Modified Thomas-Fermi theory for depletion and accumulation layers inn-type GaAs

Abstract

A modified Thomas-Fermi approximation (TFA) developed originally for inversion layers is used to calculate electron-density profiles, the spatial dependences of the potential, surface potentials, and the energies of bound states of depletion and accumulation layers in n-type CxaAs. Remarkable agreement with recently published results of self-consistent calculations of Ehlers and Mills [Phys. Rev. B 34, 3939 (1986)] is achieved. All deficiencies of the conventional TFA discussed there are removed. Methodological advantages of the modified TFA are discussed.

Structural, electrical and optical characterization of MOCVD grown In-rich InGaN layers

“…The band bending V bb has been calculated from the relative surface and bulk Fermi level positions. The electron sheet density (electron accumulation) has been determined by space charge calculations using Poisson's equation [15] within the modified Thomas-Fermi approximation (MTFA) [16][17][18].…”

Nonparabolic coupled Poisson-Schrödinger solutions for quantized electron accumulation layers: Band bending, charge profile, and subbands at InN surfaces

“…20 The MTFA approximation has been shown to be in excellent agreement with full self-consistent PS solutions for parabolic conduction band dispersions. 19,21 However, although this method generates very similar one-electron potentials and charge profiles to self-consistent PS solutions, it does not contain any information on the subband structure present when strong band bending at the semiconductor surface causes the conduction band states to become quantized. This paper presents details of a method combining the Poisson-MTFA solution with a numerical solution of the Schrödinger equation for the resulting one-electron potential to yield the conduction subband structure.…”

Effect of a skin-deep surface zone on the formation of a two-dimensional electron gas at a semiconductor surface

“…We restrict our consideration to λ > 0, see Appendix C for a justification. So far only the particular case with λ → ∞ corresponding to ξ (0) = 0 has been considered [27,28], resulting in the basis of generalized wave functions (in the direction normal to the surface) sin(kz) k>0 . We treat λ as a parameter to be fit to the data.…”

“…This is formulated as a 1D self-consistent PoissonSchrödinger problem. The problem has been solved iteratively [21][22][23][24] and also using the modified Thomas-Fermi approximation (MTFA) [25][26][27][28]. These two strategies have been found equivalent [26,29].…”