Observation of Double Injection in Long Siliconp−i−nStructures

Abstract

Double injection currents limited by space charge and recombination kinetics have been observed in silicon $p-i-n$ structures fabricated by ion-drift techniques. Current-voltage characteristics were measured and found to contain an Ohmic portion followed by a region in which $I\propto V^m$, where $m\ge 3$. This region has been identified with Lampert's insulator regime for which he predicts $I\propto \frac{V^3}{L^5}$. As predicted by Baron (in the preceding paper) it is necessary to correct for diffusion effects. The experimental results confirm qualitatively Baron's first-order prediction that $I\propto V^m$, $m=\frac{3}{(1-\frac{10L_a}{3L})}$, where $L_a$ is the ambipolar diffusion length and $L$ is the sample length. The magnitude of the current may also be predicted within a factor of 2 by a first-order approximation. This consists of use of an effective length $L_{\mathrm{eff}}=L-2.2\left(2\mathrm{}{L}_a\right)$ in Lampert's theory. The factor 2.2 is empirically determined. The carrier distribution was found by potential probe measurements (discussed in the following paper) and were well fitted by the theoretical curves derived by Baron. The carrier distribution is characterized by an exponential decrease near the junctions, from which a value for $L_a$ can be determined. The center portion of the carrier distribution is characterized by a slower, Lampert-like dependence from which an independent value of $L_a$ can be determined. These two values of $L_a$ are in agreement with each other and with the value of $L_a$ determined from the measured lifetime. The carrier concentration in the center was found to vary proportionally to $J^{\frac{2}{3}}$. As predicted for junction theory, the carrier concentrations at the junctions were found to vary proportionally to $J$; however, their magnitude is less than the theoretical value.