Stochastic Models of Surface Limited Electronic and Heat Transport in Metal and Semiconductor Contacts, Wires, and Sheets — Micro to Nano

摘要

We introduce novel statistical simulation approaches to include the e ect ofsurface roughness in coupled mechanical, electronic and thermal processesin N/MEMS and semiconductor devices in the 10 nm - 1 m range. A modelis presented to estimate roughness rms and autocorrelation L from experimentalsurfaces and edges, and subsequently generate statistical seriesof rough geometrical devices from these observable parameters. Using suchseries of rough electrodes under Holm's theory, we present a novel simulationframework which predicts a contact resistance of 80 m in MEMSgold-gold micro-contacts, for applied pressures above 0.3 mN on 1 m 1 m surfaces. The non-contacting state of such devices is simulated throughstatistical Monte Carlo iterations on percolative networks to derive a timeto electro-thermal failure through electrical discharges in the gas insulatingmetal electrodes. The observable parameters L and are further integratedin semi-classical solutions to the electronic and thermal Boltzman transportequation (BTE), and we show roughness limited heat and electronic transportin rough semiconductor nanowires and nano-ribbons. In this scope, wemodel for the rst time electrostatically con ned nanowires, where a reductionof electron - surface scattering leads to enhanced mobility in comparisonto geometrical nanowires. In addition, we show extremely low thermal conductivityin Si, GaAs, and Ge nanowires down to 0.1 W/m/K for thin Gewires with 56 nm width and = 3 nm. The dependency of thermal conductivityin (D= )2 leads to possible application in the eld of thermoelectricdevices. For rough channels of width below 10 nm, electronic transport isadditionally modeled using a novel non-parabolic 3D recursive Green functionscheme, leading to an estimation of reduced electronic transmission inrough semiconductor wires based on the quantum nature of charge carriers.Electronic and thermal simulation schemes are nally extended to such 2Dsemiconductor materials as graphene, where low thermal conductivity is approximatedbelow 1000 W/m/K for rough suspended graphene ribbons inaccordance with recent experiments.