Barker John R, Martinez Antonio
School of Engineering, University of Glasgow, Glasgow G12 8LT, United Kingdom.
J Phys Condens Matter. 2018 Apr 4;30(13):134002. doi: 10.1088/1361-648X/aaaf98. Epub 2018 Feb 15.
Efficient analytical image charge models are derived for the full spatial variation of the electrostatic self-energy of electrons in semiconductor nanostructures that arises from dielectric mismatch using semi-classical analysis. The methodology provides a fast, compact and physically transparent computation for advanced device modeling. The underlying semi-classical model for the self-energy has been established and validated during recent years and depends on a slight modification of the macroscopic static dielectric constants for individual homogeneous dielectric regions. The model has been validated for point charges as close as one interatomic spacing to a sharp interface. A brief introduction to image charge methodology is followed by a discussion and demonstration of the traditional failure of the methodology to derive the electrostatic potential at arbitrary distances from a source charge. However, the self-energy involves the local limit of the difference between the electrostatic Green functions for the full dielectric heterostructure and the homogeneous equivalent. It is shown that high convergence may be achieved for the image charge method for this local limit. A simple re-normalisation technique is introduced to reduce the number of image terms to a minimum. A number of progressively complex 3D models are evaluated analytically and compared with high precision numerical computations. Accuracies of 1% are demonstrated. Introducing a simple technique for modeling the transition of the self-energy between disparate dielectric structures we generate an analytical model that describes the self-energy as a function of position within the source, drain and gated channel of a silicon wrap round gate field effect transistor on a scale of a few nanometers cross-section. At such scales the self-energies become large (typically up to ~100 meV) close to the interfaces as well as along the channel. The screening of a gated structure is shown to reduce the self-energy relative to un-gated nanowires.
利用半经典分析方法，推导了半导体纳米结构中电子静电自能随空间的完整变化的高效解析镜像电荷模型，该变化源于介电常数失配。该方法为先进器件建模提供了快速、紧凑且物理意义清晰的计算方式。近年来，自能的基础半经典模型已经建立并得到验证，该模型依赖于对各个均匀介电区域的宏观静态介电常数进行微小修正。该模型已针对距离尖锐界面仅一个原子间距的点电荷进行了验证。在简要介绍镜像电荷方法之后，讨论并演示了该方法在推导距源电荷任意距离处的静电势时的传统失效情况。然而，自能涉及全介电异质结构与均匀等效结构的静电格林函数之差的局部极限。结果表明，对于该局部极限，镜像电荷方法可实现高度收敛。引入了一种简单的重新归一化技术，将镜像项的数量减至最少。对多个逐渐复杂的三维模型进行了解析评估，并与高精度数值计算结果进行了比较。结果表明精度可达1%。引入一种简单技术来模拟不同介电结构之间自能的转变，我们生成了一个解析模型，该模型将自能描述为硅环绕栅场效应晶体管源极、漏极和栅控沟道内位置的函数，其横截面尺度为几纳米。在这样的尺度下靠近界面以及沿沟道方向，自能会变得很大（通常高达约100毫电子伏特）。结果表明，与无栅纳米线相比，栅控结构的屏蔽作用可降低自能。
