An analytical model for electron tunneling in triangular quantum wells

Abstract

Abstract An analytical expression for the decay rate of quasi-bound states (QBS) in a triangular quantum well is derived by considering the resonance scattering of particles from the triangular potential profile. Asymptotic properties of the Airy functions that are solutions to the Schrödinger equation for a linear or triangular potential and a perturbative expansion for a small broadening of the QBS are utilized to derive the expression for its location E 0 as well as the decay rate Γ that further gives the net tunneling current from the well. The triangular well model is commonly used to represent the band-bending near a heterojunction due to the electrostatic field. This compact expression shows excellent agreement with a full numerical solver and improvement over Wentzel–Kramers–Brillouin based calculations is demonstrated.