Modelling and Calculation of Silicon Conduction Band Structure and Parameters with Arbitrary Uniaxial Stress

Guanyu Wang,Chunyu Zhou,Mingdao Yu

doi:10.4236/jamp.2018.61018

Abstract

Using the k·p theory, the coupling effect between the Δ1 and Δ2’ bands on the energy band structure of different energy valleys is studied. The analytical model of the energy-dispersion relationship applicable to uniaxial stress for arbitrary crystal plane and orientation as well as different energy valleys is established. For typical crystal orientations, the main parameters of energy band structure such as band edge level, splitting energy, density-of-state (DOS) effective mass and conductivity effective mass are calculated. The calculated results are in good agreement with the data reported in related literature. Finally, the relationship between the DOS effective mass, conductivity effective mass and the change of stress and orientation of different crystal planes is given. The proposed model and calculation results can provide a theoretical reference for the design of nano-electronic devices and TCAD simulation.

Highlights

As an important method of extending Moore’s Law, strained silicon technology can significantly improve the mobility of carriers in devices [1] [2]
In order to apply this model to different valleys of conduction band, we introduce the conversion operator Tv
The uniaxial stress was applied on these typical orientations, and the band structures of different valleys were studied

Summary

Introduction

As an important method of extending Moore’s Law, strained silicon technology can significantly improve the mobility of carriers in devices [1] [2]. Using the traditional k∙p perturbation method and deformation potential theory, the calculation results in [7] [8] [9] show that the strain effect does not change the structure of the conduction band or the shape of the constant-energy surface, but only changes the position of the conduction band edge These studies neglected the change of band structure by stress. In order to describe the effects of uniaxial stress on conduction band structure, it is necessary to further improve the two-band model and calculate the main parameters of the energy band, in order to use an arbitrary crystal plane and provide the theoretical basis for the informed selection of the orientation of a strained Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET) channel

The Model

Energy Band Model

Effective Mass

Energy Band Structure

Band Edge Level of Conduction Band

Summary