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Temperature dependence of photoluminescence of the dilute nitride semiconductor GaNA̜s₁₋ Beaton, Daniel A. 2003

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Temperature Dependence of Photoluminescence of the Dilute Nitride Semiconductor GaN^Asi-a; by Daniel A . Beaton B . S c , St. Francis Xavier University, 2001 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F THE REQUIREMENTS FOR T H EDEGREE OF MASTER OF SCIENCE in T h e Faculty of Graduate Studies (Department of Physics and Astronomy)  We accept this thesis as conforming to the required standard  T H E UNIVERSITY O F BRITISH C O L U M B I A October 3, 2003 © Daniel A . Beaton, 2003  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of B r i t i s h C o l u m b i a , I agree that the L i b r a r y 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 Physics and Astronomy  T h e University O f B r i t i s h C o l u m b i a Vancouver, C a n a d a  Abstract  ii  A b s t r a c t  The design of a closed cycle optical cryostat for semiconductor crystal characterization is discussed. The system designed and developed is capable of performing photoluminescence, resistivity, and Hall measurements as a function of temperature from 10 K to higher than 300 K. Preliminary photoluminescence experiments are carried out as a test of the system. Results from the photoluminescence measurements show evidence for the existence of nitrogen clusters in GaN Asi_ . The clusters are shown to produce states x  x  with energies inside the band gap. It has also been found that the introduction of bismuth, as a surfactant, during the growth process tends to reduce the density of the nitrogen clusters in the material.  Contents  iii  C o n t e n t s  Abstract  ii  Contents  • • iii  List of Tables  v  List of Figures  vi  1 Introduction  1  2 Background  4  2.1  2.2  Materials at L o w Temperatures  4  2.1.1  Heat Capacity  5  2.1.2  T h e r m a l Conductivity  6  III-V Semiconductor Crystals  11  2.2.1  11  2.2.2  Sample G r o w t h B a n d G a p Bowing  13  2.3  Temperature Dependence of the B a n d G a p . . .  15  2.4  Photoluminescence  16  3 System Design and Operation 3.1  C T I M o d e l 350P CryoCooler System  20 20  Contents  3 System Design and Operation 3.1  C T I M o d e l 350P CryoCooler System . . 3.1.1  3.2  3.3  Closed Cycle Refrigeration  iv  20 20 21  Heating and Cooling Considerations  24  3.2.1  Sources of Heat  25  3.2.2  Heat Shield  28  3.2.3  Modeling the Sample M o u n t  29  Sample Mount  32  3.3.1  T h e r m a l Bridge  32  3.3.2  Heater Block and Sample Stage  34  3.4  Thermometry and Temperature Control  35  3.5  V a c u u m Chamber  37  4 Temperature Dependence of PL  39  4.1  Experimental Set-up  39  4.2  Experimental Results  41  4.3  Evidence for Nitrogen Cluster States  45  5 Conclusions  59  Bibliography  61  A Design Specifications of the System  64  B Cryocooler Cooling Capacity  81  List of Tables  List  2.1  of  v.  T a b l e s  Temperature dependencies of phonon thermal conductivity for various types of crystal impurities[12]  2.2  9  Varshni fit parameters from literature, GaAs[15] and GaN[17], as well as  3.1  16  Emissivity values for the materials located inside the vacuum chamber[12]  3.2  '  Temperature ranges, of various thermal links made from  28 |"  O . D . stainless steel tubing, wall thickness 0.040" . . . . . . . . 4.1  33  Energies of nitrogen cluster states relative to conduction band minimum[24]  . .  45  vi  List of Figures  List  of  F i g u r e s  2.1  Heat capacity of copper  7  2.2  T h e r m a l conductivity of stainless steel  2.3  Cross-sections of a) bulk G a N ^ A s i - x sample and b) a single  10  quantum well sample 2.4  13  B a n d gap as a function of lattice parameter for various semiconductor compounds  2.5  .14  Recombination processes from conductio band to valence band: a) P h o t o n emission, w i t h v\ < v , b) Phonon emission, and c) 2  Auger effect 3.1  '  17  M o d e l 350P C T I Cryocooler, and cross-section of the displacer unit  22  3.2  Cryocooler displacer unit cycle  23  3.3  Electric circuit model of sample mount. .  30  3.4  M o d e l of the cooling of the sample stage for b o t h thermal links, solid line f = 4.233 x 10~ m, dashed line f - 3.35 x 10~ m  32  3.5  Cryostat sample stage  34  3.6  C a l i b r a t i o n curve of a silicon diode  36  4.1  Schematic of the P L optical set-up  40  4  3  vii  List of Figures 4.2  Photoiuminescence spectra of bulk G a N A s i _ x  x  as a function  of temperature for pulsed photoexcitation 4.3  Photoiuminescence of G a N A s i _ x  x  50  w i t h pulsed and C W exci-  tation lasers. T h e C W emission spectrum has been adjusted so that the low energy fall-offs match 4.4  51  Photoiuminescence spectra of bulk G a N A s i _ x  x  as a function  of temperature for C W photoexcitation  53  4.5  B a n d gap Energy G a N A s i _  4.6  Measured low temperature band gap for various nitrogen con-  x  centrations in G a N A s i _ x  4.7  x  x  as a function of temperature  and expected fit  . .  . . .  54  55  Comparison of the photoiuminescence spectra of samples grown w i t h and without bismuth. Pulsed excitation i n a) and C W excitation i n b)  4.8  56  Energy as a function of temperature for sample w i t h and without bismuth. T h e error in the band gap energy is ±0.002 e V for temperatures lower than 100 K  4.9  57  Sketch of the density-of-states for G a N A s i _ . A l s o shown is x  x  the expected distribution of occupied for a) various threshold energies E * relative to the conduction band m i n i m u m ( C B M ) and b) for increased temperature A.1  58  Cryostat set-up designed for semi-conductor crystal character- . ization  64  A.2  C T I Cryocooler cylinder  . . . .'  65  A.3  Assembled vacuum chamber  66  A.4  Lower piece of vacuum chamber  67  viii  List of Figures A.5  Upper piece of vacuum chamber  68  A.6  Window  A.7  Assembled sample stage  A.8  B o t t o m thermal bridge interface, mounted to second cold stage 71  A.9  Stainless steel thermal bridge  flange  69 70  72  A.10 Top interface of thermal bridge A . 11 Heater block A . 12 Sample mount  73 '  74  • • •  75  A . 13 Assembled heat shield set-up A . 14 B o t t o m piece of heat shield, mounted to first cold stage  . 76 . . .  A . 15 Center piece of the heat shielding  77 , 78  A . 16 Top most piece of the heat shielding  79  A . 17 Top most piece of the heat shielding modified for P L  80  B. l  C o o l i n g capacities of the C T I cryocooler for b o t h modes of operation  81  Chapter 1. Introduction  1  Chapter 1 Introduction In recent times the incorporation of small amounts of nitrogen into III-V semiconductor compounds (such as G a N x A s i _  x  and I n G a N x A s i - x ) , has be-  come a hot topic i n experimental and theoretical physics. Interest i n dilute nitrides has also grown i n the industrial sector, primarily for 1.3 /xm vertical cavity surface emitting lasers ( V S C E L s ) and cooler-less edge emitting lasers. T h e addition of a fraction of a percent of nitrogen can dramatically reduce the band gap of the alloyed material, allowing for the production of more technically favourable wavelength devices (1.3  JJLYO.  and 1.55 /mi). These new  materials have several advantages over ones currently i n use ( I n G a A s P / I n P and I n G a A s / I n G a A s P ) [ l ] . A s an example, lasers made from the dilute n i tride alloys are not as temperature sensitive due to a larger conduction band offset [2]. T h i s higher temperature stability is useful for the production of uncooled lasers. G a A s substrates, on which these alloys are grown are available in larger sizes and at a lower cost than I n P substrates, leading t o lower costs i n device manufacturing. T o date nitrogen's effect o n the electrical, optical and material properties of the III-V compounds is not well understood.  There are also some disadvantages associated w i t h the addition of nitrogen. For example, a large decrease i n electron mobility a n d recombination  Chapter 1. Introduction  2  lifetime[3], a n d a reduction i n photoiuminescence intensity is observed[4]. In addition to these electrical and optical deficiencies, there are also some structural problems that arise w i t h nitrogen incorporation. Because nitrogen is atomically smaller (atomic radius, r  0  = 0.74A) t h a n the arsenic,  (ro = 1.19 ^4)), which it replaces, there is a large lattice constant mismatch between substrate and the epi-layer.  T h i s puts a large amount of strain  on the grown epi-layer. T h i s strain results i n elastic and plastic relaxation processes that can lead to roughened surfaces and interfaces [5], as well as dislocations and cracks i n the material. A l l this compromises the functionality of the material. T h e introduction of In along w i t h N compensates for the size discrepancies correcting some of the lattice mismatch.  In order to achieve the very specific material properties for device fabrication, particularly i n energy and intensity of the emitted photons, attempts are being made to improve the material by varying the growth parameters and techniques[6][7][8] to reach the desired characteristics.  One area still  largely unexplored i n dilute nitride semiconductors is the dependence of the electronic and optical properties of these alloys on temperature, especially i n the range 10 K to above 300 K . A l s o unknown is the effect which the various growth methods have on temperature dependent phenomena. .  T h e following is a description of the development of an apparatus to carry out experiments characterizing the G a N A s samples. O n l y measurements on the temperature dependence of the photoiuminescence of dilute nitride alloys w i l l be discussed i n the following pages. Chapter 2 gives some background information on materials at low temperature, necessary for the discussion of  Chapter 1. Introduction  3  the design of the cryostat and a short introduction to dilute nitride semiconductors and photoluminescence. In chapter 3, the design of the cryostat is covered. Measurements on the temperature dependencies of photoluminescence ( P L ) is given i n chapter 4, w i t h concluding remarks i n chapter 5. A l l design drawings and specifications for the cryostat can be found i n the appendices.  CEapter  C h a p t e r  2.  Background  4  2  B a c k g r o u n d  2.1  Materials at Low Temperatures  T h e first step in the project was to design and b u i l d a variable temperature closed cycle helium cryostat from a second-hand cryopump. In the design of this system the heat capacity, C y ( T ) , and thermal conductivity, « ( T ) , of the materials involved are of primary importance. T h e heat capacity of a material is important when the material is to be heated or cooled i n some way. It relates the amount of energy necessary to raise or lower a unit mass one degree. Typically, the specific heat is considered to be constant above a given temperature, and below this point to be highly temperature dependent. T h e influence of temperature on the specific heat of different types of materials will be discussed below in a little more detail. It is also necessary to know the thermal conductivity of a material. Important whenever a material is to be heated to know how quickly thermal equilibrium will be reached or if using that particular material as a thermal conductor or insulator. Further notes on the thermal conductivity of materials will be covered later on, w i t h special consideration given to metal alloys, such as stainless steel.  Chapter 2.  2.1.1  Background  5  Heat Capacity  Heat capacity of a material is defined as the rate of change of energy, U, w i t h temperature, T. For a given material, the specific heat has contributions from a variety of sources, most notably electrons and phonons. T h e phonon part can be best approximated by the Debye function,  C v ( T )  I  - - j « r V  Where 6D is the Debye temperature, and M  m  w ^ f  d  x  ( 2  -  1 )  the molar mass (for M K S units,  T h e above equation is derived using the elastic continuum model of a solid, in which the number of vibrational modes in the interval u,u + du is given by; 1 2 rimodes =--4TT(-3 + ^)Vu du  (2.2)  2  Where V is the volume of the solid, v the wave velocities, and the subscripts I and t indicate longitudinal and transverse modes respectively. A m a x i m u m frequency, u  m  is given by the normalizing constraint that a solid w i t h N  atoms may have only 3A^ modes. T h i s in t u r n gives the Debye temperature as: .  0D = ^  k  -(2-3)  B  A full derivation of the Debye model for the specific heat can be found in any standard condensed matter physics text[10][ll]. A t low temperatures, T < #D, the specific heat is predicted to have a T Debye T  3  3  dependence, known as the  law. It should be noted that for real solids it is generally necessary  to go to much lower temperatures to have a pure T  3  behaviour.  Chapter 2.  Background  6  A t temperatures T > #£>, the specific heat is a constant, and given by the Dulong-Petit relation[10][12], C  v  of electrons,  = f i V ^ s . A t low temperatures the fraction  w i t h i n fc#T of the Fermi surface begins to contribute more  to the specific heat:  Tp is the Fermi temperature (f^)-  T h i s electronic  component gives a linear dependence of the specific heat on temperature at very low temperatures. In metals it is the electrons that contribute most to the specific heat at low temperatures and phonons at higher temperatures, whereas insulators have only the phonon contribution.  For the purposes of the discussion to follow on the design of the cryostat, the properties of copper will be discussed in more detail. T h e basic picture of the cryostat is a copper sample mount, w i t h a heater, weakly linked to a thermal sink operating at some low temperature. Therefore much consideration must be given to the initial cooling and subsequent reheating of the copper stage. Copper has a Debye temperature of 343 K , given by its T —> 0 limit. W h e n a more accurate measure of the specific heat is needed the Debye temperature is assumed to be a function of temperature [12]. Shown in fig 2.1 as a function of temperature is the specific heat of copper. Three regions immediately stand out: for T < 40 K there is a T  3  dependence, above  that (40 K < T < 100 K ) there is a region of linear dependence, and then for T > 300 K C (T) V  2.1.2  is a constant given by the Dulong-Petit relation as 3 8 5 ^ .  Thermal Conductivity  Heat transfer by conduction depends b o t h on the temperature gradient between two points as well as the thermal conductivity of the material bridging  7  Chapter 2. Background 400 r  100  60  160  200  250  300  Temperature (K)  Figure 2.1: Heat capacity of copper  them. T h e r m a l conductivity can be approximated by a relation borrowed from the kinetic theory of gases:  K(T) =  \pC (T)vl v  (2.4a)  Where C V ( T ) is the specific heat, v the velocity of the energy carrier, and I the mean free path of the energy carrier. Velocities of energy carriers are approximately 10 m / s for electrons and the speed of sound for phonons, and 7  b o t h can be assumed to be relatively constant w i t h temperature. T h e dependence of the specific heat on temperature has been covered i n the previous section. W h a t remains is the mean free path of the carriers involved.  In the case of electrons, the same processes that limit the electrical conductivity also affect the thermal conductivity, i.e. scattering off phonons and impurities in the crystal. One can invoke the Weidemann-Franz law, shown below, to find the thermal conductivity from the electrical conductivity.  p (T) K  = LT  (2.5)  Chapter 2.  8  Background  In equation 2.5 L is the Lorentz constant, having a value of 2.45 x I C T - ^ . 8  Note that this is only applicable where the mean free path is the same for electrical and thermal transport[11].  A t temperatures, T > Op, electron-  phonon scattering is the major process involved. A t these temperatures the wave vectors k, of the electrons, and q, of the phonons are comparable in magnitude. T h i s gives rise to an inverse relationship between mean free path and temperature:  (2.6)  l = M k -^ 6  a  Where M  a  B  is the atomic mass. A t low temperatures, where impurity scat-  tering dominates, the mean free path is constant, and therefore the electron thermal conductivity has a linear dependence on temperature.  Phonon thermal conductivity depends heavily on b o t h the wavelength of the phonon and temperature, as well as the type of scattering mechanism. A t high temperatures the phonons are chiefly scattered by other phonons, so-called U m k l a p p processes, giving rise to a T  - 1  i n K(T).  relation. A t lower  temperatures, T <C #D, where phonons are rare, crystal impurities have the greatest effect on the thermal conductivity. In this temperature regime long wavelength phonons are more likely to be excited. A s a result planar defects affect the conductivity more than point defects do.' Therefore, we need only concern ourselves w i t h the types of impurities and their respective densities. Depending on the type of impurity, different temperature dependencies are found. Table 2.1 shows the relation between several types of impurities and their effect on the temperature dependence of the thermal conductivity.  Chapter 2.  Background  9  Temperature Dependence of K(T)  Impurity G r a i n Boundaries  rp2  Dislocations  -i  Point Defects  T  Table 2.1: Temperature dependencies of phonon thermal conductivity for various types of crystal impurities [12]  Impurities also play the major role when their densities are quite high, as i n alloys. Stainless steel is typically comprised of iron w i t h 11% chromium along w i t h a variety of other elements, ( C , M n , M o , N i , S i , T i ) , at 1% or less. In treating the thermal conductivity of stainless steel, one can think of it as a metal w i t h a very large number of impurities.  Due to the high  density of impurities, the thermal conductivity becomes comparable w i t h the electronic component. A t low temperatures, there is most predominately a linear dependency.  For intermediate temperature ranges, all scattering  mechanisms can play significant roles lending to a nearly constant value from T = 150 K to T = 300 K . Above these temperatures a T  A  relationship is  seen, w i t h a < 1. F i g . 2.2 shows the thermal conductivity of stainless steel as a function of temperature.  Heat Transfer Through Solids T h e heat flow, Q, along a solid of cross-section, A , under the influence of a temperature gradient,  is given by:  Q = (T)A f K  d  (2.7)  10  Chapter 2. Background  0  50  100  150  200  250  300  Temperature, K  350  400  Figure 2.2: T h e r m a l conductivity of stainless steel  Where K(T)  is the thermal conductivity of the material as a function of  temperature, and A , its cross-sectional area. If its ends are at temperatures T2 and T i respectively, and is of length, I, w i t h uniform cross-sectional area, then the equation can be rewritten as:  Q=Y  l  r  JTI  <) T  dT  (-) 2 8  T h e above equation will be used later on to establish the proper ratio of area to length needed for the temperature ranges of the thermal bridges between the cold head and sample stage, as well as calculating the amount of heat conducted along any leads into the sample.  Chapter 2. Background  2.2 2.2.1  11  III-V Semiconductor Crystals Sample Growth  Semiconductor compound crystals are grown on site by Molecular B e a m E p i t a x y ( M B E ) onto semi-insulating G a A s wafers under ultra-high vacuum ( U H V ) conditions. T h e underlying G a A s substrate first needs to have the surface oxide removed. T h i s is done by heating the substrate to about 600 °C w i t h a n arsenic flux. A buffer layer of G a A s is then grown o n t o p of the oxide free substrate on which is grown the G a N A s semiconductor crystal. T h e buffer layer is necessary to cover the roughened condition of the original surface from which the oxide was thermally removed.  E p i t a x i a l growth of the III-V semiconductor compounds by M B E is carried out under group-V rich conditions. T h e larger vapour pressure of these elements places excess group-V atoms on the surface available during growth. For this reason the growth is controlled by the amount of the g r o u p - I l l available. T h e diffusion length of the g r o u p - I l l atoms along the surface is determined by the substrate temperature, growth rate, and step density. Higher substrate temperatures allow for greater diffusion, a n d leads to smoother surfaces. B u l k G a A s samples are grown w i t h substrate temperatures i n the range 400 °C to 620 °C. T h e best samples are grown at the higher end of this range. Using growth temperatures below this range leads to films that are non-stoichiometric, w i t h excess A s incorporated into G a sites or interstitially degrading the material properties [5]. T h e G a / A s flux ratio is kept slightly greater than 1 during growth, this allows for a 2 x 4 reconstruction. In this  Chapter 2. Background  12  reconstruction the surface unit cell lattice parameter is twice that of the bulk along [Oil] and four times as long along [Oil].  Nitrogen Incorporation The growth of G a N A s i _ x  x  requires conditions different from those used to  grow simple G a A s . A n R F plasma source developed by Adamcyk[6] produces the nitrogen atoms for the growth process. M o r e or less nitrogen is present in the chamber by raising or lowering the flux by changing input pressure to the plasma source. A s was stated, the growth rate is limited by the arrival of the g r o u p - I l l atoms. Furthermore the amount of N incorporation is inversely proportional to the growth rate [5] for constant substrate temperature. Surface desorption of nitrogen has an activation energy of 2.1 eV[5], so for a substrate temperature greater than approximately 550 °C very little nitrogen is found i n the crystals [6]. There exists also some competition between group-V elements, N and A s , for incorporation i n G a N A s i _ . x  x  It  is therefore advantageous to have a low A s flux during growth to allow for more nitrogen incorporation. A simple empirical relation exists between the nitrogen concentration, [N], and the fluxes[6]:  [N] = ^  ,  (2-9)  Where F indicates the flux of the subscripted element. Nitrogen incorporation is slightly more sensitive to the A s flux for higher growth temperatures [6], Samples are also grown either w i t h or without bismuth used as a surfactant. The effect of the B i surfactant on nitrogen incorporation and material properties is still under investigation.  Chapter 2.  Background  13  GaAs  GaAs Buffer Layer  300nm 300nm  GaAs Buffer Layer  GaAs Substrate  350 um  GaAs Substrate  . a)l  Figure 2.3:  300nm - — lOnm QW 300nm  350 um  Cross-sections of a) bulk G a N A s i _ x sample and b) a single x  quantum well sample Nitrogen content varied from 0% to 0.67% in the samples studied here. To date, samples.with concentrations as high as 4% have been grown on site. It is possible to grown crystals w i t h higher nitrogen concentrations, however cracks and dislocations form above the critical thicknesses[4]. T h u s , samples need be grown thinner to prevent these defects. F i g . 2.3 shows the structural cross-sections of the crystals investigated i n this thesis.  2.2.2  Band Gap Bowing  W h e n growing alloyed semiconductors, it is important to know how the band gap of the material is affected by the concentrations of the various elements. B o t h the band gap and the lattice constant are changed as the composition of the material changes.  A s more and more A l is added to  A l G a i _ A s , w i t h x varying from 0 (pure G a A s ) to 1 (pure A l A s ) , the band x  x  gap and lattice constant both increase. T h e band gap as a function of lattice constant is shown pictorially in fig. 2.4, w i t h the above example shown w i t h a dashed line. Insofar as the band gap of an alloyed material is concerned the variation of the band gap w i t h composition can be approximated by a simple parabolic function[13]. Ef (x) B  = xE% + (1 - x)Ef  - bx(l  - x)  (2.10)  Chapter 2. 4 |—i—i—i—|—i  Background  14  1—i—|—i—i—i—|—i—i—i—|—i 1—i-—|—i—i  r  GaN 3  -  5.0  :  5.2  5.4  5.6  5.8  6.0  6.2  Lattice Constant (A)  Figure 2.4: B a n d gap as a function of lattice parameter for various semiconductor compounds  Superscripts A and B designate the constituents of the alloy, x is the composition, and the constant b is known as the bowing parameter. For G a N A s i _ , x  A is G a A s and B is G a N ; E  G a J V  = 3.4 e V and E  G a A s  x  = 1.412 e V . T y p i c a l l y  the bowing parameter takes on values of only a fraction of an e V for most III-V alloys. G a N A s on the other hand, has been discovered to have an large anomalous bowing parameter[16]. for G a N A s i _ x  x  the bowing parameter has  been fit to the following equation:  b = b + bieo^ms + b e^k Q  2  (2-H)  T h i s bowing results in the band gap being related to the lattice parameter by the curve shown by the dotted line in fig. 2.4. Note that for a range of nitrogen incorporation, the alloy has a negative band gap and therefore acts as a metal.  Chapter 2. Background  2.3  15  Temperature Dependence of the Band Gap  To derive the temperature dependence of the photoluminescence, it is i m portant to first know how the band gap changes w i t h temperature. T h i s shift i n the relative positions of the conduction and valence bands is due to two main mechanisms: 1) a change i n the lattice parameter w i t h temperature and 2) a temperature dependent electron-lattice interaction. T h e former gives rise to a linear temperature dependence for high temperatures, contributing only a fraction to the total shift i n band gap i n this temperature regime. A t low temperatures the thermal expansion becomes a non-linear function of temperature. T h e latter effect, due to electron-phonon interaction, is the major contributor to the shift seen i n the band gap. It has been shown that this leads to the following temperature dependence: AE (xT , 2  g  AE <xT, g  for  T < 0  D  (2.12a)  for  T » 0  D  (2.12b)  A fit based on the above dependencies gives that for a given temperature, the band gap of a material, E (T), g  E (T) g  can be given by: (2.13)  = E (0) - 2^g  T h e above empirical formula is known as the Varshni expression[18],  E (0) g  is the T = 0 K band gap energy, and 7 and (3 are constants for the material. T h e constant (3 is related to the Debye temperature, 9 . Table 2.2 gives the D  parameters for G a A s and G a N .  Chapter 2. Background ™ meV . '> K  P, K  GaAs  0.5408  204  344  GaN  .939  722  614  0, D  16  K  Table 2.2: Varshni fit parameters from literature, GaAs[15] and GaN[17], as well as 9D  An expression w i t h a more obvious physical significance c a n be used, proportional to the Bose-Einstein occupation of a single phonon mode[19]. (T)  Eg  = a - b ( l + ^—) V e T — 1/  (2.14)  Where 0 B is the average frequency for b o t h optical and acoustic phonons, b represents the strength of the electron-phonon interaction, and (a-b) gives the band gap at T = 0 K .  2.4  Photoiuminescence  Photoiuminescence spectroscopy is a non-destructive, contactless method of investigating the electronic structure of a material. Light incident on a sample, typically a laser or some other intense light source of a fixed wavelength, optically excites the electrons.  A s an electron falls back into the  lower energy states, some of its energy is released i n the form of radiation. T h i s is i n t u r n collected by a detector to be analyzed. T h e spectrum of the emitted photons contains information about the electronic structure of the material. T h e process of relaxing back to the lower energy bands is called recombination.  Chapter 2.  a)  17  Background  b)  c)  Figure 2.5: Recombination processes from conductio band to valence band: a) P h o t o n emission, w i t h u\ < v , b) P h o n o n emission, and c) 2  Auger effect  A s the material returns to equilibrium, recombination processes affect the amount of luminescence. It should be noted that de-excitation can result from several different recombination processes. Shown i n fig. 2.5 are photon and phonon emission, as well as the Auger effect.  Emission of photons of  energy at the conduction band edge, hi/i,  are more likely to occur t h a n  emission of photons w i t h higher energy, hu .  T h e higher energy photons are  2  a result of thermal excitation above the band m i n i m u m , giving rise to a t a i l in the photoluminescence spectra, proportional to k g T . Phonons are emitted when the decaying electron interacts w i t h the surrounding atoms and excites a vibrational mode in the lattice.  P h o n o n emission is typically associated  w i t h defects or impurities i n the material which tend to give states inside the band gap. B o t h photon and phonon emission are unavoidable recombination processes, they are a result of the existence of energy bands. T h e Auger  18  Chapter 2. Background  effect is a result of an electron-electron interaction, the recombining electron gives .its energy up to another electron in either the valence (not shown) or conduction band. Electron-electron collisions w i l l occur more frequently for larger carrier concentrations.  T h e efficiency of the photoluminescence  of a material depends on the lifetimes of the excited state w i t h respect to both radiative and non-radiative recombination processes. In practice, the efficiency of the radiative recombination processes can be quite low if there are competing non-radiative processes.  T h e strongest radiative transition in semiconductors is the one where an electron falls back into the valence band from the conduction band.  The  energy difference between the two bands is known as the band gap, E . P L s  experiments therefore, permit a direct measure of the band gap of a semiconducting material. A t the same time the emission spectrum gives information about impurity levels, the presence of defects, recombination mechanisms, and material quality. Non-radiative recombination is associated w i t h localized defect levels, which are themselves associated w i t h poor material quality or impurities. Therefore, a material grown under certain conditions can be compared w i t h a similar material grown under slightly different condition to test the effect of growth conditions on the overall material quality. Also, changing the sample temperature during P L measurements can give more information on the recombination processes than simple room temperature or constant temperature experiments. First of a l l , there is a large increase i n efficiency of the luminescence at lower temperature. Furthermore, practical use may be made of the knowledge of how the band gap shifts w i t h tern-  Chapter 2. Background  19  perature to produce a variable wavelength source. O n the other hand, the lack of a shift could be useful i n the production of highly temperature stable devices.  i  Chapter 3. System Design and Operation  20  Chapter 3 System Design and Operation Previously there existed no set-up t o perform low and variable temperature experiments to characterize the semiconducting crystals grown on site. T h e following chapter discusses the design of such a device. Emphasis was placed on creating a system that was simple, efficient, and able to do a number of different experiments. It was therefore necessary t o consider optical access for photoiuminescence, taking into account any extra heating caused by the viewports, size constraints imposed by the available magnet set-up for H a l l measurements, and most importantly the ability to control temperature over . a large range, 10 K to greater than 300 K .  3.1  CTI Model 350P CryoCooler System  T h e cryogenic cooling system was built u p from an existing C T I model 350P closed cycle helium refrigerator, originally used as a cryopump. It consists of three main parts: a compressor, drive unit,, and the displacer unit, inside of which are the regenerators. Shown i n fig. 3.1 is a schematic of the system, along w i t h a more detailed view of the displacer unit.  Consider-  able time was spent by the author, w i t h help from J . M a c K e n z i e , repairing/replacing several components of the refrigerator unit before the system  Chapter 3. System Design and Operation  21  was operational. T h e displacer is comprised of a coiled mesh (regenerator) of high heat capacity material wrapped i n a phenolic shell.  G a s that en-  ters the cylinder first passes through the regenerator i n the lower portion of the displacer, out into the open space above arid then into, through a n d back out of the second element of t h e displacer. T h e large specific heat of the regenerators allows them to hold the temperature of the last cycle, thus the gas is cooled to the temperatures of the respective cold stages. A pair of seals, O-rings, prevents the cooled gas from escaping back through the cylinder outside of the regenerators. T h e advantage of such a set-up is that it .allows more freedom i n the design of a interfacing apparatus, particularity w i t h respect to size and accessibility, otherwise unavailable when using conventional liquid helium as a coolant (i.e. dip probes or flow cryostats). Another consideration for low temperature application is cost of the coolant. In the closed cycle set-up, little or no helium is lost during a typical r u n of the experiment.  3.1.1  Closed Cycle Refrigeration  Cooling of the two low temperature stages is done by successively compressing and expanding helium gas. High pressure gas enters the cylinder from the compressor passing through the displacer a n d regenerators v i a the inlet valve, fig. 3.2a. Shown i n fig 3.1 is a cross-section of the displacer unit. Gas entering through the inlet valve passes into the first component of the displacer through openings on its bottom face. It is then cooled by passing through the regenerator before exiting and moving on to the next unit. T h i s unit cools the gas further on its way to the inner surface of the second cold  Chapter 3. System Design and Operation  O-ring  Figure 3.1:  22  Phenolic  Model 350P C T I Cryocooler, and cross-section of the displacer unit  stage. Any gas that does not move into the second unit remains behind to cool the first cold stage. The gas then leaves by the same path through the displacer and out by the escape valve. The system of valves is timed with the movement of the displacer unit. When the gas enters the cylinder the displacer is on its way down nearing the bottom of its cycle (define bottom as fully retracted), the gas passes through the regenerators inside the two units of the displacer into the spaces left between the displacer and the cooling stages. As the gas passes through the regenerators it is cooled to a tern-  Chapter 3. System Design and Operation  23  perature slightly warmer than the temperature achieved by the previously expanded gas, warmed due to the heat load on the system. The inlet valve closes as the displacer reaches the bottom of its cycle, fig. 3.2b. On the subsequent up stroke the gas is compressed, fig. 3.2c. The escape valve opens during the up stroke and the gas is allowed to expand to the low pressure line of the compressor, cooling the regenerators as it leaves, fig. 3.2d.  Figure 3.2: Cryocooler displacer unit cycle  Cylinder Specifications Outside of the cylinder there are three interfacing surfaces, the lower flange at room temperature and the two cooling stages. These are connected by an alloy of low thermal conductivity, most likely stainless steel or a similar material. The stages themselves are made from a material of high thermal conductivity and specific heat, for uniformity and stability of temperature in the cooling stage. The vacuum chamber is mounted to the lower flange. Surface area on the inner side of the chamber was kept to a minimum to keep radiative heating from the chamber low. The first cooling stage is used  Chapter 3. System Design and Operation  24  for mounting the heat shield, and a discussion of its function w i l l follow i n section 3.2.2. T h i s stage operates at a temperature of approximately 60 K—> 77 K . T h e uppermost cooling stage holds the sample mount components, and typical temperatures range from 6 K to 10 K . T h e final temperature of either stage depends on the heat load imposed by the attached apparatus. Cooling time for the second stage, as quoted by the operation manual, is approximately 45 minutes and plus an additional 7 — 8 minutes per kilogram of load attached to the second stage [21].  3.2  Heating and Cooling Considerations  Before the design was finalized a l l possible heat sources and thermal links i n the set-up had to be taken into consideration. T h e system to be designed called for the ability to cool to low temperatures. Initially the goal was to achieve a m i n i m u m of 10 K—15 K , and to reach room temperature, 300 K , w i t h a great deal of control at a l l temperatures i n between. First a n d fore-" most, the thermal link from the cold head and the sample h a d to be set. Discussion on its design of the thermal link w i l l follow i n section 3.3.1. T h e temperature controller available i n the lab presently is limited to a m a x i m u m output of 3 W , thus the link was designed to remove much less t h a n this at room temperature. W i t h the main issues covered, other sources of heat had to dealt with; mechanical heating from the vibration caused by the displacer i n the cylinder, heat conducted along electrical leads to the sample, and heating from the excitation laser used for P L measurements, radiative heating from the inner surface of the vacuum chamber, and radiation through  Chapter 3. System Design and Operation  25  and from the optical viewports.  3.2.1  Sources of Heat  i) Mechanical Heating Significant heating can occur as a result of an experiment otherwise thermally isolated, being mechanically coupled to structure which is itself v i brating. A s the displacer cycles the helium coolant to a n d from the cooling stages, some minor heating can occur at the sample stage. Typically, heat linput from mechanical vibrations are only a serious problem for liquid hel i u m temperatures, 4.2 K and below. However, some consideration should be given to this issue beause of the relatively large vibrations of the cryocooler. T h e compressor can be set to r u n the drive unit i n one of two modes, 50 H z and 60 H z . T h e former was chosen as'the displacer runs at a lower frequency i n this case approximately 1 H z , compared w i t h 1.2 H z for the latter. T h e amount of heat input from a vibrating system is directly proportional to the frequency of the vibration, the effect being less at higher temperatures. Such heating should not prove to be problematic for the temperatures achieved w i t h the cryocooler.  A n y other vibrations of the cryostat caused by out-  side sources are kept to m i n i m u m by having it securely, anchored to a large aluminum plate.  ii) Electrical Leads T h i n brass wires are used for the electrical leads i n the system.  They  extend from the electrical feed through i n the chamber, at r o o m temperature,  Chapter 3. System Design and Operation  26  to the sample, at a m i n i m u m temperature 6 K . Brass is used since as an alloy, the thermal conductivity is significantly lower t h a n that of a pure metal. A l l the wires are insulated a n d i n addition r u n inside small teflon tubing, for safety; as a result it is very difficult to properly thermally anchor the leads to a heat sink to prevent heat input along the wire due to the extremely poor thermal link across the teflon. However, a worst case scenario calculation, using equation 2.8, w i t h the greatest possible temperature gradient T\ = 300 K to T = 6 K yielded the total heat flow along the leads t o be on the 2  order of 10 m W .  A n o t h e r source of heat input associated w i t h the connecting electrical leads is resistive losses i n the wires, which gives rise to a heat input Q = I R. 2  A  typical current used for resistivity and H a l l measurements is o n the order of / i A ' s , and the corresponding heating is on the order of few n W  iii) Photoluminescence Excitation Laser A 1046 n m laser source pulsed at 200 H z , frequency doubled w i t h roughly 10% efficiency to 523 n m is used to excite the sample for photoluminescence measurements, giving a total of 3 —> 5 m W incident on the sample. T h e amount of heat input from, the excitation laser is too small to be noticeable to the performance of the cryostat or to affect the average temperature of the sample. However, some thought had to be put toward how this heat i n put affects the sample temperature locally. A simple calculation of the local heating of the sample at the site of the beam gave the m a x i m u m temperature rise induced by the laser to be approximately 10 m K . T h i s should not  27  Chapter 3. System Design and Operation  affect the sample characteristics dramatically and is less t h a n the accuracy warranted by the experiments being performed, and we can therefore ignore this effect.  v) Radiative Heating B y and large, the most problematic source of heat is due to the radiation of the materials present inside the vacuum chamber, included the interior walls of the chamber itself and the optical viewports.  A perfect black body may be defined as any body which absorbs a l l radiation falling upon it, and for such a body the absorptivity and emissivity are 1. T h e total radiant heat energy emitted by a black body per second per unit area is given by:  E = oT  (3.1)  4  Where a is Stefan's constant, having an experimental value of 5.67x 1 0 ~  8 m  ^- 4  W h e n any two surfaces of different emissivities, E\ and £2, are exposed to one another the t o t a l amount of heat energy transfered from the higher temperature surface can be expressed as: Q = oA(Tt-n)  £  l  £  \  (3.2).  Most metals have low emissivities, 0.01 —> 0.6, depending o n the quality ;  of the surface, and non-metallic materials can approximate to black bodies having emissivities of 0.9[20] or higher.  Some intelligent guess work is required when estimating the radiant heat from the surfaces, b o t h for surface condition and approximating actual radia-  Chapter 3. System Design and Operation  Table 3.1:  28  Material  Emissivity  Copper  0.02 (polished) -> 0.6 (highly oxidized)  Aluminum  0.05 ( p o l i s h e d ) ^ 0.31 (highly oxidized)  Quartz  0.9  Emissivity values for the materials located inside the vacuum chamber[12]  tive surface area impinging on the sample mount. For the calculations of the • amount of radiant heat the area of the inside of the chamber as seen by the sample mount can roughly estimated to be comprised of 75% quartz and 25% aluminum. T h e sample mount itself is approximated by a copper surface w i t h total exposed area of 100 c m . In the worst case, 2  E Q  U  A  R  T  Z  =  0.9,  EAI =  0.31,  and ecu = 0.6. T h e calculation states that approximately 2.2 W of thermal radiation flows into the sample mount; for the best case eQ  uartz  e  Al  = 0.05, and ec  u  = 0.9,  = 0.02, approximately 0.1 W is found. For this reason  it was necessary to consider an intermediate thermal shield, a n d this is the topic of the next section. R a d i a t i o n other than that emitted from the internal surfaces, such as radiation from the environment passing i n through the viewports, was considered insignificant i n comparison.  3.2.2  Heat Shield  A s illustrated above the sample stage requires heat shielding between it and the inner walls of the chamber and the viewports, i n order to achieve the desired low temperatures.  A simple design for the heat shielding was  Chapter 3. System Design and Operation  29  developed consisting of a length- of copper tubing capped a n d surrounding the sample mount anchored to the first cold stage.  T h e first cold stage  operates at approximately T = 60 K —> 77 K . Keeping i n m i n d the need for optical access to the sample, two shields were designed; one w i t h optical access, the other without. T h e amount of heat radiated to the sample from the shielding, T hi id%n = 77 K , i n place was 17 m W for the worse case s  e  g  (ecu — 0.6) a n d 0.4 m W for best case, (ec  u  = 0.02).  For optical access, three holes were included i n the design, two smaller holes (0.45") 180° to the sides of the sample meant for i n p u t / o u t p u t of the P L laser and one larger hole (0.75") i n front for both laser i n p u t / o u t p u t and the P L output. W h e n the sample was first cooled w i t h no modification to the thermal link, the lowest temperature achieved was 65 K . Modifications to the thermal link, described later i n section 3.3.1, were made i n order to compensate for the extra radiation passing through these holes.  3.2.3  Modeling the Sample Mount  In order to have an idea of how the system would perform a number of small simulations were r u n modeling the cooling a n d re-heating of the sample stage. A n y system of heat sinks, sources, and thermal links can be modeled by an equivalent electric circuit[22]:  resistors for thermal links, capacitors  for heat sinks, and power supplies for heat sources. Temperature of the components i n a thermal system reacts to changes i n the flow of heat energy much i n the same way the elements of an D C electric circuit do for changes of voltage. Shown diagrammatically i n fig 3.3 is the equivalent circuit for  Chapter 3. System Design and Operation  30  the cryostat sample stage where the capacitor, C , is derived from the specific Sample Stage  O  Thermal Bridge  Mounted to Coldhead  O  Figure 3.3: Electric circuit model of sample mount.  heat capacity of the copper sample stage a n d heater block, the resistor, R, is related to the inverse of the thermal conductance along the stainless steel tubing, and the current souce, I, is equivalent to the input heat from the heater.  T h e cold head acts as a ground for the thermal circuit, w i t h the  following equations relating the equivalent components:  C  =  R G  (3.3a)  mC (T) v  ( T — Tfcase) G l  =  j(T-T y  l  base  (3.3b)  1  [  (3.3c)  K(T')dT'  Where the thermal conductivity of stainless steel can be closely approximated by: (T)  K  = - 0 . 4 7 1 2 7 + 0.1428T - 5.1049 x 1 0 ~ T + 6.5181 x 1 0 " T 5  2  7  3  (3.4)  T h e amount of power, P i , flowing from point T ( = temperature of the sample stage), to ground is equal to the negative of the power, P > across the 2  Chapter 3. System Design and Operation  31  capacitor. Px  =  - P  Pi  =  rnC (T)^  (3.5b)  P  =  i  (3.5c)  2  (3.5a)  2  v  /  T K  (T')^r'  To find the temperature, T , at any given time, t, we simply need to solve the differential equation:  dT  A  dt  I mC hr\ ± ) i vK ) JT vK  K { T  J T b a s e  '  ) d T  '  ( 3  -  6 )  1  ba3e  A n analytical solution was unattainable due to the complex nature of the right hand side of the equation 3.6.  It was therefore easiest to allow a n  iterative computer simulation to solve it. Codes were written, w i t h much help from A . Ballestad, to calculate the cooling curves for several different ratios of area to length. Shown i n fig. 3.4 are the cooling curves for two of the thermal bridges currently in use. B o t h cases are shown w i t h the extra radiation from the optical access i n the heat shield. W i t h o u t the optical access a base temperature of 6 K is reached i n the model.  It was discovered that the added heat load due to the openings i n the heat shield, along w i t h the upper limit o n the power output by the heater constrained the range of attainable temperatures. For certain ratios of A to I the system is unable to reheat the sample to room temperature. Table 3.2 shows the lower and upper temperature limits and the corresponding ratio. In order to have the m a x i m u m possible temperature range, two set-ups are needed. T h e ratio of 3.278 x 1 0  - 4  m allows for a m i n i m u m temperature of  Chapter 3. System Design and Operation  i 0  , 100  i 200  i 300  Time, min  i 400  1 500  32  1 600  Figure 3.4: M o d e l of the cooling of the sample stage for b o t h thermal links, solid line f = 4.233 x 1 ( T m , dashed line f = 3.35 x l C T m 4  3  65 K and a max of higher than 300 K . A second arrangement w i t h a ratio of 3.35 x 1 0  3.3 3.3.1  - 3  m allows sufficient overlap a n d a m i n i m u m temperature of 25 K .  Sample  Mount  Thermal Bridge  A t the heart of the design of the cryostat is the thermal bridge between the coldhead and the sample stage. T h e amount of heat that can travel from the sample stage and the cold stage is governed by the thermal conductivity, K(T) (see equation 3.4,) of the stainless steel tubing that runs between them. T h e ends of the stainless steel tubing are soldered to copper interfacing pieces. These can be assumed to be temperature boundary points,  T  i  samp  e  Chapter 3. System Design and Operation Low Temperature ( K )  Upper limit ( K )  I (inches)  25  200  0.35"  40  300  1.18"  65  300+  2.15"  33  Table 3.2: Temperature ranges of various thermal.links made from g" O . D . stainless steel tubing, wall thickness 0.040"  and T idhead- T h e heat that travels along any solid under the influence of a co  temperature gradient is given by equation 2.7. Since the temperature controller being used has a m a x i m u m output of 3W,  the thermal bridge was  designed to have a m a x i m u m heat flow of 1 W for T = 300 K and T i = 6 K . 2  Using equation 2.8 a ratio of area to length of the compatible bridge can be found, i n this case y = 3.378 x 1 0  - 4  m. T h i s was accomplished using  0.375" outer diameter stainless steel tubing, of thickness 0.040", and having a length of 3.1".  Modification for P L A s previously mentionned, the ratio of area to length had to be re-calculated, to remove the extra heat load from the radiation passing through the optical ports in the heat shield. T h i s was simply done by shortening the thermal bridge from 3.1" to 0.35". See table 3.2 for the upper and lower bounds of temperature imposed by these ratios. A copper clamp is used to accommodate this. B y having it well thermally anchored to the cold head and thermal bridge, it shortens the effective thermal link. It is possible to increase the  Chapter  3. System Design and  Operation  34  Sample Mount  Heater Block  Thermal Bridge  Figure 3 . 5 : Cryostat sample stage  upper temperature bound by simply having a temperature controller of a larger output power.  However the cooling power of the cold heads would  then have to be taken into consideration, see diagrams i n appendix B . T h e cooling power of the second stage is a function of b o t h its own operating temperature and the operating temperature of the first cold stage. In other words if too large a heat load is applied, the base temperature of the coldhead will be compromised.  3.3.2  Heater Block and Sample Stage  Heating is accomplished by means of a 33 Q resistor inside a copper cylinder of sufficient thermal mass as to allow for stability i n temperature i n the  Chapter 3. System Design and Operation  35  sample stage. T h e resistor is placed i n the center of a hollowed portion of the cylinder, held i n place, electrically insulated, a n d well thermally linked to the copper by sapphire laden epoxy. T h e r m a l expansion of the epoxy is well matched to that of the copper, It is expected that the thermal cycling w i l l eventually cause a break down i n the epoxy, or i n its connection to the copper. A n y such defect, cracks or separation from the copper surface, w i l l dramatically effect the performance of the heating stage. T h e heater block is thermally linked to the top end of the thermal bridge w i t h a t h i n layer of indium, a n d by a thermally conductive compound to the sample stage.  Crystals are mounted on the sample stage, the top most component of the entire sample mount, held i n place by the aforementioned thermal compound. T h e stage has a 600 /xm thick wafer of oxidized silicon on its face w i t h 8 electrical contact pads, and again the thermal compound is used to thermally link the pieces. T h e contact pads were grown by E-beam evapouration, first a t h i n layer, 30nm, of chromium is wetted to the surface and then 200nm of gold is grown. T h i s electrical contact wafer is unnecessary when P L measurements are being performed. D u r i n g P L the crystals are simply placed on a small piece of copper shim, which is itself placed on the face of the sample stage.  3.4  Thermometry and Temperature Control  F i x e d to the rear face of the sample mount is a diode thermometer, held stationary w i t h a narrow band of copper shim, which is lined w i t h thermal compound. T h e diode is positioned directly opposite the sample, and is well thermally connected to the sample mount i n order to achieve the most ac-  Chapter 3. System Design and Operation  36  curate reading of the temperature as possible. Diode thermometry is based on the temperature dependence of the forward bias drop across the p-n junction. A constant current of lOpA is r u n through a calibrated diode and its voltage measured. T h e forward bias voltage as a function of temperature is shown i n fig. 3.6. Calibration was carried out inside a S Q U I D device for a temperature range of 6 K < T < 300 K , w i t h an overall accuracy of ±0.25 K . Some thermal drift is to be expected i n the diodes, therefore the diodes are required to be replaced from time to time. Diodes will be routinely checked against original calibration data for selected temperatures, T = 77 K and  T = 273 K .  Temeprature (K)  Figure 3.6: Calibration curve of a silicon diode  In order to control the temperature of the sample stage the diode thermometer is connected a non-commercial temperature controller, manufactured by the departmental electronics shop at U . B . C . A reading from the diode is compared to a referenced voltage, corresponding to the voltage of  Chapter 3. System Design and Operation  37  the desired temperature, and the output of the heater is adjusted accordingly. T h e temperature controller uses proportional and derivative control feedback circuitry to adjust the heater output to the sample mount.  3.5  Vacuum Chamber  Everything is housed inside an aluminum vacuum chamber, equipped w i t h the necessary electrical, optical,, and vacuum feed throughs. T h e chamber is comprised of two pieces, an upper and a lower segment. T h e lower portion reaches up to just above the first cold stage. It was designed as a simple cylindrical chamber fixed w i t h the necessary electrical and vacuum feed throughs. Another valve, also on the lower portion of the chamber, is used to let i n dry nitrogen when rapid reheating of the cold stages is desired. A n O-ring is used to maintain the vacuum seal between the base flange of the cryocooler cylinder, as well as between the sections of the chamber. T h e upper half of the chamber is designed to have as little inner surface area as possible, to lower radiative heating from the chamber to the cold stage a n d heat shield. Quartz was chosen for the optical viewports for its. broad transmission spectrum. T h e viewports are positioned at the top of the of the upper portion of the chamber. T h e windows are 50.4mm i n diameter, allowing for a m a x i m u m incident angle of 26° through the front window and a m i n i m u m incident angle of 64° through the side windows. Another set-up of the windows has been designed. These are smaller i n size and inset into the chamber to be closer to the sample, and subtend approximately the same solid angle as the larger windows.  Chapter 3. System Design and Operation  38  To p u m p the system down, a combination of a mechanical scroll p u m p and a molecular drag pump is used initially.  However as the cold stages  cool, predominately the second stage, the system begins to p u m p itself more effectively than the roughing pumps.  A t this point the rough pumps are  valved off until the coldhead is to be reheated after the experiment is finished.  Chapter 4. Temperature Dependence of PL  39  Chapter 4 Temperature Dependence of PL 4.1  Experimental Set-up  W h i l e the cryostat is outfitted to perform several different types of characterization experiments, only P L measurements w i l l be discussed i n the following chapter. A s was described earlier i n section 2.4, photoiuminescence experiments are carried out by first optically exciting the electrons a n d then collecting the emitted photons from the recombination process. Shown i n fig. 4.1 is the current optical set-up i n use. Presently two lasers are used to excite the sample: a pulsed 523nm (green) laser a n d a continuous wave 633nm (red) helium-neon laser. Reasons for this w i l l be given later on. Laser light from the green laser is first passed through a filter, f l , to remove any unwanted 1046 n m beam that does not get frequency doubled.  T h e now  filtered 523 n m beam is directed, as shown, to the sample by the system of mirrors, m l a and m2, and a prism. T h e red laser beam is directed to m2 and the prism by mirror m l b . Redirecting the beam to the sample w i t h a small prism is done i n order to block as little of the emitted photons as possible reaching the detector. To this end, the prism sits atop a t h i n steel r o d of similar cross-sectional area, which blocks only a fraction of the emitted radiation. After the prism, the beam passes through the approximate  Chapter 4. Temperature Dependence of PL  40  Figure 4.1: Schematic of the P L optical set-up  center of the collecting lens, L I , which is placed at its focal length away from the sample. Before hitting the sample the beam has to pass through a 2" diameter 0.25" thick quartz window. T h e relative positions and orientations of the mirrors and prism are adjusted so that any specularly reflected beam is returned to the laser.  E m i t t e d photons are collected into a horizontal beam by a plano-convex lens, L I (plane side to the sample), as wide as the lens face (~ 2 " , 50.4mm), and sent to the focusing lens, L 2 , also a plano-convex (plane side towards the detector). T h i s lens focuses the beam of emitted radiation to the input coupler of the fiber bundle from the detector, which is placed at the focal point  Chapter 4. Temperature Dependence of PL  41  of the focusing lens. Positions of the lenses and fiber bundle are adjusted to maximize the signal received, a 3-axis stage is used to maneuver the fiber bundle. A reference sample of strong, well-known P L is used as a measure of the optical through-put, and to check the alignment of the fiber bundle. T h e current set-up has comparable measured intensities to those of the old P L set-up where the fiber bundle was placed very near, ~ 1cm from the,sample. T h e fiber bundle is connected to an A c t o n Spectra P r o 300i spectrometer. Currently it is equipped w i t h two gratings, 150 ^ and 600  T y p i c a l l y the lower ^  (groves per millimeter),  grating is used because it has a much  wider wavelength range, this gives a resolution of approximately, l . l n m .  An  I n G a A s linear photo diode array ( P D A ) is used i n collection of the signal.  4.2  Experimental Results  A s the samples are cooled the energy of the emitted photons shifts to the blue as expected. Cooling also results in sharper peaks and an increase i n intensity. Blue shifting of the band gap energy approximately follows the description given i n section 2.3. T h e band gap corresponds to the energy of the peak i n the photoluminescence. T h e increased intensity and decreased w i d t h is due to the decrease i n the thermal linewidth w i t h lower temperatures.: U p o n cooling further unexpected features begin to appear i n the luminescence spectra. A second peak, and occasionally a t h i r d peak, is observed in the luminescence spectra when the pulsed laser source is used for photoexcitation. These additional low temperature peaks appear at slightly lower energy than the band gap of the samples. Therefore they w i l l be hereafter  Chapter 4. Temperature Dependence of PL  42  referred to as in-gap peaks. T h e intensity of the in-gap peaks rises sharply as the samples are cooled below 125 K , as shown i n fig. 4.2. A b o v e 125 K the pulsed excited spectra shows only a long low energy tail.  It was found that  it was possible to observe emission from only the in-gap states by using a continuous wave ( C W ) excitation laser, as shown in fig. 4.3. A 633nm 5 m W helium-neon laser was used for this purpose. T h e shape and intensity of the in-gap peaks vary for different concentrations of nitrogen and for different growth parameters. T h e in-gap spectra are shown in fig. 4.4 for the samples whose full spectra is shown in fig 4.2.  T h e fall off at high energy of the luminescence spectra for the pulsed pump is proportional to the B o l t z m a n n distribution for the corresponding temperature. Lowering the temperature of the samples reduces the amount of thermal excitation to states above the conduction band m i n i m u m . T h i s results in sharper, more intense peaks i n the photoiuminescence. T h e slope on the high energy side of the peak for the in-gap states also shows a similar temperature dependence. T h i s suggests that electrons in these states reach thermal equilibrium w i t h the conduction band before recombination occurs. It is assumed that the low energy slope of the peak of the in-gap photoiuminescence is related to the fall off i n the density of states towards m i d gap.  T h e band gap energy of the samples tends to a constant value for temperatures below approximately 75 K , observed by a constant peak energy in the photoiuminescence spectra. F i g . 4.5 shows the band gap energy of two samples as a function of temperature, along w i t h a Varshni fit to the data. Similar results are observed for all samples regardless of growth pa-  Chapter 4. Temperature Dependence of PL  43  rameters. T h e transition temperature, where the low temperature energy limit is reached, coincides w i t h the temperature for which the intensity of the in-gap states becomes significant: refer to fig. 4.2. Above the transition temperature, the band gap appears to have a nearly linear dependence on temperature. T h i s anamalous behaviour has not been observed elsewhere in the literature for pressure dependent measurements [23]. Recall that the band gap energy also depends on the concentration of nitrogen, as described by equation 2.10. F i g . 4.6 shows the low temperature limit of the band gap energy as a function of nitrogen concentration, along w i t h a fit for the expected band gap from equation 2.10 and 2.11. T h e fit lies above the measured values of the band gap. Also note that the slopes of the fit and the experimental data do not agree.  A n increase in the overall intensity of the photoluminescence is measured when bismuth is used as a surfactant during the crystal growth process. It is also observed that some of the previously mentioned features of the photoluminescence spectra do not appear as strongly in samples where bismuth is used, as shown for example i n fig. 4.7a. Several sets of samples were measured where the only change i n the growth parameters was the introduction of bismuth.  Note that the in-gap states photoluminescence also shows a  small change w i t h C W excitation (fig. 4.7b).  F i g . 4.8 is the temperature  dependence of the band gap for one set of paired samples. Note that no change is observed in the temperature dependence of the band gap w i t h B i surfactant. These particular samples happen to have similar concentrations of nitrogen.  T h i s is not easy to achieve since the amount of nitrogen in-  Chapter 4.  Temperature Dependence of PL  44  corporation depends on bismuth flux as well as other growth parameters[5].  45  Chapter 4. Temperature Dependence of PL N atoms on G a  Energy, m e V  N atoms in C h a i n  Energy, e V  2  -90  2  -90  3  -165  3  -270  4  -260  4  -400  5  -480  6  -500  Table 4.1:  Energies of nitrogen cluster states relative to conduction band m i n i m u m [24]  4.3  Evidence for Nitrogen Cluster States  It is believed the above mentioned features in the low temperature l u m i nescence are due to the presence of randomly distributed nitrogen clusters and isolated nitrogen impurity states in the G a N x A s i - x crystals. Clusters in GaN Asi_ x  x  consist of two or more nitrogen atoms in close proximity to one  another w i t h i n the lattice. T h i s occurs when two or more nitrogen atoms are bonded to a single G a centered tetrahedron or by simply having nitrogen atoms neighbouring or near other nitrogen atoms on different G a centers. T h e neighbouring nitrogen atoms bonded to different G a centers may have a linear arrangement, i n which case they are referred to as chains.  The  assumption is made that the nitrogen is incorporated only substitutionally on A s sites a n d not interstitially. T h e small amount of interstitial nitrogen present i n the crystal maya also contribute to the in-gap states, but it is not known what the contribution is. Shown i n table 4.1 are the theoretically calculated[24] energies for the cluster states ( C S ) . T h e single nitrogen  Chapter 4. Temperature Dependence of PL  46  impurity produces a resonant state i n the conduction band approximately 150 meV[24] above the conduction band minimum. These states have been shown to be highly localized around the impurity or cluster [24] a n d have much weaker pressure dependence t h a n does the conduction band [25].  W i t h the relatively high concentrations of nitrogen i n the samples studied here, the localized states will produce a distribution of b o u n d states below the conduction band minimum, which i n t u r n gives the density of states as shown schematically i n fig. 4.9. T h e electrons i n the conduction band w i l l be in thermal equilibrium w i t h the cluster states to an energy depth, e*. T h i s means states i n the gap above e* w i l l be populated according to a B o l t z mann distribution. T h e threshold, e*, for thermal excitation corresponds to the deepest trap from which a n electron can escape during its lifetime (i.e. before recombination occurs). T h i s w i l l be referred to as the kinetic limit model[26]. In this model, e* corresponds to a demarcation energy which separates the states which are i n equilibrium w i t h the band from those that are not. T h e population of the cluster states is kinetically limited a n d governed by progressive trapping-detrapping processes. In other words, electrons have a more difficult time finding the clusters states farther below the conduction band m i n i m u m , where the states are less dense. It is also possible that the cluster states give rise to a quasi-Fermi level just below the conduction band minimum[26].  T h i s would happen if the p u m p intensity were sufficiently  strong to completely fill the cluster states up to some level, £ / . Population n  of the states i n this case is governed by the excitation intensity. B o t h models would have a distribution of occupied states similar to that shown i n fig. 4.9.  Chapter 4. Temperature Dependence of PL  47  Further investigation is needed i n order to be able to establish which model is the correct interpretation.  Recombination from electrons i n the cluster states that are not i n thermal equilibrium into the band results i n the second peak observed i n the l u m i nescence spectra. For the lower concentrations of nitrogen measured a t h i r d peak is also seen i n the spectra, leading to the belief that certain cluster configurations are more likely to form i n these crystals. T h e C W laser allows for long recombination lifetimes of the electrons through lower electron-hole pair density, therefore the excited electrons are able to thermalize deeper into the distribution of the in-gap states. T h i s results i n the spectra observed i n fig. 4.3. For increasing temperature, electrons populating the cluster states are more likely to be thermally excited to the conduction band, leading t o a less rapid variation of population w i t h temperature.  T h e single nitrogen impurity state that lies inside the band at room temperature is expected to be less temperature dependent t h a n is the C B M , based on their respective pressure dependencies[25]. Therefore, as the samples are cooled the C B M moves to higher energies approaching the energy of the impurity state. It is suspected that some of the nitrogen clusters states will move into the gap for decreasing temperature, since we expect the density of cluster states to be higher for higher energies. A t low temperatures progressively smaller clusters (next nearest neighbour dimers for example) w i l l appear i n the band gap. T h e conduction band edge may become more nitrogen-like, a n d therefore less temperature dependent t h a n the G a A s based conduction band. T h i s may explain why the temperature dependence of the  Chapter 4. Temperature Dependence of PL band gap of the G a N A s i _ x  x  48  alloys are weaker t h a n the G a A s parent material.  T h e measured differences i n the photoluminescence of samples grown w i t h and without bismuth leads to the conclusion that the introduction of bismuth during the growth of the G a N A s i _ x  nitrogen clusters present i n the material.  x  crystals reduces the number of T h e increase i n the intensity of  the room temperature P L w i t h bismuth[4] and other surfactants[7] has been previously been reported, but not explained.  A reduction i n the number  of nitrogen clusters may be expected to reduce the number of non-radiative recombination centers.  Chapter 4. Temperature Dependence of PL  49  Chapter 4. Temperature Dependence of PL  50  x 10 30K  — 27K -e- 48K  Sample R1350 [N] = 0.559% Tsub = 400 C with Bismuth  1.1  1.15  1.2  57K • 76K —B— 100K -v- 124K . 150K —  —i—  1.25  1.3  1.35  1.4  1.45  1.5  c) 2.5  x 10 —  -e.—i—  -«- B -  CD  29K 45K 57K 76K 100K 125K 150K 176K  Sample R1361 [N] = 0.34% Tsub = 430 C  co  c  CD  £  1  d) Figure 4.2: Photoluminescence spectra of bulk G a N A s i _ as a function of z  temperature for pulsed photoexcitation  x  Chapter  4.  Temperature  Dependence  of PL  51  —«- Pulsed Excitation — CW Excitation  Energy, eV Figure 4.3:  Photoiuminescence of G a N x A s i - ^ w i t h pulsed and C W excitation lasers.  T h e C W emission spectrum has been adjusted so  that the low energy fall-offs match  Chapter  4.  Temperature  Dependence of PL  52  Chapter  4.  Temperature  53  Dependence of PL  oI  i  i  i  i  i  J  1.1  1.15  1.2  1.25  1.3  1.35  1.4  1  1.45  1  1.5  Energy, e V Figure 4.4: Photoiuminescence spectra of bulk G a N A s i _ x  temperature for C W photoexcitation  x  as a function of  Chapter  4.  Temperature  54  Dependence of PL  « [N] = 0.624% * [N] = 0.536% — Varshni fit  300  Temperature, K Figure 4.5: B a n d gap Energy G a N ^ A s i - x as a function of temperature  Chapter  r  4.  i  Temperature  i  Dependence  i  55  of PL  i  i  $  Model Fit PL Data  -  -  i  * # i Y 1.34 0.3  Figure 4.6:  i  0.35  i  i  0.4  0.45  1  1  mi % 0.5  0.55  1  l  0.6  0.65  0.7  Measured low temperature band gap for various nitrogen concentrations i n G a N ^ A s i - x and expected fit  Chapter  4. Temperature  Dependence  56  of PL  w/Bismuth, R1350 w/o Bismuth, R1349 T = 30K  1.25  1.45  1.3  Energy, e V  a)  1.25  1.3  1.35  1.45  1.5  Energy, e V  Figure 4 . 7 : Comparison of the photoluminescence spectra of samples grown with and without bismuth. Pulsed excitation in a) and C W excitation in b)  Chapter 4. Temperature Dependence of PL  1.38  • o  1.37  57  w/Bismuth, R1350 w/o Bismuth, R1349  so  1.36  > o >i  E? CD C  ©o o  1.35 1.34  LU  Q. 1.33 CO  O) "O c crj  oo  1.32  CQ  1.31 1.3  °§ o  1.29  I  50  100  150  200  250  300  350  Temperature, K Figure 4.8: Energy as a function of temperature for sample with and without bismuth. The error in the band gap energy is ±0.002 eV for temperatures lower than 100 K  Chapter 4. Temperature Dependence of PL  58  a) 0.045  DOS Dist. T=30K Dist.T=100K  0.04  0.1  b) Figure 4.9: Sketch of the density-of-states for G a N A s i _ . Also shown is x  x  the expected distribution of occupied for a) various threshold energies E* relative to the conduction band minimum ( C B M ) and b) for increased temperature  Chapter 5.  Conclusions  59  Chapter 5 Conclusions A closed cycle optical cryostat has been designed a n d implementationed. It has proven to be capable of achieving the desired low temperatures. W h i l e the system that has been developed performs as well as hoped, improvements can still be made. T h e addition of a sapphire window to the heat shield would allow for even lower temperatures to be reached during photoluminescence measurements. Other small modifications could be made to improve sample turn-over time. These would improve experimental productivity. r  Photoluminescence investigations of G a N ^ A s i - x semiconducting crystals have shown evidence of in-gap states which we attribute to nitrogen clusters in the material. T h e clusters have been found to gives states w i t h energies in the band gap near the minimum of the conduction band. It is believed that these cluster states are a direct cause of the loss of photoluminescence intensity observed w i t h the incorporation of nitrogen.  Use of bismuth as  a surfactant, during the growth process, of the samples reduces the density of the nitrogen clusters. T h e bismuth surfactant increases the intensity of the photoluminescence a n d decreases the relative intensity of the photoluminescence from the in-gap states. Further investigations are warranted i n order to develop a more detailed understanding of the cluster states.' A l o n g  Chapter  5.  Conclusions  60  w i t h the emission spectra measured here, absorption spectroscopy would give an insight into the nature of the cluster states and the effect bismuth surfactant has on them. T h e addition df a tunable laser to the experimental set-up would allow for photoluminescence excitation ( P L E ) experiments to be carried out. A s always, more samples should be investigated, especially samples w i t h growth parameters different from those measured here.  The  effect of increased nitrogen content, the addition of i n d i u m and the use of other surfactants such as antimony, would also be of interest.  Bibliography  61  Bibliography [1] L A . Buyanova, W . M . Chen, and B . Monemar, M R S Internet Journal of Nitride Semiconductor Research 6, 2 (2001) [2] I. Suemure, K . Uesugi, and W . Walukiewicz, A p p l i e d Physics Letters, 77, 3021 (2000) [3] E . Strom M . S c . Thesis 2001 [4] X . Y a n g , J . B . Heroux, M . J . Jurkanovic, and W . I . W a n g , Journal of Vacu u m Science a n d Technology B , 17,1144 (1999) [5] M . A d a m c y k , S. Tixier, B . J . Ruck, J . H . Schmid, T . Tiedje, V . fink, M . Jefferies, K . L . Kavanagh, and M . Thewalt, Journal of V a c u u m Science and Technology B , 19, 1417 (2001) [6] M . A d a m c y k P h . D . Thesis 2001 [7] V . G a m b i n , W . H a , M . Wistey, S. K i m , J . S . Harris, Materials Research Society Symposium Proceedings, 692, H7.1.1 (2002) [8] S. Tixier, M . A d a m c y k , E . Young, J . H . Schmid, a n d T . Tiedje, Journal of C r y s t a l G r o w t h , 25, 449 (2003)  62  Bibliography  [9] H . Riechert, A . Y u Egorov, D. Livshits, B . Borchert, a n d S. Illek, N a n otechnology, 11, 201 (2000) [10] C . K i t t e l Introduction  to Solid State Physics 6  th  edition, 1986, W i l e y  [11] Neil W . Ashcroft a n d N . D a v i d M e r m i n Solid State Physics, 1976, Saunders [12] G u y K . W h i t e Experimental  Techniques in Low TemperaturePhysics  3  rd  edition, 1979, Claredon Press [13] G . P o z i n a , I. Ivanov, B . Monemar, J . V . Thordson, a n d T . G . Anderson, Journal of A p p l i e d Physics, 84, 3830 (1998) [14] Y . Q i u , S . A . Nikishin, H . Temkin, N . N . Faleev, a n d Y . A . K u d r i u t s e v , A p p l i e d Physics Letters, 70, 3242 (1997) [15] H . Shen, S . H . P a n , Z . Hang, J . Leng, F . H . Pollack, J . M . W o o d a l l , a n d R . N . Sacks, A p p l i e d Physics Letters, 53, 1080 (1988) [16] U . T i s c h , E . F i n k m a n , and J . Salzman, A p p l i e d Physics Letters, 81, 463 (2002) [17] H . Teisseyere, P. Perlin, T . Suski, I. Gregory, S. Porowski, J . J u n , A . Pietraszko, a n d T . D . Moustaskas, Journal of A p p l i e d Physics, 76, 2429 (1994) [18] Y . P . Varshni, Physica, 34, 149 (1967) [19] P . T . Landsberg Recombiatoin versity Press  in Semiconductors,  1991, Cambridge U n i -  Bibliography [20] R . C . Weast Handbook of Chemistry  63  and Physics  5 3 , 1973, Chemical r d  Rubber C o . [21] C T I Cryocooler Operation M a n u a l [22] Communications w i t h W . N . Hardy, D. B r o u n , a n d J . Bobowski [23] Katsuhiro Uesugi, Ikuo Suemene, Tatsuo hasegawa; T o m o y u k i A k u t a gawa, and Takayoshi Nakamura, A p p l i e d Physics Letters, 7 6 , 1285 (2000) [24] P . R . C . Kent, L Belliache, and A l e x Zunger, Semiconductor Science a n d Technology, 1 7 , 851 (2002) [25] X i a o L i u , M . - E . P i s t o l , and L Samuelson, S. Schwetick a n d W . Seifret, A p p l i e d physics Letters, 5 6 , 145 (1990) [26] Communications w i t h D r . T . Tiedje [27] E . N . Economou Green's Functions Springer-Verlag  in Quantum  Physics  2, nd  1983,  Appendix  A.  Design Specifications  of the System  64  Appendix A Design Specifications of the System In the following pages are found the design specifications for the cryostat. Shown below, fig. A.1, is a cut-away view of the entire set-up.  Figure A.1: Cryostat set-up designed for semi-conductor crystal characterization  Appendix  A.  Design Specifications  of the System  65  Appendix A. Design Specifications of the System  66  Appendix  A.  Design Specifications  of the System  67  Appendix A. Design Specifications of the System  10 —  *1  CO '  69  Appendix  A.  Design Specifications  of the System  70  Appendix  A.  Design Specifications  of the System  72  Appendix  A.  Design Specifications  of the System  77  Appendix  A.  Design Specifications  of the System  78  Appendix  A.  Design Specifications  of the System  79  Appendix  B.  Cryocooler  Cooling  Capacity  81  Appendix B Cryocooler Cooling Capacity For possible future consideration of upgrading the power input to the sample mount above the present value of 3 W , it will be necessary to consider the amount of cooling power capabilities of the cryostat. Shown i n fig. B . l as a function of both first and second stage temperature is the cooling power of the cryocooler set-up. Inputting more than the specified amount of thermal power to the cold stages will compromise the base operating temperature.  MlSf STMt tCHP.UI  Figure 1.3 Typical refrigeration capacity of the Model 22C cryodyne cryocooler (60 Hz)  Figure B . l :  FIRST SUCC fEUP.m  Figure 1.4 Typical refrigeration capacity of the Model 22C cryodyne cryocooler (50 Hz)  Cooling capacities of the C T I cryocooler for b o t h modes of operation  

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