Zener tunneling in semiconductor superlattices

Area of Science:

• Condensed Matter Physics
• Semiconductor Physics
• Quantum Mechanics

Background:

• Semiconductor superlattices exhibit unique electronic properties due to their periodic structures.
• Miniband tunneling and Wannier-Stark levels are key phenomena in superlattices, influenced by unit cell symmetry and miniband structure.
• Understanding these phenomena is crucial for designing advanced semiconductor devices.

Purpose of the Study:

• To investigate the characteristics of miniband tunneling and Wannier-Stark levels in semiconductor superlattices.
• To analyze the dependence of these characteristics on unit cell symmetry and miniband structure.
• To generalize tunneling formulas and develop a unified approach for calculating these effects.

Main Methods:

• Modification of the k ⋅ p method to a k ⋅ v form.
• Generalization of the Zener tunneling formula for inter-miniband tunneling in superlattices.
• Development of a unified matrix approach for calculating inter-miniband tunneling and Wannier-Stark levels.
• Analysis of electric field dependence and repeated electron transfers through the Brillouin minizone.

Main Results:

• A generalized Zener formula for inter-miniband tunneling was derived, accounting for inhomogeneous effective mass.
• A sum rule for effective masses in superlattices was obtained.
• A unified matrix approach was developed for calculating tunneling and Stark levels for multiple minibands.
• The electric field dependence of tunneling probability and peculiarities of inter-miniband transitions were studied.

Conclusions:

• The study provides a comprehensive theoretical framework for understanding miniband tunneling and Wannier-Stark levels in semiconductor superlattices.
• The developed methods offer insights into resonant Zener tunneling and its impact on electron transport.
• Findings are relevant for the design and optimization of novel semiconductor devices exploiting quantum phenomena.