Preparation of Thin Films and Their Use in the Hall Effect
R. Thakrar
Laboratory Partner: G. Sagoo
Department of Physics and Astronomy
University College London
22th February 2010
This experiment aimed to prepare a thin film sample of Bismuth, and use it to measure the Hall
Coefficient and charge carrier density at room temperature (~298K) and at the temperature of
liquid nitrogen (~77K). The strength of the magnetic field was also varied at room temperature to
see if this had an effect on the Hall coefficient and the charge carrier density. At room
temperature, the hall coefficients were found to be (1.8 ± 0.4) x10-5 at 14mT, and (1.9 ± 0.2) x105
at 28mT. The charge carrier densities were found to be (3.5 ± 0.8) x1023 at 14mT and (3.3 ± 0.3)
x1023. These results are within range of each other, and so it was concluded that the hall
coefficient and the number of charge carriers does not depend on the strength of the magnetic
field. At ~77K, the hall coefficient was seen to increase, and the number of charge carriers
decrease, verifying the relationship that RH ∝ 1/n
1. Introduction
The Hall Effect is seen when a current is put through a perpendicular magnetic field. The effect is
a production of voltage difference that is seen across an electrical conductor, perpendicular to
both the current and magnetic field, known as the hall voltage.
The production of the voltage is due to a Lorentz Force on a charged particle moving
through a magnetic field. The particle moves perpendicularly to the current as shown in Figure 1
below.
Figure 1- Figure showing a conductor in a magnetic field, with a current running through it. The Lorentz
force felt by the charge carriers in both cases are in the same direction.
As figure 1 shows, the Lorentz Force makes the charge move upwards (in this case) this will
cause a charge build up on one side of the conductor, and therefore a potential difference across
the axis perpendicular to the direction of current and magnetic field.
The Lorentz Force is given by the equation:
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F  q(v  B) (1)
The Hall Voltage is given by the equation:
(2)
The Hall Coefficient is described to be the ratio between the induced electric field and the
E
multiple of charge density magnetic field strength i.e. RH  H (3) where j is current density.
jB
This can be reduced to:
(4)
Where: d= thickness of bismuth sample; VH is the hall voltage; I is the current, B is the magnetic
field strength.
2. Method
2.1 Preparing the Bismuth Sample
A vacuum pump is used in this experiment, shown in figure 2. Operation of the vacuum pump
may be found in the Laboratory script.1 The Bismuth sample is placed on a heating strip in the
vacuum chamber, and a glass slide is mounted on to a mask. When the vacuum pump is turned
on, the heating strip has a current passed through it. This heats the Bismuth sample past its
boiling point, and it evaporates onto the slide. After this sample is created, wires are inserted into
its pre-drilled holes, and screws are used to keep the wires in place. To ensure a good electrical
contact, silver paint is used between the wires and the sample.
Figure 2-Experimental setup for preparation of Bismuth Sample
2.2 Measuring the Hall Voltage for Varying Current at Room Temperature
The apparatus is set up as shown in figure 3. The background reading is taken for the magnetic
field, and then the magnetic field of the electromagnet is put at a set value. While the
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electromagnet is off, a current is put through the sample, and the voltage is calibrated at zero
using a potentiometer, to allow easy measurement of the Hall voltage. At this specific current, the
voltage is then measured with the electromagnet off, and then on. The difference between these
two values is the Hall voltage. This is then repeated for various values of current.
The experiment is then repeated with a larger electric field.
Figure 3 - Experimental setup for measuring the Hall Voltage with varying current
2.3 Measuring the Hall Voltage for Varying Current at ~77k (Liquid Nitrogen)
The experiment is then set up the same as part 2.2, but with a small modification to allow the
sample to be immersed in liquid nitrogen. This modification is shown in figure 4.
Figure 4 - Modification so that the sample could be immersed in liquid nitrogen
The hall voltage is measured as before with varying current, while the sample is immersed in
LN2.
3. Results and Analysis
The results from the three experiments are shown below in Graph 1.
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The graph shows that the when the magnetic field is doubled, the gradient (VH/I) is also doubled.
The data from the graph, particularly this gradient, was used to calculate charge carrier density
and the Value of the Hall Coefficient, shown in Table 1 below.
Graph 1 - Comparison of the Hall Voltage taken with varying current. Taken in varying magnetic fields of 14mT and
28mT, and immersed in liquid nitrogen with a 28.6mT field.
Condition
Magnetic
Field (mT)
Hall Coefficient x10-5-5)
Charge Carrier Density x1023
Room Temp. (~298K)
14.0 1.8 ± 0.4
3.5 ± 0.8
Room Temp. (~298K)
N2 Temp (~77K)
28.0 1.9 ± 0.2
28.6 14.3 ± 0.4
3.3 ± 0.3
0.44 ± 0.01
Table 1 - Table Showing the Hall Coefficients and Charge Carrier Densities from the Three Experiments.
4. Conclusion
The results shown in graph 1 and table 1 show that when the temperature is reduced, the value of
the hall coefficient increased greatly (as did the gradient), and the charge carrier density
decreased. The decrease in charge carrier density at ~77K is synonymous with the increase in the
hall coefficient, as lower densities of charges in bismuth coincide with an increased resistance.
Doubling the magnetic field at the same temperature yielded similar results (within range of
uncertainty) for the hall coefficient and the charge carrier density, showing that temperature is the
a main factor effecting these values. Though the experiment successfully used the sample to
study the Hall Effect accurately and to the required precision, some improvements could have
been made. Changing the shape of the mask the glass slide is mounted on so that the surface area
is easier to calculate would have further improved the accuracy of results. Also, the container
used to hold the liquid nitrogen was crude, and improvements to this would contain the nitrogen
better (and keep the sample at a steady temperature).
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Preparation of Thin Films and Their Use in the Hall Effect – Physics and Astronomy Department, UCL
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