Field-Emission Tails and Tunneling Lifetimes

Recent observations of high- and low-energy tails in field-emission energy distributions can be interpreted in terms of quasi-stationary-state single-particle tunneling. This imposes a restriction on the observable range of energies in such studies. The tails result from the predicted breakdown of the transfer Hamiltonian theory of tunneling when fourth-order terms in the perturbation expansion of the tunneling matrix element become large. The tunneling lifetimes $\sim {10}^{-12}$ sec required to fit the experimental data are consistent with both the $R C$ time constant discussed by Thornber, McGill, and Mead and also a simple intuitive picture. Alternate theories of tunneling lifetimes are critically evaluated.