The size quantization effect in the channel of a 2D nanoscale MOSFET is studied using a self-consistent quantum method. Under this, Schrodinger-Poisson equations are solved for determining the electron density for 2D device channels from 3 nmנ3 nm to 100 nmנ100 nm. The lower dimension channels show a peak of the electron density at the middle whereas higher dimension channels show the accumulation of the electrons at the oxide/semiconductor interface. Also, the role of quantum capacitance on the threshold voltages of these nanoscale devices is investigated as a function of channel dimensions and electron effective masses. It is observed that not only the size but the electron effective masses dominate the conductivity of the channel for such nanoscale devices. Here, the channel electron densities are obtained using density matrix formalism. A block diagonal Hamiltonian Matrix [H] is constructed for this oxide/channel/oxide 2D structure and the channel is discretized by using the finite-difference method. This analysis is important for understanding the physics of the size quantization and its effect on the threshold voltage.

使用自洽量子方法研究了二维纳米级 MOSFET沟道中的尺寸量化效应。在此之下，求解薛定谔-泊松方程以确定2D器件通道的电子密度，从3 nm到3 nm100 纳米和 100 纳米。较低维度的通道在中间显示电子密度的峰值，而较高维度的通道显示在氧化物/半导体界面处电子的积累。此外，研究了量子电容对这些纳米级器件的阈值电压的作用，作为沟道尺寸和电子有效质量的函数。据观察，对于这种纳米级器件，不仅尺寸而且电子有效质量支配着沟道的导电性。这里，通道电子密度是使用密度矩阵形式获得的。为这种氧化物/通道/氧化物二维结构构建块对角哈密顿矩阵[H]，并使用有限差分法对通道进行离散化。