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Accuracy of Transfer Matrix Approaches for Solving the Effective Mass SchrÖdinger Equation

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1 Author(s)
Christian Jirauschek ; Inst. for Nanoelectron., Tech. Univ. Munchen, Munich, Germany

The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schrodinger 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 Schrodinger-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.

Published in:

IEEE Journal of Quantum Electronics  (Volume:45 ,  Issue: 9 )