Acta Physica Academiae Scientiarum Hungaricae 24. (1968)

1968 / 1. szám - G. Pataki: Velocity and Current Determination for Steadily Travelling Domains in Semiconductors I. Recombination Instability

9* VELOCITY AND CURRENT DETERMINATION 131 Assuming a proper domain shape the theory gives the domain velocity in correct order of magnitude (10—3 cmsec-1). In connection with (i) it is important to remark that the existence of the Qí(E, E', E") functions is a direct consequence of the wave-like solution* and it holds for the more general case when eq. (9) is not linearized with respect to the concentrations and, for field dependent p and D, as well. This result shows that for the general case, one cannot expect the components p,- to be a function of electric field alone in every point of the domain [7]. In comparing the present theory with experimental results, the first problem is to decide which mode is realized in a given experiment. The velocity of the fourth, omitted, mode is equal to the electron drift velocity at the peak field. One can hardly expect such a high velocity for a space charge wave to have a zero-mobility component (g2). The second mode may be excluded on the basis of the temperature-dependence of domain velocity. In fact, according to [24]** the domain velocity and the current have similar temperature dependence, namely both are determined by ——. It is obvious that Uq1^ does rg not show such a temperature dependence. On the other hand, the order of magnitude of UqU> is different from that of the measured velocity for Au— centres in Ge at about 30 °K [18], [19], [24]. The same is true for mq111^. In fact, |uq **| = 0.2 cmsec-1; [Mq1 11^| = 2.6 • 102 cmsec-1. Similarly, the Gaussian and quadratic domains lead to too high velocities, since |uog| я« I «Oïl = = 1.4 cmsec _]. The correct velocity values may be obtained from the slowest domain mode, assuming S3 ^ 0. From eq. (29) |uoaV| = 3.5 • 10-3 cmsec-1 follows, while for more complex domain shapes see data in Table 1. Finally, the following question has to be answered; what is the physical reason for the domain velocity being so sensitive to the domain shape, at least for two domain modes ? By a simple consideration this is probably connected with the fact that the low-mobility states are actually zero-mobility states (fi„ =з 0). Let us assume momentarily that /л2 0. It is clear, physically, that a condition for stable domain propagation is fi2 E0 E„, where E0 is the peak field, Ex the low field at the front of the domain. In this case, one may expect that the domain shape has no important role in the determination of domain velocity, as after all both components of space charge wave are mobile. For recombination instability _E0(k2 = 0 for arbitrary but finite values of Eu, thus if we require an invariable domain shape, the domain “migration” can be determined by the domain shape itself. This is, in our opinion, the reason for the high sensitivity of domain velocity on its shape, especially for * The wave-like solution is not the unique possibility for domain motion. One can imagine that the domain “migration” is accompanied by a small change of the domain shape itself (“caterpillar-like” movement). ** The author is indebted to Dr. I. A. Kurova and Dr. M. Vrana for letting him see the results of their paper [24] before its appearance. Ada Physica Academiae Scienliarum Hangaricae 24, 1968

Next