ANALYTIC CALCULATION OF ELECTRON TRANSMISSION PROBABILITY FOR PLANAR-DOPED POTENTIAL BARRIER DEVICES

The electron barrier transmission probability, T, is calculated for planar-doped potential barrier devices. The calculations are based on the analytic expression derived by Christodoulides et al. obtained from the exact solution to the Schrodinger time-independent equation. The original Airy function solution was recast in Bessel function form for ease of computer evaluations. The barrier is assumed to be triangular with the forward slope S1, much larger than the reverse slope S2. The quantity T is calculated for values of electron energy, E, above and below the barrier peak, U(m). It is found that T is a sensitive function of S1 for all values of E. The reverse slope, S2, is observed to have very little effect on T for values of (E - U(m)) greater-than-or-equal-to 10 meV, but have a large effect on T for values of (E - U(m)) less-than-or-equal-to 0. The quantity T is observed to increase monotonically with increasing E, for practical values of device parameters. These results are in qualitative agreement with those found from the numerical solution of Chandra and Eastman. However, their results give values of T that deviate significantly from those obtained in the present work.