2.4.2.2 Nonparabolic Band Structures

When an electron occupies higher energy levels its dispersion law deviates from (2.75). In order to improve this situation and still use the analytical description of the band structure the $\vec{k}\cdot\vec{p}$ technique [16,17] is employed and an additional nonparabolicity parameter is introduced for the conduction band extrema. This leads to a modified dependence of energy on the quasi-momentum in the conduction band [18,19]:

$$\epsilon(\vec{k})(1+\alpha\epsilon(\vec{k}))=\frac{\hbar^{2}}{2}\... ...\frac{k_{x}^{2}}{m_{x}}+\frac{k_{y}^{2}}{m_{y}}+\frac{k_{z}^{2}}{m_{z}}\biggr),$$ (2.77)

where $\alpha$ is the nonparabolicity parameter and the energy reference point is at the band minimum. S. Smirnov: