The energy spectrum of emitted electrons from a single barrier is anal
yze taking into account quantized levels of an accumulation layer. A s
elf-consistent model is developed which solves Poisson's equation, the
continuity equation, Schrodinger's equation, and the heat equation. T
he relationship between the population of the quantized levels, the en
ergy relaxation time, and the tunneling probability is formulated. The
energy spectrum consists of components from three- and two-dimensiona
l electrons. A new emitter structure is proposed which effectively rem
oves the three-dimensional current component providing a highly effect
ive method of producing electrons with a very narrow energy spread in
the direction of propagation.