Analytical Charge Model Research Articles

Poisson-Schrödinger simulation and analytical modeling of inversion charge in FDSOI MOSFET down to 0 K – Towards compact modeling for cryo CMOS application

Poisson-Schrödinger (PS) simulations and an analytical charge model for a back biased FDSOI structure operated at deep cryogenic temperatures have been developed. PS simulations have been conducted down to 0 K, where metallic statistics applies, by replacing the F0 Fermi integral by a Heaviside function. Considering, as a first approximation, two separated channels for front and back interface, a set of implicit equations has been established based on a single subband scheme within the Airy approach, providing a good description of surface potential, inversion charge and capacitance characteristics of FDSOI structures operated at very low temperature and for various back biases and silicon thicknesses. This analytical charge model is a first step towards a compact model of FDSOI MOSFET for circuit design at cryogenic condition.

A Compact Model of MoS2 Field-Effect Transistors From Drift-Diffusion to Ballistic Carrier Transport Regimes

In this letter, a compact model for charge and drain current in molybdenum disulfide (MoS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) field-effect transistors (FETs) is developed, which is valid from ballistic to quasi-ballistic to drift-diffusion electronic transport regimes. Considering the influence of trap charges in MoS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> transistors, a physical-based and analytical charge model is derived. Based on the virtual source model which applies to both ballistic and quasi-ballistic transports, the carrier number density and current expressions are combined to yield the current-voltage (I-V) characteristics. Furthermore, the presented model is validated by experimental data as well as recently reported simulations for MoS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> FETs with different gate lengths. It shows that our model is accurate, straight-forward, scalable and compatible for short- and long-channel devices.

Considering Operating Point Variation in 3-D Analytical Charge Model Used for Design of Low-Stiffness Permanent Magnet Vibration Isolator

Vibration isolators are a key technology in ultraprecision machining and ultraprecision measurements. The increasing performance requirements of magnetic vibration isolation systems (MVISs) continue to demand improvements in the accuracy on which these devices are modeled. However, a serious constraint exists in designing MVISs, as high stiffnesses will be introduced by nonlinear force–displacement characteristics. The traditional analytic magnetic charge model assumes that the relative magnetic permeability $\mu _{r} = 1$ , which causes the accuracy of the magnetic analytic model of the MVIS to decrease. To solve this defect, in this article, low-stiffness MVISs are designed by using the three-dimensional analytic magnetic charge model while considering the variations of the operating point. The optimized parameters of the MVIS are then obtained by combining the genetic algorithm. The feasibility of the proposed analytical charge method is verified from the results of experimental measurements and finite-element methods. The results of this article provide a powerful tool for the design of a high-performance MVIS and provide important support for the ultimate goal of ultraprecision machining and measurements.

An Analytical Charge Model for Double-Gate Tunnel FETs

An analytical charge model for double gate (DG) tunnel FETs (TFETs) is proposed. By splitting the TFET into a series combination of a gated tunnel diode and a DG MOSFET, we solved the Poisson equation with matching boundary conditions to obtain a surface potential model for the DG TFET. Based on that, the source depletion charge and the mobile channel charge are derived. Comparisons between the proposed model and TCAD simulations show good agreements and suggest a 100/0 drain/source channel inversion charge partition. Terminal capacitances calculated based on the proposed charge model are also evaluated and show good agreement with TCAD simulations.

High frequency and noise model of gate-all-around metal-oxide-semiconductor field-effect transistors

The surrounding gate (SGT) metal-oxide-semiconductor field-effect transistor is one of the most promising candidates for the downscaling of complementary metal-oxide-semiconductor technology toward the sub-50-nm channel length range since the SGT architecture allows excellent control of the channel charge in the silicon film, thus reducing short channel effects. However, at these dimensions, quantum effects must be considered in order to develop accurate compact models useful for circuit simulations. In this paper we study the influence of quantum effects on dc, radio frequency (rf), and microwave noise for nanoscale SGT transistors including nonstationary effects. We present an analytical charge model for adjusting the charge control computed from the self-consistent solution of the two-dimensional Schrödinger and Poisson equations. rf and noise performances are calculated using the active transmission line method. We compared, on the one hand, classical and quantum charge control models and, on the other, drift-diffusion and hydrodynamic transport models.

A compact quantum model for fin-shaped field effect transistors valid from dc to high frequency and noise simulations

Fin-shaped field effect transistors (FinFETs) are considered to be a very attractive option to improve the performance of complementary metal-oxide-semiconductor devices into the sub-50-nm gate length regime. However, for those dimensions, quantum effects must be considered in order to develop accurate compact models useful for circuit simulations. In this paper, we study the influence of the quantum effects on dc, Radio frequency (rf), and microwave noise for nanoscale FinFET transistors including nonstationary effects. We present an analytical charge model to adjust the charge control computed from the self-consistent solution of the two-dimensional Schrödinger and Poisson equations. rf and noise performances are calculated using the active transmission line method. Comparison between classical and quantum charge control and between drift-diffusion and hydrodynamic models is carried out.

A unified charge model for symmetric double-gate and surrounding-gate MOSFETs

This paper presents a unified analytical charge model for long channel symmetric double-gate (DG) and surrounding-gate (SGT) MOSFETs. The proposed analytical charge model continuously covers all the operation regions and achieves both computation efficiency and high accuracy. Unified intrinsic capacitance model for both DG and SGT MOSFETs is also presented for AC simulation. A detailed comparison between the analytical model and numerical solution is conducted to demonstrate the accuracy of the model.

Analytic Charge Model for Surrounding-Gate MOSFETs

This paper presents an analytic charge model for surrounding-gate MOSFETs. Without the charge sheet approximation, the model is based on closed-form solution of Poisson's equation, current continuity equation, and Ward-Dutton linear charge partition. It continuously covers all the operation regions, i.e., linear, saturation, and subthreshold, with unique analytic expressions. The physics-based nature makes this model free of fitting parameters and hence predictive. In addition, it is inherently not source-referenced to avoid asymmetries. It is shown that the current-voltage characteristics generated by this model agree with the numerical simulation results

A unified charge model comprising both 2D quantum mechanical effects in channels and in poly-silicon gates of MOSFETs

In this paper, an approach to modeling the tunneling current along the channel, i.e. the 2D quantum mechanical (QM) effects, on the charge distribution in the carrier confinement direction is developed using the concept of “locality” and the analytical solution to the 2D Poisson equation. Then, another approach, which is the gate-capacitance-shift (GCS) approach, is described. This approach is developed for the physical effects in decanano-scaled MOSFETs that have gate-bias-dependent nature, e.g. QM effects in polysilicon gates (poly-gates). Based on this approach, the QM effects in poly-gates are considered based on the density gradient (DG) formulation. Based on the above two corrections, a unified analytical charge model is established, which yields satisfactory results compared with numerical results under different device parameters. It is further embedded into a compact ballistic model for sub-100-nm MOSFETs. It is concluded that the 2D-QM effects on the threshold voltage are non-negligible through comparison to the experimental data of a 45 nm MOSFET from TSMC [TSMC 45 nm MOSFET, internal documentation].

Comprehensive analytical physical model of quantized inversion layer in MOS structure

A new analytical charge model in quantized inversion layer in MOS structure is developed by comprehensively considering the quantum mechanical effects. The model is based on the newly proposed concept of space charge capacitance. Explicit expressions of surface potential and inversion layer carrier density are given which have smooth transition characteristics from depletion to weak to strong inversion regions. Threshold voltage shift, finite inversion layer thickness and the increment of depletion charge after strong inversion are properly modeled. Model results are compared with numerical data by self-consistent solution of Schrodinger and Poisson equation and the high accuracy of the model is demonstrated.

A new analytical charge model for the dual-gate controlled thin-film SOI MOSFET

An analytical model for dual-gate-controlled SOI MOSFETs is presented, assuming uniformly doped p-silicon films. It is restricted to electron inversion layers and depletion regions, neglecting hole densities. It allows to account for the spatial description of electronic quantities in the silicon film. Due to the non-linearities of the semiconductor equations the model parameters must be extracted iteratively. Some applications are presented to demonstrate the usefulness of the model.