4. Mobility Modeling

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.

- 4.1 Semiconductor Device Equations
- 4.1.1 Maxwell's Equations
- 4.1.2 Transport Equations and Mobility
- 4.1.3 Current Density
- 4.1.4 Basic MOS Equations

- 4.2 Modeling Approaches

- 4.3 Bulk Mobility of Strained Si
- 4.3.1 Piezoresistance Model
- 4.3.2 Physically Based Mobility Model for Strained Si
- 4.3.3 Doping Dependence
- 4.3.4 Mobility under Shear Stress

- 4.4 Bulk Mobility of Strained Ge
- 4.5 Inversion Layer Mobility

- 4.6 High-Field Mobility
- 4.6.1 Analytical High Field Velocity Model
- 4.6.2 Parallel Velocity Model
- 4.6.3 Perpendicular Velocity Model
- 4.6.4 Total Velocity for Arbitrary Field Direction
- 4.6.5 Simplification to Two-Dimensional Simulation Domains
- 4.6.6 Implementation Issues
- 4.6.7 Discussion

- 4.7 The Onion Model

S. Dhar: Analytical Mobility Modeling for Strained Silicon-Based Devices