Two-dimensional threshold voltage analytical modes of DMG strained-silicon-on-insulator MOSFETs

For the first time, a simple and accurate two-dimensional analytical model for the surface potential variation along the channel in fully depleted dual-material gate strained-Si-on-insulator (DMG SSOI) MOSFETs is developed. We investigate the improved short channel effect (SCE), hot carrier effect (HCE), drain-induced barrier-lowering (DIBL) and carrier transport efficiency for the novel structure MOSFET. The analytical model takes into account the effects of different metal gate lengths, work functions, the drain bias and Ge mole fraction in the relaxed SiGe buffer. The surface potential in the channel region exhibits a step potential, which can suppress SCE, HCE and DIBL. Also, strained-Si and SOI structure can improve the carrier transport efficiency, with strained-Si being particularly effective. Further,the threshold voltage model correctly predicts a "rollup" in threshold voltage with decreasing channel length ratios or Ge mole fraction in the relaxed SiGe buffer. The validity of the two-dimensional analytical model is verified using numerical simulations.     

异质栅全耗尽型应变硅 SOI MOSFET二维解析模型*

本文首次并建立了异质栅全耗尽型应变Si SOI (DMG SSOI) MOSFET的二维表面势沿沟道变化的模型．并对该结构的MOSFET的短沟道效应SCE (short channel effect),热载流子效应HCE(hot carrier effect),漏致势垒降低DIBL (drain induced barrier lowering)和载流子传输效率进行了研究．该模型中考虑以下参数：金属栅长,金属栅的功函数,漏电压和Ge在驰豫SiGe中的摩尔组分．结果表明沟道区的表面势引进了阶梯分布,正是这个阶梯分布的表面势抑制了SCE,HCE和DIBL．同时,应变硅和SOI(silicon-on-insulator)结构都能提高载流子的传输效率,特别是应变硅能提高载流子的传输效率．此外阈值电压模型能者正确表明阈值电压随栅长比率L2/L1减小或应变Si膜中Ge摩尔组分的降低而升高．数值模拟器ISE验证了该模型的正确性．     

Two-dimensional analytical threshold voltage model for DMG Epi-MOSFET

A two-dimensional (2-D) analytical model of a dual material gate (DMG) epitaxial (Epi)-MOSFET for improved, SCEs, hot electron effects, and carrier transport efficiency is presented. Using a two-region polynomial potential distribution and a universal boundary condition, we calculated the 2-D potential and electric field distribution along the channel. An expression for threshold voltage for short-channel DMG Epi-MOSFETs is also derived. The ratio of gate lengths has been varied to show which gate length ratio gives the best performance. The analytical results have been validated by the 2-D device simulator ATLAS over a wide range of device parameters and bias conditions.     

Semi-Analytical Modeling of Short-Channel Effects in Si and Ge Symmetrical Double-Gate MOSFETs

A simple analytical expression of the 2-D potential distribution along the channel of silicon symmetrical double-gate (DG) MOSFETs in weak inversion is derived. The analytical solution of the potential distribution is compared with the numerical solution of the 2-D Poisson's equation in terms of the channel length L, the silicon thickness t _Si, and the gate oxide thickness t _OX. The obtained results show that the analytical solution describes, with good accuracy, the potential distribution along the channel at different positions from the gate interfaces for well-designed devices when the ratio of L/t _Si is ges 2-3. Based on the 2-D extra potential induced in the silicon film due to short-channel effects (SCEs), a semi-analytical expression for the subthreshold drain current of short-channel devices is derived. From the obtained subthreshold characteristics, the extracted device parameters of the subthreshold slope, drain-induced barrier lowering, and threshold voltage are discussed. Application of the proposed model to devices with silicon replaced by germanium demonstrates that the germanium DG MOSFETs are more prone to SCEs.     

Threshold voltage model for small geometry AlGaN/GaN HEMTs based on analytical solution of 3-D Poisson's equation

A simple and accurate analytical model for the threshold voltage of AlGaN/GaN high electron mobility transistor (HEMT) is developed by solving three-dimensional (3-D) Poisson equation to investigate the short channel effects (SCEs) and the narrow width effects present simultaneously in a small geometry device. It has been demonstrated that the proposed model correctly predicts the potential and electric field distribution along the channel. In the proposed model, the effect of important parameters such as the thickness of the barrier layer and its doping on the threshold voltage has also been included. The model is, further, extended to find an expression for the threshold voltage in the sub-micrometer regime. The accuracy of the proposed analytical model is verified by comparing the model results with 3-D device simulations for different gate lengths and widths.     

应变PMOS二维阈值电压解析模型

利用准二维方法求解二维泊松方程,建立了锗硅源漏单轴应变PMOS阈值电压的二维解析模型,理论计算结果和实验报道的结果能很好吻合。研究了不同沟道长度和漏压情况下的沟道表面势,分析了沟道长度、漏压及锗硅源漏中锗摩尔组分等参数对阈值电压的影响。利用TCAD工具进行仿真模拟,结果表明,沟道长度和漏压是单轴应变PMOS阈值电压漂移的主要影响因素,而锗摩尔组分在一定成分范围内影响较小。     

Two-dimensional numerical analysis of the narrow gate effect in MOSFET

Lateral variation of the local threshold voltage causes non-linearity in the drain conductance-gate voltage characteristics, resulting in a nonunique external threshold voltage which varies with gate voltage. Using a 16-bit minicomputer, a two-dimensional (2-D) finite-difference program for narrow gate MOSFET (NAROMOS), and an accurate and efficient new finite-difference boundary equation at the oxide-semiconductor interface, computations are carried out for the external threshold voltage and a measurable electrical channel width as a function of the applied dc gate and substrate voltages. The depletion approximation is employed in order to compare the 2-D results with the 1-D analytical solution of the depletion model. Computed curves are presented for the lateral variations of the depletion layer thickness, surface potential, normal surface electric field, local as well as external threshold voltages, and electrical channel width as a function of the device structure, material parameters, and bias voltages. Based on the 2-D results and device physics, an analytical approximation of the threshold voltage versus the gate width, simple enough for CAD of VLSI, is derived whose parameters may be determined from either a 2-D computation or experimental measurements on one test device of a known gate width. The computed increase of the external threshold voltage with decreasing gate width compares well with published experimental data.     

Physics-based analytical modeling of potential and electrical field distribution in dual material gate (DMG)-MOSFET for improved hot electron effect and carrier transport efficiency

We propose a new two-dimensional (2-D) analytical model of a dual material gate MOSFET (DMG-MOSFET) for reduced drain-induced barrier lowering (DIBL) effect, merging two metal gates of different materials, laterally into one. The arrangement is such that the work function of the gate metal near the source is higher than the one near the drain. The model so developed predicts a step-function in the potential along the channel, which ensures screening of the drain potential variation by the gate near the drain. The small difference of voltage due to different gate material keeps a uniform electric field along the channel, which in turn improves the carrier transport efficiency. The ratio of two metal gate lengths can be optimized along with the metal work functions and oxide thickness for reducing the hot electron effect. The model is verified by comparison to the simulated results using a 2-D device simulator ATLAS over a wide range of device parameters and bias conditions.     

Modeling and simulation of a nanoscale three-region tri-material gate stack (TRIMGAS) MOSFET for improved carrier transport efficiency and reduced hot-electron effects

Two-dimensional (2-D) analytical modeling for a novel multiple region MOSFET device architecture-Tri-Material Gate Stack MOSFET-is presented, which shows reduced short-channel effects at short gate lengths. Using a three-region analysis in the horizontal direction and a universal depletion width boundary condition, the 2-D potential and electric field distribution in the channel region along with the threshold voltage of the device are obtained. The proposed model is capable of modeling electrical characteristics like surface potential, electric field, and threshold voltage of various other existent MOSFET structures like dual-material-gate, electrically induced shallow junction/straddle-gate (side-gate), and single-material-gate MOSFETs, with and without the gate stack architecture. The 2-D device simulator ATLAS is used over a wide range of parameters and bias conditions to validate the analytical results.     

Analytical modelling of threshold voltage for underlap Fully Depleted Silicon-On-Insulator MOSFET

In this article, surface-potential-based analytical threshold voltage model for underlap Fully Depleted Silicon-On-Insulator MOSFET (underlap-SOI) is developed by solving two-dimensional Poisson equation. The gate underlap at source/drain (S/D) has different boundary conditions as compared to channel region under the gate dielectric that divide the whole channel into three regions. It leads us to derive the new surface potential model for three different channel regions, i.e. the region under the gate dielectric and two gate underlap regions at S/D. The effects of underlap length, channel length, body thickness, channel doping concentration, metal gate work function and gate dielectric constant on threshold voltage have been included in our model. The threshold voltage dependence on different device parameters has been studied using analytical model and simulations. The closeness between the simulation results and model results show that the analytical model accurately calculate the threshold voltage values for large range of device parameters.     

Analytical modeling of the two-dimensional potential distribution and threshold voltage of the SOI four-gate transistor

The two-dimensional (2-D) channel potential and threshold voltage of the silicon-on-insulator (SOI) four-gate transistor (G/sup 4/-FET) are modeled. The 2-D analytical body potential is derived by assuming a parabolic potential variation between the lateral junction-gates and by solving Poisson's equation. The model is used to obtain the surface threshold voltage of the G/sup 4/-FET as a function of the lateral gate bias and for all possible charge conditions at the back interface. The body-potential model is extendable to fully depleted SOI MOSFETs and can serve to depict the charge-sharing and drain-induced barrier-lowering effects in short-channel devices.     

基于二维电势分布的一种新型复合多晶硅栅 LDMOS阈值电压模型

本文提出了一种新型的复合多晶硅栅LDMOS结构.该结构引入栅工程的概念,将LDMOST的栅分为n型多晶硅栅和p型多晶硅栅两部分,从而提高器件电流驱动能力,抑制SCEs(short channel effects )和DIBL(drain-induced barrier lowering).通过求解二维泊松方程建立了复合多晶硅栅LDMOST的二维阈值电压解析模型.模型考虑了LDMOS沟道杂质浓度分布和复合栅功函数差的共同影响,具有较高的精度.与MEDICI数值模拟结果比较后,模型得以验证.     

Modeling the drain current and its equation parameters for lightly doped symmetrical double-gate MOSFETs

A 2D model for the potential distribution in silicon film is derived for a symmetrical double gate MOSFET in weak inversion. This 2D potential distribution model is used to analytically derive an expression for the subthreshold slope and threshold voltage. A drain current model for lightly doped symmetrical DG MOSFETs is then presented by considering weak and strong inversion regions including short channel effects, series source to drain resistance and channel length modulation parameters. These derived models are compared with the simulation results of the SILVACO (Atlas) tool for different channel lengths and silicon film thicknesses. Lastly, the effect of the fixed oxide charge on the drain current model has been studied through simulation. It is observed that the obtained analytical models of symmetrical double gate MOSFETs are in good agreement with the simulated results for a channel length to silicon film thickness ratio greater than or equal to 2.     

Modelling of parameters for asymmetric halo and symmetric DHDMG n-MOSFETs

This article presents an analytical surface potential, threshold voltage and drain current model for asymmetric pocket-implanted, single-halo dual material gate and double-halo dual material gate (DHDMG) n-MOSFET (MOSFET, metal–oxide–semiconductor field-effect transistor) operating up to 40?nm regime. The model is derived by applying Gauss's law to a rectangular box, covering the entire depletion region. 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 along with the inner fringing capacitances at both the source and the drain ends and the subthreshold drain and the substrate bias effect. Using the surface potential model, the threshold voltage and drain currents are estimated. The same model is used to find the characteristic parameters for dual-material gate (DMG) with halo implantations and double gate. The characteristic improvement is investigated. It is concluded that the DHDMG device structure exhibits better suppression of the short-channel effect (SCE) and the threshold voltage roll-off than DMG and double-gate MOSFET. The adequacy of the model is verified by comparing with two-dimensional device simulator DESSIS. A very good agreement of our model with DESSIS is obtained proving the validity of our model used in suppressing the SCEs.     

Two-dimensional threshold voltage analytical model of DMG strained-silicon-on-insulator MOSFETs

For the first time,a simple and accurate two-dimensional analytical model for the surface potential variation along the channel in fully depleted dual-material gate strained-Si-on-insulator(DMG SSOI) MOSFETs is developed.We investigate the improved short channel effect(SCE),hot carrier effect(HCE),drain-induced barrier-lowering(DIBL) and carrier transport efficiency for the novel structure MOSFET.The analytical model takes into account the effects of different metal gate lengths,work functions,the drain ...     

全耗尽SOI LDMOS阈值电压的解析模型

通过准二维的方法,求出了全耗尽SOILDMOS晶体管沟道耗尽区电势分布的表达式,并建立了相应的阈值电压模型。将计算结果与二维半导体器件模拟软件MEDICI的模拟结果相比较,两者误差较小,证明了本模型的正确性。从模型中可以容易地分析阈值电压与沟道浓度、长度、SOI硅膜层厚度以及栅氧化层厚度的关系,并且发现ΔVth与背栅压的大小无关。     

Three-Dimensional Closed-Form Model for Potential Barrier in Undoped FinFETs Resulting in Analytical Equations for $V_{T}$ and Subthreshold Slope

An analytical approach for modeling the electrostatic potential in nanoscale undoped FinFETs is derived. This method uses a 2-D solution for this potential within a double-gate FET and takes into account the top gate electrode as the third dimension by applying the conformal mapping technique. Herewith, an analytical closed-form model for the height of the potential barrier below threshold is defined which includes 3-D effects. From that, models for subthreshold slope and threshold voltage of nanoscale triple-gate FETs are derived. The results are in good agreement with numerical device simulation results and measurements for channel lengths down to 20 nm.      

Three-dimensional analytical subthreshold models for bulk MOSFETs

Three-dimensional device-physics-based analytical models are developed for subthreshold conduction in uniformly doped small geometry (i.e., simultaneously short channel and narrow width) bulk MOSFETs, for various isolation schemes. Inverse-narrow width effects, where the threshold voltage decreases with decreasing channel width, are predicted by the model for trench isolated MOSFETs. For LOGOS isolated MOSFETs, conventional narrow width effects, where the threshold voltage increases due to decreasing channel width, are predicted. The narrow width effects are found to be comparable to the short channel effects in the absence of significant applied drain biases. However, for larger drain biases, the short channel effects outweigh the narrow width effects due to the weaker potential perturbation at the device width edges compared to the drain end. Unlike the threshold voltage, the subthreshold swing of the device is found to increase with reduced device dimensions regardless of the isolation scheme since both conventional and inverse narrow width effects result in weaker control of the surface potential by the gate     

Quantum mechanical analytical modeling of nanoscale DG FinFET: evaluation of potential,threshold voltage and source/drain resistance

Two-dimensional (2D) quantum mechanical analytical modeling has been presented in order to evaluate the 2D potential profile within the active area of FinFET structure. Various potential profiles such as surface, back to front gate and source to drain potential have been presented in order to appreciate the usefulness of the device for circuit simulation purposes. As we move from source end of the gate to the drain end of the gate, there is substantial increase in the potential at any point in the channel. This is attributed to the increased value of longitudinal electric field at the drain end on application of a drain to source voltage. Further, in this paper, the detailed study of threshold voltage and its variation with the process parameters are presented. A threshold voltage roll-off with fin thickness is observed for both theoretical and experimental results. The fin thickness is varied from 10 nm to 60 nm. The percentage roll-off for our model is 77% and that for experimental result it is 75%. Form the analysis of source/drain (S/D) resistance, it is observed that for a fixed fin width, as the channel length increases, there is an enhancement in the parasitic S/D resistance. This can be inferred from the fact that as the channel length decreases, quantum confinement along the S/D direction becomes more extensive. For our proposed devices a close match is obtained with the results through the analytical model and reported experimental results, thereby validating our proposed QM analytical model for DG FinFET device.     

A 2D compact model for lightly doped DG MOSFETs (P-DGFETs) including negative bias temperature instability (NBTI) and short channel effects (SCEs)

In this paper, a 2D compact model for potential and threshold voltage for lightly doped symmetrical double gate (DG) p-channel MOSFETs (PMOS) including negative bias temperature instability (NBTI) and short channel effects (SCEs) is presented. The model is dedicated to nano scale MOSFETs below 30 nm. In this model, both effects of interface state generation and hole-trapping are considered. Moreover, the effects of scaling down the oxide thickness and the channel thickness on NBTI are discussed. Our model is matched very well with numerical simulations obtained from COMSOL multi-physics at different drain voltages (V_d). A 4% shift in threshold voltage roll-off and 47% shift in drain induced barrier lowering (DIBL) is achieved at a gate length of 10 nm after 10 years of operation at a frequency of 1 GHz.