Logic Circuits with Carbon Nanotube Transistors Adrian Bachtold, Peter Hadley, Takeshi Nakanishi, Cees Dekker

Supplementary Material

In our numerical calculation, we follow (25) and the work by A. A. Odintsov and Y. Tokura [J. Low Temp. Phys. 118, 509 (2000)] to consider the junction between a semiconducting SWNT and a metal electrode. In these calculations, the current variation originates from the modulation of the barrier profile formed at the nanotube-electrode junction. The barrier profile is calculated self-consistently using the density of state of semiconducting SWNTs, the Poisson equation, and the conservation equation of the total electron energy. The Poisson equation relates the electrostatic potential (z) to the charge density (z) and the gate potential V^g with _q = U_qq + M_qV_q^g, where U_q and M_q are defined below. The conservation equation of the total electron energy relates the charge neutrality level E₀(z) to (z) with E₀(z) + e(z) = W, where W is the work function difference between the nanotube and the electrode.

We have adapted the calculations for our device layout as follows. (1) The gate is described as a semi-infinite plane under the SWNT. This leads to U_q = 2/k[I₀(qR)K₀(qR) - K₀(2qR_S)] and M_q = exp(-|q|R_S), where k = 5 is the dielectric constant above the gate plane, I₀ and K₀ the modified Bessel functions, R the nanotube radius, and R_S the distance between the nanotube axe and the gate plane. (2) To describe the strong electrostatic doping in an accurate way, we have included higher/lower branch in conduction/valence bands to calculate the density of states. The overlap energy ₀ is taken equal to 2.6eV and the semiconducting gap equal to 0.7eV (35). (3) the surface charge is included in our model with the definition of equation 5 of (34) and q = 2nm^-1. (4) We also consider the doping defined as equation 1 of (25).

After the calculation of the potential near the junction, the transmission probability T is determined using the WKB approximation. Finally, we get the current at room temperature using the Landauer formula.