Compact models describing the voltage-dependent terminal current and charges (or equivalently, capacitances) are essential for small-signal and transient circuit simulation.  In this work, we extend the virtual-source (VS)-based transport model ^[1] with a self-consistent channel charge model for quasi-ballistic or fully ballistic devices, when the gradual channel approximation (GCA) and the drift transport theory are no longer valid. From a parabolic channel potential profile approximation and current continuity boundary condition, we derive a voltage-dependent charge model that is self-consistent with the transport model in the ballistic regime. The extended VS model has been implemented in Verilog-A language. ^[2]

Devices operating in the ballistic regime in saturation have less channel charge than predicted by the drift-diffusion theories, which is in principle advantageous from the performance point of view.  The quasi-ballistic (QB) model predicts 61% and 58% fewer intrinsic channel charges than the saturation velocity model (Vsat) and non-saturation drift velocity model (NVsat), respectively (Figure 1).  The difference diminishes in the linear region or because the device essentially operates with low carrier velocity and a lot of scattering with low V_gs or V_ds.   It is also shown that the benefits of fast carrier transport in tight-pitch logic circuits diminish due to the presence of extrinsic charges, particularly at higher fan-outs. As shown in Figure 2, the stage delay of a 5-stage ring oscillator predicted by QB model is only 5% and 3% less than that by Vsat and Nsat models, respectively. However, for RF applications the benefit of quasi-ballisticity in Si or near-full ballisticity in III-V HEMTs calculated by the model can be significant.

1. A. Khakifirooz, O. Nayfeh, and D. Antoniadis, “A simple semiempirical short-channel MOSFET current-voltage model continuous across all regions of operation and employing only physical parameters,” IEEE Transactions on Electron Devices,, vol. 56, pp. 1674-1680, 2009.
2. L. Wei, O. Mysore, and D. Antoniadis, “Virtual-source based self-consistent charge and transport models for near-ballistic FETs,” to be submitted to 2011 International Electron Devices Meeting.

A variety of compact MOSFET models are used for circuit simulation in both industry and academia, ranging from standard industrial models with dimensional and processing parameter dependencies ^[1] to simple, intuitive physical transport models. The virtual-source model (VS model), a recently developed, simple, semi-empirical, short channel MOSFET model, captures the essential physics with relatively few physical parameters, most of which can be directly determined from device measurements or simulations ^[2] .  Because of its accuracy, simplicity, and scalability, the VS model is excellent for technology benchmarking, performance projection and variability analysis.

Figure 1: Waveform of ring oscillator node voltages.

Previous work on this project involved the implementation of the VS model, including intrinsic charges, in a commercial simulator using Verilog-A, an analog descriptive language.  Commercial circuit simulators allow users to create Verilog-A behavioral modules, which specify the relationships between currents and voltages of the internal and external nodes of the module.  Using such a module, the VS model, including intrinsic charges, was implemented in Verilog-A.  This project uses the Verilog-A implementation of the model to simulate a number of circuits.

Circuits such as ring oscillators, adders, and FIR-filters were simulated in commercial simulators using the Verilog-A implementation of the VS model.  Ring oscillators ranging from fan-out one to seven were implemented, and the delays were compared to experimental data from fabricated ring oscillators.  For the ring oscillators, the appropriate VS model parameters were extracted from measured data, and the parameters were varied in simulations in order to obtain sensitivity analyses.  The node voltages of a fivestage ring oscillator are shown in Figure 1.  For larger circuits, such as an FIR-filter, when convergence difficulties arose, smoothing functions substantially improve convergence.  Based on the circuits implemented as part of this project, using Verilog-A modules in commercial simulators is an adequate method of simulating circuits with the VS model.

1. C. Hu. “BSIM.” Internet: http://www-device.eecs.berkeley.edu/~bsim3/bsim4.html [June 31, 2009].
2. A. Khakifirooz, “A simple semiempirical short-channel MOSFET current-voltage model continuous across all regions of operation and employing only physical parameters,” IEEE Transactions on Electron Devices, vol. 56, pp. 1674-1680, 2009.