Improved multi-band transfer matrix method for calculating eigenvalues andeigenfunctions of quantum well and superlattice structures

We present an improved transfer matrix algorithm which can be used in solvi ng general n-band effective-mass Schrodinger equation for quantum well stru ctures with arbitrary shaped potential profiles (where n specifies the numb er of bands explicitly included in the effective-mass equation). In the pro posed algorithm, specific formulas are presented for the three-band (the co nduction band and the two heavy- and light-hole bands) and two-band (the he avy- and light-hole bands) effective-mass eigensystems. Advantages of the p resent method can be taken in its simple and unified treatment for general n x n matrix envelope-function equations, which requires relatively smaller computation efforts as compared with existing methods of similar kind. As an illustration of application of the method, numerical computations are pe rformed for a single GaAs/AlGaAs quantum well using both the two-band and t hree-band formulas. The results are compared with those obtained by the con ventional variational procedure to assess the validity of the method.