Conductivity and the Hall Effect

1. Conductivity and the Hall Effect Conductivity and the Hall Effect

2. Conductivity and the Hall Effect • 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

3. 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. 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. Conductivity and the Hall Effect where R12,34 = V34/I12 R23,41 = V41/I23 F obtained from ratio of resistances from graph shown at right

6. Conductivity and the Hall Effect

7. 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. Conductivity and the Hall Effect Generation of the Hall Effect in p-type silicon.

9. Conductivity and the Hall Effect Schematic of right hand rule for positive charge moving in magnetic field.

10. Conductivity and the Hall Effect qvxxBz Generation of forces and fields caused by Hall Effect and effect of magnetic field on the movement of holes.

11. Conductivity and the Hall Effect Hall voltages generated under real and ideal conditions.

12. Conductivity and the Hall Effect Hall Effect wiring configurations and subsequent measurement.

13. Conductivity and the Hall Effect 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.