Fuchs-Sondheimer Research Articles

Functionalizing self-assembled monolayers to reduce interface scattering in ruthenium/dielectric for next-generation microelectronic interconnects

As the number of transistor increases in modern devices, the resistivity of metal lines increases with the downscaling of the vias dimension due to the increased in surface scattering of electrons. Herein, we evaluated the electrical performance and the adhesion strength of the Ru/SiO2 substrate upon functionalizing with benzyliminetriethoxysilane (BITES) and aminoproyltriethoxysilane (APTES) self-assembled monolayers (SAMs)s at the Ru/SiO2 interface. The covalent bonding and retention of the SAM film on the SiO2 surface were characterized via angle-resolved X-ray Photoelectron Spectroscopy (AR-XPS) and Time-of-Flight Secondary Ion Mass Spectrometry (Tof-SIMS), respectively. According to the Fuchs–Sondheimer (FS) model and scratch test, the specularity parameter and the adhesion strength of the Ru/BITES/SiO2 simultaneously improved after thermal annealing compared to the non-functionalized Ru/SiO2 substrate. The effect of different SAM’s terminal groups (amine and benzylimine) on the electron scattering behavior was investigated based on the formation of an interface dipole upon chemisorption of organic molecules on the metal film. Our results indicate that SAM with the benzylimine terminal group formed a larger positive dipole at the SAM layer of the Ru/BITES/SiO2 interface compared to the Ru/APTES/SiO2, leading to an increased in specular electron scattering events and, thus an enhanced electrical performance of the Ru/BITES/SiO2.

Temperature dependence of resistivity increases induced by thiols adsorption in gold nanosheets

By utilizing stable thiol self-assembled monolayers (SAMs) on gold (Au) nanosheets, we investigated the temperature dependence of the amount of resistivity increases by SAM modification. increased with increasing temperature from 5 to 375 K in all the measured nanosheets for various thicknesses (9–20 nm). We consider from the DFT calculation that the temperature dependence originates from unoccupied states of sulfur atoms above the Fermi level of Au. The available unoccupied states increase at higher temperatures, which enhances scattering rates and thus increases the resistivity. Furthermore, we calculated the temperature dependence of using the Bloch–Grüneisen theory and Fuchs–Sondheimer (FS) model. Based on the results, we conclude that for ultra-thin metal films, the temperature-dependent specularity parameter which represents the fraction of electrons scattered specularly should be introduced into the conventional FS model to predict over a wide temperature range.

Impact of post annealing on the electrical properties of silver nanofilms

This paper reports on the growth of nanostructures of silver films prepared by thermal evaporation in vacuum. We focused on the effect of annealing on the silver films’ electrical properties. The resistance of the sample was measured by the standard four-probe technique. The electrical resistivity data pertaining to the impact of annealing was analyzed with the help of Fuchs-Sondheimer (F-S) and Mayadas-Shatzkes (M-S) theories.

Morphologies, Young's Modulus and Resistivity of High Aspect Ratio Tungsten Nanowires.

High aspect ratio tungsten nanowires have been prepared by selective dissolution of Nickel-aluminum-tungsten (NiAl−W) alloys which were directionally solidified at growth rates varying from 2 to 25 μm/s with a temperature gradient of 300 K·cm−1. Young’s modulus and electrical resistivity of tungsten nanowires were measured by metallic mask template method. The results show that the tungsten nanowires with uniform diameter and high aspect ratio are well aligned. The length of tungsten nanowires increases with prolongation of etching time, and their length reaches 300 μm at 14 h. Young’s modulus of tungsten nanowires is estimated by Hertz and Sneddon models. The Sneddon model is proper for estimating the Young’s modulus, and the value of calculating Young’s modulus are 260–460 GPa which approach the value of bulk tungsten. The resistivity of tungsten nanowires is measured and fitted with Fuchs−Sondheimer (FS) + Mayadas−Shatzkes (MS) model. The fitting results show that the specific resistivity of W nanowires is a litter bigger than the bulk W, and its value decreases with decreasing diameter.

MoS2 for Enhanced Electrical Performance of Ultrathin Copper Films.

Copper nanowires are widely used as on-chip interconnects due to their superior conductivity. However, with aggressive Cu interconnect scaling, surface scattering of electrons drastically increases the electrical resistivity. In this work, we have studied the electrical performance of Cu thin films deposited on different materials. By comparing the thickness dependence of Cu films' resistivity on MoS2 and SiO2, we have demonstrated that MoS2 can be used to enhance the electrical performance of ultrathin Cu films due to improved specular surface scattering by up to 40%. By fitting the experimental data with the theoretical Fuchs-Sondheimer (FS) model, we have determined the specularity parameter at the Cu/MoS2 interface to be p ≈ 0.4 at room temperature. Furthermore, first principle calculations based on density functional theory (DFT) indicate that the localized density of states (LDOS) at the Cu/amorphous SiO2 interface is larger than the LDOS at the Cu/MoS2 interface, which is believed to be responsible for the higher resistivity in the Cu thin films that are deposited on SiO2 substrates. Our results suggest that MoS2 may serve as a performance enhancer for future generations of Cu interconnects.

Impact of substrates on the electrical properties of thin chromium films [Online First

Objective: We studied the impact of substrates on the electrical properties of thin chromium films. Substrates may serve many purposes, such as to define orientation, to conduct electrical current in vertical devices, as a gate in transistors, etc. The thickness range of the chromium films grown on both substrates was (3.5-70) nm. Methods and materials: We used Fuchs-Sondheimer(FS) and Mayadas-Shatzkes(MS) theories to analyze electrical resistivity data for chromium(Cr) films grown on both substrates simultaneously by thermal evaporation in vacuum, under identical deposition conditions. Results and discussion: The infinitely thick film resistivity (ρ0), conduction electron mean free path(l), specularity parameter(p), scattering power of the grain boundary(α') and grain boundary reflection coefficient(R') were found to depend upon the nature of the substrate and the binding force between them and evaporated chromium atoms. The growth and microstructure of the chromium films were examined using atomic force microscopy (AFM) and scanning electron microscopy (SEM). Conclusions: Our experimental data exactly fits with the MS theory in the entire thickness range grown for the chromium films deposited on both the substrates. Examination of film structure by SEM indicated that the films consist of grains of relatively pure chromium of different sizes, and depends upon deposition conditions and parameters, which are important factors that dictate the structural properties of the films.

Resistivity size effect in epitaxial Ru(0001) layers

Epitaxial Ru(0001) layers are sputter deposited onto Al2O3(0001) substrates and their resistivity ρ measured both in situ and ex situ as a function of thickness d = 5–80 nm in order to quantify the resistivity scaling associated with electron-surface scattering. All layers have smooth surfaces with a root-mean-square roughness <0.4 nm, exhibit an epitaxial relationship with the substrate: Ru[0001]||Al2O3[0001] and Ru[101¯0]||Al2O3[112¯0], and show no resistance change upon air exposure, suggesting negligible resistivity contributions from geometric surface roughness and grain boundary scattering and negligible changes in the surface scattering specularity p upon oxygen exposure. The room temperature ρ vs d data are well described by the semiclassical Fuchs-Sondheimer (FS) model, indicating a bulk electron mean free path λ = 6.7 ± 0.3 nm. However, the measured ρo × λ product at 77 K is 43% lower than at 295 K, suggesting a breakdown of the FS model and/or a thickness-dependent electron-phonon coupling and/or a temperature- or environment-dependent p. Transport simulations employing the ruthenium electronic structure determined from first-principles and a constant relaxation time approximation indicate that ρ is strongly (by a factor of two) affected by both the transport direction and the terminating surfaces. This is quantified with a room temperature effective mean free path λ*, which is relatively small for transport along the hexagonal axis independent of layer orientation (λ* = 4.3 nm) and for (0001) terminating surfaces independent of transport direction (λ* = 4.5 nm), but increases, for example, to λ* = 8.8 nm for (112¯0) surfaces and transport along [11¯00]. Direct experiment-simulation comparisons show a 12% and 49% higher λ from experiment at 77 and 295 K, respectively, confirming the limitations of the semi-classical transport simulations despite correct accounting of Fermi surface and Fermi velocity anisotropies. The overall results demonstrate a low resistivity scaling for Ru, suggesting that 10 nm half-pitch Ru interconnect lines are approximately 2 times more conductive than comparable Cu lines.

Surface roughness dependence of the electrical resistivity of W(001) layers

The resistivity ρ of epitaxial W(001) layers grown on MgO(001) at 900 °C increases from 5.63 ± 0.05 to 27.6 ± 0.6 μΩ-cm with decreasing thickness d = 390 to 4.5 nm. This increase is due to electron-surface scattering but is less pronounced after in situ annealing at 1050 °C, leading to a 7%–13% lower ρ for d < 20 nm. The ρ(d) data from in situ and ex situ transport measurements at 295 and 77 K cannot be satisfactorily described using the existing Fuchs-Sondheimer (FS) model for surface scattering, as ρ for d < 9 nm is larger than the FS prediction and the annealing effects are inconsistent with a change in either the bulk mean free path or the surface scattering specularity. In contrast, introducing an additive resistivity term ρmound which accounts for surface roughness resolves both shortcomings. The new term is due to electron reflection at surface mounds and is, therefore, proportional to the ballistic resistance times the average surface roughness slope, divided by the layer thickness. This is confirmed by a measured linear relationship between ρmound and σ/(Ld), where the root-mean-square roughness σ and the lateral correlation length L of the surfaces are directly measured using atomic force microscopy and X-ray reflectivity.

Surface Morphology and Electrical Resistivity in Polycrystalline Au/Cu/Si(100) System

This work describes the analysis of morphology and electrical resistivity (ρ) obtained in the Au/Cu/Si system. The Au/Cu bilayers were deposited by thermal evaporation technique with thicknesses from 50 to 250 nm on SiOx/Si(100) substrates. The Au : Cu concentration ratio of the samples was of 25 : 75 at%. The bilayers were annealed into a vacuum oven with argon atmosphere at 660 K for one hour. The crystalline structures of AuCu and CuSi alloys were confirmed by X-ray diffraction analysis. The scanning electron microscopy (SEM), the atomic force microscopy (AFM), and the energy dispersive spectroscopy (EDS) were used to study the morphology, final thickness, and the atomic concentration of the alloys formed, respectively. The four-point probe technique was used to measure the electrical resistivity (ρ) in the prepared alloys as a function of thickness. The ρ value was measured and it was numerically compared with the Fuchs–Sondheimer (FS) and the Mayadas–Shatzkes (MS) models of resistivity. Results show values of electrical resistivity between 0.9 and 1.9 μΩ-cm. These values are four times smaller than the values of the AuCu systems reported in literature.

Conductivity size effect of polycrystalline metal nanowires

It is well known that the conductivity of metal nanowires decreases with the wire diameter. This size effect was first studied for metal thin films when the film thickness approaches the electron mean free path. Fuchs & Sondheimer (FS) pointed out that the external surface scattering of the electrons contributes to the conductivity decrease. Mayadas and Shatzkes (MS) pointed out that the grain boundary scattering plays a major role for polycrystalline thin films. As is clear that nanowires are 2-d constrained instead of 1-d for thin film, so the size effect would be more eminent. However, today the mostly used physical model for the conductivity of metal nanowires is still the MS theory. This paper proposes a more complete model suitable for circular cross-section polycrystalline metal nanowires, which takes into account of background scattering, external surface scattering, as well as grain boundary scattering. Comparison with experiment data showed that our model can well explain the conductivity size effect of polycrystalline metal nanowires.

Current Transport in Graphene/Copper Hybrid Nano Ribbon Interconnect: A First Principle Study

In search of emerging materials replacement of copper interconnect in nanometer CMOS technology nodes, graphene (G) and carbon nanotubes (CNT) have been studied intensively. There is also ongoing research to find hybrid materials, which can have better thermal and electrical conductivity [1]. Recently, reduction in temperature has been observed in graphene encapsulated copper wires [2]. It was argued that this excellent thermal property is inherent to copper not because of graphene. During graphene deposition process, Cu becomes annealed with larger grains. In addition, graphene works as a barrier layer for copper ion to diffuse into dielectric. Motivated by recent experiments we have studied theoretically G/Cu structure in bulk and in one-dimension (1D) as next generation wires for nano-electronic applications. Our purpose is to understand this structure and to study why it outperforms graphene only or Cu only interconnect. In this paper, we report density of states (DOS), current-voltage relation (I-V), and resistance (R) of G/Cu nano ribbon interconnect.We used density functional theory (DFT) with pseudo- potential technique to study electronic band structure within Quantum-Espresso (QE) code. For ballistic transport study, we used Landauer-Buttiker (LB) formalism within Wannier90 Module [3]. We have considered a one-dimensional slice of G/Cu interconnect of width 0.6nm, height 0.8nm and length 10nm. Single layer of graphene is deposited on top of three atomic layers of Cu {111}. Cu {111} is chosen because this plane is closest to graphene lattice within 2% lattice mismatch. Among these three atomic layers, bottom two layers were fixed to their bulk lattice position to represent bulk atoms. Top Cu layer and graphene layer were relaxed to find minimum force position. After obtaining atomic positions from relaxation calculations in QE, we performed self-consistent field calculation and band structure calculation. Bloch states obtained from QE were used as an input for transport calculation in Wannier90 Code. Due to high computational cost, we have limited our study to a 10nm long wire which represent a short local interconnect and a good candidate to study ballistic transport. We believe this geometry will at least serve present purpose to compare performances with graphene only interconnect. I-V characteristics of graphene interconnect and graphene on copper interconnect have been compared. Being one-dimensional wire, we have observed several stairs like and piece wise linear relationships. At zero bias, resistance is found to be the same as quantum resistance for single electronic channel, which is ~h/2e2. Since wire length 10nm is smaller than Cu mean free path (40nm), one should not compare resistivity of G/Cu with Cu only interconnect based on Fuchs-Sondheimer (FS) and Mavadas-Shatzkes (MS) models. For this G/Cu we found resistivity 1.25x10-6 Ω-m, which is one tenth of Cu-bulk resistivity. It is expected by FS & MS theory that Cu resistivity increases with decrease of width. However, in ballistic transport regime FS & MS theories were not applicable. Hence, we have used LB formalism. For comparison, we have studied same geometry for graphene only interconnect using same methodology. From DOS, it is apparent that there is no energy states available near Fermi energy for graphene only interconnect. This is why in I-V characteristics no current is observed near 0V. On other hand, hybrid structure shows better conductivity at low bias than graphene only interconnect. Graphene only nanoribbon might better perform as device not as interconnect. This calculation is useful to understand electrical performances of various nanostructures and to find true contender of next generation interconnect. Acknowledgement: Part of the work is supported by the United States Air Force Research Laboratory under agreement number FA9453-10-1-0002. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.

Thermal conductivity of individual silicon nanoribbons.

The thermal conductivities of two groups of silicon nanoribbons of ∼20 and ∼30 nm thickness and various widths have been measured and analyzed through combining the Callaway model and the Fuchs-Sondheimer (FS) reduction function. The results show that while the data for the ∼30 nm thick ribbons can be well-explained by the classical size effect, the measured thermal conductivities for the ∼20 nm thick ribbons deviate from the prediction remarkably, and size effects beyond phonon-boundary scattering must be considered. The measurements of the Young's modulus of the thin nanoribbons yield significantly lower values than the corresponding bulk value, which could lead to a reduced phonon group velocity and subsequently thermal conductivity. This study helps to build a regime map for thermal conductivity versus nanostructures' surface-area-to-volume ratio that clearly delineates two regions where size effects beyond the Casimir limit are important or not important.

Resistivity of epitaxial copper nanolines with trapezoidal cross-section

The resistivity of epitaxial Cu nanolines with line width ranging from 20 to 180nm and line height from 40 to 50nm was measured using a four-point probe technique. The Cu nanolines were fabricated using ebeam lithography with a polymethyl methacrylate bilayer resist system for improved line edge smoothness. The cross-section profile of the lines was examined using the focused ion beam milling technique. The results indicate that the cross-section should be more accurately described as trapezoidal rather than as rectangular. Using the trapezoidal profile, the electrical resistivity was calculated from the measured resistance data. Modeling based on the Fuchs–Sondheimer (FS) theory using the trapezoidal profile was also carried out. The results were compared with the experimentally calculated resistivity data. For Cu lines with line width less than 30nm, the measured resistivity was shown to be up to 20% higher than the value predicted by the FS theory. Further examination of Cu lines using atomic force microscopy and scanning electron microscopy was conducted to extract the surface roughness and line edge roughness information. Their contribution to the resistivity increase was estimated to be only up to 3% for the Cu nanolines fabricated, which did not significantly contribute to the overall resistivity for Cu lines with line width less than 30nm. Other possible factors affecting the resistivity of the Cu nanolines were also discussed, including the oxide formation on the surface of the Cu lines.

Effective electron mean free path in TiN(001)

The measured resistivity ρ of smooth stoichiometric epitaxial TiN(001) is 13 and 3.0 μΩ cm at 298 and 77 K for bulk layers but is 8 and 25 times higher when the layer thickness d is reduced to 2 nm. The increase in ρ with decreasing d is attributed to diffuse electron-surface scattering and is well described by the classical Fuchs-Sondheimer (F-S) model. This is unexpected because the F-S model is based on the nearly free electron model, while TiN exhibits a highly non-spherical Fermi surface and three bands crossing the Fermi-level. The measured room temperature effective electron mean free path λ for bulk scattering is 45 ± 4 nm, which is an order of magnitude larger than the free-electron prediction. This deviation is attributed to ∼93% of charge transport in TiN being due to two slightly filled bands which represent only 4% of conduction electrons. The F-S model is applicable to TiN because these two bands are nearly parabolic and nearly degenerate, yielding a single value for λ, which is estimated based on the published band structure to be 49 nm, in excellent agreement with the experimental 45 nm. These results demonstrate that the F-S model is applicable to metals with non-spherical Fermi-surfaces as long as the charge transport is dominated by a single (or multiple degenerate) band(s).

Electron mean free path of tungsten and the electrical resistivity of epitaxial (110) tungsten films

This work describes a study of the classical electrical resistivity size effect in tungsten. The important length scale for this size effect is the isotropic average electron mean free path (EMFP), which was determined to be 19.1 nm for W at 293 K by employing density functional theory. To explore the size effect experimentally, (110) oriented epitaxial W films with thicknesses ranging from 9.8 to 299.7 nm were prepared by sputter deposition onto ($11\overline{2}0$) Al${}_{2}$O${}_{3}$ substrates at 520 \ifmmode^\circ\else\textdegree\fi{}C followed by postdeposition annealing in Ar-4$%$H${}_{2}$ at 850 \ifmmode^\circ\else\textdegree\fi{}C. Film resistivities were measured at room temperature and at liquid He temperature. The Fuchs-Sondheimer (FS) surface scattering model with a low specularity parameter ($p$ $=$ 0.11) was shown to provide a good description of the film resistivity as a function of film thickness. Further, it is shown that an upper bound to the EMFP cannot be established by fitting resistivity data to the FS model, whereas a lower bound can be assessed.

Electron scattering at surfaces and grain boundaries in Cu thin films and wires

The electron scattering at surfaces, interfaces, and grain boundaries is investigated using polycrystalline and single-crystal Cu thin films and nanowires. The experimental data is described by a Fuchs--Sondheimer (FS) and Mayadas--Shatzkes (MS) model that is extended to account for the large variation in the specific resistivity of different grain boundaries as well as distinct top and bottom surfaces with different scattering specularity $p$. Textured polycrystalline Cu(111) thin films with thickness $d$ $=$ 25--50 nm are deposited on a stack of 7.5-nm Ta on SiO${}_{2}$/Si(001). Subsequent annealing results in small-grain (SG) thin films with an average grain size $\overline{D}$ that increases from 90 to 120 nm with increasing $d$. Corresponding large-grain (LG) thin films with $\overline{D}$ $=$ 160--220 nm are obtained by depositing 100--200-nm-thick films, followed by an in-situ anneal and a subsequent etch to match the thickness of the SG samples. Nanowires are fabricated from the SG and LG thin films using a subtractive patterning process, yielding wire widths of 75--350 nm. Single-crystal and LG layers exhibit a 18--22$%$ and 10--15$%$ lower resistivity than SG layers, respectively. The resistivity decrease from SG to LG Cu nanowires is 7--9$%$. The thickness and grain size dependence of the resistivity of polycrystalline and single-crystal Cu layers is well described by an exact version of the existing FS $+$ MS model but is distinct from the commonly used approximation, which introduces an error that increases with decreasing layer thickness from 6.5$%$ for $d$ $=$ 50 nm to 17$%$ for $d$ $=$ 20 nm. The case of nanowires requires the FS $+$ MS model to be extended to account for variation in the grain boundary reflection coefficient $R$, which effectively increases the overall resistivity by, for example, 16$%$ for 50 \ifmmode\times\else\texttimes\fi{} 45 nm${}^{2}$ wires. The overall data from single and polycrystalline Cu layers and wires yields $R$ $=$ 0.25 \ifmmode\pm\else\textpm\fi{} 0.05, and $p$ $=$ 0 at Cu-air and Cu-Ta interfaces.

Height Dependent Resistivity of Copper Interconnects in the Size Effect

ABSTRACTWe investigated the copper grain size dependence on the interconnect line height using the EBSD (Electron Back Scattering Diffraction) pattern method. In our grain size measurements, we excluded the twin boundaries because of its small contribution to the electron scattering. Our experiments showed that the average grain size of a 70 nm-high line was about 24% smaller than for a 190 nm-high line.We estimated the grain boundary scattering components by the Fuchs-Sondheimer (FS) and the Mayadas-Shatzkes (MS) models including the line height dependence of the grain size parameter (d). In order to evaluate precisely the influence of height dependence of grain size in the FS and MS models, we also determined the surface scattering coefficient of the Ta/Cu and SiC/Cu interfaces by an independent experiment.From this, we found that grain boundary scattering components became approximately 32% larger for the 70 nm-wide line when the line height dependence of the grain size was taken into consideration.

The electrical and structural properties of gold films and mercury-covered gold films

The electrical properties and morphology of polycrystalline gold films prepared on alumina and silica substrates and epitaxial thin gold films deposited on mica are examined as a function of film thickness, substrate, structure and mercury adsorption. The resistivities were examined for these films and compared with an ideal, specular gold film in accordance with the Fuchs-Sondheimer (FS) model. According to the FS model, specular films should demonstrate optimum response to adsorbates which produce diffuse rather than specular conduction electron scatter. When the as-prepared polycrystalline films were exposed to mercury, the resistance increased for both the gold-alumina and gold-silica films, and it was found that the gold-alumina films had the greatest response and showed a pronounced thickness dependence. This is due to a rougher, more porous film produced on the polycrystalline alumina substrate which promotes diffusion of the mercury into the films' grain boundaries and the gold bulk. When the epitaxial gold films were exposed to mercury, the resistivity oscillated with increasing mercury coverage. This may be attributed to the formation of successive monolayer coverage, and a resulting oscillatory change in specularity.

Étude de l'adsorption électrochimique de l'oxygène sur des lames minces d'or par la mesure de leur résistance électrique

The electrical resistance changes of thin gold film electrodes of preferential orientation [111] with film thickness and potential have been studied. The applicability of the Fuchs-Sondheimer (FS) relation to the decrease of resistance observed at the first negative polarization and the first few potential sweeps for different thicknesses have shown that this phenomenon is due to a surface process, interpreted as a cleaning of the electrodes. The resistance changes observed during the electrochemical adsorption and desorption of oxygen also obey the FS relation. The analysis of the resistance variation with the charge exchanged during these reactions has allowed us to show that the electrochemical adsorption of oxygen, on these gold films occurs by a two-dimensional island mechanism with formation of different structures of the surface layer. The values of the resistivity change caused by the adsorption of 1% oxygen atoms (with respect to the total number of metal atoms in the films) at low coverage have been compared with those observed in other systems (metal-gas, metal-metal).

Electron transport properties of copper films. II. Thermoelectric power

Thermoelectric power (TEP) of as-deposited and annealed polycrystalline and epitaxially grown copper films of thickness 100–5000 Å has been measured. The TEP increases with the film thickness to reach a saturation value at about 3000 Å. The thickness dependence decreases markedly with increasing annealing temperature and also with increasing temperature of deposition. The saturation value of the TEP of as-deposited films is about 1.5 times the bulk value of copper and decreases rapidly with annealing to approach the single-crystal bulk value. In sharp contrast to the behavior of the TEP, the resistivity and its temperature coefficient and the carrier concentration of the same copper films exhibit little size effects and insignificant changes due to annealing for thicknesses larger than 1000 Å. The observed thickness dependence of the TEP of unannealed and annealed films shows no agreement with the Fuchs-Sondheimer (F-S) theory. Further, there is no correlation between the thickness dependence of the TEP and the temperature coefficient of resistivity as expected on the basis of the F-S theory. Since the thickness variation of the TEP changes markedly with annealing, the observed dependence is not a genuine mean free path effect. The observed linear dependence of the TEP on the inverse of the film thickness (as expected from the F-S theory) is totally accidental and, therefore, physically meaningless values of U= (∂ lnl/∂ lnE)EF are obtained from the slopes of the lines. Arguments have been advanced to suggest that the observed thickness dependence of the TEP can be understood only in terms of the effect of a large thickness-dependent concentration of structural defects frozen in the metal films. The defect-induced changes in the TEP would be caused by the distortions in the Fermi surface and, hence, changes in the energy dependence of the mean free path or relaxation time at the Fermi surface.