# Photoconductive Semiconductor Switches: Materials, Physics, and Applications
## 2 Theory of PCSS Operation  
The most common mechanism of photoconductive switch operation is the linear mode. In this mechanism, the optically injected electrons and holes produce a photocurrent driven by the electric field. This photocurrent \(J\) is proportional to the electric field \(E\), the injected electron (hole) densities, \(n\) (\(p\)) densities, and their respective mobilities \(\mu_{n\ (p)}\) as \(J=e(n\mu_{n}+p\mu_{p})E\), where \(e\) is the fundamental charge. In this conventional case, the electron and hole densities reach a steady-state density that requires continuous optical \begin{table}
\begin{tabular}{l c c c c c c c} \hline
**Property** & **Si** & **GaAs** & **4H-SiC** & **GaN** & **AlN** & \(\beta\)**-GaAs\({}_{2}\)O\({}_{3}\)** & **Diamond** \\ \hline Bandgap (eV), & & & & & & & \\ Direct or & 1.11, i & 1.43, d & 3.26, i & 3.39, d & 6.1, d & 4.5, i & 5.47, d or i \\ Indirect (d, i) & & & & & & & \\ Breakdown Electric Field & & & & & & & \\ (MV/cm) & & & & & & & \\ Electron Mobility & & & & & & & \\ (cm\({}^{2}\) V\({}^{-1}\)s\({}^{-1}\)) & 1400 & 8500 & 700 & 900 & 1100 & 200 & 4500 \\ Saturation Drift & & & & & & & \\ Velocity (\(\times 10^{7}\) cm/s) & & & & & & & \\ Relative Permittivity & & & & & & & \\ Thermal Conductivity & & & & & & & \\ (W/cm K) & & & & & & & \\ Maximum Operable & & & & & & & \\ Junction Temperature (°C) & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of electrical and thermal properties of semiconducting materials most commonly used in PCSS applications, with a comparison to Si as a baseline material. generation and is typically controlled by the density and levels of electronic traps in the material. In some cases, the optical injection stimulates the generation of electrons and holes in a non-linear way by means of one or a combination of physical mechanisms. For example, above a material-dependent threshold field, an avalanche process generates electrons and holes (\"avalanche gain\"). Once this process initiates, a sustained optical source is not necessary. Semiconductors in which these non-linear conduction mechanisms can be optically triggered can be used either as linear-mode or high-gain PCSS devices, depending on the field applied. Such switches can be very efficient in principle because the optical trigger is only necessary during the initiation process. Such switches have been made using the direct bandgap semiconductors GaAs and GaN. The proposed mechanisms are very different. The GaAs mechanism involves a non-linear avalanche mechanism that is determined by unique features of the GaAs bandstructure. The GaN switches do not have a bandstructure consistent with this mechanism. Instead, the proposed mechanism involves avalanche injection. Theoretical Foundation for Nonlinear Mode in Direct Bandgap PCSS Devices  
To distinguish the origins of lock-on behavior in different materials, a computational comparison of GaN and GaAs is presented. Both sets of calculations are implemented in a structure consisting of a 1D high-resistivity (semi-insulating) region terminated on both ends with identical Ohmic contacts. The semiconductor region is insulating due to a large density of traps caused by impurities. This high resistivity provides the non-conductive off-state that persists in the absence of optical illumination. The steady-state carrier densities during illumination are assumed to be governed by trap capture. The primary common feature to both materials is the physics of the off-state. This state is caused by the defects that trap electrons. These trapped electrons cause an electric field that inhibits the flow of current. Computational Approach  
Two methods are used: a conventional ensemble Monte Carlo (EMC), and a proprietary solver for coupled transient reactive transport equations called Radiation Effects in Oxides and Semiconductors (REOS) [9]. In both methods, the calculations include the effects of large electrical fields and large carrier densities.