AP important questions and answers

 Unit-3

Q) Types of polarization 

A)Polarization takes place through four mechanisms. They are

1)Electric polarization 

2)Ionic polarization

3)Orientation polarization

4)Space charge Polarization

 

(1) Electronic polarization: This occurs throughout the dielectric material and is due to

the separation of effective centres of positive charges from the effective centres of negative

charges in atoms or molecules of dielectric material due to applied electric field. Hence

dipoles are induced within the material.

μe ∝ E

μe = αeE

Where αe = 4πε0R3

electronic polarizability. Therefore

μe = 4πε0R

3E

Electronic Polarization Pe is given by

Pe = Nμe = NαeE where N is the number of atoms per m3

(2) Ionic polarization: This occurs in ionic solids such as sodium chloride etc. Ionic solids

possess net dipole moment even in the absence of an external electric field. But when the ex-

ternal electric field is applied the separation between the ions further increases.

hence μi = αiE

where αi

is ionic polarisability

Ionic Polarization is given by ionic dipole moment per unit volume.Hence

Pi = Nμi

(3) Orientation Polarization: This occurs in a polar dielectric material, which possesses per-

manent electric dipoles. In polar dielectrics, the dipoles are randomly oriented due to thermal

agitation. Therefore net dipole moment of the material is zero. But when the external elec-

tric field is applied all dipoles tend to align in the field direction. Therefore dipole moment

develops across the material. This is referred to as orientation polarization (P0). Orientation

polarization depends on temperature. The higher the temperature more will be the more randomness

in dipole orientation thereby reducing the dipole moment.

The orientation polarizability is given by α0 =

μ

2

3kT, where ‘k’ is Boltzman constant,

T is the absolute temperature and μ is the permanent dipole moment.

(4) Space charge polarization: This occurs in materials in which only a few charge carriers

are capable of moving through small distances. When the external electric field is applied

these charge carriers move. During their motion, they get trapped or pile up against lattice

defects. These are called localized charges. These localized charges induce their image

charge on the surface of the dielectric material. This leads to the development of net dipole

moments across the material. Since this is very small it can be neglected. It is denoted by Ps.

Q)Ferroelectricity

A)The dielectric materials which are having spontaneous polarization in the absence of an electric

field are called ferroelectric materials. The phenomenon of possessing spontaneous

polarization in the absence of an electric field is called ferroelectricity.

Properties:

1. All ferroelectric materials possess spontaneous polarization below a certain temperature.

2. As temperature increases the spontaneous polarization decreases and at a particular temperature, the spontaneous

polarization vanishes. This temperature is known as Curie

temperature.

3. Curie temperature can also be defined as the temperature at which ferroelectric material

coverts into para electric material.

4. Below curie temperature the dielectric constant depends on field strength. i.e., it is no

longer constant.

5. Above curie temperature dielectric constant varies with temperature according to curie –

wises law,

i.e.,

ε௥ =

ܥ

ܶ − ܶ௖

௖ܶ < ܶ ݀݁݀��ݒ݋ݎܲሺ

ሻ

6. All ferroelectric materials exhibit the property of piezoelectricity and pyroelectricity.

7. The most important property of ferroelectrics is hysteresis under the action of an

alternating voltage.

Ex: - BaTio3, Lithium Niobate, Lithium Tantalate, etc.

Q)Piezoelectric materials

A)The piezoelectric effect is the ability of certain materials to generate an

electric field in response to applied mechanical stress. (ex: PZT (also known as

lead zirconate titanate), barium titanate, and lithium niobate)

Those materials include crystals, ceramics, polymers, wood (cellulose

fibres), and a host of other synthetic and composite materials. Initially

discovered in 1880 by the Curie brothers.

Direct Piezoelectric Effect

As stated, compressing a piezoelectric material produces electricity

(piezoelectricity). Figure 1 explains the concept.

Electronic Design

1. The piezoelectric effect occurs through compression of a piezoelectric

material.

As shown in Fig. 1, there’s a voltage potential across the material. The

two metal plates sandwich the piezo crystal. The metal plates collect the

charges, which creates/produces a voltage (lightning bolt symbol), i.e.,

piezoelectricity. In this way, the piezoelectric effect acts like a miniature

battery, because it produces electricity. This is the direct piezoelectric effect.

Inverse Piezoelectric Effect

The piezoelectric effect can be reversed, which is referred to as the

inverse piezoelectric effect. This is created by applying electrical voltage to

make a piezoelectric crystal shrink or expand (Fig. 2). The inverse piezoelectric

effect converts electrical energy to mechanical energy.

Using the inverse piezoelectric effect can help develop devices that

generate and produce acoustic sound waves. Examples of piezoelectric acoustic

devices are speakers (commonly found in handheld devices) or buzzers. The

advantage of having such speakers is that they are very thin, which makes

them useful in a range of phones. Even medical ultrasound and sonar

transducers use the reverse piezoelectric effect. Non-acoustic inverse piezoelectric

devices include motors and actuators.

Application of piezoelectric materials

 Crystal Oscillators

 Transducer

 Delay Lines

 Medical Ultrasound Applications

 Gas Igniters

 Displacement Transducers

 Accelerometers

 Piezoelectric Transformers

 Impact Printer Head.

UNIT-1

Q)Davisson and Germer’s experiment

A)The first practical evidence for the wave nature of matter waves was given by C.J.Davisson

and L.H. Germer in 1927. This was the first experimental support for Debroglie’s

hypothesis.

Principle: The e’s which are coming from the source are incident on the target and the e’s

get diffracted. These diffracted e’s produce a diffraction pattern. It shows(explains)the

wave nature of matter waves.

The experimental arrangement of the Davisson Germer experiment is discussed below:

• An electron gun comprising a tungsten filament F was coated with barium oxide and heated through a low voltage power supply.
• While applying suitable potential difference from a high voltage power supply, the electron gun emits electrons which were again accelerated to a particular velocity.
• In a cylinder perforated with fine holes along its axis, these emitted electrons were made to pass through it, thus producing a fine collimated beam.
• The beam produced from the cylinder is again made to fall on the surface of a nickel crystal. Due to this, the electrons scatter in various directions.
• The beam of electrons produced has a certain amount of intensity which is measured by the electron detector and after it is connected to a sensitive galvanometer (to record the current), it is then moved on a circular scale.
• By moving the detector on the circular scale at different positions that is changing the θ (angle between the incident and the scattered electron beams), the intensity of the scattered electron beam is measured for different values of angle of scattering.

Observations of Davisson Germer experiment:

From this experiment, we can derive the below observations:

• We obtained the variation of the intensity (I) of the scattered electrons by changing the angle of scattering, θ.
• By changing the accelerating potential difference, the accelerated voltage was varied from 44V to 68 V.
• With the intensity (I) of the scattered electron for an accelerating voltage of 54V at a scattering angle θ = 50º, we could see a strong peak in the intensity.
• This peak was the result of constructive interference of the electrons scattered from different layers of the regularly spaced atoms of the crystals.
• With the help of electron diffraction, the wavelength of matter waves was calculated to be 0.165 nm.

Q)Schrodinger Wave Equation

A)Schrodinger describes the wave nature of a particle in mathematical form and is known as

Schrodinger wave equation(SWE). There are two types of SWE

(i). Schrodinger Time independent wave equation(STIWE)

(ii). Schrodinger Time-dependent wave equation(STDWE)

(i) Schrodinger Time independent wave equation(STIWE):-

To derive an expression for “(STIWE)” let us consider an electron (particle)moving in a

positive direction along the axes. Let x, y, z be the coordinates of the particle & ′ψ′ is the

wave-displacement or wave function of the matter wave at any time ’t’. It is assumed that ′ψ′

is a finite, single-valued, continuous and periodic function.

We can express the classical differential wave equation of the material particle in three-

dimension axes are given as

∂

2ȥ

∂t2 = vଶ ቀ

∂

2ȥ

∂୶2 +

∂

2ȥ

∂୷2 +

∂

2ȥ

∂୸2

ቁ

In Three dimension we write ∂2ȥ

∂t2 = Vଶ∇

ଶȥ − − − ሺͳሻ

The solution of eq-(1) is given by

ȥ = ȥ଴ sin Ȧt − − − ሺʹሻ

ȥ = ȥ଴ sin ʹπυt − − − ሺ͵ሻ

Where ߱ = ʹπυ is the angular frequency of the particle

Differentiating eq-(3) w.r.t. ‘t’ twice we get

∂ȥ

∂t = ȥ଴ × cos ʹπυt × ʹπυ

߲

ଶ߰

߲tଶ = − ȥ଴ × sin ʹπυt × ʹπυ × ʹπυ

∂

2ȥ

∂t2 = −Ͷπ

ଶθ

ଶ

ȥ---(3)

θ =

c

λ

=

v

λ

∂

2ȥ

∂t2 = −

ସπ

2v

2ȥ

λ

2 ---(4)

Substituting eq-(4) in eq-(1), we get,

V

ଶ∇

ଶψ = −

Ͷπଶv

ଶψ

λ

ଶ

∇

ଶȥ + ସπ2

λ

2 ȥ = Ͳ − − − ሺͷሻ

According to de-broglie wave-length

λ = ୦

p

=

୦

୫v

---(6)

Sub. eq(6) in eq(5), we get

∇

ଶȥ + ସπ2௠2v

2

h

2 ȥ = Ͳ − − − ሺ͹ሻ

We have, the total energy (E) is given by

E = P.E. + K.E.

E = V + ଵ

ଶ

mvଶ

ଵ

ଶ

mvଶ = E − V

mvଶ = ʹሺE − Vሻ

mଶv

ଶ = ʹmሺE − Vሻ − − − ሺ ͅሻ

Sub. eq-(8) in eq-(7) we get,

∇

ଶȥ +

Ͷπଶ

h

ଶ

ʹmሺE − Vሻȥ = Ͳ

∇

ଶȥ +

 ͅπଶ݉ ሺE − Vሻȥ

h

ଶ

= Ͳ − − − ሺͻሻ

∇

ଶȥ + ଶ௠ሺE−Vሻȥ

ħ

2

= Ͳ − − − ሺͳͲሻ Where ħ = h

ଶπ

Eq-(9) & Eq-(10) is called as Schrodinger time independent wave equation in three

dimension

For a free particle, V= 0 ,

∇

ଶȥ +

ʹ݉Eȥ

ħ

ଶ

= Ͳ − − − ሺͳͳሻ

(ii)Schrödinger Time dependent wave equation:-

Ĥ ȥ = Êȥ where Ĥ = −

ħ

2

ଶ୫

∇

ଶ + V = Hamiltonian operator

Ê = iħ ∂

∂t = Energy operator

Physical significance of wave-function(ψሻሺEi܏ܖ܍ − ܖܝ܎��ܜ��ܖܗሻ: −

Wave-function(ψሻ or Eigen-function(ψሻ:-

It is a variable or complex quantity that is associated with a moving particle at any

position (x,y,z) and at any time ‘t’.

(i) ‘ȥ′

of a particle is represented by ȥ = ȥ଴ e

−୧Ȧt

(ii) ‘ȥ′

explains the motion of microscopic particles.

(iii) ‘ȥ′

is a complex quantity & it does not have any meaning.

(iv) |ȥ|

ଶ = ȥȥ∗

is real and positive, it has physical meaning.

(v) |ȥ|

ଶ

represents the probability of finding the particle per unit volume.

(vi) For a given volume dτ, the probability of finding the particle is given by

probability density(p) = ∫∫∫ |ψ|

ଶ

dτ where dτ = dxdydz

(vii) ‘ȥ′ gives the information about the particle behavior.

(viii) ‘p’ values are between 0 to 1.

(xi) wave-function ‘ȥ′

is a single valued, finite and periodic function.

(x) If p = ∫∫∫ |ψ|

ଶ

dτ = 1, then ‘ȥ′

is called normalized wave function.

Application of Schrödinger Time independent wave equation(STIWE):-

(1) Particle or electron in a one dimensional box or particle in an infinite square well

potential:-

Consider a particle or electron of mass ’m’ moving along x-axis enclosed in a one

dimensional potential box as shown in figure. Since the walls are of infinite potential the

particle does not penetrate out from the box. i.e. potential energy of the particle V=∞ at

the walls.

The particle is free to move between the walls A & B at x=0 and x=L.

The potential energy of the particle between the walls is constant because no force is

acting on the particle.

∴ The particle energy is taken as zero for simplicity

i. ݁. V= 0 between x=0 & x=L.

Boundary Conditions:-

(i)The potential energy for particle is given as

V(x) = 0, for 0൑ x ൑ ܮ

--------- (1)

V(x) =∞, when 0൒ x ൒ ܮ

The Schrödinger time independent wave equation for the

particle is given by,

d

ଶȥ

dxଶ +

 ͅπ

ଶm

h

ଶ

ሺE − Vሻȥ = Ͳ

But v=0, between walls,

d

2ȥ

d୶2 + ଼π

2୫

୦

2

ሺEሻȥ = Ͳ----( 2 )

Let ଼π

2୫

୦

2

ሺEሻ = kଶ

Then eq-(2), becomes

݀

ଶ߰

݀xଶ + kଶψ = Ͳ − − − ሺ͵ሻ

The general solution of eq-(3) is given by

߰ሺxሻ = Asinkx + Bcoskx------(4)

Where A, B are two constants, ‘k’ is the wave-vector

Applying the boundary conditions eq-(4), we get

(i) ߰ = Ͳ at x = Ͳ

0 = Asink(0) + Bcosk(0)

0 = 0 +B

B=0

Then eq-(4) is written as

߰ሺxሻ = Asinkx or ψ୬

ሺxሻ = Asinሺkxሻ----(6)

(ii) ߰ = Ͳ at x = ܮ

Eq-(6) can be written as

0 =ASin(kL) => A≠ Ͳ, and sin(kL) = 0

sin(kL) = sin(nπ)

kL = nπ => k = ୬π

L

-----(7)

Q)Explain the Kronig-Penny model

A)Kronig – Penny Model:

Kronig – Penny Model proposed a simpler potential in the form of an array of square

wells as shown in fig.

Schrodinger equation for one dimensional periodic potential field denoted by V(x) can be

written as

2

2 + $

%

( − #(&))ψ=0 −−−−−(1)

According to Bloch theorem the solutions of this equation have the form

ψ(x)= e

ikx

.Uk (&) -----------(2)

Where Uk (&) is periodic with the periodicity of the lattice. That is,

Uk (& + () = Uk (&)

As Vo increases the width of the barrier ω decreases so that the product Voω remains

constant. It turns out that solutions are possible only for energies given by the relation

cos -( = . /01∝3

∝3

+ cos ∝ ( -------------(3)

Where P = 4$

3

 Voω and ∝=

$

√28

P is called the scattering power of the barrier and Voω is called barrier strength.

The left-hand side of the equation (3) is plotted as a function of ‘∝a’ for the value of P

= 3 Π / 2 which is shown in Fig, the right-hand side takes values between -1 to +1 as

indicated by the horizontal lines in Fig. Therefore equation (3) is satisfied only for

those values of ‘ka’ for which left-hand side is between ± 1.

From Fig, the following conclusions are drawn.

1) The energy spectrum of the electron consists of a number of allowed and forbidden

energy bands.

2) As ‘∝a’ increases the width of the allowed energy band increases and the width of

the forbidden band decreases.

3) With increasing potential barrier P, the width of an allowed band decreases.

4) As P→∞, the allowed energy becomes infinitely narrow and the energy spectrum is a

line spectrum as shown in Fig.

5) When P→0 then all the electrons are completely free to move in the crystal without

any constraints. Hence, no energy level exists that is all the energies are allowed to the

electrons as shown in Fig. This case supports the classical free electrons theory.

UNIT-2

Q)Hall Effect

A)The Hall effect is the production of a voltage difference across an electrical conductor. This voltage difference is transverse to the electric current and perpendicular to the applied magnetic field.

The Hall effect was discovered by Edwin Hall in 1879. It has many applications, including: Determining if a material is a semiconductor or insulator, Measuring magnetic fields, Position sensing, and Integrated circuits. 

The Hall effect is used in the following applications:

• Magnetic field sensing equipment
• Direct current measurement
• Phase angle measurement
• Proximity detectors
• Hall effect sensors and probes
• Linear or angular displacement transducers
• Anti-lock braking systems

Q)SOLAR CELLS

A)Def: A special ݌ − ݊ junction diode which converts sun light into electrical energy is

known as solar cell or photo voltaic device. The symbol of solar cell is

Materials:

Main considerations while selecting a material for solar cell fabrication:

 Band gap ሺͳ ݋ݐ ʹ ݁��ሻ :

Semiconductors commonly used for making solar cells are

ܵ݅ሺͳ.ͳ ݁Vሻ, ܩܽ ݏܣ ሺͳ.Ͷ͵ ݁Vሻ,

ܥ݀ܶ݁ሺͳ.Ͷͷ ݁Vሻ, ݑܥ ሺܫ݊ ܩܽሻ ܵ݁ଶ

ሺͳ.Ͳͳ − ͳ.ͷ ݁Vሻ.

 High optical absorption.

 Electrical Conductivity.

Construction:

1. A simple solar cell consist of a ݌ − ݊

junction diode having large junction

surface to caught large radiation.

2. In this ݌ − ݊ junction diode ݊ −

ݎ݁݃݅݋݊ ሺͲ.͵ × ͳͲ−଺݉ሻ is very thin

and ݌ − ݎ݁݃݅݋݊ ሺͳͲͲ × ͳͲ−଺݉ሻ is

thick.

3. In the solar cell the thin region is

called the emitter and the other base,

light incident on the emitter.

4. N݅ plated contacts are connected through a load resistance.

Working:

Three steps are involved in working of a solar cell, when light falls on it.

1. Generation of charge carriers ሺࢉࢋ࢒ࢋ�t�࢔࢕ − ࢋ࢒࢕ࢎ ࢏ࢇ࢖��ሻ:

When light energy falls on a ݌ − ݊ junction diode, photon collide with valence

electrons and impart them sufficient energy enabling them to leave their parent atoms.

Thus, electron – hole pairs are generated in both p and n sides of the junction.

2. Separation of charge carriers:

The electron from ݌ − ݎ݁݃݅݋݊ diffuse through the junction to a ݊ − ݎ݁݃݅݋݊

and holes from ݊ − ݎ݁݃݅݋݊ diffuse through the junction to the ݌ − ݎ݁݃݅݋݊ due to

electric field of depletion layer. Thus, hole and electrons are separated out. The

accumulation of electron and holes on the two sides of the junction gives rise to open

circuit voltageሺVை஼ሻ.

For better hole, electron separation under the effect of junction field, it is

required that photo emission takes place in the junction area only.

3. Collection of charge carriers:

The flow of electrons and holes constitutes the minority current. The ࢊ. ࢉ is

collected

by the metal electrodes and flows through the external load ሺܴ௅

ሻ. The ࢊ. ࢉ is directly

proportional to the illumination and also depends on the surface are being exposed to

light.

Q)Avalanche Photo Diode

A)Avalanche photodiode is a photodetector in which more electron-hole

pairs are generated due to impact ionisation. It is like P-N photodiode or PIN

photodiode where electron-hole pairs are generated due to absorption of

photons but in addition to this avalanche photodiode uses the impact

ionisation principle for increasing magnitude of photocurrent.

Structure and working of Avalanche Photodiode

It has four regions N+ region, P region, an intrinsic layer and P+

region. The N+ and P+ region are heavily doped and the intrinsic layer is

lightly doped. Its construction can be understood more clearly with the help

of the below diagram.

In the case of avalanche diode, an additional factor is introduced to

impact ionization, which increases photocurrent several times. This

additional factor is called avalanche multiplication factor.

Impact ionisation is the process in which one energy carrier with

sufficient high kinetic energy strikes bounded energy carrier and imparts its

energy to it so that the bounded energy carrier can move freely. This leads to

higher concentration of energy carriers and thus higher magnitude of

current.

Advantages and Disadvantages of Avalanche Photodiode

 It can detect very weak signal due to high current-gain bandwidth

product.

 The construction is quite complicated i.e. care should be taken about

the junction. The junction

 Should be uniform and the guard ring is used to protect the diode

from edge breakdown.

 Applications of Avalanche photodiode

 Due to its ability to detect low-level signals, it is used in fibre optic

communication Systems. A

 properly designed silicon avalanche photodiode can provide a

response time of about 1ns.

Applications

 Typical applications for APDs are laser rangefinders

 Long-range fiber-optic telecommunication

 Quantum sensing for control algorithms

 Antenna Analyzer bridge

 LASER scanner, Barcode reader, Speed gun, Laser microscopy, PET

scanner.

Q)Zener Diode

A)A Zener diode is a heavily doped semiconductor device that is

designed to operate in the reverse direction.

A Zener Diode, also known as a breakdown diode. When the voltage

across the terminals of a Zener diode is reversed and the potential

reaches the Zener Voltage (knee voltage), the junction breaks down and

the current flows in the reverse direction. This effect is known as the

Zener Effect.

Circuit Symbol of Zener Diode

The Zener diode circuit symbol places two tags at the end of the bar

one in the upward direction and the other in the lower direction, as shown

in the figure. This helps in distinguishing Zener diodes from other forms of

diodes within the circuit.

Zener diode symbol and package outlines

Zener Breakdown in Zener Diode

When the applied reverse bias voltage reaches closer to the Zener

voltage, the electric field in the depletion region gets strong enough to pull

electrons from their valence band. The valence electrons that gain sufficient

energy from the strong electric field of the depletion region break free from

the parent atom. At the Zener breakdown region, a small increase in the

voltage results in the rapid increase of the electric current.

Avalanche Breakdown vs Zener Breakdown

The Zener effect is dominant in voltages up to 5.6 volts and the

avalanche effect takes over above that.

They are both similar effects, the difference being that the Zener effect

is a quantum phenomenon and the avalanche effect is the movement of

electrons in the valence band like in any electric current.

Avalanche effect also allows a larger current through the diode than

what a Zener breakdown would allow.

V-I Characteristics of Zener Diode

The diagram given below shows the V-I characteristics of the Zener diode.

When reverse-biased voltage is applied to a Zener diode, it allows only a small amount of leakage current until the voltage is less than Zener voltage.

The V-I characteristics of a Zener diode can be divided into two parts as follows:

Forward characteristics

Reverse Characteristics

Forward Characteristics of Zener Diode

The first quadrant in the graph represents the forward characteristics

of a Zener diode. From the graph, we understand that it is almost identical

to the forward characteristics of any other P-N junction diode.

Reverse Characteristics of Zener Diode

When a reverse voltage is applied to a Zener voltage, a small reverse

saturation current Io flows across the diode. This current is due to thermally

generated minority carriers. As the reverse voltage increases, at a certain

value of reverse voltage, the reverse current increases drastically and

sharply. This is an indication that the breakdown has occurred. We call this

voltage breakdown voltage or Zener voltage, and Vz denotes it.

Application of Zener Diode

 voltage regulation

 switching applications

 clipper circuits.

Bipolar Transistor