Device Modeling

In this chapter we describe the modeling approaches developed for the simulation of germanium devices. The main focus will be on metal-insulator-semiconductor (MIS) devices, with particular attention on germanium-on-insulator (GOI) structures. Most of the approaches were originally developed for silicon devices, and thus we will describe them briefly, stressing the differences between Si and Ge and how they translate in different modeling requirements. The chapter is organized according to a “bottom-up” structure, beginning with Section 9.2 which describes the main differences between the basic properties of Ge and Si, and then spanning from band-structure calculation up to the determination of the drain current in MIS devices for both n-channel and p-channel transistors. However, so far, most of the models have been developed for n-channel devices and cannot be easily extended to p-channel transistors. This is reflected also in the material presented in this chapter, which is more complete and richer of examples for n-channel than it is for p-channel transistors. Section 9.3 is devoted to band-structure calculation. Since the main interest is in MIS devices, where carriers are quantized in a 2D inversion layer, a relevant fraction of the section is focused on the calculation of the energy states in 2D systems. In the semi-classical physical framework that we will consider hereafter, the transport modeling is essentially based on the Boltzmann transport equation (BTE), whose general solution is very complex because the scattering integrals make the stationary BTE an integral–differential equation in a multi-dimensional space of the phases (which has six dimensions for a bulk semiconductor and four dimensions for a 2D inversion layer). A dramatic simplification is obtained by neglecting the scattering term, which leads to the ballistic transport regime. This simplified approach is mostly useful to investigate the upper-limits of the performance that can be attained with a device structure, so that it can be used for a preliminary investigation of the possible benefits related to new device structures, such as Ge channel Metal-oxidesemiconductor field effect transistor (MOSFETs). This aspect is described in Section 9.4, where comparisons between Si and Ge devices are provided. The solution of the BTE beyond the ballistic approximation is considered in Section 9.5, starting from approximate solutions such as the Drift-Diffusion approach, and then considering more accurate approaches, such as the Monte-Carlo (MC) method. Finally, in Section 9.6 we will draw our conclusion and propose a “roadmap” for the forthcoming activities in the field of the simulation of advanced Ge devices.