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33
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84931539652
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It should be remarked explicitly that, since we solve the one-dimensional Schrödinger equation, we are tacitly embracing a ``gradual-channel'' approximation: We assume that the variation of the potential along the channel is small over an electron wavelength.
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49
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84931539647
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The nonparabolic perturbative approach has been developed by D. Ahn, and reported together with the pseudopotential approach in M. V. Fischetti and D. Ahn, IBM Research Report RC 14801 7/25/89 (unpublished).
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52
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84931539646
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Density of states and electron-phonon-scattering rates employing a numerically tabulated band structure have been employed by us before in bulk semiconductors, as presented in Ref. 22. Density of states and scattering rates, in that case, could be computed once and for all and stored, since they do not depend on variables associated with the bias conditions and geometric configuration of the device under study. In the present case, unfortunately, eigenvalues and eigenfunctions of Eq. (13) depend on these variables. Therefore, while feasible in principle and easier than what was done in Ref. 22, an evaluation of density of states and scattering rates for a ``numerical'' subband structure is computationally prohibitive.
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-
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61
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84931539644
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F. Stern, unpublished results reproduced in Ref. 1.
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70
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84931539643
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Note that Ref. 62 reports a value of -0.67 for the ratio DXI.
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-
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99
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84931539642
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See the review by Ridley (Ref. 58) for recent work on interface and slab phonons with hydrodynamics and electromagnetic boundary conditions.
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104
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0345220730
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-
According to Ridley (Ref. 58), we are committing a sin here. Electromagnetic boundary conditions are known not to yield the right result, while hydrodynamic boundary conditions, as given by
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(1986)
J. Phys. C
, vol.19
, pp. 683
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Babiker, M.1
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105
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0006068029
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-
approximate much better the results of microscopic models when there is a small mismatch of the optical-phonon frequency across the interface, as is the case for the GaAs/Ge system [see, ]. In our case, is not clear whether even mechanical boundary conditions will work and we simply follow history, perhaps blindly and acritically, in using the Fuchs-Kliever approach. Finally, we do not differentiate between the interface phonons, coupled to the electrons by a strong Fröhlich scalar coupling, and interface polaritons, coupled to the electrons rather weakly via a p vec cdot A vec interaction, according to Ref. 58 and, 7, B52, M. Babiker, Semicond. Sci. Technol.
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(1989)
Phys. Rev. B
, vol.40
, pp. 2914
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Akera, H.1
Ando, T.2
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110
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84931539641
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In SiO2, the condition ω TO,2 >> ω TO,1 is verified only approximately, as Table I shows. Therefore, the zeros of Eq. (32) are obtained by the expressions for ω LO,i given in the text only within a few meV. The same considerations apply to the expressions given for the ``flat'' region of the dispersion of the SO modes.
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-
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111
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84931539640
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See also Ref. 90, Eqs. (2) – (23).
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117
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84931539745
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See the brief review given in Ref. 1 and the relative references therein.
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131
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0020879920
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A similar equation has been given by Stern and Howard (Ref. 106) and later used in the work by Yokoyama and Hess (Ref. 27), but with a slightly different approximation for the screening parameter qs,ν ( q ), by ignoring its q dependence. Solutions of this equation assuming either zero thickness for the inversion charge, or a sinusoidal wave function, have been given by, Ap, Lett. 35, 485 (1979) and by J. Lee
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(1983)
J. Appl. Phys.
, vol.54
, pp. 6995
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Hess, K.1
Phys2
Spector, N.H.3
Arora, V.K.4
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132
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84931539747
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-
respectively.
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-
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140
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84931539750
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P. Vogl, in Physics of Nonlinear Transport in Semiconductors, edited by D. K. Ferry, J. R. Barker, and C. Jacoboni, Vol. 52 of NATO Advanced Study Institute, Series B: Physics (Plenum, New York, 1980), p. 75.
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146
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84931539751
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Here we are assuming that Ksc2ieq q2- curlepscω2/ ( curlep0c2) apeq q2, which is valid for q >> 1.8 times 103 cm-1 when omega is set equal to the LA-phonon frequency at Q vec = ( q vec ,&qmacr0), with q bar0apeq 1.7 times 107 cm-1, as obtained from Eq. (72) of the text in our case.
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-
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147
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84931539753
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The expression for the bulk dynamic polarizability given in Ref. 118 is also valid in the case of a 2DEG (except for an overall factor 2 / λν), as noted by Fetter in Ref. 117 for the static polarizability.
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-
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148
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24544470347
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It is known that in bulk materials collisional broadening cannot be accounted for by simply replacing omega in Eq. (73) with ω + i / tau, where tau is the relaxation time: this would violate conservation of particle number. An extension to 2DEG's of the result given by, is required. We are indebted to F. Stern for bringing this point to our attention.
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(1970)
Phys. Rev. B
, vol.1
, pp. 2362
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Mermin, N.D.1
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