1. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Conductivity and the Hall Effect

2. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Lab objectives  Determine resistivity using Van der Pauw method  Determine carrier type (n or p) and doping density using Hall Effect  Determine majority carrier mobility from doping density and resistivity Conductivity and the Hall Effect

3. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Can determine resistivity for arbitrary shape using Van der Pauw  Uses four small contacts at boundary  Doping must be uniform and uniformly thick  No holes in sample Conductivity and the Hall Effect

4. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 To perform Van der Pauw measurement must first  Force current across two contacts of sample and measure voltage across the other two contacts  To improve accuracy reverse current and measure again  Can also force current across other two contacts and repeat procedure to further improve accuracy  Average currents accordingly Repeat measurements across contacts in another orientation Determine correction factor F from ratio of these two resistances Determine resistivity from appropriate equation Conductivity and the Hall Effect

5. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 where R 12,34 = V 34 /I 12 R 23,41 = V 41 /I 23 F obtained from ratio of resistances from graph shown at right Conductivity and the Hall Effect

6. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Conductivity and the Hall Effect

7. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Hall Effect used to measure doping density  Magnetic field across sample creates force on flowing charges  Forces both electrons and holes in the direction of the force causing charges to build up creating field  Creates voltage across sample perpendicular to flowing current  Can relate change in voltage to semiconductor type and doping density  Can determine carrier mobility from resistivity and doping density Conductivity and the Hall Effect

8. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Generation of the Hall Effect in p-type silicon. Conductivity and the Hall Effect

9. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Schematic of right hand rule for positive charge moving in magnetic field. Conductivity and the Hall Effect

10. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Generation of forces and fields caused by Hall Effect and effect of magnetic field on the movement of holes. qv x xB z Conductivity and the Hall Effect

11. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Hall voltages generated under real and ideal conditions. Conductivity and the Hall Effect

12. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Hall Effect wiring configurations and subsequent measurement. Conductivity and the Hall Effect

13. Electronic Devices Laboratory mtinker@utdallas.edu CE/EE 3110 Measured voltage and Hall voltage generated by different currents in Configuration A using no magnetic field, a magnetic field pointing in the positive z direction, and a magnetic field pointing in the negative z direction. Conductivity and the Hall Effect