Accurate evaluation of integrals arising from the bulk electron densities in quantum wells of high electron mobility transistors

In this paper we propose a new accurate approach to compute integrals arrays of the electron density and energy density in a multi-layered high electron mobility transistors (HEMTs) device. These new formulas enable the user to calculate efficiently the certain integrals. Example results on the simulation of a certain integrals are given to demonstrate the efficiency of the new scheme. The results are compared with other theoretical calculation results. The convergence rate of the series is estimated and discussed.