4.2 Modeling Approaches

Modeling of carriers in the inversion layer poses additional complications. In the inversion layer, the carriers are subject to surface scattering, carrier-carrier scattering and quantum mechanical confinement. All these effects cause mobility degradation. The transverse electric field originating from the applied gate bias often serves as a parameter to indicate the strength of the inversion layer phenomena.

The high field behavior shows that the carrier mobility declines with electric field because the carriers that gain energy experience larger scattering rates. The mean drift velocity no longer increases linearly with increasing electric field, but rises more slowly. Eventually, the velocity saturates at a constant value. This saturation velocity is commonly denoted by the symbol . Impurity scattering is relatively insignificant for energetic carriers, and so is primarily a function of the lattice temperature.

The modeling approaches of physical parameters such as the mobility can be subdivided into three categories: [Mujtaba95]

- Physically based: Mathematical expressions describing the physical
effects are derived using first principle calculations. To capture the entire
physical model into a closed form solution in which the parameter dependencies
are obtained from fundamental calculations, considerable simplifying
assumptions have to be made.
- Semi-empirical: This approach arises because in practice it is seldom the
case that the physically-based models conform to the experimental
data. Therefore, to reconcile the model with experimental data, the
coefficients appearing in the physically-based model are allowed to vary from
their original values while certain dependencies resulting from the first
principles calculation are retained.
- Empirical: Empirically-based models are those in which all dependencies are allowed to vary. Compared to the other two approaches, this modeling approach generally tends to obscure the important physics thereby exhibiting a narrower range of validity. Empirical models are usually resorted to when the dependencies predicted by the first principles calculation do not allow a good fit between the experimental data and the corresponding semi-empirical model. These models are usually more efficient in comparison to the other two modeling approaches.

A distinct advantage of the Monte Carlo method is its ability to provide a solution of the BTE without compromising on the basic physical models for band structure and scattering processes. However, due to the statistical nature of the method, large simulation times are needed for performing full device simulations, in order to obtain meaningful average quantities of interest and to reduce the stochastic error.

In this work, the effect of strain on the electronic transport properties has been investigated using the Vienna Monte Carlo Simulator (VMC). It offers simulation algorithms for both bulk semiconductors and one-dimensional devices based on analytical band and full-band models. Additionally, a fast zero-field algorithm is included [Smirnov03]. VMC provides a mature set of scattering models including phonon scattering, ionized impurity scattering, alloy scattering, and impact ionization. Details concerning the scattering models implemented can be found in the documentation [IuE06].

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