Strain dependence of effective masses in tetrahedral semiconductors

The complete first-order strain dependences of the conduction- and valence-band effective masses of germanium and zinc-blende semiconductors at $\overrightarrow{\mathrm{k}}=0\mathrm{}$ is calculated using third-order perturbation theory and the Pikus-Bir Hamiltonian. These dependences are expressed analytically in relatively few matrix elements and self-energies using a model band structure consisting of the spin-orbit-split ${\Gamma }_{{25}^{\prime }}$ upper valence bands and the ${\Gamma }_{2^{\prime }}$, ${\Gamma }_{15}$, ${\Gamma }_{{12}^{\prime }}$, and ${\Gamma }_1$ conduction bands. These matrix elements and self-energies are evaluated from pseudopotential theory. While a two-band model consisting of the ${\Gamma }_{{25}^{\prime }}$ valence and ${\Gamma }_{2^{\prime }}$ conduction bands is adequate to describe the electron and the light-hole effective masses, more terms involving also the ${\Gamma }_{15}$, ${\Gamma }_{{12}^{\prime }}$, and the ${\Gamma }_1$ conduction bands are required to interpret the dependence of these masses on strain. Our results account for the strain dependence of conduction masses observed in GaAs. They also indicate that the anomalous strain dependence of the cyclotron hole masses observed for Ge by Hensel and Suzuki are not due to a strain-dependent spin-orbit interaction, as suggested by these authors, but to orbital terms involving the higher conduction bands.