The common approximations used in the ionized donor density calculations of terahertz quantum cascade lasers (TQCL’s) are investigated. Each approximation is computationally analyzed in order to determine its impact on the accuracy and speed of the doping calculations. The analyses are repeated across all of the lattice temperatures and donor densities that are typical in TQCL’s (T = 1 to 300 K, N<sub>D</sub> = 1.00 to 5.00 × 10<sup>16</sup> cm<sup>-3</sup> ). Additionally, an original optimized approximation is proposed and analyzed. This optimized approximation is found to out-perform the common approximations in both accuracy and speed in all cases.
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.