# A Review of Sharp-Switching Band-Modulation Devices
## Operating Principles and Models  
### Band-Modulation Mechanism  
The current-voltage characteristics of all band-modulation devices originate from the particular profile of the energy bands between the cathode and anode. At equilibrium (V\({}_{\text{A}}\) = 0, Figure 7a), the bands undulate along the body. The height of the energy barriers at the anode and cathode is set by the front- and back-gate voltages, respectively. This is what the designation 'band-modulation' is meant to capture. A positive V\({}_{\text{A}}\) forward-biases both the \(P^{+}\)-\(N^{*}\) junction at the anode and the \(N^{+}\)-\(P^{*}\) junction at the cathode. It is the \(P^{*}\)-\(N^{*}\) electrostatic junction in-between that is reverse-biased and blocks the current flow. Any further increase in V\({}_{\text{A}}\) is absorbed by this junction; the energy barriers remain tall and prevent the release of electrons and holes from their reservoirs (Figure 7b). This process continues until, eventually, the maximum voltage sustainable by the central junction is reached. At this point, a small increase in V\({}_{\text{A}}\) (or a decrease in V\({}_{\text{FG}}\)) reduces marginally the anode energy barrier (\(\approx\)V\({}_{\text{FG}}-\) V\({}_{\text{A}}\)), enabling a few holes to fly from the anode to the cathode. Since the positive charge of holes lowers the electron injection barrier at the cathode slightly, some electrons can escape and move to the anode. Their negative charge further erodes the injection barrier for holes. A higher hole current increases the electron current and vice versa. This positive feedback process triggers the abrupt collapse of the two injection barriers and the flattening of the energy bands (Figure 7c); the device turns on suddenly for V\({}_{\text{A}}\) = V\({}_{\text{ON}}\), and the current increases by many orders of magnitude [26]. In the I\({}_{\text{ON}}\) state, the high density of electron-hole plasma screens the gate-induced electric field and keeps the barriers flat. The \(Z^{2}\)-FET behaves as a regular PIN diode, where the current increases with anode voltage, first exponentially and eventually reaching a quadratic dependence I\({}_{\text{A}}\)-V\({}_{\text{A}}\)\({}^{2}\) (due to the double injection mechanism). The I\({}_{\text{ON}}\) current is largely independent of the voltage applied to the gate or to the ground-plane. The device cannot be turned off until the anode voltage becomes too low (V\({}_{\text{A}}\) = V\({}_{\text{OFF}}\) < V\({}_{\text{ON}}\)) for sustaining the electron-hole plasma within the body. At that point, the energy barriers are rebuilt and the current falls sharply to zero. The positive feedback effect is reminiscent of a thyristor. Nevertheless, the band-modulation devices are fundamentally different: (i) the doping is virtual, (ii) impact ionization does not play any role, (iii) the energy barriers are gate-controlled, and (iv) operation requires lower voltage (\(\approx\)1 V) than a thyristor, leading to improved temperature stability. Figure 7: Typical profiles of the energy bands along the body as the anode voltage increases: (**a**) equilibrium at V\({}_{\text{A}}\) = 0, (**b**) blocked I\({}_{\text{OFF}}\) state with 0 < V\({}_{\text{A}}\) < V\({}_{\text{ON}}\), and (**c**) I\({}_{\text{ON}}\) state with V\({}_{\text{A}}\) > V\({}_{\text{ON}}\). The band diagram also depends on the depth within the body, being a little different at the front and back interfaces. In a \(Z^{2}\)-FET, the front-gate voltage \(\mathrm{V_{FG}}\) controls the hole injection barrier height, the turn-on voltage \(\mathrm{V_{ON}}\) and the hysteresis window (\(\mathrm{V_{ON}}-\mathrm{V_{OFF}}\)). If the \(\mathrm{V_{FG}}\) is too low and unable to build a strong energy barrier at the anode, the device acts like a PIN diode with \(\mathrm{V_{ON}}\approx 0.3\) V, much smaller than the typical turn-on voltage of a silicon diode (0.8 V).