Electrical Engineering: Hall Effect Experiment and Semiconductor Study

This document details a practical experiment conducted to investigate the Hall effect in a semiconductor material, specifically germanium. The experiment involves applying a magnetic field to a semiconductor sample and measuring the resulting Hall voltage in relation to the magnetic flux density and drift current. The introduction explains the basic principle of the Hall effect, describing how a magnetic field interacts with current flow in a conductor or semiconductor, and highlights its applications in sensing and other electronic devices. The experiment's objective is to understand the Hall effect and use it to study the carrier properties, type of carrier, concentration, and Hall motion in a semiconductor. The theory section provides the equations for current density, conductivity, and the Hall effect field. The experimental setup includes a DC power supply, electromagnet, oscilloscope, semiconductor sample, ammeter, and potentiometer. The procedure involves connecting the semiconductor sample to a power supply, setting the magnetic flux density, and measuring the Hall voltage. The results section presents data in tables and graphs showing the relationship between magnetic flux density, drift current, and Hall voltage. The discussion analyzes the graphs using linear regression, calculates the Hall effect coefficient, and discusses the errors. The results confirm the proportionality between magnetic flux and Hall voltage, as well as between drift current and Hall voltage, illustrating the fundamental principles of the Hall effect.

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INTRUMENTATION
PROFFESSOR/TUTOR
COURSE
SCHOOL
DATE

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Introduction
When a conductor is connected to wires which are connected to a power supply, there will be a
normal flow of current, linearly from the negative end to a positive end of the conductor. But
when a magnet is introduced perpendicularly to the conductor, the current flow tends to be
disturbed, with the current flowing more towards the magnet, which in turns makes the electrons
to be accumulated on one side, hence there’ll be a potential difference discovered only when a
voltmeter is connected across the conductor. The meter will deflect on the side where there’s a
higher number of electrons. The other side, opposite side of the electrons, will experience the
presence of holes, since most of the electrons are attracted on the side where the magnetic effect
is felt. Hall effect is a way through which a magnetic field interact with the flow of a current
through a conductor or a semi-conductor. Which is why Hall effect is widely used on
semiconductor devices, Hall effect elements used in sensing and other electronics were put
together in a single chip, integrated circuit. These days Hall effect are used in various electronics
products like computers, others like aircraft etc (Storr, 2013). For Hall effect to have an impact
on microprocessors, they need to have analogue circuit integrated or interfaced in them. The
interface may include diagnostics abilities, protection from faults at the transient conditions, and
detection of closed and open short circuit. Hall effect is a technique that can be good in sensing
various parameters, usually the output voltage is very small, measured in (μV), which requires
amplification to get to a meaningful voltage level. These elements combined with Hall element
makes what is called a Hall effect sensor. Hall effect sensor might be a magnetic sensor tool, but
the principle of how it senses can be used in the measurement of other variables like current,
pressure, position, speed e.g. of a wheel etc., temperature among other parameters that uses this
principle. So long as the parameter measures involves a magnetic field, Hall sensors can perform

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the measurement (Koniar , et al., 2007). The parameters to which this effect can be used is. The
measurement is to identifying the static characteristics of a sensor, in simple terms the
experiment is to show how the voltage depends on the distance of the permanent magnet from
the sensor.
The objective of the experiment
The main objective of this experiment, having known the working mechanism of Hall effect, is
to first learn more about Hall effect, then use it in collection of conductivity investigation that
establishes the carrier properties, the type of carrier, how they concentrate and Hall motion for a
sample semiconductor.
Theory
In a conductor or a semiconductor, a particle can move linearly as described earlier, the
movement is usually random and influenced by an electric field. The average velocity at a given
direction is proportional to the electric field applied, this expression is given by:
v=μ E … … … … … … … … … … … … … … … … ..(1)
Where μ is what is known as the mobility of the particles that are charged, in a semiconductor,
this can either be negatively charged (electrons) or positively charged (holes). If the charged
particles are n in a given volume, then the current density J, is found by:
J=nqv … … … … … … … … … … … … … … … … … … … … . ( 2 )
From equation (2), we can say that
J=nqμ E≡ σ E … … … … … … … … … … … … … … … … .(3)
Where σ is conductivity of the semiconductor

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The semiconductor might be in a transverse magnetic field, and if that happens equation (1), the
component of the magnetic force acts to shift the charged particles in a transverse direction to
their motion, setting up an electric field, and the Hall field that counteracts the field deflection.
When there’s a balance, or equilibrium. The Hall effect force cancels out the force of the
magnetic field. The Hall effect field is given by the following equation
EH =−R ( J X B ) … … … … … … … … … … … …..( 4)
Where the Hall effect coefficient R, is given by
R= 1
nq … … … … … … … … … … … … … … … … … .(5)
Project description
The materials
 DC power supply
 Electromagnet
 Oscilloscope
 Semiconductor sample
 Ammeter (0 – 10mA)
 Potentiometer
The experiment arrangement is shown in figure 1, the semiconductor going to be used here is
Germanium.

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Procedure
AC/DC power supply shall be used where through appropriate wires, from the terminals, the
semiconductor materials sample shall be connected, 5mA. The oscillator is checked to check the
transverse voltages, the potentiometer which is on the semiconductor sample for the voltage to
be set to zero. The oscillator is set to a measurement ¿ 100 mV /¿ so that an accurate reading is
attained.
The sample is taken to the air gap of the electromagnet, with a connection on one side attached to
the terminals where power is supplied and the other the end of the oscilloscope
With the current set at 5mA at the AC or DC power supply, the magnetic flux density shall be set
to 0.4T, by a use of a DC power supply so that the Hall voltage is recorded by an oscilloscope.
Use the chart that shows how flux density relates to current, to ensure that the flux density is
reduced to zero, increasing it bit by bit while taking the current readings at the same time.

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Figure 1The experiment set-up
Results
When the flux density is set to 0.3T, the drift current set 10mA, then it shall indicate the Hall
voltage. The current is then slowly reduced to 0mA, and the Hall is recorded.
Remove the Ge sample from the electromagnet, and have the drift current be 5mA, afterwards,
measure longitudinally the drift voltage, V y across the specimen so that the plate’s resistance can
be calculated.
Obtained data are:
Drift current = I y=5 mA ± 0.1mA

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The dimensions of the plate are:
Length = d y=15.69mm ± 0.005 mm
Width = d x=2.87 mm ± 0.005 mm
Thickness = d z=0.99 mm ± 0.005 mm
The data recorded was obtained from the experiment, by using a magnetic flux to get the Hall
voltage which were recorded in table 1. Another set of data were obtained comparing the drift
current to the hall voltages. The two results recorded were plotted, see graph 1 and 2.
Table 1. Readings for the Magnetic flux density and the Hall voltage
Trial Magnetic flux B(T )
Hall voltage
V H (V )
1 0.42 0.352
2 0.37 0.329
3 0.31 0.315
4 0.27 0.2794
5 0.23 0.255
6 0.19 0.204
7 0.15 0.176
8 0.11 0.132
9 0.07 0.0754
10 0.05 0.0348
To obtain the results in the second part of the experiment, the magnetic flux density was set to
0.3T with the error limit of 0.0071T and the Hall voltage was obtained and recorded in table 2
Table 2 Readings of the quantity of drift current against Hall voltage
Trial
Drift Current
I y (A )
Hall voltage
V H (V )
1 0.011 0.635
2 0.01 0.565
3 0.009 0.5
4 0.008 0.478
5 0.007 0.433

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6 0.006 0.376
7 0.005 0.302
8 0.004 0.239
9 0.003 0.176
10 0.002 0.115
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
f(x) = 0.848899655923039 x + 0.0310487746647005
R² = 0.950206176197266
Hall voltage against Magnetic Flux
Magnetic Flux B,(T)
Hall Voltage (V)
Graph 1 The graph of the Hall voltage plotted against the magnetic flux density readings

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0 0.002 0.004 0.006 0.008 0.01 0.012
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
f(x) = 56.3212121212121 x + 0.0158121212121212
R² = 0.991842346590083
Hall voltage against Drift Current
Drift Current (A)
Hall Voltage (V)
Graph 2 The graph showing Hall Voltage plotted vs drift Current
Discussion
Graphs 1 and 2 were gotten by applying the linear regression technique, where the Hall voltage
was plotted against the magnetic flux. The equation of the line was obtained by obtaining the line
of best fit, that though did not intercept the Y-axis, but through the equation of the line, the Y-
intercept was obtained, that is when there’s no magnetic field. The slope or gradient of the line
was found to be 0.8489, that means:
V H =0.8489 B
We know that the equation of obtaining the Hall effect coefficient is:
RH = ε H
JB … … … … … … … … … .. ( 6 )
Where
RHis the Hall effect coefficient measured in (m3/C)

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ε H is the Hall Field measured in (V/m)
J is the Drift current density, which is measured in (A/m2)
B is the magnetic flux density measured in (T)
RH = εH
J y B = V H dz
I y B … … … … … … … … … .. ( 7 )
Where
V H is the Hall voltage, measured in (V)
d x is the width of the semiconductor material, Germanium measured in (m)
d z is the thickness of the semiconductor material, Germanium measured in (m)
Therefore, we have the equation as
V H = RH ly
dz . B … … … … … … … … … .. ( 8 )
When the values are substituted, we have
0.8489= RH 0.005
0.00099
Therefore , RH =0.1681m3 /C
When we consider the error, we have:
0.1
5 X 100 %=± 2%
Which is an error in ε I y and

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0.005
0.99 X 100=±0.505 %
Which is an error in ε dz
The total percentage error shall be ± 2.5051% with the absolute error of 0.0048 m3 /Cin RH
Therefore RH =0.1681 m3 /C ±0.0048 m3 /C
On the second graph, there equation of the trend line was obtained and found to be y = 56.321x +
0.0158, with the slope found to be 56.321. this means that:
V H =56.321 I y +0.0158
When the equation above is rearranged and then we find the values of the flux density, slope of
the trendline and the dimensions of the plate, the result shall be:
V H = RH B
dz
. I y … … … … … … … … … .. ( 9 )
56.321= RH 0.3
0.00099
RH =0.1859 m3 /C
If we consider the errors, we shall have
0.007091
0.3 X 100=± 2.634 %
This is an error in ε B
0.005
0.99 x 100 %=± 0.5051 %

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This is an error in ε dz
The total error in percentage therefore becomes 2.634 %, and the absolute error is therefore
0.00607m3/C where calculating RH
Therefore, we shall have
RH =0.1859 ± 0.00607 m3 / C
As the Hall voltage increases, so does the magnetic flux, the intensity of the magnetic flux made
the deflection of the oscilloscope to cover a wide area. The magnetic flux coming from the
electro magnetic material caused the electrical effect on the semiconductor device to increase on
one side where the oscilloscope was connected and the intensity was imminent of the
oscilloscope. On the second experiment, we can also see the Hall voltage increases with the
increase of the drift current. The drift current is the current that shifted to the side where the
magnetic effect was felt by the conductor. Since the magnetic flux relates directly to the current
in proportionality, the result obtained was a proof of that fact, because it showed the same result
as the magnetic flux.
This experiment like any others, had errors, which were coming from the following sources.
Some of them being absolute error which came from the flux density, drift current, and the Hall
voltage. The errors were considered and below is how they were considered:
Magnetic flux density
The errors here, have two sources. The error coming from the limitation in the reading that was
shown by the ammeter connected to the DC power supply, the reading values also gave some
errors, the calibration chart for the magnetic flux to current was suspected not to be as accurate