Interdiffusion process in lattice-matched <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">In</mi></mrow><mrow><mi mathvariant="italic">x</mi></mrow></msub></mrow></math><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Ga</mi></mrow><mrow><mn>1</mn><mi mathvariant="normal">−</mi><mi mathvariant="italic">x</mi></mrow></msub></mrow></math><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">As</mi></mrow><mrow><mi mathvariant="italic">y</mi></mrow></msub></mrow></math><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mn>1</mn><mi mathvariant="normal">−</mi><mi mathvariant="italic">y</mi></mrow></msub></mrow></math>/InP and GaAs/<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Al</mi></mrow><mrow><mi mathvariant="italic">x</mi></mrow></msub></mrow></math><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Ga</mi></mrow><mrow><mn>1</mn><mi mathvariant="normal">−</mi><mi mathvariant="italic">x</mi></mrow></msub></mrow></math>As quantum wells

Kohki Mukai; Mitsuru Sugawara; Susumu Yamazaki

doi:10.1103/PhysRevB.50.2273

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Interdiffusion process in lattice-matched ${In}_{x}$ ${Ga}_{1 - x}$ ${As}_{y}$ $P_{1 - y}$ /InP and GaAs/ ${Al}_{x}$ ${Ga}_{1 - x}$ As quantum wells

Kohki Mukai, Mitsuru Sugawara, and Susumu Yamazaki

Fujitsu Laboratories Ltd., 10-1 Morinosato-Wakamiya, Atsugi 243-01, Japan

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Phys. Rev. B 50, 2273 – Published 15 July, 1994

DOI: https://doi.org/10.1103/PhysRevB.50.2273

Abstract

We derive a formula that describes interdiffusion profiles of quantum wells and shows how the formula accurately models interdiffusion in quantum wells of lattice-matched ${In}_{x}$ ${Ga}_{1 - x}$ ${As}_{y}$ $P_{1 - y}$ and ${Al}_{x}$ ${Ga}_{1 - x}$ As alloy semiconductors. Our formula includes the different interdiffusion coefficients between layers and interfacial discontinuity of interdiffused species. Our formula explains how quantum energy shifts due to interdiffusion vary with annealing time and annealing temperature in various wide well layers of both ${In}_{x}$ ${Ga}_{1 - x}$ ${As}_{y}$ $P_{1 - y}$ /InP and GaAs/ ${Al}_{x}$ ${Ga}_{1 - x}$ As quantum wells. We also show the quantitative difference between interdiffusion profiles of these two materials.

References (41)

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[c1] L. L. Chang and Koma, Appl. Phys. Lett. 29, 138 (1976).

[c2] W. D. Laidig, N. Holonyak, Jr., M. D. Camras, K. Hess, J. J. Coleman, P. D. Dapkus and J. Bardeen, Appl. Phys. Lett. 38, 776 (1981).

[c3] M. Kawabe, N. Matsuura, N. Shimizu, F. Hasegawa and Y. Ninnichi, Jpn. J. Appl. Phys. 23, L623 (1984).

[c4] K. Meehan, N. Holonyak, Jr., J. M. Brown, M. A. Nixon and P. Gavrilovic, Appl. Phys. Lett. 45, 549 (1984).

[c5] E. V. K. Rao, H. Thibiergr, F. Brillouet, F. Alexandre and R. Azoulay, Appl. Phys. Lett. 46, 867 (1985).

[c6] R. L. Thornton, R. D. Burnham, T. L. Paoli, N. Holonyak, Jr., and D. G. Deppe, Appl. Phys. Lett. 48, 7 (1986).

[c7] R. L. Thornton, R. D. Burnham, T. L. Paoli, N. Holonyak, Jr., and D. G. Deppe, Appl. Phys. Lett. 47, 1239 (1985).

[c8] T. Fukuzawa, S. Semura, H. Saito, T. Ohta, Y. Uchida and H. Nakashima, Appl. Phys. Lett. 45, 1 (1984).

[c9] J. Cibert, P. M. Petroff, D. J. Werder, S. J. Pearton, A. C. Gossard and J. H. English, Appl. Phys. Lett. 49, 223 (1986).

[c10] D. G. Deppe, L. J. Guido, N. Holonyak, Jr., K. C. Hsieh, R. D. Burnham, R. L. Thornton and T. L. Paoli, Appl. Phys. Lett. 49, 510 (1986).

[c11] J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard and J. H. English, Appl. Phys. Lett. 49, 1275 (1986).

[c12] L. J. Guido, N. Holonyak, Jr., K. C. Hsieh, R. W. Kaliski, W. E. Plano, R. D. Burnham, R. L. Thornton, J. E. Epler and T. L. Paoli, J. Appl. Phys. 61, 1372 (1987).

[c13] M. D. Camras, T. L. Paoli and C. Linstrom, J. Appl. Phys. 54, 5637 (1983).

[c14] H. Leier, H. Rothfritz, and Forchel, J. Appl. Phys. 95, 277 (1989).

[c15] K. Nakashima, Y. Kawaguchi, Y. Kawamura, H. Asahi and Y. Imamura, Jpn. J. Appl. Phys. 26, L1620 (1987).

[c16] T. Fujii, N. Sugawara, S. Yamazaki and K. Nakajima, J. Cryst. Growth 105, 348 (1990).

[c17] B. Tell, B. C. Johnson, J. L. Zyskind, J. M. Brown, J. W. Sulhoff, K. F. Brown-Goebeler, B. I. Miller and U. Koren, Appl. Phys. Lett. 52, 1428 (1988).

[c18] M. Razeghi, O. Acher and F. Launay, Semicond. Sci. Technol. 2, 793 (1987).

[c19] K. Nakashima, Y. Kawaguchi, Y. Kawamura and Y. Imamura, Appl. Phys. Lett. 52, 1383 (1988).

[c20] S. A. Schwarz, P. Mei, T. Venkatesan, R. Bhat, D. M. Hwang, C. L. Schwartz, M. Koza, L. Nazar and B. J. Skromme, Appl. Phys. Lett. 53, 1051 (1988).

[c21] H. Sumida, H. Asahi, S. J. Yu, K. Asami and S. Gonda, Appl. Phys. Lett. 54, 520 (1989).

[c22] H. Ribot, K. W. Lee, R. J. Simes, R. H. Yan and L. A. Coldren, Appl. Phys. Lett. 55, 672 (1989).

[c23] E. S. Koteles, A. N. M. M. Choudhury, A. Levy, B. Elman, P. Melman, M. A. Koza, and R. Bhat, in Advanced III-V Compound Semiconductor Growth, Processing and Devices, edited by S. J. Pearton, D. K. Sadana, and J. M. Zavada, MRS Symposia Proceedings No. 240 (Materials Research Society, Pittsburgh, 1991), p. 171.

[c24] R. M. Flemming, D. B. McWhan, A. C. Gossard, W. Wiegmann and R. A. Logan, J. Appl. Phys. 51, 357 (1980).

[c25] W. Jost, Diffusion (Academic, New York, 1960), p. 68.

[c26] R. Smoluchowski, Phys. Rev. 62, 539 (1942).

[c27] H. E. Cook and J. E. Hilliard, J. Appl. Phys. 40, 2191 (1969).

[c28] H. Haken, Quantenfeldtheorie des Festkorpers (Teubner, Stuttgart, 1973).

[c29] G. E. Pikus and G. L. Bir, Fiz. Tverd. Tela (Leningrad) 1, 154 (1959) [Sov. Phys. Solid State 1, 136 (1959)].

[c30] G. E. Pikus and G. L. Bir, Fiz. Tverd. Tela (Leningrad) 1, 1642 (1959) [Sov. Phys. Solid State 1, 1502 (1960)].

[c31] A. Gavini and M. Cardona, Phys. Rev. B 1, 672 (1970).

[c32] K. Sakurai, Introduction to Quantum Mechanics by Personal Computer (Shokabo, Tokyo, 1989) [in Japanese].

[c33] M. C. Joncour, J. L. Benchimol, J. Burgeat and M. Quillec, J. Phys. (Paris) Colloq. 5, 3 (1982).

[c34] S. R. Forest, P. H. Schmidt, R. B. Wilson and M. L. Kaplan, Appl. Phys. Lett. 45, 1199 (1984).

[c35] C. P. Kuo, S. K. Vong, R. M. Cohen and G. B. Stringfellow, J. Appl. Phys. 57, 5428 (1985).

[c36] Y. Suematsu, Semiconductor Laser and OEIC (Orhm Inc., Tokyo, 1984), p. 70 [in Japanese].

[c37] H. C. Casey, Jr., , J. Appl. Phys. 49, 3684 (1978).

[c38] B. Goldstein, Phys. Rev. 121, 1305 (1961).

[c39] S. Y. Chiang and G. L. Pearson, J. Appl. Phys. 46, 2986 (1975).

[c40] D. L. Kendal, in Semicoductors and Semimetals (Academic, New York, 1968), Vol. 4, p. 163.

[c41] S. J. Yu, H. Asahi, S. Emura, S. Gonda and K. Nakashima, J. Appl. Phys. 70, 204 (1991).

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Interdiffusion process in lattice-matched ${In}_{x}$ ${Ga}_{1 - x}$ ${As}_{y}$ $P_{1 - y}$ /InP and GaAs/ ${Al}_{x}$ ${Ga}_{1 - x}$ As quantum wells

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Interdiffusion process in lattice-matched InxGa1−xAsyP1−y/InP and GaAs/AlxGa1−xAs quantum wells

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References (41)

Interdiffusion process in lattice-matched ${In}_{x}$ ${Ga}_{1 - x}$ ${As}_{y}$ $P_{1 - y}$ /InP and GaAs/ ${Al}_{x}$ ${Ga}_{1 - x}$ As quantum wells