Efficient quantum well to quantum dot tunneling: Analytical solutions

Tunneling transfer of carriers from a quantum well (collector) into a quantum dot is investigated theoretically using the transition-probability approach of Bardeen. The approach is attractive since it allows analysis of the tunneling rate using the wave function of the initial state in the quantum well and that of the final state in the quantum dot. We derive an analytical tunneling formula for the transition rate. We show that the quantum well to quantum dot tunneling can be extremely fast when the well, barrier, and dot potentials are properly designed. These calculations show that, in the recent experiment of a quantum-dot laser using an auxiliary InGaP quantum well for carrier collection and lateral transport followed by tunneling to the quantum dot layer via a thin coupling barrier, the added requirement of tunneling does not impede the population of the dot states.