Coupled numerical analysis of Suspended Gate Field Effect Transistor (SGFET)

Jayaprakash Reddy. K, Charanjeet Kaur Malhi, Rudra Pratap, Navakanta Bhat Center for Nano Science & Engineering, IISc,

Bangalore, Karnataka, India e-mail: kjpreddy@mecheng.iisc.ernet.in

AbstractSuspended gate MOSFETs exist since last few decades. Resonant gate transistors were first demonstrated as a means of getting high Q devices [1]. The advantages of transistor based transduction as compared to the capacitive detection have also been demonstrated [2,3]. The behaviors of SGFETs have been studied using equivalent lumped parameter modeling methodology [4-7]. Numerical simulations involving hybrid FEA coupling between two different tools, ANSYS Multiphysics and ISE-DESIS, with the help of an external Perl script have also been tried [8]. Here ANSYS is used for the coupled electrostatic and structural physics calculations and ISE-DESIS provides the correct boundary conditions for the electrostatic domain using semiconductor physics. Another related study [9] solved the beam equation coupled with the Poisson equation numerically using finite difference and Newton Raphson method.

Our work presents an easier modeling and analysis of a suspended gate MOSFET in COMSOL, successfully demonstrating a solution of a moving gate type device. In our analysis, we consider the air gap as a deformable continuum and we report the standard Id-Vg characteristics of the transistor. Commercially available packages such as ISE-DESIS specialize in only fixed gap analysis wherein air is also modeled as a material with a known permittivity. In such an analysis the capacitor formed due to the air gap remains fixed. We demonstrate here that this analysis can be easily carried out in COMSOL using its multiphysics features. Using two dimensional analysis involving structural mechanics domain, moving mesh ALE, convection and diffusion, and the electrostatics domain, the effect of moving gate and hence the moving air gap can be modeled and analyzed.

Keywords-component; MOSFET, Suspended gate field effective transistor, COMSOL, Multiphysics.

I. INTRODUCTION In Hybrid Micro-Electro-Mechanical (MEM)solid-state

devices, Suspended gate FET (SG-FET) is the more important device because of its potential for very low power and various memory applications. Generally, in principle SG-FET has a movable gate over a channel to delimit two stable states which are two different threshold voltages; one high, in the up-state, resulting in an extremely low off current and another low, in down state, providing a very high on current. The suspended gate FET methodology is implemented for the various micromechanical devices gas sensors, microphone and resonators like gyroscope for achieving the high sensitivity. In designing and optimizing of such a high

sensitive devices with SGFET methodology requires the complete numerical simulations package which can be provide the semiconductor electrical domain and micromechanical domain, at present the numerical simulations of these devices have been carried out with the hybrid simulations [8]. The goal of this paper is to propose, for the first time the coupling of the semiconductor electrical domain and the micromechanics in a single FEM package. Adapting these two different domains the FEM simulations have been carried out instantaneously for the characteristics of the device.

II. SGFET GEOMETRY AND CONSIDERATIONS Fig. 1 shows the 3D and cross section of a Suspended gate

field effect transistor. The electric field in the gate influenced the low doped p- type silicon beam will under go certain deflection; specifically, at a certain gate voltage a thin layer of it, close to the silicon oxide(SiO2) surface, turns into an n-type material. This process, called inversion, creates a conducting channel between the highly doped n-type source and the drain regions. With this channel present, a voltage across the source and the drain drives a drain current.

Figure 1. N-channel SGFET. (a) Three dimensional structure: The channel width is equal to the beam length (W= WFET= Lbeam), and the channel length is equal to the beam width (L=LFET=Wbeam), (b) Cross section parallel to device

length, (c) Equivalent capacitor circuit, (d) Symbol.[6]

Fig. 2 shows the schematic view of the modeled geometry. The relevant dimensions are: Gate length = 0.2 m, transistor width = 0.2 m, Air gap = 20 nm, Gate material = Polysilicon, Gate thickness = 20nm, Gate oxide thickness = 5nm.

Figure 2. Geometry of SGFET in COMSOL workplane

III. METHODOLOGY AND SIMULATIONS In SGFET model the electronic semiconductor part is

solved by using standard drift diffusion approximation coupled Poissions equation. By the accepted assumptions - such as neglecting magnetic fields, a constant density of states in both the valence and the conductance bands, and a Boltzmann distribution of the carriers, these equations are derived from Maxwells equations and Boltzmann transport theory.

The semiconductor model solved by using three dependent variables: (the electrostatic potential), n, and p. The three basic semiconductor equations are

Where p and n are the hole and electron concentrations,

respectively, and N represents the fixed charge associated with ionized donors. Jn and Jp the electron and hole current densities. RSRH, represents the Shockley-Read-Hall recombination.

Part of the moving gate (suspended beam) model is solved by the standard Euler beam equation. An electrostatic force caused by an applied potential difference between the moving gate (beam) and the ground electrode bends towards the oxide layer. To compute the electrostatic force, calculate the electric field in the surrounding air. Due to the electrostatic force as the beam bends, the geometry of the air changes continuously. In COMSOL multiphysics, using arbitrary Lagrangian-Eulerian (ALE) method, the model takes the air displacement into consideration when computing the potential field. When the beam deforms, the electric field between the gate and ground continuously changes as a result of the bending.

A. Boundary Conditions In semiconductor model, the symmetry or zero charge

(flux) boundary condition has been carried out in case of the boundaries which are in contact with the insulator or far away

from active device area. The electrostatic potential is fixed for boundaries contact with the metal.

The moving gate has been modeled as a roller-roller support at the both ends and at the interface of beam and the air given as a free deformation for accurate electrostatic results.

B. Initial-Value Calculation To solve the SGFET model for various voltages, it starts

with the initial value formulation in first step. This step replaces the carrier concentrations with the formulas [10].

This step produces the exact solution for the full system

when all applied voltages are zero.

C. Mesh: For finite element analysis of the model, the triangular

element has been selected. Maximum element size is 3E-9 m and minimum element size is 2.0E-11 m for the beam region.

Figure 3. Meshed view of SGFET

IV. RESULTS The numerical analysis has been carried out for the various

gate voltages and the following results are reported. The standard Id Vg plot has been reported for the transistor. Fig. 9 shows the variation in Id with the change in the air gap. Drain current increases with increase in deflection of the center point of the beam.

Figure 4. Id-Vg characterstics for moving gate FET

Figure 5. Initial electrical potentialvalue calculation

Figure 6. Electric potential distribution at Vg=2 volts

Figure 7. The deformation of the moving influenced by electrostatic force

Figure 8. Deflection profiles of suspended gate for various gate voltages

Figure 9. Variation in the drain current (Id) with change in the air gap

V. SUMMARY We have demonstrated the 2D suspended gate field

effective transistor in single platform COMSOL multiphysics. The present study is being extended to a 3D which can be useful for studying complicated geometry devices like Gyroscope, Microphone and Gas sensor of the moving gate.

REFERENCES

[1] Nathanson, C. H., Newell, W. E., Wickstrom, R. A., Davis, J. R., The Resonant Gate Transistor, IEEE transactions on Electron Devices, Ed-14 (3), pp. 117-133, March 1967.

[2] Abele, N., Pott, V., Boucart, K., Casset, F., Segueni, K., Ancey, P., and Ionescu, A. M., Comparison of RSG-MOSFET and capacitive MEMS resonator detection, Electron. Lett., vol. 41, no. 5, pp. 242-244, March 2005.

[3] Grogg, D., Tsamados, D., Badila, N. D., Ionescu, A. M., Integration of MOSFET transistors in MEMS resonators for improved output detection, proc. 18th Int. Solid-State sens. Actuators Conf. Tech. Dig., Lyon, France, Jun. 10-14, 2007, pp. 1709-1712.

[4] Ionescu, A. M., Pott, V., Fritschi, R., Banerjee, K., Declerq, M.J., Renaud, P., Hibert, C., Fluckiger, P., Racine, G.A., Modeling and design of a low voltage SOI suspended gate MOSFET (SG-MOSFET) with a metal over-gate architecture, proc. ISQED, 2002, pp. 496-501.

[5] Kam, H., Lee, D. T., Howe, R. T., King, T. J., A new nanolectromechanical field effect transistor (NEMFET) design for low-power electronics, in IEDM Tech. Digest, 2005, pp. 463-466.

[6] Akarvardar, K., Eggimann, C., Tsamados, D., Chauhan, Y.S., Wan, G.C., Ionescu, A.M., Howe, R.T., and Wong H.S.P., Analytical Modeling of the Suspended Gate FET and Design Insights for Low-Power Logic, IEEE transactions on Electron Devices, vol. 55 (1), pp. 48-59, 2008.

[7] Malhi, C., Pratap, R., Bhat, N. Design of a high sensitivity FET integrated MEMS microphone, 23rd Eurosensors Conference, Sep. 06-09, pp. 875-878, 2009.

[8] Tsamados, D., Chauhan, Y. S., Eggimann, C., Akarvardar, K., Phillip Wong, H. S., Ionescu, A.M., Numerical and analytical simulations of suspended gate FET for ultra-low power inverters, Proceedings of the 37th European Solid-State Devices Research Conference, ESSDERC 2007, pp. 167-170, Munich, Germany, 11-13 Sept. 2007.

[9] Kam, H., King Liu, T. J., Pull-in and release voltage design for Nanoelectromechanical Field-Effect Transistors, IEEE transactions on Electron Devices, vol. 56 (12), pp. 3072-3082, 2009.

[10] COMSOL Multiphysics example DC Characteristics of a MOS Transistor (MOSFET) model, version 3.5a.

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