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

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

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