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DEPARTMENT OF PHYSICS

PH 6251 ENGINEERING PHYSICS II

IMPORTANT TWO MARK QUESTIONS AND ANSWER

1. Give Two postulates of free electron theory.

(i) The free electrons in the metal moves freely, similar to the gas molecules

moving in a vessel and it obeys the classical kinetic theory of gases.

(ii) When field is applied the free electron moves in the direction opposite to that of the field direction.

2. What are the failures of classical free electron theory?

(i) It is a macroscopic theory.

(ii) According to classical free electron theory, all the free electrons will absorb energy, but the

quantum free electron theory states that only few electrons will absorb energy.

(iii) This theory cannot explain the Compton effect, Photo-electric effect, paramagnetism and

ferromagnetism, etc.,

(iv) This theory cannot explain the electrical conductivity of semiconductors and insulators.

(v) Dual nature of light radiation cannot be explained.

(vi) The theoretical and experimental values of specific heat and electronic specific heat are not

matched.

3. Define mobility of electrons.

In addition to thermal motion, electrons drift due to the applied field. The magnitude

of the drift velocity per unit field is defined as the mobility of electrons.

4. Mention any two important features of Quantum free electron theory.

(i) It shows that energy levels of an electron are discrete

(ii) Maximum energy level up to which the electrons can be filled is denoted by Fermi energy level.

5. State Wiedmann Franz law.

The ratio between the thermal conductivity (K) and electrical conductivity (σ) of a metal is directly

proportional to the absolute temperature of the metal. k

LT

6. Define Fermi energy and give its importance.

It is the maximum energy of the quantum state corresponding to Fermi energy level at absolute zero.

7. Give any two importance of Fermi energy.

(i)Fermi energy determines the probability of an electron occupying a given energy level at a given

temperature.

(ii) It is the reference energy level which separates the filled energy level and vacant energy levels.

8. Define Fermi level.

The Fermi level is that state at which the probability of electron occupation is ½ at any temperature

above 0K and also it is the level of maximum energy of the filled states at 0K.

9. Define density of states. What is its use.

Density of states is defined as the number of energy states per unit volume in an energy interval. It is

used to calculate the number of charge carriers per unit volume of the solid.

10. Draw the Fermi distribution curve at O K and at any temperature T k.

Fermi distribution curve at T=0 K and at above 0 K.

11. Define drift velocity of electrons.

The average velocity acquired by an electron after steady state is reached in the presence of an

electric field is called drift velocity of electrons.

12. State the properties of a semiconductor.



(i) The resistivity of semiconductor lies between conducting and insulating materials (10-4 to 0.5 ohm-

metre).

(ii) At 0 K they behave insulators.

(iii) When temperature is raised or when impurities are added, their conductivity increases.

(iv) They have negative temperature coefficient of resistance.

13. State the Law of mass action in semiconductors.

In a semiconductor at thermal equilibrium condition, the law of mass action states that the product of

the electron concentration and the hole concentration is always equal to the square of the intrinsic

carrier concentration. i.e.: np = ni2

14. Differentiate between direct and indirect band gap semiconductors.

Direct band gap semi conductors are nothing but compound semi conductors in which electron and

hole recombine directly and emit a photon. These are used in LED’s and Laser diodes. eg. GaAs, Inp

whereas Indirect band gap semi conductor does not emit photon but release heat energy (eg). Si, Ge.

These are elemental or pure semi conductors.

15. Why semi conductors have negative temperature coefficient resistance?

In the case of semiconductors when the temperature is increased electron in the valence band gain

energy and jump into the conductor band. These electrons take part in electrical conduction. In other

words when the temperature is increased conductivity increases or resistivity decreases. Therefore

semiconductors have negative temperature coefficient of resistance.

16. What is Hall Effect? Give its importance.

If a specimen carrying current ‘I’ is placed in a transverse magnetic field ‘B’ a voltage is developed

in the direction perpendicular to both ‘I’ and ‘B’. This phenomenon is known as Hall effect and the

voltage thus developed is Hall voltage. This effect can be used to determine whether a semiconductor

is n-type (or) p-type and also to find the carrier concentration.

17. Define donors and acceptors and give its ionisation energy.

Donors are the pentavalent impurity atoms like, P, As, etc… which donates on electron to the pure

semiconductors like Ge (or) Si. These energy levels are called donor energy level.

The ionisation energy of donor state is ,C dE E E which is the energy required to transfer an

electron from donor energy level to conduction band.

Acceptors are the trivalent impurity atoms like Ga, In etc…. which can easily accept an electron from

the pure semi conductors like Ge (or) Si. These energy levels are called acceptor energy level.

The ionisation energy of acceptor is a vE E E which is the energy required for an electron to

move from valence band to acceptor energy level.

18. What are the applications of Hall Effect?

i) It is used to determine whether the material is p-type or n-type semi-conductor. i.e. if RH is

positive then the material is p-type.

If RH is negative then the material is n type.

ii. It is used to determine the sign of the current carrying charges.

19. How can you distinguish p-type and n-type semiconductors using Hall effect.

If the Hall coefficient is negative, then the semiconductor is n-type and if the Hall coefficient is

positive, then the semiconductor is p-type.

20. Distinguish between soft and hard magnetic materials.

Hard magnetic material Soft magnetic material

It has large area of hysteresis Loop. It has smaller area of hysteresis loop

It has high coercivity and high retentivity. It has less coercivity and lesser retentivity.

It has irreversible domain wall movement. It has reversible domain wall movement.

It has lesser permeability. It has large permeability.



It is used for making permanent magnets. It is used for making electromagnets.

19. What is Bohr magneton?

The orbital magnetic moment and spin magnetic moment of an electron in an atom can be expressed

in terms of atomic unit of magnetic moment called Bohr magneton.

20. What is Meissner effect?

Meissner effect refers to the complete exclusion of magnetic flux inside the superconductor when it is

placed in a uniform magnetic field. Thus it indicates that superconductors are perfect diamagnetic.

21. Difference between Elemental and Compound Semiconductors

S.No Elemental semiconductors Compound semiconductors

1. These are made from single element These are made from compound

(mixed) element

2. These are made from IV group and

VI elements

These are made from III and V [or]

II and VI elements

3.

These are called as indirect band gap

semiconductor (electron-hole

recombination takes place through

traps)

These are called as direct band gap

semiconductor (electron-hole

recombination takes place directly)

4. Heat is produced in the

recombination

Photons are emitted during

recombination

5. Life time of charge carriers is more

due to indirect recombination

Life time of charge carriers is less due

to direct recombination.

6. Current amplification is more Current amplification is less.

7. These are used for making diodes These are used for making LED,

transistor, etc. laser diodes, etc.

8. Example : Ge, Si Example : GaAs, GaP, CdS, MgO

22. Draw the graph for variation of Fermi level with temperature in p-type semiconductor.

23. Draw the graph for variation of Fermi level with temperature in n-type semiconductor.

Nd = 1024 atoms/m3

Nd = 1021 atoms/m3

Na Increasing

0 500k

Temperature (k)

E



24. How are magnetic materials classified?

If the atoms do not carry permanent magnetic dipoles, those materials are called Diamagnetic. If

the atoms of the material carry permanent magnetic dipoles, further classification is based on the

interaction between the individual dipoles. If the permanent dipoles do not interact the materials is

paramagnetic. If the interactions among the permanent dipoles are strong such that all the dipole

line up in parallel direction. The material is ferromagnetic. If the permanent dipoles line up in

antiparallel direction and are equal in the material is antiferromagnetic. If the magnitudes of

permanents dipoles aligned antiparallel are not equal then exhibit magnetization then material is

ferrimagnetic.

25. What is curie – Weiss Law?

Ferromagnetic material exhibit spontaneous magnetization below a characteristic temperature

called ferromagnetic Curie temperature. Above this temperature, the substance becomes

paramagnetic & obeys curie – Weiss law.

C

T

Here, C in Curie constant & in paramagnetic curie temperature.

26. Write two applications of ferrites.

1.They are used to produce ultrasonics by magnetostriction principle.

2. Ferrites are used in audio and video transformers.

3. They are used in radio receivers to increase the sensitivity.

27. Define cooper pair of electrons?

The pair of electrons formed due to electron-lattice-electron interaction (force of attraction) by

overcoming the electron-electron interaction (force of repulsion), with equal and opposite

momentum spins are called Cooper pairs.

28. What are high TC superconductors? Give an example.

Any superconductor with a transition temperature above 30K is in general called high TC

superconductors.

Examples: YBa2 Cu3 O7 TC = 92 k

La2 – x Srx CuO4 TC = 38 k

29. What are squids?

Squids (superconductivity quantum interference devices) is a double junction quantum

interferometer. Two Josephson junctions mounted on a super conducting ring forms this

interferometer. The SQUIDS are based on the flux quantization in a superconductivity ring. The

total magnetic flux passing through the ring in quantized. Very minute magnetic signal are

detected by there SQUIDS servitors.

30. Distinguish type I & type II superconductors.

Superconductors are classified based an their diamagnetic response. Superconductors which

exhibit a complete Meissner effect are called type I super conductors. Here diamagnetism abruptly

disappears at the critical magnetic field HC & the transition from superconducting to normal state

in sharp.



In type II superconductors, the diamagnetism starts disappearing gradually at a lower critical field

HC1 & only at a upper critical field Hc2 losses complete diamagnetism & becomes normal

conductor.

31. What are the types of dielectrics? Give some examples?

There are two types of dielectric materials

(i) Active dielectrics and

(ii) Passive dielectrics

i) Active dielectrics are the materials which can be adapted to generate, amplify, modulate and

convert electrical signals. They can store electrical energy.

ii) Passive dielectrics are those which obstruct the flow of electric current.

Some examples of active dielectrics are ferroelectrics, piezoelectrics and pyroelectrics. Electrical

insulating material is a passive dielectric.

32. List out the types of polarization mechanisms.

The types of polarization mechanisms are

i) Electronic polarization.

ii) Ionic polarization

iii) Oriental polarization.

iv) Space charge polarization.

33. Define dielectric loss and dielectric loss angle.

When a dielectric is subjected to the a.c. voltage, the electrical energy is absorbed by the material

and is dissipated in the form of heat. The dissipation of energy is called dielectric loss. The

complementary angle =900 is called as dielectric loss angle.

34. Define dielectric strength.

Dielectric strength is the minimum voltage required per unit thickness of the material to produce

dielectric breakdown on dielectric breakdown or dielectric failure its unit is V/m

35. Define dielectric breakdown.

The phenomenon in which a dielectric material loses its resistivity and permits very large current

to flow through it is called dielectric breakdown.

36. What is Discharge breakdown?

Some dielectric materials may have occluded gas bubbles. If these dielectric materials are

subjected to high voltages, the gaseous substance is easily ionized and hence they produce a large

ionization current. Thus large ionization current may produce electric break down. This type

break down is known as discharge break down.

Characteristics: This type of break down can occur at low voltage where there is large number of

occluded gas bubbles.

37. What are ferro-electric materials? Give examples.

Materials which exhibit electronic polarisation even in the absence of the applied electric field are

known as ferro-electric materials.

Barium Titanate (BaTiO3)

Potassium Dihydrogen Phosphate (KH2PO4)

38. What are the remedies for dielectric materials?

1. The insulating materials should have high resistivity to reduce leakage current.

2. It should have high dielectric strength to withstand high voltage

3. It should have small dielectric loss.

4. It should have sufficient mechanical strength.

39. What are metallic glasses?

Metallic glasses are the newly developed engineering materials which shares the properties of both

metals and glasses.



40. What are the types of metallic glasses?

There are two types of metallic glasses

(1) Metal-Metalloid glasses

(2) Metal –Metal glasses

Metal-Metalloid glasses

(Fe,Co, Ni) Metal –(B, Si, c,P) Metalloid

Metal –Metal glasses

Nickel-Niobium (Ni-Nb)

41. What are the applications of metallic glasses?

(1) Metallic glasses possess high tensile strength, they are superior than common steel. This

makes them useful as reinforcing elements in concrete, plastic (or) rubber.

(2) Due to their high strength, high ductility rollability and good corrosion resistance they are used

to make razor blades.

(3) Due to their high corrosion resistance, metallic glasses are ideal materials for making surgical

instruments.

42. What is meant by shape memory alloys?

Shape memory alloys are the alloys which change its shape from its original shape to new shape

and while heating/cooling it will return to its original shape.

43. Define Pseudo-elasticity.

Pseudo-elasticity occurs in some types of shape memory alloys in which the change in its shape

will occur even without change in its temperature.

44. What are the applications of shape memory alloys?

1. SMA can act as actuators and sensors.

2. It is used as Micro – Surgical instruments.

3. They are used to correct the irregularities in teeth.

4. They are used in orthopedic devices for pulling, fractures tighter, artificial heart.

5. Fibre composite shape memory alloys are used to produce twist on the helicopter blades.

6. used to make glass frames

45. Write a note on Bio-materials.

The materials which are used for structural applications in the field of medicine are known as

biomaterials. They are used to make device to replace damaged or diseased body parts in human

and animal bodies.

46. Write few applications of nanophase materials.

1. Nanophase materials are used in nanoelectronic devices such as nanatransistors, ceramic

capacitors for energy storage, noise filters and stabilizers.

2. Quantum dots, quantum wires are mainly produced from semiconductor nanomaterials. Hence

they are used in computer storage devices.

47. What is induced birefringence?

The appearance of double refraction under the influence of an external agent is known as artificial

double refraction or induced birefringence.

48. What is Kerr effect?

Anisotropy induced in an isotropic medium under the influence of an electric filed is known as

Kerr effect.

Δμ = KλE2



1. Starting with the classical free electron theory of metals obtain an expression

for electrical and thermal conductivities and hence prove Wiedemann – Franz

law.

CLASSICAL FREE ELECTRON THEORY

1. A Solid metal has nucleus with revolving electrons. The electrons move freely like molecules

in a gas.

2. The free electrons move in a uniform potential field due to the ions fixed in the lattice.

3. In the absence of electric field (E=0), the free electrons move in random directions and collide

with each other. During this collision no loss of energy is observes since the collisions are

elastic as shown in figure.

4. When the presence of electric field (E ≠0) in the direction opposite to the direction of applied

electric field, as shown in figure.

5. Since the electrons are assumed to be perfect gas, they obey the laws of classical theory of

gases.

6. Classical free electrons in the metal obey Maxwell-Boltzmann statistics.

EXPRESSION FOR ELECTRICAL CONDUCTIVITY ( σ)

Definition

The electrical conductivity is defined as the quantity of electricity flowing

per unit area per unit time at a constant potential gradient.



When an electric field (E) is applied to a conductor the free electrons are accelerated and

give rise to current (I) which flows in the direction of electric filed flows of charges is given in

terms of current density.

Let ‘n’ be the number of electrons per unit volume and ‘e’ be the charge of the electrons.

The current flowing through a conductor per unit area in unit time (current density) is given by

J= nVd (-e)

J = – nVd (e) ... (1)

The negative sign indicates that the direction of current is in opposite direction

to the movement of electron.

Due to the applied electric field, the electrons acquire an acceleration ‘a’ can be given

by

When an electric field of strength (E) is applied to the conductor, the force experienced by

the free electrons in given by

From Newton’s second Law of motion, the force acquired by the electrons can be written as

F = ma …….(4)

Comparing equation (3) & (4) –eE = ma



Now, substituting the value of ‘a’ from the equation (2), we get

Substitute equation (6) in (1)

THERMAL CONDUCTIVITY (K)

Definition

Expression for thermal conductivity (K) of an electron Consider a metal bar with two planes A and B separated by a distance ‘λ’ from

C. Here T1 is hot end and T2 is cold end. ie., T1> T2

The thermal conductivity is defined as the amount of heat flowing through an unit area per unit temperature gradient.



Let ‘n’ be the number of conduction electrons and ‘v’ be the velocity of the electrons. KB is

the Boltzmann constant. From kinetic theory of gases

The

kinetic energy of an electron at

Let as assume that there is equal probability for the electrons to move in all the six

directions. Each electrons travels with thermal velocity ‘V’ and ‘n’ is the free electron density

then on average of 1/6 nv electron will travel in any one direction.



No. of electrons crossing per unit area in unit time at C

We know that the thermal conductivity,

The heat energy transferred per unit sec per unit area

Comparing equations (5) and (6),



WIEDEMANN-FRANZ LAW

Statement

Where L is called Lorentz number, the value of L is 2.44 × 10–8 WΩK–2

(as per Quantum Mechanical value).

Derivation

By Classical theory, we can drive Widemann-Franz law using the expressions

for electrical and thermal conductivity of metals.

The expression for thermal conductivity

The expression for electrical conductivity

We know that kinetic energy of an electron

The ratio between the thermal conductivity (K) and electrical conductivity (σ) of a metal is directly proportional to the absolute temperature of the metal.



Thus, it is proved that the ratio of thermal conductivity and electrical conductivity of a

metal is directly proportional to the absolute temperature of the metal.

It is found that the classical value of Lorentz number is only one half of the experimental

value (2.44 × 10–8 WΩK–2). The discrepancy of L value is the failure of the classical theory

(Experimental and Theoretical). This can be rectified by quantum theory.

By Quantum theory By Quantum theory the mass ‘m’ is replaced by effective mass m*

According to Quantum theory, the expression for thermal conductivity is modified by

considering the electron specific heat as



This is gives the correct value of Lorentz number and it in good agreement with

the experiment value.

2. What is density of states? Derive an expression for density of states and

carrier concentration in metals. Hence obtain an expression for Fermi energy of

a metal at 0K.

DENSITY OF STATES

Density of states is defined the as the number of energy states per unit volume in an energy interval of a metal. It is use to calculate the number of charge carriers per unit volume of any solid.



Let us constant a sphere of radius “n” in space with quantum numbers nx , ny

and nz

The sphere is further divided into many shells represents a particular combination of

quantum numbers and represents particular energy value.

Therefore, the number of energy states within a sphere of radius

Let us consider two energy values E and E + dE can be found by finding the number of

energy states between the shells of radius n and n+ dn from the origin. Since the quantum

numbers are positive integers, n values can be defined only in the positive octant of the n –

space. The number of available energy states within the sphere of radius “n” due to one octant.

Similarly the number of available energy states within the sphere of radius n+dn corresponding

energy.

The number of available energy states between the shells of radius n and n + dn

(or) between the energy levels E and E + dE



The number of available energy states between the energy interval dE

Since the higher powers of dn is very small, dn2 and dn3 terms can be neglected.

We know that the allowed energy values is

Differentiating equation (4) with respect to ‘n’

On substituting equation (6) and (5) in equation (3) we get,



If volume of the metal, V = L3

For unit volume of a metal,

Each electron energy level can accommodate two electrons as per Pauli’s exclusion

principle. (Spin up and Spin down = 2 (e) × density of states).

Carrier concentration in metals



Let N(E) dE represents the number of filled energy states between the interval of

energy dE, normally all the energy states will not be filled

The actual number of electrons in dE, F(E) = 1

Normally all the states are not filled states, filling of electrons is a given energystate is

given by Fermi-function F(E). Let dn represents the number of filled energy states.

In this case of material of absolute zero the upper occupied level is EF and for all the levels

below EF, F(E)=1 (at T = 0 K the maximum energy level that can be occupied by the electron is

called Fermi energy level EF T = 0 K F(E) = 1).

Integrating equation (8) within the limits 0 to EF0us can get the number of energy states

of electron (N)

Hence the Fermi energy of a metal depends only on the density of electrons of that metal.



Average energy of an electron at 0 K

Average energy of electron

Substitute equation (12) and (9) in equation (11)



3. a) Obtain and expression for intrinsic carrier concentration in an intrinsic

semiconductor

b) How will you determine the energy gap of an intrinsic semiconductor.

CARRIER CONCENTRATION IN INTRINSIC SEMICONDUCTORS

In a semiconductor both electrons and holes are charge carriers (know as carrier

concentration). A semiconductor in which holes and electrons are created by thermal

excitation across the energy gap is called an intrinsic semiconductor.

In an intrinsic semiconductor the number of holes is equal to the number of free

electrons.

At T = 0K, valence band is completely filled and conduction band is completely

empty. Thus the intrinsic semiconductor behaves as a perfect insulator.

At T > 0K, the electron from the valence band shifted to conduction band

across the band gap.

Density of electrons in conduction band

Let dN be the number of electrons in the energy interval E and E + dE in the conduction

band.

dN = N(E) dE F(E) ... (1)

Where N (E) dE is the density of states in the energy interval E and E + dE and

F (E) is the probability that a state of energy E is occupied.

The number of electrons in conduction band can be calculated by integrating the

equation(1) from energy Ec (ie., energy from the bottom of the conduction Ec to the



top of conduction band ∞ )

We know that,

Since, the semiconductor is a crystal, the electron motion is considered in the periodic

potential. So, the mass ‘m’ is replaced as effective mass me* and the kinetic

energy of the electron, E = E – Ec

In the above expression E >> EF , So we can neglect one (1) in the denominator.

Substituting equation (3) & (4) in equation (2)



Density of electrons in conduction band

Density of Holes in Valence band

Let dP be the number of holes in the energy interval E and E + dE in the valence

band.

dP= N (E) dE [1 – F(E)] ... (7)

(1– F (E) is the remaining probability after finding the density of electrons)

The total number of holes within limits ∞ to Ev is

We know that,



Since, the semiconductor is a crystal, the electron motion is considered in the

h* and the kinetic

energy of the electron, E = Ev – E.

In the above expression E << EF (in valence band),

Substituting eqn (9) & (10) in eqn (8)

To solve this Integral

Differentiating above equation, we get

The limits are ∞ to 0

Density of holes in valence band



Density of holes in valence band

Intrinsic Carrier Concentration

In intrinsic semiconductorsNe =Nh =ni is called intrinsic carrier concentration.



The equation (12) is called as intrinsic carrier concentration.

DETERMINATION OF BAND GAP ENERGY OF A SEMICONDUCTOR

We know that the electrical conductivity,

We know resistivity is resistance per unit area per unit length



The above equation gives us a method of determining the energy gap of an intrinsic

material. If we find the resistance of the intrinsic semiconductor using post office box or carry

Foster’s bridge at various temperatures, we can plot a graph between 1/T and logRi

Therefore by finding the slope of line we can calculate the energy band gap

with the following expression.

4. Derive the relation for carrier concentration of N-type semiconductor. Also

sketch the variation of Fermi level with temperature in the case of ‘N’ type

semiconductor.

Let us consider Nd donor levels per m3 of energy Ed lies below the conduction band. At

low temperatures small fraction of donors will be ionized and practically all donor levels are

filled with electrons.

Let, Ec – Ef > 4KT, then

Density of electrons in the conduction band will be given by

3/ 2

*

2

22 exp 1

f ceE Em KT

nh KT

If we assume that Ef lies more than a few KT above the donor level then, density of empty

donors is given by

1 expd f

d d d

E EN P E N

KT



Conduction band

Ec = Bottom energy level in conduction band

Ef = Fermi energy level

Ed = donor energy level

Ev = Top energy level valence band

Fig. N – type semiconductor

At very low temperatures, practically no electrons get insufficient energy for excitation from

valence band into conduction band. Therefore, the density of empty donors should be same as

the density of electrons in the conduction band. Here, the electrons in the conduction band are

denoted electrons from the donor level.

3/ 2*

2

3/ 2*

d 2

3/ 2*

2

f

22 exp exp

logarithm & rearranging

2log N log 2

.log2 2 2

2

T = OK,

E

f c d fed

f c d f e

d cf

e

d

E E E Em KTN

h KT KT

Taking

E E E E m KT

KT KT h

E E KT NdE

m KT

h

At

E E

2

c

Ec

Ef

Ed

Valence band Ev



It shows that Fermi level lies exactly halfway between donor level of bottom of conduction band.

As T increases Fermi level drops. As the temperature is gradually increased, the

contribution of electron to the conduction band from the valence band increases and at very high

temperature it far exceeds the donor concentration. The intrinsic behaviour predominates at

higher temperatures, because all donor / acceptor donor state might be ionized.

In the figure shown below, Ei is the centre of forbidden energy gap (or) fermi level

position in intrinsic semiconductor. As the temperature increases, the Fermi level shifts towards

the intrinsic fermi level. But by increasing the donor concentration, the extrinsic behaviour may

be maintained even at high temperatures.

Fig. Variation of Fermi level with temperature and for various concentrations in ‘n’ type

semiconductor.

ff

3/ 2*

2

1/ 2

1/ 23/ 2

*

2

E the value of E into exp

1exp exp log

2 2 22

exp exp .2

22

c

f c d c d

e

f c d c d

e

EPutting

KT

E E E E N

KT KT m KT

h

E E E E N

KT KTm KT

h

Substituting this in equation [1]

3/ 2* 1/ 2

1/ 23/ 2

*

2

22 .exp

22

2

e d d c

e

e

m KT N E En

h KTm KT

h

3/ 4

*1/ 2

2

22 exp

2

e d cd

m KT E En N

h KT

Conduction band

Ec

Ef

Ed

Ei

Ev

OK

OK

f Nd = 1024 atoms/m3

Nd = 1021 atoms/m3



So, the density of electrons in the conduction band is proportional to the square root of the

donor concentration. This equation is valid only at low temperatures. But at high temperature we

must take the intrinsic carrier concentration along with this equation.

5. Derive the relation for carrier concentration of P – type semiconductor.

Explain the effect of temperature and impurity concentration on Fermi energy

level. In the case of P – type semiconductor acceptor energy level (Ea) is just above the top of

valence band. Fermi level lies in th middle of Ea and Ev as shown in the figure.

Let NA be the number of acceptor atoms per m3 in the energy level Ea. At very low

temperature all the acceptor levels are empty. When the temperature is increased slowly. The

electrons more from valence band and occupy the vacant sites in the acceptor energy level first

and then they move to the conduction band. At very high temperature electrons can directly jump

from valence band to the conduction band.

o o o o

Ec = Bottom most energy level in conduction band

Ev = Top most energy level in valence band

Ef = Fermi energy level

Ex = Acceptor energy level

Eg = Forbidden energy gap

The density of holes in the valence band is given by

3/ 2*

/

2

22 . 1v fE E KTh Bm K T

P eh

If we assume that Ef lies more than few KBT, below the acceptor level then the density of

ionized acceptors is given by,

Conduction band

o o

Conduction band

o

Ec

EA

Ev

Ef

Eg



/

1 2f aE E KT

a a a aN N F E N e

At low temperature, the density of holes in the valence band is equal to the density of

ionized acceptor in the energy level ‘Ea’

3/ 2

*/ /

2

1 & 2

22 . v f f aE E KT E E KTh

a

equating

m KTe N e

h

Taking log on both sides and rearranging.

*

ha 2

3/ 2*

2

f 3/ 2*

2

f

2 mlog N log 2

2log

22

E .log 32 2 2

2

, T = 0K, E2

v f f a

v f a a

h

v a a

h

v a

E E E E KT

KT KT h

E E E N

KT m KT

h

E E NKT

m KT

h

E EAt

ie, Fermi level is exactly in the middle of Ea and Ev.

f the value of E from equation 1

expv f

Substituting in

E E

KT

3/ 2*

2

1exp exp log

2 2 22

v f v a a

h

E E E E N

KT KT m KT

h

1/ 2

1/ 23/ 2

*

2

=exp log 42

22

v a a

h

E E N

KTm KT

h



substituting equation (4) in (1)

3/ 2* 1/ 2

1/ 22 3/ 2*

2

3/ 4*

1/ 2

2

22 . .exp

22

2

22 . .exp 5

2

h a v a

h

v aha

m KT N E EP

h KTm KT

h

E Em KTP N

h KT

This equation represents carrier concentration in p-type semiconductor. It is found from this

equation that density of holes in the valence band at moderately low temperature is directly

proportional to the square root of acceptor concentration.

Variation of Fermi level with temperature and impurity concentration

At higher temperature intrinsic behaviour predominates the extrinsic behaviour. ie. As the

temperature is increased slowly first acceptor level is filled with electrons and then it jumps to

conduction band. At very high temperature electrons starts jumping from valence band to the

conduction band. It means intrinsic behaviour predominates. Hence, Fermi energy level is shifted

towards the centre of forbidden energy gap as shown below.

When the acceptor concentration is increased the shifting of Fermi energy level (Ef)

towards intrinsic fermi energy level (Efi) takes place only at high temperature.

Fig : Effect of temperature and acceptor concentration on Fermi level.

Ec

Efi

Ea

Ef

Ev

Na Increasing

0 500k

Temperature (k)

E



6. Give the theory of Hall Effect in the case of a semiconductor. Describe the

experiment to find the concentration of charge carriers in n-type semiconductor

using Hall effect.

Hall effect:

When a magnetic field is applied perpendicular to a current carrying conductor (or)

semiconductor, a voltage is developed across the specimen in a direction perpendicular to both

the current and the magnetic field. This phenomenon is called the hall effect and the voltage so

developed is called the hall voltage.

Theory of Hall effect:

Consider a slab of a specimen subjected to an external electric field Ex along x –axis and

a magnetic field by along z axis.

As a result of electric field Ex, a current density Jx will flow in the direction of that

electric field. If we assume that the current is carried only by electron of charge –e, then their

velocity Vx will be opposite to Jx. So, the magnetic induction ‘B’z applied perpendicular to

current will exert a transverse magnetic deflecting force (Lorentz force) on the electron which

causes the electrons to drift downward to the edge of the specimen.

Fig: Hall effect

Consequently lower surface of the slab becomes negative and its upper surface becomes

positive as shown in the diagram.

The excess of negative charge on the lower surface and positive charge at the upper

surface create a transverse electric field Ey known as Hall field which opposes the transverse

drifting of electrons.

Ultimately, an equilibrium is reached at which the electrical opposing force (eEy) force

due to accumulation of electron becomes equal to the magnetic deflecting force (-e Vx Bz) and so

the drifting of electrons stops.



Thus, the net force on the electrons becomes zero.

y

y

x

x

x

y

. . F 0

( ) E

drift speed V electrons is given by

J

n = concentration of electrons

V

E

y x z

x z

x

H x z

H x z

i e eE eV B

or V B

The of

nev

Where

JxR J B

ne

or R J B

Where the factor 1

HRne

is called the Hall coefficient for the specimen. RH is negative for free

electron and positive for holes.

Results:

11. HR

n e

for metal where only the electrons at Fermi surface have substantially the same

velocity.

2. In an intrinsic semiconductor the Hall coefficient is given by

2

H 2

e

h

nb -p-AR = =

e nb+p

Where

n=concentration of electrons

p=Concentration of holes

μ mobilities of electronsb = =

μ mobilities of holes



For a metal (or) degenerate semiconductor A = 1 for a non-degenerate semiconductor with

thermal scattering A = 3

8

, but for ionized impurity scattering A = 1.93 (i.e) for p type and n

type semiconductors.

3. Monovalent metals have –ve (RH) Hall coefficient and divalent alkaline earth metals like zinc

and cadium RH is +ve.

4. In n type semiconductor RH is –ve and so the electrons are the majority charge carriers. In P

type semiconductor RH is +ve and so the holes are the majority charge carriers.

Applications of Hall effect:

1. The sign of charge carrier is determined.

2. Carrier concentration can be determined

3. Mobility of charge carriers is measured directly.

4. Electrical conductivity of the material can be determined.

5. It can be used to determine whether the given material is metal, insulator (or)

semiconductor, based on the sign of RH.

Experimental Set up

Description

A thin specimen having a few mm wide and several cm long is placed in x- direction as

shown in the diagram. A magnetic field Bz is applied in z direction. A suitable current is placed

through the specimen in x direction.

Two potential leads are placed at A and B of the specimen which are connected to a high

sensitive digital micro voltmeter to measure the Hall voltage VH.

Magnetic field along z axis

Fig:Experimental arrangement to study the Hall effect



Procedure:

By measuring the Hall voltage, Hall coefficient can be calculated. Since, the Hall voltage

is about few microvolt, the measurement of Hall voltage is very difficult due to the development

of thermo electric effects. This can be eliminated by changing the direction of current and once

again measuring the Hall voltage.

Similarly, the error due to an improper alignment of electrodes can be eliminated by

reversing the direction of magnetic field. Thus, the measured Hall voltage is the average of four

readings (ie.. two readings when Bz is applied along +ve z axis and another two readings when

Bz is applied along –ve z axis)

Calculation:

y

y

H x

, E

d = Thickness of the specimen,

V .

1sin R and J

b = breadth of the specimen

y

y H x z

x

VSince

d

where

E d R J B d

Ice

ne bd

where

y

x z

1.

v b

I B

x z

y

I BV

ne b

en

knowing the values of Vy, b, Ix and By, the value of the concentration of charge carries can be

determines.

The mobility of the charge carrier is given by

1.

..

yx

x z x

y y

z x x z

EV

E B E

V V ll

db V V B d

where l = length of the specimen.

By measuring the applied potential difference Vx across x direction and Hall voltage Vy and

knowing the values of Bz, l and d, one can determine the mobility of the charge carrier.



Further,

= Electrical conductivity of the specimen.x

J

E

Since,

Ey = RH.Jx.Bz and

H

.

. = R . .

| |

H x z x

H

z x x

H

R J B JR

B E E

n eR

So, by determining n and the electrical conductivity of the specimen can be evaluated.

7. Describe the ferro magnetic domain theory in detail and how will you account

hysteresis of ferromagnetic material based on domain theory ?

Principle :

The group of atomic dipoles organized in tiny bounded regions in the ferro magnetic

materials are called ferromagnetic domain.

Explanation

The domain in a region of the ferromagnetic material in which all the magnetic moments

are aligned to produce a net magnetic moment in one direction only.

In demagnetized ferromagnetic materials, the domains are randomly oriented. The

boundaries separating domains are known as domain walls. When the magnetic field is applied

to the Ferromagnetic material, the magnetization is produced by two ways.

1. By the motion of domain walls.

2. By the rotation of domains.

Process of Domain magnetization

There are two ways to align a random domain structure by applying an external magnetic field.

1. By the motion of Domain walls

When a small amount of magnetic field is applied, the domains having dipoles parallel to

the applied magnetic field increases in area by the motion of domain walls.



2. By the rotation of Domains

If the applied magnetic field is further increased, the domains are rotated parallel to the

field direction by the rotation of domains.

Energies involved in the domain growth (or) Origin of Domain theory of Ferromagnetism

The total internal energy of the domain structure in a ferromagnetic material is

made up from the following contributions.

1. Exchange energy (or) Magnetic field energy.

2. Crystalline energy (or) Anisotropy energy.

3. Domain wall energy (or) Bloch wall energy.

4. Magnetostriction energy

1. Exchange energy (or) Magnetic Field energy

“The interaction energy which makes the adjacent dipoles align themselves” is the called

exchange energy (or) magnetic field energy. The interaction energy makes the adjacent dipoles

align themselves. It arises from interaction of electron spins. It depends upon the inter atomic

distance.



2. Anisotropy energy

The excess energy required to magnetize a specimen in particular direction over

that required to magnetize it along the easy direction is called the crystalline anisotropy

energy.

In ferromagnetic materials there are two types of directions of magnetization

namely,

a) Easy direction and

b) hard directions.

In easy direction of magnetization, weak field can be applied and in hard direction

of magnetization, strong field should be applied.

3. Domain wall energy or Bloch wall energy

A thin boundary or region that separates adjacent domains magnetized in different

directions is called domain wall or Bloch wall



a) Thick wall: When the spins at the boundary are misaligned and if the direction

of the spin changes gradually as shown figure, it leads to a thick Blochwall. Here the

misalignments of spins are associated with exchange energy.

b) Thin wall: When the spins at the boundaries changes abruptly, then the anisotropic

energy becomes very less. Since the anisotropic energy is directly proportional to the thickness

of the wall, this leads to a thin Bloch wall.

4. Magnetostriction energy

When a material is magnetized, it is found that it suffers a change in dimensions.This

phenomenon is known as Magnetostriction. This deformation is different along different crystal

directions.



Explanation of hysteresis on the basis of Domains

1. When a field is applied, for small H, the domain walls are displaced and gives rise to small

value of magnetization. [OA in the graph]. Now, the field is removed, the domains return to its

original state known as reversible domains.

When the field is increases, a large number of domains contribute to the magnetization and I

increases rapidly with H.

Now, when the field is removed the domain boundaries do not come back to the original

position due to the domain wall movement to a very large distance (AB in the graph). These

domains are called irreversible domains.

4. Now if the field is further increased, domains start rotating along the field direction and

anisotropic energy is stored and it is represented as BC in the graph.

Thus the specimen is said to attain maximum magnetization at this position even after the

removal of the field. The material is having magnetism called Retentivity. This Retentivity can

be destroyed by applying a high reverse magnetic field called coercivity.

6. Thus the reversible and irreversible domain wall movements give rise to hysteresis in the

Ferromagnetic materials.



8.Explain dia,para and ferro magnetic materials on the basis of spin.

S.No Properties Dia Para Ferro

1

Definition It is a material in

which there is no

permanent magnetic

moment.

It has permanent

magnetic

moment.

It has enormous

(more) permanent

magnetic moment.

2

Spin or magnetic

moment or dipole

alignment.

No spin alignment. Random

alignment

Parallel and orderly

alignment

3

Behavior Repulsion of

magnetic lines of

force from the centre

of the material.

Attraction of

magnetic lines

towards the

centre.

Heavy attraction of

lines of force towards

the centre.

4

Magnetized direction Magnetized

direction Opposite to

the External

magnetic field.

Same direction

as the External

magnetic field.

Same direction as the

External magnetic

field.

5 Permeability Permeability It is

very less

It is very high It is very high

6 Relativity

permeability

μr < 1 μr > 1 μr >> 1

7 Susceptibility Negative Low positive High positive

8

Magnetic phase

transition

Magnetic phase

transition At 0 K

diamagnetic material

is Superconductor.

When we increase

its temperature it

becomes a normal

conductor.

When

temperature is

less than the

curie temp it is

converted in to

Diamagnetic.

. When temperature

of the material is

greater than it Curie

temperature it is

converted into

Paramagnet.



9. Describe the structure , properties and applications of ferrites in detail.

FERRITES

Definition

Ferrites or Ferrimagnetic materials are the modified structure of iron without carbon. In

Ferities the spins of adjacent ion is the presence of a magnetic field are in opposite directions

with different magnitudes.

Properties 1. These are made from ceramic ferromagnetic compounds.

2. It has low tensile strength and it is brittle and soft.

3. In these materials all valence electrons are tied up by ionic bonding.

4. Ferrites have low eddy current loss and low hysteresis loss.

Structures of Ferrites Ferrites are the magnetic compounds consisting to two or more different kinds

of atoms. Generally ferrites are expressed as X²+ (Fe2)3+ O4

where X²+ stands for suitable divalent metals ions such etc Mg 2+ , Zn2+ etc.

Normally, there are two types of structures present in the ferrites

1. Regular spinel 2. Inverse spinel

In the regular spinal type, each metal atom (divalent) is surrounded by fourions in a tetragonal

fashion. For example in Mg 2+, Fe2 3+ ,O4 2+, the structure of Mg 2+ is given in the Fig. and it is

called “A’ site. Totally in a unit cell, there will be 8 tetrahedral (8A) sites. Thus in a regular

spinal, each divalent metal ion (mg 2+) exists in a tetrahedral form (A site) and each trivalent

metal ion (Fe 2+) exists in an octahedral form (B site). Hence, the sites A and B combine together

to form a regular spinal ferrite structure.

2.Inverse spinal



In this type, we consider the arrangement of dipoles of a single ferrous ferrite molecule Fe3+ [Fe

2+ Fe 3+] O4 2– Fe 3+ , ions (trivalent) occupies all A sites (tetrahedral) and half of the B sites

(octahedral) also. Thus the left out B sites will be occupied by the divalent (Fe2+).

Application of Ferrites

1. Ferrites are used to produce ultrasonic wave by Magnetostriction principle.

2. Ferrites are used in audio and video transformers.

3. Ferrites rods are used in radio receivers to increase the sensitivity.

4. Ferrites are widely used in non-reciprocal microwave devices such as gyrator,

circulator and Isolator.

10.Write a short notes on the following

(a) BCS theory of superconductivity

(b) High temperature super conductor

(c) Magnetic levitation

(a) BCS THEORY OF SUPERCONDUCTIVITY

The properties of Type I superconductors were modeled successfully by the efforts of

John Bardeen, Leon Cooper, and Robert Schrieffer in what is commonly called the BCS theory.

The BCS theory of superconductivity has successfully described the measured properties

of Type I superconductors. It envisions resistance-free conduction of coupled pairs of electrons



called Cooper pairs. This theory is remarkable enough that it is interesting to look at the chain of

ideas which led to it.

1. One of the first steps toward a theory of superconductivity was the realization that there must

be a band gap separating the charge carriers from the state of normal conduction.

a) A band gap was implied by the very fact that the resistance is precisely zero. If charge carriers

can move through a crystal lattice without interacting at all, it must be because their energies are

quantized such that they do not have any available energy levels within reach of the energies

of interaction with the lattice.

b) A band gap is suggested by specific heats of materials like vanadium. The fact that there is an

exponentially increasing specific hear as the temperature approaches the critical temperature

from below implies that thermal energy is being used to bridge some kind of gap in energy. As

the temperature increases, there is an exponential increase in the number of particles which

would have enough energy to cross the gap.

Single electrons could be eliminated as the charge carriers in superconductivity since with a

system of fermions you don’t get energy gaps. All available levels up to the Fermi energy fill up.

The needed boson behavior was consistent with having coupled pairs of electrons

with opposite spins. The isotope effect described above suggested that the coupling mechanism



involved the crystal lattice, so this gave rise to the phonon model of coupling envisioned with

Cooper pairs.

(b) High temperature super conductor

1. High TC Superconductors have high temperatures.

2. They have a modified perovskite crystal structure.

3. Superconducting state is direction dependent.

4. These are oxides of copper with other elements.

5. These are reactive, brittle, and cannot be easily modified or joined.

6. For high TC superconductors, liquid Nitrogen is used instead of liquid helium.

(c)Magnetic levitation

Maglev is a magnetic levitated train, its works under the principal of Electromagnetic induction.

This train cannot move over the rail. Instead it floats above the rails, so that it moves faster with

speed of 500 Km/hr without any frictional loss. It has two superconducting magnet on each side

of the train and there is guiding system consisting of ‘S” shaped coils on each side. Due to

actions of these magnets the train moves faster by levitation principle.

Working

This train consists of superconducting magnets placed on each side of the train.The train can run

in a guiding system, which consists of serial ‘S’ shaped coil as shown in figure.



Fig . Magnetic Levitation

Initially when the train starts, they slide on the rails. Now, when the train moves faster, the

superconducting magnets on each side of the train will induce a current in the ‘S’ shaped coils

kept in the guiding system. This induced current generates a magnetic force in the coils in such a

way that the lower half of ‘S’ shaped coil has the same magnetic pole as that of the

superconducting magnet in the train, while the upper half has the opposite magnetic pole.

Therefore, the total upward magnetic force acts on the train and the train is levitated or raised

above the rails and floats in the air. Now, by alternatively changing the poles of the

superconducting magnet in the train, alternating currents can be induced in ‘S’ shaped coils.

Thus, alternating series of north and south magnetic poles are produced in the coils,

which pulls and pushes the superconducting magnets in the train and hence the train is further

moved. This can travel a speed of 500 km per hour.

(d) SQUID

SQUID stands for Superconductors Quantum Interference Device. It is a double junction

quantum interferometer formed from two Josephson junctions mounted on a superconducting

ring. SQUID is based on the flux quantization in a superconducting ring. The total magnetic flux



passing through the ring is quantized. It is using to detect very minute magnetic field of the order

of 10-14 tesla.

11. Define local field and derive an expression for the local field in a dielectric

for a cubic structure. Hence deduce Claussius – Mossotti equation.

INTERNAL FIELD (OR) LOCAL FIELD

When a dielectric material is placed in an external electric field, it exerts a dipole moment in it.

Therefore two fields are exerted.

1. Due to external field. 2. Due to dipole moment

This long range of coulomb forces which is created due to the dipoles is called as Internal field

(or) local field. This field is responsible for polarizing the individual atoms (or) molecules.



12. Write short note on the following

(a) Dielectric break down.

(b) Temperature and frequency dependent polarization of a dielectric material

(c) Dielectric loss

(a) DIELECTRIC BREAKDOWN

When a dielectric material loses its property and permits the flow of a large current, it is said to

be dielectric breakdown

Types of dielectric breakdown

1. Intrinsic breakdown

2. Thermal breakdown.

3. Electrochemical breakdown.

4. Defect breakdown.

5. Discharge breakdown.

1. Intrinsic Breakdown



When a dielectric material is subjected to large electric field, a large number of electrons

are transferred from the valence band to the conduction band. Thus the dielectric material loses

its insulating property and becomes a conductor. This is known as intrinsic breakdown.

2. Thermal breakdown

Thermal breakdown occurs in dielectric when the rate of heat generation is greater than

the rate of heat dissipation.

3. Electrochemical breakdown

When temperature increases, mobility of ions increases and hence leakage current also

increases. This decreases the insulation resistance and finally creates a dielectric breakdown.

Hence this type of breakdown is called electrochemical breakdown.

4. Defect breakdown

If the surface of the dielectric material has defects such as cracks, pores, etc. Moisture

and other impurities can fill at these places leading to breakdown, this type of breakdown called

Defect breakdown.

5. Discharge breakdown

This type of breakdown occurs when the insulator contains occluded gas bubbles. When

the dielectic is subjected to an electric field, the gas present in the material will be easily ionized

than the solids.

(b) FREQUENCY AND TEMPERATURE DEPENDENCE OF POLARIZATION

MECHANISM



1. Electronic polarization is very fast and is completed at any instant of time even when the

frequency of the voltage is very high in the optical range (1015 Hz). Thus it occurs at all

frequencies.

2. Ionic Polarization is slower and the ions do not respond when the voltage corresponds to

visible optical frequencies, i.e., the electric field changes in polarity at very fast, so that the ions

are not able to reorient themselves due up to the field. So the ionic polarization does not occur at

visible optical frequencies. It occurs only at frequencies less than 1013 Hz.

3. Orientation Polarization is even slower than ionic polarization and occurs only at electrical

frequencies (audio and radio frequencies 106 Hz).

4. Space-charge polarization is the slowest process because the ions have to diffuse (jump) over

several inter atomic distances. This occurs at very low frequencies of 50 - 60 Hz (power

frequencies).

Thus at low frequencies all the four polarizations will occur and the total polarization is

very high, but at high frequencies, the value of the total polarization is very small. The following

graphs show the frequency dependence of polarization mechanism and the corresponding power

losses at those frequencies.

Temperature dependence

Electronic and ionic polarizations are independent of temperature and the orientation and

space charge polarizations are dependent of temperature. Orientation polarization is inversely

proportional to the temperature.

(c) DIELECTRIC LOSS



When a dielectric material is subjected to an alternating electric field, some amount of

energy is absorbed by the material and is dissipated in the form heat. This loss of energy is called

ielectric loss.

Where tan θ is called the power factor of the dielectric

Conclusions

1. The dielectric loss increases with increase of frequency, applied voltage, temperature, and

humidity.

2. The dielectric loss is maximum, when the relaxation time of a polarization process matches

the period of the applied AC voltage.

3. The dielectric loss at radio frequency is high due to diffusion of ions.



4. The dielectric losses in the optical region, associated with the electrons are referred to as

optical absorption. This absorption leads to color of materials.

5. The dielectric losses in the infrared region associated with the ionic vibrations are referred to

as Infrared absorption.

13.Definition for electronic and ionic Polarisation and derivation for electronic

polarisability

Electronic polarization occurs due to the displacement of positively charged nucleus and

negatively charged electron in opposite directions by an external electric field. It creates a

dipole moment in the dielectric.

Ionic polarization which arises due to the displacement of cations (+ve) and anions (-ve) in

opposite directions and occurs in ionic solids in the application of electric field.

Derivation for Electronic Polarizability αe



14. Give the properties, preparation and applications of Metallic Glasses



15.Give an account on Shape Memory Alloys and their applications.



16.Explain with necessary diagram the synthesis and preparation of Nano

materials using the following methods. A) Pulsed Laser Deposition and B)

Chemical Vapour Deposition.



a. Chemical Vapour Deposition

Principle

In this technique, initially the material is heated to gaseous state and then it is deposited on a

solid surface under vacuum condition to form nano powder by chemical reaction with the

substrate.

Working

Chemical Vapour Deposition involves the flow of a gas with diffused

reactants (substances to be deposited in the vapour) over a hot substrate surface.

The gas that carries the reactants is called the carrier gas.



While the gas flows over the hot solid surface, the heat energy increases chemical

reactions of the reactants that form film during and after the reactions.

The byproducts of the chemical reactions are then removed. The thin film of desired

composition can thus be formed over the surface of the substrate.

b. Pulsed Laser Deposition (PLD)

Principle

The Pulsed Laser Deposition method of thin film growth involves evaporation of a solid

target in an ultra high vacuum (UHV) chamber by means of high-energy laser pulses. A

powerful beam of laser evaporates the atoms from a solid source. These atoms collide with inert

gas atoms and cool them forming clusters. Finally, the clusters condense on the cooled substrate

Construction

The set up consists of an ultra high vacuum (UHV) system equipped with inert facility,

laser beam, solid target and cooled substrate as shown in diagram. A high power laser is used as

an external energy source to vaporize materials and to deposit thin films. A set of optical

components is used to focus the laser beam over the target surface.

Working

1. The laser beam is focused onto the surface of the target. At sufficiently high flux

densities and short pulse duration, all elements in the target are rapidly heated up to their

evaporation temperature. Materials are dissociated from the target surface and ablated

out.

2. The emitted materials tend to move towards the substrate according to the laws of gas-

dynamic. The spot size of the laser and the plasma temperature has significant effects on

the deposited film uniformity.

3. The ejected high energy species impinge onto the substrate surface and form a thin film

of nano particles.

Laser light

Substrate Plasma Plume

Target

UHV Chamber

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