Analytical expression for the total electrical conductivity of unannealed and annealed metal films

Simple analytical expression for the size effect in thin metal wires

“…4s(0, 4)) = 2alcos 4)l[sin 01 I 1 + p (4) 2(1 --p) without any limitation in the value of p, as recently demonstrated [6].…”

“…exhibiting the general form of the Cottey m.f.p, gives an interpretation for the calculation of the size effects in the pioneering work of Sondheimer [5], provided that an adequate algebraic representation of the alterations in the electron flow (due to the scattering at an external surface) be used. Moreover, the scattering phenomena due to phonons and external surfaces may be regarded as independent [4], without altering the agreement between the data derived from the FuchsSondheimer model [5] and from the extended Cottey model [4] within an inaccuracy of less than 6%, whatever the electronic specular reflection coefficient at the film surface may be.Consequently, the multidimensional models of conduction, which implement mean free paths related to any source of scattering, can be used for calculating any transport property of annealed and unannealed metal films, as recently discussed [6].In the case of thin wires, previous theoretical studies [7][8][9] have proposed general equations which could not be integrated [8], except in some limiting cases [8,9]. The aim of this letter is to analyse the size effects in thin wires in terms of Cottey-type mean free path in order to simplify the expression of the electrical conductivity.…”

Study of the size effects in the electrical resistivity of ultrathin (<Cu 40 nm) films in the framework of the statistical conduction models

“…Previous works [10] have shown that a unique equation can be used for describing the electrical conductivity of thin metal films, by taking into account simultaneously the scattering due to phonons, external surfaces and grain boundaries. It has been established [10] that whatever the film structure and the roughness of the film surface, the electrical conductivity f , is given by [10,14]:…”

“…Starting from the similar assumption made by Mayadas and Shatzkes [8] and taking into account the above features in the three dimensional models [9,10], it is assumed that the grain boundaries in polycrystalline metal films can be represented by three arrays of mutually perpendicular planar potentials with rough surfaces oriented perpendicular to the X-, Y-and Z-axes, respectively. The current is due to electron which has been transmitted through a large number of grain boundaries and it is assumed that T is the fraction of electrons which are specularly transmitted through the grain boundaries whilst for the remainder the free path is as usual terminated by collision at the boundary.…”

Comment on "Reinterpretation of the thickness-dependent conductivity of thin platinum films"

“…The reinterpretation of our experimental data by Messaadi et al [1] was done using the model published by them [1,4,5] and based only on the replotting of data given in [2] in a 0r (film resistivity) against 1/d (d = thickness) plot. A linear dependence was established "with exception of two or three experimental points, only".…”