The continuous reductions in feature sizes in the semiconductor industry have generated much interest in novel one-dimensional nanostructures such as semiconductor nanowires. Very thin silicon nanowires (SiNWs) with diameters below 2 nm have been synthesized [1] and several SiNWs based transistors have been demonstrated [2]. Due to reduced acoustic phonon scattering in quasi one-dimensional systems, long coherence lengths might be possible even at room temperature [3] but, on the other hand, scattering by defects will be increasingly important with decreasing wire diameters. At the same time sample-to-sample variations become a crucial issue: when the device length and the mean free path are comparable, and shorter than the coherence length, variations of the positions of the individual dopant atoms can affect the conductance of the wire significantly. Accurate models of the electronic transport properties in nanowires are clearly desirable.
In this work we combine the ideas of scaling theory and universal conductance fluctuations with density-functional theory and Landauer formalism to analyze the conductance properties of H-passivated SiNWs [4,5]. Specifically, we study the cross-over from ballistic to diffusive transport in B or P doped SiNWs by computing the sample averaged conductance , mean free path le, and sample-to-sample variations std(G) as a function of Fermi energy, doping density, wire length (L), and the radial dopant profile. We show that all these quantities can be understood and accurately estimated from the scattering properties of the single dopants, implying that relatively simple calculations are sufficient in practical device modelling. The sample-to-sample fluctuations at a given energy and dopant type vary with L/le in a universal way independently on the dopant concentration, and in the diffusive regime for wire length L>le, we observe good agreement with analytical predictions.
[1] D.D.D. Ma et al. , Science 299, 1874 (2003).
[2] Y.Cui et al. Nano Lett. 3, 149 (2003).
[3] W.Lu et al., Proc. Natl. Acad. Sci. USA 102, 10046 (2005).
[4] T.Markussen et al., Phys. Rev. B 74, 245313 (2006).
[5] T.Markussen et al., submitted (2007).
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