By Edwin Henry Barton
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37) and (109), ‘ac = e 2 K T E 1 2J:, 2nhc, 1: (1 - X)G(k,k) 6(6 - 6’)(k’)’ dk‘ dX (1 10) - e 2IC TE mdk (3 - 8c2 + 6 ~ ~ ) . 3nh3c, The scattering rate vac is added to ve, of Eq. (40). Acoustic scattering, from Eq. (1 12), is proportional to k and leads to a nearly constant mean free path. The corresponding partial mobility is proportional to T - 3’2. All the parameters appearing in va,, characteristic of a given material, are known from independent experiments. The deformation potential can be related to the pressure rate coefficient of the energy gap,’”’ provided the corresponding valence-band shift is negligible.
3 H. J. G. Meijer and D. Polder, Physica 19,255 (1953). 74 W. A. Harrison, Phys. Rea. 101,903 (1956). 7 5 A. R. Hutson, J . Appl. Phys. Suppl. 32, 2287 (1961). 'O " 1. ^^ and Hutson and White76 have given the piezoelectric coupling coefficientappropriate to sphalerite and wurtzite structures. Allowing for anisotropy in the effective mass, permittivity, and piezoelectric ~ provided expressions suitable to parabolic bands. interaction, 2 0 0 k ~has These expressions involve integrals which cannot be reduced analytically if the effective mass is anisotropic.
99) or (104). The deformation potential E , (units of eV per strain or simply eV) is equal to the distance the conduction band edge shifts (in eV) per unit strain due to the acoustic vibration. Note that s(k, k) is independent of the angle between k' and k for parabolic bands where G(k', k) = 1. 6 J . Bardeen and W. Shockley, Phys. Rev. 80, 72 (1950). '4 See C0nwe11,~~ p. 108. 38 D. L. RODE Their theory of multivalley conduction shows the importance of transverse modes for deformation-potential scattering.
An introduction to the mechanics of fluids by Edwin Henry Barton