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This lecture discusses the properties and characterization of materials, focusing on electronic characterization of diamond and Teflon. Topics covered include resistivity measurements, contact resistance, Schottky barriers, four-point probe resistivity, lock-in amplifiers, Hall effect, van der Pauw method, temperature dependence, and diamond superconductivity.
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Gavin W Morley Department of Physics University of Warwick Diamond Science & Technology Centre for Doctoral Training, MSc course Module 2 – Properties and Characterization of Materials (PX904) Lecture 9 – Electronic characterization
PTFE (Teflon) > 1018 -cm (room temperature) Silicon ~ 104 -cm (room temperature) Pure metal ~ 10-10 -cm (1 K) Tin ~ 10-5 -cm (room temperature) Superconductors ~ 0 Diamond ~ 1016 -cm (room temperature) 10-10 1 1010 1020 Resistivity (ohm-cm)
Bad way to measure Resistivity, Ohm’s law V = I R R = L/A sample Length, L Area, A
Bad way to measure Resistivity, Source voltage, V Measure current, I A Ohm’s law V = I R R = L/A sample Length, L Area, A
Measuring contact resistance Source voltage, V Measure current, I A Ohm’s law V = I R Study one contact at a time sample Length, L Area, A
Measuring contact resistance I–Vcharacteristics for rectifying and Ohmic contacts for aluminium on p-diamond (001). The figure shows a rectifying Al–diamond contact (curve A) and a carbide–diamond Ohmic contact (curve B) prepared by in vacuo annealing of an Al contact. D A Evans et al., Diamond–metal contacts: interface barriers and real-time characterization, J. Phys.: Condens. Matter 21, 364223 (2009) Ohm’s law V = I R
Measuring contact resistance I–Vcharacteristics for rectifying and Ohmic contacts for aluminium on p-diamond (001). The left panel shows a rectifying Al–diamond contact (curve A) and a carbide–diamond Ohmic contact (curve B) prepared by in vacuo annealing of an Al contact. D A Evans et al., Diamond–metal contacts: interface barriers and real-time characterization, J. Phys.: Condens. Matter 21, 364223 (2009) Ohm’s law V = I R Above 1020 K, bulk carbide (Al3C4) formation occurs creating Ohmic contacts
Schottky contacts Depletion layer Wolfgang Pauli: ‘‘God made the bulk; the surface was invented by the devil’’ Schottky barrier for n-type semiconductor, Page 573, Kittel, Introduction to Solid State Physics, Wiley 1996
Schottky contacts Schottky barrier height is Raymond T Tung, The physics and chemistry of the Schottky barrier height, Applied Physics Reviews 1, 011304 (2014)
Rectifying Current Time
Four Point Probe Resistivity, Source current, I V Measure voltage, V Ohm’s law V = I R R = L/A sample Length, L Area, A Experimental considerations in measuring resistivity, Pages 194-199, Singleton, Band Theory and Electronic Properties of Solids, OUP 2001
Bad way to measure Resistivity, Source Voltage, V A Measure current, I Ohm’s law V = I R R = L/A sample Length, L Area, A
Four Point Probe Resistivity, Source current, I V Measure voltage, V Ohm’s law V = I R R = L/A sample Length, L Area, A
Lock-in amplifiers AC source current, I reference V Lock-in signal sample Component of signal at reference frequency Experimental considerations in measuring resistivity, Pages 194-199, Singleton, Band Theory and Electronic Properties of Solids, OUP 2001
Hall Effect Source current, I Lorentz Force: F = q (E+ v × B) V sample Applied magnetic field, B Chapter, 8 and 10 and Appendix F, Singleton, and page 164, Kittel
Hall Effect Sample thickness, d Chapter, 8 and 10 and Appendix F, Singleton, and page 164, Kittel
Hall Effect Source current, I Make Hall bar from thin film samples with lithography Experimental considerations in measuring resistivity, Pages 194-199, Singleton, Band Theory and Electronic Properties of Solids, OUP 2001
Wire bonding Image by Holger Motzkau http://en.wikipedia.org/wiki/File:Ultrasonic_wedge_bonding.webm
van der Pauw Sample geometries The van der Pauw method L J van der Pauw, A method of measuring the resistivity and Hall coefficient on lamellae of arbitrary shape. Philips Technical Review20: 220–224 (1958) Experimental considerations in measuring resistivity, Page 197, Singleton, Band Theory and Electronic Properties of Solids, OUP 2001
Temperature dependence M Werner et al., Charge transport in heavily B-doped polycrystalline diamond films, Applied Physics Letters 64, 595 (1994) Sample A is metallic
Diamond surfaces Wolfgang Pauli: ‘‘God made the bulk; the surface was invented by the devil’’ O A Williams and RB Jackman, Surface conductivity on hydrogen terminated diamond, Semicond. Sci. Technol. 18 (2003) S34
Diamond Superconductivity k = 0 For Cooper pair Page 202, Singleton, Band Theory and Electronic Properties of Solids, OUP 2001
Diamond Superconductivity E A Ekimov et al, Superconductivity in diamond, Nature 428, 542 (2004)
Diamond Superconductivity E Bustarret et al, Dependence of the Superconducting Transition Temperature on the Doping Level in Single-Crystalline Diamond Films, Physical Review Letters, 93, 237005 (2004)