Improved analytical model of surface potential with modified boundary conditions for double gate tunnel FETs
Introduction
TUNNEL field-effect transistors (TFETs) are under intensive investigation for future logic and low power applications owing to their promise for breaking the subthreshold swing (SS) thermal limitation of 60 mV/dec and enabling power-supply scaling to below 0.5 V [1], [2], [3]. Beside a lot of significant experimental efforts, an accurate analytical model would be helpful to provide fast results to be used in circuit simulations as well as present a brief insight for the design and fabrication of TFET devices.
The modeling of electrostatics in the channel is very important for the terminal properties of TFETs. However, the operation of TFET is mainly dominated by tunneling mechanism, which is different with the drift-diffusion model in MOSFETs. The TFETs are much more sensitive to the channel electrostatics than that of MOSFETs due to the high dependence on the band bending in the tunnel junction for the band-to-band tunnel process. Hence the accuracy of the surface potential model is of much more significance in TFETs.
Several analytical models of the surface potential in TFETs have been reported [4], [5], [6]. However, these models would make improper results sometimes, because the effects of the depletion region in source and drain regions are neglected, resulting in inaccurate boundary conditions and deviation of surface potential at the source/drain ends compared with the results from TCAD, even they could be much more worse if the drain region is lightly doped to suppress the ambipolar current [7]. In addition, disregard for the depletion widths of source/drain region leads to the overestimate on the electric field and tunnel probability near the tunnel junction. Previous works [8], [9] computed the surface potential and took source/drain depletion width into consideration using an iterative approach or series expansions which is relatively complex and computationally inefficient. Therefore, an accurate analytical model of the surface potential which efficiently considers the source/drain depletion width is necessary.
In this paper, an accurate analytical model of the channel surface potential in a double gate tunnel field effect transistor (DGTFET) is proposed with considering the influence of the depletion widths in source/drain regions on the channel surface potential and the modified boundary conditions are presented in Section 2. In Section 3, based on the proposed surface potential model, the threshold voltage (VT), one of the most important electrical parameters of a solid state device, is developed. As well known in the conventional MOS transistors, the threshold voltage is defined as the gate voltage at which the surface potential reaches two times the Fermi potential. However, this definition is only valid for doped MOSFETs [10] and does not work well for TFETs with undoped body as well as different operational mechanism. The transconductance change (TC) method is used in this work. The conclusions are highlighted in Section 4.
Section snippets
The solution of 2D Poisson's equation
The studied DGTFET device is a gated p-i-n diode with a double gate over the intrinsic Si region which is compatible with the future multi-gate MOSFET technology and its cross section view is shown in Fig. 1. Typical values of the physical parameters used in this work are listed in Table 1 if not otherwise stated.
Assuming the channel region to be fully depleted in the subthreshold operation domain, the charge density in the channel region is equal to the ionized doping concentration and the
Threshold voltage model for DGTFETs
For MOS transistors, the physical definition of the threshold voltage is the gate voltage at which the density of the carriers in the inversion channel equals the doping level of the substrate, i.e., the surface potential reaches two times the Fermi potential. However, this definition of threshold voltage is only valid for doped MOSFETs and does not work well for TFETs due to the undoped body and the totally different operational mechanism. Many previous works used a constant current method
Conclusion
In this paper, the improved surface potential model of double gate TFETs has been developed with modified boundary conditions considering the effect of source and drain depletion widths. Model validation has been proven by comparing with the numerical simulation results and it has to point out that the model accuracy has been improved. Based on the proposed potential model, an analytical threshold voltage model has also been developed with the TC method and good agreement has been achieved for
Acknowledgements
This work is supported by Advance Research Foundation of China (Grant No. 9140Axxx501), and National Defense Advance Research project (Grant No. 513xxxxx306).
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