4. Mobility Modeling

An accurate description of the carrier mobility is essential for estimating the performance of semiconductor devices using numerical methods. While the mobility can be calculated from the different scattering mechanisms using numerical techniques such as Monte Carlo methods, an analytical description of mobility seems more appropriate for performing device simulations. Although much work has been done in developing analytical mobility models for unstrained Si similar efforts are lacking for strained Si.

This chapter focuses on modeling of the electron mobility in Si. In Section 4.1, the fundamental equations of electromagnetics as well as the Boltzmann's transport equation are stated and used to derive the transport equations that form the backbone for semiconductor device simulations. The different mobility modeling approaches are discussed next in Section 4.2 including a brief discussion about the Monte Carlo method. In Section 4.3, a model describing the low-field bulk mobility for electrons in strained Si layers as a function of strain is presented. It includes the effect of strain-induced splitting of the conduction band valleys in Si, inter-valley scattering, and doping dependence. The model has been extended to take into account the modification of the effective mass tensor with shear strain, as was discussed in Section 3.3.4. In addition, the applicability of the model to estimate the electron mobility in strained Ge is also demonstrated. Efforts to model the Si inversion layer mobility are discussed in Section 4.5. The electron velocity in uniaxially and biaxially strained Si in the nonlinear transport regime is investigated in Section 4.6. An analytical model describing the velocity components parallel and perpendicular to the field direction has been developed. For mobility modeling, a systematic methodology is adopted in which first the bulk mobility is treated followed by surface and high field reductions, as described in Section 4.7.