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A Schrödinger-Poisson Solver for Modeling Carbon Nanotube FETs

D.L. John, L.C. Castro, P.J.S. Pereira and D.L. Pulfrey
Department of Electrical and Computer Engineering, CA

Keywords: nanotubes, FET, Schrödinger Poisson, Schottky barrier

Abstract:
Carbon nanotubes are attracting great interest for their use in nanoscale electronic devices. Recent modeling efforts of carbon nanotube field-effect transistors (CNFETs) have been successful in examining the subthreshold behaviour of these devices through a simple solution to Laplace's equation [1, 2], while the above-threshold behaviour has been modeled using bulk device concepts [3, 4], or overly restrictive geometry or material parameters [5] that neglect the possibility of Schottky-barrier limited transport [6]. Moreover, this earlier work has not produced a solution that is fully self-consistent in charge, potential, and current. In this work, we present a detailed method for incorporating quantum transport effects through a coupled Schrodinger-Poisson solver. The Poisson solution is effected using a two-dimensional finite difference algorithm in a coaxial structure with azimuthal symmetry. The Schrodinger solution is implemented by the Airy function transfer matrix method [7], and the resultant, unbounded, wavefunctions, defined on the nanotube surface, are normalized to the flux computed by the Landauer formula. The solver illustrates the need for more detailed modeling of the nanotube regions near the CNFET end-contacts, particularly devices that are Schottky-barrier limited. Normally, the evanescent modes inside the barrier are neglected, precluding an accurate determination of the transit charge, and thus a deficient solution of Poisson's equation is obtained. Consideration of these modes, through the wave equation, allows this issue to be alleviated. Convergence issues arising due to resonance effects are discussed, current-voltage characteristics are predicted, and trends are compared to experimental results from the literature and to previous models. --- [1] D.L. John et al., IEEE Trans. Nanotechnol., 2(3):175, 2003. [2] S. Heinze et al., arXiv:cond-mat/0302175v1, Feb. 10, 2003. [3] L.C. Castro et al., Proc. IEEE COMMAD, 2002. Accepted for publication Apr. 7, 2003. [4] J.P. Clifford et al., IEEE Trans. Nanotechnol., 2(3):181, 2003. [5] J. Guo et al., Appl. Phys. Lett., 81(8):1486, 2002. [6] S. Heinze et al., Phys. Rev. Lett., 89(10):106801, 2002. [7] W.W. Lui et al., J. Appl. Phys., 60(5):1555, 1986.

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