Carbon Nanotube Transistor 2D: Barrier, Transfer & I-V Curves

Bias Controls

Gate voltage V_G 0.30 V

Drain–source V_DS 0.20 V

Tube diameter d 1.00 nm

Temperature T 300 K

Channel State

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Drain current I_DS

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Barrier height Φ_B

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Bandgap E_g

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Sub-V_T swing S

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ON/OFF ratio

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Thermal energy k_BT

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How it works

2D companion to the 3D CNTFET scene: the identical "top-of-the-barrier" ballistic transport model (Natori / Rahman–Lundstrom), computed independently and read off a device cross-section plus two analytic charts instead of a rendered nanotube.

E_g ≈ 0.8 eV·nm / d          (nanotube bandgap, d = diameter)
Φ_B(V_G) = E_g/2 − β·V_G     (barrier height, gate efficiency β ≈ 0.92)
I_DS = (4e/h)·k_T·ln[ (1+e^((E_F−Φ_B)/k_T)) / (1+e^((E_F−Φ_B−V_DS)/k_T)) ]

V_G — lowers the barrier as it rises; once Φ_B drops below the Fermi level E_F (=0 here), electrons cross ballistically with almost no scattering along the tube.
V_DS — the forward bias that pulls current once the channel opens; the output-curve panel sweeps this axis at the current V_G.
Diameter d — a narrower tube has a larger bandgap (E_g ∝ 1/d), which raises the OFF-state barrier and improves the ON/OFF current ratio at the cost of ON-current.
Temperature T — sets k_BT and the subthreshold swing S ≈ ln(10)·k_BT/β, the mV-per-decade cost of turning the channel off; CNTFETs get close to the 60 mV/decade room-temperature limit because the gate wraps a body only ~1 nm thick.
Transfer curve — log₁₀(I_DS) swept across the whole V_G range at the current V_DS, d and T; the straight subthreshold segment's slope is exactly the S readout above.

Electrons spawn at the source and either sail over the barrier to the drain (ballistic transmission, no phonon scattering in an ideal short CNT channel) or reflect elastically back toward the source, with a Fermi-function crossing probability tied directly to the same Φ_B and k_BT used in every curve.