Electron scattering at surfaces and grain boundaries in thin Au films

The electron scattering at surfaces and grain boundaries is investigated using polycrystalline Au films deposited onto mica substrates. We vary the three length scales associated with: (i) electron scattering in the bulk, that at temperature T is characterized by the electronic mean free path in the bulk ℓ0(T); (ii) electron-surface scattering, that is characterized by the film thickness t; (iii) electron-grain boundary scattering, that is characterized by the mean grain diameter D. We varied independently the film thickness from approximately 50 nm to about 100 nm, and the typical grain size making up the samples from 12 nm to 160 nm. We also varied the scale of length associated with electron scattering in the bulk by measuring the resistivity of each specimen at temperatures T, 4 K < T < 300 K. Cooling the samples to 4 K increases ℓ0(T) by approximately 2 orders of magnitude. Detailed measurements of the grain size distribution as well as surface roughness of each sample were performed with a Scanning Tunnelling Microscope (STM). We compare, for the first time, theoretical predictions with resistivity data employing the two theories available that incorporate the effect of both electron-surface as well as electron-grain boundary scattering acting simultaneously: the theory of A.F. Mayadas and M. Shatzkes, Phys. Rev. 1 1382 (1970) (MS), and that of G. Palasantzas, Phys. Rev. B 58 9685 (1998). We eliminate adjustable parameters from the resistivity data analysis, by using as input the grain size distribution as well as the surface roughness measured with the STM on each sample. The outcome is that both theories provide a fair representation of both the temperature as well as the thickness dependence of the resistivity data, but yet there are marked differences between the resistivity predicted by these theories. In the case of the MS theory, when the average grain diameter D is significantly smaller than ℓ0(300) = 37 nm, the electron mean free path in the bulk at 300 K, the effect of electron-grain boundary scattering dominates the increase in resistivity of the film over the bulk, and the electronic mean free path, ℓD(4), computed from Drudeʹs model at 4 K, is similar to the grain diameter D. The increase in resistivity attributable to electron-grain boundary scattering can be as large as 220 at low temperatures, for samples made out of 12 nm grains. On the contrary, when D is significantly larger than ℓ0(300), then electron-surface scattering dominates the increase in resistivity. When D is comparable to ℓ0(300), there is a cross over where both electron-surface and electron-grain boundary scattering do contribute to increasing the resistivity of the film over that of the bulk. These predictions are in sharp contrast with those based upon the theory of Palasantzas, that predicts an increase in resistivity—attributable to electron-grain boundary/surface scattering—that turns out to be essentially unity regardless of the size of the grains making up the sample.