An analytical model of triple‐material double‐gate metal–oxide–semiconductor field‐effect transistor to suppress short‐channel effects

This paper presents an analytical subthreshold model for surface potential and threshold voltage of a triple‐material double‐gate (DG) metal–oxide–semiconductor field‐effect transistor. The model is developed by using a rectangular Gaussian box in the channel depletion region with the required boundary conditions at the source and drain end. The model is used to study the effect of triple‐material gate structure on the electrical performance of the device in terms of changes in potential and electric field. The device immunity against short‐channel effects is evaluated by comparing the relative performance parameters such as drain‐induced barrier lowering, threshold voltage roll‐off, and subthreshold swing with its counterparts in the single‐material DG and double‐material DG metal–oxide–semiconductor field‐effect transistors. The developed surface potential model not only provides device physics insight but is also computationally efficient because of its simple compact form that can be utilized to study and characterize the gate‐engineered devices. Furthermore, the effects of quantum confinement are analyzed with the development of a quantum‐mechanical correction term for threshold voltage. The results obtained from the model are in close agreement with the data extracted from numerical Technology Computer Aided Design device simulation. Copyright © 2015 John Wiley & Sons, Ltd.     

Potential‐based threshold voltage and subthreshold swing models for junctionless double‐gate metal‐oxide‐semiconductor field‐effect transistor with dual‐material gate

On the basis of quasi‐two‐dimensional solution of Poisson's equation, an analytical threshold voltage model for junctionless dual‐material double‐gate (JLDMDG) metal‐oxide‐semiconductor field‐effect transistor (MOSFET) is developed for the first time. The advantages of JLDMDG MOSFET are proved by comparing the central electrostatic potential and electric field distribution with those of junctionless single‐material double‐gate (JLSMDG) MOSFET. The proposed model explicitly shows how the device parameters (such as the silicon thickness, oxide thickness, and doping concentration) affect the threshold voltage. In addition, the variations of threshold voltage roll‐off, drain‐induced barrier lowering (DIBL), and subthreshold swing with the channel length are investigated. It is proved that the device performance for JLDMDG MOSFET can be changed flexibly by adjusting the length ratios of control gate and screen gate. The model is verified by comparing its calculated results with those obtained from three‐dimensional numerical device simulator ISE. Copyright © 2015 John Wiley & Sons, Ltd.     

Green's function approach for modeling of electrostatic effects in nanoscale fully depleted double‐gate silicon‐on‐insulator metal‐oxide‐semiconductor field‐effect transistors

Exact solution of two‐dimensional (2D) Poisson's equation for fully depleted double‐gate silicon‐on‐insulator metal‐oxide‐semiconductor field‐effect transistor is derived using three‐zone Green's function solution technique. Framework consists of consideration of source–drain junction curvature. 2D potential profile obtained forms the basis for estimation of threshold voltage. Temperature dependence of front surface potential distribution, back surface potential distribution and front‐gate threshold voltage are modeled using temperature sensitive parameters. Applying newly developed model, surface potential and threshold voltage sensitivities to gate oxide thickness have been comprehensively investigated. Device simulation is performed using ATLAS 2D (SILVACO, 4701 Patrick Henry Drive, Bldg. Santa Clara, CA 95054 USA) device simulator, and the results obtained are compared with the proposed 2D model. The model results are found to be in good agreement with the simulated data. Copyright © 2013 John Wiley & Sons, Ltd.     

A 2‐D surface‐potential‐based threshold voltage model for short channel asymmetric heavily doped DG MOSFETs

In recent times, transistors with heavily doped body have generated much interest because of junctionless channel. In addition, proper threshold voltage regulation requires adjustment of the channel doping, as a result of which most of the compact models become invalid as they consider an intrinsic body. In this paper, a compact surface‐potential‐based threshold voltage model is developed for short channel asymmetric double‐gate metal–oxide–semiconductor field‐effect transistors with heavily/lightly doped channel. The 2‐D surface potential is computed and compared with Technology Computer Aided Design, and a relative error of 2–4 % was obtained. The threshold voltage is solved from 2‐D Poisson's equation using ‘virtual cathode’ method, and a good agreement is observed with the numerical simulations. Also, the model is compared with a reference model and a better result is obtained for heavily doped channel. Copyright © 2014 John Wiley & Sons, Ltd.     

Investigation of multi‐layered‐gate electrode workfunction engineered recessed channel (MLGEWE‐RC) sub‐50 nm MOSFET: A novel design

In this paper, a two‐dimensional (2D) analytical sub‐threshold model for a novel sub‐50 nm multi‐layered‐gate electrode workfunction engineered recessed channel (MLGEWE‐RC) MOSFET is presented and investigated using ATLAS device simulator to counteract the large gate leakage current and increased standby power consumption that arise due to continued scaling of SiO₂‐based gate dielectrics. The model includes the evaluation of surface potential, electric field along the channel, threshold voltage, drain‐induced barrier lowering, sub‐threshold drain current and sub‐threshold swing. Results reveal that MLGEWE‐RC MOSFET design exhibits significant enhancement in terms of improved hot carrier effect immunity, carrier transport efficiency and reduced short channel effects proving its efficacy for high‐speed integration circuits and analog design. Copyright © 2008 John Wiley & Sons, Ltd.     

Impact of high‐κ gate dielectric and other physical parameters on the electrostatics and threshold voltage of long channel gate‐all‐around nanowire transistor

High‐κ gate‐all‐around structure counters the Short Channel Effect (SCEs) mostly providing excellent off‐state performance, whereas high mobility III–V channel ensures better on‐state performance, rendering III–V nanowire GAAFET a potential candidate for replacing the current FinFETs in microchips. In this paper, a 2D simulator for the III–V GAAFET based on self‐consistent solution of Schrodinger–Poisson equation is proposed. Using this simulator, capacitance–voltage profile and threshold voltage are characterized, which reveal that gate dielectric constant (κ) and oxide thickness do not affect threshold voltage significantly at lower channel doping. Moreover, change in alloy composition of In_xGa_1‐xAs, channel doping, and cross‐sectional area has trivial effects on the inversion capacitance although threshold voltage can be shifted by the former two. Although, channel material also affects the threshold voltage, most sharp change in threshold voltage is observed with change in fin width of the channel (0.005 V/nm for above 10 nm fin width and 0.064 V/nm for sub‐10 nm fin width). Simulation suggests that for lower channel doping below 10²³ m⁻³, fin width variation affects the threshold voltage most. Whereas when the doping is higher than 10²³ m⁻³, both the thickness and dielectric constant of the oxide material have strong effects on threshold voltage (0.05 V/nm oxide thickness and 0.01 V/per unit change in κ). Copyright © 2014 John Wiley & Sons, Ltd.     

An equivalent‐circuit modelling on vertical and horizontal integrations for MOS flat‐band voltage simulation

The fixed oxide charge will cause the MOS capacitor (MOS‐C) flat‐band voltage to shift. We can observe the potential distribution to determine the MOS‐C flat‐band voltage. However, the potential distribution can be obtained from the integration of the electric field distribution. The integration of the electric field distribution is classified into the vertical and horizontal integrations. In this paper, we use the equivalent‐circuit model to demonstrate the flat‐band voltage of the non‐ideal MOS‐C. The equivalent‐circuit model of Poisson's equation includes two fixed charges Q′_f1 and Q′_f2 in the oxide layer region. Because the horizontal integration method is the superposition method, the equivalent‐circuit model for the horizontal integration is divided into 3 types. Hence, the flat‐band voltage for the horizontal integration is equal to the sum of the V_G1, V_G2, and V_G3 for the flat‐band condition. By comparison, the simulation results of the horizontal integration method approximate to the vertical integration method. Copyright © 2006 John Wiley & Sons, Ltd.     

Asymmetric halo and symmetric Single‐Halo Dual‐Material Gate and Double‐Halo Dual‐Material Gate n‐MOSFETs characteristic parameter modeling

This paper presents an analytical subthreshold surface potential model of novel structures called asymmetric pocket‐implanted Double‐Halo Dual‐Material Gate (DHDMG) and Single‐Halo Dual‐Material Gate (SHDMG) Metal Oxide Semiconductor Field Effect Transistor (MOSFET), which combines the advantages of both the channel engineering (halo) and the gate engineering techniques (dual‐material gate) to effectively suppress the short‐channel effects (SCEs). The model is derived using the pseudo‐2D analysis by applying the Gauss's law to an elementary rectangular box in the channel depletion region, considering the surface potential variation with the channel depletion layer depth. The asymmetric pocket‐implanted model takes into account the effective doping concentration of the two linear pocket profiles at the source and the drain ends. The inner fringing field capacitances are also considered in the model for accurate estimation of the subthreshold surface potential at the two ends of the MOSFET. The same model is used to find the characteristic parameters for dual‐material gate with single‐halo and double‐halo implantations. It is concluded that the DHDMG device structure exhibits better suppression of the SCEs and the threshold voltage roll‐off than a pocket‐implanted and SHDMG MOSFET after investigating the characteristics parameter improvement. In order to validate our model, the modeled expressions have been extensively compared with the simulated characteristics obtained from the 2D device simulator DESSIS. A nice agreement is achieved with a reasonable accuracy over a wide range of device parameter and bias condition. Copyright © 2012 John Wiley & Sons, Ltd.     

Modeling the threshold voltage of PNIN SSOI tunnel field‐effect transistor

In this paper, a physically based analytical threshold voltage model for PNIN strained‐silicon‐on‐insulator tunnel field‐effect transistor (PNIN SSOI TFET) is proposed by solving the two‐dimensional (2D) Poisson equation in narrow N⁺ layer and intrinsic region. In the proposed model, the effect of strain (in terms of equivalent Ge mole fraction), narrow N⁺ layer and gate dielectric, and so on, is being considered. The validity of the proposed model is verified by comparing the model results with 2D device simulation results. It is demonstrated that the proposed model can correctly predicts the trends in threshold voltage with varying the device parameters. This proposed model can be effectively used to design, simulate, and fabricate the PNIN SSOI TFETs with the desired performance. Copyright © 2015 John Wiley & Sons, Ltd.     

Monte Carlo analysis of dynamic characteristics and high‐frequency noise performances of nanoscale double‐gate MOSFETs

In this paper, a full‐band Monte Carlo simulator is employed to study the dynamic characteristics and high‐frequency noise performances of a double‐gate (DG) metal–oxide–semiconductor field‐effect transistor (MOSFET) with 30 nm gate length. Admittance parameters (Y parameters) are calculated to characterize the dynamic response of the device. The noise behaviors of the simulated structure are studied on the basis of the spectral densities of the instantaneous current fluctuations at the drain and gate terminals, together with their cross‐correlation. Then the normalized noise parameters (P, R, and C), minimum noise figure (NF_min), and so on are employed to evaluate the noise performances. To show the outstanding radio‐frequency performances of the DG MOSFET, a single‐gate silicon‐on‐insulator MOSFET with the same gate length is also studied for comparison. The results show that the DG structure provides better dynamic characteristics and superior high‐frequency noise performances, owing to its inherent short‐channel effect immunity, better gate control ability, and lower channel noise. Copyright © 2012 John Wiley & Sons, Ltd.     

An analytic drain current model for long‐channel undoped gate stack surrounding‐gate MOSFETs including interface fixed charges

On the basis of the exact solution of Poisson's equation and Pao–Sah double integral for long‐channel bulk MOSFETs, a continuous and analytic drain current model for the undoped gate stack (GS) surrounding‐gate (SRG) metal–oxide–semiconductor field‐effect transistor (MOSFET) including positive or negative interface fixed charges near the drain junction is presented. Considering the effect of the interface fixed charges on the flat‐band voltage and the electron mobility, the model, which is expressed with the surface and body center potentials evaluated at the source and drain ends, describes the drain current from linear region to saturation region through a single continuous expression. It is found that the surface and body center potentials are increased/decreased in the case of positive/negative interface fixed charges, respectively, and the positive/negative interface fixed charges can decrease/increase the drain current. The model agrees well with the 3D numerical simulations and can be efficiently used to explore the effects of interface fixed charges on the drain current of the gate stack surrounding‐gate MOSFETs of the charge‐trapped memory device. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical modeling of threshold voltage for symmetrical silicon nano-tube field-effect-transistors (Si-NT FETs)

In this paper, an analytical model of the threshold voltage for short-channel symmetrical silicon nano-tube field-effect-transistors (Si-NT FETs) is presented. The three-dimensional (3D) Poisson equation in cylindrical coordinates has been solved with suitable boundary conditions to find the surface potential along the channel length. The inversion charge density \((Q_{inv} )\) has been calculated in the channel region of the device in the subthreshold regime of device operation, using the Boltzmann relationship. Subsequently, the calculated inversion charge density \((Q_{inv} )\) has been equated to a threshold charge density \((Q_{th})\) in order to find the threshold voltage \((V_{th})\) expression. The effect of physical device parameters, including the tube thickness, on the threshold voltage and drain induced barrier lowering (DIBL) of the device has been discussed. The model results have been verified with the simulation data obtained by the device simulation software ATLAS.     

Semi-analytical modeling of Ag and Au nanoparticles and fullerene (C60) embedded gate oxide compound semiconductor MOSFET memory devices

In this paper we present an analytical simulation study of Non-volatile MOSFET memory devices with Ag/Au nanoparticles/fullerene (C60) embedded gate dielectric stacks. We considered a long channel planar MOSFET, having a multilayer SiO₂–HfO₂ (7.5?nm)–Ag/Au nc/C60 embedded HfO₂ (6?nm)–HfO₂ (30?nm) gate dielectric stack. We considered three substrate materials GaN, InP and the conventional Si substrate, for use in such MOSFET NVM devices. From a semi-analytic solution of the Poisson equation, the potential and the electric fields in the substrate and the different layers of the gate oxide stack were derived. Thereafter using the WKB approximation, we have investigated the Fowler-Nordheim tunneling currents from the Si inversion layer to the embedded nanocrystal states in such devices. From our model, we simulated the write-erase characteristics, gate tunneling currents, and the transient threshold voltage shifts of the MOSFET NVM devices. The results from our model were compared with recent experimental results for Au nc and Ag nc embedded gate dielectric MOSFET memories. From the studies, the C60 embedded devices showed faster charging performance and higher charge storage, than both the metallic nc embedded devices. The nc Au embedded device displayed superior characteristics compared to the nc Ag embedded device. From the model GaN emerged as the overall better substrate material than Si and InP in terms of higher threshold voltage shift, lesser write programming voltage and better charge retention capabilities.     

Two-dimensional analytical model of threshold voltage and drain current of a double-halo gate-stacked triple-material double-gate MOSFET

We have developed a two-dimensional analytical model for the channel potential, threshold voltage, and drain-to-source current of a symmetric double-halo gate-stacked triple-material double-gate metal–oxide–semiconductor field-effect transistor (MOSFET). The two-dimensional Poisson’s equation is solved to obtain the channel potential. For accurate modeling of the device, fringing capacitance and effective surface charge are considered. The basic drift–diffusion equation is used to model the drain-to-source current. The midchannel potential of the device is used instead of the surface potential in the current modeling, considering the fact that the punch-through current is not confined only to the surface in a fully depleted MOSFET. An expression for the pinch-off voltage is derived to model the drain current in the saturation region accurately. Various short-channel effects such as drain-induced barrier lowering, gate leakage, threshold voltage, and roll-off have also been investigated. This structure shows excellent ability to suppress various short-channel effects. The results of the proposed model are validated against data obtained from a commercially available numerical device simulator.     

Performance analysis of fully depleted triple material surrounding gate (TMSG) SOI MOSFET

In this paper, analytical model for threshold voltage is derived for fully depleted Triple material Surrounding gate (TMSG) SOI MOSFET. Three gate material of different work functions are introduced in the SOI MOSFET structure to reduce the short channel effects. The two dimensional Poisson equation is solved and based on parabolic approximation method, the model for threshold voltage is developed. The threshold voltage is analyzed for device parameters such as gate length ratios, oxide thickness, silicon thickness, doping concentration. The results of the analytical model values are validated using MEDICI simulation.     

A physically based,accurate compact model of direct tunneling gate current considering quantum mechanical effects in nanoscale metal‐oxide‐semiconductor field‐effect transistors

We present a physically based, accurate model of the direct tunneling gate current of nanoscale metal‐oxide‐semiconductor field‐effect transistors considering quantum mechanical effects. Effect of wave function penetration into the gate dielectric is also incorporated. When electrons tunnel from the metal oxide semiconductor inversion layer to the gate, the eigenenergies of the quasi‐bound states turn out to be complex quantities. The imaginary part of these complex eigenenergies, Γ_ij, are required to estimate the finite lifetimes of these states. We present an empirical equation of Γ_ij as a function of surface potential. Inversion layer electron concentration is determined using eigenenergies, calculated by modified Airy function approximation. Hence, a compact model of direct tunneling gate current is proposed using a novel approach. Good agreement of the proposed compact model with self‐consistent numerical simulator and published experimental data for a wide range of substrate doping densities and oxide thicknesses states the accuracy and robustness of the proposed model. The proposed model can well be extended for devices with high‐κ/stack gate dielectrics introducing necessary modifications. Copyright © 2011 John Wiley & Sons, Ltd.     

A low‐power technique for high‐resolution dynamic comparators

A low‐power technique for high‐resolution comparators is introduced. In this technique, p‐type metal‐oxide‐semiconductor field‐effect transistors are employed as the input of the latch of the comparator just like the input of the preamplifier. The latch and preamplifier stages are activated in a special pattern using an inverter‐based controller. Unlike the conventional comparator, the preamplification delay can be set to an optimum low value even if after the preamplification, the output voltages is less than n‐channel metal‐oxide semiconductor voltage threshold. As a result, the proposed comparator reduces the power consumption significantly and enhances the speed. The speed and power benefits of the proposed comparator were verified using analytical derivations, PVT corners, and post layout simulations. The results confirm that the introduced technique reduces the power consumption by 60%, also, provides 57% better comparison speed for an input common mode voltage (V_cm) range of 0‐Vdd/2.     

An ultra‐thin oxide sub‐1 V CMOS bandgap voltage reference

This paper presents a sub‐1 V CMOS bandgap voltage reference that accounts for the presence of direct tunneling‐induced gate current. This current increases exponentially with decreasing oxide thickness and is especially prevalent in traditional (non‐high‐κ/metal gate) ultra‐thin oxide CMOS technologies (t_ox < 3 nm), where it invalidates the simplifying design assumption of infinite gate resistance. The developed reference (average temperature coefficient, T_{C_AVG}, of 22.5 ppm/°C) overcomes direct tunneling by employing circuit techniques that minimize, balance, and cancel its effects. It is compared to a thick‐oxide voltage reference (T_{C_AVG} = 14.0 ppm/°C) as a means of demonstrating that ultra‐thin oxide MOSFETs can achieve performance similar to that of more expensive thick(er) oxide MOSFETs and that they can be used to design the analog component of a mixed‐signal system. The reference was investigated in a 65 nm CMOS technology with a nominal V_DD of 1 V and a physical oxide thickness of 1.25 nm. Copyright © 2013 John Wiley & Sons, Ltd.     

A study of threshold voltage fluctuations of nanoscale double gate metal-oxide-semiconductor field effect transistors using quantum correction simulation

In this paper, we computationally investigate fluctuations of the threshold voltage introduced by random dopants in nanoscale double gate metal-oxide-semiconductor field effect transistors (DG MOSFETs). To calculate variance of the threshold voltage of nanoscale DG MOSFETs, a quantum correction model is numerically solved with the perturbation and the monotone iterative techniques. Fluctuations of the threshold voltage resulting from the random dopant, the gate oxide thickness, the channel film thickness, the gate channel length, and the device width are calculated. Quantum mechanical and classical results have similar prediction on fluctuations of the threshold voltage with respect to different designing parameters including dimension of device geometry as well as the channel doping. Fluctuation increases when the channel doping, the channel film thickness, and/or the gate oxide thickness increase. On the other hand, it decreases when the channel length and/or the device width increase. Calculations of the quantum correction model are quantitatively higher than that of the classical estimation according to different quantum confinement effects in nanoscale DG MOSFETs. Due to good channel controllability, DG MOSFETs possess relatively lower fluctuation, compared with the fluctuation of single gate MOSFETs (less than a half of the fluctuation[-11pc] of SG MOSFETs). To reduce fluctuations of the threshold voltage, epitaxial layers on both sides of channel with different epitaxial doping are introduced. For a certain thickness of epitaxial layers, the fluctuation of the threshold voltage decreases when epitaxial doping decreases. In contrast to conventional quantum Monte Carlo approach and small signal analysis of the Schrödinger-Poisson equations, this computationally efficient approach shows acceptable accuracy and is ready for industrial technology computer-aided design application.     

Explicit modelling of the double‐gate MOSFET with VHDL‐AMS

This paper presents a new compact model for the undoped, long‐channel double‐gate (DG) MOSFET under symmetrical operation. In particular, we propose a robust algorithm for computing the mobile charge density as an explicit function of the terminal voltages. It allows to greatly reduce the computation time without losing any accuracy. In order to validate the analytical model, we have also developed the 2D simulations of a DG MOSFET structure and performed both static and dynamic electrical simulations of the device. Comparisons with the 2D numerical simulations give evidence for the good behaviour and the accuracy of the model. Finally, we present the VHDL‐AMS code of the DG MOSFET model and related simulation results. Copyright © 2006 John Wiley & Sons, Ltd.