Comment on "Single-carrier space-charge controlled conduction vs. ballistic transport in GaAs devices at 77°K"

Abstract

UBMICRON-DEVICE literature has seen a major upset during the past two years in the field of “ballistic transport,” beginning with the publication of the first paper by Shur and Eastman [ 11 . Their assumption that collisions could be neglected for very small devices seemed reasonable; however, the theory and experiments failed to agree completely. Barker, Ferry and Grubin [2] then emphasized the importance of correctly treating the boundary conditions. On further reflection, diffusion effects appear to be of equal importance [3] . In an effort to develop a simple description of small devices that considers the short-comings above, Schmidt, Octavio and Esqueda [4] used the drift-diffusion equation to describe current flow in “ballistic diodes” [l] . Their results seem very encouraging, predicting a linear I-V characteristic for low currents. (They also predict a power-law behavior for high currents, with an exponent of l .63 .) However, it is a bit disturbing that their I-Vcurves lie above (higher current) the pure ballistic prediction, at least for most of the voltage range plotted. We can check their results with a simple calculation. The current density is given by j = qnv, so we may calculate the average carrier velocity if we know the current density j and the electron density n. For an applied voltage of 0.1 V, and for Q = 0, their predicted current density is 6 x lo5 A/cm2. Schmidt et al. provided a, plot of the zero-bias carrier concentration, from which we estimate the carrier concentration to be 2 x lo1’ at the center of the channel. This should be a close estimate even for 0.1 P applied voltage. The resulting velocity is 1.9 x lo9 cm/s, 19 times greater than the velocity limit of GaAs. Clearly something is amiss. Before proceeding, let us see what limits the velocity of electrons in GaAs. If the energy-band structure is known, then the velocity at any energy can be calculated from