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

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization 2 Diamond properties

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization 3 Resistivity (ohm-cm) Diamond  ~  -cm (room temperature) PTFE (Teflon)  >  -cm (room temperature) Silicon  ~ 10 4  -cm (room temperature) Superconductors  ~ 0 Pure metal  ~  -cm (1 K) Tin  ~  -cm (room temperature)

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Length, L Area, A sample R =  L/A Ohm’s law V = I R Bad way to measure Resistivity,  4

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Bad way to measure Resistivity,  Length, L Area, A sample R =  L/A A Source voltage, V Measure current, I Ohm’s law V = I R 5

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Measuring contact resistance Length, L Area, A sample Study one contact at a time A Source voltage, V Measure current, I Ohm’s law V = I R 6

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Measuring contact resistance I–V characteristics 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, (2009) Ohm’s law V = I R 7

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Measuring contact resistance I–V characteristics 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, (2009) Ohm’s law V = I R 8 Above 1020 K, bulk carbide (Al 3 C 4 ) formation occurs creating Ohmic contacts

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Schottky contacts Schottky barrier for n-type semiconductor, Page 573, Kittel, Introduction to Solid State Physics, Wiley Wolfgang Pauli: ‘‘God made the bulk; the surface was invented by the devil’’ Depletion layer

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Schottky contacts Raymond T Tung, The physics and chemistry of the Schottky barrier height, Applied Physics Reviews 1, (2014) 10 Schottky barrier height is 

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Rectifying 11 Time Current

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Four Point Probe Resistivity,  Length, L Area, A sample R =  L/A Source current, I Ohm’s law V = I R V Measure voltage, V Experimental considerations in measuring resistivity, Pages , Singleton, Band Theory and Electronic Properties of Solids, OUP

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Length, L Area, A sample R =  L/A Source Voltage, V Ohm’s law V = I R A Measure current, I Bad way to measure Resistivity,  13

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Four Point Probe Resistivity,  Length, L Area, A sample R =  L/A Source current, I Ohm’s law V = I R V Measure voltage, V 14

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Lock-in amplifiers sample AC source current, I V Lock-in reference signal Component of signal at reference frequency Experimental considerations in measuring resistivity, Pages , Singleton, Band Theory and Electronic Properties of Solids, OUP

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Hall Effect sample Chapter, 8 and 10 and Appendix F, Singleton, and page 164, Kittel 16 Source current, I V Applied magnetic field, B Lorentz Force: F = q (E+ v × B)

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Hall Effect Chapter, 8 and 10 and Appendix F, Singleton, and page 164, Kittel 17 Sample thickness, d

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Hall Effect Experimental considerations in measuring resistivity, Pages , Singleton, Band Theory and Electronic Properties of Solids, OUP Source current, I Make Hall bar from thin film samples with lithography

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Wire bonding 19 Image by Holger Motzkau :Ultrasonic_wedge_bonding.w ebm

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization van der Pauw Sample geometries Experimental considerations in measuring resistivity, Page 197, Singleton, Band Theory and Electronic Properties of Solids, OUP 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 Review 20: 220–224 (1958)

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Temperature dependence 21 M Werner et al., Charge transport in heavily B-doped polycrystalline diamond films, Applied Physics Letters 64, 595 (1994) Sample A is metallic

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Diamond surfaces 22 O A Williams and RB Jackman, Surface conductivity on hydrogen terminated diamond, Semicond. Sci. Technol. 18 (2003) S34 Wolfgang Pauli: ‘‘God made the bulk; the surface was invented by the devil’’

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization 23 Page 202, Singleton, Band Theory and Electronic Properties of Solids, OUP 2001 Diamond Superconductivity k = 0 For Cooper pair

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Diamond Superconductivity 24 E A Ekimov et al, Superconductivity in diamond, Nature 428, 542 (2004)

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization Diamond Superconductivity 25 E Bustarret et al, Dependence of the Superconducting Transition Temperature on the Doping Level in Single-Crystalline Diamond Films, Physical Review Letters, 93, (2004)

Module 2 – Properties and Characterization of Materials - Lecture 9 – Electrical Characterization 26 Lecture 9Electrical characterization - Schottky and Ohmic contacts - 4 point probe measurements - Lock-in measurements - Hall effect - Sample geometries - Temperature dependence - Superconductivity 10Electron microscopy: - Scanning electron microscopy - Transmission electron microscopy