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Tunneling through a tilted tight-binding band.

Alexander Onipko¹, Lyuba Malysheva

¹Division of Physics, Luleå University of Technology, S-971 87 Luleå, Sweden. alex@mt.luth.se

Annals of the New York Academy of Sciences

|April 25, 2002

Summary

This study analytically describes quantum tunneling through crystals under electric fields. It details the transmission spectrum and tunneling current, revealing quantized energy levels.

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Area of Science:

Solid-state physics
Quantum mechanics

Background:

Quantum tunneling is crucial for understanding electron transport in materials.
Electric fields significantly influence tunneling phenomena in crystalline structures.

Purpose of the Study:

To derive an analytical expression for the exponential factor governing tunneling.
To describe the quantization features in the transmission spectrum and tunneling current.

Main Methods:

Single-band approximation was employed.
Analytical derivation of the exponential factor for tunneling.

Main Results:

Explicit expression for the tunneling exponential factor derived.
Wannier-Stark, Airy, and intermediate quantization features identified.
Transmission spectrum and tunneling current analyzed.

Conclusions:

Analytical description of quantum tunneling through thin crystals under electric fields achieved.
Quantization effects on tunneling current are analytically characterized.

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