Electrical Resistivity of thin metal films-Peter Wibmann, Hans-Ulrich Finzel

Springer Tracts in Modern Physics Volume 223 Managing Editor: G Höhler, Karlsruhe Editors: A Fujimori, Chiba J Kühn, Karlsruhe Th Müller, Karlsruhe F Steiner, Ulm J Trümper, Garching C Varma, California P Wölfle, Karlsruhe Starting with Volume 165, Springer Tracts in Modern Physics is part of the [SpringerLink] service For all customers with standing orders for Springer Tracts in Modern Physics we offer the full text in electronic form via [SpringerLink] free of charge Please contact your librarian who can receive a password for free access to the full articles by registration at: springerlink.com If you not have a standing order you can nevertheless browse online through the table of contents of the volumes and the abstracts of each article and perform a full text search There you will also find more information about the series Springer Tracts in Modern Physics Springer Tracts in Modern Physics provides comprehensive and critical reviews of topics of current interest in physics The following fields are emphasized: elementary particle physics, solid-state physics, complex systems, and fundamental astrophysics Suitable reviews of other fields can also be accepted The editors encourage prospective authors to correspond with them in advance of submitting an article For reviews of topics belonging to the above mentioned fields, they should address the responsible editor, otherwise the managing editor See also springer.com Managing Editor Gerhard Höhler Institut für Theoretische Teilchenphysik Universität Karlsruhe Postfach 69 80 76128 Karlsruhe, Germany Phone: +49 (7 21) 08 33 75 Fax: +49 (7 21) 37 07 26 Email: gerhard.hoehler@physik.uni-karlsruhe.de www-ttp.physik.uni-karlsruhe.de/ Solid-State Physics, Editors Atsushi Fujimori Editor for The Pacific Rim Department of Complexity Science and Engineering University of Tokyo Graduate School of Frontier Sciences 5-1-5 Kashiwanoha Kashiwa, Chiba 277-8561, Japan Email: fujimori@k.u-tokyo.ac.jp http://wyvern.phys.s.u-tokyo.ac.jp/welcome_en.html Elementary Particle Physics, Editors Johann H Kühn C Varma Editor for The Americas Institut für Theoretische Teilchenphysik Universität Karlsruhe Postfach 69 80 76128 Karlsruhe, Germany Phone: +49 (7 21) 08 33 72 Fax: +49 (7 21) 37 07 26 Email: johann.kuehn@physik.uni-karlsruhe.de www-ttp.physik.uni-karlsruhe.de/∼jk Department of Physics University of California Riverside, CA 92521 Phone: +1 (951) 827-5331 Fax: +1 (951) 827-4529 Email: chandra.varma@ucr.edu www.physics.ucr.edu Thomas Müller Institut für Experimentelle Kernphysik Fakultät für Physik Universität Karlsruhe Postfach 69 80 76128 Karlsruhe, Germany Phone: +49 (7 21) 08 35 24 Fax: +49 (7 21) 07 26 21 Email: thomas.muller@physik.uni-karlsruhe.de www-ekp.physik.uni-karlsruhe.de Fundamental Astrophysics, Editor Joachim Trümper Max-Planck-Institut für Extraterrestrische Physik Postfach 13 12 85741 Garching, Germany Phone: +49 (89) 30 00 35 59 Fax: +49 (89) 30 00 33 15 Email: jtrumper@mpe.mpg.de www.mpe-garching.mpg.de/index.html Peter Wölfle Institut für Theorie der Kondensierten Materie Universität Karlsruhe Postfach 69 80 76128 Karlsruhe, Germany Phone: +49 (7 21) 08 35 90 Fax: +49 (7 21) 69 81 50 Email: woelfle@tkm.physik.uni-karlsruhe.de www-tkm.physik.uni-karlsruhe.de Complex Systems, Editor Frank Steiner Abteilung Theoretische Physik Universität Ulm Albert-Einstein-Allee 11 89069 Ulm, Germany Phone: +49 (7 31) 02 29 10 Fax: +49 (7 31) 02 29 24 Email: frank.steiner@uni-ulm.de www.physik.uni-ulm.de/theo/qc/group.html Peter Wißmann Hans-Ulrich Finzel Electrical Resistivity of Thin Metal Films With 110 Figures ABC Professor Peter Wißmann Professor Hans-Ulrich Finzel Institut für Physikalische und Theoretische Chemie Universität Erlangen-Nürnberg Egerlandstr 91058 Erlangen, Germany Hochschule Niederrhein FB Chemie Adlerstr 32 47798 Krefeld, Germany E-mail: HU.Finzel@web.de Library of Congress Control Number: 2006935051 Physics and Astronomy Classification Scheme (PACS): 73.50.-h, 73.50.Bk, 73.61.-r, 73.61.At, 73.90.+f ISSN print edition: 0081-3869 ISSN electronic edition: 1615-0430 ISBN-10 3-540-48488-4 Springer Berlin Heidelberg New York ISBN-13 978-3-540-48488-2 Springer Berlin Heidelberg New York This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable for prosecution under the German Copyright Law Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Typesetting: by the authors using a Springer LATEX macro package Cover production: WMXDesign GmbH, Heidelberg Printed on acid-free paper SPIN: 11905196 56/techbooks 543210 Preface The technical application of thin metal films in such diverse fields as microelectronics (e.g chips, sensor design, solar cells), optical filters, catalysis or corrosion-resistant coatings have led to a large database on the electrical properties The interpretation of the data has, however, often been controversial A remarkable progress in understanding the physical basis of the phenomena was achieved by first depositing monometallic films under welldefined ultra-high-vacuum conditions, and then by studying the influence of the residual gas by additional gas adsorption experiments in a second step Polycrystalline as well as single-crystalline films could be prepared by varying the substrate material and the deposition conditions in a proper manner Modern structure investigations and high-resolving spectroscopic techniques have helped to obtain a more accurate picture of the character and strength of the metal/gas interaction during the crystal growth So, general approval is presently given to the idea that gaseous adatoms should display features similar to alloy formation on a pure metal surface, e.g the generation of new scattering centres for the conduction electrons The so-called scattering hypothesis holds quantitatively in many cases as has been previously shown for the dependence of the resistivity on film thickness Here we will concentrate on the effect of annealing and gas adsorption on films of the noble metals silver and gold which have model character with respect to a weak metal/gas interaction Corresponding phenomena on the resistivity of bulk metal samples are widely unknown for obvious reasons The experimental data have been accumulated in the last three decades and allow a detailed and independent check regarding whether the scattering hypothesis can be used for a theoretical prediction of the film resistivity or not A sufficient structural characterisation of the films is an important prerequisite for such efforts Moreover, possibilities to recalculate the resistivity from optical, photoelectric or infrared absorption data will be critically discussed The conclusions drawn may shed new light on the interpretation of the electrical properties of films with more complicated structures, compositions and chemical reactivities These films are usually prepared under worse vacuum conditions but represent the centre of practical interest VI Preface Acknowledgements The authors are deeply obliged to all coworkers of the Institute of Physical and Theoretical Chemistry of the University Erlangen-Nă urnberg With their engaged scientic eorts, they have enabled us to present this survey Also we are obliged Frau B Eichel for typing the script and to Springer Verlag for the excellent cooperation Erlangen/Krefeld September 2006 P Wissmann H.-U Finzel Contents Introduction References 2 The Scattering Hypothesis References The Effect of Annealing on the Electrical Resistivity of Thin Silver Films References 32 The Effect of Annealing on the Electrical Resistivity of Thin Gold Films 35 References 51 The Interaction of Oxygen and Ethylene with Silver and Gold Films 53 References 78 Other Adsorbates on Silver and Gold Films 6.1 Xenon on Silver and Gold Films 6.2 CO on Silver and Gold Films 6.3 Hydrogen on Gold Films 6.4 Palladium on Gold Films References 81 81 86 91 93 95 Further Selected Adsorption Systems 7.1 Adsorption of CO and O2 on Palladium Films 7.2 The Fe/O System 7.3 The Ge/CO System References 97 97 103 115 120 Conclusions and Outlook 123 References 124 Index 125 Introduction Thin metal films have received widespread attention for technical applications like conducting connections in microelectronics, optical elements tailored with desired spectral properties or supported adsorbents in heterogeneous catalysis The electrical resistivity is an easily accessible and informative quantity to characterise the material K Fuchs [1] has predicted in a famous theoretical paper published in 1938 that the electrical resistivity of thin metal films increases with decreasing thickness The scattering of conduction electrons at the film surfaces was considered to be responsible for this phenomenon Since good agreement was found with early experimental data [2, 3], the interpretation was not called in question for a long period Later, however, it became obvious that grain boundary scattering [4, 5] and surface roughness [6, 7] play a decisive role in the resistivity behaviour of polycrystalline films Moreover, ultra-thin films may crack and form an island structure [8, 9] Thus, the measured thickness dependence of the electrical resistivity differs from Fuchs’ results in such a way that the resistivity increase with decreasing thickness is more pronounced than the theoretical prediction The corresponding extension of Fuchs’ theory leads to the scattering hypothesis [10,11], where not only surface scattering, but also crystallic boundary scattering, surface roughness and adsorption phenomena are included into description A brief survey of this hypothesis is presented in Chap In special cases, however, more complicated mechanisms must be included into discussion in order to explain the results The aim of the present booklet is to report on selected examples of such complications and to show possibilities for solving the problems The influence of annealing on the resistivity of silver and gold films is treated in Chaps and It is shown that the pure grain boundary scattering is not sufficient to explain the resistivity properties of polycrystalline films Obviously, the healing of lattice defects in the interior of the grains must be additionally taken into consideration On the other hand, both effects can be neglected in the case of single-crystal films Then, we elucidate in Chap the problems of a theoretical calculation of the scattering cross section for the example of oxygen and ethylene adsorption on silver and gold films The application of the model described in Chap is P Wissmann and H.-U Finzel: Electrical Resistivity of Thin Metal Films, STMP 223, 1–2 (2007) c Springer-Verlag Berlin Heidelberg 2007 DOI 10.1007/3-540-48490-6 Introduction critically reviewed for these examples In Chap 6, we discuss other adsorbates on silver and gold films Xe, CO and H2 are bound rather weakly and hence are particularly suitable to be compared with the results obtained so far Palladium is a metal that also enhances the gold-film resistivity in the ultrathin thickness range of the overlayer In this connection, special emphasis is put on the reactivity with oxygen and carbon monoxide Details of the interaction of both these gases on Pd films of moderate thickness are discussed in Chap Moreover, an example is included where the gas can penetrate into the interior of the film Oxygen on iron films at higher temperatures shows such a behaviour Finally, we discuss the adsorption of carbon monoxide on semiconducting Ge films, where the scattering hypothesis totally fails to explain the results Doping phenomena cannot be excluded in this case, even if the thickness dependence of the resistivity seems to be in agreement with a scattering mechanism References K Fuchs Proc Cambridge Phil Soc 94, 100 (1938) H Mayer Physik dă unner Schichten, wissenschaftliche, Vol II Verlagsgesellschaft Stuttgart, p 178 (1955) K.L Chopra Thin Film Phenomena, Mc Graw-Hill, New York (1969) A.F Mayadas and M Shatzkes Phys Rev B1, 1382 (1970) P Wissmann Thin Solid Films 5, 329 (1970) Y Namba Japan J Appl Phys 9, 1326 (1970) H.-U Finzel and P Wissmann Ann Phys 43, (1986) T.J Coutts Electrical Conduction in Thin Metal Films, Elsevier, Amsterdam p 205 (1974) H.-U Finzel and P Wissmann Z Naturforsch 40a, 161 (1985) 10 P Wissmann The Electrical Resistivity of Pure and Gas Covered Metal Films Springer Tracts Mod Phys., 77, (Springer-Verlag, Berlin, 1975) 11 P Wissmann Thin metal films and gas chemisorption in: Studies in Surface Science and Catalysis, 32, 53 (Elsevier, Amsterdam, 1987) The Scattering Hypothesis The scattering hypothesis is based on the assumption that Matthiessen’s rule can be applied, i.e all scattering contributions compose additively [1] according to (2.1) ρ = ρ0 + ρGB + ρSS + ρSR with the grain boundary scattering contribution K D (2.1a) C d (2.1b) CB d3 (2.1c) ρGB = ρ0 the surface scattering contribution ρSS = ρ0 and the roughness contribution ρSR = ρ0 where d is the film thickness and D the mean crystallite extension parallel to the film plane ρ0 is the resistivity of the bulk metal with the same lattice fault density as the films; K and C are scattering constants and hence proportional to the mean free path l0 of the electrons, and B is a measure of the asperity height [2] Equation (2.1) approaches the well-known Fuchs–Sondheimer relation [3] for K = B = and (2.2) C = (1 − p) l0 where p is the fraction of electrons specularly reflected at the film surfaces It is easily recognised that an upper limit Cmax = (3/16)l0 is implied in Eq (2.2) since the quantity p is defined to vary between and at the outer film surface For C = B = 0, Eq (2.1) changes into the Mayadas–Shatzkes relation [4] with η (2.3) K= l0 1−η P Wissmann and H.-U Finzel: Electrical Resistivity of Thin Metal Films, STMP 223, 3–7 (2007) c Springer-Verlag Berlin Heidelberg 2007 DOI 10.1007/3-540-48490-6 114 Further Selected Adsorption Systems Fig 7.23 Plot for checking Eq (7.5) with the data of Fig 7.22 (pO2 ) = 10 mbar of iron ions via cation vacancies is the dominant process and the diffusion via grain boundaries as a path of easy diffusion looses its importance As a consequence, the growth rate of the oxide layer depends on the orientation of the crystallites Figure 7.24 shows a typical example for a 200-nm-thick polycrystalline iron film oxidised in air of 1-bar pressure at 573 K [29] Obviously the oxidation velocity for more open (200) surfaces is much higher than for rather closed (110) surfaces Here also the strong strain impressed on the (200) surface (refer to Fig 7.12) may play an important role Summarising, we may state that the formation of oxides on iron single crystals covers a large area of actuality in surface science The dependence on Fig 7.24 Progress of the oxide layer formation with time Parameter is the crystallite orientation [29] For details, see the text 7.3 The Ge/CO System 115 temperature as well as oxygen pressure is rather complicated A good survey for the most densely packed Fe(110) surface is presented in [43] New aspects arise when polycrystalline films with a high density of grain boundaries are investigated Then the influence of grain boundary diffusion on shape and growth rate of the oxide layers becomes dominating Consequently, we observe a distinct thickness dependence due to changes in the grain boundary density Future efforts are necessary to get a better insight into the competition of the various mechanisms involved 7.3 The Ge/CO System In the last section we have mentioned that the oxidation of iron films leads to an increase of the resistivity of several orders of magnitude Correspondingly, the free electron density in the films is strongly reduced Such films exhibit a negative temperature coefficient of resistivity and thus behave like a semiconducting film The marked influence of the substrate on the electrical properties cannot be neglected any more, and gas adsorption induces relatively huge changes in the resistivity, because doping is now more important than scattering of the conducting electrons We therefore decided to finally include the properties of germanium interacting with gases into this survey Germanium has achieved increasing attention as a basic material in microelectronics [51] Recent results concerning the influence of various gases like oxygen [52], ammonia [53, 54] or hydrogen [55], important for intermediary steps in the technical preparation procedures, are also available Our films have been deposited at room temperatures on glass substrates, and we have concentrated on the adsorption of CO as a strongly disturbing component of the residual gas [56] Field effect measurements were considered to be particularly useful to obtain further information on the conduction mechanism [57] We have constructed a glass cell, schematically shown in Fig 7.25 The substrate consists of a thin rectangular plate of AR glass fixed on one field electrode FP The second mobile field electrode RP could be adjusted magnetically to the final position with the help of distance pearls and guiding edges after completion of the film deposition process The final distance of both field electrodes was 0.8 mm, thus making possible in situ adsorption experiments under UHV conditions (C is the connection to the pump line) The substrate was equipped with two thick pre-deposited chromium layers serving as contacts for a four-pole resistivity determination Chromium was considered to realize the best quasi-ohmic transition to the film It should be emphasised that both the field and resistance measurement networks were mutually isolated by the glass pearls GP in order to minimise the non-uniformity of the surface charging Further details of the construction of the cell have been described elsewhere [58, 59] The deposition of the film F was performed by heating a weighted amount of specpure Ge fixed in a tungsten helix EH Only small Ge layers were pre- 116 Further Selected Adsorption Systems Fig 7.25 Schematics of the glass cell used in the field effect investigations For details, see the text deposited on a closed shutter for cleaning purposes [58] The film thickness was then calculated from the known film area and the distance between film and evaporation source The accuracy of the thickness determination was estimated to be about 10% for the comparison of various films If the adsorption measurements were performed on one and the same film, then the accuracy was much higher for obvious reasons Figure 7.26 shows the dependence of the resistivity on the film thickness d Deposition and measuring temperature is room temperature and the rate of deposition is nm/min This deposition rate is much lower than that applied in the work of Davey et al [60]; correspondingly the resistivities in Fig 7.26 are higher by two orders of magnitude Information on the mean crystallite size in dependence on the various deposition parameters is missing in the literature for polycrystalline films as described here Generally speaking, however, the degree of order should increase with decreasing deposition rate [34] The dashed curve in Fig 7.26 is the theoretical dependence calculated on the basis of Eqs (2.1b) and (2.2) At the first glance, a reasonable agreement seems to be established A formal evaluation yields ρo = 71 Ω cm and 7.3 The Ge/CO System 117 Fig 7.26 Thickness dependence of the resistivity of thin Ge films [58] For details, see the text (1 − p)l0 = 160 nm The detailed analysis, however, reveals that the assumption of a predominating electron scattering as compared to doping processes is very dangerous in the case of semiconductors Moreover, the use of the free electron gas approximation looses its real justification here The films are p-conducting for reasons that are not quite clear up to now [60] We believe that the distortion of the lattice near the grain boundaries results in a charging-up with drastic consequences for the resistivity Note that the resistivity is enhanced by several orders of magnitude as compared to Ge(111) single-crystal films epitaxially grown on well-oriented substrates [61, 62] In order to specify this point, we have induced changes in the surface charge by the field effect electrode and studied the changes in the resistivity depending on the film thickness The results are presented in Fig 7.27 in a doubly logarithmic plot One easily recognises that the resistivity change is independent of the film thickness With the aid of Eq (2.1b) we derive that the charging is a volume effect rather than a pure surface effect A possible interpretation is based on the relatively large Debye length L = Cn−1/2 p (7.7) where C is a characteristic constant For typical semiconductors at room temperature C ≈ 0.14 nm−1/2 [63] should hold np is the density of the majority charge carriers and can be estimated from ρ−1 = eµp np (7.8) with µp being the mobility of the defect electrons at room temperature (µp = 3500 cm2 /Vs [64]) We obtain then np ≈ 2×1013 cm−3 and L ≈ 103 nm from Eq (7.7) so that the Debye length is larger than the mean crystallite size in our films (D ≈ 102 nm [65]) Therefore, we conclude that the p-conduction is probably generated in the grain boundaries that can be considered as an area of a strongly disturbed lattice arrangement of Ge atoms Here the concentration of defect electrons is drastically enhanced, and their mobility is 118 Further Selected Adsorption Systems 3 d ∆ρ  × 109 Ω cm d ∆Q  As  1.0 0.2 0.1 0.02 101 102 103 d (nm) Fig 7.27 Thickness dependence of the quantity d∆ρ/d∆Q for the films of Fig 7.26 [58] reduced A charging-up at the grain boundaries modifies the charge density in the whole interior of the grains Moreover, the charging at the transitions Ge/glass and Ge/vacuum cannot be neglected On the other hand, the condition L D (7.9) should not be fulfiled for epitaxially grown films and for films with a higher defect electron density np [61, 62] L is smaller than the lattice spacing for metals due to the extremely high electron density; hence it does not play a comparable role for the conduction mechanism in that case [63] Further information is obtained from adsorption experiments with CO Here it should be emphasised that NFE in Figs 7.28 and 7.29 characterises the amount of admitted CO divided by the film area This quantity should not be confused with the coverage n because the arrangement of Fig 7.25 implies severe complications like (a) adsorption of CO on other metal parts of the cell, for example on the chromium contacts (b) a non-uniform gas distribution between the film surface and the very closely spaced mobile field effect electrode Nevertheless, NFE can be used without problems as a qualitative measure of the CO coverage A suitable quantity to describe the influence of adsorbed gases is the field effect mobility [66] µFE = d (∆σ) |∆Q→0 d∆Q (7.10) which can be easily derived from the measured ∆σ versus ∆Q curves [59] Here, ∆σ is the surface conductivity that accounts for the deviations from the bulk value [66] µFE is negative for sufficiently small gas doses due to the 2  µFM mm  Vs  7.3 The Ge/CO System 119 −100 d = 620 nm −50 NFE(1014 molecules CO/cm2) Fig 7.28 Field effect mobility for a 620-nm-thick Ge film in dependence on CO coverage [58] p-conductivity of the Ge films Figure 7.28 makes evident that small oscillations are observed in the beginning of the µFE versus NFE curves Similar effects were reported for the Ge(111)/O2 system by Henzler [67] and were interpreted by a structural conversion of the surface at small gas exposures and by an adsorption without further structural changes at higher exposures At very high CO exposures, the field effect mobility can even change its sign, and so films of sufficiently small thickness become n-conducting Figure 7.29 shows a typical example, obviously an electron transfer from the adsorbed gas molecules to the film is the reason for this drastic change in the conduction mechanism As a consequence, a new light is shed on the coverage dependence schematically shown in Fig 7.30 which was observed, for example, for the Ge/O-system [68] The similarity to the maximum observed for the Pd/H [5] system should not be an argument for an overweighting scattering process On the contrary, the maximum of the resistivity versus coverage curves for semiconducting films more likely indicates that the p-conduction of the pure films is neutralised by the doping of electrons The resistivities reported by Suhrmann et al [68, 69] adapt to the values of Fig 7.26 quite well A discrepancy, however, arises with respect to the adsorption properties at room temperature These authors could not realise any CO adsorption on a 59-nm-thick Ge film deposited at 77 K and annealed for h at 373-K [69] Here again the strong influence of various preparation parameters like annealing treatment, residual gas pressure, quality of the Ge material used for deposition, evaporation rate etc on the Ge/gas interaction becomes evident 120 Further Selected Adsorption Systems Fig 7.29 Field effect mobility for a 71-nm-thick film in dependence on CO coverage [58] Fig 7.30 Schematical change of the resistivity of thin Ge films with O2 coverage at 273 K [68] The CO adsorption at 77 K, on the contrary, results in a maximum increase in resistivity of 20% for a film of 73-nm-thickness [69] This value is extremely high as compared to metal/CO systems and may be a further hint for a doping mechanism dominating the electrical properties of the films As expected, the resistivity increase becomes larger for thinner films [69] References K Christmann Surface Physical Chemistry, Springer Verlag, New York (1991) G.A Somorjai Surface Chemistry and Catalysis, Wiley, New York (1993) G Ertl In: Catalysis, Science and Technology, 4, 238 (J.R Anderson and M Boudart (Eds.)), (Springer Verlag, Berlin, 1983) References 121 T Engel and G Ertl In: Physics of Solid Surfaces and Heterogeneous Catalysis, 4, 73 (D.A King and D.P Woodruff (Eds.)), (Elsevier, Amsterdam, 1982) P Wissmann, G Wedler and M Watanabe Nichtmetalle in Metallen, Verlag DGM, Wiesbaden, 49 (1990) R Gebhardt Thesis, University of Erlangen Nă urnberg (1987) G Wedler and R Chander Thin Solid Films 65, 53 (1980) G Wedler and G Alshorachi Thin Solid Films 74, (1980) J Angilello, F d’Heurle, S Peterson and A Segmă uller J Vac Sci Technol 17, 471 (1980) 10 K Hă aupl Thesis, U Erlangen-Nă urnberg (1984) 11 R.W Vook In: Epitaxial Growth, Part A, J.W Matthews (Ed.) Academic Press, London (1975) 12 D.E Eastman Phys Rev B2, (1970) 13 W Fischer and P Wissmann Z Naturforsch 31a, 190 (1976) 14 H Hloch Thesis, University of Erlangen-Nă urnberg (1993) 15 H Hloch and P Wissmann Phys Stat Sol (a) 145, 521 (1994) 16 I.Z Jones, R.A Bennett and M Bowker Surface Sci 402, 595 (1998) 17 M Kittel, R Terborg, M Polcik, A.M Bradshaw, D.L Toomes, D.P Woodruff and E Rotenberg Surface Sci 511, 34 (2002) 18 B Heping, M Rauh and P Wissmann unpublished 19 M Rauh, B Heping and P Wissmann Appl Phys A 61, 587 (1995) 20 N.F Mott and H Jones The Theory of the Properties of Metals and Alloys, Dover, New York, 268 (1958) 21 D Dayal and P Wissmann Thin Solid Films 44, 185 (1977) 22 P Sato, K Houkala, M Alatalo and K Laasonen Surface Sci 516, 247 (2002) 23 H.-U Finzel, B Heping and P Wissmann Z Naturforsch 52a, 640 (1997) 24 M Eriksson and L.G Ekedahl Surface Sci 412/413, 430 (1998) 25 P Wissmann In: Handbook of Optical Properties II, R.E Hummel and P Wissmann (Eds.), CRS Press, Boca Raton, FL 401 (1997) 26 M Rauh Diploma Thesis, University of Erlangen-Nă urnberg (1988) 27 J Kră uger, H.D Kunze and E Schă urmann In: Gase und Kohlenstoff in Metallen, E Fromm and A Gebhardt (Eds.), Springer Verlag, Berlin, 578 (1976) 28 P Wissmann and H Zitzmann Fresenius Z Anal Chem 319, 591 (1984) 29 H Zitzmann Thesis, University of Erlangen Nă urnberg (1980) 30 S.S Lau, S.Y Feng, J.O Olowolafe and M.A Nicolet Thin Solid Films 25, 415 (1975) 31 G Wedler and P Wissmann Z Naturforsch 23a, 1537 (1968) 32 R Schmidt Thesis, U Erlangen-Nă urnberg (1988) 33 R Schmidt, G Wedler and P Wissmann Vacuum 41, 1590 (1990) 34 K.L Chopra Thin Film Phenomena, McGraw-Hill, New York (1969) 35 G Wedler Z Phys Chem (Frankfurt) 27, 388 (1961) 36 G Alshorachi and G Wedler Appl Surface Sci 20, 279 (1985) 37 A.J Melmed and J.J Carroll J Vac Sci Technol 10, 164 (1973) 38 C.F Brucker and T.N Rhodin Surface Sci 57, 523 (1976) 39 A Hodgson, A Wight and G Worthy Surface Sci 319, 119 (1999) 40 W.E Boggs, R.H Kachik and G.E Pellisier J Electrochem Soc 112, 53 (1965) 41 D.A Channing and M.J Graham J Electrochem Soc 117, 389 (1970) 42 W Meisel and P Gă utlich Werkstoe Korrosion 32, 296 (1981) 122 Further Selected Adsorption Systems 43 V.S Smentkowski and J.T Yates Surface Sci 232, 113 (1990) 44 M Rauh, H.-U Finzel and P Wissmann Z Naturforsch 54a, 117 (1999) 45 G Hă orz In: Gase und Kohlensto in Metallen, E Fromm and E Gebhardt (Eds.), Springer Verlag Berlin, 84 (1976) 46 R.E Hummel Phys Stat Sol (a)76, 11 (1983) 47 K Hauffe Reaktionen in und an festen Stoffen, Springer Verlag, Berlin, 710 (1966) 48 E Fromm Kinetics of Metal-Gas Interactions at Low Temperatures, Springer Verlag, Berlin, 83 (1988) 49 I.M Ritchie In: Chemisorption and Reactions on Metallic Films, Vol 2, J.A Anderson (Ed.), Academic Press, London, 257 (1971) 50 B.A Irving Corros Sci 5, 471 (1965) 51 M Henzler Surface Sci 357, 809 (1996) 52 E.J.J Kirchner and E.J Baerends Surface Sci 311, 126 (1994) 53 W Ranke and J Wasserfall Surface Sci 303, 45 (1994) 54 C Bater, M Sanders and J.H Craig Surface Sci 451, 226 (2000) 55 H Kim, A Vailiouis, D.G Cahill and J.E Greene Surface Sci 457, 337 (2000) 56 H Gentsch Z Phys Chem (Frankfurt) 24, 55 (1960) 57 V.F Kiselev and O.V Krylov Electronic Phenomena in Adsorption and Catalysis on Semiconductors and Dielectrics, Springer Series in Surface Science, Vol 7, Springer, Berlin (1987) 58 H.-U Finzel Thesis, U Erlangen-Nă urnberg (1976) 59 H.-U Finzel and P Wissmann Surface Sci 86, 83 (1979) 60 K.L Chopra Thin Film Phenomena, McGraw Hill, New York, 441 (1969) 61 J.E Davey Appl Phys Lett 8, 164 (1966) 62 B.W Sloope and C.O Tiller J Appl Phys 38, 140 (1967) 63 W Mă onch Semiconductor Surfaces and Enterfaces, Springer-Verlag, Berlin, 22 (1993) 64 E.M Conwell Proc IRE 40, 1327 (1952) 65 R.L Ramey and W.D McLennan J Appl Phys 38, 3491 (1967) 66 W Mă onch Semiconductor Surfaces and Interfaces, Springer-Verlag, Berlin, 67 (1993) 67 M Henzler Surface Sci 24, 209 (1971) 68 R Suhrmann, M Kruel and G Wedler Z Naturforsch 18a, 119 (1963) 69 R Suhrmann, M Kruel and G Wedler Z Naturforsch 18a, 633 (1963) Conclusions and Outlook The electrical resistivity of thin silver [1] and gold [2] films deposited at room temperature on glass and silicon substrates was previously studied mainly with respect to the thickness dependence The results were explained with the help of the so-called scattering hypothesis where grain boundary scattering is the decisive process for polycrystalline films while surface scattering becomes effective for single-crystal films, in particular at the metal/silicon transition In the present booklet, we have extended our discussion to the influence of the annealing treatment Special emphasis was put on excellent UHV conditions and all other parameters were kept as constant as possible In spite of these endeavours, the agreement between experiment and theory is less satisfactory; we have to include into consideration also a healing of lattice distortions inside the crystallites, a smoothening of the surface roughness and an increasing alignment of the crystallites to the (111) orientation The comparison of the properties of silver and gold films seems to be particularly promising, because both noble metals exhibit nearly the same lattice structure but differ in their chemical activity Silver tends to coagulate on glass substrates, and the characteristic cracking temperature decreases with decreasing film thickness [1] On silicon substrates, silver behaves quite inert Gold films exhibit at higher temperatures very flat surfaces but react with silicon Gas adsorption on the films can be also described by scattering hypothesis within certain limits Here, the theoretical prediction is that the gas always induces an increase in film resistivity contrary to early assumptions (see, for example, [3]) Exceptions are observed only for inhomogeneous films, higher coverages and chemical reactions between various species adsorbed on the surface The excess charging of the surface atoms is found to be the decisive quantity for a quantitative description, and it can be calculated on the basis of the density functional formalism or self-consistent field approximation, using Mulliken’s population analysis This procedure leads to a very good agreement between experiments and theory for the Ag/O system If z is estimated from a linear dipole model, the agreement becomes worse because some important assumptions are not fulfiled for most of the investigated gases Moreover, the correlation with work function measurements and optical data as postulated by many authors could P Wissmann and H.-U Finzel: Electrical Resistivity of Thin Metal Films, STMP 223, 123–124 (2007) c Springer-Verlag Berlin Heidelberg 2007 DOI 10.1007/3-540-48490-6 124 Conclusions and Outlook not be realised Further studies are necessary to develop a complete picture, including the information power of the damping of frustrated IR vibrations as discussed by Persson et al [4, 5] In conclusion we would like to encourage theoretical chemists to perform cluster calculations on further adsorption systems mentioned in this booklet to set reliable z-values at our disposal By this procedure a theoretical prediction of the resistivity increase produced by gas adsorption seems to be very promising The interpretation of adsorption experiments with metals is much more complicated because of problems in the exact determination of coverage Three-dimensional clusters and islands can then be formed on the surface Further problems arise when the gas is incorporated into the metal films (i.e volume effects) or when semiconducting adsorbents are used (i.e doping effects) Here, future studies are necessary to achieve a comprehensive description Our next analysis will deal with the Ni/CO system Reliable experimental resistivity data [6] as well as calculated z-values [7] are available in the literature so that a further check of Eq (2.7) seems to be prosperous Moreover, ultra-thin nickel films on glass substrates behave like semiconductors as far as a negative ATCR [8], a resistivity decrease during CO adsorption [9], and an oscillating field effect mobility [10] are concerned Here new models for a better understanding of the phenomena have to be developed References P Wissmann Thin Metal Films and Gas Chemisorption In: Studies in Surface Science and Catalysis, 32, 53 (Elsevier, Amsterdam, 1987) D Dayal and P Wissmann Vakuum – Technik 38, 121 (1989) J.J Wortmann and K.S Canady Appl Phys Lett 9, 75 (1966) B.N.J Persson Phys Rev B44, 3277 (1991) B.N.J Persson, D Schumacher and A Otto Chem Phys Lett 178, 204 (1991) P Wissmann Springer Tracts Mod Phys., 77, (Berlin, 1975) X Xu, N Wang and O Zhang Surface Sci 274, 386 (1992) H.-U Finzel and P Wissmann, Z Naturforsch 40a, 1066 (1985) H.-U Finzel, D Lazarov, M Rauh and P Wissmann Verhandl German Phys Soc VI 25, 657 (1990) 10 H.-U Finzel and P Wissmann Surface Sci 86, 83 (1979) Index activation energy, 49 adsorption of gases, 51 adsorption of metals, 92 Auger-electron-spectroscopy, 21, 25, 43 lattice mismatch, 94, 99 lattice parameter, 93, 105 layer-by-layer growth, 21, 93 local density approximation, 103, 123 low electron energy diffraction, 41 Born’s approximation, catalytic reaction, 54, 97 coverage dependence, 51 crystalline structure, 11 Debye length, 117 dielectric constants, 26 doping mechanism, 119 Drude’s theory, 26, 28 ellipsometry, 27 epitaxial growth, 20, 21, 117 eutectic temperature, 44, 45, 47 Fermi energy, field effect mobility, 119 film growth, 10, 25 Fowler theory, 17, 112 free electron gas model, Fresnel’s formulae, 27 frustrated IR vibrations, Fuchs–Sondheimer theory, 3, 77 Matthiessen’s rule, Maxwell–Garnett theory, 32 Mayadas–Shatzkes theory, Mean crystallite size, 10, 14 mean free path of electrons, Melnyk–Harrison theory, 91 metal–silicon transition, 46 Mie theory, 32, 35 Monte-Carlo simulation, 51 Mulliken’s population analysis, oxidation kinetics, 109 Persson theory, photoelectric yield, 17 resistivity measurements, jellium model, 82 satellite maxima in XRD spectra, 11, 99 scanning electrons microscopy, 17 scanning tunnelling micrograph, 23, 35 scattering cross section, scattering hypothesis, self-consistent field approximation, 56 semiconducting metal/silicon systems, 49 semiconductor films, 114 space charge limited diode, 10, 17 specularity parameter, surface roughness, 1, 4, 17 kinetics of metal/gas interaction, 109 temperature coefficient of resistivity, 19 glass cells, 9, 10, 54, 59, 97 grain boundary diffusion, 3, 111 grain boundary scattering, interdiffusion, 41 126 Index texture analysis, 13, 99 thermally induced strains, 105 ultra-thin films, 1, 18, 50 Vand’s theory, 10 work function, 6, 16 X-ray diffraction, 11 Ziman–Mott formula, Springer Tracts in Modern Physics 181 Emulsion Science Basic Principles An Overview By J Bibette, F Leal-Calderon, V Schmitt, and P Poulin 2002 50 figs., IX, 140 pages 182 Transmission Electron Microscopy of Semiconductor Nanostructures An Analysis of Composition and Strain State By A Rosenauer 2003 136 figs., XII, 238 pages 183 Transverse Patterns in Nonlinear Optical Resonators By K Stali¯unas, V J Sánchez-Morcillo 2003 132 figs., XII, 226 pages 184 Statistical Physics and Economics Concepts, Tools and Applications By M Schulz 2003 54 figs., XII, 244 pages 185 Electronic Defect States in Alkali Halides Effects of Interaction with Molecular Ions By V Dierolf 2003 80 figs., XII, 196 pages 186 Electron-Beam Interactions with Solids Application of the Monte Carlo Method to Electron Scattering Problems By M Dapor 2003 27 figs., X, 110 pages 187 High-Field Transport in Semiconductor Superlattices By K Leo 2003 164 figs.,XIV, 240 pages 188 Transverse Pattern Formation in Photorefractive Optics By C Denz, M Schwab, and C Weilnau 2003 143 figs., XVIII, 331 pages 189 Spatio-Temporal Dynamics and Quantum Fluctuations in Semiconductor Lasers By O Hess, E Gehrig 2003 91 figs., XIV, 232 pages 190 Neutrino Mass Edited by G Altarelli, K Winter 2003 118 figs., XII, 248 pages 191 Spin-orbit Coupling Effects in Two-dimensional Electron and Hole Systems By R Winkler 2003 66 figs., XII, 224 pages 192 Electronic Quantum Transport in Mesoscopic Semiconductor Structures By T Ihn 2003 90 figs., XII, 280 pages 193 Spinning Particles – Semiclassics and Spectral Statistics By S Keppeler 2003 15 figs., X, 190 pages 194 Light Emitting Silicon for Microphotonics By S Ossicini, L Pavesi, and F Priolo 2003 206 figs., XII, 284 pages 195 Uncovering CP Violation Experimental Clarification in the Neutral K Meson and B Meson Systems By K Kleinknecht 2003 67 figs., XII, 144 pages 196 Ising-type Antiferromagnets Model Systems in Statistical Physics and in the Magnetism of Exchange Bias By C Binek 2003 52 figs., X, 120 pages 197 Electroweak Processes in External Electromagnetic Fields By A Kuznetsov and N Mikheev 2003 24 figs., XII, 136 pages 198 Electroweak Symmetry Breaking The Bottom-Up Approach By W Kilian 2003 25 figs., X, 128 pages 199 X-Ray Diffuse Scattering from Self-Organized Mesoscopic Semiconductor Structures By M Schmidbauer 2003 102 figs., X, 204 pages 200 Compton Scattering Investigating the Structure of the Nucleon with Real Photons By F Wissmann 2003 68 figs., VIII, 142 pages 201 Heavy Quark Effective Theory By A Grozin 2004 72 figs., X, 213 pages Springer Tracts in Modern Physics 202 Theory of Unconventional Superconductors By D Manske 2004 84 figs., XII, 228 pages 203 Effective Field Theories in Flavour Physics By T Mannel 2004 29 figs., VIII, 175 pages 204 Stopping of Heavy Ions By P Sigmund 2004 43 figs., XIV, 157 pages 205 Three-Dimensional X-Ray Diffraction Microscopy Mapping Polycrystals and Their Dynamics By H Poulsen 2004 49 figs., XI, 154 pages 206 Ultrathin Metal Films Magnetic and Structural Properties By M Wuttig and X Liu 2004 234 figs., XII, 375 pages 207 Dynamics of Spatio-Temporal Cellular Structures Henri Benard Centenary Review Edited by I Mutabazi, J.E Wesfreid, and E Guyon 2005 approx 50 figs., 150 pages 208 Nuclear Condensed Matter Physics with Synchrotron Radiation Basic Principles, Methodology and Applications By R Röhlsberger 2004 152 figs., XVI, 318 pages 209 Infrared Ellipsometry on Semiconductor Layer Structures Phonons, Plasmons, and Polaritons By M Schubert 2004 77 figs., XI, 193 pages 210 Cosmology By D.-E Liebscher 2005 Approx 100 figs., 300 pages 211 Evaluating Feynman Integrals By V.A Smirnov 2004 48 figs., IX, 247 pages 213 Parametric X-ray Radiation in Crystals By V.G Baryshevsky, I.D Feranchuk, and A.P Ulyanenkov 2006 63 figs., IX, 172 pages 214 Unconventional Superconductors Experimental Investigation of the Order-Parameter Symmetry By G Goll 2006 67 figs., XII, 172 pages 215 Control Theory in Physics and other Fields of Science Concepts, Tools, and Applications By M Schulz 2006 46 figs., X, 294 pages 216 Theory of the Muon Anomalous Magnetic Moment By K Melnikov, A Vainshtein 2006 33 figs., XII, 176 pages 217 The Flow Equation Approach to Many-Particle Systems By S Kehrein 2006 24 figs., XII, 170 pages 219 Inelastic Light Scattering of Semiconductor Nanostructures By C Schüller 2007 105 figs., XII, 178 pages 220 Precision Electroweak Physics at Electron-Positron Colliders By S Roth 2007 107 figs., X, 174 pages 221 Free Surface Flows under Compensated Gravity Conditions By M Dreyer 2007 128 figs., X, 272 pages 222 Theory of Light Hydrogenic Bound States By M.I Eides, H Grotch, and V.A Shelyuto 2007 108 figs., XVI, 260 pages 223 Electrical Resistivity of Thin Metal Films By P Wißmann, H.-U Finzel 2007 110 figs., VII, 150 pages ... www.physik.uni-ulm.de/theo/qc/group.html Peter Wißmann Hans-Ulrich Finzel Electrical Resistivity of Thin Metal Films With 110 Figures ABC Professor Peter Wißmann Professor Hans-Ulrich Finzel Institut für Physikalische... that of cooling The amount of the deviation can vary remarkably as several measurements of The Effect of Annealing on the Electrical Resistivity of Thin Gold Films 45 Fig 4.14 Changing of resistivity. .. Finzel: Electrical Resistivity of Thin Metal Films, STMP 223, 9–34 (2007) c Springer-Verlag Berlin Heidelberg 2007 DOI 10.1007/3-540-48490-6 10 The Effect of Annealing on the Electrical Resistivity of