For engineering applications, macroscopic transport models based on the Boltzmann Transport Equation (BTE) like the Drift-Diffusion (DD), model are very efficient compared to the time-consuming Monte Carlo (MC) simulation. However, with the further decrease of the device geometry into the deca-nanometer regime, the inaccuracy of the DD model increases steadily. Investigations have demonstrated that higher-order macroscopic models can cover the gate length range from 100nm down to about 25nm. To derive higher-order models, such as the six moments model, one has to multiply the BTE with special weight functions (for instance, the velocity of the carriers, or the energy) and integrate over k-space. Approximations used during the derivation of the models include the macroscopic relaxation time approximation for modeling the scattering operator of the BTE, the diffusion approximation, the modeling of the tensorial components, and the closure relation.
In the analysis of these models, it is essential to describe the transport parameters, namely the carrier mobility, the energy-flux mobility, the energy relaxation time, the second-order energy-flux mobility, and the second-order energy relaxation time with as few simplifying assumptions as possible. A rigorous study of the behavior of these parameters in the bulk case has already been carried out using bulk MC tables. A crucial issue is the description of the parameters in an inversion layer, which has not yet accomplished satisfactorily. To take important inversion layer effects like surface roughness scattering, quantization, and non-parabolic bands for high fields on the transport parameters into account, a 2D six moments transport model based on Subband Monte Carlo (SMC) tables has been developed (see Fig.). A device simulator calculates the effective field through the channel of a device and extracts higher-order transport parameters from the SMC tables. A UTB SOI MOSFET with a film thickness of 5 nm was investigated as an example.