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Stanford University Virtual Source CNFET Model

The Stanford Virtual-Source Carbon Nanotube Field-Effect Transistors (VSCNFET) model is a semi-empirical model that describes the current-voltage and charge-voltage (i.e. capacitance-voltage) characteristics in a short-channel metal-oxide-semiconductor field-effect transistor (MOSFET) with carbon nanotubes as the channel material. The intrinsic drain current (Id) and terminal charges are based on the virtual source (VS) model, with the virtual source velocity extracted from experimental data for different channel lengths (ranging from 3-um down to 15-nm). Parasitic effects are modeled: (i) direct source-to-drain and band-to-band tunneling current calibrated by numerical simulations; (ii) metal-to-CNT contact resistances calibrated by experimental data; (iii) parasitic capacitance including gate-to-CNT fringe capacitances and gate-to-contact coupling capacitances. The inputs to the VSCNFET model are the physical device design including device dimensions, CNT diameter, gate oxide thickness, etc.


Download the VS-CNFET model.

Note: The key difference between the old Stanford CNFET (S-CNFET) model and the VS-CNFET model is the modeling of carrier transport. The S-CNFET model is physics-based using the quasi-ballistic Landauer formula, while the VS-CNFET model is based on the semi-empirical virtual source concept calibrated to experimental data. One issue of the S-CNFET model is that the longitudinal wave vectors along the channel direction are quantized and then summed up numerically to calculate the drain current and terminal charges, leading to a decreasing drain current as the channel length decreases below 100 nm. The VS-CNFET model also includes data-calibrated contact resistance and direct source-to-drain tunneling current, which are not captured in the S-CNFET model.

The following table summarizes the differences between the two models:



Stanford CNFET Model

Virtual-Source CNFET Model

Device Structure Top gate; 4-terminal Cylindrical gate-all-around and top gate; 3-terminal (without the body terminal, which is insulated by the thick buried oxide)
Carrier Transport Quasi-ballistic Landaur formula including empirical acoustic and optical phonon scattering mean free paths in the calculation of the transmission coefficient. The surface potential is calculated by the charge neutrality iteratively. Semi-empirical virtual source approach with data-calibrated carrier injection velocity and mobility. Both the velocity and mobility are functions of the CNT diameter and the gate length.
Terminal charge (capacitance) Summation of the occupied quantized states (i.e. E-k dispersion) Virtual source charge model interpolating between the ballistic and diffusive regimes.
Short-channel effect Empirical constant parameters to adjust the subthreshold slope and drain-induced barrier lowering. Electrostatic scale length theory (i.e. SS and DIBL change exponentially with the gate length) calibrated to TCAD numerical simulation.
Parasitic contact resistance Tunneling through the Schottky barrier at the metal-to-CNT interface. No dependence on the contact length. Transmission line model with the coupling conductance characterized by the Schottky barrier height; calibrated to experimental data; capture the length and CNT diameter dependence.
Tunneling leakage current Junction band-to-band tunneling leakage (relatively simple) Direct source-to-drain and junction band-to-band tunneling leakage currents calibrated to TCAD numerical simulation (numerical integration is involved.)


Chi-Shuen (Vince) Lee - chishuen [at] stanford [dot] edu

Carlo Gilardi - cgilardi [at] stanford [dot] edu


Chi-Shuen Lee, Jieying Luo


The authors would like to thank Prof. L. Wei (Waterloo), Prof. S. Rakheja (NYU), G. Hills (Stanford), Prof. S. Mitra (Stanford), and Prof. Z. Chen (Purdue) for the useful discussion.

Related Publications

C.-S. Lee, E. Pop, A. Franklin, W. Haensch, and H.-S. P. Wong, “A Compact Virtual-Source Model for Carbon Nanotube Field-Effect Transistors in the Sub-10-nm Regime—Part I: Intrinsic Elements,” arXiv:1503.04397

C.-S. Lee, E. Pop, A. Franklin, W. Haensch, and H.-S. P. Wong, “A Compact Virtual-Source Model for Carbon Nanotube Field-Effect Transistors in the Sub-10-nm Regime—Part II: Extrinsic Elements and Performance Assessment,” arXiv:1503.04398

J. Luo, L. Wei, C.-S. Lee, A. D. Franklin, X. Guan, E. Pop, D. A. Antoniadis and H.-S. P. Wong, “Compact Model for Carbon Nanotube Field-Effect Transistors Including Nonidealities and Calibrated With Experimental Data Down to 9-nm Gate Length,” IEEE Trans. Electron Devices, vol. 60, no. 6, pp. 1834-1843, Jun. 2013.