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3. Hall-Effect in Semiconductors. Conduction type, Concentration of Charge Carriers and
Their Mobility
3.1. Objectives
1. Familiarizing with the measurements of Hall-effect on semiconductors.
2. Measurement of concentration of majority charge carriers and their mobility in silicon.
3.2. Principles
Charge carrier concentration and mobility can be found measuring Hall-effect on van der Pauw sample placed in magnetic field. Magnetic field makes charge carriers to deviate from their straight drift between the contacts. This deviation results in generation of Hall voltage V
H
in the direction perpendicular to the direction of current flow (Fig. 3).
Fig. 3
. (a) Principle of measurement of Hall-effect. (b) Example of measurement of Hall-voltage
V
42
. Current is applied between contacts 3 and 1 ( I
31
), while voltage is measured between contacts 4 and 2 .
In order to measure Hall-voltage on van der Pauw sample, two sets of measurements are made: one with magnetic field in the positive z
-direction, and one with it in the negative z
-direction.
The voltages recorded with positive field will have a subscript
P
P
(for example, V
13, P
= V
3, P
- V
1,
), whereas those recorded with negative field will have a subscript
N
(such as V
13, N
= V
3, N
- V
1,
N
). For all of the measurements, the magnitude of the injected currents should be kept the same.
The magnitude of the magnetic field must be the same in both directions also. Hall voltage is then calculated as:
, (6) where
V
13
= V
13, P
− V
13, N
,
V
24
= V
24, P
− V
24, N
,
V
31
= V
31, P
− V
31, N
,

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V
42
= V
42, P
− V
42, N.
The polarity of the Hall voltage indicates the type of material the sample is made of. If it is positive, the material is p -type, and if it is negative, the material is n -type.
When Hall-voltage V
H
is known, sheet concentration of charge carriers n
S
can be found as:
, (7) where I is the current flowing along the sample and e is the electron charge.
Density of the majority charge carriers n m
and their mobility µ m
can be found as:
, (8)
μ .
3.3. Experimental Equipment
- LabView controlled measuring unit
- Holder with silicon van der Pauw samples
- DC Power Supply
- Permanent Co-Sm magnet of magnetic field strength B = 0.5 T
3.4. Procedure
1. Assemble the measurement set-up.
2. Place magnet over the silicon sample.
3. Apply 1 mA current through one diagonal of the sample. This is the current I shown in formula (7) and (8). Measure voltage over the other perpendicular diagonal. Flip the magnet and repeat the measurement. Calculate difference between the measured voltages. The obtained value is the voltage V
13
in formula (6).
4. Reverse the direction of current 1 mA and repeat the procedure 3. The obtained value is the voltage V
31
in formula (6).
5. Repeat the procedures 4 and 5 applying current to the other diagonal and measuring voltage over the perpendicular one. The obtained values are the voltages V
42
correspondingly in formula (6).
24
and V
6. Measure thickness of the silicon sample t .
3.5. Calculations and Discussion
1. Retrieve the data on van der Pauw resistance R , sheet resistance R
S extrinsic silicon samples you measured in lab work 2.
and resistivity ρ of the

22
2. Calculate Hall-voltage V
H
using the voltages measured in procedures 4-6 and formulae (6).
3. Using the values of R , V
H
, t , I and B calculate density of the majority charge carriers n m mobility of majority charge carriers µ m
, sheet resistance R
S
and sheet carrier density n
Determine type of the majority charge carriers: electrons, or holes.
S
,
.
4. Compare the obtained values with that known for the sample you measured and with that known for silicon used in electronic industry.
5. Discuss your measurements and the obtained results.
3.6. Questions
1. Is it possible to measure Hall-effect on intrinsic semiconductor? Explain your answer.
2. Is it possible to measure Hall-effect on compensated semiconductor? Explain your answer.
3. How temperature influences Hall-effect measurements?
3. Predict Hall-voltage on your samples when they would be measured at a temperature of
100°C.
4. Is it possible to measure Hall-effect on your samples at liquid nitrogen temperature? Support your answer with calculations of charge carrier concentration.
Appendix
(a) The intrinsic carrier density in silicon at 300 K equals:
(b) Table of the intrinsic carrier density in semiconductors at different temperatures.

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Taking Measurements with LabView
1) Using a similar setup as the Van der Pauw resistance measurement, assemble the sample and breadboard as shown
2) Adjust the DC Power supply such that the current is 1mA
3) Take Voltage measurement with no external magnetic field, with a positive field, and a negative field respectively
4) Rotate the wires and repeat 4 times to measure , , ,
5) Repeat with both P type and N type samples