I am looking for the eigen value part and the in-plane dispersion for this equation for a MOS structure where electrons are quantized in the z direction. Stern and Howard (PRB 1967) have a very good discussion on it for parabolic case. What about the nonparabolic case?
The following papers might be of interest to you:
Nonresonant nonlinearity due to intersubband transitions in nonparabolic semiconductor quantum wells, S. Mukhopadhyay, J. Appl. Phys. 90, 5441 (2001).
Interface roughness-limited electron mobility in AlAs/GaAs and GaInP/GaAs quantum wells, B.R. Nag, S. Mukhopadhyay, and M. Das, J. Appl. Phys. 86, 459. (1999).
Intrinsic electron mobility in narrow Ga0.47In0.53As quantum wells, S. Mukhopadhyay, and B.R. Nag, Phys. Rev. B 48, 17960 (1993).
In-plane effective mass in narrow quantum wells of nonparabolic semiconductors, B.R. Nag, and S. Mukhopadhyay, Appl. Phys. Lett. 62, 2416 (1993).
Energy levels in quantum wells of nonparabolic semiconductors, B.R. Nag, and S. Mukhopadhyay, Phys. Status Solidi(b), 175, 103 (1993).
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