Carbon Nanotube Transistor: Ballistic Switching

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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How it works

A semiconducting carbon nanotube channel sits between metal source/drain contacts, with a gate electrode capacitively raising or lowering an electrostatic barrier at mid-channel — the "top-of-the-barrier" ballistic FET model (Natori / Rahman–Lundstrom):

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 ≈ 1 for a CNT's thin body)
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 visible flow rate is set by V_DS together with the barrier transparency.
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_T = 8.617×10⁻⁵·T eV and the subthreshold swing S ≈ ln(10)·k_T/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.

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 — visualised here with a Fermi-function crossing probability tied directly to the same Φ_B and k_T used in the current formula above.

Ballistic electron Reflected electron Gate-controlled barrier

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