Discussion

In unstrained Si the constant energy surfaces of the conduction band valleys along [001] have a prolate ellipsoidal shape, where one of the three semiaxes is characterized by $\ensuremath{m_\mathrm{l}}$ and two semiaxes by $\ensuremath{m_\mathrm{t}}$. At small shear strain $\varepsilon_{xy}$ the constant energy surfaces take the form of scalene ellipsoids characterized by three masses, $m_{\mathrm{l},[001]}, m_{\mathrm{t},[110]}$, and $m_{\mathrm{t},[\,\bar{1}10]}$. These masses change under the influence of $\varepsilon_{xy}$ and can be modeled using the equations (3.94), (3.98), and (3.99). From Figure 3.13 it can be seen that under shear strain $\varepsilon_{xy}$, the lines of constant energies in the ${\ensuremath{\mathitbf{k}}}_x{\ensuremath{\mathitbf{k}}}_y$-plane develop into ellipses with their semiaxes rotated 45${^\circ}$ about the $k_z$ axis. For levels of shear strain that significantly change the location of the conduction band edge, ${\ensuremath{\varepsilon_{xy}}} \approx 1/\kappa$, a large deformation of the shape of the conduction band takes place. In principle equations (3.94), (3.98), and (3.99) describe the change of the effective masses, but it will be shown in Section 6.1 that a (non-)parabolic approximation for the conduction band minimum is not valid in this case and full-band modeling is required for simulations of electron transport even at low electric fields.

As pointed out previously a key advantage of the kp method is that it allows one to derive analytical expressions for the energy dispersion with the knowledge of only a small number of parameters. In the expressions derived in this section, the knowledge of only three parameters $\Delta, \eta$, and $\kappa$ is required to characterize the energy dispersion around the conduction band minimum under shear strain. These parameters can be calculated using the empirical pseudopotential method, which is briefly described in the next section.

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