Dynamic and Steady-State Injection of Electron-Hole Plasma in p-Type InSb

Abstract

Potential measurements as a function of time and space show in detail the passage of an injected electron-hole plasma front, and the eventual establishment of a nonequilibrium steady state in a long bar of p-type InSb at 77°K. The front is preceded by a depletion layer which vanishes as plasma reaches the anode. Thereafter the current, with the voltage held constant, grows exponentially until just before the steady-state plasma density is reached. These results are compared with a theory by Dean and by Ancker-Johnson, Robbins, and Chang describing plasma injection into a semiconductor with deep traps. The measured front arrival time as a function of constant applied voltage agrees satisfactorily with Dean's prediction. Four observations are at variance with his theory: the time constants of the exponential current growth are density-dependent instead of being independent as predicted; the current at the front arrival is not a function of voltage as his theory states; the electric field behind the front is not proportional to the square root of distance; and the steady-state injected current has a higher power dependence on voltage than the predicted square-law dependence. The extended analysis accounts for all the observed growth time behavior, namely a growth time which is independent of steady-state density at high and low densities, and which increases with density in the intermediate range. Also, a new theory of the steady-state conduction characteristic, based on the density-dependent plasma lifetime, reproduces quite well the measured conduction characteristics, I ∝ Vn with 2<n<8, until the interference of pinching, which causes a sub-Ohmic conduction. In the nonequilibrium steady state the plasma density has a uniform spatial distribution within a factor of two over the central 80% of the sample length. The steady-state density decreases monotonically from cathode to anode, or alternatively, a U-shaped distribution is observed with high plasma densities occurring also at the anode, a characteristic which is attributed to copious hole injection. All the observed dynamic and steady-state properties of double injection into p-InSb are in good agreement with theory except for the constancy of the current magnitude at the front arrival and the form of the dependence of electric field on distance.