Injected Current and Quantum Transmission Coefficient in Low Schottky Barriers: WKB and Airy Approaches

An exact solution of the quantum transmission coefficient has been obtained by using an Airy-transfer-matrix formalism to solve Schrödinger equation. The procedure is applied to the calculation of the transmission coefficient in reverse-biased low Schottky diodes. The barrier profiles are given by Monte Carlo device simulations. As compared to the exact calculation, results indicate that injected current is much exacerbated when considering Wentzel–Kramers–Brillouin (WKB) approach or when neglecting quantum mechanical reflections for energies over the potential barrier. However, WKB could reasonably predict the total current if properly modifying the model parameters. Influence of barrier lowering is also discussed.