German Kremer

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 in thin gold films: Discrimination between electron-surface and electron-grain boundary scattering by measuring the Hall effect at 4 K

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.

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).

Size effects on the Hall constant in thin gold films

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.

Resistivity of thin gold films on mica induced by electron-surface scattering from a self-affine fractal surface

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 publishe...

Control circuit for a scanning tunneling microscope

We have successfully built and tested a circuit designed to control a piezoelectric tube scanner having the standard single inner-electrode quartered outer-electrode configuration, using digital-to-analog (D/A) converters commercially available. To avoid noise associated with the PC, the signals transmitted by the D/A channels to the control electronics are received by instrumentation amplifiers INA 105 at the control circuit, providing 86 dB common mode rejection, thereby over four orders of magnitude of immunity to common mode noise. To prevent ground loops in the communication between the control electronics and the analog-to-digital (A/D) converters, a novel approach was used. The signals sent by the control electronics to the A/D converters were transmitted via isolation amplifiers ISO 122 followed by a 10 kHz Sallen–Key low pass filter incorporated at each output of the control circuit, providing galvanic isolation between the control electronics and the PC, thereby eliminating ground loops. The con...

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.

The Initial Stages of Growth of a Metal Film on a Single-Crystal Metal Substrate

The initial stages of growth of copper, nickel, and cobalt, deposited in ultrahigh vacuum onto a clean (111) silver single-crystal film have been studied by reflection high-energy electron diffraction in situ. Oriented nuclei and single-crystal films (with double positioning) were obtained for all substrate temperatures and thicknesses. No signs of a pseudomorphic growth were detected even in the thinnest deposits. The detection limit of the deposits was 0.05 A. The sticking coefficient of the first metal nuclei on the substrate was determined as a function of substrate temperature. The present results differ considerably from those obtained previously in conventional high vacuum, demonstrating the influence of contaminants in the latter.

High‐precision low‐cost quartz‐crystal thin‐film monitor with temperature control

An accurate thin‐film thickness monitor capable of a resolution of at least 0.01 nm is described. The errors arising from the temperature dependence of the crystal resonant frequency are minimized by heating a closely matched reference crystal until their temperatures are equalized; and by subtracting their frequencies of oscillations. These functions are performed by simple electronic devices.

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.