Quantum calculations of the carrier mobility: Methodology, Matthiessen's rule, and comparison with semi-classical approaches

• Published in: Journal of applied physics Vol. 115; no. 5
• Main Authors: Niquet, Yann-Michel, Nguyen, Viet-Hung, Triozon, François, Duchemin, Ivan, Nier, Olivier, Rideau, Denis
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 07.02.2014
• Subjects: Applied physics; CARBON; CARRIER MOBILITY; COMPARATIVE EVALUATIONS; Condensed Matter; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Contact resistance; CORRELATIONS; COULOMB SCATTERING; Elastic scattering; GREEN FUNCTION; Green's functions; INTERFERENCE; Materials Science; Mathematical analysis; MATTHIESSEN RULE; NANOSCIENCE AND NANOTECHNOLOGY; Nanowires; PHONONS; Physics; Quantum transport; QUANTUM WIRES; ROUGHNESS; SILICON; Silicon films; Surface roughness; SURFACES; THIN FILMS
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/1.4864376

We discuss carrier mobilities in the quantum Non-Equilibrium Green's Functions (NEGF) framework. We introduce a method for the extraction of the mobility that is free from contact resistance contamination and with minimal needs for ensemble averages. We focus on silicon thin films as an illustration, although the method can be applied to various materials such as semiconductor nanowires or carbon nanostructures. We then introduce a new paradigm for the definition of the partial mobility μM associated with a given elastic scattering mechanism “M,” taking phonons (PH) as a reference (μM−1=μPH+M−1−μPH−1). We argue that this definition makes better sense in a quantum transport framework as it is free from long range interference effects that can appear in purely ballistic calculations. As a matter of fact, these mobilities satisfy Matthiessen's rule for three mechanisms [e.g., surface roughness (SR), remote Coulomb scattering (RCS) and phonons] much better than the usual, single mechanism calculations. We also discuss the problems raised by the long range spatial correlations in the RCS disorder. Finally, we compare semi-classical Kubo-Greenwood (KG) and quantum NEGF calculations. We show that KG and NEGF are in reasonable agreement for phonon and RCS, yet not for SR. We discuss the reasons for these discrepancies.