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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 T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in The Faculty of Graduate Studies (Department of Physics and Astronomy) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A October 3, 2003 © Daniel A . Beaton, 2003 In presenting this thesis in part ial fulfilment of the requirements for an advanced degree at the University of Br i t ish Columbia, I agree that the L ibrary 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 The University Of Br i t ish Columbia Vancouver, Canada 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 pho-toluminescence 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 xAsi_ x. The clusters are shown to produce states with energies inside the band gap. It has also been found that the introduc-tion of bismuth, as a surfactant, during the growth process tends to reduce the density of the nitrogen clusters in the material. Contents i i i C o n t e n t s Abstract i i Contents • • i i i List of Tables v List of Figures v i 1 Introduction 1 2 Background 4 2.1 Materials at Low Temperatures 4 2.1.1 Heat Capacity 5 2.1.2 Thermal Conduct iv i ty 6 2.2 III-V Semiconductor Crystals 11 2.2.1 Sample Growth 11 2.2.2 Band G a p Bowing 13 2.3 Temperature Dependence of the Band Gap . . . 15 2.4 Photoluminescence 16 3 System Design and Operation 20 3.1 C T I Model 350P CryoCooler System 20 Contents iv 3 System Design and Operation 20 3.1 C T I Model 350P CryoCooler System . . 20 3.1.1 Closed Cycle Refrigeration 21 3.2 Heating and Cool ing Considerations 24 3.2.1 Sources of Heat 25 3.2.2 Heat Shield 28 3.2.3 Model ing the Sample Mount 29 3.3 Sample Mount 32 3.3.1 Thermal Bridge 32 3.3.2 Heater Block and Sample Stage 34 3.4 Thermometry and Temperature Control 35 3.5 Vacuum 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 v. L i s t o f T a b l e s 2.1 Temperature dependencies of phonon thermal conductivi ty for various types of crystal impurities[12] 9 2.2 Varshni fit parameters from literature, GaAs[15] and GaN[17], as well as 16 3.1 Emissivi ty values for the materials located inside the vacuum chamber[12] ' 28 3.2 Temperature ranges, of various thermal l inks made from | " O .D. stainless steel tubing, wall thickness 0.040" . . . . . . . . 33 4.1 Energies of nitrogen cluster states relative to conduction band minimum[24] . . 45 List of Figures v i L i s t o f F i g u r e s 2.1 Heat capacity of copper 7 2.2 Thermal conductivity of stainless steel 10 2.3 Cross-sections of a) bulk G a N ^ A s i - x sample and b) a single quantum well sample 13 2.4 Band gap as a function of lattice parameter for various semi-conductor compounds .14 2.5 Recombination processes from conductio band to valence band: a) Photon emission, with v\ < v2, b) Phonon emission, and c) Auger effect ' 17 3.1 Mode l 350P C T I Cryocooler, and cross-section of the displacer unit 22 3.2 Cryocooler displacer unit cycle 23 3.3 Electr ic circuit model of sample mount. . 30 3.4 Mode l of the cooling of the sample stage for both thermal l inks, solid line f = 4.233 x 10~ 4 m, dashed line f - 3.35 x 10~ 3 m 32 3.5 Cryostat sample stage 34 3.6 Cal ibrat ion curve of a silicon diode 36 4.1 Schematic of the P L optical set-up 40 List of Figures v i i 4.2 Photoiuminescence spectra of bulk G a N x A s i _ x as a function of temperature for pulsed photoexcitation 50 4.3 Photoiuminescence of G a N x A s i _ x wi th pulsed and C W exci-tat ion lasers. The C W emission spectrum has been adjusted so that the low energy fall-offs match 51 4.4 Photoiuminescence spectra of bulk G a N x A s i _ x as a function of temperature for C W photoexcitation 53 4.5 Band gap Energy G a N x A s i _ x as a function of temperature . . 54 4.6 Measured low temperature band gap for various nitrogen con-centrations in G a N x A s i _ x and expected fit . . . 55 4.7 Comparison of the photoiuminescence spectra of samples grown wi th and without bismuth. Pulsed excitation in a) and C W excitation in b) 56 4.8 Energy as a function of temperature for sample wi th and with-out bismuth. The error in the band gap energy is ±0.002 eV for temperatures lower than 100 K 57 4.9 Sketch of the density-of-states for G a N x A s i _ x . A lso shown is the expected distr ibution of occupied for a) various threshold energies E* relative to the conduction band min imum ( C B M ) and b) for increased temperature 58 A.1 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 List of Figures v i i i A .5 Upper piece of vacuum chamber 68 A.6 Window flange 69 A .7 Assembled sample stage 70 A.8 Bot tom thermal bridge interface, mounted to second cold stage 71 A .9 Stainless steel thermal bridge 72 A.10 Top interface of thermal bridge 73 A . 11 Heater block ' 74 A . 12 Sample mount • • • 75 A . 13 Assembled heat shield set-up . 76 A . 14 Bot tom piece of heat shield, mounted to first cold stage . . . 77 A . 15 Center piece of the heat shielding , 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 Cool ing capacities of the C T I cryocooler for both 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 in experimental and theoretical physics. Interest in dilute nitrides has also grown in the industrial sector, pr imari ly for 1.3 /xm vertical cavity surface emitt ing lasers ( V S C E L s ) and cooler-less edge emitt ing lasers. The addit ion of a fraction of a percent of nitrogen can dramatical ly reduce the band gap of the alloyed material, allowing for the product ion of more technically favourable wavelength devices (1.3 JJLYO. and 1.55 /mi). These new materials have several advantages over ones currently in use ( I n G a A s P / I n P and InGaAs / InGaAsP) [ l ] . As an example, lasers made from the dilute ni-tride alloys are not as temperature sensitive due to a larger conduction band offset [2]. Th is higher temperature stabil ity is useful for the product ion of un-cooled lasers. G a A s substrates, on which these alloys are grown are available in larger sizes and at a lower cost than InP substrates, leading to lower costs in device manufacturing. To date nitrogen's effect on the electrical, optical and material properties of the III-V compounds is not well understood. There are also some disadvantages associated wi th the addit ion of nitro-gen. For example, a large decrease in electron mobil i ty and recombination Chapter 1. Introduction 2 lifetime[3], and a reduction in photoiuminescence intensity is observed[4]. In addit ion to these electrical and optical deficiencies, there are also some structural problems that arise wi th nitrogen incorporation. Because nitro-gen is atomically smaller (atomic radius, r 0 = 0.74A) than the arsenic, (ro = 1.19 ^4)), which it replaces, there is a large lattice constant mismatch between substrate and the epi-layer. Th is puts a large amount of strain on the grown epi-layer. Th is strain results in elastic and plastic relaxation processes that can lead to roughened surfaces and interfaces [5], as well as dislocations and cracks in the material. A l l this compromises the function-ality of the material. The introduction of In along wi th N compensates for the size discrepancies correcting some of the lattice mismatch. In order to achieve the very specific material properties for device fabrica-t ion, part icularly in 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 st i l l largely unexplored in dilute nitride semiconductors is the dependence of the electronic and optical properties of these alloys on temperature, especially in the range 10 K to above 300 K. Also unknown is the effect which the various growth methods have on temperature dependent phenomena. . The following is a description of the development of an apparatus to carry out experiments characterizing the G a N A s samples. Only measurements on the temperature dependence of the photoiuminescence of dilute nitr ide alloys wi l l be discussed in 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 semi-conductors and photoluminescence. In chapter 3, the design of the cryostat is covered. Measurements on the temperature dependencies of photolumi-nescence (PL) is given in chapter 4, wi th concluding remarks in chapter 5. A l l design drawings and specifications for the cryostat can be found in the appendices. CEapter 2. Background 4 C h a p t e r 2 B a c k g r o u n d 2.1 Materials at Low Temperatures The first step in the project was to design and bui ld 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. The heat capacity of a material is important when the material is to be heated or cooled in some way. It relates the amount of energy necessary to raise or lower a unit mass one degree. Typical ly, the specific heat is considered to be constant above a given temperature, and below this point to be highly temperature dependent. The influence of temperature on the specific heat of different types of materials wi l l 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 equil ibrium wi l l be reached or if using that particular material as a thermal conductor or insulator. Further notes on the thermal conductivity of materials wi l l be covered later on, wi th special consideration given to metal alloys, such as stainless steel. Chapter 2. Background 5 2.1.1 Heat Capacity Heat capacity of a material is defined as the rate of change of energy, U, with temperature, T. For a given material, the specific heat has contributions from a variety of sources, most notably electrons and phonons. The phonon part can be best approximated by the Debye function, C v ( T ) - - j « r V I w ^ f d x ( 2 - 1 ) Where 6D is the Debye temperature, and Mm the molar mass (for M K S units, The above equation is derived using the elastic continuum model of a solid, in which the number of vibrat ional modes in the interval u,u + du is given by; 1 2 rimodes =--4TT(-3 + ^)Vu2du (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 maximum frequency, um is given by the normalizing constraint that a solid wi th N atoms may have only 3A^ modes. This in turn gives the Debye temperature as: 0D = ^ . -(2-3) kB 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 3 dependence, known as the Debye T 3 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], Cv = f i V ^ s . A t low temperatures the fraction of electrons, wi th in fc#T of the Fermi surface begins to contribute more to the specific heat: Tp is the Fermi temperature (f^)- Th is 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 wi l l be discussed in more detail. The basic picture of the cryostat is a copper sample mount, wi th a heater, weakly l inked to a thermal sink operating at some low temperature. Therefore much consid-eration must be given to the ini t ial cooling and subsequent reheating of the copper stage. Copper has a Debye temperature of 343 K, given by its T —> 0 l imit. When a more accurate measure of the specific heat is needed the De-bye 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 re-gions 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 CV(T) is a constant given by the Dulong-Peti t relation as 3 8 5 ^ . 2.1.2 Thermal Conductivity Heat transfer by conduction depends both on the temperature gradient be-tween two points as well as the thermal conductivity of the material bridging Chapter 2. Background 7 400 r 60 100 160 Temperature (K) 200 250 300 Figure 2.1: Heat capacity of copper them. Thermal conductivity can be approximated by a relation borrowed from the kinetic theory of gases: 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 7 m/s for electrons and the speed of sound for phonons, and both can be assumed to be relatively constant wi th temperature. The depen-dence of the specific heat on temperature has been covered in the previous section. What remains is the mean free path of the carriers involved. In the case of electrons, the same processes that l imit the electrical con-ductivi ty 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. K(T) = \pCv(T)vl (2.4a) pK(T) = LT (2.5) Chapter 2. Background 8 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. Th is gives rise to an inverse relationship between mean free path and temperature: l = MakB6-^ (2.6) Where Ma is the atomic mass. A t low temperatures, where impuri ty 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 both 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 Umklapp processes, giving rise to a T - 1 in K(T). relation. A t lower temperatures, T <C #D, where phonons are rare, crystal impurit ies 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 wi th 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 impurit ies and their effect on the temperature dependence of the thermal conductivity. Chapter 2. Background 9 Impurity Temperature Dependence of K(T) Gra in Boundaries Dislocations rp2 Point Defects T-i 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 in alloys. Stainless steel is typically comprised of iron wi th 11% chromium along wi th 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 wi th a very large number of impurit ies. Due to the high density of impurit ies, the thermal conductivity becomes comparable wi th the electronic component. A t low temperatures, there is most predominately a linear dependency. For intermediate temperature ranges, al l scattering mechanisms can play significant roles lending to a nearly constant value from T = 150 K to T = 300 K. Above these temperatures a TA relationship is seen, wi th a < 1. F ig . 2.2 shows the thermal conductivity of stainless steel as a function of temperature. Heat Transfer Through Solids The heat flow, Q, along a solid of cross-section, A , under the influence of a temperature gradient, is given by: Q = K(T)Adf (2.7) Chapter 2. Background 10 0 50 100 150 200 250 300 350 400 Temperature, K Figure 2.2: Thermal 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, wi th uniform cross-sectional area, then the equation can be rewritten as: Q=Y r <T)dT (2-8) l JTI The above equation wi l l 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 11 2.2 III-V Semiconductor Crystals 2.2.1 Sample Growth Semiconductor compound crystals are grown on site by Molecular Beam Epi taxy ( M B E ) onto semi-insulating G a A s wafers under ultra-high vacuum ( U H V ) conditions. The underlying G a A s substrate first needs to have the surface oxide removed. This is done by heating the substrate to about 600 °C wi th an arsenic flux. A buffer layer of G a A s is then grown on top of the oxide free substrate on which is grown the G a N A s semiconductor crystal. The buffer layer is necessary to cover the roughened condit ion of the original surface from which the oxide was thermally removed. Epi tax ia l growth of the III-V semiconductor compounds by M B E is car-ried out under group-V rich conditions. The 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 group-I l l avail-able. The diffusion length of the group-I l l atoms along the surface is deter-mined by the substrate temperature, growth rate, and step density. Higher substrate temperatures allow for greater diffusion, and leads to smoother surfaces. Bu lk G a A s samples are grown wi th substrate temperatures in the range 400 °C to 620 °C. The best samples are grown at the higher end of this range. Using growth temperatures below this range leads to films that are non-stoichiometric, wi th excess As incorporated into G a sites or interstit ial ly degrading the material properties [5]. The 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 x A s i _ x requires conditions different from those used to grow simple GaAs . A n R F plasma source developed by Adamcyk[6] produces the nitrogen atoms for the growth process. More or less nitrogen is present in the chamber by raising or lowering the flux by changing input pressure to the plasma source. As was stated, the growth rate is l imited by the ar-rival of the group-I l l atoms. Furthermore the amount of N incorporation is inversely proportional to the growth rate [5] for constant substrate temper-ature. Surface desorption of nitrogen has an activation energy of 2.1 eV[5], so for a substrate temperature greater than approximately 550 °C very lit-tle nitrogen is found in the crystals [6]. There exists also some competi t ion between group-V elements, N and As , for incorporation in G a N x A s i _ x . It is therefore advantageous to have a low As 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 incorpora-t ion is slightly more sensitive to the As flux for higher growth temperatures [6], Samples are also grown either wi th or without bismuth used as a surfactant. The effect of the B i surfactant on nitrogen incorporation and material prop-erties is st i l l under investigation. Chapter 2. Background 13 GaAs Buffer Layer . GaAs Substrate a)l Figure 2.3: Cross-sections of a) bulk G a N x A s i _ x sample and b) a single 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 wi th higher nitrogen concentrations, however cracks and dislocations form above the crit ical thicknesses[4]. Thus, samples need be grown thinner to prevent these defects. F ig . 2.3 shows the structural cross-sections of the crystals investigated in this thesis. 2.2.2 Band Gap Bowing When growing alloyed semiconductors, it is important to know how the band gap of the material is affected by the concentrations of the various elements. Bo th 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 x G a i _ x A s , wi th x varying from 0 (pure GaAs) to 1 (pure A l A s ) , the band gap and lattice constant both increase. The band gap as a function of lattice constant is shown pictorial ly in fig. 2.4, wi th the above example shown wi th a dashed line. Insofar as the band gap of an alloyed material is concerned the variation of the band gap wi th composition can be approximated by a simple parabolic function[13]. EfB(x) = xE% + (1 - x)Ef - bx(l - x) (2.10) 300nm 300nm 350 um GaAs GaAs Buffer Layer GaAs Substrate 300nm - — lOnm QW 300nm 350 um Chapter 2. Background 14 4 |—i— i— i—|— i 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: Band gap as a function of lattice parameter for various semicon-ductor compounds Superscripts A and B designate the constituents of the alloy, x is the composi-t ion, and the constant b is known as the bowing parameter. For G a N x A s i _ x , A is G a A s and B is G a N ; E G a J V = 3.4 eV and E G a A s = 1.412 eV. Typical ly the bowing parameter takes on values of only a fraction of an eV 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 x A s i _ x the bowing parameter has been fit to the following equation: b = bQ + bieo^ms + b2e^k (2-H) This 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 15 2.3 Temperature Dependence of the Band Gap To derive the temperature dependence of the photoluminescence, it is im-portant to first know how the band gap changes wi th temperature. Th is shift in the relative positions of the conduction and valence bands is due to two main mechanisms: 1) a change in the lattice parameter wi th temperature and 2) a temperature dependent electron-lattice interaction. The former gives rise to a linear temperature dependence for high temperatures, contr ibuting only a fraction to the total shift in band gap in this temperature regime. A t low temperatures the thermal expansion becomes a non-linear function of tem-perature. The latter effect, due to electron-phonon interaction, is the major contributor to the shift seen in the band gap. It has been shown that this leads to the following temperature dependence: AEg(xT2, for T < 0 D (2.12a) AEg<xT, 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, Eg(T), can be given by: Eg(T) = Eg(0) - 2^- (2.13) The above empirical formula is known as the Varshni expression[18], Eg(0) is the T = 0 K band gap energy, and 7 and (3 are constants for the material. The constant (3 is related to the Debye temperature, 9D. Table 2.2 gives the parameters for G a A s and G a N . Chapter 2. Background 16 ™ meV . '> K P, K 0D, K G a A s 0.5408 204 344 G a N .939 722 614 Table 2.2: Varshni fit parameters from literature, GaAs[15] and GaN[17], as well as 9D An expression wi th a more obvious physical significance can be used, proportional to the Bose-Einstein occupation of a single phonon mode[19]. Eg(T) = a - b ( l + ^—) (2.14) V e T — 1 / Where 0 B is the average frequency for both 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, typical ly a laser or some other intense light source of a fixed wave-length, optically excites the electrons. As an electron falls back into the lower energy states, some of its energy is released in the form of radiation. Th is is in turn collected by a detector to be analyzed. The spectrum of the emitted photons contains information about the electronic structure of the material. The process of relaxing back to the lower energy bands is called recombination. Chapter 2. Background 17 a) b) c) Figure 2.5: Recombination processes from conductio band to valence band: a) Photon emission, wi th u\ < v2, b) Phonon emission, and c) Auger effect As the material returns to equil ibrium, recombination processes affect the amount of luminescence. It should be noted that de-excitation can result from several different recombination processes. Shown in 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 l ikely to occur than emission of photons with higher energy, hu2. The higher energy photons are a result of thermal excitation above the band minimum, giving rise to a tai l in the photoluminescence spectra, proportional to k g T . Phonons are emitted when the decaying electron interacts with the surrounding atoms and excites a vibrat ional mode in the lattice. Phonon emission is typical ly associated wi th defects or impurit ies in the material which tend to give states inside the band gap. Bo th photon and phonon emission are unavoidable recombination processes, they are a result of the existence of energy bands. The Auger Chapter 2. Background 18 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 wi l l occur more frequently for larger carrier concentrations. The efficiency of the photoluminescence of a material depends on the lifetimes of the excited state wi th 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. The strongest radiative transit ion 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 s . P L experiments therefore, permit a direct measure of the band gap of a semicon-ducting material. A t the same time the emission spectrum gives information about impuri ty levels, the presence of defects, recombination mechanisms, and material quality. Non-radiative recombination is associated wi th local-ized defect levels, which are themselves associated wi th poor material quality or impurities. Therefore, a material grown under certain conditions can be compared wi th a similar material grown under slightly different condit ion 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 in efficiency of the luminescence at lower temperature. Furthermore, practical use may be made of the knowledge of how the band gap shifts wi th 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 in 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 to perform low and variable temperature experiments to characterize the semiconducting crystals grown on site. The 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 to 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 Ha l l measurements, and most importantly the abil i ty to control temperature over . a large range, 10 K to greater than 300 K. 3.1 CTI Model 350P CryoCooler System The cryogenic cooling system was built up from an existing C T I model 350P closed cycle helium refrigerator, originally used as a cryopump. It con-sists of three main parts: a compressor, drive unit,, and the displacer unit, inside of which are the regenerators. Shown in fig. 3.1 is a schematic of the system, along wi th a more detailed view of the displacer unit. Consider-able time was spent by the author, wi th help from J . MacKenz ie , repair-ing/replacing several components of the refrigerator unit before the system Chapter 3. System Design and Operation 21 was operational. The displacer is comprised of a coiled mesh (regenerator) of high heat capacity material wrapped in a phenolic shell. Gas that en-ters the cylinder first passes through the regenerator in the lower port ion of the displacer, out into the open space above arid then into, through and back out of the second element of the displacer. The 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. The advantage of such a set-up is that it .allows more freedom in the design of a interfacing apparatus, particular-ity wi th respect to size and accessibility, otherwise unavailable when using conventional l iquid 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, l itt le or no helium is lost during a typical run of the experiment. 3.1.1 Closed Cycle Refrigeration Cool ing of the two low temperature stages is done by successively com-pressing and expanding helium gas. High pressure gas enters the cylinder from the compressor passing through the displacer and regenerators v ia the inlet valve, fig. 3.2a. Shown in 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. Th is unit cools the gas further on its way to the inner surface of the second cold Chapter 3. System Design and Operation 22 O-ring Phenolic Figure 3.1: Model 350P CTI 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 sub-sequent 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 wi l l follow in section 3.2.2. Th is stage operates at a temperature of approximately 60 K—> 77 K. The uppermost cooling stage holds the sample mount components, and typical temperatures range from 6 K to 10 K. The final temperature of either stage depends on the heat load imposed by the attached apparatus. Cool ing time for the second stage, as quoted by the operation manual, is approximately 45 minutes and plus an addit ional 7 — 8 minutes per ki logram of load attached to the second stage [21]. 3.2 Heating and Cooling Considerations Before the design was finalized al l possible heat sources and thermal l inks in the set-up had to be taken into consideration. The system to be designed called for the abil i ty to cool to low temperatures. Init ial ly the goal was to achieve a min imum of 10 K—15 K, and to reach room temperature, 300 K, wi th a great deal of control at al l temperatures in between. First and fore-" most, the thermal l ink from the cold head and the sample had to be set. Discussion on its design of the thermal l ink wi l l follow in section 3.3.1. The temperature controller available in the lab presently is l imited to a maxi-mum output of 3 W , thus the link was designed to remove much less than this at room temperature. W i t h the main issues covered, other sources of heat had to dealt wi th; mechanical heating from the vibrat ion caused by the displacer in 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 radiat ion 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 ther-mally isolated, being mechanically coupled to structure which is itself v i -brating. As the displacer cycles the helium coolant to and from the cooling stages, some minor heating can occur at the sample stage. Typical ly, heat l input from mechanical vibrations are only a serious problem for l iquid he-l ium temperatures, 4.2 K and below. However, some consideration should be given to this issue beause of the relatively large vibrations of the cryocooler. The compressor can be set to run the drive unit in one of two modes, 50 Hz and 60 Hz. The former was chosen as'the displacer runs at a lower frequency in this case approximately 1 Hz, compared wi th 1.2 Hz for the latter. The amount of heat input from a vibrat ing system is directly proport ional to the frequency of the vibrat ion, the effect being less at higher temperatures. Such heating should not prove to be problematic for the temperatures achieved wi th the cryocooler. Any other vibrations of the cryostat caused by out-side sources are kept to minimum 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 in the system. They extend from the electrical feed through in the chamber, at room temperature, Chapter 3. System Design and Operation 26 to the sample, at a minimum temperature 6 K. Brass is used since as an alloy, the thermal conductivity is significantly lower than that of a pure metal. A l l the wires are insulated and in addit ion run 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 l ink across the teflon. However, a worst case scenario calculation, using equation 2.8, wi th the greatest possible temperature gradient T\ = 300 K to T 2 = 6 K yielded the total heat flow along the leads to be on the order of 10 m W . Another source of heat input associated wi th the connecting electrical leads is resistive losses in the wires, which gives rise to a heat input Q = I2R. A typical current used for resistivity and Hal l measurements is on the order of / iA ' s , and the corresponding heating is on the order of few n W iii) Photoluminescence Excitation Laser A 1046 nm laser source pulsed at 200 Hz, frequency doubled wi th roughly 10% efficiency to 523 nm is used to excite the sample for photoluminescence measurements, giving a total of 3 —> 5 m W incident on the sample. The 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 in-put affects the sample temperature locally. A simple calculation of the local heating of the sample at the site of the beam gave the maximum tempera-ture rise induced by the laser to be approximately 10 m K . Th is should not Chapter 3. System Design and Operation 27 affect the sample characteristics dramatically and is less than 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 radiat ion 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 al l ra-diation fall ing upon it, and for such a body the absorptivity and emissivity are 1. The total radiant heat energy emitted by a black body per second per unit area is given by: E = oT4 (3.1) Where a is Stefan's constant, having an experimental value of 5.67x 1 0 ~ 8 m ^ - 4 -When any two surfaces of different emissivities, E\ and £2, are exposed to one another the total amount of heat energy transfered from the higher temper-ature surface can be expressed as: Q = oA(Tt-n) £ l £ \ (3.2). Most metals have low ; emissivities, 0.01 —> 0.6, depending on 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, both for surface condit ion and approximating actual radia-Chapter 3. System Design and Operation 28 Mater ia l Emissivi ty Copper 0.02 (polished) -> 0.6 (highly oxidized) A luminum 0.05 (po l i shed)^ 0.31 (highly oxidized) Quartz 0.9 Table 3.1: Emissivi ty 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. The sample mount itself is approximated by a copper surface wi th total exposed area of 100 c m 2 . In the worst case, E Q U A R T Z = 0.9, EAI = 0.31, and ecu = 0.6. The calculation states that approximately 2.2 W of ther-mal radiat ion flows into the sample mount; for the best case eQuartz = 0.9, eAl = 0.05, and ecu = 0.02, approximately 0.1 W is found. For this reason it was necessary to consider an intermediate thermal shield, and this is the topic of the next section. Radiat ion other than that emitted from the inter-nal surfaces, such as radiation from the environment passing in through the viewports, was considered insignificant in comparison. 3.2.2 Heat Shield As i l lustrated above the sample stage requires heat shielding between it and the inner walls of the chamber and the viewports, in 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 and surrounding the sample mount anchored to the first cold stage. The first cold stage operates at approximately T = 60 K —> 77 K. Keeping in mind the need for optical access to the sample, two shields were designed; one wi th optical access, the other without. The amount of heat radiated to the sample from the shielding, Tshieid%ng = 77 K, in place was 17 m W for the worse case (ecu — 0.6) and 0.4 m W for best case, (ecu = 0.02). For optical access, three holes were included in the design, two smaller holes (0.45") 180° to the sides of the sample meant for input /output of the P L laser and one larger hole (0.75") in front for both laser input /output and the P L output. When the sample was first cooled wi th no modif ication to the thermal link, the lowest temperature achieved was 65 K. Modif icat ions to the thermal l ink, described later in section 3.3.1, were made in 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 run modeling the cooling and re-heating of the sample stage. Any system of heat sinks, sources, and thermal l inks can be modeled by an equivalent electric circuit[22]: resistors for thermal l inks, capacitors for heat sinks, and power supplies for heat sources. Temperature of the components in a thermal system reacts to changes in the flow of heat energy much in the same way the elements of an D C electric circuit do for changes of voltage. Shown diagrammatical ly in 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 O O Sample Stage Thermal Bridge Mounted to Coldhead Figure 3.3: Electr ic circuit model of sample mount. heat capacity of the copper sample stage and 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. The cold head acts as a ground for the thermal circuit, wi th the following equations relating the equivalent components: (3.3a) C = mCv(T) R (3.3b) (3.3c) (T — Tfcase) lG 1 G = j(T-Tbaseyl [ K(T')dT' Where the thermal conductivity of stainless steel can be closely approximated by: K(T) = -0 .47127 + 0.1428T - 5.1049 x 1 0 ~ 5 T 2 + 6.5181 x 1 0 " 7 T 3 (3.4) The amount of power, P i , flowing from point T (= temperature of the sam-ple stage), to ground is equal to the negative of the power, P2> across the Chapter 3. System Design and Operation 31 capacitor. Px = - P 2 (3.5a) P i = rnCv(T)^ (3.5b) P 2 = i / T K(T')^r' (3.5c) To find the temperature, T , at any given time, t, we simply need to solve the differential equation: dT A hr\ i K { T ' ) d T ' ( 3 - 6 ) vK1 ) JTba3e dt I mCvK± ) J T b a s e 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 an iterative computer simulation to solve it. Codes were writ ten, wi th much help from A . Ballestad, to calculate the cooling curves for several different ratios of area to length. Shown in fig. 3.4 are the cooling curves for two of the thermal bridges currently in use. Bo th cases are shown wi th the extra radiation from the optical access in the heat shield. Wi thout the optical access a base temperature of 6 K is reached in the model. It was discovered that the added heat load due to the openings in the heat shield, along wi th the upper l imit on 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 l imits and the corresponding ratio. In order to have the maximum possible temperature range, two set-ups are needed. The ratio of 3.278 x 1 0 - 4 m allows for a min imum temperature of Chapter 3. System Design and Operation 32 i , i i i 1 1 0 100 200 300 400 500 600 Time, min Figure 3.4: Mode l of the cooling of the sample stage for both thermal links, solid line f = 4.233 x 1(T 4 m, dashed line f = 3.35 x l C T 3 m 65 K and a max of higher than 300 K . A second arrangement wi th a ratio of 3.35 x 1 0 - 3 m allows sufficient overlap and a minimum temperature of 25 K . 3.3 S a m p l e M o u n t 3.3.1 Thermal Bridge A t the heart of the design of the cryostat is the thermal bridge between the coldhead and the sample stage. The amount of heat that can travel from the sample stage and the cold stage is governed by the thermal conductiv-ity, K(T) (see equation 3.4,) of the stainless steel tubing that runs between them. The ends of the stainless steel tubing are soldered to copper interfacing pieces. These can be assumed to be temperature boundary points, Tsampie Chapter 3. System Design and Operation 33 Low Temperature (K) Upper l imit (K) I (inches) 25 200 0.35" 40 300 1.18" 65 300+ 2.15" Table 3.2: Temperature ranges of various thermal. l inks made from g" O .D . stainless steel tubing, wall thickness 0.040" and Tcoidhead- The heat that travels along any solid under the influence of a temperature gradient is given by equation 2.7. Since the temperature con-troller being used has a maximum output of 3W, the thermal bridge was designed to have a maximum heat flow of 1 W for T 2 = 300 K and T i = 6 K. Using equation 2.8 a ratio of area to length of the compatible bridge can be found, in this case y = 3.378 x 1 0 - 4 m. Th is was accomplished using 0.375" outer diameter stainless steel tubing, of thickness 0.040", and having a length of 3.1". Modification for PL A s previously mentionned, the ratio of area to length had to be re-calculated, to remove the extra heat load from the radiat ion passing through the opt ical ports in the heat shield. Th is 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 accommo-date 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 in appendix B . The cooling power of the second stage is a function of both 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 wi l l 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 in temperature in the Chapter 3. System Design and Operation 35 sample stage. The resistor is placed in the center of a hollowed port ion of the cylinder, held in place, electrically insulated, and well thermally l inked to the copper by sapphire laden epoxy. Thermal expansion of the epoxy is well matched to that of the copper, It is expected that the thermal cycling wi l l eventually cause a break down in the epoxy, or in its connection to the copper. A n y such defect, cracks or separation from the copper surface, wi l l dramatical ly effect the performance of the heating stage. The heater block is thermally linked to the top end of the thermal bridge wi th a th in layer of indium, and 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 in place by the aforementioned thermal compound. The stage has a 600 /xm thick wafer of oxidized sil icon on its face wi th 8 electrical contact pads, and again the thermal compound is used to thermally l ink the pieces. The contact pads were grown by E-beam evapouration, first a th in layer, 30nm, of chromium is wetted to the surface and then 200nm of gold is grown. Th is electrical contact wafer is unnecessary when P L measurements are being performed. Dur ing 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 Fixed to the rear face of the sample mount is a diode thermometer, held stationary wi th a narrow band of copper shim, which is l ined wi th thermal compound. The diode is positioned directly opposite the sample, and is well thermally connected to the sample mount in 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 junc-tion. A constant current of lOpA is run through a calibrated diode and its voltage measured. The forward bias voltage as a function of temperature is shown in fig. 3.6. Cal ibrat ion was carried out inside a S Q U I D device for a temperature range of 6 K < T < 300 K, wi th an overall accuracy of ±0.25 K. Some thermal drift is to be expected in the diodes, therefore the diodes are required to be replaced from time to time. Diodes wi l l be routinely checked against original calibration data for selected temperatures, T = 77 K and T = 273 K. Temeprature (K) Figure 3.6: Cal ibrat ion curve of a sil icon diode In order to control the temperature of the sample stage the diode ther-mometer is connected a non-commercial temperature controller, manufac-tured 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 accord-ingly. The 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 wi th the necessary electrical, optical,, and vacuum feed throughs. The chamber is comprised of two pieces, an upper and a lower segment. The lower port ion reaches up to just above the first cold stage. It was designed as a simple cyl in-drical chamber fixed wi th the necessary electrical and vacuum feed throughs. Another valve, also on the lower port ion of the chamber, is used to let in dry nitrogen when rapid reheating of the cold stages is desired. A n O-r ing is used to maintain the vacuum seal between the base flange of the cryocooler cylinder, as well as between the sections of the chamber. The upper half of the chamber is designed to have as l itt le inner surface area as possible, to lower radiative heating from the chamber to the cold stage and heat shield. Quartz was chosen for the optical viewports for its. broad transmission spec-trum. The viewports are positioned at the top of the of the upper port ion of the chamber. The windows are 50.4mm in diameter, allowing for a maximum incident angle of 26° through the front window and a min imum incident angle of 64° through the side windows. Another set-up of the windows has been designed. These are smaller in 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 pump the system down, a combination of a mechanical scroll pump and a molecular drag pump is used initially. However as the cold stages cool, predominately the second stage, the system begins to pump itself more effectively than the roughing pumps. A t this point the rough pumps are valved off unt i l 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 Whi le the cryostat is outfitted to perform several different types of char-acterization experiments, only P L measurements wi l l be discussed in the following chapter. As was described earlier in section 2.4, photoiuminescence experiments are carried out by first optically exciting the electrons and then collecting the emitted photons from the recombination process. Shown in fig. 4.1 is the current optical set-up in use. Presently two lasers are used to excite the sample: a pulsed 523nm (green) laser and a continuous wave 633nm (red) helium-neon laser. Reasons for this wi 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 nm beam that does not get frequency doubled. The now filtered 523 nm beam is directed, as shown, to the sample by the system of mirrors, m l a and m2, and a prism. The red laser beam is directed to m2 and the prism by mirror m l b . Redirecting the beam to the sample wi th a small prism is done in order to block as litt le of the emitted photons as possible reaching the detector. To this end, the prism sits atop a th in steel rod of similar cross-sectional area, which blocks only a fraction of the emit-ted 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 hit t ing the sample the beam has to pass through a 2" diameter 0.25" thick quartz window. The relative positions and orientations of the mirrors and prism are adjusted so that any specularly reflected beam is returned to the laser. Emi t ted 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, L2 , also a plano-convex (plane side towards the detector). Th is lens focuses the beam of emitted radiat ion to the input cou-pler 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. The 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. The fiber bundle is connected to an Ac ton Spectra Pro 300i spectrometer. Currently it is equipped with two gratings, 150 ^ (groves per mil l imeter), and 600 Typical ly the lower ^ grating is used because it has a much wider wavelength range, this gives a resolution of approximately, l . l n m . A n InGaAs linear photo diode array ( P D A ) is used in 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. Cool ing also results in sharper peaks and an increase in intensity. Blue shifting of the band gap energy approximately follows the de-scription given in section 2.3. The band gap corresponds to the energy of the peak in the photoluminescence. The increased intensity and decreased width is due to the decrease in the thermal l inewidth wi th lower temperatures.: Upon cooling further unexpected features begin to appear in the lumines-cence spectra. A second peak, and occasionally a th i rd peak, is observed in the luminescence spectra when the pulsed laser source is used for photoex-citation. These addit ional low temperature peaks appear at slightly lower energy than the band gap of the samples. Therefore they wi l l be hereafter Chapter 4. Temperature Dependence of PL 42 referred to as in-gap peaks. The intensity of the in-gap peaks rises sharply as the samples are cooled below 125 K, as shown in fig. 4.2. Above 125 K the pulsed excited spectra shows only a long low energy tai l . It was found that it was possible to observe emission from only the in-gap states by using a continuous wave (CW) excitation laser, as shown in fig. 4.3. A 633nm 5 m W helium-neon laser was used for this purpose. The shape and intensity of the in-gap peaks vary for different concentrations of nitrogen and for different growth parameters. The in-gap spectra are shown in fig. 4.4 for the samples whose full spectra is shown in fig 4.2. The fall off at high energy of the luminescence spectra for the pulsed pump is proportional to the Bol tzmann distr ibution for the corresponding temper-ature. Lowering the temperature of the samples reduces the amount of ther-mal excitation to states above the conduction band minimum. Th is results in sharper, more intense peaks in the photoiuminescence. The slope on the high energy side of the peak for the in-gap states also shows a similar temper-ature dependence. This suggests that electrons in these states reach thermal equil ibrium wi th the conduction band before recombination occurs. It is as-sumed that the low energy slope of the peak of the in-gap photoiuminescence is related to the fall off in the density of states towards mid gap. The band gap energy of the samples tends to a constant value for tem-peratures below approximately 75 K, observed by a constant peak energy in the photoiuminescence spectra. F ig . 4.5 shows the band gap energy of two samples as a function of temperature, along wi th a Varshni fit to the data. Similar results are observed for al l samples regardless of growth pa-Chapter 4. Temperature Dependence of PL 43 rameters. The transit ion temperature, where the low temperature energy l imit is reached, coincides with the temperature for which the intensity of the in-gap states becomes significant: refer to fig. 4.2. Above the transit ion temperature, the band gap appears to have a nearly linear dependence on temperature. Th is anamalous behaviour has not been observed elsewhere in the literature for pressure dependent measurements [23]. Recal l that the band gap energy also depends on the concentration of nitrogen, as described by equation 2.10. F ig . 4.6 shows the low temperature l imit of the band gap en-ergy as a function of nitrogen concentration, along wi th a fit for the expected band gap from equation 2.10 and 2.11. The 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 pho-toluminescence spectra do not appear as strongly in samples where bismuth is used, as shown for example in fig. 4.7a. Several sets of samples were mea-sured where the only change in the growth parameters was the introduction of bismuth. Note that the in-gap states photoluminescence also shows a small change wi th C W excitation (fig. 4.7b). F ig . 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 wi th B i surfactant. These particular samples happen to have similar concentrations of nitrogen. Th is is not easy to achieve since the amount of nitrogen in-44 Chapter 4. Temperature Dependence of PL corporation depends on bismuth flux as well as other growth parameters[5]. Chapter 4. Temperature Dependence of PL 45 N atoms on G a Energy, meV N atoms in Cha in Energy, eV 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 min imum [24] 4.3 Evidence for Nitrogen Cluster States It is believed the above mentioned features in the low temperature lumi-nescence are due to the presence of randomly distr ibuted nitrogen clusters and isolated nitrogen impuri ty states in the G a N x A s i - x crystals. Clusters in G a N x A s i _ x consist of two or more nitrogen atoms in close proximity to one another wi th in the lattice. This 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. The neighbouring nitrogen atoms bonded to different G a centers may have a linear arrangement, in which case they are referred to as chains. The assumption is made that the nitrogen is incorporated only substitut ionally on A s sites and not interstitially. The small amount of intersti t ial nitrogen present in the crystal maya also contribute to the in-gap states, but it is not known what the contribution is. Shown in table 4.1 are the theoreti-cally calculated[24] energies for the cluster states (CS). The single nitrogen Chapter 4. Temperature Dependence of PL 46 impuri ty produces a resonant state in the conduction band approximately 150 meV[24] above the conduction band minimum. These states have been shown to be highly localized around the impuri ty or cluster [24] and have much weaker pressure dependence than does the conduction band [25]. W i t h the relatively high concentrations of nitrogen in the samples studied here, the localized states wi l l produce a distr ibution of bound states below the conduction band minimum, which in turn gives the density of states as shown schematically in fig. 4.9. The electrons in the conduction band wi l l be in thermal equil ibrium with the cluster states to an energy depth, e*. Th is means states in the gap above e* wi l l be populated according to a Bol tz-mann distr ibution. The threshold, e*, for thermal excitation corresponds to the deepest trap from which an electron can escape during its lifetime (i.e. before recombination occurs). This wi l l be referred to as the kinetic l imit model[26]. In this model, e* corresponds to a demarcation energy which sep-arates the states which are in equil ibrium wi th the band from those that are not. The population of the cluster states is kinetically l imited and governed by progressive trapping-detrapping processes. In other words, electrons have a more difficult t ime finding the clusters states farther below the conduction band minimum, 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]. Th is would happen if the pump intensity were sufficiently strong to completely fill the cluster states up to some level, £ / n . Populat ion of the states in this case is governed by the excitation intensity. Bo th models would have a distr ibution of occupied states similar to that shown in fig. 4.9. Chapter 4. Temperature Dependence of PL 47 Further investigation is needed in order to be able to establish which model is the correct interpretation. Recombination from electrons in the cluster states that are not in thermal equil ibrium into the band results in the second peak observed in the lumi-nescence spectra. For the lower concentrations of nitrogen measured a th i rd peak is also seen in the spectra, leading to the belief that certain cluster configurations are more likely to form in these crystals. The 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 distr ibution of the in-gap states. This results in the spectra observed in fig. 4.3. For increasing temperature, electrons populat ing the cluster states are more likely to be thermally excited to the conduction band, leading toa less rapid variation of population wi th temperature. The single nitrogen impurity state that lies inside the band at room tem-perature is expected to be less temperature dependent than is the C B M , based on their respective pressure dependencies[25]. Therefore, as the sam-ples 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 wi l l move into the gap for decreasing temperature, since we expect the den-sity of cluster states to be higher for higher energies. A t low temperatures progressively smaller clusters (next nearest neighbour dimers for example) wi l l appear in the band gap. The conduction band edge may become more nitrogen-like, and therefore less temperature dependent than the G a A s based conduction band. This may explain why the temperature dependence of the Chapter 4. Temperature Dependence of PL 48 band gap of the G a N x A s i _ x alloys are weaker than the G a A s parent material. The measured differences in the photoluminescence of samples grown wi th and without bismuth leads to the conclusion that the introduction of bis-muth during the growth of the G a N x A s i _ x crystals reduces the number of nitrogen clusters present in the material. The increase in the intensity of the room temperature P L wi th bismuth[4] and other surfactants[7] has been previously been reported, but not explained. A reduction in 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 5 0 x 10 Sample R1350 [N] = 0.559% Tsub = 400 C with Bismuth 30K — 27K -e- 48K — 57K • — i — 76K —B— 100K -v- 124K . 150K c) 2.5 x 10 CD co c CD — 29K 45K - e - 57K . — i — 76K - « - 100K - B - 125K 150K 176K £ 1 Sample R1361 [N] = 0.34% Tsub = 430 C 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 d) Figure 4.2: Photoluminescence spectra of bulk G a N z A s i _ x as a function of temperature for pulsed photoexcitation 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 - ^ wi th pulsed and C W excita-t ion lasers. The 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 Dependence of PL 53 o I i i i i i J 1 1 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 Energy, eV Figure 4.4: Photoiuminescence spectra of bulk G a N x A s i _ x as a function of temperature for C W photoexcitation Chapter 4. Temperature Dependence of PL 54 « [N] = 0.624% * [N] = 0.536% — Varshni fit 300 Temperature, K Figure 4.5: Band gap Energy G a N ^ A s i - x as a function of temperature Chapter 4. Temperature Dependence of PL 55 1.34 r i i i i i Model Fit $ PL Data - i -* # i i i i 1 1 1 Y l 0.3 0.35 0.4 0.45 0.5 0.55 mi % 0.6 0.65 0.7 Figure 4.6: Measured low temperature band gap for various nitrogen con-centrations in G a N ^ A s i - x and expected fit Chapter 4. Temperature Dependence of PL 56 w/Bismuth, R1350 w/o Bismuth, R1349 T = 30K a) 1.25 1.3 Energy, eV 1.45 1.25 1.3 1.35 Energy, eV 1.45 1.5 Figure 4 . 7 : Comparison of the photoluminescence spectra of samples grown with and without bismuth. Pulsed excitation in a) and C W ex-citation in b) Chapter 4. Temperature Dependence of PL 57 1.38 1.37 1.36 > o 1.35 > i E? CD C 1.34 LU Q. CO 1.33 O) "O 1.32 c crj CQ 1.31 1.3 1.29 s o © o o • w/Bismuth, R1350 o w/o Bismuth, R1349 o o °§ o I 50 100 150 200 250 Temperature, K 300 350 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 0.04 b) DOS Dist. T=30K Dist.T=100K 0.1 Figure 4.9: Sketch of the density-of-states for G a N x A s i _ x . Also shown is the expected distribution of occupied for a) various threshold energies E* relative to the conduction band minimum (CBM) and b) for increased temperature Chapter 5. Conclusions 59 Chapter 5 Conclusions A closed cycle optical cryostat has been designed and implementationed. It has proven to be capable of achieving the desired low temperatures. Whi le the system that has been developed performs as well as hoped, improvements can sti l l be made. The addit ion 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 attr ibute to nitrogen clusters in the material. The clusters have been found to gives states wi th 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 wi th the incorporation of nitrogen. Use of bismuth as a surfactant, during the growth process, of the samples reduces the density of the nitrogen clusters. The bismuth surfactant increases the intensity of the photoluminescence and decreases the relative intensity of the photolu-minescence from the in-gap states. Further investigations are warranted in order to develop a more detailed understanding of the cluster states.' A long Chapter 5. Conclusions 60 wi th the emission spectra measured here, absorption spectroscopy would give an insight into the nature of the cluster states and the effect bismuth sur-factant has on them. The addit ion 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 wi th growth parameters different from those measured here. The effect of increased nitrogen content, the addit ion of ind ium 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 Nitr ide Semiconductor Research 6, 2 (2001) [2] I. Suemure, K. Uesugi, and W . Walukiewicz, App l ied Physics Letters, 77, 3021 (2000) [3] E. Strom M.Sc. Thesis 2001 [4] X . Yang, J . B . Heroux, M . J . Jurkanovic, and W.I . Wang, Journal of Vac-uum Science and Technology B, 17,1144 (1999) [5] M . Adamcyk, S. Tixier, B . J . Ruck, J . H . Schmid, T . Tiedje, V . fink, M . Jefferies, K . L . Kavanagh, and M . Thewalt, Journal of Vacuum Science and Technology B, 19, 1417 (2001) [6] M . Adamcyk P h . D . Thesis 2001 [7] V . Gambin , W . Ha , M . Wistey, S. K i m , J .S. Harris, Mater ials Research Society Symposium Proceedings, 692, H7.1.1 (2002) [8] S. Tix ier , M . Adamcyk, E . Young, J . H . Schmid, and T . Tiedje, Journal of Crysta l Growth, 25, 449 (2003) Bibliography 62 [9] H. Riechert, A . Y u Egorov, D. Livshits, B. Borchert, and S. Illek, Nan-otechnology, 11, 201 (2000) [10] C . K i t te l Introduction to Solid State Physics 6th edit ion, 1986, Wi ley [11] Nei l W . Ashcroft and N. David Mermin Solid State Physics, 1976, Saun-ders [12] Guy K. Whi te Experimental Techniques in Low TemperaturePhysics 3rd edition, 1979, Claredon Press [13] G . Pozina, I. Ivanov, B. Monemar, J . V . Thordson, and T . G . Anderson, Journal of Appl ied Physics, 84, 3830 (1998) [14] Y . Q iu , S.A. Nik ishin, H. Temkin, N .N . Faleev, and Y .A .Kudr iu tsev , Appl ied Physics Letters, 70, 3242 (1997) [15] H. Shen, S .H . Pan , Z. Hang, J . Leng, F . H . Pollack, J . M . Wooda l l , and R . N . Sacks, Appl ied Physics Letters, 53, 1080 (1988) [16] U. T isch, E. F inkman, and J . Salzman, Appl ied Physics Letters, 81, 463 (2002) [17] H. Teisseyere, P. Perl in, T . Suski, I. Gregory, S. Porowski, J . Jun , A . Pietraszko, and T . D . Moustaskas, Journal of Appl ied Physics, 76, 2429 (1994) [18] Y . P . Varshni, Physica, 34, 149 (1967) [19] P.T. Landsberg Recombiatoin in Semiconductors, 1991, Cambridge Un i -versity Press Bibliography 63 [20] R . C . Weast Handbook of Chemistry and Physics 5 3 r d , 1973, Chemical Rubber Co . [21] C T I Cryocooler Operation Manual [22] Communications with W . N . Hardy, D. Broun, and J . Bobowski [23] Katsuhiro Uesugi, Ikuo Suemene, Tatsuo hasegawa; Tomoyuki Aku ta -gawa, and Takayoshi Nakamura, Appl ied Physics Letters, 7 6 , 1285 (2000) [24] P . R . C . Kent, L Belliache, and A lex Zunger, Semiconductor Science and Technology, 1 7 , 851 (2002) [25] X iao L i u , M . - E . Pisto l , and L Samuelson, S. Schwetick and W . Seifret, Appl ied physics Letters, 5 6 , 145 (1990) [26] Communications wi th Dr . T . Tiedje [27] E. N. Economou Green's Functions in Quantum Physics 2nd, 1983, Springer-Verlag 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 characteri-zation 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 69 10 —*1 CO ' 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 sam-ple mount above the present value of 3 W , it wi l l be necessary to consider the amount of cooling power capabilities of the cryostat. Shown in 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 wi l l compromise the base operating temperature. MlSf STMt tCHP.UI FIRST SUCC fEUP.m Figure 1.3 Typical refrigeration capacity of the Model 22C Figure 1.4 Typical refrigeration capacity of the Model 22C cryodyne cryocooler (60 Hz) cryodyne cryocooler (50 Hz) Figure B . l : Cool ing capacities of the C T I cryocooler for both modes of op-eration 

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