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.

Compact Models are the physically based accurate mathematical description of the cir-cuit elements, which are computationally efficient enough to be incorporated in circuit simulators so that the outcome becomes useful for the circuit designers. As the multi-gate MOSFETs have appeared as replacements for bulk-MOSFETs in sub-32nm technology nodes, efficient compact models for these new transistors are required for their successful utilization in integrated circuits. Existing compact models for common double-gate (CDG) MOSFETs are based on the fundamental assumption of having symmetric gate oxide thickness. In this work we explore the possibility of developing models without this approximation, while preserving the computational efficiency at the same level. Such effort aims to generalize the compact model and also to capture the oxide thickness asymmetry effect, which might prevail in practical devices due to process uncertainties and thus affects the device performance significantly. However solution to this modeling problem is nontrivial due to the bias-dependent asym-metric nature of the electrostatic. Using the single implicit equation based Poisson so-lution and the unique quasi-linear relationship between the surface potentials, previous researchers of our laboratory have reported the core model for such asymmetric CDG MOSFET. In this work effort has been put to include Non-Quasistatic (NQS) effects, different small-geometry effects, and noise model to this core, so that the model becomes suitable for practical applications. It is demonstrated that the quasi-linear relationship between the surface potentials remains preserved under NQS condition, in the presence of all small geometry effects. This property of the device along with some other new techniques are used to develop the model while keeping the mathematical complexity at the same level of the models reported for the symmetric devices. Proposed model is verified against TCAD simulation for various device geometries and successfully imple-mented in professional circuit simulator. The model passes the source/drain symmetry test and good convergence is observed during standard circuit simulations.

La réduction des transistors MOSFETs, briques de base des circuits intégrés, ne permet plus d'améliorer efficacement leurs performances. Des leviers technologiques ont été mis en place dans les procédés de fabrication de ces transistors pour y remédier. L'introduction intentionnelle de contraintes constitue l'une de ces solutions. De fait, l'orientation des contraintes en fonction de la direction du canal influence fortement les propriétés de transport des transistors MOSFETs. Les méthodes de calculs de structures de bandes semi-empiriques EPM et */k.p/* dans l'approximation de la fonction enveloppe, ont été développées afin d'étudier les perturbations occasionnées sur la structure électronique des matériaux par l'action conjuguée des contraintes mécaniques et du confinement. L'influence de ces dernières perturbations sur les propriétés de transport a, par la suite, été analysée à l'aide de simulations avancées Monte Carlo "fullband" et Kubo-Greenwood. Les résultats théoriques obtenus ont été confrontés aux données expérimentales de flexion à quatre pointes (Wafer Bending), mesurées au cours de cette thèse. Il apparaît clairement que la prise en compte du couplage complexe des effets de confinement et de contrainte joue un rôle essentiel dans les propriétés de transport des dispositifs MOSFETs actuels. Enfin, chaque étape de modélisation a donné lieu à une discussion des domaines de validité des outils de simulation Dérive-Diffusion et Hydrodynamique, classiquement utilisés dans l'industrie pour la modélisation des dispositifs MOSFETs.