Tanta University
Faculty of Science
Physics Department
Graduation Research
Submitted To physics Department Faculty of
Science Tanta University
By
Ahmed Abdou El-Menawy
Supervised by
Dr. Samia Ahmed Saafan
Physics Department
2012
Acknowledgment
At first I thank God for that he helped me to finish this research and give me a great chance, valuable gift to be graduated at the physics department with the care and encouragement of
Prof Dr. Mohamed Amer
Head of Physics Department
And all my dear professors
Also I offer my sincere thanks to
My Supervisor
Prof. Dr. Samia Ahmed Saafan
For her effective help and encouragement
Ahmed Abdou El-Menawy
Acknowledgment 1
Contents 2
The aim of the work 3
Introduction 4
Theory of the Hall Effect 5
Hall Effect Applications 12
Experimental Procedure 14
Results And Discussion 18
References 19
The aim of the present work is to investigate the Hall effect in a stainless steel sample and to determine the Hall constant of the sample
The Hall effect has been known for over one hundred years, but has only been put to noticeable use in the last three decades. The first practical application (outside of laboratory experiments) was in the 1950s as a sensor. With the mass production of semiconductors, it became feasible to use the Hall effect in high volume products. By introducing the first solid state keyboard using the Hall effect, a revolution in the keyboard industry has occurred in 1968. For the first time, a Hall effect sensing element and its associated electronics were combined in a single integrated circuit. Today, Hall effect devices are included in many products, ranging from computers to sewing machines, automobiles to aircraft, and machine tools to medical equipment.
The Hall effect was discovered by Dr. Edwin Hall in 1879 while he was a doctoral candidate at Johns Hopkins University in Baltimore. Hall was attempting to verify the theory of electron flow proposed by Kelvin some 30 years earlier. Dr. Hall found when a magnet was placed so that its field was perpendicular to one face of a thin rectangle of gold through which current was flowing, a difference in potential appeared at the opposite edges. He found that this voltage was proportional to the current flowing through the conductor, and the flux density or magnetic induction perpendicular to the conductor.
Although Hall’s experiments were successful and well received at the time, no applications outside of the realm of theoretical physics were found for over 70 years. With the advent of semiconducting materials in the 1950s, the Hall effect found its first applications. However, these were severely limited by cost. In 1965, Everett Vorthmann and Joe Maupin, development engineers, teamed up to find a practical, low-cost solid state sensor. Many different concepts were examined, but they chose the Hall effect for one basic reason: it could be entirely integrated on a single silicon chip. This breakthrough resulted in the first low-cost, high-volume application of the Hall effect, that is, “the solid state keyboard”.
When a current-carrying conductor is placed into a magnetic field, a voltage will be generated perpendicular to both the current and the field. This principle is known as the Hall effect.
Figure 1 illustrates the basic principle of the Hall effect . It shows a thin sheet of semiconducting material (Hall element) through which a current is passed. The output connections are perpendicular to the direction of current. When no magnetic field is present (Figure -1) , current distribution is uniform and no potential difference
is seen across the output.
Figure (1)
Hall effect principle, no magnetic field
Figure (2)
Hall effect principle, magnetic field present
When a perpendicular magnetic field is present, as shown in Figure 2 a Lorentz force is exerted on the current. This force disturbs the current distribution, resulting in a potential difference (voltage) across the output. This voltage is the Hall voltage (VH). The interaction of the magnetic field and the current is shown in equation form as : VH µ I ´B.
The Hall voltage is proportional to the vector cross product of the current (I) and the magnetic field (B). It is on the order of 7 mv in silicon and thus requires amplification for practical applications.
The Hall effect is an important diagnostic tool for the characterization of materials – particularly semiconductors. It provides a direct determination of both the sign of the charge carriers.
To deduce a mathematical formulation of the Hall effect consider the basic setup shown in Figure (3): A thin strip (thickness δ) of the material to be studied is placed in a magnetic field B oriented at right angles to the strip.
Figure (3)
A current I is arranged to flow through the strip from left to right (x – direction), and the voltage difference between the top and bottom (y-direction) is measured. Assuming the voltmeter probes are vertically aligned, the voltage difference is zero when B = 0.
The current I flows in response to an applied electric field E, with its direction is
established by convention. However, on the microscopic scale I is the result of either
positive charges moving in the direction of I, or negative charges moving backwards. In either case, the magnetic Lorentz force (qv ×B) causes the carriers to curve upwards.
Since charge cannot leave the top or bottom of the strip, a vertical charge imbalance
builds up in the strip. This charge imbalance produces a vertical electric field which
counteracts the magnetic force, and a steady-state situation is reached. The vertical
electric field can be measured as a transverse potential difference on the voltmeter.
Suppose now that the charge carriers where electrons ( q =- e . (In this case
negative charge accumulates on the strip’s top so the voltmeter would read a negative
potential difference. Alternately, should the carriers be holes q = +e we measure positive voltage.
The force acting on the moving charge carriers in a magnetic field is the Lorentz force:
……………………………… (1)
F, v and B form a right-handed Cartesian co-ordinate system. Since we have arranged v and B to be perpendicular to each other, the resultant force is also perpendicular to both v and B as shown in the following equations:
...... (2)
The force in (2) is reduced to two simple equations which describe the motion of the carriers.
……..………………………………………….(3a)
…………………………………………………(3b)
The movement of charge carriers sets up an electric field Ey in the opposite direction to the Lorentz force and this field continues to grow as the charge carriers move to one side of the semiconductor until it balances the Lorentz force. In this situation we have
…………………………………………… (4)
The electric field can be calculated from the Hall voltage, VH, since for a constant electric field,
…………………………………………… (5)
where w is the width of the sample.
Since the velocity can be expressed in terms of the current density, Ey can be written as:
…………………………………………… (6)
Where RH is the Hall constant which is negative if the majority carriers are electrons and positive if the majority carriers are holes.
If the sample contains both electrons and holes, then the Hall constant is given by
……………………………………………….(7)
Since we measure VH and set the values or measure the values of Bz, I, A and w, we can calculate the n, the carrier density. In addition to being able to measure the charge of the majority carriers the Hall effect can be used to measure the Hall mobility. With a measurement of the Hall coefficient the mobility can be found:
; where r is the resistivity of the sample. [2], [3].
Hall effect devices produce a very low signal level and thus require amplification. While suitable for laboratory instruments, the vacuum tube amplifiers available in the first half of the 20th century were too expensive, power consuming, and unreliable for everyday applications. As mentioned before, it was only with the development of the low cost integrated circuit that the Hall effect sensor became suitable for mass application. Many devices now sold as "Hall effect sensors" are in fact a device containing both the sensor described above and a high gain integrated circuit (IC) amplifier in a single package. Recent advances have resulted in the addition of ADC (Analog to Digital) converters and I²C (Inter-integrated circuit communication protocol) IC for direct connection to a microcontroller's I/O port being integrated into a single package.
What Is A Hall Sensor?
A Hall sensor is a four-terminal, solid-state device capable of producing an
output voltage VH, proportional to the product of the input current, lc, the
magnetic flux density, B, and the sine of the angle between B and the plane
of the Hall sensor.
A reversal in the direction of either the magnetic field or the control
current will result in a polarity change of VH. A reversal in the direction of both
will keep the polarity the same. By holding the control current constant, the
Hall voltage may be used to measure magnetic flux density. Multiplication may
be accomplish by varying both the control current and the magnetic field.
Typical Applications
The following are just some of the many applications where Hall sensors are used:
• Magnetic Card Readers - Proximity Sensors
• Rotary Speed Sensors
• Multipliers
• Magnet Field Measurements
• Electrical Power Measurements
• Current Sensors
• Brushless dc Motors
• Gauss-meters
• Watt-hour Meters
• Permanent Magnet Measurements
• Air Gap Measurements
• Magnetic Circuit design
• Flux Leakage Measurements
• Nondestructive Memory Readouts
• Linear/Angular Transducers
• Magnetic Tape Heads
• Guidance Systems
• Ignition Systems
1- Images below show the experimental setup arranged to determine the Hall voltage and the Hall constant in a stainless steel sample (commercial razor ).
2- Five copper wires have been soldered in the stainless steel sample as shown in image (1).
Image 1
Image (1): The sample, 5 wires and a potentiometer
3- Two wires (1, 2) for the current and the three other wires are for measuring the voltage (3, 4 and 5).
4- Wires (4 and 5) have been connected to a Potentiometer to adjust the zero point of the voltage at zero magnetic filed.
5- The electromagnet current has been adjusted to 1.5 ampere and the hall voltage has been taken as a function of the sample current I.
image 2: The power supply of the electromagnet
6- The results are shown in table 1.
Image 3: The electromagnet, the power supply that provides the sample current and the multimeter that measures the Hall voltage
7- has been plotted against I as shown in the following graph.
(V) / 0.0365 / 0.072 / 0.107 / 0.1445 / 0.183
8- From the graph has been calculated by using the relation
Where has been taken as 1.5 Tesla and W=.00005 m
slope=.0135135
then = .00000045
[1] HALL EFFECT SENSING AND APPLICATION
[2] Internet material, http://britneyspears.ac/physics/halleffect/hall.htm.
[3] [1] R. P. Feynman, Feynman Lectures on Physics, 3 , ch. 14