# Photoconductive Semiconductor Switches: Materials, Physics, and Applications
## 2 Theory of PCSS Operation
The donor densities in the _n_-regions are \(10^{19}\) cm\({}^{-3}\), and the Mn-doped acceptor-like doping is \(5\times 10^{19}\) cm\({}^{-3}\). The total thickness is 2 \(\upmu\)m.  
A series of calculations explored the effects of Mn acceptor-like defects [20]. The first role of the acceptors is to trap the injected electrons. The resultant electric field halts the injection of additional electrons. The trapped charge produces a space charge barrier that stops the current flow. This mechanism provides the off-state of the switch. The band-to-band impact ionization mechanism supplies electrons from the right-hand-side contact [21]. In this mechanism, the optical pulse initiates the triggering by injecting electrons that are trapped and holes that reduce the barrier at the left-hand side. The reduced barrier allows the flow of current that starts injection at the right-hand side. Figure 2 shows the temporal evolution of the current. During the initial stage, transient current flows after the application of a large electrical potential of 110 V (550 kV/cm). The  
Figure 1: Schematic of doping in a simulated _n-i-n_ switch structure. contribution of injected electrons leads to a slight rise in the current. However, the field from the acceptor traps at the left-hand side halts this current flow. At time \(t=10^{-8}\) s, the optical pulse is applied. The photoconductivity causes a steady increase in the current. In this calculation, the electron and hole densities reach unphysical values because the growth has no Auger mechanism. Figure 3 shows the spatial variation in the conduction and valence bands caused by the applied potential. This figure reveals that the band bending is very abrupt at the right-hand side. The band bending at the timestep immediately prior to the growth of current is shown in Figure 2. This figure shows that the voltage has a large variation at the right-hand side. In other words, the electric field is modest except at the right-hand side. The change in potential at the right-hand side is enabled by the applied electric potential. However, the field is provided by the electron charged defects. This result suggests that the average field will be modest outside of a few hundred nm near the biased switch electrode. The defect mechanism provides a field that is somewhat independent of the external circuit. Instead, it is a field created by the optically injected electrons. Once the threshold is exceeded, the carrier growth is not controlled by the circuit. However, the field provided by the circuit causes a modest carrier drift contribution to the current. Figure 3: Computed band diagram of GaN _n-i-n_ structure at the last computed time increment before the optical pulse (shown in Figure 2), varying from the left-hand contact (0) and right-hand contact (0.0002 cm). The i region is noted at the top center in green and the n region at the top sides in purple (color online). Figure 2: Time-evolution calculation of _n-i-n_ device current in the dark (\(t<10^{8}\) s) and after an instantaneous light pulse (\(t>10^{8}\) s). Additional calculations using a capacitive source (an important circuit element for applications as described in Sections 7 and 8) lead to new insights about these calculations. In both the calculation and measurement of a fabricated PCSS pulse-charged by a capacitive circuit, both the current and the switch voltage decrease as the capacitor discharges. After approximately \(4\times 10^{-7}\) s, the current becomes very small, but the voltage remains constant. That voltage is defined as the lock-on voltage. This use of the term lock-on differs from the previous usage for GaAs switches. In experiments on those switches, the voltage during the on-state remained approximately constant. This constant voltage corresponds to a field of approximately 4 kV/cm, the lock-on field. New calculations using a capacitive current source were performed to obtain insight into the ways in which behavior may diverge.