Theoretical consideration of band-structure determination from tunneling in thin-film heterojunctions

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Abstract
The energy dependence of the exact numerically calculated transmission coefficient of a thin-film heterojunction is compared with the analytic results derived from the energy-band model of the junction. Several modified WKB approximations are utilized in the analysis and their respective reliability is examined. This is accomplished by considering a one-dimensional model consisting of a square barrier, containing uniformly spaced square wells between two Bohr-Sommerfeld metals. The transmission coefficients are calculated over the energy ranges where the barrier material is both insulating and conducting for a variety of externally applied electric fields. We examine several approximation schemes, each of which employs the band structure applicable to the periodic potential of which the barrier is a segment. The results obtained from these approximations are found to be in error by factors ranging from unity to several orders of magnitude. We conclude that application of the methods of band theory to thin-film tunneling experiments must be carried out with caution or serious errors could result.

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