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Conductivity and the Hall Effect
Conductivity and the Hall Effect
Electronic Devices Laboratory
[email protected]
CE/EE 3110
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
Electronic Devices Laboratory
[email protected]
CE/EE 3110
Conductivity and the Hall Effect
•
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
Electronic Devices Laboratory
[email protected]
CE/EE 3110
Conductivity and the Hall Effect
•
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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
Electronic Devices Laboratory
[email protected]
CE/EE 3110
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
Electronic Devices Laboratory
[email protected]
CE/EE 3110
Conductivity and the Hall Effect
Van der Pauw Configuation (A)
5.00E-01
Voltage (V)
4.00E-01
Vad (V)
3.00E-01
Vda (V)
2.00E-01
Vbc (V)
1.00E-01
Vcb (V)
0.00E+00
0
2
4
6
8
10
Current (mA)
Van der Pauw Configuration (B)
5.00E-01
Voltage (V)
4.00E-01
Vab (V)
3.00E-01
Vba (V)
2.00E-01
Vdc (V)
1.00E-01
Vcd (V)
0.00E+00
0
2
4
6
8
10
Current (mA)
Electronic Devices Laboratory
[email protected]
CE/EE 3110
Conductivity and the Hall Effect
•
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
Electronic Devices Laboratory
[email protected]
CE/EE 3110
Conductivity and the Hall Effect
Generation of the Hall Effect in p-type silicon.
Electronic Devices Laboratory
[email protected]
CE/EE 3110
Conductivity and the Hall Effect
Schematic of right hand rule for positive charge moving in magnetic field.
Electronic Devices Laboratory
[email protected]
CE/EE 3110
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.
Electronic Devices Laboratory
[email protected]
CE/EE 3110
Conductivity and the Hall Effect
Hall voltages generated under real and ideal conditions.
Electronic Devices Laboratory
[email protected]
CE/EE 3110
Conductivity and the Hall Effect
Hall Effect wiring configurations and subsequent measurement.
Electronic Devices Laboratory
[email protected]
CE/EE 3110
Conductivity and the Hall Effect
Measured Voltage Versus Current Configuration (A)
Hall Voltage Versus Current Configuration (A)
3.00E-02
2.00E-02
V0AConf (V)
1.50E-02
VPosAConf (V)
1.00E-02
VNegAConf (V)
5.00E-03
0.00E+00
0
2
4
6
8
10
Hall Voltage (V)
Voltage (V)
2.50E-02
2.50E-03
2.00E-03
1.50E-03
1.00E-03
5.00E-04
0.00E+00
-5.00E-04 0
-1.00E-03
-1.50E-03
-2.00E-03
HallVPosAConf (V)
HallVNegAConf (V)
2
4
6
8
10
Current (mA)
Current (mA)
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.
Electronic Devices Laboratory
[email protected]
CE/EE 3110