Knudsen Diffusion in Silicon Nanochannels

TL;DR

This study investigates gas diffusion in silicon nanochannels, confirming classical Knudsen diffusion behavior over a wide range of conditions and analyzing deviations due to channel shape imperfections.

Contribution

The paper provides experimental validation of Knudsen diffusion in silicon nanochannels across a broad Knudsen number range and accounts for shape deviations affecting diffusivity.

Findings

Knudsen diffusion observed from Kn=10^2 to 10^7

Temperature dependence of D_He ~ sqrt(T) confirmed

Channel shape deviations reduce diffusivity compared to ideal tubes

Abstract

Measurements on helium and argon gas flow through an array of parallel, linear channels of 12 nm diameter and 200 micrometer length in a single crystalline silicon membrane reveal a Knudsen diffusion type transport from 10^2 to 10^7 in Knudsen number Kn. The classic scaling prediction for the transport diffusion coefficient on temperature and mass of diffusing species,D_He ~ sqrt(T), is confirmed over a T range from 40 K to 300 K for He and for the ratio of D_He/D_Ar ~ sqrt(m_Ar/m_He). Deviations of the channels from a cylindrical form, resolved with transmission electron microscopy down to subnanometer scales, quantitatively account for a reduced diffusivity as compared to Knudsen diffusion in ideal tubular channels. The membrane permeation experiments are described over 10 orders of magnitude in Kn, encompassing the transition flow regime, by the unified flow model of Beskok and Karniadakis.