Size Effects and Piezoresistance in Metal Films

Abstract

Recently, it has been shown that the scattering of electrons by grain boundaries is the major contribution to the electrical resistivity ρ of fine grained metal films. Using this model for the thin film electrical resistivity, the strain coefficient of resistivity, η=Δρ/ρ/ΔL/L [ΔL/L is the longitudinal strain], can be calculated in terms of the film thickness t and a grain size parameter α. The value of η thus obtained decreases with increasing α (i.e., decreasing grain size). For values of α between 0.001 and 0.1, η decreases by about 10%; however, for α from 0.1 to 1, η decreases by about 50%. As α increases from 1, η decreases monotonically towards 0. The effect of film thickness is most apparent for α<0.1 and in the range of film thickness from 10 l0 to l0, a decrease of η of only about 5% occurs. For α>1 the effect of film thickness on η is negligible.