Measure band structure energies using photon-assisted tunneling and calculate rectangular barrier tunneling probabilities. Use when analyzing electron penetration through potential barriers, measuring characteristic band energies, or studying quantum tunneling effects in semiconductors.
Use this technique when measuring energy of characteristic points in the E(k) behavior of any band.
Initiate Optical Excitation
Complete Transition via Tunneling
Measure Energy
Use when electron wave impinges on rectangular potential barrier.
Outside barrier (k_0):
k_0 = sqrt(2mE) / ħ
Inside barrier (k_1):
k_1 = sqrt(2m(eV_0 - E)) / ħ
Exact Formula:
T_e = 1 / [1 + ((k_0² + k_1²)² / (4k_0²k_1²)) × sinh²(k_1 × a)]
Approximation for k_1 × a >> 1:
T_e ≈ 16 × (k_0 × k_1 / (k_0² + k_1²))² × exp(-2 × k_1 × a)
Approximation for eV_0 >> E:
T_e ≈ 16 × (E / eV_0) × (1 - E / eV_0) × exp(-2 × k_1 × a)
| Variable | Description |
|---|---|
| E(k) | Energy-momentum relationship of the band |
| eV_0 | Barrier height |
| a | Barrier width |
| E | Kinetic energy of tunneling electron |
| k_0 | Wavenumber outside barrier |
| k_1 | Wavenumber inside barrier |
| T_e | Transmission probability |