Electromagnetic analogies to general-Hamiltonian effective-mass electron wave propagation in semiconductors with spatially varying effective mass and potential energy

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Abstract
It is shown that exact, quantitative electromagnetic analogies exist for all forms of the general Hamiltonian [R. A. Morrow and K. R. Brownstein, Phys. Rev. B 30, 678 (1984)], which applies to single-band effective-mass electron wave propagation in semiconductors. It is further shown that these analogies are valid for propagation in the bulk, propagation past abrupt interfaces between materials, and propagation within one- and two-dimensionally inhomogeneous materials. These results indicate that the correct form of the single-band effective-mass Hamiltonian can be determined through appropriate wave-function-amplitude-sensitive experiments. Wave-function-phase-sensitive experiments (such as the measurement of electron wave refraction directions) are not adequate to specify completely the Hamiltonian. The present analogies suggest many wave-function-amplitude-sensitive experiments that can be used to determine the correct form of the Hamiltonian. The results of the present analysis are broadly applicable to general effective-mass propagation, unlike other recent work that has treated specific cases.