Limitations of step profile models in describing the space-charge distribution near semiconductor surfaces

Abstract

High-resolution electron energy-loss (HREEL) spectra have been analysed using local dielectric theory in a study of the depletion layer formed at the InSb(100) surface. Two-, three-and four-layer models were used to simulate a series of low-incidence-energy HREEL spectra (1.25-10 eV). An abrupt charge profile (the two-layer model) provided good agreement with experimental data when spatial dispersion and wavevector-dependent plasmon damping were included in the local dielectric model. This was in spite of the fact that the twolayer model does not accurately reflect the charge distribution, which was calculated using the modified Thomas-Fermi approximation (MTFA). Smoothing of the step profile by the inclusion of an intermediate layer (the three-layer model) introduced 'plasmaron' modes, unless the plasma damping in the middle layer was set to a very high level. These modes were not observed experimentally, indicating that the abrupt charge profile in fact produced more accurate simulations. A four-layer model more closely approximating the calculated charge profile produced superior fits to the experimental spectra, but only when the plasma damping in each layer was carefully controlled. The limitations of step profile approximations and the local dielectric theory approach in describing regions of highly non-uniform charge density are discussed. In particular, the spatial and wavevector dependence of the plasmon damping is considered.

Evolution of electron states at a narrow-gap semiconductor surface in an accumulation-layer formation process

“…For simplicity of calculation, we describe the charged surface by a uniform distribution of surface charges that extends right outside and along each background surface. 10,[22][23][24][25][26][27][28][29]31,32,35 We assume the charge neutrality of the whole system that is composed of the carrier system, the positive background, and the surface-charge distribution.…”

“…19,20 At light doping, quasi-two-dimensional plasmons occur in a sharply localized accumulation layer, 20 while, at heavy doping, electronic excitations in the accumulation layer are virtually surface plasmons in a semi-infinite system with the carrier density enhanced near the surface. 19 In relation to the EELS measurements, the surface excitations in the absence and the presence of a surface spacecharge layer have been calculated by means of a hydrodynamic theory combined with a step density-profile model, 19,28,29 a semiclassical local-response theory formulated in Ref. 30,10,20,25 the random-phase approximation, [31][32][33][34] and the time-dependent LDA.…”

“…In another scheme treating an accumulation layer, the EEL spectrum has been calculated by using a step profile of the carrier density that approximates to the accurate density profile in thermal equilibrium taking account of the nonparabolicity. 28,29 The latter density profile is calculated by the modified Thomas-Fermi approximation that involves the NP band obtained by the simplified version of the k"p method. 40 However, this is a simplified scheme to calculate the EEL spectrum with reasonable effort.…”

Evolution of elementary excitations at a doped polar semiconductor surface in a depletion-layer formation process

“…Furthermore, the clean ͑001͒ surface of n-type InSb is also reported to have a considerable depletion layer. 29,30 The carrier density distribution and the effective oneelectron potential in the absence and the presence of a surface space-charge layer can be calculated self-consistently by several schemes. To perform self-consistent calculations with reasonable efforts, carrier charges in surface states are so often replaced by a uniform distribution of surface charges.…”

“…In passing, surface excitations on the clean n-doped GaAs ͑001͒ or InSb ͑001͒ surface with its intrinsic surface states in Refs. [27][28][29][30] correspond to the latter case of the higher doping level.…”