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.     

Charge-based model for symmetric double-gate MOSFETs with inclusion of channel doping effect

This paper presents a unified charge-based model for symmetric double-gate (DG) MOSFETs with a wide range of channel doping concentrations. From one dimensional (1D) Poisson–Boltzmann equation in the DG MOSFET structure, an accurate inversion charge model is proposed, which predicts the inversion charge density precisely from weak inversion, through moderate inversion and finally to strong inversion region for both heavily doped and lightly doped condition. Based on that, the unified drain current model is developed from Pao-Sah’s dual integral. The unified terminal charge and trans-capacitance models are derived out from Ward and Dutton’s linear-charge-partition scheme. Extensive numerical simulations are performed on DG MOSFETs to verify the unified charge-based models and good agreements between them are obtained, proving the validity of the proposed model for further circuit simulation.     

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.     

A continuous, analytic drain-current model for DG MOSFETs

This letter presents a continuous analytic current-voltage (I-V) model for double-gate (DG) MOSFETs. It is derived from closed-form solutions of Poisson's equation, and current continuity equation without the charge-sheet approximation. The entire I/sub ds/(V/sub g/,V/sub ds/) characteristics for all regions of MOSFET operation: linear, saturation, and subthreshold, are covered under one continuous function, making it ideally suited for compact modeling. By preserving the proper physics, this model readily depicts "volume inversion" in symmetric DG MOSFETs-a distinctively noncharge-sheet phenomenon that cannot be reproduced by standard charge-sheet based I-V models. It is shown that the I-V curves generated by the analytic model are in complete agreement with two-dimensional numerical simulation results for all ranges of gate and drain voltages.     

短沟道MOSFET解析物理模型

本文基于修正的二维泊松方程导出了适用于深亚微米ＭＯＳＦＥＴ的值电压解析模型,并进而通过反型区电荷统一表达式并考虑到载流子速度饱和、ＤＩＢＬ、相关迁移率、反型层电容和沟道长度调制等主要小尺寸与高场效应,最后得以了较为准确、连续和可缩小的漏极电流模型,模型输出与华晶等榈测试ＭＩＮＩＭＯＳ模拟结果较为吻合,可用于ＶＬＳＩ器件与电路预测模拟。     

Performance analysis of long Ge channel double gate (DG) p MOSFETs with high-k gate dielectrics based on carrier concentration formulation

In this paper, electrical behavior of symmetric double gate Ge channel MOSFETs with high-k dielectrics is reported on the basis of carrier concentration formalism. The model relies on the solution of Poisson-Boltzmann equations subject to suitable boundary conditions taking into account the effect of interface trap charge density (D_it) and the Pao-Sah’s current formulation considering field dependent hole mobility. It is continuous as it holds good for sub-threshold, weak and strong inversion regions of device operation. The proposed model has been employed to calculate the drain current of DG MOSFETs for different values of gate voltage and drain voltage along with various important device parameters such as transconductance, output conductance, and transconductance per unit drain current for a wide range of interface trap charge density, equivalent oxide thickness (EOT) and bias conditions. Moreover, most of the important device parameters are compared with their corresponding Si counter parts. Accuracy of the model has been verified by comparing analytical results with the numerical simulation data. A notable improvement of the drive current and transconductance for Ge devices is observed with reference to Si devices, particularly when D_it is small.     

Accounting for quantum effects and polysilicon depletion from weak to strong inversion in a charge-based design-oriented MOSFET model

This paper presents a simple, physics-based, and continuous model for the quantum effects and polydepletion in deep-submicrometer MOSFETs with very thin gate oxide thicknesses. This analytical design-oriented MOSFET model correctly predicts inversion and depletion charges, transcapacitances, and drain current, from weak to strong inversion and from nonsaturation to saturation. One single additional parameter is used for polysilicon doping concentration, while the quantum correction does not introduce any new parameter. Comparison to experimental data of deep-submicrometer technologies is provided, showing accurate fits both for I-V and C-V data. The model offers simple relationships among effective electrical parameters and physical device parameters, providing insight into the physical phenomena. This new model thereby supports device engineering, analog circuit design practice, as well as efficient circuit simulation.     

Quantum mechanical compact modeling of symmetric double-gate MOSFETs using variational approach

A physics-based analytical model for symmetrically biased double-gate (DG) MOSFETs considering quantum mechanical effects is proposed. Schrödinger's and Poisson's equations are solved simultaneously using a variational approach. Solving the Poisson and Schrödinger equations simultaneously reveals quantum mechanical effects (QME) that influence the performance of DG MOSFETs. The inversion charge and electrical potential distributions perpendicular to the channel are expressed in closed forms. We systematically evaluated and analyzed the potentials and inversion charges, taking QME into consideration, in Si based double gate devices. The effect of silicon thickness variation in inversion-layer charge and potentials are quantitatively defined. The analytical solutions provide good physical insight into the quantization caused by quantum confinement under various gate biases.     

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 analytic potential model for symmetric and asymmetric DG MOSFETs

This paper presents an analytic potential model for long-channel symmetric and asymmetric double-gate (DG) MOSFETs. The model is derived rigorously from the exact solution to Poisson's and current continuity equation without the charge-sheet approximation. By preserving the proper physics, volume inversion in the subthreshold region is well accounted for in the model. The resulting analytic expressions of the drain-current, terminal charges, and capacitances for long-channel DG MOSFETs are continuous in all operation regions, i.e., linear, saturation, and subthreshold, making it suitable for compact modeling. As no fitting parameters are invoked throughout the derivation, the model is physical and predictive. All parameter formulas are validated by two-dimensional numerical simulations with excellent agreement. The model has been implemented in Simulation Program with Integrated Circuit Emphasis version 3 (SPICE3), and the feasibility is demonstrated by the transient analysis of sample CMOS circuits.     

Precise Modeling Framework for Short-Channel Double-Gate and Gate-All-Around MOSFETs

A precise modeling framework for short-channel nanoscale double-gate (DG) and gate-all-around (GAA) MOSFETs is presented. For the DG MOSFET, the modeling is based on a conformal mapping analysis of the potential distribution in the device body arising from the interelectrode capacitive coupling, combined with a self-consistent procedure to include the effects of the inversion charge. The DG interelectrode coupling, which dominates the subthreshold behavior of the device, can also be applied with a high degree of precision to the cylindrical GAA MOSFET by performing a simple geometric scaling transformation to account for the difference in gate control in the two devices. Near threshold, self-consistent procedures invoking Poisson's equation in combination with boundary conditions and suitable modeling expressions for the potential are applied to the two devices. In strong inversion, these solutions converge to those of the respective long-channel devices. The drain current is calculated as part of the self-consistent treatment. The results for both the electrostatics and the current are in excellent agreement with numerical simulations.     

Explicit Analytical Charge and Capacitance Models of Undoped Double-Gate MOSFETs

An analytical, explicit, and continuous-charge model for undoped symmetrical double-gate (DG) MOSFETs is presented. This charge model allows obtaining analytical expressions of all total capacitances. The model is based on a unified-charge-control model derived from Poisson's equation and is valid from below to well above threshold, showing a smooth transition between the different regimes. The drain current, charge, and capacitances are written as continuous explicit functions of the applied bias. We obtained very good agreement between the calculated capacitance characteristics and 2-D numerical device simulations, for different silicon film thicknesses.     

An explicit analytical charge-based model of undoped independent double gate MOSFET

This paper describes an explicit analytical charge-based model of an undoped independent double gate (DG) MOSFET. This model is based on Poisson equation resolution and field continuity equations. Without any fitting parameter or charge sheet approximation, it provides explicit analytical expressions of both inversion charge and drain current considering long undoped transistor. Consequently, this is a fully analytical and predictive model allowing describing planar DG MOSFET as well as FinFET structures. The validity of this model is demonstrated by comparison with Atlas simulations.     

Continuous analytic I-V model for surrounding-gate MOSFETs

We present a continuous analytic current-voltage (I-V) model for cylindrical undoped (lightly doped) surrounding gate (SGT) MOSFETs. It is based on the exact solution of the Poisson's equation, and the current continuity equation without the charge-sheet approximation, allowing the inversion charge distribution in the silicon film to be adequately described. It is valid for all the operation regions (linear, saturation, subthreshold) and traces the transition between them without fitting parameters, being ideal for the kernel of SGT MOSFETs compact models. We have demonstrated that the I-V characteristics obtained by this model agree with three-dimensional numerical simulations for all ranges of gate and drain voltages.     

A surface potential-based non-charge-sheet core model for undoped surrounding-gate MOSFETs

A surface potential based non-charge-sheet core model for cylindrical undoped surrounding-gate (SRG) MOSFETs is presented. It is based on the exact surface potential solution of Poisson's equation and Pao-Sah's dual integral without the charge-sheet approximation, allowing the SRG-MOSFET characteristics to be adequately described by a single set of the analytic drain current equation in terms of the surface potential evaluated at the source and drain ends. It is valid for all operation regions and traces the transition from the linear to saturation and from the sub-threshold to strong inversion region without fiRing-parameters, and verified by the 3-D numerical simulation.     

非掺杂环栅MOSFETs的基于表面电势和非薄层电荷的核心模型

A surface potential based non-charge-sheet core model for cylindrical undoped surrounding-gate （SRG） MOSFETs is presented. It is based on the exact surface potential solution of Poisson＇s equation and Pao-Sah＇s dual integral without the charge-sheet approximation, allowing the SRG-MOSFET characteristics to be adequately described by a single set of the analytic drain current equation in terms of the surface potential evaluated at the source and drain ends. It is valid for all operation regions and traces the transition from the linear to saturation and from the sub-threshold to strong inversion region without fitting-parameters, and verified by the 3-D numerical simulation.     

New short-channel n-MOSFET current-voltage model in stronginversion and unified parameter extraction method

A semiempirical strong inversion current-voltage (I-V) model for submicrometer n-channel MOSFETs which is suitable for circuit simulation and rapid process characterization is proposed. The model is based on a more accurate velocity-field relationship in the linear region and finite drain conductance due to the channel length modulation effect in the saturation region. The parameter extraction starts from the experimental determination of the MOSFET saturation current and saturation voltage by differentiating the output characteristics in a unified and unambiguous way. These results are used in order to systematically extract the device and process parameters such as the effective electron saturation velocity and mobility, drain and source series resistances, effective gate length and characteristic length for channel length modulation, and short-channel effects. The values agree well with other independent measurements. The results of experimental studies of wide n-MOSFETs with nominal gate length of 0.8, 1.0, and 1.2 μm fabricated by an n-well CMOS process are reported. The calculated I-V characteristics using the extracted parameters show excellent agreement with the measurement results     

Drain current model for undoped Gate Stack Double Gate (GSDG) MOSFETs including the hot-carrier degradation effects

In this paper, analytical models of drain current and small signal parameters for undoped symmetric Gate Stack Double Gate (GSDG) MOSFETs including the interfacial hot-carrier degradation effects are presented. The models are used to study the device behavior with the interfacial traps densities. The proposed model has been implemented in the SPICE circuit simulator and the capabilities of the model have been explored by circuit simulation example. The developed approaches are verified and validated by the good agreement found with the 2D numerical simulations for wide range of device parameters and bias conditions. GSDG MOSFET design and the accurate proposed model can alleviate the critical problem and further improve the immunity of hot-carrier effects of DG MOSFET-based circuits after hot-carrier damage.     

A self-consistent analytic threshold voltage model for thin SOI n-channel MOSFETs

An accurate analytical threshold voltage model is presented for fully-depleted SOI n-channel MOSFETs having a metal-insulator-semiconductor-insulator-metal structure. The threshold voltage is defined as the gate voltage at which the second derivative of the inversion charge with respect to the gate voltage is maximum. Since the inversion charge is proportional to the drain current at low bias, the model is self-consistent with the measurement scheme when the threshold voltage is measured as the gate voltage at which the variation of the transconductance at low drain bias is maximum. Numerical simulations show good agreement with the model with less than 3% error.     

An analytic saturation model for drain and substrate currents ofconventional and LDD MOSFETs

An analytic saturation model for conventional and lightly doped drain (LDD) MOSFETs is developed by using the pseudo-two-dimensional approximation in the channel and drain regions to obtain both the channel length modulation factor and the maximum electric field. Using the established I-V model in the linear region, the drain currents of conventional and LDD MOSFETs can be explicitly calculated. The substrate currents of conventional/LDD MOSFETs are calculated by using an existing simplified substrate current formula and the maximum electric field model. It is shown that the accuracy of the maximum electric field is acceptable for calculating the substrate currents of conventional/LDD MOSFETs. The parameters used in the model can be determined by the existing extraction methods and the optimization technique. The saturation model is shown to be valid for a wide range of channel lengths and bias conditions