Resonant Tunneling — Double Barrier WKB

A quantum particle tunnels through two rectangular barriers. Transmission resonances occur when the well between barriers supports quasi-bound states — T→1 at resonance energies. Transfer matrix method.

Geometry

Barrier height V₀: 3.0 eV Barrier width d: 0.5 nm Well width L: 1.0 nm Particle energy E: 1.5 eV

Transmission

T(E): —

Resonance #1: — eV

Resonance #2: — eV

κ (in barrier): — nm⁻¹

Transfer matrix method
M = M_barrier · M_well · M_barrier
T = 1/|M₁₁|²

Resonance when:
kL = nπ (standing wave in well)

Resonant Tunneling Through Double Barrier

Geometry

Transmission