1494 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 61, NO. 5, MAY 2014 A 2-D Analytical Model for Double-Gate Tunnel FETs Mahdi Gholizadeh and Seyed Ebrahim Hosseini Abstract—This paper presents a 2-D analytic potential model for double-gate (DG) tunnel field effect transistors (TFETs) by solving the 2-D Poisson’s equation. From the potential profile, the electric field is derived and then the drain current expression is extracted by analytically integrating the band-to-band tunneling generation rate over the tunneling region. The model well predicts the potential, subthreshold swing (SS), and transfer and output characteristics of DG TFETs. We analyze the dependence of the tunneling current on the device parameters by varying the gate oxide dielectric constant, gate oxide thickness, body thickness, channel length and channel material and also demonstrate its agreement with TCAD simulation results. The SS which describes the switching behavior of TFETs, is derived from the current expression. The comparisons show that the SS of our model well coincides with that of simulations. Index Terms— Analytical model, band-to-band tunneling (BTBT), BTBT generation rate, double-gate (DG) tunnel field effect transistor (TFET), electric field, mobile charge, Poisson’s equation, subthreshold swing (SS). I. I NTRODUCTION I T HAS been highlighted that increasing power density is a challenge for continued MOSFET scaling, due to nonscal- ability of subthreshold swing (SS). The SS of a MOSFET is limited to 60 mV/decade, which causes the leakage current to increase. One of the promising devices to replace the MOSFET for lowpower applications is the tunnel field effect transistor (TFET), which has demonstrated the potential to surmount the SS limit of MOSFETs [1]–[5]. The operation principle of the TFETs relies on the band-to-band tunneling (BTBT) of electrons, so that they are able to operate as steeper switches at lower supply voltages [6]. The cross-sectional view of an n-type double-gate (DG) TFET is shown in Fig. 1(a). The energy band profile in the OFF and ON-state is shown in Fig. 1(b). When a positive gate voltage is applied, the conduction band of the channel goes down and a sufficiently high lateral electric field is created at the source-channel junction. This electric field forces the electrons to tunnel from the occupied valence-band states of the source to the unoccupied conduction-band states of the channel. Manuscript received May 11, 2013; revised December 19, 2013, February 4, 2014, and March 12, 2014; accepted March 18, 2014. Date of current version April 18, 2014. The review of this paper was arranged by Editor M. Ieong. The authors are with the Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad 91779-48974, Iran (e-mail: mahdi.gholizadeh@stu.um.ac.ir; ehosseini@um.ac.ir). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2014.2313037 Fig. 1. (a) Schematic diagram of a symmetric DG n-TFET with x - y coordinates. (b) Energy band profile of an n-TFET in the OFF and ON state. E is the energy pass window between E V,SOURCE and E C,CHANNEL . The performance of TFETs has been simulated using 2-D TCAD simulations [1]–[6]. However, a physics-based analyt- ical model is essential for better understanding of the device operation and facilitates compact modeling for circuit-level studies. It is also useful to obtain fast results. Several analytical studies on TFETs have been carried out in [7]–[19]. Some 1-D analytical models without considering the impact of the drain voltage have derived the drain current [7]–[9]. Many 2-D studies on TFET modeling analytically calculate the tunneling generation rate using 2-D electric field, but the tunneling current is computed by numerically integrating over the volume of the device [10]–[13]. In some pseudo-2-D analytical models [14], [15], the tunneling current has analytically been derived. They have assumed that the electric field is constant over both the tunneling distance (along the channel) and depth of the device (perpendicular to the channel) in their models, whereas simulations and different analytical models such as [10] and [12] demonstrate that the distribution of the electric field is nonuniform in the channel. In a different method in [16], Landauer approach is used to derive the dc characteristics of TFETs. In this model, the width of the energy pass window E [Fig. 1(b)] is considered to have a linear relationship with the gate voltage, but in fact increasing the gate voltage leads to a rise in the voltage drop across the gate oxide. Therefore, increasing of the gate voltage leads to less increase in the width of the energy pass window (E ). In this paper, we develop a 2-D analytical model to derive analytical expressions for different electrical parameters of DG TFETs i.e., potential profile, SS, and transfer and output characteristics. In our calculations, the influences of the mobile 0018-9383 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.