Non-vanishing Current, Steady State

When a bias is applied, the flow of a net current results. The carrier density distribu­tion is deformed from equilibrium; now carriers generated in one volume element

Fig. 27.6 Shockley-Read – Hall center with all transitions to both bands

are moved to another one by the current before they recombine. In forward bias this results in a carrier surplus, while in reverse bias it results in a carrier depletion within a Schottky barrier.

The balance between the two transitions of a center to its adjacent band is dis­turbed, and a net generation or recombination through such centers results.

As a consequence the Fermi level splits into two quasi-Fermi levels and the two demarcation lines separate; hence some levels which acted as traps before will now act as recombination centers.

When changing the bias, this distribution changes. One, therefore, needs to in­clude all four transitions to the two bands for deeper centers that may become re­combination centers (Fig. 27.6).[156] These centers are called Schottky-Read-Hall cen­ters. The net traffic through these centers is conventionally identified as U, given by

Ccr Crv Nr(np П – )

U = i (27.29)

Crc[П + Пі expC^-^)] + Crv[p + Пі expC^-^)]



and the intrinsic energy level, Ei

This equation is representative for the sequential nature of the re-combination through a recombination center: an electron from the conduction band and a hole from the valence band must both find their way to the recombination center; the equation for the net recombination traffic [Eq. (27.30)] is therefore of the type (1/п + 1/p) – 1.

Thus, only when both carrier densities are high, is the recombination traffic large; the minority carrier limits the recombination. This will be of importance in pn-junctions, where only in the inner part of the junction region both densities are on the same order of magnitude, causing a substantially higher recombination here than in the adjacent bulk regions (see Sect. 27.4 and Fig. 27.9).

FromEq. (27.29) one confirms also that U vanishes for thermal equilibrium; i. e., for np = n2 U represents a net thermal generation when, with reverse bias, the np product in the space charge region has decreased below its equilibrium value[157] я2. A net recombination through the center occurs when with forward bias[158] the np – product exceeds n2.

A simplified relation is occasionally used, assuming a center with equal capture coefficients[159] for electrons and holes (ccr = crv = c). Equation (27.29) can then be reduced to

Updated: August 16, 2015 — 6:09 am