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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 and k>1 (k: wave vector).

We report measurements of the temperature dependent resistivity ρ(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 δ (r.m.s. amplitude) and ξ (lateral correlation length) corresponding to a Gaussian and to an exponential representation of the average autocorrelation function (ACF). We use the parameters δ and ξ determined via STM measurements to calculate the quantum reflectivity R, and the temperature dependence of both the bulk resistivity ρ 0 (T ) and of the increase in resistivity ρ(T ) = ρ(T ) − ρ 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 ρ 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 ρ 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.

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Erratum: "A high-speed variable-temperature ultrahigh vacuum scanning tunneling microscope" [Rev. Sci.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/A͒ 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/D͒ 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 control circuit was designed to allow analog as well as digital feedback, selectable via a toggle switch. The design also incorporates the possibility of using two independent external signals to modulate the polarization of the sample and two independent external signals to modulate the piezoelectric transducer drive along the Z direction. It also incorporates the possibility of electronically canceling the slope that might occur while scanning due to the sample being tilted along the X axis ͑fast scan direction͒ and/or along the Y axis ͑slow scan direction͒. The circuit was tested using two 12 bit A/D-D/A converters DAS 1602 to control the scanner of a scanning tunneling microscope, with a home-built scanning head, electrometer, and preamplifier. With the complete system in operation but in the absence of tunneling current, the electrometer exhibits a current noise under 3 pA rms and a response time of 30 s to a step input current, a performance that compares well with that of bulkier and more expensive commercial low noise current amplifiers. To calibrate the instrument and verify proper control operation, we obtained images of a commercial holographic grating covered with gold running the instrument in the digital feedback mode, using the algorithm described by Piner and Reifenberger ͓Rev. Sci. Instrum. 60, 3123 ͑1989͔͒. The control circuit and the electrometer turn out to be about one order of magnitude less expensive than commercially available control circuits and low noise current amplifiers of similar performance.

We report measurements of the topography of a gold film deposited on a mica substrate using scanning tunneling microscope ͑STM͒, and measurements of the conductivity of the film performed between 4 and 300 K. From images obtained with the STM running in air in the constant current mode of a gold sample 70-nm-thick deposited under UHV on a mica substrate preheated to 300°C, we compute the average autocorrelation function ͑ACF͒ that characterizes the surface of the film in the scale of 10ϫ10 nm 2 , and determine by least-squares fitting the parameters ␦ ͑rms. amplitude͒ and ͑lateral correlation length͒ corresponding to an exponential that best describes the average ACF data. Using an exponential representation of the ACF, the parameters ␦ and determined from STM measurements, and a modified version of the theory of Sheng, Xing, and Wang recently proposed ͓R. C. Munoz et al., J. Phys.: Condens. Matter 11, L299 ͑1999͔͒, we calculate the temperature dependence of the bulk resistivity 0 (T) and of the increase in resistivity ⌬(T)ϭ(T)Ϫ 0 (T) induced by electron-surface scattering on this film. The result is that 1Ϫ/ 0 ϭ1Ϫ 0 /ϭ⌬/ amounts to about 2.6% at 300 K, and increases linearly with increasing mean free path, to about 10.5% at 4 K. The increase in resitivity ⌬ turns out to be weakly temperature dependent.

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