## A theory of lock-on and electrical breakdown

##### Résumé

In this dissertation, a theory of electrical breakdown of insulators is developed. This theory is based on collective impact ionization, which includes both the electric field dependence and the carrier density dependence of impact ionization. This theory is applied to photoconductive semiconductor switches (PCSS's) and is used to explain the lock-on effect, an optically triggered breakdown that occurs in GaAs PCSS's. The basic principle of collective impact ionization theory is that, at high carrier densities, carrier-carrier scattering will enhance the impact ionization rate. This occurs because these interactions increase the number of carriers with energies above the impact ionization threshold.
This generalized breakdown theory uses a rate equation approach to obtain the carrier density or densities which, at a given electric field, result in a steady state or a zero net carrier growth rate. In this approach, the competition between carrier generation (by impact ionization) and carrier recombination (by Auger and defect mechanisms) leads to a steady state condition for the net carrier growth rate. It is the existence of this steady state that governs whether or not electrical breakdown occurs. This approach leads to a definition of the bulk breakdown field as the lowest field for which the injection of an infinitesimally small carrier density will result in a steady state with a large carrier density. It also leads to the definition of the lock-on field as the lowest field for which a stable, steady state carrier density is possible.
To implement this theory for PCSS materials, the Ensemble Monte Carlo (EMC) method is used to calculate the carrier distribution function, including the effects of carrier-carrier scattering. This distribution function is used to calculate the impact ionization and Auger recombination rates and thus the steady state carrier growth rate. Since the EMC calculations which include cc-scattering are computationally intense and time consuming, this theory is also implemented using both low and high density approximations for the distribution function. The low density limit is obtained using the EMC method without including cc-scattering. The high density limit is obtained by approximating the distribution function as a steady state Maxwellian. Using this theory, predictions are made for both the lock-on field and the bulk breakdown field in several materials and the results are compared, where possible, with experiment.
In this theory, the lock-on effect is a type of carrier-density dependent electrical breakdown which occurs in all insulating materials. Further, it is the difference between the predicted lock-on and the breakdown fields which determines whether or not the lock-on effect will observable as a phenomenon distinct from ordinary breakdown. If the two fields are sufficiently distinct, it is likely that the two phenomena can be distinguished. However, if they are similar, it is likely that they will be difficult to distinguish experimentally.

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