Excess Carriers in Semiconductors in .NET Add barcode code 128 in .NET Excess Carriers in Semiconductors

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Excess Carriers in Semiconductors generate, create barcode 128 none in .net projects Web application framework several types of devic .net framework code-128c es. In this section we shall examine the mechanisms by which excess electrons and holes recombine and apply the recombination kinetics to the analysis of photoconductive devices.

However, the importance of recombination is not limited to cases in which the excess carriers are created optically. In fact, virtually every semiconductor device depends in some way on the recombination of excess electrons and holes. Therefore, the concepts developed in this section will be used extensively in the analyses of diodes, transistors, lasers, and other devices in later chapters.

. Direct Recombination of Electrons and Holes It was pointed out in barcode 128a for .NET Section 3.1.

4 that electrons in the conduction band of a semiconductor may make transitions to the valence band (i.e., recombine with holes in the valence band) either directly or indirectly.

In direct recombination, an excess population of electrons and holes decays by electrons falling from the conduction band to empty states (holes) in the valence band. Energy lost by an electron in making the transition is given up as a photon. Direct recombination occurs spontaneously; that is, the probability that an electron and a hole will recombine is constant in time.

As in the case of carrier scattering, this constant probability leads us to expect an exponential solution for the decay of the excess carriers. In this case the rate of decay of electrons at any time t is proportional to the number of electrons remaining at r and the number of holes, with some constant of proportionality for recombination, a,. The net rate of change in the conduction band electron concentration is the thermal generation rate a.

rn} from Eq. (3-7) minus the recombination rate ~ . ^ = arn] - arn{t)p{t) (4-4). Let us assume the exce code 128 barcode for .NET ss electron-hole population is created at t = 0, for example by a short flash of light, and the initial excess electron and hole concentrations An and Ap are equal.3 Then as the electrons and holes recombine in pairs, the instantaneous concentrations of excess carriers n(f) and hp(t) are also equal.

Thus we can write the total concentrations of Eq. (4-4) in terms of the equilibrium values o andp 0 and the excess carrier concentrations hn(t) = 8p(r). Using Eq.

(3-24) we have d n(t) = arn] - ar[n0 + hn(t)][p{) + hp(t)] dt = - ar[(n0 + p0)hn(t) + hn2(t)] (4-5). We will use 8n(/) and 5p(f) to mean instantaneous excess carrier concentrations, and An, Ap for their values al t = 0. Later we will use similar symbolism for spatial distributions, such as 5n(x) and An(x = 0)..

This nonlinear equatio code 128b for .NET n would be difficult to solve in its present form. Fortunately, it can be simplified for the case of low-level injection.

If the excess carrier concentrations are small, we can neglect the hn2 term. Furthermore, if the material is extrinsic, we can usually neglect the term representing the equihbrium minority carriers. For example, if the material is p-type (p0 > n0), Eq.

(4-5) becomes && a*W) (4-6). The solution to this e quation is an exponential decay from the original excess carrier concentration Arc: hn(t) = Ane-a"p " = Ane~"/r" (4-7). Excess electrons in a visual .net Code-128 p-type semiconductor recombine with a decay constant T = (arpo)_1> called the recombination lifetime. Since the calculation is made in terms of the minority carriers, T is often called the minority carrier lifetime.

The decay of excess holes in n-type material occurs with ip = (CI/IQ)"1. In the case of direct recombination, the excess majority carriers decay at exactly the same rate as the minority carriers. There is a large percentage change in the minority carrier electron concentration in Example 4-2 and a small percentage change in the majority hole concentration.

Basically, the approximations of extrinsic material and low-level injection allow us to represent n{t) in Eq. (4-4) by the excess concentration hn(t) and p(t) by the equilibrium value p0. Figure 4-7 indicates that this is a good approximation for the example.

A more general expression for the carrier lifetime is. , \ v <*A*o + Po). (4-8).
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