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

Abstract

We introduce novel statistical simulation approaches to include the e ect of surface roughness in coupled mechanical, electronic and thermal processes in N/MEMS and semiconductor devices in the 10 nm - 1 m range. A model is presented to estimate roughness rms and autocorrelation L from experimental surfaces and edges, and subsequently generate statistical series of rough geometrical devices from these observable parameters. Using such series of rough electrodes under Holm's theory, we present a novel simulation framework which predicts a contact resistance of 80 m in MEMS gold-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 through statistical Monte Carlo iterations on percolative networks to derive a time to electro-thermal failure through electrical discharges in the gas insulating metal electrodes. The observable parameters L and are further integrated in semi-classical solutions to the electronic and thermal Boltzman transport equation (BTE), and we show roughness limited heat and electronic transport in rough semiconductor nanowires and nano-ribbons. In this scope, we model for the rst time electrostatically con ned nanowires, where a reduction of electron - surface scattering leads to enhanced mobility in comparison to geometrical nanowires. In addition, we show extremely low thermal conductivity in Si, GaAs, and Ge nanowires down to 0.1 W/m/K for thin Ge wires with 56 nm width and = 3 nm. The dependency of thermal conductivity in (D= )2 leads to possible application in the eld of thermoelectric devices. For rough channels of width below 10 nm, electronic transport is additionally modeled using a novel non-parabolic 3D recursive Green function scheme, leading to an estimation of reduced electronic transmission in rough semiconductor wires based on the quantum nature of charge carriers. Electronic and thermal simulation schemes are nally extended to such 2D semiconductor materials as graphene, where low thermal conductivity is approximated below 1000 W/m/K for rough suspended graphene ribbons in accordance with recent experiments.