The Hall effect

Prepared by :Mariam Ahmed & Amira Shaban & Ayat Abdelnaby

[Date] [Course title]

Table of Contents
Aim of the experiment:.............................................................................2
Background:..............................................................................................2
Principle of Hall effect..............................................................................3
Theory:......................................................................................................3
Evaluation.................................................................................................4
Procedure:.................................................................................................6
Results.......................................................................................................7

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Aim of the experiment:
-To study the hall effect and determine the type of the material (p-type
or N-type)
-study the relation between the hall voltage and the applied magnetic
field at constant current
- study the relation between the hall voltage and the current at constant
magnetic field.

Background:
In this experiment, the Hall Effect will be used to study some of
the physics of charge transport in metal and semiconductor samples. In
1879 E. H. Hall observed that when an electrical current passes through
a sample placed in a magnetic field, a potential proportional to the
current and to the magnetic field is developed across the material in a
direction perpendicular to both the current and to the magnetic field [1].
This effect is known as the Hall effect, and is the basis of many practical
applications and devices such as magnetic field measurements, and
position and motion detectors. With the measurements he made, Hall
was able to determine for the first time the sign of charge carriers in a
conductor. Even today, Hall effect measurements continue to be a useful
technique for characterizing the electrical transport properties of metals
and semiconductors. Indeed, the failure of the simple model of metallic
conductivity, which we discuss below, to account for many experimental
measurements of the Hall effect has been one of the principal motivators
leading to a better understanding of electronic properties of materials

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Principle of Hall effect
The principle of the Hall effect states that when a current-carrying
conductor or a semiconductor is introduced to a perpendicular magnetic
field, a voltage can be measured at the right angle to the current path.
This effect of obtaining a measurable voltage is known as the Hall
effect.

Theory:
When a conductive plate is connected to a circuit with a battery,
then a current starts flowing. The charge carriers will follow a linear

path from
Figure 1: sample in Hall effect experiment.

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 one end of the plate to the other end. The motion of charge carriers
results in the production of magnetic fields. When a magnet is placed
near the plate, the magnetic field of the charge carriers is distorted. This
upsets the straight flow of the charge carriers. The force which upsets
the direction of flow of charge carriers is known as Lorentz force.
Due to the distortion in the magnetic field of the charge carriers, the
negatively charged electrons will be deflected to one side of the plate
and positively charged holes to the other side. A potential difference,
known as the Hall voltage will be generated between both sides of the
plate which can be measured using a metre.

Evaluation
The charge carriers give rise to the current flowing through the
sample is effected by the applied magnetic field which is given by:
F m= qvB =evB
And the electric field which is given by:
F e=qE=eE

We know that the current will pass through the circuit only when the
electric field equals the magnetic field, then by equaling both equation
we get the hall voltage:
VH = vBb
where,
v: the velocity of the charge
B: is the magnetic field strength

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b: is the length of the sensor

Hall Coefficient

The Hall coefficient R H is mathematically expressed as

μ
R H=
σ

Where,
μ: is the mobility of the charge
σ: the conductivity of the material
Then the hall coefficient is given by:
d∗V H V∗A
R H= = I
B∗I

Where,
v: the velocity of the charge
A: the area of the slide
I: electric current
Since the electric current is given by:
I=neAV
Then, the hall coefficient is given by:
1
R H=
n∗e

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The hall coefficient is positive if the number of positive charges is more
than the negative charges. Similarly, it is negative when electrons are
more than holes.

Procedure:

Variation of the Hall voltage with the current at room temperature

and constant magnetic field:-
 Choose the Hall voltage, the current and the magnetic field "Tesla"
as measurement parameters from the start screen, and click "Ok".
 Set the current and the magnetic field to zero and calibrate the Hall
voltage to zero.
 Set the magnetic field to a certain value of by changing the voltage
and the current on the power supply.
 Determine the Hall voltage as a function of the current in steps of
1v
.
Variation of the hall voltage with the magnetic field at room
temperature and constant current:-
 Choose the Hall voltage, the current and the magnetic field
"Tesla" as measurement parameters from the start screen. and
click "Ok".
 Set the current and the magnetic field to values of zero and
calibrate the Hall voltage to zero.
 Set the current to a value of30mA.
 Determine the Hall voltage as a function of the magnetic
induction. Start with by changing the polarity of the coil-
current on the power supply and increase the magnetic

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 induction in steps of nearly. At zero point, you have to
change the polarity again.

Results
Part (1):
At constant magnetic field, B=-110.6 mT
VH I 40

-3012 -57.7 20
-2722 -52
-2195 -47 0
Hall voltage (volt)

0 2 4 6 8 10 12 14 16
-1941 -40
-1572 -35.25 -20
-949.2 -31.1
-353 -25.48 -40
-90.3 -16.6
320 -12.6 -60
863 -6.8
1048 1.59 -80
1370 4.3 current (mA)
1792 9.5
2219 16.2
2873 25.5

slope =71.4 v/A

slope∗d
R= B = 0.65V*m/A*T

Part(2):

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at constant current, I= -75.39 Ma

hall magnetic -2.8

-3.3
voltage field -7.7
-13
832.3 -2.8 -16.9
-20.8
826.36 -3.3
-29
647.3 -7.7 -33
420.9 -13 -39.3
-41.3

hall voltage(V)
-45.2
267.6 -16.9
135.9 -20.8 -56.4
-85.2 -29 -63.7
-71.5
-222.2 -33
-422.7 -39.3
-517.6 -41.3 -89.3
-92
-622.3 -45.2
-1023.6 -56.4
-1298.3 -63.7 magnetic field(mT)
-1582 -71.5
-1888.9 -89.3
-2321 -92

Slope =33.65 V/T

slope∗d
R= I =0.617 V*m/T*A

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Rtotal =( R1+ R2 ¿/2=0.6335 Vm/TA

So , the material is p-type

The number of charge carriers are :
1
N= ℜ =9.9*1018 holes

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