Method of Solving the General Equation

As described above, the DLTS experiment consists basically of applying a forward bias to a normally reverse-biased Schottky barrier or p-n junction [8,9]. In reverse bias, more of the traps are in a region depleted of free electrons, and thus experience a very low free-electron concentration, n = nr 3C rib, where rib is the bulk (neutral) value, 1018 cm-3 in our case. Thus, c o(nr,T) is very small, so that emission dominates and the traps are almost empty. Then, in forward bias, the traps are suddenly exposed to the bulk free-electron concentration n = rib for a time tp, the filling 

When the filling pulse has ended at time tp, i.e. upon reapplication of the reverse bias, the traps are once again suddenly exposed to a very small value of n, i.e. n = nr. [Note that the solution of Equation (9.4) is very insensitive to the exact value of nr, as long as nr C w/,. The traps now emit their carriers, so that the original fractional occupation fp is now reduced to fe, in total time tp + te. Thus, in emission, Equation (9.4) is solved for fe under the conditions fa = fp, fp =fe,n = nr, t = tp, and tp = tp + te. As mentioned above, the boxcar method of DLTS analysis defines the signal as S = fitf) - fiti). Such a signal is simulated simply by solving Equation (9.4) at two times, tp + t, and tp + t].  

Before applying Equation (9.4) to the problem at hand, it is instructive to solve it in two special cases, which apply to the majority of present-day DLTS analyses. In the first case, the most common of all, we set rp,f) = 0 (or a constant). Then, Equation (9.4) immediately yields closed-form exponential capture and emission equations, as shown earlier. The other special case of interest is realized under two conditions (1) small f, such that the denominator of the integrand in Equation (9.4) can be approximated by unity and (2) (rp,f) oc f. Then, Equation (9.4) yields a logarithmic solution for f[ci. Equation (3) of Hierro et al. [12]], which has been seen experimentally for trapping along dislocation lines [12,13]. 

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