5.3.3 Coupling to the Schrödinger Poisson Solver

In this work the Schrödinger-Poisson solver SCHRED 2.0 [Vasileska00] was extended to allow general strain conditions and arbitrary substrate orientation. The dependence of the subband spectrum on the Si substrate orientation has been implemented by taking the proper masses $m_{\shortparallel,1}, m_{\shortparallel,2}$, and $m_{\perp}$ according to Table 4.1. Recently, a coupling with VSP [Karner06] has been established.

The impact of strain is implemented by taking into account the strain-induced effective mass change using the analytic expressions (3.94),(3.98), and (3.99). Furthermore, the energy shifts of the subbands induced by strain are superimposed to the subband energies during the self-consistent solution of the Schrödinger-Poisson system.

The tool flow for a transport simulation in Si inversion layers is depicted in Figure 5.3. First, values for the input parameters of the Schrödinger-Poisson solver, such as $N_\mathrm{dop}, V_g$ or $T_\mathrm{si}$, have to be specified in an according input file. These values, together with the strain and the substrate orientation are passed to the Schrödinger-Poisson solver. In a postprocessing step the eigenenergies and wave functions of the subbands and the Fermi level are used to calculate the

• effective widths (5.27) which enter the phonon scattering rates,
• surface roughness scattering matrix elements (5.31),
• polarization function (5.40) and form factors (5.41) entering the static dielectric function.

Figure: Flow chart for coupled Schrödinger-Poisson solver and Monte Carlo simulation.

Hereafter, the Monte Carlo parameters have to be initialized and are passed to the MC simulator together with the postprocessed output of the Schrödinger-Poisson solver. If the quantity of interest is the effective electron mobility, a special Monte Carlo algorithm can be used [Kosina00a,Smirnov03]. It was originally designed for small signal analysis of the three dimensional electron gas, and in this work generalized for the simulation of the zero field mobility in inversion layers [Ungersboeck06b,Sverdlov06].

E. Ungersboeck: Advanced Modelling Aspects of Modern Strained CMOS Technology