Coherent and sequential tunneling in series barriers

A simple approach which can describe both coherent tunneling and sequential tunneling is applied to resonant tunneling through a double-barrier structure. This approach models phase-randomizing events by connecting to the conductor a side branch leading away from the conductor to a reservoir. The reservoir does not draw or supply a net current, but permits inelastic events and phase randomization. A conductance formula is obtained which contains contributions due to both coherent and sequential tunneling. We discuss the limiting regimes of completely coherent tunneling and completely incoherent transmission, and discuss the continuous transition between the two. Over a wide range of inelastic scattering times tunneling is sequential. The effect of inelastic events on the peak-to-valley ratio and the density of states in the resonant well is investigated. We also present an analytic discussion of the maximum peak conductance e/h of an isolated resonance in a many-channel conductor.