Silicon nanowire based multiple gate metal oxide field effect transistors(MG-MOSFET) appear as replacements for conventional bulk transistors in post 45nm technology nodes. In such transistors the short channel effect(SCE) is controlled by the device geometry, and hence an undoped (or, lightly doped) ultra-thin body silicon nanowire is used to sustain the channel. The use of undoped body also solves several issues in bulk MOSFETs e.g., random dopant fluctuations, mobility degradation and compatibility with midgap metal gates. The electrostatic integrity of such devices increases with the scaling down of the body thickness. Since the quantization of electron energy cannot be ignored in such ultra-thin body devices, it is extremely important to consider quantum effects in their threshold voltage models. Most of the models reported so far are valid for long channel double gate devices. Only Munteanu et al. [Journal of non-crystalline solids vol 351 pp 1911-1918 2005] have reported threshold voltage model for short channel symmetric double gate MOSFET, however it involves unphysical fitting parameters. Only Munteanu et al.[Molecular simulation vol 31 pp 839-845 2005] reported threshold voltage model for quad gate transistor which is implicit in nature. On the other hand no modeling work has been reported for other types of MG-MOSFETs (e.g., tri gate, cylindrical body)apart from numerical simulation results. In this work we report physically based closed form quantum threshold voltage models for short channel symmetric double gate, quad gate and cylindrical body gate-all-around MOSFETs. In these devices quantum effects aries mainly due to the structural confinement of electron energy. Proposed models are based on the analytical solution of two or three-dimensional Poisson equation and one or two-dimensional Schrodinger equation depending on the device geometries. Judicial approximations have been taken to simplify the models in order to make them closed form and efficient for large scale circuit simulation. Effort has also been put to model the quantum threshold voltage of tri gate MOSFET. However it is found that the energy quantization in tri gate devices are mainly due to electronic confinement and hence it is very difficult to develop closed form analytical equations for the threshold voltage. Thus in this work the modeling of tri gate devices have been limited to long channel cases. All the models are validated against the professional numerical simulator.

Undoped body multi gate (MG) Metal Oxide Semiconductor Field Effect Transistors (MOSFET) are appearing as replacements for single gate bulk MOSFET in forthcoming sub-45nm technology nodes. It is therefore extremely necessary to develop compact models for MG transistors in order to use them in nano-scale integrated circuit design and simulation. There is however a sharp distinction between the electrostatics of traditional bulk transistors and undoped body devices. In bulk transistor, where the substrate is sufficiently doped, the inversion charges are located close to the surface and hence the surface potential solely controls the electrostatic integrity of the device. However, in undoped body devices, gate electric field penetrates the body center, and inversion charge exists throughout the body. In contrast to the bulk transistors, depending on device geometry, the potential of the body center of undoped body devices could be higher than the surface in weak inversion regime and the current flows through the center-part of the device instead of surface. Several crucial parameters (e.g. Sub-threshold slope) sometimes become more dependable on the potential of body center rather than the surface. Hence the body-center potential should also be modeled correctly along with the surface-potential for accurate calculation of inversion charge, threshold voltage and other related parameters of undoped body multi-gate transistors. Although several potential models for MG transistors have been proposed to capture the short channel behavior in the subthreshold regime but most of them are based on the crucial approximation of coverting the 2D Poisson’s equation into Laplace equation. This approximation holds good only at surface but breaks down at body center and in the moderate inversion regime. As a result all the previous models fail to capture the potential of body center Correctly and remain valid only in weak-inversion regime. In this work we have developed semiclassical compact models for potential distribution for double gate (DG) and cylindrical Gate-All-Around (GAA) transistors. The models are based on the analytical solution of 2D Poisson’s equation in the channel region and valid for both: a) weak and strong inversion regimes, b) long channel and short channel transistors, and, c) body surface and center. Using the proposed model, for the first time, it is demonstrated that the body potential versus gate voltage characteristics for the devices having equal channel lengths but different body thicknesses pass through a single common point (termed as crossover point). Using the concept of “crossover point” the effect of body thickness on the threshold voltage of undoped body multi-gate transistors is explained. Based on the proposed body potential model, a new compact model for the subthreshold swing is formulated. Some other parameters e.g. inversion charge, threshold voltage roll-off etc are also studied to demonstrate the impact of body center potential on the electrostatics of multi gate transistor. All the models are validated against professional numerical device simulator.

For the past 40 years, relentless focus on Moore’s Law transistor scaling has provided ever-increasing transistor performance and density. In order to continue the technology scaling beyond 22nm node, it is clear that conventional bulk-MOSFET needs to be replaced by new device architectures, most promising being the Multiple-Gate MOSFETs (MuGFET). Intel in mid 2011 announced the use of bulk Tri-Gate FinFETs in 22nm high volume logic process for its next-gen IvyBridge Microprocessor. It is expected that soon other semiconductor companies will also adopt the MuGFET devices. As like bulk-MOSFET, an accurate and physical compact model is important for MuGFET based circuit design. Compact modeling effort for MuGFET started in late nineties with planar double gate MOSFET(DGFET),as it is the simplest structure that one can conceive for MuGFET devices. The models so far proposed for DG MOSFETs are applicable for common gate symmetric DG (SDG) MOSFETs where both the gates have equal oxide thicknesses. However, for practical devices at nanoscale regime, there will always be some amount of asymmetry between the gate oxide thicknesses due to process variations and uncertainties, which can affect device performance significantly. At the same time, Independently controlled DG(IDG) MOSFETs have gained tremendous attention owing to its ability to modulate threshold voltage and transconductance dynamically. Due to the asymmetric nature of the electrostatic, developing efficient compact models for asymmetric/independent DG MOSFET is a daunting task. In this thesis effort has been put to provide some solutions to this challenge. We propose simple surface-potential based compact terminal charge models, applicable for Asymmetric Double gate MOSFETs (ADG) in two configurations1) Common-gate 2) Independent-gate. The charge model proposed for the common-gate ADG (CDG) MOSFET is seamless between the symmetric and asymmetric devices and utilizes the unique so-far-unexplored quasi-linear relationship between the surface potentials along the channel. In this model, the terminal charges could be computed by basic arithmetic operations from the surface potentials and applied biases, and can be easily implemented in any circuit simulator and extendable to short-channel devices. The charge model proposed for independent ADG(IDG)MOSFET is based on a novel piecewise linearization technique of surface potential along the channel. We show that the conventional “charge linearization techniques that have been used over the years in advanced compact models for bulk and double-gate(DG) MOSFETs are accurate only when the channel is fully hyperbolic in nature or the effective gate voltages are same. For other bias conditions, it leads to significant error in terminal charge computation. We demonstrate that the amount of nonlinearity that prevails between the surface potentials along the channel for a particular bias condition actually dictates if the conventional charge linearization technique could be applied or not. We propose a piecewise linearization technique that segments the channel into multiple sections where in each section, the assumption of quasi-linear relationship between the surface potentials remains valid. The cumulative sum of the terminal charges obtained for each of these channel sections yield terminal charges of the IDG device. We next present our work on modeling the non-ideal scenarios like presence of body doping in CDG devices and the non-planar devices like Tri-gate FinFETs. For a fully depleted channel, a simple technique to include body doping term in our charge model for CDG devices, using a perturbation on the effective gate voltage and correction to the coupling factor, is proposed. We present our study on the possibility of mapping a non-planar Tri-gate FinFET onto a planar DG model. In this framework, we demonstrate that, except for the case of large or tall devices, the generic mapping parameters become bias-dependent and an accurate bias-independent model valid for geometries is not possible. An efficient and robust “Root Bracketing Method” based algorithm for computation of surface potential in IDG MOSFET, where the conventional Newton-Raphson based techniques are inefficient due to the presence of singularity and discontinuity in input voltage equations, is presented. In case of small asymmetry for a CDG devices, a simple physics based perturbation technique to compute the surface potential with computational complexity of the same order of an SDG device is presented next. All the models proposed show excellent agreement with numerical and Technology Computer-Aided Design(TCAD) simulations for all wide range of bias conditions and geometries. The models are implemented in a professional circuit simulator through Verilog-A, and simulation examples for different circuits verify good model convergence.