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FACULTY OF ENGINEERING
LAB SHEET
ENT2016 SOLID STATE ELECTRONICS
TRIMESTER 1 (2014-2015)
SSE 1 – Measurement of Conductivity and Hall Effect in a
semiconductor
*Note: On-the-spot evaluation will be carried out during or at the end of the experiment based on
preparatory questions. Students are advised to read through this lab sheet before doing
experiment. Your performance, teamwork effort, and learning attitude will count towards the
marks.
ENT2016 Solid State Electronics
Experiment SSE1
Experiment SSE1: Measurement of Conductivity and Hall Effect in a Semiconductor
Objectives:
1. To understand the principle of Hall effect by investigating the conductivity and Hall voltage
of a rectangular strip of germanium as a function of current, temperature and magnetic field.
2. To apply Hall effect to determine the type of charge carrier and its mobility.
Equipment/components required:
a)
b)
c)
d)
Tripod support
DC Power Supply
Teslameter
Multimeter x 2
e) Electromagnet
f) Germanium sample carrier board
Preparatory Questions
1.
2.
3.
4.
What is a semiconductor? What does its energy band structure look like?
How does doping make semiconductor useful?
What are intrinsic and extrinsic carriers? How are they used?
What is the mean free path between collisions? How is it related to conductivity? What is the
temperature dependence on conductivity?
5. What is the Hall effect?
6. Describe the Hall effect apparatus and what are the precautions measures taken during the
experiment.
Introduction
The dc conduction properties of a homogenous semiconductor sample depend on the
carrier concentrations (number of charge carriers per unit volume) and mobilities (average
velocity of drift acquired per unit electric field). In extrinsic materials, investigation of the
conduction properties gives information about the majority carriers; in intrinsic materials, we
obtain information about the combined effects of conduction electrons and holes.
The conductivity, , is defined from the equation J = E and, in terms of the charge
carrier concentrations and mobilities,  :
  nq e  pq h
(1)
where n and p are the concentration of electron and hole, respectively. In a thin and homogeneous
semiconductor bar of length l, with ideal and uniform contacts, the current density J is constant
across the cross section A. The voltage drop across the sample Vl is obtained by integrating the
electric field E, which is directed along the sample and does not vary with position. Thus the
conductivity can be calculated as :
 = J / E = ( I / A) . (l / V)
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ENT2016 Solid State Electronics
Experiment SSE1
When a magnetic field is applied in a direction perpendicular to the current flow in a material, a
voltage known as the Hall voltage is developed perpendicular to both the current and the
magnetic field, as shown in Fig. 1. This phenomenon arises from the Lorentz force, F , which
deflects the charge carriers in the presence of a magnetic field, B, as a function of their velocity,
v. This may be represented mathematically as :



F  q.( v x B)
(3)
which also gives the direction of the force with respect to the direction of the carrier drift and the
magnetic field as well as the sign of the charge carriers.
B
+
w
I
VH
l
d
Figure 1: Hall effect in rectangular bar of semiconductor
Since negative and positive charge carriers in a semiconductor move in opposite directions under
the influence of an external electric field, they are deflected in the same direction by the Lorentz
force. The majority charge carrier responsible for the current flow can therefore be determined
from the polarity of the Hall voltage VH, knowing the direction of the current and the magnetic
field. We can express this effect in terms of a Hall coefficient RH :
VH = RH (B. I/ d)
RH = -1/ nq for n-type
= 1/pq for p-type
(4),
where d is the thickness of the sample.
In this model, the conductivity and Hall coefficient are assumed to be independent of the
magnetic field, regardless of its size. The sign of the Hall coefficient provides further evidence of
the existence of two types of charge carriers. It may be extended to consider the Hall effect when
both electrons and holes are present. If the magnetic field is not too large, the result for the Hall
coefficient is :
RH 
( p h2  n e2 )
q( p h2  n e2 )
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ENT2016 Solid State Electronics
Experiment SSE1
The simple quantitative results given below are in only fair agreement with experiment. In
particular, the Hall coefficient does depend on the strength of the magnetic field at large fields,
and at small fields its value differs from those quoted above by factors that depend on the specific
kinds of carriers scattering processes involved in the material. Moreover, even at moderate
magnetic fields, the resistivity (i.e. reciprocal of conductivity) does depend noticeably on both
strength and direction of the magnetic field, in a phenomenon known as magneto-resistance. To
explain these effects, we must give up the assumption that all carriers of a given type have the
same mean free time. It must be admitted that the free time is a function of thermal speed.
Moreover, even then differences as large as 25% in Hall coefficient will remain unexplained
because they depend on details of the energy-band structure which are sufficiently specialized
that we have not been able to, and cannot here, take the space to discuss them. The conclusions of
a more comprehensive theory may be summarized for our purposes as :
1. For n-type germanium, RH = -0.93/ (nq)
2. For p-type germanium, RH = 1.4/ (pq)
3. The magneto-resistance depends on 2B2 at low and moderate fields.
With rising temperature, the Hall voltage will decrease due to an increase in the number of
charge carriers and the associated reduction in drift velocity and mobility. At a sufficiently high
temperature, the concentrations of holes and electrons are approximately equal. The properties of
the sample change from extrinsic conduction to intrinsic conduction (both electrons and holes
contribute to the values of the conductivity and Hall effect). A reversal of sign of the Hall voltage
may be observed, typical of p-type materials, above a particular temperature.
C
B
VH
A
A
.
Figure 2: Electrical alignment for Hall voltage measurement
In Fig 1, the two contacts must be aligned accurately opposite to each other so that V H
measures only the Hall effect. If there is some misalignment, V H will include a component arising
from the potential drop along the bar. To avoid this, an experimental arrangement for Hall voltage
measurement is shown in Fig 2. By varying the position of the moving contact on the
potentiometer, we can make the potential at point A equal to that at point B. At this condition, VH
will be zero in the absence of magnetic field. When a magnetic field is applied, the potential
between A and C is the same as that between B and C as desired.
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ENT2016 Solid State Electronics
Experiment SSE1
Another arrangement, which is used in this experiment, is shown in Fig. 5. Unfortunately,
the voltage offset changes with the current and the electrical alignment must therefore be
performed, in the absence of magnetic field, every time the current is varied.
Temperature
and current
display
(selectable)
Hall voltage tap
LED
display
selector
Sample
current
adjusting
switch
Hall voltage
compensation
Sample voltage tap
WARNING: DO NOT CONNECT THE POWER SUPPLY
TO THE VOLTAGE TAP!
Figure 3: Front view of the sample plate
Power
supply
Heater on/off
(only for experiment C)
Figure 4: Back view of the sample plate
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ENT2016 Solid State Electronics
Experiment SSE1
Figure 5: Experimental Arrangement for conductivity and Hall effect measurements.
Experiment Procedures:
WARNING: DO NOT CONNECT THE POWER SUPPLY TO THE VOLTAGE TAP!
A. Relationship of Conductivity and Hall Voltage to Magnetic Flux
1. Set the current I flowing through the germanium sample to 25 mA. With the electromagnet
switched off and the pole shoes removed (to avoid residual magnetism), set the Hall voltage
to zero using the compensating potentiometer.
2. Replace the pole shoes and switch on the DC power supply connected to the electromagnet.
Position the Teslameter probe at the center of the magnetic field, then measure the magnetic
flux density B. Set B to 10 mT by adjusting the current control knob. In this way the power
supply acts as a current source (instead of a voltage source) so that the field strength is not
affected by changes in coil resistance caused by temperature rise.
3. Measure and record the voltage across the sample Vl and the Hall voltage VH at room
temperature. Repeat the measurements for magnetic field B from 10 to 50 mT.
4. Plot the graphs for Conductivity and Hall voltage as a function of magnetic field strength.
From these, determine the Hall coefficient and the relationship between conductivity and the
magnetic flux density.
5. The dimensions of the sample are given as d= 1 mm, l = 20 mm and w = 10 mm. Calculate
the charge concentration and mobility of the majority carrier. Neglect the effect of minority
carrier.
6. Explain briefly the difference between intrinsic and extrinsic behavior. What determines
which behavior applies at a given temperature?
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ENT2016 Solid State Electronics
Magnetic field, B (mT)
10
15
20
25
30
35
40
45
50
Experiment SSE1
Hall voltage, VH
Vl
Conductivity, σ
B. Relationship of Hall Voltage to Electric Current
1. Set the current I flowing through the germanium sample to 5mA.
2. Switch off the electromagnet and remove the pole shoes. Set the Hall voltage to zero using
the compensating potentiometer.
3. Replace the pole shoes and switch on the electromagnet. Set the magnetic flux density B to
50 mT.
4. Measure the record the Hall voltage VH at room temperature.
5. Repeat steps 2 to 4 for current I from 5 to 30 mA.(When the current I is changed, the Hall
voltage offset will also change. Remember to adjust the Hall voltage offset to zero in the
absence of a magnetic field for each current setting.)
6. Plot the results on a graph. Explain the relationship between the Hall voltage and the current
flowing through the germanium sample.
Electric current, I (mA)
5
8
10
13
15
18
20
23
25
30
Hall voltage, VH
C. Relationship of Conductivity and the Hall Voltage to Temperature
CAUTION: IMMEDIATELY TURN OFF THE HEATER ONCE YOU REACH 90C.
FAILING TO DO THIS WILL DAMAGE THE SAMPLE PLATE.
1. Set the current I flowing through the germanium sample to 25 mA.
2. Switch off the electromagnet and remove the pole shoes. Set the Hall voltage to zero using
the compensating potentiometer.
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ENT2016 Solid State Electronics
Experiment SSE1
3. Replace the pole shoes and switch on the electromagnet. Set the magnetic flux density B to
50 mT.
4. Connect the 6 VAC output of the power supply to the heating coil and remove the Teslameter
probe from the heating zone. Use the temperature display to record the temperature.
5. Measure and record the voltage across the sample Vl and the Hall voltage VH as the sample
temperature rises from 25 to 95C. Plot the graphs for conductivity and Hall voltage vs.
temperature.
6. Explain the reasons for these variation patterns as the germanium sample is heated up.
Temperature, T (C)
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
Hall voltage, VH
Vl
Conductivity, σ
Reference:
Richard B. Adler, Arthur C. Smith and R. L. Longini, Introduction to Semiconductor Physics,
volume 1 of Semiconductor Electronics Education Committee Series. Wiley, New York. pg 194209
NOTE:
Report: Submit your report within 7 days of performing the experiment to the same laboratory
with neat diagrams of circuits, waveforms, and data recorded. Also include the discussion on the
results obtained in the experiment. All report must be type-written, except for diagrams which
can be computer generated or hand-drawn.
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ENT2016 Solid State Electronics
Experiment SSE1
Marking Scheme
Lab
(10%)
Assessment Components
Hands-On & Efforts (2%)
On the Spot Evaluation
(2%)
Lab Report
(6%)
Details
The hands-on capability of the students and their efforts during the
lab sessions will be assessed.
The students will be evaluated on the spot based on the lab
experiments and the observations on the semiconductor
characteristics.
Each student will have to submit his/her lab final report within 7
days of performing the lab experiment. The report should cover the
followings:
1. Introduction, which includes background information on
Hall effect measurement and their relationship with
semiconductor materials.
2. Experimental section, which includes the general summary
of the lab experiment work.
3. Results and Discussions, which include the Hall effect
measurement results, analysis, and evaluations, with neat
graphs/images of the results and recorded data.
4. Conclusion, which includes a conclusion on the
experimental.
5. List of References, which includes all the technical
references cited throughout the entire lab report.
The report must have references taken from online scientific
journals (e.g. www.sciencedirect.com,
http://ieeexplore.ieee.org/xpl/periodicals.jsp,
http://www.aip.org/pubs/) and/or conference proceedings (e.g.
http://ieeexplore.ieee.org/xpl/conferences.jsp).
Format of references: The references to scientific journals and text
books should follow following standard format:
Examples:
[1] William K, Bunte E, Stiebig H, Knipp D, Influence of low
temperature thermal annealing on the performance of
microcrystalline silicon thin-film transistors, Journal of
Applied Physics, 2007, 101, p. 074503.
[2] Hodges DA, Jackson HG, Analysis and design of digital
integrated circuits, New York, McGraw-Hill Book Company,
1983, p. 76.
Reports must be typed and single-spaced, and adopt a 12-point
Times New Roman font for normal texts in the report.
Any student found plagiarizing their reports will have the
assessment marks for this component (6%) forfeited.
The lab report has to be submitted to the Electronics lab staff.
Please make sure you sign the student list for your submission. No
plagiarism is allowed. Though the electrical characteristics of the
measured sample from the same group can be similar, the report
write-up cannot be duplicated for group members. The individual
report has to be submitted within 7 days from the date of your lab
session. Late submission is strictly not allowed.
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