Evaluation of an Equivalent Hole Effective Mass for Si/SiGe Structures

Abstract

We have studied the carrier profile and calculated a unique effective mass for a two-dimensional hole gas confined in a SiO₂/Si/Si₁__xGe_x/Si structure when an external voltage is applied. For this purpose, we have solved the system of differential equations provided by the 6 x 6 Luttinger Hamiltonian [1] simultaneously with the Poisson equation, applying an iterative process until convergence was achieved. This enabled us to incorporate the warping and the strong coupling among the subbands that constitute the band structure [2].From the calculated density of carriers we were able to evaluate an average effective mass. Although our calculations indicate that this effective mass varies notably with the hole confinement level, in general, we observed a decrease in the calculated effective mass as the molar fraction of Ge increases, which might justify the use of this kind of device.