Threshold Voltage Calculation in Ultra-Thin Film SO1 MOSFETs using the Effective Potential zyxw S. M. Ramey and D. K. Ferry Department of Electrical Engineering and Center for Solid State Electronics Research Arizona State University, Box zyxwvu 875706, Tempe, AZ 85287-5706 zyx Abshncf- The success of the effective potential method of including quantum confinement effects in simulations of MOSFETs is based on the ability to calculate ahead of time the extent of the Gaussian wavepacket used to describe the electron. In the calculation of the Gaussian, the inversion layer is assumed to form in a triangular potential well, from which a suitable standard deviation can he obtained. The situation in an ultra-thin zyxwvutsrq SO1 MOSFET is slightly different, in that the potential well has a triaugnlar bottom, but there is a significant contribution to the Confinement from the rectangular barriers formed by the gate oxide and the buried oxide (BOX). For this more complex potential well, it is of interest to determine the range of applicability of the constant standard deviation effective potential model. In this work, we include this effective potential model in 3D Monte Carlo calculations of the threshold voltage of ultra-thin SO1 MOSFETs. We find that the effective potential recovers the expected trend in threshold voltage shift with shrinking silicon thickness, down to a thickness of approximately 3 nm. I. INTRODUCTION It is well known that simulations of current bulk MOSFETs need to incorporate some type of method to account for the quantum mechanical effects of camer confinement in the inversion layer, which influence the gate capacitance and threshold voltage [1,2]. Similar quantum effects are seen in SO1 MOSFETs, especially such devices built on ultra-thin SO1 layers. In addition to the inversion layer confinement, the carriers in these thin SO1 layers are confined by the gate and buried oxide interfaces, which produce additional confinement and enhanced quantum mechanical effects [3]. The effective potential method of accounting for quantum mechanical effects has been shown to be a useful means of incorporating these effects into both bulk [4] and SO1 MOSFETs [5]. This method relies on mapping the wave nature of the electrons onto the background potential of the device obtained from a solution of the Poisson equation. The electrons are considered to be in the form of Gaussian wavepackets, with a standard deviation of known extent. However, since a constant-sized, Gaussian wave packet is usually assumed, it is of interest to explore the range of validity over which this form of the wave packet can he used. In this work, we examine the range of silicon film thicknesses for which the effective potential method can be appropriately used to obtain the threshold 189 voltage in Monte Carlo simulations of extremely thin zyx (40 nm) SO1 MOSFETs. 11. SIMULATION METHODS We have included the effective potential into a Monte Carlo transport model coupled to a 3-D Poisson solver to simulate the SO1 MOSFET. The gate length was taken to be 40 nm, the source and drain lengths were 50 nm, the gate oxide was 2 nm with a 2 nm source and drain overlap, the channel doping was constant at NA = lxIO1’ 4, the sourcddrain doping was constant at ND= 2xlOI9 cm”, and there was a 10 nm spacer region between the gate and the sourceldrain contacts. The gate contact is taken to be n+- polysilicon, with a Fermi level at the silicon conduction band edge. The buried oxide was thick enough that substrate depletion was not significant. Therefore, the substrate contact was taken to be at the bottom of the buried oxide. The silicon film thickness is vaned over a range of 2 to 10 nm for different simulations. The implementation of the effective potential has been described in detail elsewhere zyxw [6], but it will be worthwhile to review several of the concepts here. The effective potential is a means of transferring the wave-like nature of the electrons onto the Hartree potential obtained from solution of the Poisson equation. The electron is assumed to be in the form of a Gaussion wave-packet, and then the effective potential is obtained by convolving this Gaussian with the potential. The resulting effective potential profile is used to calculate the electric fields used in the Monte Carlo transport kernel. Of specific importance for this work is the origin of the standard deviations assumed for the Gaussian function in the various directions. For a free particle, the standard deviation was found to be of the form zyxwvut [6]: .2:, (1) -_ - h2 6 2 = 12m*kBT 24n where &, is the thermal de Broglie wavelength and m’ the effective mass. The transverse mass is used here since the wave-packet is propagating parallel to the (100) Si-SiO2 interfaces. This results in a value for the standard deviation of 1.14 nm at room temperature. For the direction normal to the gate oxide interface, the electron is