Electron Transport in Highly Textured Metal Films Grown by Partially Ionized Beam Deposition
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ABSTRACT In principle, the resistivity of bulk FCC cubic materials should not depend on the orientation due to the fact that the conductivity tensor is single valued. However, we show that this conclusion is not valid for thin films. Deposition of highly oriented Al, Ag, and Cu films on amorphous substrates using the partially ionized beam (PIB) technique exhibit a resistivity which is strongly correlated with the texture, i.e., the tighter the texture, the lower the film resistivity. We model the film as an array of grains whose grain boundaries can be considered as delta function potentials for electron scattering and the strength of the potentials can be calculated from the measured resistivity of the films. On the other hand, the fiber texture distribution of the the films is obtained from X-ray pole figure measurements, and Monte-Carlo simulations are then performed using this data to determine the average dislocation density at the grain boundaries due to the grain to grain crystallographic mismatch. We show that the transmittance coefficient for electron scattering, and therefore the film resistivity, is a monotonically increasing function of the average dislocation density. We therefore conclude that the structure of grain boundaries in a thin film provides the necessary mechanism by which the resistivity of an FCC cubic metal can depend on the texture. INTRODUCTION One of the first researchers to identify that resistivity could depend on the size of 2 the sample was Fuchsl1l, whose work was later extended and corrected by Sondheimer.[ ] Mayadas and Shatzkes extended the work of Fuchs- Sondheimer to include the surfaces at the grain boundary.[31 The Mayadas-Shatzkes model consists of an array of grains whose boundaries are perpendicular to the electronic flow in the medium. Later Tellier, et. al., were to extend the results of the Mayadas-Shatzkes model into three dimensions.14 ' 5] Due to recent demands on interconnect technology, another look into resistivity mechanisms is warranted. With the increased control of film microstructure made possible by current deposition technology, it is necessary to explore the effects of microstructure on the resistivity. In keeping with the models presented by Mayadas-Shatzkes as well as Tellier, the film is assumed to be composed of grains which are cube-like in nature. The cube length is assumed to coincide with the average grain size in the film. In this manner, the grain size is not limited to that of the film thickness, but can instead be treated quite independently. In the case of a film with grains, the mean free path is due to the interactions of the electrons with lattice distortions, as well as the interactions with the grain boundaries. The simplest form for this effective mean free path is to assume that the two are independent scattering mechanisms. This is certainly not correct, however deviations from this rule are 4 not expected to be large. The mean free path due to grain boundaries alone is given by[ ' 5]
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