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By Arash Hazeghi1, Tejas Krishnamohan1, H.-S. Philip Wong1
1. Stanford University
Simulate Carbon Nanotube field Effect transistor with Schottky Barriers
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Version 1.1.1w - published on 17 Mar 2015
doi:10.4231/D3R49G98F cite this
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11 Feb 2010
3.0 out of 5 stars
The tool Schottky-Barrier CNFET allows users to generate source-drain current versus source-drain bias of a carbon nanotube field effect transistor (CNFET) with Schottky-Barrier (SB) contacts. The tool is adapted from code that was used to generate the same plots from the group’s paper (A. Hazeghi et al., IEEE TED, 2004). The group uses a Landauer–Büttiker model to calculate the current. They assume that the nanotube has a length of 100 nm, diameter of 1.5 nm, is single-walled, and transports ballistically. The SBs are modeled through a transmission expression calculated using the Wentzel–Kramers–Brillouin (WKB) method. To calculate the potential near the profile, seemingly to get the correct tunneling barrier, they use evanescent mode analysis which self-consistently solves the laplace equation. The adjustable variables for the simulation are gate bias, drain bias, oxide thickness, dielectric constant, SB height, and temperature.
Since the tool is analytical one would not expect it to run slowly and it doesn’t. Computation is indeed very quick as it never takes more than a minute or two to finish running simulations. As for correctness, the tool delivers qualitatively but not quantitatively in my opinion. The correct qualitative trends of decreasing current with increasing SB height, increasing oxide thickness, decreasing dielectric constant, and decreasing gate bias are displayed. Another nice feature is the tool considers both electron and hole transport, unlike many transport models for nanotubes, which consider electron transport only.
Quantitatively, it is my belief that the values for current are wrong. First, I think there is a units mistake when they uploaded the tool because it produces currents that are on the order of 10^-5 uAm, which is 10s of pA. Their paper shows curves with currents on the order of 10s of uA, so I think they actually mean to plot in amps. I suggest they correct this as this can lead to some initial confusion. Assuming they are plotting in amps I still believe their currents are too high as they are higher than any reported experimental value in literature. In their paper they point this out as well. They attribute the lower currents seen in experiments to imperfect contacts and the presence of optical phonon scattering. In addition since their paper has been published effects from the surrounding substrate such as surface phonon polaritons (SPPs) have also been predicted to have an effect on current. While they do allow for manipulation of ambient temperature, nanotubes have also shown to get locally hot from joule heating. However since the bias range is so low, temperature variations are not going to cause much current variation. The problem with their calculation method is that the Landauer–Büttiker model assumes a ballistic channel when this is not necessarily so in real life, even at a length of 100 nm.
For improvement, I would suggest trying to incorporate at least optical phonon scattering to get more reasonable values for current (~20-30uA at 1.5V bias as opposed to 50-70uA). From an experimentalist standpoint it would be nice to be able to do calculations for various diameters as well since the energy gap changes as a function of diameter(~0.8/d eVnm). Also, it is generally difficult for most experimentalists (like me!) at universities to grow quality oxides that are 1-30nm thick. It would be better to include a larger range for oxide thickness, possibly up to 100nm. Finally, a gate-all-around CNFET has never been fabricated as far as I know. Most research is currently focused on bottom or top gated devices so it would be nice to be able to change the configuration as well, although I realize the difficulty in solving the electrostatics becomes exponentially more difficult for those geometries. All in all, I would say that the tool is good for giving researchers an idea of what trends to expect for SB-CNFETs, but needs work to produce currents that are more realistic.
-Albert Liao (UIUC)
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12 Feb 2008
5.0 out of 5 stars