# A Review of Sharp-Switching Band-Modulation Devices
## 2 Basic Characteristics
### Transient Operation  
In a transient or pulsed mode of operation, the concentrations of electrons and holes do not reach the equilibrium values and the \(\mathrm{I_{A}-V_{A}}\) characteristics differ from the behavior shown in DC operation. Consider the case where the gate is pulsed from 0 V to a positive voltage: electrons are expected to fill the gated region, but they are not readily available. Since electrons cannot be supplied promptly through the generation process, junctions, and gate leakage, the body potential is forced out of equilibrium, like in the deep-depletion regime of a MOS capacitor [2]. It follows that the energy barrier opposing the injection of holes from the anode is temporarily taller than in DC mode, hence the effective turn-on voltage \(\mathrm{V_{ON}}\) increases. The shorter the gate pulse, the higher the \(\mathrm{V_{ON}}\). The same mechanism raises the electron injection barrier at the cathode after pulsing the back gate.  
A positive pulse on the anode is expected to attenuate the electron concentration underneath the gate. However, the change in concentration takes place in the electron recombination time scale. While carrier generation dominates the \(\mathrm{I_{OFF}}\) region, recombination governs the turn-on and high-current regions.  
The carrier lifetime is of uppermost importance in the formation of the electrostatic barriers needed for sharp-switching. [PERSON] et al. demonstrated the critical role that the carrier lifetime plays in the transient operation of \(Z^{2}\)-FETs [25]. TCAD simulations of their transient behavior were performed with different values of carrier lifetime. Figure 6a,b reproduce the \(\mathrm{I_{A}-V_{A}}\) characteristics for two cases (1 ns and 0.1 ns), as \(\mathrm{V_{A}}\) is pulsed from 0 to 2 V with rise times ranging from 100 ns to 50 s (DC mode).  
Faster rise times have two remarkable effects: the \(\mathrm{V_{ON}}\) increases, widening the hysteresis window, but the leakage current in the \(\mathrm{I_{OFF}}\) state increases as well. The latter is not an intrinsic consequence of band modulation, but rather is due to the displacement current that depends on the device capacitance and increases proportionately with the voltage ramp rate, as seen in Figure 6.  
A very fast rise time does not allow the readjustment of the carrier concentration: the electrostatic barriers remain tall and block the current conduction more effectively. The change in \(\mathrm{V_{ON}}\) depends upon the carrier lifetime, for example a longer lifetime leads to more pronounced transient effects (Figure 6a). If the lifetime is short, the carrier generation by Shockley-Read-Hall mechanisms is faster. Hence, for a 0.1 ns lifetime, the steady-state  
Figure 6: \(\mathrm{I_{A}-V_{A}}\) characteristics of \(Z^{2}\)–FET for different ramp times (100 ns to 50 s) of anode voltage, from zero to 2 V. The carrier lifetime is (**a**) \(\tau=10^{-9}\) s and (**b**) \(10^{-10}\) s. The two wells were filled with carriers by gate pulses before ramping \(\mathrm{V_{A}}\) (adapted from [25]).  
V\({}_{\text{ON}}\) is achieved with a 100 \(\upmu\)s ramp, and the shift between the transient and steady state V\({}_{\text{ON}}\) values is 130 mV (Figure 6b). On the other hand, this shift in V\({}_{\text{ON}}\) is 300 mV for a 1 ns lifetime and the device recovers the steady state V\({}_{\text{ON}}\) with a longer ramp time of \(\sim\)10 ms (Figure 6a).