HALL- EFFECT SK-006

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QMO11
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Objectives:

1. To study Hall effect and to determine

(i) Hall voltage VH
(ii) Hall coefficient RH
2. To determine the type of majority carriers i.e. whether the semiconductor crystal is of
n – type or p-type.
3. To determine the charge carrier density or carrier concentration per unit volume in the
semiconductor crystal.
4. To determine the magnitude of Poynting Vector.
5. To determine the Hall angle q H.

Introduction:
In 1879, E.H. Hall observed that on placing a current carrying conductor perpendicular to a
magnetic field, a voltage is observed perpendicular to both the magnetic field and the current. It
was observed that the charge carriers, which were assumed to be electrons ,experienced a
sideways force opposite to what was expected. This was later explained on the basis of band
theory.
The number of conducting charges and the sign of charge carriers cannot be determined by the
measurement of conductivity of a specimen. In metals/conductors ,the current carriers are only
electrons whereas in semiconductors ,both electrons and holes act as current carriers .Therefore,
in semiconductor, it is quite necessary to determine whether a material is of n-type or p-type .The
Hall effect can be used to distinguish the two types of charge carriers and also to determine the
density of charge carriers.

Theory :

When a magnetic field is applied perpendicular to a current carrying specimen(metal or

semiconductor),a voltage is developed in the specimen in a direction perpendicular to both the
current and the magnetic field. This phenomenon is called Hall effect. The voltage so generated is
called Hall voltage.
We know that a static magnetic field has no effect on charges unless they are in motion. When the
charges flow , a magnetic field directed perpendicular to the direction of flow produces a mutually
perpendicular force on the charges. Consequently, electrons and holes get separated by opposite
forces and produce an electric field EH ,thereby setting up a potential difference between the ends
of a specimen. This is called Hall potential VH.

Exaplanation:

Consider a semiconductor in the form of a flat strip .Let a current I flows through the strip along X-
axis . P and P¢ are two points on the opposite faces of a b c d and a¢ b¢ c¢ d¢ respectively. If a
millivoltmeter is connected between points P and P¢ ,it does not show any reading ,indicating that
there is no potential difference setup between these points. But, when a magnetic field is applied
along Y-axis , i.e. perpendicular to the direction of current, a deflection is produced in the
millivoltmeter indicating that a potential difference is set up between P and P ¢. This potential
difference is known as Hall voltage or Hall potential VH .
As shown in fig. 1, if a current is passed along X-axis , then the electrons move along negative
direction of x-axis .The force on electron due to the applied magnetic field B is given by,

F = e (v x B)

F = e v B sin 90°

Or F = e v B ............................................ (1)

where, v is the drift velocity of electron and e is the charge of electron.

Using Fleming's left hand rule it is seen that force on the electrons will be directed towards the
face a b c d , i.e. along positive Z-axis ,thereby making the face a b c d negative and a¢ b¢ c¢ d¢
positive.
If the current is carried by positively charged carriers i.e. holes , the carriers move in the same
direction as that of the current . The magnetic force causes the positive charge carriers to move
towards the face a b c d , thereby making the face a b c d positive and a¢ b¢ c¢ d¢ negative.
Thus, by determining the polarities of the surface of the strip , we can determine the sign of the
charge carriers.

At thermal equilibrium ,when the Lorentz force exactly matches the force due to the electric
field EH (the Hall voltage) we have :

e v B= e EH = eVH ... ................................................(2)

b
VH
or v = bB

If b be the width and t is the thickness of the specimen (crystal),its cross sectional area A is given
by :

A= b t ................................................... (3)

The current density J= I/A ..............................(4)

or I = n e v A ..........................................(5)

where, n is the number of charge carriers per unit volume .

or 1 vA VH
ne = I = bBI A

or 1 VH VHt .......................................(6)
ne = bBIx bt =
BI
The Hall coefficient is given by:
VHt 1
RH = ................................................(7)
BI = ne
and charge carrier density is given by:

n =1/ e RH .......... ... ..................................(8)

If the conduction is primarily due to one type of charge carriers , then conductivity is related to
mobility mm :

mm=s RH ................................................(9)

therefore,

mm= RH/r .............................................. (10)

where , r is the resistivity.

There is another interesting quantity called the Hall angle( qH) defined by equation

tan q H= EH /EX ........................................ ...(11)

but EH = vxB ...........................................(12)
hence tan qH=vxB/EX = mmB ...........................................(13)

Apparatus: INDOSAW SK006 Hall effect apparatus.

HALL EFFECT EXPERIMENT SET - UP:

It consists of :

1. Power supply for electromagnet:

· Specifications: 0-20 V, 5 Amps.
2. Power supply (Constant current source):
· Specifications: 0-20 mA
3. Gauss meter with Hall Probe
4. Semiconductor( Ge single crystal)mounted on a PCB
Specifications:
- p-type Ge crystal.
- Thickness: 0.5 mm
- Width : 4 mm
- Length : 6mm
5. Multimeter for measuring Hall voltage
6. Hall Effect Apparatus consisting of two 500 turns coils.
Block Diagram of Experimental set up

MV METER MA METER

Power Supply
0-20 V, 5A DC

Fig.2 Shows the block diagram for experimental set up with connections . A p-type Ge crystal is
mounted on PCB. PCB is provided with four sockets and a pot to make the Hall voltage zero,
when there is no current flowing through the crystal and also when there is no magnetic field .The
upper two sockets are connected to a constant current dc source and the lower two to a
multimeter/millivoltmeter.
Hall probe with Gauss meter is kept in the center between the electromagnet.
Formula used:
3 -1
(1) Hall coefficient RH= VHt / BI m C
where, VH= Hall voltage in volts.
t = Thickness of the sample in m.
B = Magnetic flux density in Tesla.

(2) Concentration of charge carriers per unit volume

n =1/e RH carriers m-3
where, e = 1.6 x 10-19 C

(3) Resistivity of the material of the sample

r = Vl b t / I L m
Where, Vl =voltage between two points situated l cm apart on one face of sample
b = width of the sample in m .
t = thickness of the specimen in m.

(4) Mobility mm= RH/ r m2V-1 s-1

(5) Hall angle qH= tan-1(m B)

(6) Magnitude of Poynting vector:

EXPERIMENT SET UP PROCEDURE:
1. Mount the PCB (with mounted crystal) on one of the pillars and hall probe in another pillar.
2. Complete all the connections as shown fig.-2
3. Switch ON the Gauss Meter and place the hall probe away from the electromagnet. Select
the range of the gauss meter as X1 and using the adjustment knob of the Gauss Meter, adjt
the reading of the Gauss Meter as zero.

DO NOT SWITCH ON THE ELECTROMAGNET AT THIS STAGE.

4. Switch ON the constant current source and set the current, say at 5 mA in constant current
source. Keep the magnetic field at zero as recorded by Gauss meter.

DO NOT SWITCH ON THE ELECTROMAGNET AT THIS STAGE.

5. Complete the circuit diagram as shown in fig.-2. When a current of 5 mA is passed through
the crystal without application of magnetic field the hall voltage as recorded by the
multimeter should be zero.

The zero set should be adjusted carefully and gradually.

DO NOT SWITCH ON THE ELECTROMAGNET AT THIS STAGE.

6. Bring the current reading of the constant current source to Zero by
Adjusting the knob of the constant current source.
7. Switch ON the electromagnet (say at about 1 7V, 3.5A)
8. Select the range of the Gauss meter as x10 and measure the magnetic flux density at the
center between the pole pieces. The tip of the Hall Probe and the crystal should be placed
between the center of the pole pieces.
The pole pieces should be very close to the crystal and the tip ofthe Hall Probe.
POLE PIECES SHOULD NOT TOUCH THE CRYSTAL OR THE TIP OF THE HALL
PROBE

FOR CARRYING OUT THE EXPERIMENT THE MAGNETIC FLUX DENSITY SHOULD BE
MORE THAN 1500 GAUSS.

9. Do not change the current in the electromagnet i.e. keep the magnetic field constant for the
whole of the experiment.
10 Vary the current through the constant current source in small increments. Note the current
I (mA) from the constant current source passing through the sample and the Hall voltage
(mV)as recorded by the multimeter. Record these values in the observation table.
11 . Reverse the direction the magnetic field by interchanging the ‘ +’ and ‘-’ connections of the
coils (i.e by interchanging Red and Black wires to the coils of the electromagnet ). Again
note down the Hall Voltage for the same values of current as in step 10.
Take the magnitude of magnetic flux density. In this particular case the hall voltage
should be noted without taking care of negative sign of voltage.
Observations:

Width of the specimen, b = 4 mm

= 4 x 10 -3 m
Length of the specimen, l = 6mm
= 6 x 10-3 m
Thickness of the specimen, t = 0.5 mm
= 5 x 10-4 m
Magnetic flux density, B = 3600 Gauss
= 3600 x 10-4 Tesla
Table for I and V:

Sr No Current I(mA) Reading of (mV) Reading of (mV) Mean value VH

millivoltmeter millivoltmeter of VH
(B&I in one direction) (B&I in reverse direction)
I
mV ohm
1 5 9.3 -8.2 8.75 1.75
2 5.5 10.1 -9 9.55 1.73
3 5.91 11 -9.7 10.35 1.75
4 6.49 12 -10.6 11.3 1.74
5 6.9 12.8 -11.2 12 1.73
6 7.31 13.5 -11.8 12.65 1.73
7 7.73 14.4 -12.5 13.45 1.73
8 8.03 14.9 -13 3.95 1.73
9 8.54 15.9 -13.7 14.8 1.73
10 8.91 16.5 -14.3 15.4 1.72
11 9.24 17.1 -14.8 15.95 1.72
12 9.77 18.1 -15.6 16.85 1.72
13 10.1 18.5 16.1 17.3 1.71
14 10.55 19.2 -16.8 18 1.7
15 11.05 20.9 -17.5 19.2 1.73
16 11.55 21.9 -18.2 20.05 1.73
17 12.02 22.9 -18.8 20.85 1.73
18 12.72 24.3 -19.8 22.05 1.73
19 13.05 25.8 -20.3 23.05 1.76
20 13.72 26.3 -21.4 23.85 1.73

VH
mean =1.73 Ω
I

Table for resistivity : l = 6 x 10-3m

1. 0.35 110 .104

2. 0.58 188.2 .108

3. 1.1 360.00 .108

4. 2.2 721 .109

mean p =0.107 Ω m
Calculations :
1. Mean value of VH/I = 1.73 ohm

2. RH = VH t/I x B = 2.4 x 10-3 ohm m T-1

3. Sign of Hall coefficient is positive, thus the semiconductor crystal is of p-type.(to check `
whether a crystal is of p-type or n-type we have first used a crystal of known type)
1
4. n = 1/(1.6 x 10-19 x RH) =
1.6 x 10 x 2.4 x 10-3
-19

= 2.6 x 1021 m-3

5. r = 0.107W m

6. mm = R /r = ....... m2 V-1 s-1 = 2.2 x 10-2 m2 v-1 s-1

H

7. In an electromagnet wave in free space the magnetic field H and the electric field E are
perpendicular to each other . A semiconductor placed parallel to E will derive a current I in the
semiconductor . The semiconductor is subjected simultaneously to a transverse magnetic field
H producing a Hall voltage across the sample. The Hall voltage will be proportional to the
product of E and H, which is the magnitude of the Poynting vector of electromagnetic wave.
Therefore, Hall effect can be used to determine power flow in an electromagnetic wave and
the magnitude of Poynting vector .
.8. The Hall angle qH = tan-1 (mmB) = 281 (nearby)

Sources of error :

The experiment has the potential to have systematic errors which could skew the final
calculations. This may be due to slight misalignment of the magnetic field, irregularity in the grain
of germanium crystal, stray magnetic fields generated by nearby electrical equipments

Before starting the experiment, check the Gauss meter is showing zero value. For this put the
probe in separate place and switch on the Gauss meter, it will show zero value.

Ensure that the specimen is located at he center between the pole pieces and exactly
perpendicular to the magnetic field.

To measure the magnetic flux the Hall probe should placed at the center between the pole
pieces, parallel to semiconductor sample.

Check th direction of electromagnet coils so that it generates the maximum magnetic field, this
can be checked by placing a soft iron near the generated magnetic field. If soft iron attracts
forcefully, the magnetic field is strong.
9. What is the significance of Hall effect ?
10. Name some practical applications of Hall effect ?
11. How can you find the charge carrier concentration and the mobility using Hall effect ?
12. Can you study Hall effect using Si sample instead of Ge sample ?
13. Should you prefer Ge or Si ?
14. Which has higher resistivity Ge or Si ?
15. What happens if the current is not perpendicular to the magnetic field applied ?
16. On what factors the sign of Hall potential depends?
17. Write down the dimensional formula of Hall coefficient?
18. What do you mean by charge carrier density?
19. Define mobility?
20. Write down the units of mobility and its dimensional formula?
21. Should you use ammeter or milliammeter in this experiment?

Applications of Hall effect :

1. The Hall effect can be used to determine whether the semiconductor is of n-type or p-type.
2. The Hall effect can be used to determine the carrier concentration.
3. The Hall effect can be used in magnetic flux density meter.
4. The Hall effect can be used to find the magnitude of Poynting vector.