Devenlopment of Compact Small Signal Quasi Static Models for Multiple Gate Mosfets

En esta tesis hemos desarrollado los modelos compactos explícitos de carga y de capacitancia adaptados para los dispositivos dopados y no dopados de canal largo (DG MOSFETs dopados, DG MOSFETs no dopados, UTB MOSFETs no dopados y SGT no dopados) de un modelo unificado del control de carga derivado de la ecuación de Poisson. El esquema de modelado es similar en todos estos dispositivos y se adapta a cada geometría. Los modelos de la C.C. y de la carga son completamente compatibles. Las expresiones de la capacitancia se derivan del modelo de la carga. La corriente, la carga total y las capacitancias se escriben en términos de las densidades móviles de la carga en los extremos de fuente y drenador del canal. Las expresiones explícitas e infinitamente continuas se utilizan para las densidades móviles de la carga en la fuente y drenador. Las capacitancias modeladas demuestran el acuerdo excelente con las simulaciones numéricas 2D y 3D (SGT), en todos los regímenes de funcionamiento. Por lo tanto, el modelo es muy prometedor para ser utilizado en simuladores del circuito. Desafortunadamente, no mucho trabajo se ha dedicado a este dominio de modelado. Las cargas analíticas y las capacitancias, asociadas a cada terminal se prefieren en la simulación de circuito. Con respecto al SGT MOSFET, nuestro grupo fue el primero en desarrollar y publicar un modelo de las cargas y de las capacitancias intrínsecas, que es también analítico y explícito. La tesis es organizada como sigue: el capítulo (1) presenta el estado del arte, capítulo (2) el modelado compacto de los cuatro dispositivos: DG MOSFETs dopados, DG MOSFETs no dopados, UTB MOSFETs no dopados y SGT no dopados; en el capítulo (3) estudiamos las capacitancias de fricción en MuGFETs. Finalmente el capítulo (4) resuma el trabajo hecho y los futuros objetivos que necesitan ser estudiados. Debido a la limitación de los dispositivos optimizados disponibles para el análisis, la simulación numérica fue utilizada como la herramienta principal del análisis. Sin embargo, cuando estaban disponibles, medidas experimentales fueron utilizadas para validar nuestros resultados. Por ejemplo, en la sección 2A, en el caso de DG MOSFETs altamente dopados podríamos comparar nuestros resultados con datos experimentales de FinFETs modelados como DG MOSFETs. La ventaja principal de este trabajo es el carácter analítico y explícito del modelo de la carga y de la capacitancia que las hace fácil de implementar en simuladores de circuitos. El modelo presenta los resultados casi perfectos para diversos casos del dopaje y para diversas estructuras no clásicas del MOSFET (los DG MOSFETs, los UTB MOSFETs y los SGTs). La variedad de las estructuras del MOSFET en las cuales se ha incluido nuestro esquema de modelado y los resultados obtenidos, demuestran su validez absoluta. En el capítulo 3, investigamos la influencia de los parámetros geométricos en el funcionamiento en RF de los MuGFETs. Demostramos el impacto de parámetros geométricos importantes tales como el grosor de la fuente y del drenador o, el espaciamiento de las fins, la anchura del espaciador, etc. en el componente parásito de la capacitancia de fricción de los transistores de la múltiple-puerta (MuGFET). Los resultados destacan la ventaja de disminuir el espaciamiento entre las fins para MuGFETs y la compensación entre la reducción de las resistencias parásitas de fuente y drenador y el aumento de capacitancias de fricción cuando se introduce la tecnología del crecimiento selectivo epitaxial (SEG). La meta de nuestro estudio y trabajo es el uso de nuestros modelos en simuladores de circuitos. El grupo de profesor Aranda, de la Universidad de Granada ha puesto el modelo actual de SGT en ejecución en el simulador Agilent ADS y buenos resultados fueron obtenidos.In this thesis we have developed explicit compact charge and capacitance models adapted for doped and undoped long-channel devices (doped Double-Gate (DG) MOSFETs, undoped DG MOSFETs, undoped Ultra-Thin-Body (UTB) MOSFETs and undoped Surrounding Gate Transistor (SGT)) from a unified charge control model derived from Poisson's equation. The modelling scheme is similar in all these devices and is adapted to each geometry. The dc and charge models are fully compatible. The capacitance expressions are derived from the charge model. The current, total charges and capacitances are written in terms of the mobile charge sheet densities at the source and drain ends of the channel. Explicit and infinitely continuous expressions are used for the mobile charge sheet densities at source and drain. As a result, all small signal parameters will have an infinite order of continuity. The modeled capacitances show excellent agreement with the 2D and 3D (SGT) numerical simulations, in all operating regimes. Therefore, the model is very promising for being used in circuit simulators. Unfortunately, not so much work has been dedicated to this modelling domain. Analytical charges and capacitances, associated with each terminal are preferred in circuit simulation. Regarding the surrounding-gate MOSFET, our group was the first to develop and publish a model of the charges and intrinsic capacitances, which is also analytic and explicit. The thesis is organized as follows: Chapter (1) presents the state of the art, Chapter (2) the compact modeling of the four devices: doped DG MOSFETs, undoped DG MOSFETs, undoped UTB MOSFETs and undoped SGT; in Chapter (3) we study the fringing capacitances in MuGFETs. Finally Chapter (4) summarizes the work done and the future points that need to be studied. Due to the limitation of available optimized devices for analysis, numerical simulation was used as the main analysis tool. However, when available, measurements were used to validate our results. The experimental part was realised at the Microelectronics Laboratory, Université Catholique de Louvain, Louvain-la Neuve, Belgium. For example, in section 2A, in the case of highly-doped DG MOSFETs we could compare our results with experimental data from FinFETs modeled as DG MOSFETs. The main advantage of this work is the analytical and explicit character of the charge and capacitance model that makes it easy to implement in circuit simulators. The model presents almost perfect results for different cases of doping (doped/undoped devices) and for different non classical MOSFET structures (DG MOSFET, UTB MOSFETs and SGT). The variety of the MOSFET structures in which our modeling scheme has been included and the obtained results, demonstrate its absolute validity. In chapter 3, we investigate the influence of geometrical parameters on the RF performance in MuGFETs. We show the impact of important geometrical parameters such as source and drain thickness, fin spacing, spacer width, etc. on the parasitic fringing capacitance component of multiple-gate field-effect transistors (MuGFET). Results highlight the advantage of diminishing the spacing between fins for MuGFETs and the trade-off between the reduction of parasitic source and drain resistances and the increase of fringing capacitances when Selective Epitaxial Growth (SEG) technology is introduced. The goal of our study and work is the usage of our models in circuit simulators. This part, of implementing and testing our models of these multi gate MOSFET devices in circuit simulators has already begun. The group of Professor Aranda, from the University of Granada has implemented the SGT current model in the circuit simulator Agilent ADS and good results were obtained

An analytical model for the inversion charge distribution in square GAA MOSFETs with rounded corners

In this work we introduce an analytical model for square Gate All Around (GAA) MOSFETs with rounded corners including quantum effects. With the model developed it is possible to provide an analytical description of the 2D inversion charge distribution function (ICDF) in devices of different sizes and for all the op erational regimes. The accuracy of the model is verified by comparing with data obtai ned by means of a 2D numerical simulator that self-consistently solves the Poi sson and Schr ̈odinger equations. The expressions presented here are useful to achieve a good d escription of the physics of these transistors; in particular, of the quantization effect s on the inversion charge. The analytical ICDF obtained is used to calculate important par ameters from the device compact modeling viewpoint, such as the inversion charge ce ntroid and the gate-to- channel capacitance, which are modeled for different device g eometries and biases.Universidad de Granada. Departamento de Electrónica y Tecnología de los Computadores. Máster Métodos y Técnicas Avanzadas en Física (MTAF)

Analitical modeling for square gate-all-around MOSFETs

Two analytical models for square Gate All Around (GAA) MOSFETs has been introduced. The first part of this report include a quantum viewpoint and this first work has been published, while the second part approach a classical developed. With the model developed in the first part, it is possible to provide an analytical description of the 2D inversion charge distribution function (ICDF) in square GAA MOSFETs of difeerent sizes and for all the operational regimes. The accuracy of the model is verified by comparing the data with that obtained by means of a 2D numerical simulator that self-consistently solves the Poisson and Schrödinger equations. The expressions presented here are useful to achieve a good description of the physics of these transistors; in particular, of the quantization effects on the inversion charge. The analytical ICDF obtained is used to calculate important parameters from the device compact modeling viewpoint, such as the inversion charge centroid and the gate-to-channel capacitance, which are modeled for different device geometries and biases. The model presented accurately reproduces the simulation results for the devices under study and for different operational regimes. Anyway the second part of this report is focus on square GAA MOSFETs with a classical view point, which have not been analytically described in depth due to their particular geometrical complexity. The analytical description of cylindrical GAA MOSFETs is simpler since the symmetry of the structure around the rotation angle allows a 1D description, accounting just for the radial component. In the case of square GAA MOSFETs other modeling strategies are necessary, as will be shown below. Firstly, a technique to obtain analytical functions which are solutions of the 2D Poisson equation where the charge density in the silicon channel has been calculated, and the total inversion charge is introduced. Among all these functions a simple one for the electric potential in the silicon core of the square GAA MOSFETs was proposed. Secondly, the model introduced has been used to calculate the total inversion charge making use of Gauss's Law. The models obtained are finally validated with simulations data obtained with a 2D simulator developed in our group for Multiple-gate MOSFETs.Universidad de Granada. Departamento de Electrónica y Tecnología de los Computadores. Máster Métodos y Técnicas Avanzadas en Física (MTAF)This work was partially carried out within the framework of Research Projects of Department of Electronic and Computer Technology from the Faculty of Sciences, University of Granada

Vertical InAs Nanowire Devices and RF Circuits

Recent decades have seen an exponential increase in the functionality of electronic circuits, allowing for continuous innovation, which benefits society. This increase in functionality has been facilitated by scaling down the dimensions of the most important electronic component in modern electronics: the Si-based MOSFET. By reducing the size of the device, more transistors per chip area is possible. Smaller MOSFETs are also faster and more energy-efficient. In state of the art MOSFETs, the key dimensions are only few nanometers, rapidly approaching a point where the current scaling scheme may not be maintained. Research is ongoing to improve the device performance, mainly focusing on material and structural improvements to the existing MOSFET architecture. In this thesis, MOSFETs based on nanowires, are investigated. Taking advantage of the nanowire geometry, the gate can be wrapped all-around the nanowires for excellent control of the channel. The nanowires are made in a high-mobility III-V semiconductor, InAs, allowing for faster electrons and higher currents than Si. This device type is a potential candidate to either replace or complement Si-based MOSFETs in digital and analogue applications. Single balanced down-conversion mixer circuits were fabricated, consisting of three vertically aligned InAs nanowire MOSFETs and two nanowire resistors. These circuits are shown to operate with voltage gain in the GHz-regime. Individual transistors demonstrated operation with gain at several tens of GHz. A method to characterise the resistivity and metal-semiconductor contact quality has been developed, using the transmission line method adapted for vertical nanowires. This method has successfully been applied to InAs nanowires and shown that low-resistance contacts to these nanowires are possible. To optimise the performance of the device and reach as close to intrinsic operation as possible, parasitic capacitances and resistances in the device structure need to be minimised. A novel self-aligned gate-last fabrication method for vertical InAs nanowire transistors has been developed, that allows for an optimum design of the channel and the contact regions. Transistors fabricated using this method exhibit the best DC performance, in terms of a compromise between the normalised transconductance and sub-threshold swing, of any previously reported vertical nanowire MOSFET

Analytical Modeling of Ultrashort-Channel MOS Transistors

Les geometries de transistors d'avui són al rang de nanòmetres d'un sol dígit. En conseqüència, les funcionalitats dels dispositius es veuen afectades negativament pels efectes de canal curt i de mecànica quàntica (SCE i QMEs). Una transició de la geometria del transistor d'efecte de camp de tipus FinFET a Gate-All-Around (GAA) FETs com FETs de nanofils cilíndrics (NW) i de nanoplaques de silici (SiNS) es preveuen en els propers nodes tecnològics per suprimir els SCE i garantir una major miniaturització del MOSFET Aquesta dissertació se centra en el modelat analític de FETs de tipus NW i SiNS de canal ultracurt.S'introdueix un concepte de dimensions de doble porta (DG) equivalent per transferir un model de potencial de DG analític a FET de NW. Un model de corrent de DG compacte es modifica aprofitant la simetria rotacional dels FET de NW. L'efecte del confinament quàntic (QC) és implementat considerant l'eixamplament addicional de la banda prohibida al càlcul d'una concentració de portadors de càrrega intrínseca efectiva i al càlcul del voltatge llindar. L'efecte de corrent túnel directe de font a drenador (DSDT) a SiNS FET ultraescalats es modela amb el nou mètode de wavelets. Aquest model calcula analíticament la probabilitat de tunelització per a cada energia de l'electró, aproximant la forma de la barrera potencial mitjançant una barrera rectangular amb una altura de barrera equivalent. A causa de la fórmula de corrent túnel de Tsu-Esaki no analíticament integrable, es presenta un mètode analític anomenat model quasi-compacte (QCM). Aquest enfocament requereix, entre altres aproximacions, una iteració de Newton i una interpolació lineal de la densitat de corrent amb efecte túnel. A més, es realitza una anàlisi criogènica de temperatura i dopatge. S'investiga la forta influència de la distància del nivell de Fermi a la font des de la vora de la banda de conducció sobre el pendent subumbral, el corrent i la reducció de la barrera induïda per drenador (DIBL). A més, es demostra i explica la fusió de dos efectes relacionats amb el pendent subumbral i el DIBL. La validesa del concepte de dimensions DG equivalents es demostra mitjançant el mesurament i les dades de simulació de TCAD Sentaurus, mentre que el mètode de wavelets es verifica mitjançant simulacions NanoMOS NEGF.Las geometrías de transistores de hoy están en el rango de nanómetros de un solo dígito. En consecuencia, las funcionalidades de los dispositivos se ven afectadas negativamente por los efectos de canal corto y de mecánica cuántica (SCE y QMEs). Una transición de la geometría del transistor de efecto de campo de tipo FinFET a Gate-All -Around (GAA) FETs tales como FETs de nanohilos cilíndricos (NW) y de nanoplacas de silicio (SiNS) se prevén en los próximos nodos tecnológicos para suprimir los SCE y garantizar una mayor miniaturización del MOSFET. Esta disertación se centra en el modelado analítico de FETs de tipo NW y SiNS de canal ultracorto. Se introduce un concepto de dimensiones de doble puerta (DG) equivalente para transferir un modelo de potencial de DG analítico a FET de NW. Un modelo de corriente de DG compacto se modifica aprovechando la simetría rotacional de los FET de NW. El efecto del confinamiento cuántico (QC) es implementado considerando el ensanchamiento adicional de la banda prohibida en el cálculo de una concentración de portadores de carga intrínseca efectiva y en el cálculo del voltaje de umbral. El efecto de corriente túnel directa de fuente a drenador (DSDT) en SiNS FET ultraescalados se modela con el nuevo método de wavelets. Este modelo calcula analíticamente la probabilidad de tunelización para cada energía del electrón aproximando la forma de la barrera de potencial mediante una barrera rectangular con una altura de barrera equivalente. Usando la fórmula de corriente túnel de Tsu-Esaki no analíticamente integrable, se presenta un método analítico denominado modelo cuasi-compacto (QCM), querequiere una iteración de Newton y una interpolación lineal de la densidad de corriente de efecto túnel. Además, se realiza un análisis criogénico en temperatura y dopaje. Se investiga la fuerte influencia del nivel de Fermi de la fuente la sobre la pendiente subumbral, la corriente y la reducción del efecto DIBL. Además, se demuestra y explica la fusión de dos efectos relacionados con la pendiente subumbral y el DIBL. La validez del concepto de dimensiones DG equivalentes se demuestra mediante datos de mediciones y de simulaciones TCAD Sentaurus, mientras que el método de wavelets se verifica mediante simulaciones NanoMOS NEGF.Today's transistor geometries are in the single-digit nanometer range. Consequently, device functionalities are negatively affected by short-channel and quantum mechanical effects (SCEs & QMEs). A transition from fin field-effect transistor (FinFET) geometry to gate-all-around (GAA) FETs such as cylindrical nanowire (NW) and silicon nanosheet (SiNS) FETs is envisioned in the upcoming technology nodes to suppress SCEs and ensure further MOSFET miniaturization. This dissertation focuses on the analytical modeling of ultrashort-channel NW and SiNS FETs. An equivalent double-gate (DG) dimensions concept is introduced to transfer an analytical DG potential model to NW FETs. A compact DG current model is modified by exploiting the rotational symmetry of NW FETs. The effect of quantum confinement (QC) is implemented by considering the additional bandgap widening in the calculation of an effective intrinsic charge carrier concentration and in the calculation of the threshold voltage. The effect of direct source-to-drain tunneling (DSDT) current in ultrascaled SiNS FETs is modeled with the new wavelet approach. This model calculates the tunneling probability analytically for each electron energy by approximating the potential barrier shape by a rectangular barrier with an equivalent barrier height. Due to the nonanalytically integrable Tsu-Esaki tunneling formula an analytical approach named quasi-compact model (QCM) is presented. This approach requires, among other approximations, a Newton iteration, and a linear interpolation of the tunneling current density. Furthermore, a cryogenic temperature and doping analysis is performed. The strong influence of the distance of the source related Fermi level from the conduction band edge on the subthreshold swing, current, and drain-induced barrier lowering (DIBL) saturation is investigated. Also, the merging of two subthreshold swing and DIBL effects is demonstrated and explained. The validity of the equivalent DG dimensions concept is proven by measurement and TCAD Sentaurus simulation data, while the wavelet approach is verified by NanoMOS NEGF simulations

Design and analytical performance of subthreshold characteristics of CSDG MOSFET.

Masters Degree. University of KwaZulu-Natal, Durban.The downscaling of the Metal-Oxide-Semiconductor Field Effect Transistors (MOSFET) devices have been the driving force for Nanotechnology and Very Large-Scale Integration (VLSI) systems. This is affirmed by Moore’s law which states that “The number of transistors placed in an Integrated Circuit (IC) or chip doubles approximately every two years”. The main objectives for the transistor scaling are: to increase functionality, switching speed, packing density and lower the operating power of the ICs. However, the downscaling of the MOSFET device is posed with various challenges such as the threshold roll-off, Drain Induced Barrier Lowing (DIBL), surface scattering, and velocity saturation known as Short Channel Effects (SCEs). To overcome these challenges, a cylindrically structured MOSFET is employed because it increases the switching speed, current flow, packing density, and provides better immunity to SCEs. This thesis proposes a Cylindrical Surrounding Double-Gate (CSDG) MOSFET which is an extended version of Double-Gate (DG) MOSFET and Cylindrical Surrounding-Gate (CSG) MOSFET in terms of form factor and current drive respectively. Furthermore, employing the Evanescent-Mode analysis (EMA) of a two-dimensional (2D) Poisson solution, the performance analysis of the novel CSDG MOSFET is presented. The channel length, radii Silicon film difference, and the oxide thickness are investigated for the CSDG MOSFET at the subthreshold regime. Using the minimum channel potential expression obtained by EMA, the threshold voltage and the subthreshold swing model of the proposed CSDG MOSFET are evaluated and discussed. The device performance is verified with various values of radii Silicon film difference and gate oxide thickness Finally, the low operating power and switching characteristics of the proposed CSDG MOSFET has been employed to design a simple CSDG bridge rectifier circuit for micropower electricity (energy harvester). Similar to the traditional MOSFETs, the switching process of CSDG MOSFET is in two operating modes: switch-ON (conduction of current between the drain and source) or switched-OFF (no conduction of current). However, unlike the traditional diode bridge rectifier which utilizes four diodes for its operation, the CSDG bridge rectifier circuits employs only two CSDGs (n-channel and p- channel) for its operation. This optimizes cost and improves efficiency. Finally, the results from the analyses demonstrate that the proposed CSDG MOSFET is a promising device for nanotechnology and self-micro powered device system application

Design evolution of dual-material gate structure in cylindrical surrounding double-gate (CSDG) MOSFET using physics-based analytical modeling.

Doctoral Degree. University of KwaZulu- Natal, Durban.The Metal Oxide Semiconductor Field Effect Transistor (MOSFET) is the fundamental component in present Micro and Nano-electronics device applications, such as switching, memory devices, communication devices, etc. MOSFET’s dimension has shrunk down following Moore’s law to attain high-speed operation and packing density integration. The scaling of conventional MOSFET has been the most prominent technological challenge in the past few years because the decreasing device dimensions increase the charge sharing from the source to the drain and that in turn give rises to the reduced gate-control over the channel, hot carrier induced degradation, and other SCEs. These undesired effects devaluate the device performance that compels optimum device design analysis for particular operating conditions. Therefore, several innovative device design/architectures, including Double-gate, FinFET, Surrounding gate MOSFET, etc., have been developed to mitigate device scaling challenges. Comprehensive research can be traced long for one such promising gate-all-around MOSFET, i.e., Cylindrical Surrounding Double-Gate (CSDG) MOSFET centrally hollow concentric structure, provides an additional internal control gate that improves the device electrical performance and offers easy accessibility. There have been several developments in terms of improvements, and applications of CSDG MOSFET have been practiced since after its evolution. This thesis’s work has been targeted to incorporate the gate material engineering in the CSDG structure after appropriate analysis of device physics-based modeling. In particular to the proposed structure, the electric field, pinch off capacitance, and after that thickness of the device parameters’ dependence have been mathematically derived from attaining the objective. Finally, a model based on a dual-material gate in CSDG MOSFET has been proposed. The electrical field in CSDG MOSFET has been analyzed in detail using a mathematical derivation of device physics, including the Surface-Potential, threshold voltage, and the gate-oxide capacitances of the internal and external part of the device. Further, the gate-oxide capacitance of CSDG MOSFET, particularly to the device pinch-off condition, has been derived. Since the device operation and analysis at the shorter channel are not similar to conventional long-channel MOSFETs, the depletion-width variation has been studied. The identified notion has been applied to derive the approximate numerical solution and silicon thickness inducing parameters for CSDG MOSFET to deploy the improvements in the device performance and novel design modifications. As the gate-material and gate-stack engineering is an alternative to overcome the device performance degradation by enhancing the charge transport efficiency, the CSDG MOSFET in a novel Dual-Metal Gate (DMG) structure design has been proposed and analyzed using the solution of 2D Poisson’s equations in the geometrical boundary conditions of the device. The model expressions obtained solution using the proposed structure has been compared with a single metal gate structure. Finally, it has been analyzed that the proposed model exhibits an excellent match with the analytical model. The obtained DMG device structure advances the carrier velocity and transport efficiency, resulting in the surface-potential profile caused by dissimilar gate metal work-function. The superior device characteristics obtained employing a dual-material structure in CSDG are promising and can reduce the threshold voltage roll-off, suppress the hot-carrier effects and SCEs

A Subthreshold Analysis of Triple-Material Cylindrical Gate-All-Around (TM-CGAA) MOSFETs

With the technological leap to another milestone in sub 20nm regime, the conventional FETs seems to be of little use in continuing scaling with the least short channel effects (SCEs). Hence, non-conventional devices had to intervene in the rescue of the ITRS. Where the devices with the silicon-on-insulator substrates, strain, double gate, finned gate, omega and pi gates upheld the Moore’s law, the Gate-All-Around (GAA) emerged to be the ultimate solution. To further improve the sub threshold electrical parameters, a multi material gate may be inserted as the gate material. Thus, extending the idea of a triple material gate in the cylindrical GAA (CGAA) MOSFET, a TM-CGAA is obtained with better SCE characteristics. In this work, an accurate analytical sub threshold models has been developed for an undoped tri-material cylindrical gate-all-around (TM-CGAA) MOSFET considering parabolic approximation of the channel. The centre (axial) as well as the surface potential model is obtained by solving the 2-D Poisson’s equation in the cylindrical co-ordinates. The work refutes the estimation of the characteristic length using surface potential as in the previous work and proposes the use of centre potential based characteristic length formulation for an accurate analysis

Compact modeling of the rf and noise behavior of multiple-gate mosfets

La reducción de la tecnología MOSFET planar ha sido la opción tecnológica dominante en las últimas décadas. Sin embargo, hemos llegado a un punto en el que los materiales y problemas en los dispositivos surgen, abriendo la puerta para estructuras alternativas de los dispositivos. Entre estas estructuras se encuentran los dispositivos DG, SGT y Triple-Gate. Estas tres estructuras están estudiadas en esta tesis, en el contexto de rducir las dimensiones de los dispositivos a tamaños tales que los mecanismos cuánticos y efectos de calan coro deben tenerse n cuenta. Estos efectos vienen con una seria de desafíos desde el pun to de vista de modelación, unos de los más grandes siendo el tiempo y los recursos comprometidos para ejecutar las simulaciones. para resolver este problema, esta tesis propone modelos comlets analíticos y compactos para cada una de las geometrías, validos desde DC hasta el modo de operación en Rf para los nodos tecnológicos futuros. Dichos modelos se han extendido para analizar el ruido de alta frecuencia en estos diapositivos