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Microgravity Science and Technology

, Volume 27, Issue 5, pp 313–320 | Cite as

A Numerical Study on the Growth Process of InGaSb Crystals Under Microgravity with Interfacial Kinetics

  • H. Mirsandi
  • T. Yamamoto
  • Y. Takagi
  • Y. OkanoEmail author
  • Y. Inatomi
  • Y. Hayakawa
  • S. Dost
Original Article

Abstract

InxGa1−xSb bulk crystals are to be grown using a GaSb(seed)/InSb/GaSb(feed) sandwich-structured sample onboard the International Space Station (ISS). The InGaSb crystals will be grown on top of GaSb seed single crystals with different orientations viz., (111)A, (111)B, (110), (100) in order to examine and understand the growth kinetics of the crystals. In the present work, a numerical model of the crystal growth system has been developed to investigate the interface kinetics effects on the growth process by taking kinetics coefficient into account. The proposed numerical model was applied to evaluate the effect of crystal orientation on growth rate. Simulation results showed that the kinetics coefficient, whose value depends on crystal orientation, affected the growth rate of InGaSb crystal and the dissolution rate of GaSb feed crystal in the sandwich system.

Keywords

Microgravity conditions Numerical simulation Alloys Growth from solution 

Nomenclature

C

concentration of GaSb (-)

cp

specific heat (J⋅kg−1⋅K−1)

D

diffusion coefficient (m2⋅s−1)

ey

unit vector in the vertical direction

f

interface position (m)

g

gravity acceleration (m⋅s−2)

La

latent heat (J⋅kg−1)

m

slope of the interface

n

unit vector normal to the interface

p

pressure (Pa)

T

temperature (K)

u

fluid velocity component in the horizontal direction (m⋅s−1)

t

time (s)

v

fluid velocity vector (m⋅s−1)

v

fluid velocity component in the vertical direction (m⋅s−1)

x

horizontal direction coordinate (m)

y

vertical direction coordinate (m)

y+

dimensionless wall distance (-)

G

acceleration normalised by gravity of Earth (m⋅s−2)

Greek symbols

α

thermal diffusivity (m2⋅s−1)

β

kinetics coefficient (m⋅s−1)

β(0)

kinetics coefficient at the unperturbed interface (m⋅s−1)

βst

kinetics coefficient of steps (m⋅s−1)

βC

solutal expansion coefficient (-)

βT

thermal expansion coefficient (K−1)

λ

thermal conductivity (W⋅m−1⋅K−1)

μ

viscosity (kg⋅m−1⋅s−1)

ρ

density (kg⋅m−3)

ν

kinematic viscosity (m2⋅s−1)

ΔC

concentration difference (-)

ΔT

temperature difference (K)

ξ

ξ-direction coordinate

η

η-direction coordinate

Subscripts

BN

boron nitride

I

interface

L

solution (liquid)

S

crystal (solid)

Q

quartz

W

wall

Notes

Acknowledgments

This work was financially supported by a Grant-in-Aid for Scientific Research (B) (No. 23360343) and (No. 25289087) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

References

  1. Antypas, G.A., Houng, Y.M., Hyder, S.B., Escher, J.S., Gregory, P.E.: The incorporation of Ga during LPE growth of In0.53Ga0.47As on (111)B and (100) InP substrates. Appl. Phys. Lett. 33, 463–465 (1978)CrossRefGoogle Scholar
  2. Chernov, A.A.: Stability of faceted shapes. J. Cryst. Growth 24/25, 11–31 (1974)CrossRefGoogle Scholar
  3. Chernov, A.A., Scheel, H.J.: Extremely flat surfaces by liquid phase epitaxy. J. Cryst. Growth 149, 187–195 (1995)Google Scholar
  4. Christoffersen, J., Christoffersen, M.R.: The kinetics of dissolution of calcium sulphate dehydrate in water. J. Cryst. Growth 35, 79–88 (1976)CrossRefGoogle Scholar
  5. Duffar, T., Serrano, M.D., Moore, C.D., Camassel, J., Contreras, S., Dusserre, P., Rivoallant, A., Tanner, B.K.: Bridgman solidification of GaSb in space. J. Cryst. Growth 192, 63–72 (1998)CrossRefGoogle Scholar
  6. Dutta, P.S., Bhat, H.L., Kumar, V.: The physics and technology of gallium antimonide: An emerging optoelectronic material. J. Appl. Phys. 81, 5821–5870 (1997)CrossRefGoogle Scholar
  7. Dutta, P.S., Ostrogorsky, A.G.: Suppression of cracks in InxGa1−xSb crystals through forced convection in the melt. J. Cryst. Growth 194, 1–7 (1998)CrossRefGoogle Scholar
  8. Haneveld, H.B.K.: Growth of crystals from solution: rate of growth and dissolution of KCl. J. Cryst. Growth 10, 111–1112 (1971)CrossRefGoogle Scholar
  9. Hayakawa, Y., Okano. Y., Hirata A., Imaishi, N., Kumagiri, Y., Zhong, X., Xie, X., Wu, F., Liu, H., Yamaguchi, T., Kumagawa, M.: Experimental and numerical investigations on dissolution and recrystallization processes of GaSb/InSb/GaSb under microgravity and terrestrial conditions. J. Cryst. Growth 213, 40–50 (2000)CrossRefGoogle Scholar
  10. Inatomi, Y., Kikuchi, M., Nakamura. R., Kuribayashi. K., Jimbo, I.: In situ observation for semiconductor solution growth using a near-infrared microscope. J. Cryst. Growth 275, 193–200 (2005)CrossRefGoogle Scholar
  11. Inatomi, Y., Kuribayashi, K.: Morphological stability of GaP(111)B in LPE under static magnetic field. J. Cryst. Growth 241, 395–403 (2002)CrossRefGoogle Scholar
  12. Murakami, N., Arafune, K., Koyama, T., Kumagawa, M., Hayakawa, Y.: Effect of gravitational direction on dissolution and growth in GaSb/InSb/GaSb sandwich system. J. Cryst. Growth 263, 320–326 (2004)CrossRefGoogle Scholar
  13. Nobeoka, M., Takagi, Y., Okano, Y., Hayakawa, Y., Dost, S.: Numerical simulation of InGaSb crystal growth by temperature gradient method under normal- and micro-gravity fields. J. Cryst. Growth 385, 66–71 (2014)CrossRefGoogle Scholar
  14. Okano, Y., Suzumura, T., Sakai, S., Hayakawa, Y., Kumagawa, M., Hirata, A., Dost, S.: Oscillatory behavior in melting of a GaSb/InSb/GaSb system. Mech. Res. Commun. 31, 605–610 (2004)CrossRefGoogle Scholar
  15. Okano, Y., Umemura, S., Enomoto, Y., Hayakawa, Y., Kumagawa, M., Hirata, A., Dost, S.: Numerical study of Marangoni convection effect on the melting of GaSb/InSb/GaSb. J. Cryst. Growth 235, 135–139 (2002)CrossRefGoogle Scholar
  16. Okitsu, K., Hayakawa, Y., Hirata, A., Fujiwara, S., Okano, Y., Imaishi, N., Yoda, S., Oida, T., Yamaguchi, T., Kumagawa, M.: Gravitational Effects on Mixing and Growth Morphology of an In0.5Ga0.5Sb System. Cryst. Res. Technol. 31, 969–978 (1996)CrossRefGoogle Scholar
  17. Onuma, K., Tsukamoto, K., Sunagawa, I.: Dissolution kinetics of K-alum crystals as judged from the measurements of surface undersaturations. J. Cryst. Growth 110, 724–732 (1991)CrossRefGoogle Scholar
  18. Rajesh, G., Arivanandhan, M., Morii, H., Aoki, T., Koyama, T., Momose, Y., Tanaka, A., Ozawa, T., Inatomi, Y., Hayakawa, Y.: In-situ observations of dissolution process of GaSb into InSb melt by X-ray penetration method. J. Cryst. Growth 312, 2677–2682 (2010)CrossRefGoogle Scholar
  19. Rajesh, G., Arivanandhan, M., Suzuki, N., Tanaka, A., Morii, H., Aoki, T., Koyama, T., Momose, Y., Ozawa, T., Inatomi, Y., Takagi, Y., Okano, Y., Hayakawa, Y.: Effects of solutal convection on the dissolution of GaSb into InSb melt and solute transport mechanism in InGaSb solution: Numerical simulations and in-situ observation experiments. J. Cryst. Growth 324, 157–162 (2011)CrossRefGoogle Scholar
  20. Sato, Y., Nishizuka, T., Takamizawa, T., Yamamura, T., Waseda, Y.: Viscosity of molten GaSb and InSb. Int. J. Thermophysics 23, 235–243 (2002)CrossRefGoogle Scholar
  21. Stelian, C., Duffar, T., Nicoara, I.: Comparison between numerical simulation and experimental measurement of solute segregation during directional solidification. J. Cryst. Growth 255, 40–51 (2003)CrossRefGoogle Scholar
  22. Stringfellow, G.B.: Calculation of ternary phase diagrams of III-V systems. J. Phys. Chem. Solids 33, 665–677 (1972)CrossRefGoogle Scholar
  23. Takagi, Y., Suzuki, N., Okano, Y., Tanaka, A., Hayakawa, Y., Dost, S.: Numerical simulation of the dissolution process of GaSb into InSb melt under normal and microgravity conditions. Trans. JSASS Aerospace Tech. Japan 10, Ph_1–Ph_7 (2012)Google Scholar
  24. Tomažić, B., Nancollas, G.H: The kinetics of dissolution of calcium oxalate hydrates. J. Cryst. Growth 46, 355–361 (1979)CrossRefGoogle Scholar
  25. Yan, Z., Naritsuka, S., Nishinaga, T.: Interface supersaturation dependence of step velocity in liquid-phase Epitaxy of InP. J. Cryst. Growth 198(/199), 1077–1081 (1999)CrossRefGoogle Scholar
  26. Yee, J.F., Lin, M., Sarma. K., Wilcox, W.R.: The influence of gravity on crystal defect formation in InSb-GaSb alloys. J. Cryst. Growth 30, 185–192 (1975)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • H. Mirsandi
    • 1
  • T. Yamamoto
    • 1
  • Y. Takagi
    • 1
  • Y. Okano
    • 1
    Email author
  • Y. Inatomi
    • 2
  • Y. Hayakawa
    • 3
  • S. Dost
    • 4
  1. 1.Department of Materials Engineering ScienceOsaka UniversityToyonakaJapan
  2. 2.Japan Aerospace Exploration AgencyTsukubaJapan
  3. 3.Research Institute of ElectronicsShizuoka UniversityHamamatsuJapan
  4. 4.Crystal Growth LaboratoryUniversity of VictoriaVictoriaCanada

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