3.2.1. Calibration of the Fabricated Devices
In modeling the fabricated devices, p-channel devices are considered first due to their steeper subthreshold characteristics and a parallel memory window. The off-state current is tuned by considering donor type bulk traps in the silicon substrate. The bulk trap density is set as 1x10
16 cm
3 and the trap level is 0.63 eV. The capture cross section for electrons and holes are set to 10
-13 cm
2 and 10
-14 cm
2 respectively in accordance with experimental reports [
1,
20,
30]. Further, the literature survey suggests the role of fixed charges and charge trapping at the HZO/SiO
2 interfacial layer (IL) interface in modulating the subthreshold characteristics and thus limiting the memory window of the fabricated devices [
1,
20,
30]. Accordingly, acceptor type interface traps were tuned at the HZO/IL interface to obtain a best fit to the experimental data. In this regard, an interface trap density of 1.8x10
13 cm
2, trap energy level of 0.20 eV and capture cross sections of 10
-13 cm
2 and 10
-14 cm
2 for electrons and holes respectively were defined at the HZO/IL interface [
31]. In addition to these, Fermi and SRH models were invoked to capture carrier statistics and the interaction of carriers with traps that evolved during the fabrication process. The Priesach Ferroelectric model was also invoked to model the doping dependent mobility, CVT model [
32] and to capture the ferroelectric polarization. The calibrated simulation deck for the p-channel device was then used as the basis for realizing n-channel FeFETs. The off-state current was tuned again by considering the donor type bulk traps in the silicon substrate. The trapping conditions defined in the substrate were similar to that of p-channel devices in order to mimic similar bulk conditions, except that the OFF–state current was tuned by changing the energy of the trap level to 0.43 eV. The interface trap density at the HZO/IL interface was similar to the p-channel case, except that the trap levels were tuned to 0.26 eV to capture the slow subthreshold characteristics observed in
Figure 5a for n-FeFETs. In addition to this, to capture the GIDL effect observed in n-FeFETs, as seen in
Figure 5a, Kane’s BTBT model was invoked, and its coefficients were tuned to achieve the best fit to the GIDL current [
27]. The calibrated simulation decks for the n- and p-channel devices are shown in
Figure 8.
It is observed that the subthreshold characteristics of n-FeFETs are more affected due to charge trapping at the HZO/SiO2(IL) interface suggesting that electrons are more easily trapped than holes. The presence of IL further participates in a tunneling current, due to charge trapping at the HZO/SiO2 (IL). This results in a charge transfer directly between the HZO and Si channel and is responsible for modulating the subthreshold characteristics of the n-FeFETs.
The characteristic crossover point observed in the n-channel devices during the downward sweep was also captured in the TCAD simulations, as shown in
Figure 8a. A closer insight into this reveals that there is a temporary switching of the ferroelectric based operation to the charged based operation, which arises due to the presence of the fixed charges and charge trapping at the HZO/IL interface and HZO bulk layer.
The devices are further investigated by recording the contour plots of electron/hole concentrations and conduction current densities after forward and reverse sweeps at 1 nA/µm. These are depicted in
Figure 9a for n-FeFETs and in
Figure 9b for p-FeFETs. For the n-channel device, as observed from
Figure 9a, the shift in electron concentration and conduction current density is not significant after the respective program/erase cycles. In contrast, for the p-channel device, a significant change in both the hole concentration as well as the conduction current density is observed in
Figure 9b, which accounts for the shift in V
TH observed in both
Figure 7c,d and
Figure 5b after subjecting the gate stack to the necessary program cycle.
The trapping effects on the MW can be understood by observing the band diagrams recorded at erase and program conditions. This is shown in
Figure 10a,b for the n-and p-channel devices, respectively. For the n-FeFET devices, as depicted in
Figure 10a, the carriers can directly tunnel through the HZO and the IL (SiO
2) through Fowler-Nordheim (FN) tunneling [
33]. The carriers can also participate in tunneling with the help of acceptor type traps defined at the HZO/IL interface and at the HZO bulk through the trap-assisted tunneling (TAT) [
33]. The injected carriers are ‘hot’, in the sense that these carriers are energetic and can further participate in the generation of interface traps at the SiO
2 (IL)/Si interface, thereby degrading the quality of the memory window or the devices over time. Consequently, there is a charge sharing directly between the HZO and the silicon channel, which is responsible for modulating the subthreshold characteristics observed in
Figure 5a and
Figure 8a. Under the program cycle, as depicted in
Figure 10b, the electron carriers tunnel through the SiO
2 layer, which is translated to the shift observed in the device threshold voltage. Further, on observing the position of the traps with respect to the fermi level under both erase and program conditions, as seen in
Figure 10a, it can be inferred that most of the tunneled carriers during the program pulse are trapped courtesy of the bulk traps in HZO and at HZO/IL interface. Consequently, the span of the memory window for the n-FeFETs gets limited.
The band diagrams under erase/program conditions depicted in
Figure 10b for p-channel devices follow a similar approach. The tunneling probabilities for the holes, however, is much lower than that of the electrons and the charge sharing through FN/TAT is effectively minimized. At a sufficiently higher gate bias, there is still a possibility of ‘hot’ hole injection, which may result in the generation of traps at the SiO
2/Si interface. Under the program cycle, similar to the n-channel case, the tunneling of the hole carriers through the SiO
2 is responsible for the shift in the device threshold voltage observed in
Figure 5b and
Figure 8b. Further, it is also identified that there are multi-level traps present at the HZO/IL interface. These traps are relatively deeper, as discussed in
Section 3.1.1, and are responsible for the roll-off in the device V
TH observed during the pulse characterization of the p-FeFET devices in
Figure 7c.