Electron tunneling rate in quantum dots under a uniform electric field

A stabilization method is used to evaluate the tunneling rate of an electron in isolated quantum dots of conical shape under uniform electric field. A stabilization graph is obtained by plotting the eigenvalues of a single quantum dot embedded in a confining box made of barrier material as functions of the size of the box. The eigenvalues of the system are calculated within the effective mass approximation via the Raleigh-Ritz variational method. The density of states associated with the quasibound state is constructed from the stabilization graph and is shown to have a Lorentzian profile. The width of the Lorentzian profile gives the tunneling rate. We show that the tunneling rate of the quantum dot system is 2–3 times smaller than that of a quantum well system with the same bound-to-continuum transition energy.