INTRODUCTION
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. 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.
In this
experiment, we want to determine
relationship between Hall Current IH and voltage UH, to
measure sensitivity of Hall element KH from GaAs semiconductor, and
to determine magnetization curve of silicon steel with Hall element. We use LEEI-35 Hall Effect Experimental
Apparatus. So, that is the reason Hall Effect Experiment must done.
THEORY
When an electric current passes
through a conductor in the direction perpendicular to the external magnetic
field, there will be the potential difference in the direction perpendicular to
the electric current and the magnetic field. This phenomenon is known as the
Hall effect, discovered in 1879 by American physicist Hall. Hall effect in
metals generally small but on the type of semiconductor materials such as
germanium-N, InSb, and GaAs Hall effect is quite large. GaAs elements commonly
used in the measurement of the magnetic field due to its high sensitivity, wide
linear range, and a low temperature coefficient.
Figure 1 shows the electric
currentIHpassing through the Hall element P type, the charge carrier
drift current hole (holes) of v, the magnetic field B causes the Lorentz force
F on a moving charge:
FIGURE 1. Diagram formation of
Hall voltage
(1.1)
In this case q is the electron
charge. Lorentz force will deflect the charge carrier to the horizontal
direction and gathered at the edges of the sample and generate an electric
field E.
Collection continued until the
electric field (Fe = qE) and magnetic field (FB) are deployed by
carriers mutually exclusive, in this case:
(1.2)
For samples with a p-type charge
carrier concentrations of p, width w and thickness d, the current through the
sample is IH (IH = pqυωd), so the speed of the charge
carriers holes into υ = IH / pqωd. Then from equation (1.3) is
obtained,
(1.3)
If both members of equation (1.3)
multiplied by ω then obtained,
(1.4)
with RH = 1/pq and called the Hall
coefficient. In summary, equation (1.4) is generally written as:
(1.5)
In this case the coefficient KH=RH/d=1/pqd and
referred to as the Hall element sensitivity, expressed in units of mV/(mA•T).
In general, the larger the KH, the better. Therefore KH
inversely proportional to the concentration of the charge carrier p and
concentration is smaller than in the metal, the semiconductor material is
better used as a Hall element. Of the equation (1.5) it appears that by knowing
KH, IH and UH values can be measured.
As with
NMR, Hall effect can be used to measure AC and DC magnetic fields with fast and
simple. Figure 2 shows the DC source that generates a magnetic current IM
can be arranged the magnitude through the resistance R1. E2
source generate currents Hall IH to Hall elements through resistance
R2. E2 source can be either DC or AC. A voltmeter is used
to measure current Hall IH and Hall voltage UH.
FIGURE 2. Circuit to measure
Hall difference voltage
Semiconductors are generally
composed of n-type and p-type with charge carriers different signs. Therefore,
if the material type is known, the direction of the magnetic field can be
determined by looking at the sign of UH. Because of the time used to
generate an electric field through the Hall effect is very short (10-12
- 10-14 s), then the current AC or DC can be used. If the current
Hall expressed as IH = I0 sin (ωt), then we obtain
(1.6)
Potential Hall is back and forth. In the case of AC,
equation (1.6) remains valid but the value of IH and UH
is an effective value.
EXPERIMENTAL
METHOD
In this experiment, we used a set
of Hall Effect Experimental Apparatus production by Lambda Scientific.
The first thing to do in this experiment
is check all the component of Hall Effect Devices are well connected as the
following figure
FIGURE 3. Hall Effect Experimental
Apparatus production by Lambda Scientific
FIGURE 4. Electric circuit of Hall
Effect Apparatus
After checking the components,
then we implement for three activities. The first activity is determine
relationship between IH and UH. In this activity, we
connecting the Hall apparatus to the PLN voltage source. We must sure that all
the display point to the 0 value. Then, we regulate electromagnetic
magnetization current IM in 400 mA, no more. Then, regulate Hall
current (The current that flow to the Hall element) with turn slowly the Hall Current Adj. start from 0,5 mA, 1,0
mA, 1,5 mA, 2,0 mA, and 2,5 mA. We must attention that Hall current cannot more
than 5 mA because can make the Hall element burn. Next, in every IH
value, measure Hall voltage. To get good UH value, press reverse switch back and forth in UH
panel. And plot the curve UH - IH, then make sure the
relationship both of them is linear.
The second activity is measuring
sensitivity KH from GaAs Hall element. The first thing to do is
understand how to use Teslameter for measuring magnetic field. We must be
careful to use it because probe of Teslameter is very brittle. Next step is
regulate and hold out Hall current IH in 1.00 mA. After that,
regulate magnetization current IM with Current Adj in 50 mA, 100 mA, 150 mA, 200 mA, …, 400 mA. Then,
every value of IM, write down the magnetic field B by Teslameter and
Hall voltage UH in the sample, both of toggle switchbetter to use for return the polarity. And, calculate
sensitivity of Hall element with use equation
.
The third activity is determine magnetization
curve of silicon steel with Hall element. In this activity, Hall element will
use to measure magnetic field B in electromagnetic slit. The first thing to do
in this activity is regulate Hall current IH in 1 mA while change
excitation current IM from 0 to 400 mA with interval 100 mA. Then,
every value of IM, write down Hall voltage UH. Remember
that to eliminate the effect use toggle
switch. Then, calculate magnetic field B for every value of IM with
equation
. Use value of KH that we got in activity
two. Then plot curve of B-IM.
RESULT OF
EXPERIMENT AND DATA ANALYSIS
Experiment
Result
Activity 1. Determine Relation
between Hall Current (IH) dengan
hall voltage (UH).
IM = 400 mA
TABLE 1. Relation between Hall
Current (IH) and Hall Voltage (UH)
NO.
|
IH (mA)
|
UH (mV)
|
B (mT)
|
1
|
0,5
|
3,4
|
294,3
|
2
|
1,0
|
5,7
|
294,4
|
3
|
1,5
|
7,5
|
294,4
|
4
|
2,0
|
9,7
|
294,4
|
5
|
2,5
|
11,8
|
294,5
|
Activity 2. Measure Sensitivity KH from GaAs Hall Element
IH = 1,0 mA
TABLE 2. Relation between
Magnetic Current (IM),Magnetic Field (B), and Hall Voltage (UH)
No.
|
IM (mA)
|
UH(mV)
|
B (mT)
|
1
|
50
|
46,3
|
35,4
|
2
|
100
|
24,3
|
69,7
|
3
|
150
|
16,0
|
105,4
|
4
|
200
|
12,2
|
141,0
|
5
|
250
|
9,5
|
178,9
|
6
|
300
|
8,1
|
217,5
|
7
|
350
|
6,4
|
255,6
|
8
|
400
|
6,0
|
293,9
|
Activity 3. Determine Magnetization
Curve of Silicon Steel with Hall Element
IH = 1,0 mA
TABLE 3. Relation between
Magnetic Current (IM), Magnetic Field (B),and Hall Voltage (UH)
No.
|
IM (mA)
|
UH(mV)
|
B (mT)
|
1
|
0
|
0
|
0
|
2
|
100
|
24,5
|
68,8
|
3
|
200
|
12,0
|
140,2
|
4
|
300
|
8,0
|
216,7
|
5
|
400
|
5,8
|
293,0
|
Data
Analysis
Activity 1. Curve
relationship between hall current and hall voltage.
FIGURE 5. Curve of Relation between
Hall Current (IH) and Hall Voltage (UH)
Based on the curve of relation
between Hall Current (IH) and Hall Voltage (UH) is
directly proportional or linear and from the curve we find the equation y = 4.16x + 1.38 or UH = 4,16IH + 1.38 and
get it too the value of R2=0,999.
The gradient (m) from the curve is the ratio between Hall Voltage (UH)
and Hall Current (IH), where the unit of Hall Voltage (UH)
is mV and the unit of Hall Current (IH) is mA. So the gradient (m) is 4,16 V/A and the
calculate hall element that’s :
Tan θ = m
=
where, UH=
IH KH B
So that,
m =
m
= KH B
KH =
with: m= 4,16
dan B= 353,28 mT
KH =
= 0,0118.103 mV/(mA.T)
R2 =
0,999
DK = R2 x
100 %
DK = 0,999 x 100%
DK = 99,9 %
KR = 100 % - DK
KR = 100% - 99,90%
KR = 0,10 %
KR =
KR x KH
= 0,10 % x
0,0118.103
= 0,001 x
0,0118.103
= 0,0118
PF = |KH ±
|
PF = |11,8 ± 0,0118| mV/(mA.T)
Activity 2. Measure Sensitivity KH from GaAs Hall Element.
·
Just Data 1
KH =
KH =
KH = 1,308.103 mV/(mA.T)
=
1,308.103
mV/mA.T
=0,137.103 mV/mA.T
**Untuk Nilai P
.10-6 cm-3
Table
of Measurement result
IM (mA)
|
UH (mV)
|
B (mT)
|
KH (mV/mA.T)
|
(mV/mA.T)
|
P cm-3
|
50
|
46,3
|
35,4
|
1,308.10-3
|
|1,308±0,137|103
|
8,458.1021
|
100
|
24,3
|
69,7
|
0,349.103
|
|0,349±0,037|103
|
6,241.1022
|
150
|
16,0
|
105,4
|
0,152.103
|
|0,152±0,016|103
|
2,167.1023
|
200
|
12,2
|
141,0
|
0,087.103
|
|0,087±0,010|103
|
5,065.1023
|
250
|
9,5
|
178,9
|
0,053.103
|
|0,053±0,006|103
|
8,945.1023
|
300
|
8,1
|
217,5
|
0,037.103
|
|0,037±0,004|103
|
18,370.1023
|
350
|
6,4
|
255,6
|
0,025.103
|
|0,025±0,003|103
|
31,950.1023
|
400
|
6,0
|
293,9
|
0,020.103
|
|0,020±0,002|103
|
45,922.1023
|
Based on the calculation by using
formula
we find that if the value of UH is
great, the value of KH is great too. It is mean that relation
between UH and KH is directly proportional.
Activity 3. Determine Magnetization
Curve of Silicon Steel with Hall Element
FIGURE 6. Curve of Relation between
Magnetic Current (IM) and Magnetic Field (B)
Based on the curve of relation
between Magnetic Current (IM) and Magnetic Field (B) is directly
proportional or linear and from the curve we find the equation y = 0.7339x – 3.04 or B = 0,7339IM – 3.04. The gradient (m) from the curve is the ratio
between Magnetic Field (B) and Magnetic Current (IM), where the unit
of Magnetic Field (B) is mT and the unit of Magnetic Current (IM) is
mA. So the gradient (m) is 0.7339 T/A.
And by using the equation
so we find :
·
·
·
·
·
Discussion
Based on the
observation table that describes the relationship between the strong currents Hall
and Hall voltage
at a constant magnetic
field strength, the greater his Hall current
strength, the greater his Hall
voltage. If drawn
comparisons between the magnetic
field strength (B) against strong currents
Hall (IH), the
greater the magnetic field strength of his strong
Hall currents will
be smaller.
For a graph
illustrating the relationship between
the current Hall (IH) and Hall voltage
(VH) is directly
proportional to the value of
the Besa its
IH VH then
its going to be
greater. of the observations,
obtained for IH
= 0,5 obtained
UH = 3,4; for IH = 1,0 obtained UH = 5,7; for IH = 1,5 obtained UH = 7,5; for IH = 2,0 obtained UH = 9,7; for IH = 2,5 obtained UH = 11,8. This is
consistent with the theory that
the greater the current of his Haall the greater
his Hall voltage.
CONCLUSION
Hall effect occurs
following the Lorentz force law, so from here will cause the Hall voltage is proportional to the amount of current flowing, but to meet the Hall voltage based on the temperature of the exponential function
which initially rose
and then fell.
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. This effect is known as the Hall effect. Based on the experiment result
about Effect Hall, we find that relation between Hall Current (IH)
and Hall Voltage (UH) is directly proportional or linear. We can see
the relation in the curve of UH – IH. Beside that,
relation between Magnetic Current (IM) and Magnetic Field (B) is
directly proportional or linear. And we can see the relationship from curve of
B- IM. we can calculate sensitivity of Hall element KH
with use equation
. Based on the equation, if the value of UH
is great so, the value of KH is great too. So the relation is linear
or directly proportional.
REFERENCE
Lambda Scientific, 2011.
LEEI-35 Hall Effect Experimental Apparatus, Lambda Scientific Inc. Miami, USA.
Subaer, dkk. 2013. Penuntun Praktikum Eksperimen Fisika I. Unit Laboratorium Fisika Modern Jurusan Fisika FMIPA UNM.
Albert Einstein (1879-1955, warga Jerman-Amerika Serikat). Seorang filsuf dan pencita damai yang ramah. Ia adalah guru intelektualbagi dua generasi fisikawan teori yang meninggalkan sidik karyanya dalam hampir setiap bidang kajian fisika moderen.