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We present a rigorous comparison between resistivity data and theoretical predictions involving the theory of Palasantzas [G. Palasantzas and J. Barnas, Phys. Rev. B 56, 7726 (1997)], and the modified Sheng, Xing, and Wang-fractal theory [R. C. Munoz et al., Phys. Rev. B 66, 205401 (2002)], regarding the resistivity arising from electron scattering by a self-affine fractal surface on gold films using no adjustable parameters. We find that both theories lead to an approximate description of the temperature dependence of the resistivity data. However, the description of charge transport based upon fractal scaling seems oversimplified, and the predicted increase in resistivity arising from electron-surface scattering seems at variance with other experimental results. If the samples are made up of grains such that the mean grain diameter D > ℓ0(300), the electronic mean free path in the bulk at 300 K, then the predicted increase in resistivity at 4 K is of the order of a few percent. This contradicts published measurements of magnetomorphic effects arising from size effects where electron-surface scattering is the dominant electron scattering mechanism at 4 K. On the contrary, if the samples are made out of grains such that D < ℓ0(300), then the dominant electron scattering mechanism controlling the resistivity is not electron-surface scattering but rather electron-grain boundary scattering, and the latter electron scattering mechanism is not included in either theory. [ABSTRACT FROM AUTHOR]

We report the Hall constant RH, drift mobility μD, and Hall mobility μH measured at 4 K in thin gold films deposited on mica substrates, where the dominant electron scattering mechanism is electron-surface scattering. RH increases with increasing film thickness and decreases with increasing magnetic field. For high magnetic fields B≥6 T, RH turns out to be approximately independent of magnetic field, and its value is close to that of the free electron model. We use the high magnetic field values of RH to determine film thickness. This nondestructive method leads to a determination of film thickness that agrees to within 10% with the thickness measured by other techniques. The theoretical predictions, based upon the theory of Fuchs-Sondheimer and the theory of Calecki, are at variance with experimental observations. [ABSTRACT FROM AUTHOR]

A formalism to calculate the time delay experienced by a particle undergoing scattering is presented. The formalism is a natural extension of Wigner’s delay time to wave packets which do not exhibit a well defined angular momentum. The delay depends only on the partial wave phase shifts characterizing the scattering event. The formalism is tested by applying it to the 3D square well. The results are shown to agree with the known properties of resonant scattering as deduced from a study of the poles of the scattering matrix in the complex energy plane. [ABSTRACT FROM AUTHOR]

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 measured in thin films where surface roughness has also been measured with a STM, and where electron-grain boundary scattering can be neglected. We also review the theory of Mayadas and Shatzkes (MS) [Phys. Rev. B 1, 1382 (1970)] used for decades, and discuss its severe conceptual difficulties that arise out of the fact that: (i) MS employed plane waves to describe the electronic states within the metal sample having periodic grain boundaries, rather than the Bloch states known since the thirties to be the solutions of the Schr€odinger equation describing electrons propagating through a Kr€onig-Penney [Proc. R. Soc. London Ser. A 130, 499 (1931)] periodic potential; (ii) MS ignored the fact that the wave functions describing electrons propagating through a 1-D disordered potential are expected to decay exponentially with increasing distance, a fact known since the work of Anderson [Phys. Rev. 109, 1492 (1958)] in 1958 for which he was awarded the Nobel Prize in 1977; (iii) The current in the sample should be proportional to TN, the probability that an electron traverses N consecutive (disordered) grains found along a mean free path; MS assumed that TN=1. We review unpublished details of a quantum transport theory based upon a model of diffusive transport and Kubo's linear response formalism recently published [Arenas et al., Appl. Surf. Sci. 329, 184 (2015)], which permits estimating the increase in resistivity of a metallic specimen (over the bulk resistivity) under the combined effects of electron scattering by phonons, impurities, disordered grain boundaries, and rough surfaces limiting the sample. We evaluate the predicting power of both the MS theory and of the new quantum model on samples where the temperature dependence of the resistivity has been measured between 4K and 300K, and where surface roughness and grain size distribution has been measured on each sample via independent experiments. We find that the quantum theory does exhibit a predicting power, whereas the predicting power of the MS model as well as the significance and reliability of its fitting parameters seems questionable. We explore the power of the new theory by comparing, for the first time, the resistivity predicted and measured on nanometric Cu wires of (approximately) rectangular cross section employed in building integrated circuits, based upon a quantum description of electron motion. [ABSTRACT FROM AUTHOR]

We report the Hall effect measured in gold films evaporated onto mica substrates, the samples having an average grain diameter D that ranges between 12 and 174 nm, and a thickness t of approximately 50 nm and 100 nm. The Hall mobility was determined at low temperatures T (4 K ≤ T ≤ 50 K). By tuning the grain size during sample preparation, we discriminate whether the dominant collision mechanism controlling the resistivity of the samples at 4 K is electron-surface or electron-grain boundary scattering, based upon whether the Hall mobility depends linearly on film thickness t or on grain diameter D. [ABSTRACT FROM AUTHOR]

Examines the control circuit for a scanning tunneling microscope. Role in analog-digital feedback selectability and scanning slope elimination; Use of converters in circuit testing for microscopy control; Effect of converter electrometer on noise current and response time.