A lumped-circuit nonquasi-static (NQS) model, that is applicable for both large-signal transient simulations and a small-signal ac analysis, is developed in this paper. An improved physical equivalent circuit, capturing NQS effects in the millimeter waveband, is derived using a transmission line model, by incorporating the high-frequency longitudinal gate electrode and a channel distributed RC network. The proposed model is implemented in a BSIM-BULK MOSFET model and validated with dc and RF data, obtained from technology computer-aided design device simulations and experimental data. The proposed model is in very good agreement with the data up to ${50}{f}_{t}$ . The transient currents, for a gate-voltage switching rate of ${5}\times {10}^{{10}}$ V/s, show excellent match with the data. The dc, transient, and ac simulations using the proposed model are much faster than a 10-segmented MOSFET model. This shows that the proposed model is better than other computationally complex compact models, for most RF applications.

Accurate and Computationally Efficient Modeling of Nonquasi Static Effects in MOSFETs for Millimeter-Wave Applications

First-principles-based device models are in demand in the semiconductor industry to assess the impact of new materials at very early phases of the technology development. Existing models for the 2D metal–oxide–semiconductor field-effect transistor work under quasi-static limit and can only be used for designing circuits operating under half of the transistor's intrinsic cut-off frequency. Here, we develop a compact device model for phosphorene-based transistor that takes into account its band structure anisotropy as well as the carrier inertia, which is crucial for high-frequency operation. In a multi-scale approach, density functional theory based calculation is first carried out to obtain the material specific parameters, which are then used to develop a continuity equation based non-quasi-static model to gain insight into the high-frequency behaviors. We find that channel orientation has a strong impact on both the low and high frequency conductances; however, it affects only the high-frequency component of capacitances. The model is then implemented in an industry-standard circuit simulator using relaxation-time-approximation technique and simulations are conducted to demonstrate its applicability for near cut-off frequency circuit operation. The proposed modeling methodology, which connects material to circuit, thus helps us to expand the design space, where technology downscaling could be very challenging and expensive.

A predictive model for high-frequency operation of two-dimensional transistors from first-principles

With the unique quasi-linear relationship between the surface potentials along the channel, recently we have proposed a quasi-static terminal charge model for common double-gate MOSFETs, which might have asymmetric gate oxide thickness. In this brief, we extend this concept to develop the nonquasi-static (NQS) charge model for the same by solving the governing continuity equations. The proposed NQS model shows good agreement against TCAD simulations and appears to be useful for efficient circuit simulation.

Nonquasi-Static Charge Model for Common Double-Gate MOSFETs Adapted to Gate Oxide Thickness Asymmetry

The semiconductor industry has relied on accurate device models for analyzing, predicting and innovating integrated circuit design. Multi-gate MOSFET device architectures like FinFETs are beginning to replace their planar MOSFET counterparts at the 22nm technology node to enable continued technology scaling. Vertical cylindrical gate (CG) MOSFET are touted to replace planar MOSFETs as the memory device for DRAM and NAND Flash offering increased area density. New device architectures together with relentless scaling of MOSFETs for performance mean increased complexity and new device physics that need to be comprehended. This new understanding needs to be translated into device models for technology progress. Newer device models also require newer methodologies for model creation process and usage for circuit design. In this thesis we develop a comprehensive compact SPICE model for a CG MOSFET. Relying on fundamental physics based electrostatics description (Poisson Equation) of the device analytic equations for terminal current and capacitance are derived forming the core model. Including all requisite real device effects we validate this model to both numerical simulations (TCAD) and hardware silicon data showing < 1% RMS error when the model is tuned to the data. For channel diameters < 20nm quantum mechanical confinement effects tend to dominate. The complex bias and geometry dependence of the inversion charge centroid is captured through a phenomenological model. This model helps accurate prediction of the reduction in gate capacitance of a CG MOSFET. This model was also extended to carrier confinement in thin channels such as the double gate FET or FinFET. The vertical CG MOSFET exhibits asymmetry w.r.t. source and drain. With the aid of TCAD we propose that non-uniform vertical channel doping and structural differences in the top and bottom (source/drain) junction regions as the major contributors to the asymmetric behavior. We then create a mathematical framework to capture these asymmetries in the compact model developed above. We validate this approach by showing excellent agreement to hardware silicon data from a high voltage vertical CG MOSFET technology. All these models have been incorporated in BSIM-CMG the first industry standard multi-gate MOSFET model. Despite including many complex physical effects the resultant model can be executed in the order of few 10's of secs (per operating point) enabling rapid very large scale integrated circuit design. A compact SPICE model maintains a balance of predictive nature and flexibility with many sub-components describing various physics and tunable parameters in order to capture data from various sources accurately. This could quickly become unmanageable during a model creation process. For this we propose a RF model extraction procedure that does not require any additional sub-circuit elements and takes advantage of advances in parameter optimization tools available today in an efficient manner. We demonstrate this procedure on high frequency data from multiple planar MOSFET technologies discussing various use cases. Using BSIM6, a bulk planar MOSFET compact model the resultant procedure was able to capture silicon data even beyond the cut-off frequency of the MOSFET and predict various RF circuit design figure of merits with great accuracy.

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From poisson to silicon - advancing compact spice models for ic design

An accurate physics-based lumped-circuit model, representing the nonquasi-static effect and the distributed polygate electrode resistance in bulk MOSFET is proposed. In our approach, an improved physical equivalent circuit capturing NQS effect is developed by using pole-zero compensation technique. The new model takes into account the inherent delay in the response of channel charges to the applied voltage. The proposed model is implemented in BSIM6 MOSFET model, and it is validated with Y-parameter data obtained from technology computer-aided design device simulations. The proposed model is in very good agreement with the device data up to 50/t, which ensures that it is suitable for most RF applications over any other computationally complex compact models.

Compact modeling of nonquasi-static effect in bulk MOSFETs for RF circuit design in sub-THz regime

A new relaxation-time-approximation-based nonquasi-static (NQS) MOSFET model, consistent between transient and small-signal simulations, has been developed for surface-potential-based MOSFET compact models. The new model is valid for all regions of operation and is compatible with, and at low frequencies recovers, the quasi-static description of the MOSFET. The model is implemented in two widely used circuit simulators and is tested for speed and convergence. It is verified by comparison with technology computer-aided design simulations and experimental data and by application of a recently developed benchmark test for NQS MOSFET models.

Zeqin Zhu

Papers

Accurate RTA-Based Nonquasi-Static MOSFET Model for RF and Mixed-Signal Simulations