Controlling Heat and Mass Transport during the Vertical Bridgman Growth of Homogeneous Ternary III-V Semiconductor Alloys

Transcription

1 Trans. Indian Inst. Met. Vol.60, Nos. 2-3, April-June 2007, pp TP 2117 Controlling Heat and Mass Transport during the Vertical Bridgman Growth of Homogeneous Ternary III-V Semiconductor Alloys P.S. Dutta, H.J. Kim and A. Chandola Department of Electrical, Computer, and Systems Engineering Rensselaer Polytechnic Institute, Troy, New York 12180, USA (Received 30 June 2006 ; in revised form 20 November 2006) ABSTRACT Large separations between the solidus and liquidus curves in the pseudo-binary phase diagrams are characteristics of all III- V ternary semiconductor alloys such as Ga 1-x Sb, Ga 1-x As, InAs 1-y P y, etc. Hence during crystal growth from melt, alloy segregation and constitutional supercooling is a major issue due to which the mechanical properties of the crystals suffer. Since the solidification temperatures vary with alloy composition, a control over both heat and mass transport during crystal growth is necessary for achieving spatial compositional homogeneity in the grown crystals. In this paper, it has been demonstrated that by appropriately choosing axial temperature gradient, melt mixing scheme, growth rate and solute feeding rate, homogeneous bulk Ga 1-x Sb crystals could be grown. 1. INTRODUCTION Research and development of ternary III-V compound semiconductor alloy based substrates is of high interest for numerous optoelectronic and optical applications. The binary counterparts (such as GaSb and InSb) are totally miscible, both in liquid and in solid state. Therefore, the physical, electronic and optical properties of the resulting ternary (such as Ga 1-x Sb) vary continuously with the alloy composition. However mixed alloy semiconducting substrates are far from being commercially viable and require a lot of fundamental research. In particular, the heat and mass transport issues during crystal growth need to be understood carefully to improve the crystalline quality of these materials. Presence of microscopic cracks in the crystals is the most common problem. This is related to the large separation between the liquidus and the solidus in the pseudo-binary phase diagrams 1. During a typical directional solidification experiment (such as by vertical Bridgman growth), the composition of the growing crystal changes continuously (alloy segregation) due to the solidus-liquidus separation. Unless the growth rates are extremely low, constitutional supercooling occurs leading to solid-liquid interface breakdown and spatial compositional fluctuations. The spatial compositional fluctuations coupled with the variations in lattice parameters and thermal expansion coefficients with alloy composition leads to excessive local strain and hence cracking in the crystals. Once these cracks are formed, they cannot be eliminated by post growth annealing. Hence the only way to eliminate cracking is by avoiding constitutional supercooling during the growth. For avoiding constitutional supercooling, a higher temperature gradient at the melt-solid interface and/or a slower growth rate is desirable. However, high temperature gradient is not suitable for obtaining a planar solid-liquid interface which is extremely important for obtaining homogeneous alloy composition perpendicular to the growth direction (across the sliced wafers). Higher temperature gradient also leads to lowering the stress level necessary for cracking. Hence increasing the temperature gradient to solve the cracking problems is not possible. Lowering the growth rate is another option for eliminating cracks. However for commercial viability, the growth rates cannot be too slow unless there are novel applications that could justify the high cost of the substrates. Therefore, a fundamental study of the trade-off between the growth rate and temperature gradient is necessary to solve the radial homogeneity issue and the cracking problem. Forced convection could also help in eliminating supercoooling if temperature fluctuation resulting from the fluid motion is eliminated. Unfortunately this occurs only when the axial temperature gradient in the melt is low (in other words if an isothermal melt or solution is used). Therefore, temperature gradient becomes the most important parameter that dictates the quality and radial homogeneity of the semiconductor alloys, the topic of discussion in this paper. Another issue with ternary crystal growth is the changing alloy composition along the growth direction. External solute feeding strategies are necessary to replenish the depleting compounds or elements in the melt during the growth In this paper, we will discuss the sensitivity of the solute feeding process on the alloy composition along the growth direction. 2. EXPERIMENTAL DETAILS For the Ga 1-x Sb growth, a vertical Bridgman configuration coupled with crucible rotation options and external solute feeding was used Pre-synthesized polycrystalline GaSb and InSb of mm diameter were used in the experiments. All the experiments reported here were conducted in quartz crucibles with flat bottom. Melt was encapsulated by alkali halide salt (LiCl-KCl eutectic mixture). Inert argon gas up to 1.2 atmospheres was used to pressure the melt to avoid

2 156 Dutta et al. : Vertical Bridgman Growth of Homogeneous Ternary III-V Semiconductor Alloys volatilization of the antimony during growth. A single zone semi-transparent furnace with gold coated tube around the heaters was used. Hence the seed re-melting, solidification and the melt-solid interface position could be seen clearly. Due to the parabolic temperature profile, by changing the maximum set point of the furnace, the axial temperature gradient near the melt-solid interface could be varied between 5 and 30 o C/cm 18. The gradient of the furnace also changes along the axial direction (crystal growth direction). During the experiments, a variety of melt mixing schemes have been used, the results of which will be discussed in the paper. The schematic of experimental growth configuration and crystal growth sequence (from left to right) is shown in Fig To start with, a InSb poly-crystalline seed was placed at the bottom of the crucible and a GaSb poly-crystal feed was suspended from the top of the growth chamber on to a specially designed stainless steel feed holder. The stainless steel holder was designed in such a way that it would never come in contact with the crucible or melt at any time. After heating and stabilizing the furnace to obtain a specific temperature gradient, the crucible was raised into the furnace. A part of the InSb seed was melted to obtain a melt-solid interface. At this point, the GaSb feed was lowered and allowed to touch the top of the InSb melt. This led to GaSb feed dissolution and the crystal growth was initiated in a stationary crucible as a result of increasing level of the solute concentration at the solid-liquid interface with time. The crystal grown by this method was compositionally graded along the growth axis with increasing gallium concentration in Ga 1-x Sb (decreasing indium concentration). The rate of compositional grading is decided by the solidus temperature in the pseudo-binary phase diagram and the axial furnace temperature gradient. The axial composition was graded till a desirable alloy composition was achieved and then a homogeneous composition crystal length was grown. During the compositionally graded crystal growth, the melt-solid interface automatically rises from the cooler to the hotter zone in the furnace. Thus the melt-solid interface shape was also change continuously during the growth. The effect of temperature gradient on the melt-solid interface shape and the radial compositional variation will be discussed in this paper. For growing the axially uniform composition crystal, the crucible was translated into the lower temperature zone of the furnace at a rate of 0.4 mm/hr while the GaSb feed dissolution was continued by a periodic dipping method (as discussed later). While the GaSb at the melt-solid interface was depleted by preferential incorporation in the crystal, it was replenished by the feed dissolution. Hence the melt-solid interface remained at the same position in the furnace till the entire melt solidified. After the solidification, the crucibles were cooled to room temperature at a rate of o C/hr. The crystals could be removed from the crucible by dissolving the alkali halide salt encapsulation in hot water. Figure 2 shows a 50 mm diameter as-grown Ga 1- x Sb poly-crystal. The crystals were then sliced by a diamond wheel saw along the growth direction and polished to mirror shining by a specially developed polishing process for ternary alloys. Spatial compositional analyses of the grown crystals were carried out by JEOL-733 electron probe micro-analysis (EPMA). The indium, gallium and antimony concentrations perpendicular to the growth axis (radial direction) at various axial positions (along the growth direction) were measured. 3. RESULTS AND DISCUSSION The heat and mass transport during the growth of ternary alloys dictates the spatial compositional homogeneity of the substrates (wafers) and the yield of wafers of the same composition (from the same ingot). As discussed above, radial compositional homogeneity requires planar melt-solid interface and axial homogeneity requires constant melt composition with time that could be achieved only via solute feeding (of the depleted species during growth). Hence the growth parameters that need to be optimized during the Fig. 1 : Schematic diagram of the GaInSb crystal growth process 18.

3 Dutta et al. : Vertical Bridgman Growth of Homogeneous Ternary III-V Semiconductor Alloys 157 growth of ternary crystals are temperature gradient at the melt-solid interface, growth rate and solute feeding rate. The latter two parameters are related to each other since excessive dissolution of the feed will lead to rapid precipitation (uncontrolled growth) and inadequate feeding will lead to change in the axial alloy composition. In this section, we will first present the effects of furnace temperature gradient and various melt mixing processes on the radial alloy composition in the wafers. Then we will discuss the result of axial compositional profile for an optimized solute feeding condition. 3.1 Effect of Axial Temperature Gradient on Radial Compositional Profile In this section, the radial compositional profiles have been discussed for 50 mm diameter crystals grown without any intentional melt stirring (only natural convection), with melt stirring by a stirrer, and with accelerated crucible rotation technique (ACRT) 7. Three ranges of axial temperature gradients, namely 5-10 o C/cm, o C/cm and o C/cm were evaluated in our experiments 18. For the growth experiments without melt mixing, the crucible was simply translated into the cooler zone of the furnace without any rotational motion. Melt stirring by a stationary stirrer and with uniform crucible rotation has been found to be very effective. In this case, a flat quartz (silica) plate of diameter slightly less than the diameter of the crucible was inserted in the melt. Crucible rotation rate of at least 30 rpm in conjunction with a stationary stirrer in the melt was found to be necessary in providing melt mixing. Finally, we also experimented with accelerated crucible rotation technique (ACRT). The accelerated crucible rotation was performed by gradually increasing the crucible rotation from 0 to 75 rpm in 1 minute followed by deceleration from 75 rpm to 0 rpm in 1 minute. This sequence was then repeated continuously. The crucible rotation was in the same direction during the entire experiment. The acceleration and deceleration between 0 and 75 rpm was found to be adequate for radial melt mixing in 50 mm diameter crucibles. With a specific maximum set-point temperature in a single zone furnace, the growth of InSb rich alloy compositions in Ga 1-x Sb (with lower solidus temperature) takes place in the higher axial temperature gradient region (cooler zone). Hence while presenting effects of low temperature gradient, GaSb rich alloys have been shown. On the other hand, InSbrich alloy compositions have been grown at high temperature gradients. The effect of optimum temperature gradient on the entire range of alloy compositions from GaSb to InSb will also be presented. Figures 3(a-c) show the radial InSb profiles in different wafers extracted from crystals grown using axial temperature gradients of 5-10 o C/cm and o C/cm under three different conditions, namely, (a) without any melt mixing, (b) with a stationary stirrer in the melt along with uniform crucible rotation and (c) with ACRT (without any stirrer). In the crystals grown without any melt mixing, constitutional supercooling resulted in interface breakdown. Hence compositional fluctuations could be seen in the radial compositional profile as shown in Fig. 3a. Under low gradients, the isotherms are expected to be flat. However due to weak natural convection and poor melt mixing, one could see accumulated indiums on the left side of the crystal resulting in constitutional supercooling. Numerous cracks could be seen in the crystal where there is a high fluctuation in indium content. The crystals grown by a stationary stirrer and constant crucible rotation of 100 rpm exhibited an exceptional degree of compositional homogeneity (Fig. 3b) and improved microstructure for the grown crystal. The stirrer disperses the accumulated solute near the interface and hence a flat melt-solid interface with a uniform radial profile is seen in Fig. 3(b). The radial InSb profiles in crystals grown using ACRT are shown in Fig. 3(c). Similar to the crystal grown with a stirrer, excellent radial compositional homogeneity could be seen. (a) (b) (c) Fig. 2 : As-grown Ga 1-x Sb poly-crystal (2-inch diameter). Fig. 3 : Radial InSb concentration profiles in Ga 1-x Sb polycrystal grown (a) without melt stirring, (b) with melt stirring using stirrer and (c) with ACRT. The axial temperature gradients used in the experiment were 5-10 o C/cm ( ) and o C/cm ( ).

4 158 Dutta et al. : Vertical Bridgman Growth of Homogeneous Ternary III-V Semiconductor Alloys Under high axial temperature gradient of o C/cm, the radial compositional profiles obtained for the above three melt mixing conditions are shown in Figs 4(a-c). Without any melt stirring, the melt-solid interface is extremely curved as depicted by the radial composition profile (Fig. 4a). As expected, with increase in the axial temperature gradient, the growth interface became concave with respect to the solid (leading to a convex InSb radial profile). However, unlike in the case of low temperature gradient, there are no random compositional fluctuations and no micro-cracking could be seen in the crystals grown under these axial temperature gradients. This clearly indicates that constitutional supercooling did not occur. Figure 4(b) shows the radial profile with the stirrer in the melt and constant crucible rotation of 100 rpm. The curved compositional profile clearly indicates that high axial gradients lead to curved interfaces which are very difficult to flatten even with fluid stirring. It is worthwhile mentioning that the radial composition profile obtained for the crystal grown with stirrer in the melt at high crucible rotation speed (100 rpm) is comparable to that of a crystal grown with stirrer at low crucible rotation speed (30 rpm). The convex radial profile is also seen in the crystal grown with ACRT (Fig. 4c). From the results presented above, it is clear that the axial temperature gradient plays a crucial role in solute transport from the solid-liquid interface to the bulk melt and thereby affecting the radial compositional homogeneity. Under low gradients, the natural convection is not strong enough and the only mechanism for solute transport is via diffusion leading to constitutional supercooling in crystals without any forced convection. Forced convection does help in avoiding constitutional supercooling. By increasing the axial temperature gradient, the constitutional supercooling could be eliminated. However, the overall radial compositional variation is very large (corresponding to the solid-liquid interface shape). Thus an optimum axial temperature gradient should be maintained during the entire growth experiment in order to achieve planar melt-solid interface shape. This could be experimentally verified and implemented in our system by simultaneously cooling the furnace while the crucible is being lowered into the cooler zone of the furnace. A crystal was grown by continuously maintaining a temperature gradient of 15 o C/cm (at the melt-solid interface) by lowering the furnace set-point temperature during the growth. The crucible was subjected to the same ACRT motion as described above. Figure 5 shows the radial InSb compositional profiles scanned from various axial positions in the crystal. As can be seen, the profiles are flat for the entire composition range from GaSb to InSb. No micro-cracking could be seen in the entire crystal indicating the absence of supercooling during the entire growth experiment. 3.2 Effect of Solute Feeding Rate on Axial Compositional Homogeneity The heat transport dictates the solid-liquid interface shape during the growth. A planar solid-melt interface is the most (a) (a) (b) (b) (c) (c) Fig. 4 : Radial InSb concentration profiles in Ga 1-x Sb polycrystal grown (a) without melt stirring, (b) with melt stirring using stirrer and (c) with ACRT. The axial temperature gradient used in these experiments was o C/cm. Fig. 5 : Radial InSb concentration profiles in a Ga 1-x Sb polycrystal grown with an axial temperature gradient of 15 o C/cm and using ACRT. The various curves are for wafers of different alloy compositions extracted from various axial locations in the crystal.

5 Dutta et al. : Vertical Bridgman Growth of Homogeneous Ternary III-V Semiconductor Alloys 159 ideal one and leads to uniform radial composition. Having optimized the growth conditions for radial compositional homogeneity, the axial compositional homogeneity in the crystal needs to be achieved under the same axial temperature gradient and melt mixing scheme. The axial compositional profile is dependent on the growth rate and the melt composition. To maintain a constant melt composition with time, the mass transport rate (solute feeding rate) must be optimized. Figure 6 shows the cross-section of a Ga 1-x Sb crystal grown with a continuously fed GaSb into the melt 19. As shown, rapid crystallization via random nucleation in the melt occurred giving rise to an extremely poor and nonhomogeneous crystal. To optimize the solute feeding process, we used a GaSb polycrystalline feed of 10 mm in diameter introduced at the top of the InSb melt. A large number of growth experiments were conducted to study the effect of solute dipping frequency and dipping time along with the crucible lowering rate on the axial compositional profile 19. A dipping frequency of 3-4 times in 1 hour with a dipping time of 2-5 seconds was found to be optimum for avoiding interface breakdown and rapid growth. These optimum solute feeding parameters were found to differ slightly depending on the temperature gradient in the melt, crucible diameter, Fig. 7 : Axial indium, gallium and antimony profiles in a graded followed by homogeneous Ga 1-x Sb crystal grown from a InSb seed. controlling the heat and mass transport during the vertical Bridgman growth. We have experimentally shown that by optimizing the axial furnace temperature gradient, one could achieve planar interface shape and thereby homogeneous alloy compositions along the radial direction (perpendicular to growth direction) in ternary III-V bulk crystals. Suitable melt mixing such as via ACRT or a stirrer in the melt helps in avoiding constitutional supercooling or interface breakdown during growth. Finally, periodic solute feeding is necessary for growing axially homogeneous crystals from which a large number of wafers of the same alloy composition could be extracted. These results are universal for crystal growth under open crucibles and could be applied to other ternary alloy systems by fine tuning the above mentioned growth parameters. Fig. 6 : Cross-section of a Ga 1-x Sb crystal grown with a continuously dissolved GaSb feed into the melt. ACKNOWLEDGEMENT The authors would like to acknowledge the support from National Science Foundation (NSF) through the Faculty Early Career Development Award ECS feed contact area, etc. Hence it is necessary to optimize the solute feeding parameters for any new experimental set-up and configuration. Figure 7 shows the axial indium, gallium and antimony profiles in a Ga 1-x Sb crystal grown from a InSb seed. The graded composition region (7-15 mm portion) was grown by periodically dipping the GaSb feed into the InSb melt. During the growth of graded region, the crucible was kept at the same position in the furnace while the melt was stirred using ACRT. After the graded composition region, the crucible was lowered for sometime without solute feeding resulting in decrease in gallium concentration (15-20 mm portion). The periodic solute feeding process was then continued while the crucible was translated leading to a uniform composition region (20-30 mm portion). At the end of the growth, the solute feeding was terminated and the crystal was cooled to room temperature. 4. CONCLUSIONS In conclusion, we have successfully demonstrated radially and axially homogeneous ternary Ga 1-x Sb crystals by REFERENCES 1. Bachmann K J, Thiel F A and Schreiber H, Jr., Prog. in Crystal Growth and Characterization 2 (1979) Bonner W A, Skromme B J, Berry E, Gilchrist H L and Nahory R E, in: Harris J S, (Ed.), Inst. Phys. Conf. Ser. 96 (1989) Nakajima K, Osamura K, Yasuda K and Murakami Y, J. Crystal Growth 41 (1977) Nakajima K, Kodama S, Miyashita S, Sazaki G and Hiyamizu S, J. Crystal Growth 205 (1999) Hashio K, Tatsumi M, Kato H and Kinoshita K, J. Crystal Growth, 210 (2000) Tanaka A, Watanabe A, Kimura M and Sukagawa T, J. Crystal Growth, 135 (1994) Elwell D and Scheel H J, Crystal Growth from High Temperature Solutions, Academic Press (1975). 8. Dutta P S and Ostrogorsky A G, J. Crystal Growth 194 (1998) Ciszek T F, Method for Preparing Homogeneous Single Crystal Ternary III-V Alloys, US Patent 5,047,112 (1991). 10. Miotkowski I, Vogelgesang R, Alawadhi H, Seong M J, Ramdas A K, Miotkowska S and Paszkowicz W, J. Crystal Growth 203 (1999) 51.

6 160 Dutta et al. : Vertical Bridgman Growth of Homogeneous Ternary III-V Semiconductor Alloys 11. Lin M H and Kou S, J. Crystal Growth 132 (1993) 461; Y. Tao and Kou S, J. Crystal Growth 181 (1997) Ashley T, Bewisk J A, Cockayne B and Elliott C T, Inst. Phys. Conf. Ser. 144 (1995) Dutta P S, Methods for growing multi-component semiconductor alloys US Patent (2003). 14. Dutta P S and Miller T R, J. Electronic Mater., 29 (2000) Dutta P S and Ostrogorsky A G, Alloys and methods for their preparation, US Patent US B1 (2001). 16. Dutta P S, J. Crystal Growth 275 (2005) Kim H J, Chandola A, Bhat R and Dutta P S, J. Crystal Growth 289 (2006) Kim H J, Ph.D. Thesis, Bulk crystal growth process for Compositionally homogeneous GaInSb Substrates, Rensselaer Polytechnic Institute, Troy, New York, USA (2005). 19. Chandola A, Ph.D. Thesis, Bulk crystal growth and infrared absorbtion studies of GaInSb, Rensselaer Polytechnic Institute, Troy, New York, USA (2005).