Gate-Capacitance-Shift Approach and Compact Modeling for Quantum Mechanical Effects in Poly-Gates

A new approach,gate-capacitance-shift (GCS) approach,is described for compact modeling.This approach is piecewise for various physical effects and comprises the gate-bias-dependent nature of corrections in the nanoscale regime.Additionally,an approximate-analytical solution to the quantum mechanical (QM) effects in polysilicon (poly)-gates is obtained based on the density gradient model.It is then combined with the GCS approach to develop a compact model for these effects.The model results tally well with numerical simulation.Both the model results and simulation results indicate that the QM effects in poly-gates of nanoscale MOSFETs are non-negligible and have an opposite influence on the device characteristics as the poly-depletion (PD) effects do.

New Method of Total Ionizing Dose Compact Modeling in Partially Depleted Silicon-on-Insulator MOSFETs

On the basis of a detailed discussion of the development of total ionizing dose （TID） effect model, a new commercial-model-independent TID modeling approach for partially depleted silicon-on-insulator metal-oxide- semiconductor field effect transistors is developed. An exponential approximation is proposed to simplify the trap charge calculation. Irradiation experiments with 60Co gamma rays for IO and core devices are performed to validate the simulation results. An excellent agreement of measurement with the simulation results is observed.

Compact Modeling for Inversion Charge in Nanoscale DG-MOSFETs

A compact model for the integrated inversion charge density Qi in double-gate （DG-） MOSFETs is developed. For nanoscale applications,quantum confinement of the inversion carriers must be taken into account. Based on the previous work of Ge, we establish an expression for the surface potential with respect to Qi, and form an implicit equation, from which Qi can be solved. Results predicted by our model are compared to published data as well as results from Schred,a popular 1D numerical solver that solves the Poisson＇s and Schr6dinger equa- tions self-consistently. Good agreement is obtained for a wide range of silicon layer thickness,confirming the supe- riority of this model over previous work in this field.

A review for compact model of graphene field-effect transistors

Graphene has attracted enormous interests due to its unique physical, mechanical, and electrical properties. Specially, graphene-based field-effect transistors （FETs） have evolved rapidly and are now considered as an option for conventional silicon devices. As a critical step in the design cycle of modem IC products, compact model refers to the development of models for integrated semiconductor devices for use in circuit simulations. The purpose of this review is to provide a theoretical description of current compact model of graphene field-effect transistors. Special attention is devoted to the charge sheet model, drift-diffusion model, Boltzmann equation, density of states （DOS）, and surface-potential-based compact model. Finally, an outlook of this field is briefly discussed.

BSIM-CMG Compact Model for IC CAD: from FinFET to Gate-All-Around FET Technology

We discuss the BSIM-CMG compact model for SPICE simulations of any common multi-gate(CMG)device.This is an industry standard model which has been used extensively for FinFETs IC design and simulation,and has now been extended to accurately model gate-allaround FET(GAAFET).We present the core framework of BSIM-CMG and discuss the latest updates that capture various physical phenomena originating from the quantum confinement of electrons by the small cross section of the GAAFET channel.Special attention is paid to providing suitable model parameters that can be adjusted using software tools to match the model with manufactured transistors very accurately.Furthermore,the model’s speed allows the use of Monte Carlo circuit simulation to account for random device variations encountered in manufacturing.This model is the industry standard compact model for GAAFETs and will help bridge the wide divide between GAA IC manufacturing and design,starting at 3nm/2nm technologies.

A review of compact modeling for phase change memory

Phase change memory(PCM)attracts wide attention for the memory-centric computing and neuromorphic comput-ing.For circuit and system designs,PCM compact models are mandatory and their status are reviewed in this work.Macro mod-els and physics-based models have been proposed in different stages of the PCM technology developments.Compact model-ing of PCM is indeed more complex than the transistor modeling due to their multi-physics nature including electrical,thermal and phase transition dynamics as well as their interactions.Realizations of the PCM operations including threshold switching,set and reset programming in these models are diverse,which also differs from the perspective of circuit simulations.For the purpose of efficient and reliable designs of the PCM technology,open issues and challenges of the compact modeling are also discussed.

Compact modeling of quantum confinements in nanoscale gate-all-around MOSFETs

In this work,a surface-potential based compact model focusing on the quantum confinement effects of ultimately scaled gate-all-around(GAA)MOSFET is presented.Energy quantization with sub-band formation along the radius direction of cylindrical GAAs or thickness direction of nanosheet GAAs leads to significant quantization effects.An analytical model of surface potentials is developed by solving the Poisson equation with incorporating sub-band effects.In combination with the existing transport model framework,charge-voltage and current-voltage formulations are developed based on the surface potential.The model formulations are then extensively validated using TCAD numerical simulations as well as Si data of nanosheet GAA MOSFETs.Simulations of typical circuits verify the model robustness and convergence for its applications in GAA technology.

Compact Threshold Voltage Model for FinFETs

A 2D analytical electrostatics analysis for the cross-section of a FinFET (or tri-gate MOSFET) is performed to calculate the threshold voltage.The analysis results in a modified gate capacitance with a coefficient H introduced to model the effect of tri-gates and its asymptotic behavior in 2D is that for double-gate MOSFET.The potential profile obtained analytically at the cross-section agrees well with numerical simulations.A compact threshold voltage model for FinFET,comprising quantum mechanical effects,is then proposed.It is concluded that both gate capacitance and threshold voltage will increase with a decreased height,or a decreased gate-oxide thickness of the top gate,which is a trend in FinFET design.

A simplified compact model of miniaturized cross-shaped CMOS integrated Hall devices

A simplified compact model for a miniaturized cross-shaped CMOS integrated Hall device is presented. The model has a simple circuit structure,only consisting of a passive network with eight non-linear resistors and four current-controlled voltage sources.It completely considers the following effects：non-linear conductivity,geometry dependence of sensitivity,temperature drift,lateral diffusion,and junction field effect.The model has been implemented in Verilog-A hardware description language and was successfully performed in a Cadence Spectre simulator.The simulation results are in good accordance with the classic experimental results reported in the literature.

Ambipolar Transport Compact Models for Two-Dimensional Materials Based Field-Effect Transistors

Three main ambipolar compact models for Two-Dimensional(2D)materials based Field-Effect Transistors(2D-FETs)are reviewed:(1)Landauer model,(2)2D Pao-Sah model,and(3)virtual Source Emission-Diffusion(VSED)model.For the Landauer model,the Gauss quadrature method is applied,and it summarizes all kinds of variants,exhibiting its state-of-art.For the 2D Pao-Sah model,the aspects of its theoretical fundamentals are rederived,and the electrostatic potentials of electrons and holes are clarified.A brief development history is compiled for the VSED model.In summary,the Landauer model is naturally appropriate for the ballistic transport of short channels,and the 2D Pao-Sah model is applicable to long-channel devices.By contrast,the VSED model offers a smooth transition between ultimate cases.These three models cover a fairly completed channel length range,which enables researchers to choose the appropriate compact model for their works.

A novel compact model for on-chip stacked transformers in RF-CMOS technology

A novel compact model for on-chip stacked transformers is presented.The proposed model topology gives a clear distinction to the eddy current,resistive and capacitive losses of the primary and secondary coils in the substrate.A method to analytically determine the non-ideal parasitics between the primary coil and substrate is provided.The model is further verified by the excellent match between the measured and simulated S-parameters on the extracted parameters for a 1：1 stacked transformer manufactured in a commercial RF-CMOS technology.

Numerical modeling and simulation of metal powder compaction of balancer

The constitutive relation of powder material was derived based on the assumption that metal powder is a kind of elasto-plastic material, complying with an elliptical yield criterion. The constitutive integration algorithm was discussed. A way to solve the elastic strain increment in each iteration step during elasto-plastic transition stage was formulated. Different integration method was used for elastic and plastic strain. The relationship between model parameters and relative density was determined through experiments. The model was implemented into user-subroutines of Marc. With the code, computer simulations for compaction process of a balancer were performed. The part is not axisymmetric and requires two lower punches and one upper punch to form. The relative density distributions of two design cases, in which different initial positions of the punches were set, were obtained and compared. The simulation results indicate the influence of punch position and movement on the density distribution of the green compacts.

BSIM Model Research and Recent Progress

The continued development of CMOS technology and the emergence of new applications demand continued improvement and enhancement of compact models. This paper outlines the recent work of the BSIM project at the University of California, Berkeley,including BSIM5 research, BSIM4 enhancements, and BSIMSOI development. BSIM5 addresses the needs of nano-CMOS technology and RF high-speed CMOS circuit simulation. BSIM4 is a mature industrial standard MOSFET model with several improvements to meet the technology requirements. BSIMSOI is developed into a generic model framework for PD and FD SOI technology. An operation mode choice,via the calculation of the body potential △Vbi and body current/charge,helps circuit designers in the trend of the coexistence of PD and FD devices.

On Numerical Modelling of Industrial Powder Compaction Processes for Large Deformation of Endochronic Plasticity at Finite Strains

Compaction processes are one the most important par ts of powder forming technology. The main applications are focused on pieces for a utomotive, aeronautic, electric and electronic industries. The main goals of the compaction processes are to obtain a compact with the geometrical requirements, without cracks, and with a uniform distribution of density. Design of such proc esses consist, essentially, in determine the sequence and relative displacements of die and punches in order to achieve such goals. A.B. Khoei presented a gener al framework for the finite element simulation of powder forming processes based on the following aspects; a large displacement formulation, centred on a total and updated Lagrangian formulation; an adaptive finite element strategy based on error estimates and automatic remeshing techniques; a cap model based on a hard ening rule in modelling of the highly non-linear behaviour of material; and the use of an efficient contact algorithm in the context of an interface element fo rmulation. In these references, the non-linear behaviour of powder was adequately desc ribed by the cap plasticity model. However, it suffers from a serious deficiency when the stress-point reaches a yield surface. In the flow theory of plasticit y, the transition from an elastic state to an elasto-plastic state appears more or less abruptly. For powder material it is very difficult to define the locati on of yield surface, because there is no distinct transition from elastic to ela stic-plastic behaviour. Results of experimental test on some hard met al powder show that the plastic effects were begun immediately upon loading. In such mater ials the domain of the yield surface would collapse to a point, so making the di rection of plastic increment indeterminate, because all directions are normal to a point. Thus, the classical plasticity theory cannot deal with such materials and an advanced constitutive theory is necessary. In the present paper, the constitutive equations of powder materials will be discussed via an endochronic theory of plasticity. This theory provides a unifi ed point of view to describe the elastic-plastic behaviour of material since it places no requirement for a yield surface and a ’loading function’ to disting uish between loading an unloading. Endochronic theory of plasticity has been app lied to a number of metallic materials, concrete and sand, but to the knowledge of authors, no numerical scheme of the model has been applied to powder material . In the present paper, a new approach is developed based on an endochronic rate independent, density-dependent plasticity model for describing the isothermal deformation behavior of metal powder at low homologous temperature. Although the concept of yield surface has not been explicitly assumed in endochronic theory, it is shown that the cone-cap plasticity yield surface (Fig.1), which is the m ost commonly used plasticity models for describing the behavior of powder materi al can be easily derived as a special case of the proposed endochronic theory. Fig.1 Trace of cone-cap yield function on the meridian pl ane for different relative density As large deformation is observed in powder compaction process, a hypoelastic-pl astic formulation is developed in the context of finite deformation plasticity. Constitutive equations are stated in unrotated frame of reference that greatly s implifies endochronic constitutive relation in finite plasticity. Constitutive e quations of the endochronic theory and their numerical integration are establish ed and procedures for determining material parameters of the model are demonstra ted. Finally, the numerical schemes are examined for efficiency in the model ling of a tip shaped component, as shown in Fig.2. Fig.2 A shaped tip component. a) Geometry, boundary conditio n and finite element mesh; b) density distribution at final stage of

Ternary analytic porosity-reduction model of sandstone compaction trend and its significance in petroleum geology: A case study of tight sandstones in Permian Lower Shihezi Formation of Shilijiahan area, Ordos Basin, China

The tight sandstones in the Permian Lower Shihezi Formation of Shilijiahan area in the Ordos Basin was taken as study object in this research to quantitatively determine the effects of burial depth, burial time and compaction strength on porosity during densification of reservoir. Firstly, sandstone compaction profiles were analyzed in detail. Secondly, the theoretical study was performed based on visco-elasto-plastic stress–strain model. Thirdly, multiple regression and iterative algorithm were used respectively to ascertain the variation trends of Young's modulus and equivalent viscosity coefficient with burial depth and burial time. Accordingly, the ternary analytic porosity-reduction model of sandstone compaction trend was established. Eventually, the reasonability of improved model was tested by comparing with thin-section statistics under microscope and the models in common use. The study shows that the new model can divide the porosity reduction into three parts, namely, elastic porosity loss, visco-plastic porosity loss and porosity loss from cementation. And the results calculated by the new model of litharenite in He 2 Member are close to the average value from the thin-section statistics on Houseknecht chart, which approximately reveals the relative magnitudes of compaction and cementation in the normal evolution trend of sandstone porosity. Furthermore, the model can more exactly depict the compaction trend of sandstone affected little by dissolution than previous compaction models, and evaluate sandstone compaction degree and its contribution to reservoir densification during different burial and uplift processes.

Parameter Extraction for 2-π Equivalent Circuit Model of RF CMOS Spiral Inductors

A novel parameter extraction method with rational functions is presented for the 2-πequivalent circuit model of RF CMOS spiral inductors. The final S-parameters simulated by the circuit model closely match experimental data. The extraction strategy is straightforward and can be easily implemented as a CAD tool to model spiral inductors. The resulting circuit models will be very useful for RF circuit designers.

Performance and analytical modelling of halo-doped surrounding gate MOSFETs

Halo structure is added to sub-100 nm surrounding-gate metal-oxide-semiconductor fieldeffect-transistors （MOS- FETs） to suppress short channel effect. This paper develops the analytical surface potential and threshold voltage models based on the solution of Poisson＇s equation in fully depleted condition for symmetric halo-doped cylindrical surrounding gate MOSFETs. The performance of the halo-doped device is studied and the validity of the analytical models is verified by comparing the analytical results with the simulated data by three dimensional numerical device simulator Davinci. It shows that the halo doping profile exhibits better performance in suppressing threshold voltage roll-off and drain-induced barrier lowering, and increasing carrier transport efficiency. The derived analytical models are in good agreement with Davinci.

Analysis of characteristic functions for equivalent circuit model in monolithic transformer

A model of monolithic transformers is presented, which is analyzed with characteristic functions. A closed- form analytical approach to extract all the model parameters for the equivalent circuit of Si-based on-chip transformers is proposed. A novel de-coupling technique is first developed to reduce the complexity in the Y parameters for the transformer, and the model parameters can then be extracted analytically by a set of characteristic functions. Simulation based on the extracted parameters has been carried out for transformers with different structures, and good accuracy is obtained compared to a 3-demensional full-wave numerical electro- magnetic field solver. The presented approach will be very useful to provide a scalable and wide-band compact circuit model for Si-based RF transformers.

An improvement to computational efficiency of the drain current model for double-gate MOSFET

As a connection between the process and the circuit design, the device model is greatly desired for emerging devices, such as the double-gate MOSFET. Time efficiency is one of the most important requirements for device modeling. In this paper, an improvement to the computational efficiency of the drain current model for double-gate MOSFETs is extended, and different calculation methods are compared and discussed. The results show that the calculation speed of the improved model is substantially enhanced. A two-dimensional device simulation is performed to verify the improved model. Furthermore, the model is implemented into the HSPICE circuit simulator in Verilog-A for practical application.

A unified charge-based model for SOI MOSFETs applicable from intrinsic to heavily doped channel

A unified charge-based model for fully depleted silicon-on-insulator （SOI） metal oxide semiconductor field-effect transistors （MOSFETs） is presented. The proposed model is accurate and applicable from intrinsic to heavily doped channels with various structure parameters. The framework starts from the one-dimensional Poisson Boltzmann equa- tion, and based on the full depletion approximation, an accurate inversion charge density equation is obtained. With the inversion charge density solution, the unified drain current expression is derived, and a unified terminal charge and intrinsic capacitance model is also derived in the quasi-static case. The validity and accuracy of the presented analytic model is proved by numerical simulations.