.  Fig.  ELECTRICAL  4.13.  TRANSPORT  PROPERTIES  Resistivity vs temperature, sample  no.13.  CHAPTER 4.  ELECTRICAL  Fig. 4.14.  TRANSPORT  PROPERTIES  Hall coefficients vs temperature, sample no.13.  CHAPTER 4.  Fig. 4.15.  ELECTRICAL  TRANSPORT  PROPERTIES  Calculated conduction band electron concentration vs  temperature (solid curve).  Data points (•) are derived from l/(eR ). H  The data points at low temperatures show the presence of conduction in the donor band.  CHAPTER 4.  Fig.  ELECTRICAL  4.16.  TRANSPORT  PROPERTIES  Hall mobility vs temperature, sample no. 13.  IQ  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: • Ga cell temperature:  600 ° C , 1040 °C,  • As cell temperature: 350 °C, • vacuum pressure: • growth rate:  substrate  8  103 A/min,  • layer thickness: The  1.4xl0" mbar,  2.88 u.m.  temperature  during  growth  was  unique optical method as described in Ref. [4.8]. found with the techniques  measured  with a  The thickness was  of the selective etching and S E M 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: • Ga cell temperature:  580-600 ° C ,  1067 °C,  • As cell temperature: 392 °C, • Si cell teamperature: • vacuum pressure:  1100 °C,  1.1 xlO'  • growth rate: 213 A/min, • layer thickness:  4260.A.  8  mbar,  CHAPTER 4,  The  ELECTRICAL  TRANSPORT  transport properties  PROPERTIES  are governed  7_2  by the carriers in  different bands and by a combination of several scattering processes, including  neutral impurity scattering,  longitudinal acoustic  ionized impurity scattering,  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  semiconductor.  The  temperatures  © is given by [4.7]  T «  mobility  M= -  where  lattice  due  - ^ 2m* a co  to  e  V  vibration in  this  scattering  e / T  0  q = electron charge, m* = effective mass of a carrier, a = polar constant, co = optical phonon angular frequency, and 0  0 = Debye temperature. At high temperatures, T > 0 [4.7]  2m*aa>  0  3 y n®  a polar at  low  (4.21)  CHAPTER 4.  In  ELECTRICAL  TRANSPORT PROPERTIES  the intermediate range of temperatures  ( T ~0  7_3_  ), 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 vibration.  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  where  3  *5/2  m  k  3/2  £ a c  2  - T  (4.23)  C = pco^q, , the average longitudinal elastic constant, {  co, = angular frequency of the longitudinal phonon, q, = wave number of the longitudinal phonon, 1/2  l kTm , 2  acoustic deformation potential constant,  a c  l  ac  = 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  *  TI  where  3/2  PROPERTIES  2 (47ce) (kT) Z e m ^ ^ N ^ l n C l + p ) - (3 /(l + p )] 7/2  =  TRANSPORT  2  2  14  3/2  3  2  2  2  3 / 2  ~  T  '  ( 4  '  2 4 )  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 2kT"\J6me/n  P The  £  •  -  (4  25)  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]: — =!, —  where  ,  (4.26)  Z. is a sum over i, the individual scattering process, M- = the overall Hall mobility, H  h= the component drift mobility due to certain scattering process, and r = the corresponding Hall factor. H  Obviously, the combined mobility is smaller than the mobility due to one scattering process as shown in Fig. 4.14.  CHAPTER 4.  ELECTRICAL  15  TRANSPORT PROPERTIES  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. high temperatures R = r /(en ). -  H  H  D  R = - r /(en ), H  H  c  At  and at very low temperatures  At intermediate range of temperatures,  electrons  transfer exponentially from the conduction band to the donor band with decreasing temperature.  At the maximum point of R , n u. =n u. , H  which is derived from Eq. 4.17.  c  c  D  D  Although, it was not intentionally  doped, sample no.32 still has an electron concentration of order 10 cm  3  (Fig.4.9).  15  This was caused by the residual or background  impurity that existed in the M B E 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  extrapolation  low from  temperatures n  c  theoretical formula [3.9]:  at  high  is  obtained temperatures  by  the  exponential  according to  the  CHAPTER 4  ELECTRICAL  TRANSPORT  I  J '  fNc(N„-N )V/2  where  d  2  PROPERTIES (  AE  C  (4.27)  exp - 2kT  N=  By fitting the electron concentration data in Fig. 4.10, we found that the activation energy for sample no.32 is AE = 6.0 ± 0.5 meV. C  Similarly, for the Si-doped sample no.13, it is found that AE = 5 ± 1 meV. C  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 ntype dopant we have been used in our M B E system, the residual or background impurity in the M B E 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 cm /Vs at 2  300 K to 19,000 cm /Vs at 70 K because of the weaker  polar optical  phonon  deformation  2  scattering  and longitudinal  the  domination  of  phonon  At temperatures lower than 65 K , because  potential scattering [4.15]. of  acoustic  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. B, C and D are compensation  10 , 5 x l 0 ,  1 3  15  1 5  and 5 . 5 x l 0  15  cm" . 3  The  ratios N / N are 0.3 to 0.4 for curves A, B, and C, and a  0.5 for curve D. Stillman.  5xl0 ,  The electron concentrations of curve A,  d  Our result curve D is consistent with the results of  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) level  have an extreme point at some temperature. increases,  temperature,  which  these  extreme  indicates  points  stronger  shift  ionized  because of the higher impurity concentration.  As the dopant towards  impurity  higher scattering  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. that  the  ELECTRICAL  electrical  TRANSPORT  properties  of  the  PROPERTIES  undoped  sample  7JS change  with respect to temperature than those of the doped sample. the  resistivities  of  these two  samples,  it is  clear that  the  more From 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 G a i . A s x  x  epitaxial films grown by molecular beam epitaxy. The topographic properties of cleaved ends of grown layers were investigated techniques  by means  including  of selective etching  scanning  electron  scanning tunneling microscopy (STM).  and microscopic  microscopy  (SEM) and  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 A l G a i - A s . x  Al  mole fraction in A l G a i - A s x  x  was  measured  x  by x-ray  diffractometry. An x-ray machine designed for powders was used to measure A l mole fraction in single crystal A l G a i - A s with sufficient x  accuracy.  The resolution of x-ray diffractometry  x  was discussed.  mole fraction was calculated with a newly derived formula.  Al  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  accurate  results.  to  achieve  and  reproducible  measurement  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. interpret  the  electrical  The two-band theory was used to  transport  results.  The  temperature  dependence of the electron concentration in the conduction band was fit with an exponential function. activation energy of the impurity. impurity is  silicon.  From this fit, we obtained the We conclude that the residual  The undoped GaAs  material that we  measured has a residual Si donor impurity concentration of cirr  3  at room temperature.  19,000 cm /Vs at 70 K. 2  have 5xl0  15  The highest Hall electron mobility is  REFERENCE  &1  References [1.1]  P. Boucaud, F. 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