ENT2016 Solid State Electronics Experiment SSE1
FACULTY OF ENGINEERING
LAB SHEET
ENT2016 SOLID STATE ELECTRONICS
TRIMESTER 2 (2017-2018)
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.
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) Tripod support e) Electromagnet
b) DC Power Supply f) Germanium sample carrier board
c) Teslameter
d) Multimeter x 2
Preparatory Questions
1. What is a semiconductor? What does its energy band structure look like?
2. How does doping make semiconductor useful?
3. What are intrinsic and extrinsic carriers? How are they used?
4. 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, s, is defined from the equation J = sE and, in terms of the charge carrier concentrations and mobilities, m :
(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 :
s = J / E = ( I / A) . (l / V) (2)
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 :
(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.
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) (4),
RH = -1/ nq for n-type
= 1/pq for p-type
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 :
(5)
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 m2B2 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.
.
Figure 2: Electrical alignment for Hall voltage measurement
In Fig 1, the two contacts must be aligned accurately opposite to each other so that VH measures only the Hall effect. If there is some misalignment, VH 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.
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.
Figure 3: Front view of the sample plate
Figure 4: Back view of the sample plate
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?
Magnetic field, B (mT) / Hall voltage, VH / Vl / Conductivity, σ10
15
20
25
30
35
40
45
50
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) / Hall voltage, VH5
8
10
13
15
18
20
23
25
30
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.
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) / Hall voltage, VH / Vl / Conductivity, σ25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
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 194-209
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.
Marking Scheme
Lab (10%) / Assessment Components / DetailsHands-On & Efforts (2%) / The hands-on capability of the students and their efforts during the lab sessions will be assessed.
On the Spot Evaluation (2%) / The students will be evaluated on the spot based on the lab experiments and the observations on the semiconductor characteristics.
Lab Report
(6%) / 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.
Page 9 of 9