Analysis of the I(V) characteristics of p+-n-π-p+structures for the determination of hole velocity in silicon

The method of obtaining the velocity field relation from the characteristics of p⁺-n-π-p⁺structures is analyzed using detailed numerical techniques and semiquantitative analytic descriptions. Rodriguez, Ruegg, and Nicolet (RRN) [1] have concluded from differential resistance measurements above punch-through that the hole velocity was saturated and gave 7.5 × 10⁶cm/s for 0.4 × 10⁵<E<1.1 × 10⁵V/cm. The differential resistance above punch-through is composed of l) the space-charge resistance component considered by RRN, and 2) a term which has its origin in the spillover of holes into the depleted region of the p⁺-n junction, but which is enhanced in proportion to the length of the π region. A detailed analysis of the spillover shows that as the current is increased, the built-in field of the p⁺-n junction is markedly reduced by neutralization of the depleted space charge. This effect, which leads to typically 25 percent of the total differential resistance, is an important factor in the determination of the hole velocity. In independent experiments of p⁺-p-p⁺structures, the authors have found that the velocity increases by ∼ 30 percent (to an accuracy of ± 5 percent) over the range of fields in the RRN experiment. It is shown for the p⁺-n-π-p⁺structure that the J(V) curve is rather insensitive to the υ(E) relation, and that a nonsaturated velocity also fits the RRN experimental results. An additional correction to the space-charge resistance itself comes from the effect of a nonsaturated velocity.