Engineering Phase Formation Thermo-Chemistry for Crystal Growth of Homogeneous Ternary and Quaternary III-V Compound Semiconductors from Melts

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1 956 Journal of ELECTRONIC MATERIALS, Vol. 29, No. 7, 2000 Dutta Special and Issue Miller Paper Engineering Phase Formation Thermo-Chemistry for Crystal Growth of Homogeneous Ternary and Quaternary III-V Compound Semiconductors from Melts P.S. DUTTA 1,3 and T.R. MILLER 2 1. Rensselaer Polytechnic Institute, Department of Electrical, Computer and Systems Engineering, Center for Integrated Electronics and Electronics Manufacturing, Troy, New York Lockheed Martin Inc., Schenectady, New York duttap@rpi.edu Based on intrinsic alloy phase formation chemistry and thermodynamics, a novel and unique way of producing compositionally homogeneous multi-component (binary, ternary, quaternary) semiconductor materials is presented. A free energy minimization computer program licensed from AEA Technology Engineering Software, Inc., has been employed to study the composition of the solidifying phases from Ga-In-As-Sb melts at different temperatures and with various liquid compositions. The solid phases have been identified (theoretically and experimentally) to be either ternary compounds of Ga 1 x In x Sb, Ga 1 x In x As, GaAs y Sb 1 y, and InAs y Sb 1-y, or quaternary Ga 1 x In x As y Sb 1 y depending on the melt temperature and composition. By engineering the thermochemistry of preferential phase formation in the Ga-In-As-Sb melt, compositionally uniform, single phase, crack free, large polycrystalline Ga 1 x In x Sb and Ga 1 x In x As have been grown. INTRODUCTION Substrates of III-V compound semiconductors with variable band gaps and lattice constants are desirable to obtain high performance electronic and optoelectronic devices. Unfortunately, at the present time, device grade, single crystal, substrates of only binary compounds (such as GaAs, GaSb, InP) with discrete energy band gaps and lattice constants are commercially available. Ternary and quaternary based devices are fabricated on thin epitaxial layers grown by non-equilibrium techniques (from vapor or solid phase) on binary substrates using buffer layers. The buffer layer technology necessary to relieve misfit (lattice mismatch) related stresses at the epilayer-substrate interface is not optimized for all systems and often devices exhibit large leakage currents due to poor interfacial regions. Availability of substrates with tunable band gap and lattice constant will open up numerous possibilities of interesting band gap engineering in homo- and hetero-epitaxial devices, and would reduce the complexity and cost of the epitaxial technology. Results of rigorous investigation in the area of bulk crystal growth of ternary and quaternary compounds over the past few decades have indicated the unfeasi- (Received September 19, 1999; accepted March 30, 2000) bility of large scale production of multi-component substrates by the conventional melt growth techniques. 1 Melt grown ternary and quaternary substrates are of poor quality primarily due to spatial compositional inhomogeneity arising from the wide separation between the liquidus and solidus curves in the phase diagrams. 1 6 Hence, new thermodynamic approaches of preparing homogeneous semiconductor alloys from melt should be considered. The development and optimization of materials and processes are generally time-consuming and costly operations. As a result, significant delays are frequently encountered before important materials advances can be introduced in technological applications. For these reasons, thermodynamic calculations and simulations based on critically evaluated data are now finding wide and increasing use as a basic tool in materials and process design. Commercial software packages incorporating thermodynamic databases are already available for this purpose. 7 Their use enables the number of direct measurements to be minimized, as information on necessary process conditions can be obtained very rapidly and inexpensively to achieve the required product with minimum waste of energy and materials. For III-V compounds, even though thermodynamic calculations have been widely used since ,9 to 956

2 Engineering Phase Formation Thermo-Chemistry for Crystal Growth of Homogeneous Ternary and Quaternary III-V Compound Semiconductors from Melts 957 predict liquid or gas mixtures required to grow alloys of various target compositions, and to predict solidsolid miscibility gaps, experimenters working with systems of three or more components still cannot rely exclusively on phase diagrams that have already been published in the literature. It is impossible for a journal article to cover all of the composition-temperature space that may be of interest. Moreover, published liquidus and solidus curves for a fixed temperature are often drawn on a composition plot without tie-lines (connecting equilibrium liquid and solid compositions). Similarly, isotherms representing the boundaries of a miscibility gap are often shown without tie-lines (indicating pairs of solids in equilibrium with each other). Furthermore, liquidsolid and solid-solid equilibria are rarely shown on the same plot. This last omission tends to obscure an important point: For some compositions that are within a miscibility gap at one temperature, there may be a higher temperature at which they can be grown as single phase solids. Other compositions, deeper within the miscibility gap, are not stable as single phase solids at any temperature, because on heating, they begin to melt before the solids become miscible. The incompleteness of the information in the literature makes it essential for any group trying to grow multi-component solids to be able to perform phase diagram calculations for their own conditions of interest. Recently, based on thermodynamic calculations, Dutta and Miller 10 proposed a novel method of deriving large quantities of homogeneous ternary and quaternary alloys from melts by monitoring the nucleation temperature and melt composition. Isothermal phase diagram calculations in the present work concentrated on guiding efforts to grow Ga 1-x In x Sb, Ga 1 x In x As, GaAs y Sb 1 y, InAs y Sb 1 y and Ga 1 x In x As y Sb 1 y from Ga-In-As-Sb melts. Results presented herein are limited to conditions where the liquid is stoichiometric, that is, the sum of the mole fractions of the group III components equals that of the group V components. The calculations were undertaken using MTDATA, the National Physical Laboratory (NPL, UK) Database for Metallurgical Thermochemistry. THERMODYNAMIC MODEL Models and Data Sources MTDATA determines equilibrium compositions by minimizing the Gibbs free energy of the system. It requires an input file containing free energies of pure substances as a function of temperature, and excess free energies of solution phases as functions of temperature and composition. Data for the pure elements in their solid and liquid phases and for the pure solid compounds were taken from the assessment of Ansara et al. 11 The published free energy expressions were multiplied by two because the compounds were formulated in the present work as AB, rather than as A 0.5 B 0.5 (MTDATA reads the stoichiometry of each substance in the system from the input file and accounts for it in the calculations). The liquid was modeled as comprised only of atoms. The strong attraction between group III elements and group V elements in the liquid was accounted for by negative excess free energy terms rather than by postulating the existence of III-V compounds in the liquid phase. The excess free energy of a solution phase is defined as the difference between the actual free energy of mixing and the free energy change that would result from the entropy of mixing of an ideal solution. The excess free energy of the liquid was represented using a Redlich-Kister model 12 having non-zero coefficients for all of the six possible binary interactions and for two of the four possible ternary interactions. The contribution of an interaction to the excess free energy is G excess = W 0 (T)X 1 X 2 + W 1 (T)X 1 X 2 (X 1 -X 2 ) + W 2 (T)X 1 X 2 (X 1 -X 2 ) 2. for a binary interaction, and G excess = W 0 (T)X 1 X 2 X 3 for a ternary interaction, where X n is the mole fraction of species n. Redlich-Kister coefficients for the binary interactions in the liquid were taken from Ansara et al. 11 A coefficient for the ternary interaction among Ga, In, and Sb in the liquid was taken from Ref. 13. The zincblende phase was treated using a twosublattice model, with gallium and indium occupying one sublattice, while arsenic and antimony occupy the other. Using Y X to represent the fraction of sites on its appropriate sublattice occupied by element X, the free energy of the solid was calculated as: G = Y Ga Y As G o GaAs + Y In Y As G o InAs + Y Ga Y Sb G o GaSb + Y In Y Sb G o InSb + RT (Y Ga ln Y Ga + Y In ln Y In ) + RT (Y As ln Y As + Y Sb ln Y Sb ) + G excess where G excess = Y Ga Y As Y Sb a o + Y Ga Y In Y As b o + Y Ga Y In Y Sb c o + Y In Y As Y Sb d o Solid solutions of III-V compounds were not included in the Ansara et al. assessment. 11 Expressions for the a o, b o, c o, and d o coefficients were taken from other literature sources. 13,14 Calculations of the pseudobinary phase diagrams of GaAs-InAs, GaAs- GaSb, and GaSb-InSb agreed well with experimental data from the literature, with the exception of the InAs-InSb. Improved agreement for this subsystem was achieved by addition of a ternary As, In, Sb interaction in the liquid, and adjustment of the d o coefficient. The values for these two coefficients were arrived at by trial-and-error rather than by a rigorous optimization procedure. All interaction terms from sources other than the Ansara et al. 11 assessment are listed in Table I. All interactions listed in Table I used only the first term (W 0 ) in the Redlich-Kister series. Calculations were performed using the MULTIPHASE module of MTDATA. At each temperature, overall compositions (moles of each ele-

3 958 Dutta and Miller Table I. Redlich-Kister Coefficients Used for Phase Diagram Calculations (Other than from Ref. 11) Interacting Coefficient Species Phase Joule/mole, T in Kelvin Source As,In,Sb Liquid W o = T Present Work Ga,In,Sb Liquid W o = T Ref. 13 GaAs, GaSb Zincblende a o =17866 Ref. 14 GaAs, InAs Zincblende b o = Ref. 14 GaSb, InSb Zincblende c o = T Ref. 13 InAs, InSb Zincblende d 0 = T Present Work ment) corresponding to selected points expected to be in the interior of two phase or three phase regions were input. The program then calculated the compositions and amounts of the phases present at equilibrium. Each point that was within a two-phase region generated a tie line, and each point within a three phase region generated the three lines forming the boundaries of the region. Calculated Diagrams Phase diagrams for the Ga 1 x In x As y Sb 1 y system were calculated for temperatures from 200 C to 1200 C. Representative diagrams are presented in Figs In these diagrams, dotted lines represent solid-liquid tie lines, while dashed lines represent solid-solid tie lines. Dashed-Dotted lines ending in filled circles [in Figs. 2, 3, and 4] are the experimental tie lines of Nakajima et al. 15 Between 720 C and the melting point of GaAs (1237 C), there is only a single solid, which is rich in gallium and arsenic, and a liquid which is rich in indium and antimony (shown in Figs. 1 and 2). The only change with increasing temperature in this range is a continuous shift of both the liquidus and solidus curves toward the GaAs corner. Below the melting point of InAs (942 C), the In-rich ends of both curves are on the InSb-InAs axis (Figs. 1 and 2). Above the melting point of InAs, both curves end on the GaAs-InAs axis. In the temperature range ~ C, three-phase regions are predicted to exist, where an arsenic-rich solid and an antimonyrich solid are simultaneously in equilibrium with a liquid that is richer than either solid in indium and antimony (Figs. 3 and 4). At 400 C and below, a threesolid region appears within the solid-solid miscibility gap, as the arsenic-rich solid decomposes further into separate gallium-rich and indium-rich phases. The calculations predict that Ga 0.78 In 0.22 As 0.1 Sb 0.9 for example is within the miscibility gap at 500 C, but at 600 C it is stable as a single solid in equilibrium with a liquid of composition Ga 0.25 In 0.75 As Sb In contrast, Ga 0.8 In 0.2 As 0.2 Sb 0.8 is also within the miscibility gap at 500 C, but it is not stable as a single phase solid at any temperature. Solid with bulk composition Ga 0.8 In 0.2 As 0.2 Sb 0.8 does not separate from a liquid until the liquid has been cooled to about 600 C. When the solid does form, it will be a two phase mixture of antimony-rich and arsenic-rich solids, because it is already below the minimum temperature at which the solids would be miscible if they did not melt. Modeling of Solidification Many models for growth of solid solutions from melts have been developed, with varying degrees of complexity. One of the simplest models assumes that the actively growing zone of the solid is constantly in quasi-equilibrium with the entire bulk liquid (not a true equilibrium to the extent that the temperature is non-uniform). Solid is frozen in composition and cannot exchange matter with the liquid. Also, solid phase diffusion is extremely low and hence neglected. As the solid grows, the liquid becomes depleted in the elements that preferentially enter the solid; so with time, the solid also gets depleted in those elements. The interface temperature is assumed to decrease as the liquid becomes richer in the lower melting components. Quantitative treatment of such a model usually begins by defining effective solid-liquid distribution coefficients, k i, for the components i. The distribution coefficients are often assumed to remain constant, and may or may not be assumed to be the same as the equilibrium distribution coefficients. Experimentally, it is usually found that attempts to grow pseudo-binary solid solutions such as Ga 1 x In x As or Ga 1 x In x Sb from a ternary liquid produce solids with a gradation in composition that conforms to a model of this first type. The crystal growth experiments described herein more nearly followed a second type of model. In this model, the interface solid is in equilibrium only with a thin zone of liquid at the liquid-solid interface. The temperature at the liquid-solid interface is assumed to be constant, but lower than the bulk liquid temperature. The interface liquid exchanges matter with the bulk liquid on a time scale that is slow compared to the equilibration between solid and interface liquid. As the solid grows, the interface liquid becomes depleted in the elements that preferentially enter the solid, but they are continuously replenished by exchange with the bulk liquid. As the process continues, the solid composition remains uniform, and the interface liquid composition remains constant, but the composition of the bulk liquid gradually approaches that of the interface liquid. When the composition of the bulk liquid becomes the same as the interface liquid, the growth of solid stops unless the temperature decreases (in which case the composition of the solid will change), or the bulk liquid is replenished by adding the elements that have become depleted. The second type of model can be represented by

4 Engineering Phase Formation Thermo-Chemistry for Crystal Growth of Homogeneous Ternary and Quaternary III-V Compound Semiconductors from Melts 959 Fig. 1. Calculated phase diagram of Ga-In-As-Sb system at T = 900 C. Fig. 3. Calculated phase diagram of Ga-In-As-Sb system at T = 700 C. Dashed-Dotted lines ending in filled circles are the experimental tie lines of Nakajima et al. 15 Fig. 2. Calculated phase diagram of Ga-In-As-Sb system at T = 800 C. Dashed-Dotted lines ending in filled circles are the experimental tie lines of Nakajima et al. 15 Fig. 4. Calculated phase diagram of Ga-In-As-Sb system at T = 600 C. three points on an isothermal phase diagram for the growth temperature. In Figs. 1 and 4, point A represents an initial bulk liquid composition. Point B is the composition of the solid, and point A* is the composition of the interface liquid. As the growth continues, the solid composition remains at point B, and the interface liquid composition remains at point A*, but the bulk liquid composition moves along the tie line from point A toward point A*. The theoretical maximum fraction of the original liquid charge that can be solidified at constant temperature is equal to the ratio of the length of line segment AA* to that of segment BA*. While the model predicts that yield can be maximized by starting with a liquid composition as close as possible to the desired solid composition, that increases the risk of nucleation within the bulk liquid. For example, a bulk liquid corresponding to point A1 on Fig. 1 has a calculated liquidus temperature of 950 C. Random nucleation could occur in the bulk if the bulk liquid temperature is any less than 50 C above the interface temperature (900 C) at the start of the experiment. While the model predicts that the same solid could be grown at a theoretical yield of 70% by starting with a bulk composition close to point A1, the calculated liquidus temperature for composition A1 is 1000 C. Hence, to increase the maximum yield of the uniform composition region in the crystal using the present approach, the temperature gradient in the melt needs to be increased. It was theoretically predicted that alloy concentra-

5 960 Dutta and Miller a Fig. 5. Experimentally grown uniform Ga 0.88 In 0.12 Sb polycrystal (growth temperature ~630 C; melt composition: 75 mol.% Ga, 25 mol.% In, 98 mol.% Sb, and 2 mol.% As). tions in the solid should remain constant, provided the growth temperature was constant, in spite of the fact that the segregation coefficients of individual elements were all much different than unity. Figure 1 above demonstrated the growth of uniform Ga-In- As from a Ga-In-As-Sb melt. A similar concept can be applied for the growth of uniform Ga-In-Sb, In-As-Sb and Ga-As-Sb from Ga-In-As-Sb by choosing appropriate melt compositions and growth temperatures. The results presented here on uniform ternary solids from quaternary melts are in accordance with the second type of model. EXPERIMENTAL RESULTS Charge Synthesis and Crystal Growth The quaternary melts were synthesized by either (a) melting Ga, In, Sb and InAs, or GaAs or (b) by mixing pre-synthesized binary compounds GaSb, InSb, GaAs, and InAs. Synthesis was performed in silica crucibles by keeping the melt in a linear temperature gradient zone of the furnace to promote mixing through natural convection for hours. The maximum temperature in the melt was approximately 50 C above the liquidus temperature. The bottom of the crucible where solidification (nucleation) initiates was monitored carefully and was decided based on the MTDATA simulations. 10 Melt was encapsulated by boric oxide or alkali halide salt. Inert argon gas up to 1.5 atmospheres was used to pressure the melt to avoid volatilization of the group V components during synthesis. After synthesis, crystal growth was performed by the conventional vertical Bridgman method. The crucible lowering rate was in the range of 2 3 mm/hr. Typical temperature gradients of the furnace near the melt-solid interface used in this work ranged between C/cm. Growth of Ga 1 x In x Sb By using the above described procedure, we were able to produce compositionally uniform polycrystalline Ga 1 x In x Sb (shown in Fig. 5) from Ga-In-As-Sb melts. Melt composition and growth temperature is b Fig. 6. Radial indium profiles for the two wafers A and B (from the crystal shown in Fig. 5) as measured using EPMA technique. indicated in the figure caption. Due to spatial compositional homogeneity, cracks usually seen in ternary boules are absent in this crystal. The elemental concentrations in the solid obtained in these crystals are close to the predicted values from MTDATA calculations (simulations performed at the respective growth temperatures with the experimental melt compositions). Using electron micro-probe x-ray analysis (EPMA), the radial and axial indium concentration in the grown crystals was evaluated. Figure 6 shows the radial indium profile of two wafers A and B taken from two axial positions of the grown ingot. The radial position 0 mm represents the edge of the crystal and the position 10 mm corresponds to the center of the crystal. As clearly seen in the two plots, the axial as well as the radial indium concentration is very uniform and close to 12 mol.%. The compositional homogeneity of the crystal is also evident from the Fourier transform infrared transmission plots of the two wafers (Fig. 7). Both the transmission spectra show a band edge of ~0.6 ev. Growth of Ga 1 x In x As By using the procedure similar to that above, we were also able to produce homogeneous polycrystalline Ga 1 x In x As from Ga-In-As-Sb melts. As in the earlier case, no cracks were observed due to spatial alloy homogeneity of the crystals. Figure 8a shows an experimentally grown Ga 0.2 In 0.8 As polycrystal at a growth temperature of ~900 C from a melt (A1) comprising of 10 mol.% Ga, 90 mol.% In, 20 mol.% Sb, and

6 Engineering Phase Formation Thermo-Chemistry for Crystal Growth of Homogeneous Ternary and Quaternary III-V Compound Semiconductors from Melts 961 a hibit miscibility gaps in solid phases. This is due to differences in chemical interaction between the constituent elements in the melt, which leads to multiple compounds or phase formation. Multi-phase semiconductor alloys are not suitable for any applications. However, it is possible to obtain a single phase homogeneous alloy, if the chemistry and thermodynamics of phase formation is well understood and carefully monitored during experimental synthesis. Recently, an innovative way for preparing homogeneous quaternary compounds with variable band gaps, but discrete lattice constants termed as quasi-binary was demonstrated by Dutta and Ostrogorsky. 16 Quasibinary (GaSb) 1 x (InAs) x could be grown in the GaSb rich side. However, as the growth temperature increases with the increase in InAs content, the melt tends to decompose to form a quaternary Ga-In-As-Sb solution and multi-phase formation takes place. Hence the composition (and band gap tuning) in Quasi- Binary compounds is limited by the solubility of the higher melting binary (such as InAs in GaSb) at growth temperatures slightly above the lower melting one (GaSb) due to a stringent requirement of melt association. In the present work, a unique approach is presented through which compositionally homogea b Fig. 8. (a) Experimentally grown Ga 0.2 In 0.8 As polycrystal (Growth temperature ~900 C; melt composition: 10 mol.% Ga, 90 mol.% In, 20 mol.% Sb, and 80 mol.% As). The axial compositional profile of indium in the first to freeze 18 mm of the crystal (the uniform region) is shown in Fig. 8b. b Fig. 7. (a) and (b) Room temperature Fourier transform infrared transmission plots for wafers A and B respectively of the crystal shown in Fig. 5. The band gap evaluated from the two plots is ~0.6 ev. 80 mol.% As. From the MTDATA predictions in Fig. 1, the solid composition (B1) should be close to 20 mol.% Ga, 80 mol.% In, negligible amount of Sb, and nearly 100% As. The total length of the uniform region of the crystal expected is ~40% of the total melt volume (proportional to the length of the tie line A1-A1* with respect to the length of B1-A1*), which is experimentally verified using the axial EPMA measurements for the first to freeze 18 mm of the crystal as shown in Fig. 8b. Figure 9a and b are room temperature Fourier transform infrared transmission plots for wafers A and B respectively of the crystal shown in Fig. 8a. The transmission cut-off edge lies at the same point in the two wafers, indicating the axial compositional homogeneity in the crystal (in the first to freeze one-third portion). The band gap evaluated from the two plots is ~0.5 ev. DISCUSSION As mentioned above, multi-component alloys ex-

7 962 Dutta and Miller a b Fig. 9. (a) and (b) Room temperature Fourier transform infrared transmission plots for wafers A and B respectively of the crystal shown in Fig. 8a. The band gap evaluated from the two plots is ~0.5 ev. neous ternary and quaternary semiconductors can be synthesized and grown from a multi-component melt. This new alloy growth process is thermodynamically driven and based on preferential alloy phase formation chemistry. The methodology presented in this work is universal for all III-V, II-VI, and IV-IV alloys. Homogeneous compounds can be grown in the entire band gap-lattice constant plane by properly selecting the melt compositions and nucleation temperatures. 10 It is worth mentioning that single phase, stable alloys can be synthesized and grown from melts only for those compositions lying outside the solid-solid miscibility gaps. The approach of growing ternary crystals from quaternary melts is also applicable if one chooses melt composition from the solid+liquid region of the pseudobinary phase diagram such as GaAs-InAs. The important experimental parameters are the temperature gradient above the solid-liquid interface, the interface temperature and the temperature of the bulk melt. With the present approach, at least a portion of the bulk melt should be higher than the liquidus temperature. This will avoid any random nucleation in the melt. Any randomly precipitated solid will float to the top of the melt due to density difference and melt back into the liquid. The key thing in achieving uniform composition is the solid-liquid interface temperature. Any fluctuation in the solidliquid temperature will change the alloy concentration in the solid. Conceptually, the approach used in this study is different from the conventional normal solidification. During normal solidification (with a fully mixed melt), the alloy concentration changes continuously due to segregation. 1 Hence no two wafers sliced from two different axial positions in the crystal will have the same composition. By adopting the present approach, a perfectly uniform alloy composition is achieved in the first to freeze certain region and then the composition changes drastically. Thus, two wafers taken from the uniform region will be identically the same. The length of the uniform region in the crystal depends on growth and melt temperatures, and melt composition as discussed above. In general, the addition of the fourth component in the ternary melt allows one to vary the growth temperature and provide seeding with the binary compounds. For example, the addition of antimony to the Ga-In- As solution provides an additional degree of freedom by lowering the growth temperatures; as a result GaInAs can be easily grown using InAs single crystalline seed, which is not possible using a GaAs-InAs psuedobinary melt (due to InAs melting point). Similarly, by adding arsenic to the Ga-In-Sb melt, the liquidus and solidus temperatures can be varied, which is useful in seeding with GaSb. SUMMARY An innovative method for the melt growth of compositionally uniform ternary and quaternary alloys is presented. A thermo-chemistry simulation code MTDATA has been employed to study the solidification of homogeneous ternary GaInSb, GaInAs, InAsSb and GaAsSb from Ga-In-As-Sb melt. This approach is applicable to other III-V, II-VI, IV-IV compound semiconductor alloys as well. Using this scheme, crack free, polycrystals of compositionally homogeneous GaInSb and GaInAs have been grown by the vertical Bridgman method. REFERENCES 1. K.J. Bachmann, F.A. Thiel, and H. Schreiber, Jr., Prog. Cryst. Growth and Charact. 2, 171 (1979). 2. T.F. Ciszek, Method for Preparing Homogeneous Single Crystal Ternary III-V Alloys, U.S. patent 5,047,112 (1991). 3. I. Miotkowski, R. Vogelgesang, H. Alawadhi, M.J. Seong, A.K. Ramdas, S. Miotkowska, and W. Paszkowicz, J. Cryst.

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