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Physical Electronics and SemiconductorsB39MB1

Introduction/Revision of Some Fundamental Concepts

Kinetic Energy

It can be shown that kinetic energy 2mv2

1where m is mass and v is velocity.

Potential Energy

A body has potential energy by virtue of its position. The reference level of potential energy

is arbitrary; only differences in potential energy at two different levels have physical

significance.

Velocity

The average velocity of a particle during a specified time interval is a vector quantity definedas the displacement of the particle during that time interval divided by the time interval.

Acceleration

In most cases, the velocity of a moving body changes as the motion proceeds and the body is

said to move with accelerated motion or to have an acceleration.

The average acceleration of a particle during a specified time interval is a vector quantity

defined as the change in velocity of the particle during the time interval divided by the time

interval.

Motion in Circle at Constant Speed

A particle moving in a circle of radius r at constant speed v has acceleration a which at each

instant is directed towards the centre of the circle and has magnituder

v2. This is called the

centripetal (centre seeking) acceleration. It is this acceleration that accomplishes the

continuous turning of the velocity vector in direction, without change of speed.

Newtons Principles

From the second principle we conclude that maF . For motion in a circle as discussed in

the previous section, the acceleration is given byr

v2. If the particle has mass m, it must be

acted upon by a force maF if it is to have this acceleration. This force is called thecentripetal force and its magnitude is

r

mvF

2

Since the centripetal acceleration is directed towards the centre of the circle, the centripetalforce is also directed towards the centre of the circle.

Principle of Universal Gravitation

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Every particle of matter in the universe attracts every other with a gravitational force. The

equation expressing this relation for a given pair of particles of masses m 1 and m2 is

221

r

mmGF where r is the distance between the two particles and G is a fixed

proportionality constant called the gravitation constant. The value of G is2211 Kg/m.N10670.6

Coulombs Principle

The electric force between two point charges is proportional to the magnitude of each of the

charges and inversely proportional to the square of the distance between the charges

02

21

4r

QQF where 0 is a dimensional constant known as the permittivity of free space,

2

2120

m.N

C1085.8 .

Electric Field

An electric field is said to exist at a point if a force of electrical origin is exerted on a charged

body placed at the point. The magnitude of the field at any point, represented by E, is

defined as the quotient obtained when the force F on a test charge placed at the point, is

divided by the quantity of charge Q on the test charge.

QFE or sometimes lower case

qF

In other words, the magnitude of an electric field is the force per unit charge.

Current

The rate at which charge is transported across a section of a wire, ordt

dq, is called the current

in the wire. Current is represented by the letter i (or I)

dt

dqi

nevAi where n is the number of free electrons per unit volume, e the electron charge, v theaverage velocity of the electrons and A the cross section of the wire. The current density in

the wire, represented by J, is defined as the ratio of the current to the cross-sectional area.

nevA

iJ

The direction of the current is in the opposite direction to the direction of motion of the

electrons.

Force on a Moving Charge

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A positive charge q, moving with velocity v perpendicular to the direction of a uniform

magnetic field, B, is found to experience a force F in a direction as given by the left-hand

rule. First finger points in the direction of the field, second finger in the direction of speed or

velocity. The thumb then points in the direction of the Thrust or force.

BqvF

Clearly, the force on electrons having negative charge is in the opposite direction to the force

on positive charges.

Electron Volt

The electron volt is a very small slang unit of energy and is equal to19

106.1 Joules. It is

the energy gained by an electron in being accelerated through 1 volt. Clearly, the gain in

energy in being accelerated through 100 volts is 100 electron volts1719

106.1106.1100 Joules, etc. This energy gain manifests itself as an increase in

kinetic energy, i.e. 2mv2

1eV where V is the accelerating potential.

Electromagnetic Radiation

The electromagnetic spectrum covers an extremely large frequency range. The energy of the

photons or quanta is given by hfE where h is Plancks constant equal to s.J1063.6 34

and F is the frequency. Photons or quanta always travel at the velocity of light, c, which in

free space or vacuum can be taken to be s/m103 8 . The relationship between c, f and the

wavelength, is fc . Note carefully,contrary to what is shown in programmes such as StarTrek, particles of matter cannot travel at the velocity of light. As very high velocities are

achieved, an increase in mass starts to take place. In nuclear reactions and particle

accelerators, velocities for entitites such as electrons and protons can approach to within a

few per cent of those for light, but never actually reach it.

Useful Data

1

A or Angstrom is nm1.0cm10m10 810

1 nanometre =

A10nm1metres10

9

1 micrometre = nmmmetres 1000110 6

Electron Charge = Coulombs10x6.1 19

Electron Mass = 9.1 x 10 kg31

Velocity of Light is 3 x 10 sec/8m

Mass of electron is 9.1 x 10 31kg

Plancks Constant is 6.63 x 10 34

J.s

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Wave Particle Duality

Photoelectric Effect

Pre

1900

Classical Theories

Light

This was thought of as purely a wave phenomenon and its properties could beexplained by Maxwell type of equations.

Electrons and NucleiDistinct particles since they possess charge and mass and properties could beexplained by Newtonian Mechanics.

Post

1900- Wave Mechanical, Quantum Mechanical Theories

Phenomena such as black body radiation and photoelectric effect could not beexplained satisfactorily by classical theory.

Waveparticle duality is fundamental to understanding modern physical electronics.

The Photoelectric Effect- First observed by Heinrich Hertz in 1887.

If light of sufficiently short wavelength impinges on the surface of certain solids,

(usually metals), then it is possible for electrons to be emitted from the solid. This iscalled the Photoelectric Effect. The effect may be demonstrated by using anapparatus of the type shown in the diagram.

Vg Va

photocathode

Incident light

(frequency f)

grid

electrons

collector

anode

vacuum envelope

photocurrent

microammeter

A photoelectric experiment.

Light of frequency f, illuminates a cold cathode situated inside a vacuum tube. Ifelectrons are emitted, then provided they have sufficient energy to overcome theretarding force field set up by voltage Vg between grid and cathode, they will beswept to the anode and a current registered on the microammeter in series with it.

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A diagram illustrating the emission of electrons from a metal plate, requiring energy gained

from an incoming photon to be more than the work function of the material.

Experimental Results

Two points to note.

Unless the frequency of the incident light is greater than some critical value f0, whichis dependant on the cathode material, no emission is observed, no matter howintense the light.

For constant light frequency and provided f is greater than f0, the photocurrent can

be measured as a function of grid voltage Vg and of light intensity keeping collectorvoltage, constant to give typical collector current data of the form shown.

collector

photocurrent

-V0 Grid voltage,Vg

high light intensity

low light intensity

retarding accelerating

0

Variation of photocurrent with grid voltage in the photoelectric experiment.

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No matter what the intensity of the light, there is a constant retarding voltage, in this

case, 0V (stopping potential) which entirely inhibits emission. This implies that the

maximum kinetic energy of emitted electrons is constant and independent of theintensity of the incident light. If we plot a graph of stopping potential against incident

light frequency, a straight line is produced with a slope ofe

h.

Stopping

Potential

Incident Light Frequency

f

Constant

Slope

(V0)

Classical Theory Explanation

According to the Classical Theory electrons can gain sufficient energy to be emittedif the light is bright enough, ie., if the light is of sufficient intensity.

Contradictions to Classical Theory

Electrons are emitted instantaneously, s10~ 14 , providing the frequency is highenough.

There is no explanation for the threshold frequency.

The maximum energy of emitted photoelectrons is not dependent on the intensity ofthe incoming radiation.

Quantum Explanation of Einstein 1905

Each photon has an energy equal to hf and this is the total energy used in theinteraction. Some of the energy is used to overcome the binding forces and theremainder is converted to kinetic energy of the emitted electron. is known as the

work function of the material.

K.E. of emitted electron = photon energywork function

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02 eVhfmv

2

1

The limiting case when the photon energy is equal to the work function and anelectron is just emitted with zero kinetic energy.

Then 0hf

hf0 , 0f is the critical frequency or threshold frequency.

The wave theory of light and the quantum theory of light complement each other.

Quantum Theory - Individual Events

Wave Theory- Statistical average of a large number of events.

1 electron volt (eV) = 1.6 X 10-19Joules and is the energy gained by an electron in

going through a potential difference of 1 volt.

1 Watt =1 Joule per sec

1 Amp =1 Coulomb per sec

1 = 10- m

known as an Angstrom Unit

The photoelectric yield is the number of electrons given off or emitted by a singlephoton or quantum.

Example 1.

When ultraviolet light of wavelength 300 nm falls on a zinc surface, a retardingpotential of 0.5 V must be applied to keep the most energetic electrons fromreaching the collector. Determine the work function, the wavelength of thephotoelectric threshold and the retarding potential required for light of 200 nmwavelength.

Solu t ion

Since 0.5 volts is required to stop the most energetic electrons, this is equal to theenergy required in accelerating an electron through a potential difference of 0.5 voltsi.e., 0.5 electron volts (eV). The frequency f can be obtained from

Hz10110300

103f;fc 15

9

8

Energy of a photon, E = hf = 6.63 x3410 1 x 1015

= 6.63 x 10-19Joules

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eV14.4106.1

1063.619

19

hfmv2

1 2

eV5.0volts5.0mv

2

1 2max

eV64.3eV5.0eV14.4mv2

1hf 2max

hfE

34

19

34

19

1063.6

10824.5f

1063.6

196.164.3

14

34

19

1078.81063.6

10824.5HZ

200 nm wavelength, fc ; Hzf 159

8

105.110200

103

Joules10945.9105.11063.6hfE 191534

eV22.6106.1

10945.919

19

eV58.264.322.6

Thus a retarding potential of 2.58 volts would be needed for the light of 200 nm

wavelength.

Example 2

The threshold wavelength to stop all emission from a photoelectric surface is600 nm. Light of wavelength 500 nm is incident on the surface. Determine:

(a) the work function of the material

(b) the maximum velocity of the emitted electrons

Solu t ion

At the threshold condition, fcandhf0

Hz10510600

103cf 14

9

8

1434 1051063.6

Joules10315.3 19

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voltselectroneV07.2106.1

10315.319

19

hmv2

1 2

Hz106f;nm500for 14

1914342 10315.31061063.6mv2

1

19202 10315.31078.39mv2

1

Joules10663.0mv2

1 192

192 10326.1mv

31

19

2101.9

10326.1v

112 10457.1v

s/m10817.3v 5