No description available.

No description available.

No description available.

The Tunnel Field Effect Transistor (TFET) with sub-60mV/decade Sub-threshold slope and extremely high ION/IOFF ratio has attracted enough attention for low standby power (LSTP) applications where the battery life is very important. So far research in this area has been limited to numerical simulation and experimental analysis. It is however extremely necessary to develop compact models for TFET in order to use them in nano-scale integrated circuit design and simulation. In this work, for the first time, we develop analytical Sub-threshold slope model for n-channel double gate TFET (nDGTFET). Unlike conventional FETs, current in TFET is mainly controlled by the band-to-band tunneling mechanism at source/channel interface. As the total drain current is proportional to band-to-band generation rate, the main challenge in the present work is to find an explicit relationship between average electric field over the tunneling path and the applied gate voltage under nonlocal tunneling condition. Two dimensional Poisson’s equation (with Laplace approximation)is first solved in a rectangular coordinate system in order to obtain analytical expression for electron energy distribution over the channel region.Kane’s Model[J. Phy. Chem.Solids 12(181)1959]for band-to-band tunneling along with some analytical approximation techniques are then used to derive the expression for the Sub-threshold slope under nonlocal tunneling conditions. This Sub-threshold slope model is verified against professional numerical device simulator (MEDICI) for different device geometries. Being an asymmetric device, TFET fabrication suffers from source misalignment with gate. As the doping in source and drain-gate are different, conventional-FET-like self-aligned gate stack formation is not possible for TFET. Such misalignment, at source side, seriously degrades the performance of TFETs. To overcome this problem, in this work we explore the possibility of using “gate replacement” technique for TFET fabrication. We first develop process flow for single gate bulk nTFET, and then we extend it to n-channel double gate TFET (nDGTFET) using modified FinFET process. Good alignments between source and gate are observed with TCAD-simulations in both the cases.

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.

Neste trabalho, é apresentada uma análise da operação analógica de transistores de múltiplas portas, avaliando a tensão Early, o ganho de tensão em malha aberta, a razão da transcondutância pela corrente de dreno (gm/IDS), a condutância de dreno e, em especial, a distorção harmônica, exibida por estes dispositivos. Ao longo deste trabalho, foram estudados FinFETs, dispositivos de porta circundante (Gate-All-Around GAA) com estrutura de canal gradual (Graded-Channel GC) e transistores MOS sem junções (Junctionless - JL). Inicialmente, foi efetuada a análise da distorção harmônica apresentada por FinFETs com e sem a presença de tensão mecânica biaxial, com diversas larguras de fin (Wfin) e comprimentos de canal (L), quando estes operavam em saturação, como amplificadores de um único transistor. Nesta análise, as não-linearidades foram avaliadas através da extração das distorções harmônicas de segunda e terceira ordens (HD2 e HD3, respectivamente), mostrando que a presença de tensão mecânica tem pouca influência em HD2, mas altera levemente a HD3. Quando os ganhos de tensão em malha aberta dos dispositivos são levados em conta, transistores sem tensão, também chamados de convencionais, mais estreitos apresentam grande vantagem em termos de HD2 em relação aos tensionados. Ainda nesta análise, percebeu-se que HD2 e HD3 de transistores tensionados pioram com a redução da temperatura, especialmente em inversão mais forte. Na seqüência, foi efetuada uma análise de HD3 em FinFETs com e sem tensão mecânica de vários comprimentos e larguras de canal, operando em região triodo e aplicados a estruturas balanceadas 2-MOS, mostrando que presença de tensão mecânica traz pouca influência em HD3, mas reduz a resistência do canal dos dispositivos (RON), o que não é bom em estruturas resistivas, como as avaliadas. Nesta análise, ainda, pode-se perceber uma melhora em HD3 superior a 30 dB ao se incrementar VGT de zero a 1,0 V, em cuja tensão dispositivos mais estreitos apresentam curvas mais lineares que os mais largos. Então, foi estudada a distorção apresentada por transistores GAA e GC GAA operando em regime triodo, aplicados a estruturas 2-MOS, onde se pôde perceber que GC GAAs com maiores comprimentos da região fracamente dopada apresentam vantagem em HD3 em relação aos demais, para valores de VGT superiores a 2 V. Na avaliação destas estruturas em função da temperatura, percebeu-se que, para VGT superiores a 1,1 V, HD3 depende fortemente da temperatura e piora conforme a temperatura diminui. O estudo envolvendo transistores sem junções foi mais focado em seus parâmetros analógicos, comparando-os aos apresentados por dispositivos de porta tripla ou FinFETs. Em inversões moderada e forte, transistores sem junção apresentaram menores valores para gm/IDS em relação a dispositivos de FinFETs polarizados em um mesmo nível de corrente, entretanto, a dependência de gm/IDS com a temperatura em transistores sem junção também foi menor que a apresentada por FinFETs. JL e FinFETs apresentaram comportamentos distintos para a tensão Early e o ganho de tensão em malha aberta em função da temperatura. Estes parâmetros sempre melhoram com o aumento da temperatura em dispositivos JL, enquanto que exibem seu máximo valor em temperatura ambiente em FinFETs. Nas proximidades da tensão de limiar, transistores sem junção com largura de fin de 30 nm exibiram tensão Early e ganho superiores a 80 V a 57 dB, respectivamente, enquanto que FinFETs mostraram Tensão Early de 35 V e ganho de 50 dB. Em todos os estudos efetuados ao longo do trabalho, procurou-se apontar as causas das não-linearidades apresentadas pelos dispositivos, a partir de modelos analíticos que pudessem relacionar a física de funcionamento dos transistores com os resultados experimentalmente obtidos. / In this work it is presented an analysis of the analog operation of multiple gate transistors, evaluating the Early Voltage, the open-loop voltage gain, the transconductance over the drain current ratio (gm/IDS), the drain conductance and, especially, the harmonic distortion exhibited by these devices. Along the work, FinFETs, Gate-All-Around (GAA) devices with the Graded-Channel (GC) structure and MOS transistors without junctions (Junctionless - JL) were studied. Initially, an analysis of the harmonic distortion presented by conventional and biaxially strained FinFETs with several fin widths (Wfin) and channel lengths (L) was performed, when these devices were operating in saturation as single transistor amplifiers. In this analysis, the non-linearities were evaluated through the extraction of the second and the third order harmonic distortions (HD2 and HD3, respectively), and it was shown that the presence of strain has negligible influence in HD2, but slightly changes HD3. When the open loop voltage gain of the devices is taken into consideration, narrower conventional transistors present a huge advantage with respect to the strained ones in terms of HD2. Also, it was perceived that both HD2 and HD3 of strained FinFETs worsen with the temperature decrease, especially in stronger inversion. In the sequence, an analysis of the HD3 presented by conventional and strained FinFETs of several fin widths and channel lengths operating in the triode regime was performed. These devices were applied to 2-MOS balanced structures, showing that the presence of the strain does not influence significantly the HD3, but reduces the resistance in the channel of the transistors (RON), which is not good for resistive structures as the ones evaluated. In this analysis, it can also be observed an HD3 improvement of 30 dB when VGT is increased from zero up to 1,0 V, where narrower devices present transfer characteristics more linear than the wider ones. Then, it was studied the distortion presented by GAA and GC GAA devices operating in the triode regime, applied to 2-MOS structures. In this case, it could be perceived that GC GAAs with longer lightly doped regions present better HD3 in comparison to the other devices for VGT higher than 2.0 V. In the evaluation of these structures as a function of the temperature, it could be seen that for VGT higher than 1.1 V, HD3 strongly depends on the temperature and worsens as the temperature decreases. The study involving JL transistors was focused on their analog parameters, comparing them to the ones presented by triple gate devices or FinFETs. In moderate and strong inversions, Junctionless showed lower values for gm/IDS with respect to triple gate devices biased at a similar current level. However, the dependence of gm/IDS from Junctionless with the temperature was also smaller than the one presented by FinFETs. Junctionless and FinFETs exhibited distinct behaviors for the Early voltage and the open-loop voltage gain as a function of the temperature. These parameters always improve with the temperature raise in JL devices whereas they exhibit their maximum values around room temperatures for FinFETs. In the proximity of the threshold voltage, Junctionless with fin width of 30 nm presented Early voltage and intrinsic gain larger than 80 V and 57 dB, respectively, whereas FinFETs exhibited Early voltage of 35 V and gain of 50 dB. For all the studies performed in this work, the probable causes of the non-linearities were pointed out, from analytic models that could correlate the physical work of the devices with the experimental results.

Neste trabalho, é apresentada uma análise da operação analógica de transistores de múltiplas portas, avaliando a tensão Early, o ganho de tensão em malha aberta, a razão da transcondutância pela corrente de dreno (gm/IDS), a condutância de dreno e, em especial, a distorção harmônica, exibida por estes dispositivos. Ao longo deste trabalho, foram estudados FinFETs, dispositivos de porta circundante (Gate-All-Around GAA) com estrutura de canal gradual (Graded-Channel GC) e transistores MOS sem junções (Junctionless - JL). Inicialmente, foi efetuada a análise da distorção harmônica apresentada por FinFETs com e sem a presença de tensão mecânica biaxial, com diversas larguras de fin (Wfin) e comprimentos de canal (L), quando estes operavam em saturação, como amplificadores de um único transistor. Nesta análise, as não-linearidades foram avaliadas através da extração das distorções harmônicas de segunda e terceira ordens (HD2 e HD3, respectivamente), mostrando que a presença de tensão mecânica tem pouca influência em HD2, mas altera levemente a HD3. Quando os ganhos de tensão em malha aberta dos dispositivos são levados em conta, transistores sem tensão, também chamados de convencionais, mais estreitos apresentam grande vantagem em termos de HD2 em relação aos tensionados. Ainda nesta análise, percebeu-se que HD2 e HD3 de transistores tensionados pioram com a redução da temperatura, especialmente em inversão mais forte. Na seqüência, foi efetuada uma análise de HD3 em FinFETs com e sem tensão mecânica de vários comprimentos e larguras de canal, operando em região triodo e aplicados a estruturas balanceadas 2-MOS, mostrando que presença de tensão mecânica traz pouca influência em HD3, mas reduz a resistência do canal dos dispositivos (RON), o que não é bom em estruturas resistivas, como as avaliadas. Nesta análise, ainda, pode-se perceber uma melhora em HD3 superior a 30 dB ao se incrementar VGT de zero a 1,0 V, em cuja tensão dispositivos mais estreitos apresentam curvas mais lineares que os mais largos. Então, foi estudada a distorção apresentada por transistores GAA e GC GAA operando em regime triodo, aplicados a estruturas 2-MOS, onde se pôde perceber que GC GAAs com maiores comprimentos da região fracamente dopada apresentam vantagem em HD3 em relação aos demais, para valores de VGT superiores a 2 V. Na avaliação destas estruturas em função da temperatura, percebeu-se que, para VGT superiores a 1,1 V, HD3 depende fortemente da temperatura e piora conforme a temperatura diminui. O estudo envolvendo transistores sem junções foi mais focado em seus parâmetros analógicos, comparando-os aos apresentados por dispositivos de porta tripla ou FinFETs. Em inversões moderada e forte, transistores sem junção apresentaram menores valores para gm/IDS em relação a dispositivos de FinFETs polarizados em um mesmo nível de corrente, entretanto, a dependência de gm/IDS com a temperatura em transistores sem junção também foi menor que a apresentada por FinFETs. JL e FinFETs apresentaram comportamentos distintos para a tensão Early e o ganho de tensão em malha aberta em função da temperatura. Estes parâmetros sempre melhoram com o aumento da temperatura em dispositivos JL, enquanto que exibem seu máximo valor em temperatura ambiente em FinFETs. Nas proximidades da tensão de limiar, transistores sem junção com largura de fin de 30 nm exibiram tensão Early e ganho superiores a 80 V a 57 dB, respectivamente, enquanto que FinFETs mostraram Tensão Early de 35 V e ganho de 50 dB. Em todos os estudos efetuados ao longo do trabalho, procurou-se apontar as causas das não-linearidades apresentadas pelos dispositivos, a partir de modelos analíticos que pudessem relacionar a física de funcionamento dos transistores com os resultados experimentalmente obtidos. / In this work it is presented an analysis of the analog operation of multiple gate transistors, evaluating the Early Voltage, the open-loop voltage gain, the transconductance over the drain current ratio (gm/IDS), the drain conductance and, especially, the harmonic distortion exhibited by these devices. Along the work, FinFETs, Gate-All-Around (GAA) devices with the Graded-Channel (GC) structure and MOS transistors without junctions (Junctionless - JL) were studied. Initially, an analysis of the harmonic distortion presented by conventional and biaxially strained FinFETs with several fin widths (Wfin) and channel lengths (L) was performed, when these devices were operating in saturation as single transistor amplifiers. In this analysis, the non-linearities were evaluated through the extraction of the second and the third order harmonic distortions (HD2 and HD3, respectively), and it was shown that the presence of strain has negligible influence in HD2, but slightly changes HD3. When the open loop voltage gain of the devices is taken into consideration, narrower conventional transistors present a huge advantage with respect to the strained ones in terms of HD2. Also, it was perceived that both HD2 and HD3 of strained FinFETs worsen with the temperature decrease, especially in stronger inversion. In the sequence, an analysis of the HD3 presented by conventional and strained FinFETs of several fin widths and channel lengths operating in the triode regime was performed. These devices were applied to 2-MOS balanced structures, showing that the presence of the strain does not influence significantly the HD3, but reduces the resistance in the channel of the transistors (RON), which is not good for resistive structures as the ones evaluated. In this analysis, it can also be observed an HD3 improvement of 30 dB when VGT is increased from zero up to 1,0 V, where narrower devices present transfer characteristics more linear than the wider ones. Then, it was studied the distortion presented by GAA and GC GAA devices operating in the triode regime, applied to 2-MOS structures. In this case, it could be perceived that GC GAAs with longer lightly doped regions present better HD3 in comparison to the other devices for VGT higher than 2.0 V. In the evaluation of these structures as a function of the temperature, it could be seen that for VGT higher than 1.1 V, HD3 strongly depends on the temperature and worsens as the temperature decreases. The study involving JL transistors was focused on their analog parameters, comparing them to the ones presented by triple gate devices or FinFETs. In moderate and strong inversions, Junctionless showed lower values for gm/IDS with respect to triple gate devices biased at a similar current level. However, the dependence of gm/IDS from Junctionless with the temperature was also smaller than the one presented by FinFETs. Junctionless and FinFETs exhibited distinct behaviors for the Early voltage and the open-loop voltage gain as a function of the temperature. These parameters always improve with the temperature raise in JL devices whereas they exhibit their maximum values around room temperatures for FinFETs. In the proximity of the threshold voltage, Junctionless with fin width of 30 nm presented Early voltage and intrinsic gain larger than 80 V and 57 dB, respectively, whereas FinFETs exhibited Early voltage of 35 V and gain of 50 dB. For all the studies performed in this work, the probable causes of the non-linearities were pointed out, from analytic models that could correlate the physical work of the devices with the experimental results.

La forte demande et le besoin d’intégration hétérogène de nouvelles fonctionnalités dans les systèmes mobiles et autonomes, tels que les mémoires, capteurs, et interfaces de communication doit prendre en compte les problématiques d’hétérogénéité, de consommation d’énergie et de dissipation de chaleur. Les systèmes mobiles intelligents sont déjà dotés de plusieurs composants de type capteur comme les accéléromètres, les thermomètres et les détecteurs infrarouge. Cependant, jusqu’à aujourd’hui l’intégration de capteurs chimiques dans des systèmes compacts sur puce reste limitée pour des raisons de consommation d’énergie et dissipation de chaleur principalement. La technologie actuelle et fiable des capteurs de gaz, les résistors à base d’oxyde métallique et les MOSFETs (Metal Oxide Semiconductor- Field Effect Transistors) catalytiques sont opérés à de hautes températures de 200–500 °C et 140–200 °C, respectivement. Les transistors à effet de champ à grille suspendu (SG-FETs pour Suspended Gate-Field Effect Transistors) offrent l’avantage d’être sensibles aux molécules gazeuses adsorbées aussi bien par chemisorption que par physisorption, et sont opérés à température ambiante ou légèrement au-dessus. Cependant l’intégration de ce type de composant est problématique due au besoin d’implémenter une grille suspendue et l’élargissement de la largeur du canal pour compenser la détérioration de la transconductance due à la faible capacité à travers le gap d’air. Les transistors à double grilles sont d’un grand intérêt pour les applications de détection de gaz, car une des deux grilles est fonctionnalisée et permet de coupler capacitivement au canal les charges induites par l’adsorption des molécules gazeuses cibles, et l’autre grille est utilisée pour le contrôle du point d’opération du transistor sans avoir besoin d’une structure suspendue. Les transistors monoélectroniques (les SETs pour Single Electron Transistors) présentent une solution très prometteuse grâce à leur faible puissance liée à leur principe de fonctionnement basé sur le transport d’un nombre réduit d’électrons et leur faible niveau de courant. Le travail présenté dans cette thèse fut donc concentré sur la démonstration de l’intégration 3D monolithique de SETs sur un substrat de technologie CMOS (Complementary Metal Oxide Semiconductor) pour la réalisation de la fonction capteurs de gaz très sensible et ultra basse consommation d’énergie. L’approche proposée consiste à l’intégration de SETs métalliques à double grilles dans l’unité de fabrication finale BEOL (Back-End-Of-Line) d’une technologie CMOS à l’aide du procédé nanodamascene. Le système sur puce profitera de la très élevée sensibilité à la charge électrique du transistor monoélectronique, ainsi que le traitement de signal et des données à haute vitesse en utilisant une technologie de pointe CMOS disponible. Les MOSFETs issus de la technologie FD-SOI (Fully Depleted-Silicon On Insulator) sont une solution très attractive à cause de leur pouvoir d’amplification du signal quand ils sont opérés dans le régime sous-le-seuil. Ces dispositifs permettent une très haute densité d’intégration due à leurs dimensions nanométriques et sont une technologie bien mature et modélisée. Ce travail se concentre sur le développement d’un procédé de fonctionnalisation d’un MOSFET FD-SOI comme démonstration du concept du capteur de gaz à base de transistor à double grilles. La sonde Kelvin a été la technique privilégiée pour la caractérisation des matériaux sensibles par le biais de mesure de la variation du travail de sortie induite par l’adsorption de molécules de gaz. Dans ce travail, une technique de caractérisation des matériaux sensibles alternative basée sur la mesure de la charge de surface est discutée. Pour augmenter la surface spécifique de l’électrode sensible, un nouveau concept de texturation de surface est présenté. Le procédé est basé sur le dépôt de réseaux de nanotubes de carbone multi-parois par pulvérisation d’une suspension de ces nanotubes. Les réseaux déposés servent de «squelettes» pour le matériau sensible. L’objectif principal de cette thèse de doctorat peut être divisé en 4 parties : (1) la modélisation et simulation de la réponse d’un capteur de gaz à base de SET à double grilles ou d’un MOSFET FD-SOI, et l’estimation de la sensibilité ainsi que la puissance consommée; (2) la caractérisation de la sensibilité du Pt comme couche sensible pour la détection du H[indice inférieur 2] par la technique de mesure de charge de surface, et le développement du procédé de texturation de surface de la grille fonctionnalisée avec les réseaux de nanotubes de carbone; (3) le développement et l’optimisation du procédé de fabrication des SETs à double grilles dans l’entité BEOL d’un substrat CMOS; et (4) la fonctionnalisation d’un MOSFET FD-SOI avec du Pt pour réaliser la fonction de capteur de H[indice inférieur 2]. / Abstract : The need of integration of new functionalities on mobile and autonomous electronic systems has to take into account all the problematic of heterogeneity together with energy consumption and thermal dissipation. In this context, all the sensing or memory components added to the CMOS (Complementary Metal Oxide Semiconductor) processing units have to respect drastic supply energy requirements. Smart mobile systems already incorporate a large number of embedded sensing components such as accelerometers, temperature sensors and infrared detectors. However, up to now, chemical sensors have not been fully integrated in compact systems on chips. Integration of gas sensors is limited since most used and reliable gas sensors, semiconducting metal oxide resistors and catalytic metal oxide semiconductor- field effect transistors (MOSFETs), are generally operated at high temperatures, 200–500 °C and 140–200° C, respectively. The suspended gate-field effect transistor (SG-FET)-based gas sensors offer advantages of detecting chemisorbed, as well as physisorbed gas molecules and to operate at room temperature or slightly above it. However they present integration limitations due to the implementation of a suspended gate electrode and augmented channel width in order to overcome poor transconductance due to the very low capacitance across the airgap. Double gate-transistors are of great interest for FET-based gas sensing since one functionalized gate would be dedicated for capacitively coupling of gas induced charges and the other one is used to bias the transistor, without need of airgap structure. This work discusses the integration of double gate-transistors with CMOS devices for highly sensitive and ultra-low power gas sensing applications. The use of single electron transistors (SETs) is of great interest for gas sensing applications because of their key properties, which are its ultra-high charge sensitivity and the ultra-low power consumption and dissipation, inherent to the fundamental of their operation based on the transport of a reduced number of charges. Therefore, the work presented in this thesis is focused on the proof of concept of 3D monolithic integration of SETs on CMOS technology for high sensitivity and ultra-low power gas sensing functionality. The proposed approach is to integrate metallic double gate-single electron transistors (DG-SETs) in the Back-End-Of-Line (BEOL) of CMOS circuits (within the CMOS interconnect layers) using the nanodamascene process. We take advantage of the hyper sensitivity of the SET to electric charges as well from CMOS circuits for high-speed signal processing. Fully depleted-silicon on insulator (FD-SOI) MOSFETs are very attractive devices for gas sensing due to their amplification capability when operated in the sub-threshold regime which is the strongest asset of these devices with respect to the FET-based gas sensor technology. In addition these devices are of a high interest in terms of integration density due to their small size. Moreover FD-SOI FETs is a mature and well-modelled technology. We focus on the functionalization of the front gate of a FD-SOI MOSFET as a demonstration of the DGtransistor- based gas sensor. Kelvin probe has been the privileged technique for the investigation of FET-based gas sensors’ sensitive material via measuring the work function variation induced by gas species adsorption. In this work an alternative technique to investigate gas sensitivity of materials suitable for implementation in DG-FET-based gas sensors, based on measurement of the surface charge induced by gas species adsorption is discussed. In order to increase the specific surface of the sensing electrode, a novel concept of functionalized gate surface texturing suitable for FET-based gas sensors are presented. It is based on the spray coating of a multi-walled-carbon nanotubes (MW-CNTs) suspension to deposit a MW-CNT porous network as a conducting frame for the sensing material. The main objective of this Ph.D. thesis can be divided into 4 parts: (1) modelling and simulation of a DG-SET and a FD-SOI MOSFET-based gas sensor response, and estimation of the sensitivity as well as the power consumption; (2) investigation of Pt sensitivity to hydrogen by surface charge measurement technique and development of the sensing electrode surface texturing process with CNT networks; (3) development and optimization of the DG-SET integration process in the BEOL of a CMOS substrate, and (4) FD-SOI MOSFET functionalization with Pt for H[subscript 2] sensing.

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.