Scaling theory put into practice: first-principles modeling of transport in doped silicon nanowires

TL;DR

This paper integrates scaling theory and density-functional theory to model transport in doped silicon nanowires, revealing universal conductance fluctuations and validating DMPK theory predictions in the diffusive regime.

Contribution

It presents a first-principles approach combining scaling theory with DFT to analyze transport crossover in doped silicon nanowires, highlighting universality and theoretical agreement.

Findings

Conductance trends are predicted by dopant scattering properties.

Sample-to-sample fluctuations are energy-dependent but doping-independent.

DMPK theory accurately describes diffusive transport in the studied nanowires.

Abstract

We combine the ideas of scaling theory and universal conductance fluctuations with density-functional theory to analyze the conductance properties of doped silicon nanowires. Specifically, we study the cross-over from ballistic to diffusive transport in boron (B) or phosphorus (P) doped Si-nanowires by computing the mean free path, sample averaged conductance <G>, and sample-to-sample variations std(G) as a function of energy, doping density, wire length, and the radial dopant profile. Our main findings are: (i) the main trends can be predicted quantitatively based on the scattering properties of single dopants; (ii) the sample-to-sample fluctuations depend on energy but not on doping density, thereby displaying a degree of universality, and (iii) in the diffusive regime the analytical predictions of the DMPK theory are in good agreement with our ab initio calculations.