Finite-element analysis of quantum wells of arbitrary semiconductors with arbitrary potential profiles

A finite-element method for the analysis of eigenstates in a quantum well, which is based on the Galerkin procedure, is discussed. A general boundary condition of the envelope function at the heterointerface is introduced by using the transfer matrix. The validity of the method is confirmed by calculating the eigenstates of GaAs/AlGaAs and InAs/GaSb rectangular quantum wells. Numerical examples of voltage-applied quantum wells are presented.