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 I(V) characteristics of P+FNπP+ structures is analyzed using detailed numerical techniques and semiquantitative analytic descriptions. RRN concluded from differential resistance measurements above punch-through that the velocity was saturated and gave cm/sec for volts/cm. The differential resistance above puncil-through is composed of: first the space-charge resistance component considered by RRN and second, a term which has its origin in the spill-over of holes into the depleted region of the p+n junction. A detailed analysis of the spill-over 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, typically 20% of the total differential resistance, is a factor in the accuracy of the hole velocity. In independent experiments on p+pp+ structures, we have found that the velocity increases by ∼ 30% (to an accuracy of ±5%)over the range of fields in the RRN experiment. It is shown for the p+πp+ structure that the J(V) curve is rather insensitive to the v(E) relation and that a non-saturated velocity also fits the RRN experimental results. An additional correction to the space-charge resistance itself comes from the effect of a nonsaturated velocity.