Closed formulas for tunneling time in superlattices

Area of Science:

• Solid-state physics
• Quantum mechanics
• Materials science

Background:

• Superlattices are periodic semiconductor nanostructures.
• Electron and photon transport through superlattices is crucial for quantum devices.
• Understanding phase time in quantum tunneling is key to device performance.

Purpose of the Study:

• Derive new, simple formulas for evaluating phase time in finite superlattices.
• Analyze the behavior of superlattice-tunneling time (tau(n)) based on particle energy.
• Compare theoretical results with experimental measurements of optical-pulse and superluminal delay times.

Main Methods:

• Development of exact analytical formulas for phase time.
• Analysis of superlattice-tunneling time (tau(n)) in energy bands and gaps.
• Investigation of substrate effects on tunneling time.
• Comparison with experimental data from Spielmann et al. and Steinberg et al.

Main Results:

• Superlattice-tunneling time (tau(n)) exhibits resonant-band structure in energy bands.
• Superluminal phase time behavior is observed when particle energy is in a gap.
• In bands, tau(n) exceeds free motion time (tau(f)); in gaps, tau(n) can be less than tau(f) but greater than single-cell time (tau(1)).
• Excellent agreement found with experimental optical-pulse and superluminal delay times, including substrate effects.

Conclusions:

• The derived formulas accurately predict superlattice-tunneling time.
• Particle energy dictates distinct behaviors of tau(n) in bands versus gaps.
• Experimental validation confirms the theoretical model, offering insights into electron and photon transport phenomena.