Electronic Effects in the Elastic Constants of <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math></span>-Type Silicon

John J. Hall

doi:10.1103/PhysRev.161.756

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Electronic Effects in the Elastic Constants of $n$ -Type Silicon

John J. Hall

IBM Watson Research Center, Yorktown Heights, New York

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Phys. Rev. 161, 756 – Published 15 September, 1967

DOI: https://doi.org/10.1103/PhysRev.161.756

Abstract

The temperature dependence of the second-order elastic moduli, and the 25°C third-order elastic constants, are reported for pure silicon and for silicon doped with ∼2× $10^{19}$ ( $P$ atoms)/ ${cm}^{3}$ . Certain combinations of the elastic constants are unaffected by the doping; others show large changes which are interpreted in the light of Keyes's theory of the electronic contribution to the elastic constants. The agreement between theory and experiment is excellent, and permits a thermodynamic determination of the carrier concentration of the doped sample and of the shear deformation potential constant $Ξ_{u}$ for the silicon conduction band of 8.6 eV at 25°C.

References (24)

R. W. Keyes, IBM J. Res. Develop. 5, 266 (1961)
C. Herring and E. Vogt, Phys. Rev. 101, 944 (1956)
L. J. Bruner and R. W. Keyes, Phys. Rev. Letters 7, 55 (1961)
N. G. Einspruch and P. Csavinszky, Appl. Phys. Letters 2, 1 (1963)
J. J. Hall, Phys. Rev. 137, A960 (1965)
J. R. Drabble and J. Fendley, Solid State Commun. 3, 269 (1965)
J. J. Hall and P. J. Price (to be published)
Omitted endnote
Omitted endnote
D. F. Gibbons, Phys. Rev. 112, 136 (1958)
R. H. Carr, R. D. McCammon, and G. K. White, Phil. Mag. 12, 157 (1965)
S. I. Novikova, Fiz. Tverd. Tela 6, 333 (1964) [English transl.: Soviet Phys.—Solid State 6, 269 (1964)]
Omitted endnote
A. Smakula and V. Sils, Phys. Rev. 99, 1744 (1955) A. Smakula, J. Kalnajs, and V. Sils, ibid. 99, 1747 (1955)
B. G. Cohen, Solid State Electron. 10, 33 (1967)
R. J. Blume, Rev. Sci. Instr. 34, 1400 (1963)
H. J. McSkimin and P. Andreatch, Jr., J. Appl. Phys. 35, 3312 (1964)
R. N. Thurston and K. Brugger, Phys. Rev. 133, A1604 (1964)
K. Brugger, Phys. Rev. 133, A1611 (1964)
J. R. Neighbours and C. S. Smith, Acta. Met. 2, 591 (1954) R. Bacon and C. S. Smith, ibid. 4, 337 (1956)
J. McDougall and E. C. Stoner, Phil. Trans. Roy. Soc. A237, 67 (1938)
J. E. Aubrey, W. Gubler, T. Henningsen, and S. H. Koenig, Phys. Rev. 130, 1667 (1963)
I. Balslev, Phys. Rev. 143, 636 (1966)
J. C. Hensel, H. Hasegawa, and M. Nakayama, Phys. Rev. 138, A225 (1965)

[c1] R. W. Keyes, IBM J. Res. Develop. 5, 266 (1961)

[c2] C. Herring and E. Vogt, Phys. Rev. 101, 944 (1956)

[c3] L. J. Bruner and R. W. Keyes, Phys. Rev. Letters 7, 55 (1961)

[c4] N. G. Einspruch and P. Csavinszky, Appl. Phys. Letters 2, 1 (1963)

[c5] J. J. Hall, Phys. Rev. 137, A960 (1965)

[c6] J. R. Drabble and J. Fendley, Solid State Commun. 3, 269 (1965)

[c7] J. J. Hall and P. J. Price (to be published)

[c8] Omitted endnote

[c9] Omitted endnote

[c10] D. F. Gibbons, Phys. Rev. 112, 136 (1958)

[c11] R. H. Carr, R. D. McCammon, and G. K. White, Phil. Mag. 12, 157 (1965)

[c12] S. I. Novikova, Fiz. Tverd. Tela 6, 333 (1964) [English transl.: Soviet Phys.—Solid State 6, 269 (1964)]

[c13] Omitted endnote

[c14] A. Smakula and V. Sils, Phys. Rev. 99, 1744 (1955) A. Smakula, J. Kalnajs, and V. Sils, ibid. 99, 1747 (1955)

[c15] B. G. Cohen, Solid State Electron. 10, 33 (1967)

[c16] R. J. Blume, Rev. Sci. Instr. 34, 1400 (1963)

[c17] H. J. McSkimin and P. Andreatch, Jr., J. Appl. Phys. 35, 3312 (1964)

[c18] R. N. Thurston and K. Brugger, Phys. Rev. 133, A1604 (1964)

[c19] K. Brugger, Phys. Rev. 133, A1611 (1964)

[c20] J. R. Neighbours and C. S. Smith, Acta. Met. 2, 591 (1954) R. Bacon and C. S. Smith, ibid. 4, 337 (1956)

[c21] J. McDougall and E. C. Stoner, Phil. Trans. Roy. Soc. A237, 67 (1938)

[c22] J. E. Aubrey, W. Gubler, T. Henningsen, and S. H. Koenig, Phys. Rev. 130, 1667 (1963)

[c23] I. Balslev, Phys. Rev. 143, 636 (1966)

[c24] J. C. Hensel, H. Hasegawa, and M. Nakayama, Phys. Rev. 138, A225 (1965)

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Electronic Effects in the Elastic Constants of $n$ -Type Silicon

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Electronic Effects in the Elastic Constants of n-Type Silicon

Abstract

References (24)

Electronic Effects in the Elastic Constants of $n$ -Type Silicon