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X-ray imaging of silicon die within fully packaged semiconductor devices
- Brian K. Tanner, Patrick J. McNally, Andreas N. Danilewsky
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- Journal:
- Powder Diffraction / Volume 36 / Issue 2 / June 2021
- Published online by Cambridge University Press:
- 30 March 2021, pp. 78-84
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X-ray diffraction imaging (XRDI) (topography) measurements of silicon die warpage within fully packaged commercial quad-flat no-lead devices are described. Using synchrotron radiation, it has been shown that the tilt of the lattice planes in the Analog Devices AD9253 die initially falls, but after 100 °C, it rises again. The twist across the die wafer falls linearly with an increase in temperature. At 200 °C, the tilt varies approximately linearly with position, that is, displacement varies quadratically along the die. The warpage is approximately reversible on cooling, suggesting that it has a simple paraboloidal form prior to encapsulation; the complex tilt and twisting result from the polymer setting process. Feasibility studies are reported, which demonstrate that a divergent beam and quasi-monochromatic radiation from a sealed X-ray tube can be used to perform warpage measurements by XRDI in the laboratory. Existing tools have limitations because of the geometry of the X-ray optics, resulting in applicability only to simple warpage structures. The necessary modifications required for use in situations of complex warpage, for example, in multiple die interconnected packages are specified.
Neuropsychological Profile of Parkin Mutation Carriers with and without Parkinson Disease: The CORE-PD Study
- Elise Caccappolo, Roy N. Alcalay, Helen Mejia-Santana, Ming-X. Tang, Brian Rakitin, Llency Rosado, Elan D. Louis, Cynthia L. Comella, Amy Colcher, Danna Jennings, Martha A. Nance, Susan Bressman, William K. Scott, Caroline M. Tanner, Susan F. Mickel, Howard F. Andrews, Cheryl Waters, Stanley Fahn, Lucien J. Cote, Steven Frucht, Blair Ford, Michael Rezak, Kevin Novak, Joseph H. Friedman, Ronald F. Pfeiffer, Laura Marsh, Brad Hiner, Andrew D. Siderowf, Barbara M. Ross, Miguel Verbitsky, Sergey Kisselev, Ruth Ottman, Lorraine N. Clark, Karen S. Marder
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- Journal of the International Neuropsychological Society / Volume 17 / Issue 1 / January 2011
- Published online by Cambridge University Press:
- 24 November 2010, pp. 91-100
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The cognitive profile of early onset Parkinson’s disease (EOPD) has not been clearly defined. Mutations in the parkin gene are the most common genetic risk factor for EOPD and may offer information about the neuropsychological pattern of performance in both symptomatic and asymptomatic mutation carriers. EOPD probands and their first-degree relatives who did not have Parkinson’s disease (PD) were genotyped for mutations in the parkin gene and administered a comprehensive neuropsychological battery. Performance was compared between EOPD probands with (N = 43) and without (N = 52) parkin mutations. The same neuropsychological battery was administered to 217 first-degree relatives to assess neuropsychological function in individuals who carry parkin mutations but do not have PD. No significant differences in neuropsychological test performance were found between parkin carrier and noncarrier probands. Performance also did not differ between EOPD noncarriers and carrier subgroups (i.e., heterozygotes, compound heterozygotes/homozygotes). Similarly, no differences were found among unaffected family members across genotypes. Mean neuropsychological test performance was within normal range in all probands and relatives. Carriers of parkin mutations, whether or not they have PD, do not perform differently on neuropsychological measures as compared to noncarriers. The cognitive functioning of parkin carriers over time warrants further study. (JINS, 2011, 17, 1–10)
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. Chapman, James H. Charlesworth, Kenneth R. Chase, Chen Zemin, Luciano Chianeque, Philip Chia Phin Yin, Francisca H. Chimhanda, Daniel Chiquete, John T. Chirban, Soobin Choi, Robert Choquette, Mita Choudhury, Gerald Christianson, John Chryssavgis, Sejong Chun, Esther Chung-Kim, Charles M. A. Clark, Elizabeth A. Clark, Sathianathan Clarke, Fred Cloud, John B. Cobb, W. Owen Cole, John A Coleman, John J. Collins, Sylvia Collins-Mayo, Paul K. Conkin, Beth A. Conklin, Sean Connolly, Demetrios J. Constantelos, Michael A. Conway, Paula M. Cooey, Austin Cooper, Michael L. Cooper-White, Pamela Cooper-White, L. William Countryman, Sérgio Coutinho, Pamela Couture, Shannon Craigo-Snell, James L. Crenshaw, David Crowner, Humberto Horacio Cucchetti, Lawrence S. Cunningham, Elizabeth Mason Currier, Emmanuel Cutrone, Mary L. Daniel, David D. Daniels, Robert Darden, Rolf Darge, Isaiah Dau, Jeffry C. Davis, Jane Dawson, Valentin Dedji, John W. de Gruchy, Paul DeHart, Wendy J. Deichmann Edwards, Miguel A. De La Torre, George E. Demacopoulos, Thomas de Mayo, Leah DeVun, Beatriz de Vasconcellos Dias, Dennis C. Dickerson, John M. Dillon, Luis Miguel Donatello, Igor Dorfmann-Lazarev, Susanna Drake, Jonathan A. Draper, N. Dreher Martin, Otto Dreydoppel, Angelyn Dries, A. J. Droge, Francis X. D'Sa, Marilyn Dunn, Nicole Wilkinson Duran, Rifaat Ebied, Mark J. Edwards, William H. Edwards, Leonard H. Ehrlich, Nancy L. Eiesland, Martin Elbel, J. Harold Ellens, Stephen Ellingson, Marvin M. Ellison, Robert Ellsberg, Jean Bethke Elshtain, Eldon Jay Epp, Peter C. Erb, Tassilo Erhardt, Maria Erling, Noel Leo Erskine, Gillian R. Evans, Virginia Fabella, Michael A. Fahey, Edward Farley, Margaret A. Farley, Wendy Farley, Robert Fastiggi, Seena Fazel, Duncan S. Ferguson, Helwar Figueroa, Paul Corby Finney, Kyriaki Karidoyanes FitzGerald, Thomas E. FitzGerald, John R. Fitzmier, Marie Therese Flanagan, Sabina Flanagan, Claude Flipo, Ronald B. Flowers, Carole Fontaine, David Ford, Mary Ford, Stephanie A. Ford, Jim Forest, William Franke, Robert M. Franklin, Ruth Franzén, Edward H. Friedman, Samuel Frouisou, Lorelei F. Fuchs, Jojo M. Fung, Inger Furseth, Richard R. Gaillardetz, Brandon Gallaher, China Galland, Mark Galli, Ismael García, Tharscisse Gatwa, Jean-Marie Gaudeul, Luis María Gavilanes del Castillo, Pavel L. Gavrilyuk, Volney P. Gay, Metropolitan Athanasios Geevargis, Kondothra M. George, Mary Gerhart, Simon Gikandi, Maurice Gilbert, Michael J. Gillgannon, Verónica Giménez Beliveau, Terryl Givens, Beth Glazier-McDonald, Philip Gleason, Menghun Goh, Brian Golding, Bishop Hilario M. Gomez, Michelle A. Gonzalez, Donald K. Gorrell, Roy Gottfried, Tamara Grdzelidze, Joel B. Green, Niels Henrik Gregersen, Cristina Grenholm, Herbert Griffiths, Eric W. Gritsch, Erich S. Gruen, Christoffer H. Grundmann, Paul H. Gundani, Jon P. Gunnemann, Petre Guran, Vidar L. Haanes, Jeremiah M. Hackett, Getatchew Haile, Douglas John Hall, Nicholas Hammond, Daphne Hampson, Jehu J. Hanciles, Barry Hankins, Jennifer Haraguchi, Stanley S. Harakas, Anthony John Harding, Conrad L. Harkins, J. William Harmless, Marjory Harper, Amir Harrak, Joel F. Harrington, Mark W. Harris, Susan Ashbrook Harvey, Van A. Harvey, R. Chris Hassel, Jione Havea, Daniel Hawk, Diana L. Hayes, Leslie Hayes, Priscilla Hayner, S. Mark Heim, Simo Heininen, Richard P. Heitzenrater, Eila Helander, David Hempton, Scott H. Hendrix, Jan-Olav Henriksen, Gina Hens-Piazza, Carter Heyward, Nicholas J. Higham, David Hilliard, Norman A. Hjelm, Peter C. Hodgson, Arthur Holder, M. Jan Holton, Dwight N. Hopkins, Ronnie Po-chia Hsia, Po-Ho Huang, James Hudnut-Beumler, Jennifer S. Hughes, Leonard M. Hummel, Mary E. Hunt, Laennec Hurbon, Mark Hutchinson, Susan E. Hylen, Mary Beth Ingham, H. Larry Ingle, Dale T. Irvin, Jon Isaak, Paul John Isaak, Ada María Isasi-Díaz, Hans Raun Iversen, Margaret C. Jacob, Arthur James, Maria Jansdotter-Samuelsson, David Jasper, Werner G. Jeanrond, Renée Jeffery, David Lyle Jeffrey, Theodore W. Jennings, David H. Jensen, Robin Margaret Jensen, David Jobling, Dale A. Johnson, Elizabeth A. Johnson, Maxwell E. Johnson, Sarah Johnson, Mark D. Johnston, F. Stanley Jones, James William Jones, John R. Jones, Alissa Jones Nelson, Inge Jonsson, Jan Joosten, Elizabeth Judd, Mulambya Peggy Kabonde, Robert Kaggwa, Sylvester Kahakwa, Isaac Kalimi, Ogbu U. Kalu, Eunice Kamaara, Wayne C. Kannaday, Musimbi Kanyoro, Veli-Matti Kärkkäinen, Frank Kaufmann, Léon Nguapitshi Kayongo, Richard Kearney, Alice A. Keefe, Ralph Keen, Catherine Keller, Anthony J. Kelly, Karen Kennelly, Kathi Lynn Kern, Fergus Kerr, Edward Kessler, George Kilcourse, Heup Young Kim, Kim Sung-Hae, Kim Yong-Bock, Kim Yung Suk, Richard King, Thomas M. King, Robert M. Kingdon, Ross Kinsler, Hans G. Kippenberg, Cheryl A. Kirk-Duggan, Clifton Kirkpatrick, Leonid Kishkovsky, Nadieszda Kizenko, Jeffrey Klaiber, Hans-Josef Klauck, Sidney Knight, Samuel Kobia, Robert Kolb, Karla Ann Koll, Heikki Kotila, Donald Kraybill, Philip D. W. Krey, Yves Krumenacker, Jeffrey Kah-Jin Kuan, Simanga R. Kumalo, Peter Kuzmic, Simon Shui-Man Kwan, Kwok Pui-lan, André LaCocque, Stephen E. Lahey, John Tsz Pang Lai, Emiel Lamberts, Armando Lampe, Craig Lampe, Beverly J. Lanzetta, Eve LaPlante, Lizette Larson-Miller, Ariel Bybee Laughton, Leonard Lawlor, Bentley Layton, Robin A. Leaver, Karen Lebacqz, Archie Chi Chung Lee, Marilyn J. Legge, Hervé LeGrand, D. L. LeMahieu, Raymond Lemieux, Bill J. Leonard, Ellen M. Leonard, Outi Leppä, Jean Lesaulnier, Nantawan Boonprasat Lewis, Henrietta Leyser, Alexei Lidov, Bernard Lightman, Paul Chang-Ha Lim, Carter Lindberg, Mark R. Lindsay, James R. Linville, James C. Livingston, Ann Loades, David Loades, Jean-Claude Loba-Mkole, Lo Lung Kwong, Wati Longchar, Eleazar López, David W. Lotz, Andrew Louth, Robin W. Lovin, William Luis, Frank D. Macchia, Diarmaid N. J. MacCulloch, Kirk R. MacGregor, Marjory A. MacLean, Donald MacLeod, Tomas S. Maddela, Inge Mager, Laurenti Magesa, David G. Maillu, Fortunato Mallimaci, Philip Mamalakis, Kä Mana, Ukachukwu Chris Manus, Herbert Robinson Marbury, Reuel Norman Marigza, Jacqueline Mariña, Antti Marjanen, Luiz C. L. Marques, Madipoane Masenya (ngwan'a Mphahlele), Caleb J. D. Maskell, Steve Mason, Thomas Massaro, Fernando Matamoros Ponce, András Máté-Tóth, Odair Pedroso Mateus, Dinis Matsolo, Fumitaka Matsuoka, John D'Arcy May, Yelena Mazour-Matusevich, Theodore Mbazumutima, John S. McClure, Christian McConnell, Lee Martin McDonald, Gary B. McGee, Thomas McGowan, Alister E. McGrath, Richard J. McGregor, John A. McGuckin, Maud Burnett McInerney, Elsie Anne McKee, Mary B. McKinley, James F. McMillan, Ernan McMullin, Kathleen E. McVey, M. 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Stewart, Cynthia Stokes Brown, Ken Stone, Anne Stott, Elizabeth Stuart, Monya Stubbs, Marjorie Hewitt Suchocki, David Kwang-sun Suh, Scott W. Sunquist, Keith Suter, Douglas Sweeney, Charles H. Talbert, Shawqi N. Talia, Elsa Tamez, Joseph B. Tamney, Jonathan Y. Tan, Yak-Hwee Tan, Kathryn Tanner, Feiya Tao, Elizabeth S. Tapia, Aquiline Tarimo, Claire Taylor, Mark Lewis Taylor, Bishop Abba Samuel Wolde Tekestebirhan, Eugene TeSelle, M. Thomas Thangaraj, David R. Thomas, Andrew Thornley, Scott Thumma, Marcelo Timotheo da Costa, George E. “Tink” Tinker, Ola Tjørhom, Karen Jo Torjesen, Iain R. Torrance, Fernando Torres-Londoño, Archbishop Demetrios [Trakatellis], Marit Trelstad, Christine Trevett, Phyllis Trible, Johannes Tromp, Paul Turner, Robert G. Tuttle, Archbishop Desmond Tutu, Peter Tyler, Anders Tyrberg, Justin Ukpong, Javier Ulloa, Camillus Umoh, Kristi Upson-Saia, Martina Urban, Monica Uribe, Elochukwu Eugene Uzukwu, Richard Vaggione, Gabriel Vahanian, Paul Valliere, T. J. 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Yee, Viktor Yelensky, Yeo Khiok-Khng, Gustav K. K. Yeung, Angela Yiu, Amos Yong, Yong Ting Jin, You Bin, Youhanna Nessim Youssef, Eliana Yunes, Robert Michael Zaller, Valarie H. Ziegler, Barbara Brown Zikmund, Joyce Ann Zimmerman, Aurora Zlotnik, Zhuo Xinping
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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Elastic Constants of Nanometer Thick Diamond-like Carbon Films
- Marco G. Beghi, Carlo E. Bottani, Andrea LiBassi, Rosanna Pastorelli, Brian K. Tanner, Andrea C. Ferrari, John Robertson
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- MRS Online Proceedings Library Archive / Volume 675 / 2001
- Published online by Cambridge University Press:
- 21 March 2011, W11.6.1
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Carbon films of thickness down to 2 nanometers are necessary to achieve a storage density of 100 Gbit/in2 in magnetic hard disks. Reliable methods to measure the properties of these ultrathin films still have to be developed. We show for the first time that combining Surface Brillouin Scattering (SBS) and X-ray reflectivity measurements the elastic constants of such films can be obtained. Tetrahedral amorphous carbon films were deposited on silicon, by an S bend filtered cathodic vacuum arc, which provides a continuous coverage on large areas free of macroparticles. Films of thickness down to 2 nm and density of ∼3 g/cm3 were produced and characterized. The dispersion relations of surface acoustic waves are measured by SBS for films of different thickness and for the bare substrate. Waves can be described by a continuum elastic model. Fitting of the dispersion relations, computed for given film properties, to the measured dispersion relations allows the derivation of the elastic constants. Fora 8 nm thick film we find a Young's modulus E around 400 GPa, with a shear modulus G lying in the 130 – 210 GPa interval. For a 4.5 nm thick film, E is around 240 GPa, with G lying in the 70 – 130 GPa interval. Results for even thinner films become highly sensitive to the precision of the substrate properties, and indicate that the above values are lower bounds. We thus show that we can grow and characterize nanometer size tetrahedral amorphous carbon films, which maintain their density and mechanical properties down to the nm range.
4 - Energy bands
- Brian K. Tanner
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- Introduction to the Physics of Electrons in Solids
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- 05 June 2012
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- 30 March 1995, pp 52-97
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Appendix 3 - Derivation of the Landé g factor
- Brian K. Tanner
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- Introduction to the Physics of Electrons in Solids
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- 30 March 1995, pp 242-243
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Contents
- Brian K. Tanner
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- Introduction to the Physics of Electrons in Solids
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- 30 March 1995, pp ix-xii
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1 - The classical free electron model
- Brian K. Tanner
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- Introduction to the Physics of Electrons in Solids
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Summary
In practical terms, the enormous range of values of resistivity of solids is something which we take for granted. Every day, we happily touch the polymer sleeving or fitments surrounding conductors bearing potentially lethal currents at quite high voltages. Only when one is reminded that the difference of almost 30 orders of magnitude found between the resistivity of the noble metals and some synthetic polymers represents the largest variation of any physical parameter does this apparently mundane phenomenon suddenly appear intriguing. It is tempting to enquire whether the same physical process can be responsible for electrical conduction in all materials. Even if the same process extends over half the range it would be a remarkable achievement. Perhaps we would then appreciate why so much time and effort is devoted to measurements of electrical conductivity.
It is hard to conceive that, prior to the turn of the century, very little was known about the physics of solids. Some ideas on crystal structure had been anticipated from the morphology of natural and synthetic crystals but there existed little understanding of the electrical, thermal or magnetic properties of solids. Solid state physics is a twentieth century branch of science and as such deserves recognition as an important section of ‘modern physics’. As we shall see later, it was not until quantum mechanics was applied to the physics of solids that many real advances were made.
8 - Localized electrons
- Brian K. Tanner
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- Introduction to the Physics of Electrons in Solids
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Summary
In this chapter we examine the way in which the simple model of an electron in a box can be applied to understand the optical properties of the alkali halides. We then proceed to consider the magnetic properties of electrons which are localized at specific lattice sites. With this discussion of the phenomena of diamagnetism and paramagnetism, we lead up to the next chapter on magnetic order where we see the breakdown of the independent electron approximation giving quite dramatic results.
Point defects in alkali halides
The band gaps of the alkali halides, such as NaCl or KCl, are high and they are found to be excellent insulators. Thus, in the pure and perfect state, the alkali halides are transparent to visible light. However, as a result of either irradiation with X-rays, heating in the vapour of the alkali metal or electrolysis at high temperature, it is possible to create large numbers of negative ion vacancies (Fig. 8.1). These defects correspond to unoccupied lattice sites which would normally contain a halide ion. If the lattice site was simply vacant, the site would appear to be positively charged due to the removal of negative charge on the halide ion. In order to preserve electrical neutrality, it is favourable for an electron to become trapped at this negative ion vacancy. Such an electron trapped at a negative ion vacancy is called an F or colour centre.
2 - Quantum mechanical free electron model
- Brian K. Tanner
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- Introduction to the Physics of Electrons in Solids
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Summary
The years of the third decade of the present century were heady times. Old social orders were being swept away, monarchies becoming republics and the United States of America was emerging as a world power. In physics too, revolutions were taking place, none more potent than that which resulted in the emergence of quantum mechanics as a model for the behaviour of sub-atomic particles.
It was Newton who first suggested that light was particulate but during the nineteenth century this view had fallen into neglect. Indeed a number of experiments, for example the classic Young's slits experiment, demonstrated quite conclusively that light was a wave motion. How else could interference fringes occur? However, the experiments on the photoelectric effect demonstrated just as conclusively that light energy was carried in packets, or quanta, and that a continuous wave description was not applicable.
This ‘wave or particle’ dilemma was not unique to the behaviour of light. J. J. Thompson showed that cathode rays were charged, had a well defined mass and had all the properties expected of a beam of particles. Nevertheless, Davisson and Germer showed that diffraction of electrons could take place, an effect made visually much more dramatic by G. P. Thompson's transmission electron diffraction patterns. Nowadays, electron diffraction is used as a routine analytical tool in all advanced metallurgical and materials science laboratories (Fig. 2.1). Clearly new axioms were required.
10 - Superconductivity
- Brian K. Tanner
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- Introduction to the Physics of Electrons in Solids
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- 30 March 1995, pp 213-236
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Summary
Probably the most spectacular phenomenon associated with the breakdown of the independent electron approximation is that of superconductivity. In the superconducting state, the material loses all resistivity and becomes a perfect conductor. The discovery in 1986 of oxide materials which were superconducting at temperatures above that of the boiling point of nitrogen sparked an unprecedented surge of activity in the field which remains an area of high profile and popular interest.
The discovery of superconductivity
In 1908 Kammerlingh Onnes succeeded in liquefying helium and set about the task of studying the properties of metals at these extremely low temperatures. As we saw in Chapter 1, the resistivity of metals such as platinum fell to a small, non-zero value when extrapolated to T = 0. This residual resistivity fell with improvements in purity and thus Onnes studied mercury, which was the most pure metal available at that time. To the great surprise of Onnes and the whole scientific community, the resistivity fell monotonically until just above the boiling point of helium and then fell abruptly to zero. Fig. 10.1 shows an example of the superconducting phase transition in yttrium barium copper oxide, one of the high temperature superconducting oxides. Onnes was unable to measure precisely the transition width or whether the resistivity was genuinely zero. However, in 1963 File and Mills measured the decay of a persistent current set up in a superconducting ring using nuclear magnetic resonance as the probe.
6 - Electrical conduction in semiconductors and insulators
- Brian K. Tanner
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- Introduction to the Physics of Electrons in Solids
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- 30 March 1995, pp 111-137
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7 - Semiconductor devices
- Brian K. Tanner
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Summary
One of the most remarkable developments of the last decade has been the growth of the semiconductor industry. The exploitation of the properties of semiconducting materials to build large logic arrays on a single piece of crystal has led to a dramatic increase in the processing power and memory capacity of small computers, with a simultaneous fall in price. Development of single chip microprocessors has revolutionized our mode of working in a whole range of fields from the factory floor to the office. In this chapter we will examine the basic physics associated with a number of devices, and as many devices rely on the properties of junctions between n- and p-type semiconductors a fairly detailed discussion of such junctions is given before individual devices are treated. However, because all devices require connection to metallic wires in order to join components together we will first examine the metal–semiconductor junction. As it turns out this proves to be an excellent introduction to the p–n junction as well as providing a glimpse into some of the not-so-obvious pitfalls associated with device manufacture.
Metal–semiconductor junctions
The Schottky barrier
Let us suppose that a piece of metal is brought into contact with a piece of n-type semiconductor. (Of course, in practice, the metal would be evaporated on the semiconductor as a thin film, or attached with a soldered connection in which an alloy is formed, but such a naive picture is useful to fix our ideas.)
Appendix 2 - Elements of statistical mechanics
- Brian K. Tanner
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Preface
- Brian K. Tanner
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Summary
Most textbooks on solid state physics begin the exposition from what might be called a ‘structural position’. Space and point groups are discussed, followed by consideration of the Bravais lattice. The reader is thus led on to elementary ideas about crystallography and the use of diffraction techniques for the solution of crystal structures. Having laid the foundation of how atoms and molecules order to form crystalline structures, electron motion in such periodic structures is treated and band theory developed. The free electron model is seen as an approximation of the more general band theory. In many, rather formal, ways this approach is very satisfying. It would seem obvious that in the first instance one must understand the structure of the material on which one is working before attempting to understand its other physical properties. However, in practice, it proves rather hard to teach solid state physics this way and to retain student enthusiasm in the early stages of the teaching of crystallography where one is dealing with rather difficult geometrical concepts and very little physics. There is a very real danger of making the introduction to the subject so unexciting that the inspiration is lost and students come to regard solid state physics as the ‘dull and dirty’ branch of their physics course. However, elementary quantum mechanics, including the one-dimensional solution of the time independent Schrödinger equation, is included quite early in many undergraduate courses and there is much attraction in illustrating at this early stage the important technological context of the apparently abstruse quantum mechanics.
Appendix 1 - Elements of kinetic theory
- Brian K. Tanner
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5 - Experimental evidence for band structure and effective mass
- Brian K. Tanner
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Summary
At the beginning of the previous chapter, we reviewed some experimental data which could not be explained using the free electron model. While the Hall effect unequivocally indicates the breakdown of the free electron model, it does not provide direct evidence for the existence of energy bands. There are, however, a number of techniques which do provide a direct measure of the energy gaps and the density of states.
Optical techniques for band structure measurements
Infra-red absorption in semiconductors
The first technique is both the easiest to understand and the easiest to perform experimentally. If one looks at a piece of polished silicon or germanium, it has the appearance of a metal. However, if thinned to below a few micrometres in thickness a piece of silicon is translucent, having a red appearance. A certain amount of light is transmitted in the red end of the spectrum. If one goes further into the infra-red, we find that these semiconductors are transparent.
Monochromatic radiation can be obtained from the continuous spectrum of infra-red radiation emitted by a hot filament by use of a diffraction grating spectrometer. The intensity transmitted through the semiconductor is measured as a function of wavelength, and, as illustrated in Fig. 5.1, a very abrupt drop in transmission is observed at a frequency characteristic of the semiconductor. For germanium and other common semiconductors this ‘absorption edge’, as it is called, occurs at around 1–2 μm wavelength. This is in the near infra-red.
9 - Magnetism
- Brian K. Tanner
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We have until now made use of the independent electron approximation, in which it is assumed that we can treat each electron independently of all of the others. In this chapter we will examine the consequence of the breakdown of this phenomenon.
It has been known for centuries, indeed it was known to the ancient Chinese, that magnetite or lodestone was attracted by the earth's field. Two pieces of lodestone attracted or repelled each other depending on which end of the lump of rock was pointed at the other. These chunks of material possess a spontaneous magnetic moment, i.e. they have a magnetization in zero external magnetic field.
We find that the elements iron, nickel and cobalt, bunched together in the middle of the periodic table, can also be induced to have a spontaneous moment at room temperature. The spontaneous magnetization M (defined as the magnetic moment per unit volume) is very large compared with that induced by a magnetic field in materials such as copper or zinc, which are very close in the periodic table. Alloys of iron, cobalt and nickel also have such properties which became known as ferromagnetism.
Basic phenomena
Hysteresis loops
Ferromagnetic materials show a characteristic M – H (or M – B0) loop. The susceptibility, defined by k = M/B0 where B0 is the external field, is very large and the magnetization displays hysteresis (Fig. 9.1). In sufficiently high field the magnetization saturates, this saturation magnetization being a characteristic of the material.
Frontmatter
- Brian K. Tanner
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Index
- Brian K. Tanner
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