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.<>     

Parametric expression of subthreshold slope using threshold voltageparameters for MOSFET statistical modeling

In this paper, we propose a newly developed subthreshold slope (ideality factor) model, whose parameters are solely determined from the threshold voltage data. We succeed in expressing the ideality factor in terms of the threshold voltage parameters obtained from the body and DIBL effects, which can take care of its dependence on the process data such as channel length, oxide thickness, substrate doping profile, and junction depth in a parametric way. We prove the validity of our model by comparing it with simulation and measurement results from nMOSFET devices with various oxide thickness, channel length, and doping profile     

A new threshold voltage model for deep-submicron MOSFETs with nonuniform substrate dopings

A simple but accurate threshold voltage model for deep-submicron MOSFETs with nonuniform dopings is described in this paper. In this model, a simplified quasi-delta substrate doping profile is used to approximate the nonuniformity. We apply a hyperbola function to avoid the discontinuous problem at the boundary between different doping regions. By adjusting the parameter δ, the actual gradual doping profile can be obtained. A substrate-bias dependent model of short channel effect is also introduced which describes the reduction of substrate-bias effect in deep-submicron devices. The model developed is in good agreement with two-dimensional numerical simulation.     

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.     

一种非均匀掺杂的全耗尽SOI-MOSFET阈值电压模型(英文)

对垂直于沟道的二维电势分布函数提出了一种新的近似,给出了基于这种近似的杂质浓度呈高斯分布的非均匀掺杂全耗尽SOI-MOSFET的阈值电压解析模型.模型结果与MEDICI数值模拟结果符合得很好,表明了模型的准确性,这为实践中分析与控制非均匀掺杂的全耗尽SOI-MOSFET的阈值电压提供了一种新的途径.     

一种非均匀掺杂的全耗尽SOI-MOSFET阈值电压模型

对垂直于沟道的二维电势分布函数提出了一种新的近似,给出了基于这种近似的杂质浓度呈高斯分布的非均匀掺杂全耗尽SOI-MOSFET的阈值电压解析模型.模型结果与MEDICI数值模拟结果符合得很好,表明了模型的准确性,这为实践中分析与控制非均匀掺杂的全耗尽SOI-MOSFET的阈值电压提供了一种新的途径.     

一种非均匀掺杂的全耗尽SOI-MOSFET阈值电压模型

对垂直于沟道的二维电势分布函数提出了一种新的近似,给出了基于这种近似的杂质浓度呈高斯分布的非均匀掺杂全耗尽SOI-MOSFET的阈值电压解析模型.模型结果与MEDICI数值模拟结果符合得很好,表明了模型的准确性,这为实践中分析与控制非均匀掺杂的全耗尽SOI-MOSFET的阈值电压提供了一种新的途径.     

A new method for extracting the counter-implanted channel profileof enhancement-mode p-MOSFETs

A new methodology is proposed to extract the nonuniform channel doping profile of enhancement mode p-MOSFETs with counter implantation, based on the relationship between device threshold voltage and substrate bias. A selfconsistent mathematical analysis is developed to calculate the threshold voltage and the surface potential of counter-implanted long-channel p-MOSFET at the onset of heavy inversion. Comparisons between analytic calculation and two-dimensional (2-D) numerical analysis have been made and the accuracy of the developed analytic model has been verified. Based on the developed analytic model, an automated extraction technique has been successfully implemented to extract the channel doping profile. With the aid of a 2-D numerical simulator, the subthreshold current can be obtained by the extracted channel doping profile. Good agreements have been found with measured subthreshold characteristics for both long- and short-channel devices. This new extraction methodology can be used for precise process monitoring and device optimization purposes     

An accurate two-dimensional CAD-oriented model of retrograde doped MOSFETs for improved short channel performance

An analytical CAD-oriented model for short channel threshold voltage of retrograde doped MOSFETs is developed. The model is extended to evaluate the drain induced barrier lowering parameter (R) and gradient of threshold voltage. The dependence of short channel threshold voltage and R on thickness of lightly doped layer (d) has also been analyzed in detail. It is shown that a retrograde doping profile reduces short channel effects to a considerable extent. A technique is developed to optimize the device parameters for minimizing short channel effects. The results so obtained are in close proximity with published data.     

由等价掺杂转换理论得到非对称线性缓变P-N结的击穿特性

基于等价掺杂转换理论的应用,得到了解析计算非对称线性缓变P-N结击穿特性.由于非对称线性缓变P-N结是单扩散P-N结的一个恰当近似,因而,研究其击穿特性可以更好地理解和设计功率器件P-N结的终端结构.运用等价掺杂转换方法的基本理论得到了不同扩散掺杂梯度和衬底浓度组合系列的击穿电压.研究了最大耗尽层宽度在扩散侧和衬底侧的扩展,给出了它们随扩散掺杂梯度和衬底浓度组合的变化而出现的不同特点.本方法预言的最大击穿电压较之单纯的突变结和对称线性缓变P-N结更接近文献报道的结果,显示了等价掺杂转换理论的理论计算非对称线性缓变P-N结击穿电压的有效性.     

Model for DMOST threshold voltage

An analytical model for the channel region in MOS-gated power transistors has been developed. The model takes into account the effect of substrate doping gradient on the threshold voltage of the transistor and it can be applied to lateral and vertical DMOS and IGBT transistor structures. The model has been tested by comparing the calculated I-V characteristics for an MOS structure having various doping gradients to the results from a 2-D device simulator.<>     

由等价掺杂转换理论得到非对称线性缓变P-N结的击穿特性

基于等价掺杂转换理论的应用,得到了解析计算非对称线性缓变P-N结击穿特性.由于非对称线性缓变P-N结是单扩散P-N结的一个恰当近似,因而,研究其击穿特性可以更好地理解和设计功率器件P-N结的终端结构.运用等价掺杂转换方法的基本理论得到了不同扩散掺杂梯度和衬底浓度组合系列的击穿电压.研究了最大耗尽层宽度在扩散侧和衬底侧的扩展,给出了它们随扩散掺杂梯度和衬底浓度组合的变化而出现的不同特点.本方法预言的最大击穿电压较之单纯的突变结和对称线性缓变P-N结更接近文献报道的结果,显示了等价掺杂转换理论的理论计算非对称线性缓变P-N结击穿电压的有效性.     

An analytical model for the threshold voltage of a narrow-width MOSFET

A closed form analytical expression is derived to predict the threshold voltage of a narrow-width MOSFET. The present calculation utilizes the Fourier transform technique to analyze the voltage over the width cross section of the basic MOS device structure. No fitting parameter with experimental data is necessary because the fringe electric field is calculated directly from the relevant physical parameters to deduce the threshold voltage. The dependence of threshold voltage on channel width and substrate bias thus obtained is in reasonable agreement with experimental and numerical results. The effects of field doping and field oxide thickness on the threshold voltage are also taken into consideration. A comparison is made of the present analytical expression for threshold voltage with that, based on an adjustable weighting factor, of earlier analytical models.     

A new 2-D model for the potential distribution and threshold voltage of fully depleted short-channel Si-SOI MESFETs

A new two-dimensional (2-D) analytical model for the threshold voltage of a fully depleted short-channel Si-MESFETs fabricated on the silicon-on-insulator (SOI) has been presented in this paper. The 2-D potential distribution functions in the active layer of the device is approximated as a parabolic function and the 2-D Poisson's equation has been solved with suitable boundary conditions to obtain the bottom potential at the Si/oxide layer interface. The calculations have been carried out for both uniform and nonuniform doping profiles in two dimensions. The minimum bottom potential is used to monitor the drain-induced barrier lowering effect and consequently an analytical expression for the threshold voltage of the device has been derived. The numerical results for the bottom potential and threshold voltage considering a wide range of device parameters have also been presented. The model has been compared with the simulated results obtained by using the ATLAS Device Simulation Software to show the validity of the proposed model. For uniform doping profile, the numerical results have also been compared with the reported data in the literature and a good agreement is observed among the three. The proposed model is simple and easy to understand the behavior of the fully depleted short-channel SOI-MESFETs as compared to the other models reported in the literature.     

Ion-implanted threshold tailoring for insulated gate field-effect transistors

This paper develops a general threshold equation for long-channel insulated gate field-effect transistors which accounts for the effects of ion-implant profiles used in threshold tailoring. Although any integrable function used to describe the nonuniform doping will yield an analytical expression for threshold, a Gaussian function is chosen because it accurately describes the implanted profile following proper annealing, regardless of subsequent high-temperature steps during fabrication. Most profiles of interest are quasi-neutral, i.e., the spatial dependence of the majority carriers in the undepleted bulk is adequately described by the doping profile, but the threshold equation is shown to be an excellent approximation for non quasi-neutral profiles as well. Comparison with experimental results show the analytical expression to be in good agreement with data over a wide range of implant conditions and starting substrate resistivity.     

A new approach to threshold voltage modelling of short-channel MOSFETS

A simple analytical model has been developed to predict the threshold voltage on drain bias dependence of an arbitrarily doped short-channel MOSFET. Based on an analytical solution of the two-dimensional Poisson equation, the potential distribution in the channel depletion region has been derived. The maximum surface field and the minimum surface potential are used to determine the threshold voltage. The influence of drain voltage on threshold voltage has been included by an equivalent shrinkage of the virtual channel length hereafter called “voltage-length transformation”. This simple but general procedure enables us to account for the drain effect and to extend other threshold voltage models derived under assumption of low drain-source voltage. Predictions for threshold voltage have been compared with results of two-dimensional numerical analysis and experimental data. The comparison has been made for a wide variety of doping profiles, channel length, substrate and drain bias, gate oxide thickness and junction depth. Excellent agreement has been obtained down to submicron channel length.     

MOSFET doping profiling

An automated technique was developed for rapid measurement of MOSFET channel doping profiles. The technique is based on the well-known relationship between the device threshold voltage and substrate bias. It uses only DC voltage measurements and is not subject to the limitations of conventional capacitance-voltage (C-V) methods. An operational amplifier feedback circuit is used to determine the threshold voltage automatically as the substrate bias voltage is varied. Doping profiles determined with this technique agree very well with those obtained from C-V and from spreading resistance measurements, as well as with those predicted by SUPREM-3. The devices were fabricated with processes representing two generations of CMOS technology. The doping concentrations, channel implants, and gate oxide thicknesses varied significantly between the two, allowing the assessment of the accuracy of doping profile extraction techniques for devices representing a wide performance range     

Continuous model for gate-induced charge in short-channel MOSFETs

The threshold voltage in a short-channel MOS transistor is a sensitive function of the effective channel length, substrate bias and the channel impurity profile. A continuous model is developed in this letter to obtain a simple analytical expression for the above described sensitivities suitable for CAD program implementation. The calculated values for the threshold voltage are compared with the measurements on MOSFETs with effective channel lengths between 9.7 ?m and 1.2 ?m.     

Two-dimensional analytical modeling of fully depleted DMG SOI MOSFET and evidence for diminished SCEs

A two-dimensional (2-D) analytical model for the surface potential variation along the channel in fully depleted dual-material gate silicon-on-insulator MOSFETs is developed to investigate the short-channel effects (SCEs). Our model includes the effects of the source/drain and body doping concentrations, the lengths of the gate metals and their work functions, applied drain and substrate biases, the thickness of the gate and buried oxide and also the silicon thin film. We demonstrate that the surface potential in the channel region exhibits a step function that ensures the screening of the drain potential variation by the gate near the drain resulting in suppressed SCEs like the hot-carrier effect and drain-induced barrier-lowering (DIBL). The model is extended to find an expression for the threshold voltage in the submicrometer regime, which predicts a desirable "rollup" in the threshold voltage with decreasing channel lengths. The accuracy of the results obtained using our analytical model is verified using 2-D numerical simulations.     

Equivalent doping profile transformation: a semi-empirical,analytical method for predicting breakdown characteristics of anapproximate single-diffused parallel-plane junction

In this paper, a semi-empirical analytical method called the equivalent doping profile transformation method (EDPTM) has been proposed for the first time to predict the breakdown characteristics of an approximate single-diffused parallel-plane pn-junction that has a doping profile of the combination of a diffused side linear gradient constant and a constant substrate doping concentration, which considers the influence of the diffusion gradient level on the space charge region of the substrate side. Through the equivalent doping profile transformation, this approximate pn-junction turns into a double-sided asymmetric linear-graded junction (Jin et al., 1999). As a result, the breakdown voltage, critical peak electrical field, and the maximum depletion layer width can be carefully evaluated at different doping substrate concentration and gradient constant combinations. Compared with previous approximations such as abrupt and classical symmetrical linear-graded junctions, this method can give exact breakdown characteristics of a single-diffused pn-junction. The results are in excellent agreement with the numerical analysis, which proves the validity of this new method