Current-Voltage Behavior of Atomic-Sized Transition Metal Contacts Søren Kynde Nielsen PhDthesis Preface his thesis is submitted to the Faculty of Science at the University T of Aarhus, Arhus,˚ Denmark, in order to fulfill the requirements for obtaining the PhD degree in physics.The studies have been carried out under the supervision of Flemming Besenbacher in the scanning tunneling microscopy (STM) laboratory at the Center for Atomic-Scale Materials Physics (CAMP) at the Department of Physics and Astronomy from August 1998 to July 2002.CAMP is sponsored by the Danish National Research Foundation. Many of the experimental results were obtained during two visits to the Solid State Physics Group (VSM) at the Kamerlingh Onnes Labora- tory, University of Leiden, Leiden, The Netherlands in the autumn and winter of 2000 and the summer of 2001. Søren Kynde Nielsen Department of Physics and Astronomy Center for Atomic-scale Materials Physics University of Aarhus, Denmark PhDthesis September 2002 ii Acknowledgments irst of all I would like to thank my supervisor Flemming Besenbacher for his F enthusiastic approach and his motivating behavior concerning getting the job done! His greatest influence on my life came about when he encouraged me to go abroad, resulting in my two visits at the Kamerlingh Onnes Laboratory at the University of Leiden in Holland.This turned out to be a great learning experience, and it must have strengthened my character tremendously. Fellow CAMP member Kim Hansen acted as my co-supervisor for the first three years of my PhD.During the last year, he has been available for correspon- dence offering continued support and guidance.Kim’s enthusiasm for physics in general and nano-science in particular has been a great inspiration and help to me.I have on numerous occasions benefitted from his huge knowledge on subjects related to our work, and his corrections, comments and suggestions on the chapters of this thesis are invaluable.For all this I am very grateful. I would also like to thank the other two senior members of CAMP, Erik Lægsgaard for his technical support and Ivan Stensgaard for his guidance in the early stages of my PhD.They both have an always present and warm, but very dry humour, which I have enjoyed at several occasions after I finally learned to appreciate it. I am grateful to professor Jan M.van Ruitenbeek for welcoming me into the VSM group in Leiden.His calm presence in the lab was a great help, providing a pleasant working environment.Through interesting discussions and comments on my work he has contributed to the writing of several chapters. I was especially pleased on the occasions where he and his wife invited our little group to visit them in their beautiful home. It was a pleasure to work with Yves Noat in Leiden.While he introduced me to the mechanically controllable break-junction (MCBJ) we performed, in close collaboration, the experiments presented in Chapter 9.His great enthusiasm for the experimental work and especially for infinite discussions had a positive influence on my work in Leiden. I owe Roel Smit thanks for providing extra data and figures which helped elucidate the experimental results presented in Chapter 9. iii In general I extend my thanks to all members of the VSM group for making my stay pleasant, especially Luca Bai, Carlos Untiedt and Roel Smit, for sharing many evenings and cinema experiences, making me feel at home. I have enjoyed collaborating with Mads Brandbyge at the Microelectronic Center, Technical University of Denmark.Apart from fruitful discussions he contributed with the theoretical input to Chapters 6–8, greatly enhancing their quality.His calculations guided the understanding of our experimental observa- tions and have been vital for the publication of articles in high-impact journals; an outcome which is highly appreciated. I would furthermore like to thank all the people who have been part of the CAMP group in the past four years, for creating a very interesting research environment which it has been a pleasure to be part of. Special thanks to both Jeanette Dandanell and Anette Skovgaard for proof reading my manuscript, correcting numerous typos and grammatical errors.If there are some left, they will have entered with later changes. A thanks also to Marianne Larsen for allowing me to use her drawings for the making of the very first and most amusing figure. Having finished with all the professional acknowledgments, a few, but to me very important people still remain.To all my friends and family, thanks for being there for me. I can never thank my parents enough for their continued support through my entire study at the University.They always offered their support both during happy times but more importantly also when I was down. Finally I extend my deepest gratitude to my girlfriend Line.For the past six months where I have worked almost continously on this thesis she was always there to cheer me up and help me through the tough times.For this and a multitude of other reasons, I owe her all my love. Søren Kynde Nielsen Arhus,˚ September 2002 iv List of Publications n this thesis, the references listed below are referred to with capital Roman I numerals, whereas other references are cited using Arabic numerals. Publications [I] Fast and accurate current-voltage curves of metallic quantum point contacts, K.Hansen, S.K.Nielsen, E.Lægsgaard, I.Stensgaard, and F.Besenbacher, Rev.Sci.Instr. 71, 1793–1803 (2000). [II] Current-voltage curves of gold quantum point contacts revisited, K.Hansen, S.K.Nielsen, M.Brandbyge, E.Lægsgaard, I.Stensgaard, and F.Besenbacher, Appl.Phys.Lett. 77, 708–710 (2000). [III] Current-Voltage Curves of Atomic-Sized Transition Metal Contacts: An Explanation Why Au is Ohmic and Pt is Not, S.K.Nielsen, M.Brandbyge, K.Hansen, K.Stokbro, J.M.van Ruitenbeek and F.Besenbacher, Phys.Rev.Lett. 89, 066804 (2002). [IV] Current-voltage curves of atomic-sized transition metal contacts, S.K.Nielsen, K.Hansen, M.Brandbyge, J.M.van Ruitenbeek and F.Besenbacher, in preparation (unpublished). [V] Current-induced disruptions of monatomic transition metal contacts, S.K.Nielsen, K.Hansen, M.Brandbyge, J.M.van Ruitenbeek and F.Besenbacher, in preparation (unpublished). [VI] Bias-dependent peak shift in conductance histograms of atomic-sized platinum contacts, S.K.Nielsen, Y.Noat, M.Brandbyge, R.H.M.Smit, K.Hansen, L.Y.Chen, A.I.Yanson, F.Besenbacher and J.M.van Ruitenbeek, in preparation (unpublished). v Contents 1 Introduction 1 1.1 Why study nano-sized structures? ................. 2 1.2Feynman’sbottom!.......................... 3 1.3 The six metals: Au, Pt, Ag, Cu, Pd and Ni ............ 4 1.4Structureofthethesis........................ 6 References............................... 9 2 Theory of Conductance 11 2.1 From macroscopic to atomic-sized contacts ............ 11 2.2Thecircularorifice.......................... 15 2.3 The Landauer-B¨uttikerformalism.................. 18 2.4Theadiabaticapproximation.................... 21 2.5 Quantized conductance ........................ 22 2.6Eigenchannels............................. 23 References............................... 24 3 Experimental Realization of ASCs29 3.1Introduction.............................. 30 3.2 Scanning tunneling microscope ................... 32 3.3 Mechanically controllable break-junction .............. 34 References............................... 37 4 Conductance Histograms 41 4.1Concept................................ 42 4.2Review................................. 45 4.3 The noble metals: Au, Ag and Cu ................. 48 4.4Theplatinummetals:Pt,PdandNi................ 51 References............................... 56 vii 5 Fast and Accurate Electronic Setup 61 5.1Introduction.............................. 61 5.2 Block diagram of the setup ..................... 62 5.3Thecurrent-to-voltageconverter.................. 63 5.4Modelofthecircuit......................... 68 5.5Calibration.............................. 70 5.6 Calculating G, I,andV ....................... 71 5.7Timingtheburst........................... 72 5.8 Performance on resistors ....................... 76 5.9 Performance on a breaking Au ASC ................ 79 5.10Summary............................... 81 References............................... 82 6 Effect of Impuritieson I-V Curvesof Au 85 6.1Introduction.............................. 86 6.2Experimentaldetails......................... 86 6.3Current-voltagecurves........................ 88 6.4 Tight-binding calculations ...................... 90 6.5 Tunneling through a thin insulating film .............. 92 6.6Conclusion.............................. 94 6.7 Other effects of contamination on ASCs .............. 95 6.7.1 Exposing ASCs of Au to ambient conditions ........ 95 6.7.2 Monatomic chains with extremely long bond lengths . 96 6.7.3 Influence of hydrogen on platinum .............100 6.7.4 Conclusion..........................103 References...............................104 7 Current-Voltage Curvesof ASCs 111 7.1Experimentaldetails.........................112 7.2 Why gold is Ohmic and platinum is not ..............115 7.2.1 Examples of current-voltage curves .............115 7.2.2 Fitting to a polynomial ...................116 7.2.3 Density functional theory calculations ...........120 7.2.4 Discussion...........................124 7.2.5 Conclusion..........................126 7.3 Current-voltage curves of noble metals ...............127 7.4 Current-voltage curves of platinum metals .............131 7.5Discussion...............................137 7.6Conclusion..............................140