Quantum Tunneling — Double Barrier Resonant Transmission

Resonant tunneling diode (RTD) physics: transmission peaks, quasi-bound states, negative differential resistance

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Transmission T(E)
Reflection R(E)
Resonance n=1 (eV)
Resonance n=2 (eV)
Resonant Tunneling Diode (RTD): Two potential barriers with a quantum well between them. At quasi-bound state energies E_n ≈ n²π²ℏ²/(2m b²), transmission reaches T = 1 (perfect transmission through classically forbidden barriers). This is the quantum analog of Fabry-Pérot resonance. Transfer matrix method: each region contributes a 2×2 matrix; T = |t|² where t is the transmission amplitude. RTDs exhibit negative differential resistance (I decreases as V increases) when a resonance passes below the Fermi energy — enabling THz oscillators and logic devices.