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Theory of Electron Tunneling in Semiconductors (Direct Tunneling across p - n Junctions)

1965; Physical Society of Japan; Volume: 20; Issue: 10 Linguagem: Inglês

10.1143/jpsj.20.1854

1347-4073

Yosihisa Takeuti, Hiroshi Funada,

Quantum and electron transport phenomena

The time-dependent theory of the tunneling problem is developed for the ideal semiconductor junction with an inhomogeneous electric field. It is shown that the tunneling probability of Fredkin and Wannier type can be derived from the rigorous formula for transition probability between an incident and an outgoing wave packet. The tunneling probability of the final form is obtained by using the difference equation and the variation principle of Lippmann and Schwinger. The weak field approximation hitherto supposed is not used but a strong field approximation is taken on the junction potential. The result obtained resembles that of a free electron tunneling through one-dimensional barrier. The time-independent formulation is added in Appendix.