Compact Model for Nano-Wire Tunnel Field-Effect Transistor
Authors: Sato Shingo , Omura Yasuhisa , Mallik Abhijit 
Published: February 2020

This abstract presents a compact current model of the Nano-Wire-Tunnel-Field-Effect-Transistor (NW-TFET). We have already proposed a simple channel-length-dependent current model for NW-TFET with WKB approximation; it uses a piece-wise-linear potential. The validity of this model has been confirmed near the subthreshold region [1]. However, the characteristics of the drain current with gate voltages over threshold voltage cannot be well characterized since our model uses the electric field at source-channel junction, which underestimates the tunneling distance. To realize a highly precise compact current model for NW-TFET, the tunneling probability near the on-state must be reconsidered. The tunneling probability T(E) with constant effective electric field is expressed as shown in eq. (1). Some models of the effective electric field near the source-channel junction for NW-TFET have already been reported [2, 3]. One of them is often used in estimating the tunneling probability due to its simple and powerful expression for characterizing TFET operation [3]. The tunneling probabilities of that model (model ‘A’) and ours near the on-state (model ‘B’ [1]) at source Fermi level as a function of gate voltage are compared in Fig.1. The parameters of tunnel electron mass, energy band gap, channel length and natural length assumed in the simulation are 0.3m0, 0.5eV, 20nm and 2.63nm, respectively. We find that both models have the same trend against gate voltage and overestimate the tunneling probability near the on-state because they underestimate the tunneling distance. Model ‘A’ has slightly smaller tunneling probability than model ‘B’. To analyze the probability difference between the models, analytical expressions of the effective electric field for each model with the potential profile applying the depletion approximation in the channel are shown by eqs. (2) and (3). First and second terms of these equations reveal terms for control of the drain and gate voltages, respectively. In the case of L >> λ, the effective electric field of model ‘A’ is consistent with that of model ‘B’ and the tunneling probability is only controlled by the second term, the effective electric field, which means no dependence on the drain voltage. Model ‘B’ offers better control of the gate voltage than model ‘A’ due to the property of the hyperbolic function included in the former’s formula. The difference in tunneling probability between the models is expected to appear in short channel devices (L < 10λ). To reveal the effect of the channel length dependence of the effective electric field, the tunneling probability of NW-TFET with channel length of 10nm calculated as a function of the gate voltage is shown in Fig. 2. The difference in tunneling probability between the models near the on-state is clear. Model ‘A’ traces the exact simulation result although the gate-voltage dependence of the tunneling probability is slightly different. On the other hand, model ‘B’ overestimates the tunneling probability; however, the gate-voltage dependence of the tunneling probability seems to match the exact simulation result if the gate voltage is offset. From the viewpoint of model compactness, it is easy to add voltage fitting to the tunneling probability of model ‘B’ to exactly match the simulation results. The characteristic of the gate voltage offset as a function of the energy band gap is calculated in Fig. 3. We find that the gate voltage offset is proportional to the effective band gap energy. The reason is that the underestimation of the tunneling distance in model ‘B’ becomes noticeable because of the exponential dependence of the potential profile even though a constant electric field is assumed at the source-channel junction when the band gap energy is large. The gate voltage offset depends only on energy band gap in the range studied here. Figure 4 shows the tunneling probability with gate voltage offset as a function of gate voltage near the on-state. The result of model ‘B’ with gate voltage offset can exactly trace the simulation results for any band gap energy, even in short channel devices. We compared the validity of the models and successfully reproduced the exact simulation results in this study.
[1] S. Sato et al., in Proc. Compact Modeling Dig., 2014, pp. 28-31.
[2] E. Gnani et al., Solid-State Electronics, vol.84, 2013, pp. 96–102.
[3] J. Knoch et al., in Proc. DRC Dig., 2005, pp. 153–156.
[4] J. P. Colinge, in Proc. SISPAD Dig., 2014, pp. 313-316.

Figure 1