Application of an efficient algorithm for solving the one‐band effective mass equation self‐consistently in the modelling of some low‐dimensional structure devices

An efficient algorithm is presented for the self‐consistent numerical solution of the single‐band effective mass equation. This algorithm has a different form depending on whether the effective mass is modelled as continuous or piecewise continuous. Coupled with a Poisson solver, an established algorithm is applied for the attainment of self‐consistency. The rate of convergence to a self‐consistent solution is investigated, and the solvers are applied to three different structures to demonstrate its versatility and robustness. The first of these is a nominally undoped quantum well AlGaAs/GaAs heterostructure, the second a doubly δ‐doped GaAs homostructure and lastly a quasi‐square well modulation‐doped field effect transistor. The algorithm is of sufficient efficiency so as to allow the software to run reasonably quickly on a modern microcomputer.