An analytic and accurate model for the threshold voltage of short channel MOSFETs in VLSI

Based on the two-dimensional Poisson equation, the surface potential distribution along the surface channel of a MOSFET has been analytically derived by assuming negligible source and drain junction depths and its minimum potential is then used to determine the threshold voltage. The existence of a minimum surface potential point along the channel of a MOSFET under an applied drain bias is consistent with the numerical results of the two-dimensional analysis. The effects of finite source and drain junction depths have been elegantly included by modifying the depletion capacitance under the gate and the resulted threshold voltage model has been compared to the results of the two-dimensional numerical analysis. It has been shown that excellent agreement between these results has been obtained for wide ranges of substrate doping, gate oxide thickness, channel length (< 1 μm), substrate bias, and drain voltage. Moreover, comparisons between the developed model and the existing experimental data have been made and good agreement has been obtained. The major advantages of the developed model are that no iterations and no adjustable fitting parameters are required. Therefore, this simple and accurate threshold voltage model will become a useful design tool for ultra short channel MOSFETs in future VLSI implementation.     

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 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.     

A new approach to analytically solving the two-dimensional Poisson's equation and its application in short-channel MOSFET modeling

An analytical solution for the potential distribution of the two-dimensional Poisson's equation with the Dirichlet boundary conditions has been obtained for the MOSFET device by using Green's function method and a new transformation technique, in which the effects of source and drain junction curvature and depth are properly considered. Based on the calculated potential distribution, the subthreshold current considering the drain-induced barrier lowering effects has been computed by a simple current equation that considers only the diffusion component with an effective length determined by the potential distribution at the SiO2-Si interface. From the calculated subthreshold current, the threshold voltage of the MOSFET's is determined. It has been verified that the dependences of the calculated threshold voltage and subthreshold current on device channel length, drain, and substrate biases are in good agreement with those computed by whole two-dimensional numerical analysis and experimental data.     

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.     

Threshold voltage model for deep-submicrometer fully depleted SOIMOSFET's

The threshold voltage, V_th, of fully depleted silicon-on-insulator (FDSOI) MOSFET with effective channel lengths down to the deep-submicrometer range has been investigated. We use a simple quasi-two-dimensional model to describe the V_th roll-off and drain voltage dependence. The shift in threshold voltage is similar to that in the bulk. However, threshold voltage roll-off in FDSOI is less than that in the bulk for the same effective channel length, as predicted by a shorter characteristic length l in FDSOI. Furthermore, ΔV_th is independent of back-gate bias in FDSOI MOSFET. The proposed model retains accuracy because it does not assume a priori charge partitioning or constant surface potential. Also it is simple in functional form and hence computationally efficient. Using our model, V _th design space for Deep-Submicrometer FDSOI MOSFET is obtained. Excellent correlation between the predicted V_th design space and previously reported two-dimensional numerical simulations using MINIMOS5 is obtained     

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.     

Analytical modeling of InSb/AlInSb heterostructure dual gate high electron mobility transistors

This paper presents an approximate solution of a 2D Poisson’s equation within the channel region for Double-Gate AlInSb/InSb High Electron Mobility Transistors (DGHEMTs), using variable separation technique. The proposed model is used to obtain the surface potential, electric field, threshold voltage and drain current of both tied and separated gate bias conditions for Double-Gate AlInSb/InSb HEMTs. The surface potential and electric field are derived for both effective conduction paths of front and back heterointerface by a simple analytical expression and an analytical solution is verified with sentarus TCAD device simulator.     

A simple theory to predict the threshold voltage of short-channel IGFET's

A simple expression for the threshold voltage of an IGFET is derived from a charge conservation principle which geometrically takes into account two-dimensional edge effects. The expression is derived for zero drain voltage and is valid for short and long-channel lengths. The dependence of the threshold voltage on the source and drain diffusion depth, r_j, and channel length, L, is explicitly given. In the limit, L/r_j → ∞, the threshold voltage equation reduces to the familiar expression for the long-channel case.The theory is compared with the measured threshold voltages on IGFET's fabricated with 1·4, 3·8 and 7·4 μm channel lengths. The dependence of the threshold voltage under backgate bias voltages ranging from zero to breakdown agrees closely with the theory.     

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。     

An analytical threshold voltage and subthreshold current model forshort-channel MESFETs

Short-channel effects on the subthreshold behavior are modeled in self-aligned gate MESFETs with undoped substrates through an analytical solution of the two-dimensional Poisson equation in the subthreshold region. Based on the resultant potential solution, simple and accurate analytical expressions for short-channel threshold voltage, subthreshold swing, and subthreshold drain current are derived. These are then used to develop an expression for minimum acceptable channel length. A comparative study of the short-channel effects in MESFETs with doped and undoped substrates indicates that channel lengths will be limited to 0.15-0.2 μm by subthreshold conduction. Besides offering insight into the device physics of the short-channel effects in MESFETs, the model provides a useful basis for accurate analysis and simulation of small-geometry GaAs MESFET digital circuits     

Two-dimensional analytical model of double-gate tunnel FETs with interface trapped charges including effects of channel mobile charge carriers

A two-dimensional analytical model of double-gate(DG) tunneling field-effect transistors(TFETs) with interface trapped charges is proposed in this paper. The influence of the channel mobile charges on the potential profile is also taken into account in order to improve the accuracy of the models. On the basis of potential profile, the electric field is derived and the expression for the drain current is obtained by integrating the BTBT generation rate. The model can be used to study the impact of interface trapped charges on the surface potential, the shortest tunneling length, the drain current and the threshold voltage for varying interface trapped charge densities, length of damaged region as well as the structural parameters of the DG TFET and can also be utilized to design the charge trapped memory devices based on TFET. The biggest advantage of this model is that it is more accurate, and in its expression there are no fitting parameters with small calculating amount. Very good agreements for both the potential, drain current and threshold voltage are observed between the model calculations and the simulated results.     

Compact modeling of the effects of parasitic internal fringe capacitance on the threshold voltage of high-k gate-dielectric nanoscale SOI MOSFETs

A compact model for the effect of the parasitic internal fringe capacitance on the threshold voltage of high-k gate-dielectric silicon-on-insulator MOSFETs is developed. The authors' model includes the effects of the gate-dielectric permittivity, spacer oxide permittivity, spacer width, gate length, and the width of an MOS structure. A simple expression for the parasitic internal fringe capacitance from the bottom edge of the gate electrode is obtained and the charges induced in the source and drain regions due to this capacitance are considered. The authors demonstrate an increase in the surface potential along the channel due to these charges, resulting in a decrease in the threshold voltage with an increase in the gate-dielectric permittivity. The accuracy of the results obtained using the authors' analytical model is verified using two-dimensional device simulations.     

双离子注入短沟道MOS FET的阈值电压解析模型

本文对短沟道MOSFET沟道区的硼、砷离子注入分布采用二次函数及指数函数的分段函数分布近似,并利用格林函数法求解二维泊松方程,从而导出非均匀分布短沟道MOS FET的表面势和阈值电压的解析模型.它计及注入能量、剂量、退火温度、退火时间等工艺参数的影响,也包含了漏极电压V_D和栅氧化层厚度等因素的影响.本解析模型的结果与用MINI-MOS数值模拟的结果符合得很好,具有简单、实用的特点.适用于改进有关电路分析程序例如SPICE中的模型.     

The voltage-doping transformation: a new approach to the modelingof MOSFET short-channel effects

It is shown that the influence of the drain-source field on the potential barrier height is physically equivalent to and can be replaced by a reduction in channel doping concentration according to a formula derived from the two-dimensional Poisson equation. The actual barrier height for any drain bias and channel length, on which the derived equation depends, can be calculated easily using well-known one-dimensional (long-channel) solutions. This simple but general procedure, called the voltage-doping transformation (VDT), is shown to lead to analytically calculated potential distributions in fairly good agreement with two-dimensional numerical simulation. An application of the VDT to threshold voltage (V_tj) calculations also is shown. The V_th model is compared with measurements taken on implanted n-MOSFETs with various channel lengths. Good agreement demonstrates the accuracy of both the VDT and the new V_th model     

一种非对称双栅应变硅HALO掺杂沟道MOSFET阈值电压解析模型

提出了一种非对称双栅应变硅HALO掺杂沟道金属氧化物半导体场效应管结构.该器件前栅和背栅由两种不同功函数的金属构成,沟道为应变硅HALO掺杂沟道,靠近源区为低掺杂区域,靠近漏区为高掺杂区域.采用分区的抛物线电势近似法和通用边界条件求解二维泊松方程,分别求解了前背栅表面势、前背栅表面电场及前背栅阈值电压,建立了双栅器件的表面势、表面电场和阈值电压解析模型.详细讨论了物理参数对解析模型的影响.研究结果表明,该器件能够很好的抑制短沟道效应、热载流子效应和漏致势垒降低效应.模型解析结果与DESSIS仿真结果吻合较好,证明了该模型的正确性.     

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.     

Analytical threshold voltage model for cylindrical surrounding-gate MOSFET with electrically induced source/drain extensions

Physics-based analytical threshold voltage model for cylindrical surrounding-gate MOSFET with electrically induced source/drain extensions is presented. The effect of inversion carriers on the channel’s potential is considered in presented model. Using this analytical model, the characteristics of EJ-CSG are investigated in terms of surface potential and electric field distribution, threshold voltage roll-off, and DIBL. Results show that the application of electrically induced S/D extensions to the cylindrical surrounding-gate MOSFET will successfully suppress the hot-carrier effects, threshold voltage roll-off, and DIBL. It is also revealed that a moderate side-gate bias voltage, a small gate oxide thickness, and a small silicon channel radius are needed to improve device characteristics. The derived analytical model is verified by its good agreement with the three-dimensional numerical device simulator ISE.     

Two-dimensional analytical modeling of threshold voltages of short-channel MOSFET's

We present an analytical model of the threshold voltage of a short-channel MOSFET based on an explicit solution of two-dimensional Poisson's equation in the depletion region under the gate. This model predicts an exponential dependence on channel length (L), a linear dependence on drain voltage (VD), and an inverse dependence on oxide capacitance (εox/tox). An attractive feature of this model is that it provides an analytical closed-form expression for the threshold voltage as a function of material and device parameters (tox, VD, L, substrate bias, and substrate doping concentration) without making premature approximations. Also, this expression reduces to the corresponding expression for long-channel devices.