Claudio Arenas

Surface roughness and surface-induced resistivity of gold films on mica: influence of roughness modelling

We report measurements of the temperature dependent resistivity (T ) of a gold film 70 nm thick deposited on mica preheated to 300 °C in UHV, performed between 4 K and 300 K, and measurements of the surface topography of the same film performed with a scanning tunnelling microscope (STM). From the roughness measured with the STM we determine the parameters (r.m.s. amplitude) and (lateral correlation length) corresponding to a Gaussian and to an exponential representation of the average autocorrelation function (ACF). We use the parameters and determined via STM measurements to calculate the quantum reflectivity R , and the temperature dependence of both the bulk resistivity 0 (T ) and of the increase in resistivity (T ) = (T ) - 0 (T ) induced by electron-surface scattering on this film, according to a modified version of the theory of Sheng, Xing and Wang recently proposed (Munoz et al 1999 J. Phys.: Condens. Matter 11 L299). The resistivity 0 in the absence of surface scattering predicted for a Gaussian representation of the ACF is systematically smaller than that predicted for an exponential representation of the ACF at all temperatures. The increase in resistivity induced by electron-surface scattering predicted for a Gaussian representation of the average ACF data is about 25% larger than the increase in resistivity predicted for an exponential representation of the ACF data.

Size effects and charge transport in metals: Quantum theory of the resistivity of nanometric metallic structures arising from electron scattering by grain boundaries and by rough surfaces

We discuss recent progress regarding size effects and their incidence upon the coefficients describing charge transport (resistivity, magnetoresistance, and Hall effect) induced by electron scattering from disordered grain boundaries and from rough surfaces on metallic nanostructures; we review recent measurements of the magneto transport coefficients that elucidate the electron scattering mechanisms at work. We review as well theoretical developments regarding quantum transport theories that allow calculating the increase in resistivity induced by electron-rough surface scattering (in the absence of grain boundaries) from first principles—from the parameters that describe the surface roughness that can be measured with a Scanning Tunnelling Microscope (STM). We evaluate the predicting power of the quantum version of the Fuchs-Sondheimer theory and of the model proposed by Calecki, abandoning the method of parameter fitting used for decades, but comparing instead theoretical predictions with resistivity m...

Surface-induced resistivity of gold films on mica: comparison between the classical and the quantum theory

We report an extension of the theory of Sheng, Xing and Wang (SXW) (Sheng L, Xing D Y and Wang Z D 1995 Phys. Rev. B 51 7325), which permits the calculation of size effects from the statistical properties that characterize the surface on a microscopic scale, for samples in which the average height-height autocorrelation function (ACF) is described either by a Gaussian or by an exponential. We also report measurements of the topography of a gold film deposited on a mica substrate using a scanning tunnelling microscope (STM) on a gold sample 70 nm thick deposited under ultrahigh vacuum on a mica substrate preheated to 300 °C. From the STM images we compute the average ACF which characterizes the surface of the film on the scale of 10 nm × 10 nm, and determine by least-squares fitting the r.m.s. amplitude and the lateral correlation length corresponding to a Gaussian and to an exponential that best represent the ACF data. Using the modified SXW (mSXW) theory and a Gaussian and an exponential representation of the ACF data, we calculate the quantum reflectivity R characterizing the interaction between the electrons and the surface, and the decrease in conductivity attributable to electron-surface scattering, for mean free paths 2.5 nm 1000 nm. We compare the predictions of the classical Fuchs-Sondheimer (FS) model for the average quantum reflectivity R = R, calculated with the mSXW model, with the predictions of the quantum theory, using both the Gaussian and the exponential representation of the ACF. We find that predicted by FS theory for R = R exceeds that predicted by the quantum mSXW theory, by an amount that increases with increasing . This discrepancy can be traced to the angular dependence of the quantum reflectivity R[cos()]. We also find that the decrease in conductivity predicted by mSXW theory for a Gaussian representation of the data is larger than that predicted for an exponential representation of the same ACF data. We attribute this to the fact that the reflectivity R is determined by the Fourier transform of the ACF, and the Gaussian and the exponential that best represent the ACF data exhibit Fourier transforms that are similar in the regions where k~1, but are different in the regions where k 1 (k: wave vector).

Surface roughness and surface-induced resistivity of gold films on mica: influence of the theoretical modelling of electron-surface scattering

We analyse the thickness and temperature dependence of the resistivity for several gold films on mica reported by Sambles, Elsom and Jarvis (SEJ: Sambles J R, Elsom K C and Jarvis J D 1982 Phil.?Trans.?R.?Soc.?A 304 365). Data analysis proceeds according to an iteration procedure proposed recently (Munoz R C, Concha A, Mora F, Espejo R, Vidal G, Mulsow M, Arenas C, Kremer G, Moraga L, Esparza R and Haberle P 2000 Phys.?Rev.?B 61 4514; Munoz R C, Vidal G, Kremer G, Moraga L, Arenas C and Concha A 2000 J.?Phys.:?Condens.?Matter 12 2903), that permits the calculation of the temperature-dependent bulk conductivity ?0(T) from the parameters ? (r.m.s.?roughness amplitude) and ? (lateral correlation length) that describe the surface roughness. To assess the influence of the theoretical modelling of the electron-surface scattering, we use the theory of Tesanovic, Jaric and Maekawa (TJM), the theory of Trivedi and Aschroft (TA) and the modified theory of Sheng, Xing and Wang (mSXW). With the parameters ? and ? measured for a 70?nm gold film deposited on mica, under similar conditions of evaporation, all three models reproduce approximately the thickness and temperature dependence of the resistivity (between 4?K and 300?K) of the SEJ films without using any adjustable parameter. Agreement between theory and experiment improves according to the sequence TJM, TA, mSXW.

Surface Roughness and Surface-Induced Resistivity of Thin Gold Films On Mica

Abstract. We report measurements of the surface topography of a 70 nm gold film deposited on mica preheated to 300 oC in UHV performed with a Scanning Tunneling Microscope (STM). From these measurements we determine the rms roughness amplitude and the lateral correlation length characterizing the average height-height autocorrelation function on a nanometric scale.We also report a method of analyzing thin film resistivity data that departs sharply from the traditional method of parameter fitting. This method allows the determination of the resistivity and mean free path characterizing the bulk from the measured thin film resistivity by means of a new iteration procedure, that uses as input data the roughness parameters experimentally determined with the STM and any of the available quantum transport theories, without adjustable parameters. We examine the resistivity data reported by Sambles et al. [Philos. Trans. R. Soc. London, Ser. A304, 365 (1982)] for gold films deposited on mica under similar substrate temperature and similar speed of evaporation. The remarkable outcome is that any of the quantum transport theories available, describe approximately both the temperature as well as the thickness dependence of the resistivity data without any adjustable parameter. Another surprise is that the parameters characterizing the bulk—assumed to be independent of thickness for many years—turn out to be thickness dependent.