The effects of a common approximation used in the polarizability calculations of electron-electron subband screening in quantum well devices

Quantum well devices can be investigated through the use of computational predictions of the electron-electron subband scattering rates. A high-accuracy prediction requires the calculation of the quantum well electron polarizability. An approximation is sometimes made that renders the integral in the polarizability equation analytically solvable. This study comprehensively quantifies the error and the limitations introduced through the use of this approximation. The approximate polarizability equation is found to introduce significant error for certain scenarios. Furthermore, the approximate polarizability equation is found to fail to give any numeric answer at all for relatively high temperatures and low electron densities.