Electrons confined in ultrathin metal films provide a window on the peculiar world of quantum mechanics.

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The Hall coefficient R H of ultrathin epitaxial Pb films is determined experimentally. A comparison with electrical conductivity data leads to the conclusion that the investigated Pb layers behave like a size-quantized metal. Pronounced variations of R H with the film thickness were found. The observed reversal of the sign of R H is discussed within the available theory of the quantum size effect describing the galvanomagnetic properties of metals. We find that the observed phenomenon cannot be explained by the free electron model of a quantized layer. [S0031-9007(96)00249-9] PACS numbers: 73.20.Dx, 68.55.Jk, 73.50.Jt There is growing interest in quantum size effects (QSE) in ultrathin metallic films [1]. Recent studies have clearly shown the occurrence of the QSE in the electrical conductivity of ultrathin Pb films [2] but, to our knowledge, the influence of the size quantization on the Hall effect in ultrathin metallic film has never been investigated experimentally before. From the theoretical point of view the Hall effect in quantized metallic systems was discussed only by Calecki [3]. He studied the galvanomagnetic properties of thin quantized metallic films for the case in which electrons are scattered elastically by surface roughness and volume impurities. The conclusions that could be derived from this work are as follows. In the presence of bulk impurities only, represented by d-function scattering potentials, the Hall constant is equal to 21͞ne. Scattering by the surface roughness causes a variation of the Hall coefficient with the film thickness d. When the correlation length of the surface roughness is sufficiently small compared to the Fermi wavelength l F , then R H 21͞ne when only one subband is occupied by electrons (n F 1). When the number of occupied subbands is large (n F ¿ 1), R H ͑21͞ne͒ ͑4͞15͒n F ϳ d. Calecki [3] also states that in the low-correlation-length limit the Hall constant does not depend on the parameters describing the surface roughness and does not give directly the value of electron density.In this Letter we present results of the experimental determination of the Hall coefficient in a weak magnetic field as a function of film thickness and compare the experimental data with predictions of existing theory of the Hall effect in quantized ultrathin metallic films. Ultrathin Pb films provide a promising starting point for obtaining a general understanding of the influence of the QSE on the Hall effect because we have previously observed pronounced QSE effects in such films [2]. In the present study we combine the UHV technology used previously to study the QSE in the specific conductivity [2] with a new experimental method used specifically to detect the weak signals produced by the Hall effect.The sample preparation and the measurements were performed in an ultrahigh vacuum system with a base pressure ,7 3 10 211 mbar. It was equipped with a He cryostat and a reflection high-energy electron diffraction (RHEED) system. Semi-insulating Si(111) oriented to within 0.05 ± was used...

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The quantum-size-effect structure of ultrathin Pb and Pb-In alloy films on Si(111)surfaces is studied by photoemission spectroscopy in the thickness range from 0 to about 30 monolayers and analyzed, taking into account electron scattering and film structure, which is characterized by high-energy-reflectionelectron diffraction.