Abstract

We generalize the method proposed previously for a self-consistent solution of the system of the Kohn–Sham and Poisson equations to the case of high density of electrons localized near the surface of a semiconductor due to size quantization of the electron spectrum in a potential well in the band banding region. We obtain a completely self-consistent iterative solution for a quasi two-dimensional electron gas in the accumulation layer at the surface of a semiconductor with a degenerate electron gas in the bulk. Both parabolic and non-parabolic energy spectra of conduction electrons are considered. For a parabolic conduction band, we obtain the spatial distributions of the electron density and electrostatic potential, as well as the energies of size-quantized levels and their dependence on the depth of the near-surface potential well. A significant decrease in the density of three-dimensional electrons was revealed in the region where the quasi two-dimensional electron gas occupied the accumulation layer. We calculated the dependencies of the excess electron surface density and the capacitance of the structure on the surface potential. The results are presented in dimensionless form that can be used to semi-quantitatively evaluate the parameters of accumulation layers by the known level of doping and the value of band bending. In the case of the nonparabolic conduction band, due to the finite bandgap width, the spectrum of quasi two-dimensional electron gas is obtained in the two-band Franz–Kane approximation by solving the eigenvalue problem for the new single-band equation of the effective-mass method. The density of states and the effective mass of electrons in the 2D subbands is found to increase linearly with energy. We have derived the expression that analytically approximates the calculated energy spectrum. The position of levels, the dispersion of energy spectrum, and the dependence of effective mass on energy, which were found for the size-quantized sub-bands, are in agreement with the published results for characteristics of quasi two-dimensional electrons at n-InAs surface that were directly measured by angle resolved photoelectron spectroscopy and magnetotunneling spectroscopy. Conditions are considered when the nonparabolicity of the conduction band enables quasi two-dimensional electrons to absorb the normally incident radiation due to intersubband transitions.

中文翻译：

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具有非抛物线能带的半导体积层中准二维电子气的自洽Kohn-Sham和Poisson方程的解

摘要

我们将先前针对Kohn-Sham和Poisson方程组的自洽解提出的方法推广到由于势阱中电子光谱的尺寸量化而使高密度电子位于半导体表面附近的情况在乐队的乐队区域。我们获得了半导体表面堆积层中准二维电子气与整体中简并电子气的完全自洽迭代解。传导电子的抛物线和非抛物线能谱都被考虑了。对于抛物线导带，我们获得了电子密度和静电势的空间分布，以及尺寸量化的能级及其对近表面势阱深度的依赖性。在准二维电子气占据累积层的区域中，三维电子的密度显着降低。我们计算了过量电子表面密度和结构电容对表面电势的依赖性。结果以无量纲形式呈现，可用于通过已知的掺杂水平和能带弯曲值半定量评估累积层的参数。在非抛物线导带的情况下，由于有限的带隙宽度，通过求解新的单带方程的特征值问题，可以在两带Franz-Kane近似中获得准二维电子气的光谱。有效质量法。发现二维子带中的状态密度和电子的有效质量随能量线性增加。我们已经得出了可以解析地近似计算出的能谱的表达式。对于尺寸量化的子带，能级的位置，能谱的散布以及有效质量对能量的依赖性与已发表的关于准二维电子的特性的结果一致。通过角分辨光电子能谱和磁隧道技术直接测量n -InAs表面。当导带的非抛物线性使准二维电子由于子带间跃迁而吸收垂直入射的辐射时，应考虑以下条件。