## Simulation of high field transport in photoconductive semiconductor switches

##### Résumé

An impact ionization theory is proposed to explain an unusual phenomenon in GaAs photoconductive semiconductor switches under high-voltage bias and optical illumination. The effect is characterized by a persistent electric field across the switch after illumination is turned off. The field appears to remain 'locked-on' leading to the name 'lock-on' for the effect. It is found that these switches are bistable with filamentary current flow in the ON state. The theory, originally proposed by Hjalmarson, is based on a band-to-band impact ionization mechanism which becomes increasingly efficient due to carrier-carrier scattering as the carrier density increases. The key mechanism of the theory is collective impact ionization.
The theory focuses on the dependence of impact ionization on carrier density. Impact ionization requires a hot carrier. For an electron initiated process, the electron must be heated to a bandgap of energy above the conduction band edge, which allows it to generate an electron-hole pair by colliding with a valence band electron. The collective impact ionization idea is that, above a critical carrier density, the heating of these high energy carriers is very efficient due to energy redistribution by carrier-carrier scattering. At low carrier density, the carrier-carrier scattering rate is negligible so that each carrier must acquire all of its energy from the electric field. The theory has been implemented by approximating the distribution function by an interpolation between the low and high density extremes. This involves a two temperature approximation to the low density distribution function. Although this implementation works well for the lock-on field, it is expected to be inadequate in explaining the growth of a filament.
To develop a more microscopic theory requires a better calculation of the carrier distribution function. This involves solving a kinetic equation for the time evolution of the distribution function. In this dissertation, the kinetic equation is approximated by the Boltzmann equation, which is solved by a Monte Carlo method. The method includes the carrier density dependence of impact ionization as well as carrier-phonon scattering, carrier-carrier energy redistribution, and impact ionization. The results show that the density dependence of carrier-carrier scattering is the key mechanism for the initiation of lock-on.

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