exp . 12 hall effect as experimental proof of positive charg

8/3/2019 Exp . 12 Hall Effect as Experimental Proof of Positive Charg

1/14

1

University of Technology

Laser and Optoelectronics Engineering Department

Optoelectronic Engineering Branch

Detector lab 2010-2011

EXP No12

HALL EFFECT AS EXPERIMENTAL PROOF OF

POSITIVE CHARGE CARRIERS IN SEMICONDUCTORSPrinciple and task

The Hall Effect in thin zinc and copper foils is studied and the Hall coefficient

determined. The effect of temperature on the Hall voltage is investigated.

The resistivity and Hall voltage of a rectangular germanium sample are measured

as a function of temperature and magnetic field. The band spacing, the specificconductivity, the type of charge carrier and the mobility of the charge carriers are

determined from the measurements.

Purpose and aim of the experiment

The suggested experiment was implemented as a demonstration experiment in the

Modern physics course and as well as a laboratory exercise conducted by students

Individually. It has been used to demonstrate the existence of positive charge

carriers in a p-type semiconductor and contributes to better understanding not only

of the hole

concept, but also of other physical quantities and phenomena included in the

proposed experiment:

intrinsic conductivity, extrinsic conductivity, electrons, holes, band theory,

forbidden zone, valence band, conduction band, conductivity, mobility,

magnetic resistance, Hall constant, Lorentz force

Physics textbooks intended for the fourth year in the high schools in Croatia are

extremly rich in subjects covering different fields of modern physics [1]. Concepts

mentioned above (except mobility, magnetic resistance and Hall constant) appear

in the investigated sample of physics textbooks. In view of this, the proposed

experiment can also be adapted for the high school level. The Hall voltage and thevoltage across the sample of p-Ge are measured as a function of current,

temperature and magnetic field. From the measurements, the following quantities

can be determined: band spacing, magneto resistance, conductivity, the sign of the

charge carriers, their mobility and concentration, Hall constant.

Equipment

1-Hall effect, Cu, carrier board 11803.00 1

2-Hall effect, zinc, carrier board 11804.01 1

3-Coil, 300 turns 06513.01 2

Exp no 12


POSITIVE CHARGE CARRIERS IN SEMICONDUCTORS


2/14

2





4-Iron core, U-shaped, laminated 06501.00 1

5-Pole pieces, plane, 30330348 mm, 2 06489.00 1

6-Power supply 0-30 VDC/20 A, stabil 13536.93 1

7-Power supply, universal 13500.93 1

8-Hall probe, tangent, prot. cap 13610.02 1

9-Digital multimeter 07134.00 1

10-Meter, 10/30 mV, 200 deg.C 07019.00 1

Set-up and procedure

The experimental set-up is shown in Fig. 1.

The plate must be brought up to the magnet very carefully, so as not to damage thecrystal In particular, avoids bending the plate.

1. The control current is derived from the alternating voltage output of the power

unit, using a bridge rectifier.

To do this, the rectifier is connected on the one hand to the lower socket of the

power supply unit and on the other to the socket marked 15 V on the selector

ring above it (see Fig. 1).

An electrolytic condenser is connected to the rectifier output for smoothing. (Note

the polarity). The control current is set with the aid of a potentiometer. A 330 V

resistor is connected in series to limit the current and so prevent accidentaloverstepping

of the maximum permissible current (50 mA).

In this measurement, the crystal is connected directly (terminals A and B in Fig. 1);

hence the constant-current source and the defect voltage compensation are inactive.

Exp no 12HALL EFFECT AS EXPERIMENTAL PROOF OF



3/14

3





Fig. 1 Experimental set-up of the Hall effect in the metals.

The magnetic field is produced by the two series-connected coils fed from the DC

outlet of the main supply unit. It is advisable for this purpose to set the voltage to

the maximum value and to adjust the magnetic field to the desired value by use of

the current control knob.

The power supply unit then acts as a constant-current source, so ensuring that

temperature-induced resistance changes have no effect on the field strength. The

magnetic induction of the field is measured by the teslameter, the Hall probe ofwhich is placed at the centre of the field (after the apparatus has been adjusted).

The Hall voltage is measured by the high-resistance digital multimeter.

2. The control-current supply is now connected to the outer terminals A and C

(Fig. 2), so that the incorporated constant current source becomes effective. The

560 V potentiometer is set to the maximum voltage. The control current should

now e about 30 mA. (If it is not, the value can be readjusted using the trimmer on

the supplementary board). The voltage across the sample is measured between the




4/14

4





terminals A and B using the digital multimeter (see Fig. 2). The sample resistance

in the absence of the magnetic field,R0, is calculated and the change in resistance

R=

is plotted as a function of the magnetic inductionB (RB sample resistance with the

magnetic field).3. The sample is heated to temperatures up to 175C using the heating coil. The

heating current required is taken from the 6 V AC output of the power supply unit.

The sample temperature Tcan be determined by the built-in Cu/CuNi

thermocouple, using the voltmeter :

UTT= + T0

(UT = voltage across the thermocouple; = 40 V/K;

T0 = room temperature).

CAUTION: The sample temperature must in no case rise

above 190C.

RB R0

R0

Exp no 12




5/14

5





Fig. 2:

Fig3




6/14

6





4. With the magnetic field switched off and the pole pieces removed (remanence!),

the control current is switched on (terminals

A and C in Fig. 2) and the Hall voltage set to zero by the compensating

potentiometer. The pole pieces are replaced and the Hall voltage is measured as a

function of the magnetic induction for both field directions.

5. With the magnetic field constant, the sample temperature is slowly raised to the

maximum temperature and the Hall voltage measured. The Hall probe of theTeslameter is removed from the heating zone during heating up.The layout follows

Fig. 1 and the wiring diagram in Fig. 2.

Arrange the field of measurement on the plate midway between the pole pieces.

Carefully place Hall probe in the centre of the magnetic field.

The measuring amplifier takes about 15 min. to settle down free from drift and

should therefore be switched on correspondingly earlier.

To keep interfering fields at a minimal level, make the connecting cords to the

amplifier input as short as possible.

Take the transverse current I for the Hall probe from the power supply unit13536.93. It can be up to 15 A for short periods.

The Hall probe will show a voltage at the Hall contacts even in the absence of a

magnetic field, because these contacts are never exactly one above the other but

only within manufacturing tolerances. Before measurements are made, this voltage

must be compensated with the aid of the potentiometer as follows:

Disconnect the transverse current I.

Set the measuring amplifier to an output voltage of 1 V, for example, by

adjusting the compensation-voltage. he = 104 , amplification = 105)

Connect the transverse current.

Twist the connecting cords between hall voltage sockets and amplifier input in

order to avoid as much as possible stray voltages.

Adjust the compensating potentiometer, using a screwdriver, until the instrument

again shows an output voltage of 1 V.

Repeat this operation several times to obtain a precise adjustment.The determination of the Hall voltage is not quite simple since

Voltages in the microvolt range are concerned where the Hall voltages are

superposed by parasitic voltages such as thermal voltages, induction voltages due

to stray fields, etc. The following procedure is recommended:

Exp no 12




7/14

7





Set the transverse current I to the desired value.

Set the field strengthB to the desired value (on the power supply, universal, and

13500.93).

Set the output voltage of the measuring amplifier to about 1.5 V by adjusting the

compensation-voltage.

Using the mains switch on the power supply unit, switch the magnetic field on

and off and read the Hall voltages at each on and off position of the switch (after

the measuring amplifier and the multi-range meter have recovered from their peakvalues). The difference between the two values of the voltage, divided by the gain

factor 105, is the Hall voltage UH to be determined.

Hall Effect Theory

The Hall Effect, discovered by Edwin Hall in 1879, consists of the generation of a

ifference in electric potential between the sides of a conductor through which a

current is flowing while in a magnetic field perpendicular to the current. This was

later predicted for semiconductors and the transistor soon after its development in

the late 1950s.

Figure 5 An illustration of the electromagnetic theory behind the Hall Effect. The

figure above illustrates a conductor subjected to a magnetic field. The magnetic

field is at a right angle to the current flowing through the material. An electron

enters the right electrode and travels towards the left electrode (Note* the

Exp no 12




8/14

8





convention that electrons move opposite to the current flow is being used). A force

known as the Lorentzforce acts upon the electron.

Lorenz Force: F= q*v*B

Where F= Lorenz Force

q= Charge of electron (1.6 X 10-19 C)

v= Velocity of electron (m/s)

B= Flux density of magnetic field [Wb/m2 or tesla (T)]

This force causes the electron to move towards the bottom of the conductor. Thismeans that all electrons traveling as shown in the slab of conductor will congregate

towards the bottom of the conductor. As a result, the lower edge of the conductor

will become negatively charged while the upper edge will become positively

charged. In other words, an EMF (electromotive force, potential, Ey) will develop

across the width of

the slab that is in proportion to the amount of flux, current, and resultant charge

separation, t.

The amount of generated voltage due to the Hall Effect, VH, can be calculated

using the relationshipVH = [B*KH*I]/z

WhereB= Flux density of magnetic field [Wb/m2 or tesla (T)]

KH= Hall Effect constant (m3/number of electrons-C)

I= Current flowing through the conductor (A)

z= Thickness of conductor (m)

The Hall Effect constant, KH, is a factor of the number of electrons per unit

volume and the electron charge. Up to this point we have been using a conductor to

illustrate the behavior of the Hall Effect. Actually, semi conducting material is

used to manufacture Hall effect devices, but the explanation of how electrons are

deflected at right angles to the magnetic

flux remains the same. The only difference is that with semi conducting materials

you are working with charge carriers and holes instead of electrons. Hall Effect

devices can be manufactured from either p-type or n-type semi conducting

materials. The only difference between the way these two materials behave is in

the internal flow direction of electrons. When you are using n-type material, you

are dealing with a flow of electrons whereas when you are working with p-type

material, you are working with a flow of hole carriers. For all practical purposes

these

Exp no 12




9/14

9





are the same as positively charged particles, or positrons, that flow in the opposite

direction from the n-type electrons. Consequently, the outward results of using

these two types of material are identical; only the polarities of the biasing currents

are reversed. The Hall voltage generated VH depends upon the thickness of the

material and the electrical properties of the material (charge density and carrier

mobility). The behavior described by the Hall Effect equation above is somewhat

ideal. The Hall voltage depends in practice on other factors such as the mechanical

pressure and the temperature. The dependence on the mechanical pressure(piezoresistive effect) is a factor to be considered mainly for the manufacturer

when encapsulating the device. It is not of much concern for the user. The

temperature has a double influence. On one hand it affects the electrical resistance

of the element. On the other hand, the temperature affects the mobility of majority

carriers thus also the sensitivity. So if we keep a constant supply voltage and the

device heats up, the bias current will decrease with temperature. Thus VH goes

down. The sensitivity (gain) of the device goes up because of the

increased mobility of the charge carriers. Since these two effects have opposite

signs, it is possible to compensate for them. Nevertheless it is always useful tolimit the supply current so that self-heating is negligible. It is much better to apply

a constant current. With a constant current supply you get an error of 0.12%/K.

With a constant voltage supply you get an error of 0.4%/K

If a current I flows through a strip conductor of thickness dand if the conductor is

placed at right angles to a magnetic fieldB, the Lorenz force

F= Q (v xB )

acts on the charge carriers in the conductor, n being the drift velocity of the charge

carriers and Q the value of their charge. This leads to the charge carriers

concentrating in the upper or lower regions of the conductor, according to their

polarity, so that a voltage the so-called Hall voltage UH is eventually set up

between two points located one above the other in the strip:

UH=d

IBRH ...

RH is the Hall coefficient.

The type of charge carrier can be deduced from the sign of the Hall coefficient: a

negative sign implies carriers with a negative charge (normal Hall effect), and a




10/14

10





positive sign, carriers with a positive charge (anomalous Hall effect). In metals,

both negative carriers, in the form of electrons, and positive carriers, in the form of

defect electrons, can exist. The deciding factor for the occurrence of a Hall voltage

is the difference in mobility of the charge carriers: a Hall voltage can arise only if

the positive and negative charge carriers have different nobilities. The

measurements for copper shown in Fig. 3 are related by the expression UH, B.

Linear regression using the relation

UH = a + bB shows these values to be represented by aStraight line with the slope b = -0.0384 10

-6m

2/s and a standard deviation sb =

0.0004 06m/s. From this, with d= 18 10

-6m and I = 10 A, we derive the Hall

coefficient RH = (0.576 0.006) 10-10 m3/As.

Fig. 6

6




11/14

11





Fig. 7

Exp no 12




12/14

12





Fig. 8




13/14

13





Fig. 9:

Problems

1. The Hall voltage is measured in thin copper and zinc foils.

2. The Hall coefficient is determined from measurements of the current and the

magnetic induction.

Exp no 12




14/14

14





3. The temperature dependence of the Hall voltage is investigated on the copper

sample.

4. The Hall voltage is measured at room temperature and constant magnetic field

as a function of the control current and plotted on a graph (measurement without

compensation for defect voltage).

5. The voltage across the sample is measured at room temperature and constant

control current as a function of the magnetic inductionB.

6. The voltage across the sample is measured at constant control current as afunction of the temperature. The band spacing of germanium is calculated from the

measurements.

7. The Hall voltage UH is measured as a function of the magnetic inductionB, at

room temperature. The sign of the charge carriers and the Hall constantRH

together with the Hall mobility mH and the carrier concentrationp are calculated

from the measurements.

8. The Hall voltage UH is measured as a function of temperature at constant

magnetic inductionB and the values are plotted on a graph.

Materials used in Hall-effect

The material used in the manufacture of Hall-effect devices is a p-type or an n-type

semiconductor. Typical examples are indium arsenide, indium arsenide phosphide,

indium antimony, gallium arsenide, germanium, and doped silicon. Silicon has the

advantage that signal conditioning circuits can be integrated on the same chip. One

type of Hall effect integrated circuit yields a differential output superimposed on a

common mode output. Whereas a second type yields a single ended output

superimposed on a quiescent output. Hall elements are manufactured in different

shapes; rectangles, butterfly (which concentrates the flux in the central zone), and

also as a symmetrical cross, which permits the interchange of electrodes. Hall

devices can be manufactured to fit into a variety of packages. Most packages are

similar to those used with transistors and other solid state devices. In many cases it

is very difficult to single out the Hall device within a transducer system because of

the integral design packaging that is often used.

Exp no 12



exp . 12 hall effect as experimental proof of positive charg

Documents