Magnetic Field Effect on an Electron Tunneling out of a Confining Plane

The influence of a magnetic field on the tunneling of an electron out of a confining plane is studied by a path integral method. We map this 3-d problem on to a 1-d one, and find that the tunneling is strongly affected by the field. Without a perpendicular field the tunneling at zero temperature can be completely suppressed by a large parallel field, but in the small parallel field and low temperature limit the tunneling rate is finite. An explicit formula is obtained in this case. A quantitative explanation without fitting parameter to a recent experiment is provided.