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4.1.1 The Si-SiO$ _2$ Interface

In the following section the subband structure of electrons confined near the Si-SiO$ _2$ interface is discussed. As shown in Section 3.4.1 the conduction band edge of Si is located along the $ \Delta $ direction and is located in the vicinity of the $ X$ symmetry point. Each valley is characterized by a longitudinal mass $ \ensuremath{m_\mathrm{l}}$ and a transverse mass $ m_\mathrm{t}$. In the following only the three valley pairs along the equivalent $ \Delta $ axes are considered, whereas the valleys at the $ L$ points are neglected. In the principal crystallographic system the inverse effective mass tensors describing the energy dispersion of the three valley pairs are given by

$\displaystyle \ensuremath{{\underaccent{\bar}{\nu}}}'^{(1)}= \begin{pmatrix}\fr... ...m_\mathrm{t}}} & 0\\ 0 & 0 & \frac{1}{\ensuremath{m_\mathrm{l}}} \end{pmatrix}.$ (4.18)


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