5.3.3 Coupling to the Schrödinger Poisson Solver


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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.
$\includegraphics[scale=1.0, clip]{inkscape/simToolFlow.eps}$

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].

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