Accuracy of transfer matrix approaches for solving the effective mass schrödinger equation

The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schrödinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a constant and a position-dependent effective mass are considered. Comparisons with a finite difference method are also performed. Based on analytical model potentials as well as self-consistent Schrödinger-Poisson simulations of a heterostructure device, it is shown that a symmetrized transfer matrix approach yields a similar accuracy as the Airy function method at a significantly reduced numerical cost, moreover avoiding the numerical problems associated with Airy functions.