Analytical modeling of the subthreshold current in short-channel MOSFET's

In this paper an analytical model for subthreshold current for both long-channel and short-channel MOSFET's is presented. The analytical electrostatic potential derived from the explicit solution of a two-dimensional Poisson's equation in the depletion region under the gate for uniform doping is used. The case for nonuniform doping can easily be incorporated and will be published later. The results are compared to a numerical solution obtained by using MINIMOS, for similar device structures. An analytical expression for the channel current is obtained as a function of drain, gate, substrate voltages, and device parameters for devices in the subthreshold region. The short-channel current equation reduces to the classical long-channel equation as the channel length increases.     

Threshold voltage model for deep-submicron fully depleted SOI MOSFETs with back gate substrate induced surface potential effects

A simple analytical threshold voltage model for short-channel fully depleted SOI MOSFETs has been derived. The model is based on the analytical solution of the two-dimensional potential distribution in the silicon film (front silicon), which is taken as the sum of the long-channel solution to the Poisson's equation and the short-channel solution to the Laplace equation, and the solution of the Poisson's equation in the silicon substrate (back silicon). The proposed model accounts for the effects of the back gate substrate induced surface potential at the buried oxide-substrate interface which contributed an additional 15–30% reduction in the threshold voltage for the devices used in this work. Conditions on the back gate supply voltage range are determined upon which the surface potential at the buried oxide-substrate interface is accumulated, depleted, or inverted. The short-channel associated drain induced barrier lowering effects are also included in the model. The model predications are in close agreement with PISCES simulation results. The equivalence between the present model and previously reported models is proven. The proposed model is suitable for use in circuit simulation tools such as Spice.     

A 2-D analytical solution for SCEs in DG MOSFETs

A two-dimensional (2-D) analytical solution of electrostatic potential is derived for undoped (or lightly doped) double-gate (DG) MOSFETs in the subthreshold region by solving Poissons equation in a 2-D boundary value problem. It is shown that the subthreshold current, short-channel threshold voltage rolloff and subthreshold slope predicted by the analytical solution are in close agreement with 2-D numerical simulation results for both symmetric and asymmetric DG MOSFETs without the need of any fitting parameters. The analytical model not only provides useful physics insight into short-channel effects, but also serves as basis for compact modeling of DG MOSFETs.     

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     

A two-dimensional analytical model of threshold voltages ofshort-channel MOSFETs with Gaussian-doped channels

A two-dimensional analytical model for the threshold voltage of a short-channel MOSFET with a Gaussian-doped channel has been developed. The Gaussian profile has been simulated by a novel integrable function. This makes possible a purely analytical solution of the two-dimensional Poissons equation in the channel region of the MOSFET     

A two-dimensional analytical threshold voltage model for MOSFET's with arbitrarily doped substrates

A threshold voltage model is presented which is valid for short- and long-channel MOSFET's with a nonuniform substrate doping profile. The model is based upon an approximate two-dimensional analytical solution of Poisson's equation for a MOSFET of arbitrary substrate doping profile which takes into account the effect of curved junctions of finite depth. The analytical model is compared to MINIMOS simulations showing that it can accurately predict short-channel threshold voltage falloff and threshold voltages in this vicinity without the use of fitting parameters.     

An analytical threshold voltage and subthreshold current model forshort-channel AlGaAs/GaAs MODFETs

Short-channel effects on the subthreshold behavior are modeled in self-aligned gate AlGaAs/GaAs MODFETs 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 short-channel effects in enhancement-mode MODFETs with and without i-AlGaAs spacer layers indicates that channel lengths will be limited to 0.18-0.25 μm by subthreshold conduction. Minimum gate lengths for MODFETs with a spacer layer are notably larger than those without a spacer layer. Besides offering insights into the physics of short-channel effects in MODFETs, the model provides a useful basis for efficient design, analysis, and simulation of small geometry AlGaAs/GaAs MODFET digital circuits     

An improved analytical solution of energy balance equation forshort-channel SOI MOSFET's and transverse-field-induced carrier heating

This paper presents a method for solving the one-dimensional (1-D) energy balance equation for fully depleted short-channel SOI MOSFET's. This method takes the exact kinetic energy into account and provides a new analytical solution for the non-saturated drain current region. The carrier temperature for spatially homogeneous case is described as a function of the longitudinal electric field and the carrier concentration deviation. The electron temperature is higher than that predicted by old models, which is examined by the two-dimensional simulation. The experimental data on gate current characteristics in short-channel SOI nMOSFET's can be physically interpreted by the proposed 1-D model     

A new two-dimensional analytical subthreshold behavior model for short-channel tri-material gate-stack SOI MOSFET’s

On the basis of the exact solution of the two-dimensional Poisson equation, a new analytical subthreshold behavior model consisting of the two-dimensional potential, threshold voltage, and subthreshold current for the short-channel tri-material gate-stack SOI MOSFET’s is developed. The model is verified by its good agreement with the numerical simulation of the device simulator MEDICI. The model not only offers physical insight into the device physics but also provides guidance for the basic design of the device.     

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.     

Compact Subthreshold Current Modeling of Short-Channel Nanoscale Double-Gate MOSFET

A physics-based compact subthreshold current model for short-channel nanoscale double-gate MOSFETs is presented. The potential is modeled using conformal mapping techniques in combination with parabolic approximations. For subthreshold conditions, we have assumed that the electrostatics is dominated by capacitive coupling between the body electrodes. Hence, the potential is obtained as an analytical solution of the 2-D Laplace equation. The current modeling is based on drift-diffusion theory. The modeling results are in good agreement with those of numerical simulations without the use of adjustable parameters.     

二维短沟道MOSFET阈值电压分析模型

随着器件尺寸的进一步减小,由量子效应导致的能带分裂对MOSFET中阈值电压特性的影响变得越来越重要.提出了一个包含量子效应(QME)的短沟道金属氧化物场效应晶体管(MOSFET)分析的阈值电压模型,该模型建立在求解包含量子校正的泊松方程的基础上.分析在泊松方程中考虑量子效应后建立的分析的阈值电压模型可知:随着器件尺寸的减小,由量子效应和短沟道效应引起的阈值电压的升高变得越来越严重.本模型的优点是没有引入额外的物理参数.     

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.     

Subthreshold surface potential and drain current models for short-channel pocket-implanted MOSFETs

An analytical subthreshold surface potential model for short-channel pocket-implanted (double-halo) MOSFET is presented. The effect of the depletion layers around the source and drain junctions on channel depletion layer depth, which is very important for short-channel devices, is included. Using this surface potential, a drift-diffusion based analytical subthreshold drain current model for short-channel pocket-implanted MOSFETs is also proposed. A physically-based empirical modification of the channel conduction layer thickness that was originally proposed for relatively long-channel conventional device is made for such short-channel double-halo devices. Very good agreement for both the surface potential and drain current is observed between the model calculation and the prediction made by the 2-D numerical device simulation using Dessis.     

双栅肖特基源漏MOSFET的阈值电压模型

通过求解泊松方程得到了双栅肖特基势垒MOSFET的解析模型. 这个解析模型包括整个沟道的准二维电势分布和适用于短沟双栅肖特基势垒MOSFET的阈值电压模型.数值模拟器ISE DESSIS验证了模型结果.     

Deep submicrometer double-gate fully-depleted SOI PMOS devices: aconcise short-channel effect threshold voltage model using a quasi-2Dapproach

This paper reports a concise short-channel effect threshold voltage model using a quasi-2D approach for deep submicrometer double-gate fully-depleted SOI PMOS devices. By considering the hole density at the front and the back channels simultaneously, the analytical threshold voltage model provides an accurate prediction of the short-channel threshold voltage behavior of the deep submicrometer double-gate fully-depleted SOI PMOS devices as verified by 2D simulation results. The analytical short-channel effect threshold voltage model can also be useful for SOI NMOS devices     

双栅肖特基源漏MOSFET的阈值电压模型

通过求解泊松方程得到了双栅肖特基势垒MOSFET的解析模型. 这个解析模型包括整个沟道的准二维电势分布和适用于短沟双栅肖特基势垒MOSFET的阈值电压模型.数值模拟器ISE DESSIS验证了模型结果.     

Semianalytical Modeling of Short-Channel Effects in Lightly Doped Silicon Trigate MOSFETs

A simple analytical expression of the 3-D potential distribution along the channel of lightly doped silicon trigate MOSFETs in weak inversion is derived, based on a perimeter-weighted approach of symmetric and asymmetric double-gate MOSFETs. The analytical solution is compared with the numerical solution of the 3-D Poisson's equation in the cases where the ratios of channel length/silicon thickness and channel length/channel width are ges 2. Good agreement is achieved at different positions within the channel. The perimeter-weighted approach fails at the corner regions of the silicon body; however, by using corner rounding and undoped channel to avoid corner effects in simulations, the agreement between model and simulation results is improved. By using the extra potential induced in the silicon film due to short-channel effects, the subthreshold drain current is determined in a semianalytical way, from which the subthreshold slope, the drain-induced barrier lowering, and the threshold voltage are extracted.     

A new simplified threshold-voltage model for n-MOSFETs with nonuniformly doped substrate and its application to MOSFET's miniaturization

The formulation, verification, and application of a new simplified 2-D threshold voltage model for n-MOSFETs with nonuniformly doped substrate profile are provided, in which the averaged normal field at the Si/SiO/sub 2/ interface in the active channel is quoted from a simplified solution of two-dimensional Poisson equation using the Green function technique. Starting with the expression of this average normal field, a simple threshold-voltage model for short-channel n-MOSFETs with nonuniformly doped substrate profile is explicitly expressed in terms of device structures and terminal voltages by considering parabolic source-drain boundary potentials. Moreover, the effects of the junction depth on the threshold voltage are examined in detail. It is shown that the DIBL effect cannot be completely eliminated by simply increasing the substrate doping concentration. Comparisons among developed model, 2-D numerical analysis, and experimental data have been made and the accuracy of the developed analytical model has been verified. In addition, a direct extension of our model to the case of uniformly doped substrates leads to a new constraint equation for device miniaturization.<>     

A physical short-channel threshold voltage model for undoped symmetric double-gate MOSFETs

A compact, physical, short-channel threshold voltage model for undoped symmetric double-gate MOSFETs has been derived based on an analytical solution of the two-dimensional (2-D) Poisson equation with the mobile charge term included. The new model is verified by published numerical simulations with close agreement. Applying the newly developed model, threshold voltage sensitivities to channel length, channel thickness, and gate oxide thickness have been comprehensively investigated. For practical device designs the channel length causes 30-50% more threshold voltage variation than does the channel thickness for the same process tolerance, while the gate oxide thickness causes the least, relatively insignificant threshold voltage variation. Model predictions indicate that individual DG MOSFETs with good turn-off behavior are feasible at 10 nm scale; however, practical exploitation of these devices toward gigascale integrated systems requires development of novel technologies for significant improvement in process control.