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^-^)]
or
with
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
