1

Workbook on Semiconductor Physics

BSC001PT

For

B.Tech 1st year CSE students

Of

University of Engineering and Management, Jaipur

Name of the student

College Roll number

2

Subject code: BSC001PT

Credit: 4

Lecture Plan: 3L+1T

Prerequisites: Basics of Semiconductors discussed in class 12th.

Total number of Modules: 5

Detailed Syllabus Module-wise:

Module 1: Introduction to Quantum Mechanics [10]

Wave Particle duality- De-Broglie Hypothesis, Heisenberg’s uncertainty principle, wave packet

Wave Function and Physical Significance of a wave function Probability Density and Normalization of a wave function Expectation Value and Operator Correspondence Schrödinger Wave Equations (Time dependent and Independent) Particle in a 1D box and its energy states Particle in a 3D box and its energy states Degeneracy

Module 2: Electronic materials [8]

Free electron theory Density of states and energy band diagrams Kronig-Penny model (to introduce origin of band gap) Energy bands in solids, E-k diagram Direct and indirect bandgaps Types of electronic materials: Metals, Semiconductors, and Insulators Occupation probability and Fermi level Effective mass and Phonons.

Module 3: Semiconductors [12]

Intrinsic and extrinsic semiconductors Dependence of Fermi level on carrier-concentration and temperature Carrier generation and recombination Carrier transport: diffusion and drift current

3

p-n junction Metal-semiconductor junction (Ohmic and Schottky) Semiconductor materials of interest for optoelectronic devices.

Module 4: Measurements [5]

Four-point probe measurements for resistivity. Hall Effect- Measurement of Hall coefficient for carrier density and Hall

Mobility Hot Probe Method measurements.

Module 5: Lasers [8]

Optical transitions in bulk semiconductors: absorption, spontaneous emission, and stimulated emission

Einstein’s Relation Lasers: Ruby laser Semiconductor laser He Ne laser Applications of lasers

References:

1. J. Singh, Semiconductor Optoelectronics 2. P. Bhattacharya, Semiconductor Optoelectronic Devices 3. Online course: “Semiconductor Optoelectronics” by M R Shenoy on

NPTEL 4. Malik and Singh, Quantum Mechanics 5. Dr. Pradeep Kumar Sharma, Engineering Physics

Content Pages

Module 1 4-37 Module 2 38-67 Module 3 68-85 Module 4 86-99 Module 5 100-112 Solutions **will be uploaded on departmental website**

(https://drpradeepatuem.wordpress.com/)

4

Module 1

Quantum Mechanics

1. What do you mean by duality of matter?

2. Explain why classical mechanics cannot be applied to study motion of electrons?

3. What is the de-Broglie wavelength of an electron having velocity equal to half of speed of light?

5

4. Compute the de Broglie wavelength of the following: A 1000kg automobile travelling at 100m/s A 10g bullet travelling at 500m/s An electron with a kinetic energy of 1ev An electron with a kinetic energy of 100Mev

6

5. Derive an expression to obtain a relation between de-Broglie wavelength and kinetic energy of a particle having mass m and temperature.

7

6. Derive a formula expressing de-Broglie wavelength of an electron in terms of potential energy (V) in volts through which it is accelerated.

7. Calculate the de-Broglie wavelength of a 1 MeV proton.

8. State Heisenberg’s Uncertainty Principle.

8

9. An electron moves in x direction with a speed of 3.6 X 10^6 m/s. We can measure its speed to a precision of 1%. With what precision can we measure its position?

10. A hydrogen atom is 0.53Å in radius. Use uncertainty principle to estimate the minimum energy an electron can have in this atom.

9

11. Estimate the minimum velocity of a billiard ball (m~100g) confined to a billiard hole of dimension 1 m.

12. The momentum of an electron is 5 x 1027 kg m/s and is measured to an accuracy of 0.003%. Calculate uncertainty in the determining position of the electron.

10

13. A free 10 eV electron moves in the x-direction with a speed of 1.88 x 106 m/s. Assuming that one can measure its speed to a precision of 1 %, what will be the precision with which its position is simultaneously measured? If electron is replaced by a golf ball of mass 45 g moving at a speed of 40 m/s, what is the precision in position in this case? What conclusion do you draw?

11

14. In a radio transmitter, pulse lasts for 1 millisecond. Find the uncertainty in the momentum and the frequency of photons transmitted.

15. What are the mathematical conditions that a wave function must follow?

12

16. None of the following are permitted as solutions of the Schrödinger equation. Give reason in each case

a) Ψ(x) = A cos 푘푥 for x<0 , Ψ(x)= Bsin 푘푥 for x>0 b) Ψ(x) = A/x for -L<x<L c) Ψ(x) = A tan푘푥 for x>0

17. Determine the conjugate for the given wave functions i) 푒 − 푒

ii) 푖 sin 푥+cos 푖푥 iii) N푒

13

18. What is the physical significance of a wave function?

19. Why do we must normalize a wave function?

20. What is normalization constant?

21. What is the physical meaning of ∫ |훹| 푑푥 = 1

14

22. Normalize 훹 = 퐴 sin for 0<x<L

15

23. Normalize Ψ = A (1-x2) for -1<x<1

24. A particle is trapped in a 1D box of width L and is in its ground state. Evaluate the probability to find the particle

a) Between x=0 and x=L/3 b) Between x= L/3 and x=2L/3 c) Between x=2L/3 and x= L

16

17

25. The wave function of a particle is given by Ψ(x) = A푒 for 0<x<∞ and is zero elsewhere. Find the value of A and the probability of finding the particle lying in between 2/k to 3/k.

18

26. For a particle in 1D box, show that the average value of x is L/2, independent of the quantum state.

19

27. Show that the average value of x2 in the one dimensional well is ⟨푥 ⟩ = 퐿 ( − )

20

28. The wave function of a particle in its ground state in one dimensional

box of length L is given by 2 sin xL L

. Calculate the probability of

finding the particle with an interval of 1 Ȧ at the center of the box. The length of the box is 10 Ȧ.

21

29. Find the lowest energy of an electron confined to move in one dimensional box of length 1 Ȧ.

30. An electron is trapped in an infinitely deep well of a width ‘a’. if the electron is in its ground state, what is the probability of finding it in the central 1/3rd of the well.

22

31. Assuming that the proton is inside the nucleus as a free particle in a box where surface of the nucleus plays the role of wall of the box. What energy it is expected to release when nucleus transits from the first excited state to round state. The size of the nucleus is 1.0 x 10-14 m.

23

32. Consider a particle confined in a one dimensional box of width ‘a’. Find probability that the particle is found between x = 0 and x = a/n when it is in the nth state.

24

33. Find out the expectation value of the following quantities for a particle trapped in one dimensional box of size ‘a’ (i) Position (ii) Momentum

25

34. For the wave function Ψ(x) = 푒 and consider the dimensionless Hamilton aoperator 퐻= 푝 + 푥 for 푝̂ = -i Calculate the Eigen value of H.

26

35. Show that position and momentum operator do not commute with each

other.

36. Starting from the wave equation and introducing energy and momentum of the particle obtain an expression for three dimensional Schrödinger’s equation in time dependent form.

27

37. Obtain three dimensional time independent Schrodinger’s wave equation from time dependent Schrodinger’s equation.

28

38. Give the formulation of time independent Schrodinger’s equation for a free particle.

29

39. Solve the Schrodinger equation for a particle in a 1D box with perfectly rigid walls.

30

40. What are the values of Eigen energies of a particle trapped in a 1D box?

41. An electron is trapped in a one dimensional region of length 1.0X10-10m. How much energy must be supplied to excite the electron from the ground state to the first excited state? In ground state, what is the probability of finding the electron in the region from x=0.090 Å to 0.110Å?

31

42. What is the minimum energy of an electron trapped in a 1D region of size of an atomic nucleus (1.0X10-14m)?

32

43. An electron trapped in a one dimensional infinite well of width L=1nm. Consider the transition from the excited state n=2 to the ground state n=1. Calculate the wavelength of light emitted. In which region of electromagnetic spectrum does it fall?

44. Write down the Schrödinger wave function for a particle of mass m trapped in a one dimensional box of size a. How does the function modify if the particle were in a 3D cubical box of each side a?

33

45. What is degeneracy?

46. Find the lowest energy of the states having following degeneracy: a) Non-degenerate b) Doubly degenerate c) Triply degenerate d) Six fold degeneracy for 3D cubical box

34

47. Answer the following questions with respect to a particle in cubical box of side ‘a’. (i) Is nx = ny = nz = 1 state degenerate? (ii) What is the order of degeneracy for nx+ny+nz = 4? (iii) What shall happen to the degeneracy of the above states if the

box is not cubical but rectangular parallelepiped with side a, b, and c such that a = b ≠ c?

35

48. An electron is trapped in a cubical box of side 1 Ȧ. Find energy and momentum for the ground state and the first excited state.

49. A particle in a cubical box of side ‘a’ in its ground state. Find the probability that the particle is found in 1/8th region of box.

36

Objective type questions

1. Which of the following phenomenon cannot be explained by the classical theory? (a) Photoelectric effect (b) Compton Effect (c) Raman Effect (d) All of above

2. Which of the following shows the particle nature of light? (a) Photoelectric effect (b) Raman effect (c) Compton effect (d) All of above

3. Which of the following characteristic(s) photon has(have)? (a) M0=0 (b) E h

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(c) 2

hmc

(d) All of above 4. Which of the following relation can be used to determine deBroglie

wavelength associated with a particle of mass a and having energy E (a)

2hmq

(b) 3

hmkT

(c) 2hmE

(d) All of above 5. The phase velocity of deBroglie wave associated with an electron is

given by (a) E

p

(b) h

(c) hc

(d) k 6. Electron behave like a wave as it

(a) Can be deflected by an electric field (b) Can be deflected by a magnetic field (c) They ionize a gas (d) Can be diffracted by a crystal

7. A material particle is in thermal equilibrium at temperature T. The wavelength of de Broglie wave associated with it is (a)

2hkT

(b) 28hmkT

(c) 2

hmkT

(d) 24hmkT

8. Photoelectric effect involves only (a) Free electrons (b) Bound electrons (c) Both (a) and (b) (d) None

9. The de Broglie hypothesis is concerned with (a) Wave nature of radiation (b) Wave nature of all material particles

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(c) Wave nature of electrons only (d) Wave nature of α-particles only

10. The ratio of de Broglie wavelengths of a hydrogen atom and helium atom at room temperature, when they move with thermal velocities, is (a) 1:2 (b) 2:1 (c) 3:1 (d) 1:3

11. Which of the following relations is correct for Heisenberg’s uncertainty principal?

(a) 2

E t

(b) 4hx p

(c) 2

L

(d) None of above 12. Heisenberg Uncertainty principal holds good for

(a) Microscopic as well as macroscopic particles both (b) Only microscopic particles (c) Only macroscopic particles (d) None of above

13. The energy of a particle in infinite potential well is (a) Proportional to n2 (b) Inversely proportional to n2 (c) Proportional to n (d) Inversely proportional to n

14. The momentum of a particle in infinite potential well of length l is (a) Proportional to l (b) Inversely proportional to l (c) Proportional to l2 (d) Inversely proportional to l2

15. The momentum of a particle in infinite potential well is (a) Proportional to n2 (b) Inversely proportional to n2 (c) Proportional to n (d) Inversely proportional to n

16. Which of the following operator is associated with energy

(a) 2

2

2V

m

(b) 2

2

2m

(c) i

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(d) it

17. Which of the following operator is associated with Kinetic energy

(a) 2

2

2V

m

(b) 2

2

2m

(c) i

(d) it

18. Which of the following operators is associated with momentum

(a) i

(b) 2

2

i

(c) 2

2

i

(d) 2

2

2m

19. Which one of the following values of a particle in infirnite potential well of length l are allowed

(a) 2 2 2

2n

ml

(b) 2 2 2

22n

ml

(c) 2 2

22mn l

(d) 2 2

22nml

20. The entire information of a system can be gathered with the help of (a) Position (b) Eigen value (c) Momentum operator (d) Wave function

21. The expression 2,x t stands for

(a) Normalization (b) Position (c) Time probability density (d) Position probability density

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Summary for Module 1

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Module 2

Electronic materials

1. What do you understand by free electron gas model of metals?

2. What is the difference between electrical conductivity and thermal conductivity?

3. Define and discuss Wiedemann-Franz law.

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4. What are the limitations of free electron theory?

5. Calculate the drift velocity of electrons in an intrinsic in an Aluminum wire of diameter 0.9 mm carrying current of 6 A. Assume that 4.5. x 1028 electrons /m3 are available for conduction.

43

6. The density of Cu is 8.92 x 103 kg/m3 and its atomic weight is 63.5. Determine the current density if the current of 5.0 A is maintained in Cu wire of radius 0.7 mm. assuming that only one electron of an atom takes part in conduction. Also calculate the drift velocity of electrons.

7. State the salient features of quantum theory of free electrons?

44

8. Write down the expression by which you can calculate the probability of finding an electron having energy E and temperature T.

9. What is fermi energy?

10. What is the value of Fermi Dirac function for a) T= O K b) E equals to fermi energy c) For T= 273K and E= Ef

45

11. Show that the density of states g (E) dE is proportional to E1/2.

46

12. Determine a relation between fermi energy and number of conduction electrons present per unit volume?

47

13. How can you determine fermi velocity and fermi temperature from fermi energy?

14. Show that the average kinetic energy per unit particle density is 3/5 of fermi energy.

48

15. Show that the Fermi level EF has the property that the sum of the

probability that an electron state ΔE above EFis occupied and the probability that astate ΔE below EFis unity.

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16. Evaluate the temperature at which there is one percent probability that a

state with energy above 0.5eV above the Fermi level will be occupied by an electron?

17. In Cu, each atom provides one valence electron. The density of copper is

8.92g/cc and its atomic mass is 63.546. Calculate the Fermi energy and the average kinetic energy per unit volume.

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18. Explain why the value of Fermi energy for different materials

isdifferent. 19. If the mass of a Cu wire is 1g and the area of cross section is 1cm2. Find

out the number density of electrons in it if the length is given to be 1m and each Cu atom donates 2 electrons.

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20. Show that the Fermi energy of Cu is 7.07eV if the density of Cu is given to be 8.92g/cc (Take valency =1 )

21. Estimate the average drift velocity of conduction electrons in a Al wire of

cross section area 200 X 10-7 cm2 carrying a current of 5mA. The number density of Al is given to be 7 x 1028/m3.

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22. If the absolute temperature of a metal is raised to 10,000 K then what will

be the probability of finding an electron in the energy level 2eV above Fermi level?

23. Explain the meaning of periodic potential and its origin in atoms? 24. Explain graphically how the Fermi Dirac equation changes as we increase

the temperature?

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25. For potassium the Fermi energy is 2.14 eV and the electron density is 1.4 x

1028 /m3. Find the electron density for the metal for which the Fermi energy is 4.72 eV.

26. Calculate the Fermi energy for copper, given that the number of conduction electron per unit volume is 8.49 x 1028 m-3.

54

27. Given that the electron density in silver is 5.8 x 1028 m-3. Calculate the Fermi energy for free electron gas. What is the speed of electron at this energy?

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28. Calculate the probability of occupancy for a state whose energy is (a) 0.1 eV above the Fermi energy, (b) 0.1 eV below the Fermi energy, and (c) equal to the Fermi energy. Assume the temperature to be 800 K. (Boltzmann constant k = 1.38 x 10-23 J/K.).

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29. A cube of copper is 1 cm on edge. How many states are available for its conduction electrons in the energy interval E = 5.00 eV to E = 5.01 eV? Assume that free electrons behave as quantum gas.

30. The Fermi energy for copper is 7 eV. Calculate (i) the number of energy states available for conduction electrons below the Fermi energy in a cube of copper of edge 1 cm and (ii) the density of conduction electrons.

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31. Calculate the Fermi energy, Fermi velocity and Fermi temperature for free electron gas for silver having conduction electrons per unit volume to be 5.8 x 1028 m-3.

58

32. Calculate the Fermi energy in copper assuming that each copper atom contributes one free electron to the electron gas. Given density of copper to be 8.94 x 103 kg/m3 and its atomic mass is 63.54.

33. Determine the average kinetic energy and speed of electron at its mean energy at 0 K, if the Fermi energy is 10 eV.

59

34. Fermi energy of a given substance is 7.9 eV. What is the average energy and speed of electrons in this substance at 0 K?

35. There are 2.5. x 1028 free electrons per cubic meter of sodium. Calculate the Fermi energy and Fermi velocity.

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36. The density of copper is 8940 kg/m3 and atomic energy weight is 63.55. Determine the Fermi energy of copper. Also obtain the average energy of free electrons of copper at 0 K.

37. Consider silver in the metallic state with one free electron per atom. Calculate the Fermi energy. Given that density of silver is 10.5 g/cm3 and atomic weight is 108.

61

38. Aluminum metal crystallizes FCC structure. If each atom contributes single electron as free electron and the lattice constant ‘a’ is 4.0 Ȧ, treating conduction electron as free electron Fermi gas , find (i) Fermi energy EF (ii) Fermi Vector (kF) and total kinetic energy of free electron gas per unit volume at 0 K.

62

39. Discuss Kronig-Penny model. Using this model show the energy spectrum of electrons consisting of a number of allowed energy bands separated by forbidden bands.

63

40. What is the effect of periodic potential on the energy of electrons in a metal? Explain it on the basis of Kronig-Penny model and explain the formation of energy bands.

64

41. Discuss the formation of Brillouin zones for (i) linear lattice (ii) two dimensional lattice.

42. Define and prove that effective mass of an electron is 2

*2 2/

md E dk

. Give

the physical basis of effective mass and explain its physical significance.

65

43. Differentiate among metals, semiconductors and insulators on the basis of

band theory.

44. What are phonons?

66

Objective type questions

1. With the increase in temperature, the resistance of a metal (a) Remain constant (b) Increases (c) Decreases (d) Becomes zero

2. Average kinetic energy of a free electron gas at 0 K is

(a) 25 FE

(b) 53 FE

(c) 35 FE

(d) FE 3. The density of states of electrons between the energy range E and

E+dE is proportional to

(a) 12E

(b) E2 (c) E

(d) 32E

4. The phase space is a (a) Two dimensional space (b) One dimensional space (c) Three dimensional space (d) Six dimensional space

5. At low temperature, the resistivity of a metal is proportional to (a) T2 (b) T (c) T5 (d) T1/2

6. Which of the following relation is correct for current density (a) dJ nev

(b) 1

d

Jnev

(c) d

neJv

(d) dJ neAv 7. Which one of the following relation is correct for the conductivity of

metals

(a) 2

2nemt

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(b) 2

2mne t

(c) 2

2ne t

m

(d) 22n

mte

8. The value of Fermi-distribution function at absolute zero (T=0 K) is 1, under the condition (a) FE E (b) FE E (c) FE E (d) FE E

9. The free electron theory of metals was initiated by (a) Pauli (b) Sommerfeld (c) Lorentz and Drude (d) Fermi-Dirac

10. The energy Eigen value in a free electron model is given by

(a) 2

2 28hEk m

(b) 2 2

2h kE

m

(c) 2 2

2kEm

(d) 2 22E m k 11. The first Brillouin zone is defines between the region k =

(a) 0 to a

(b) 2a

to a

(c) a

to 2a

(d) a

to a

12. The second Brillouin zone is defined between the region k=

(a) K=a to

a

(b) 2ka

to a and

a to 2

a

(c) ka

to 2a

(d) 2ka

to 2a

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13. Which one of the following relation is correct for effective mass of an electron

(a) 2 2

*2 24

h d Emdk

(b) 12 2

*2 24

h dkmd E

(c) 12

* 22

d Em hdk

(d) 12 2

*2 24

h d Emdk

14. Pure semiconductor behaves as an insulator at (a) 273 K (b) -273 0C (c) 373 K (d) None of the above

15. The group velocity of the electron in one dimensional lattice is given as

(a) gdkvd

(b) gdvdk

(c) gvk

(d) gv k 16. When we increase the temperature of extrinsic semiconductor, after a

certain temperature it behaves like (a) An insulator (b) An intrinsic semiconductor (c) A conductor (d) A superconductor

17. In an n-type semiconductor the Fermi level lies (a) Above the top of the valence band (b) Below the bottom of the conduction band (c) In the middle of the forbidden gap (d) Near the conduction band

18. The concentration of electrons in the conduction band of an intrinsic semiconductor is proportional to (a) T (b) T2 (c) T3/2 (d) T3

19. The energy gap between the valence and conduction bands in a semiconductor is of the order of

69

(a) 26 eV (b) 1.0 eV (c) 7.0 eV (d) 0.001 eV

20. For semiconductors, the resistivity is inversely proportional to the temperature for semiconducting materials. True or false? a) True b) False

Summary for Module 2

70

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Module 3

Semiconductors

1. Draw the energy band diagram(label Ec ,Ev&Ef)of the following a) Intrinsic semiconductor b) p-type semiconductor (mention the acceptor level) c) n-type semiconductor (mention the donor level)

72

2. Write down the expression for density of states in a metal?

3. Modify the earlier density of states expression for electron in conduction band and holes in valence band.

4. Why are we taking effective mass of electron in place of mass?

73

5. Calculate the number density of electrons in conduction band using density of states of conduction band.

74

6. Calculate the number density of holes in valence band using density of states of valence band.

75

7. For an intrinsic semiconductor having band gap Eg = 0.7 eV, calculate the density of holes and electrons at room temperature

8. State the Law of Mass Action?

76

9. Obtain the expression for fermi energy in an intrinsic semiconductor at any temperature T. how does this expression changes for T=OK.

77

10. Using the law of mass action, derive the expression for intrinsic concentration.

78

11. Prove that the fermi level is above the average of conduction and valence energy in an n-type semiconductor.

12. Why the mobility of holes is always lesser that that of electron?

13. Calculate the intrinsic concentration of Silicon for energy band gap = 1

eV at temperature T=300 K. (given * *0h em m m ).

79

14. Determine the position of Fermi level for an intrinsic semiconductor with gap Eg=0.7 eV at T=300 K. if * *6h em m , calculate the density of electrons at 300 K.

80

15. Calculate the ratio of intrinsic concentration of an intrinsic semiconductor at temperature 570C and 270C. The energy band gap is 1.1 eV. Write down the conclusion.

16. Calculate the value of intrinsic concentration for a semiconductor having band gap energy 1eV at 300K.

81

17. Explain how drift and diffusion current are different from each other?

18. What is the Einstein’s relation for these?

82

19. Find the diffusion coefficients of electrons and holes at 270C for given that the mobilities of electrons and holes are 0.17 and 0.025 m2/V-s respectively at 270C.

20. The minority charge carrier lifetime in p-type semiconductor is 10-7 s. the mobility of electron is 0.15 m2/V-s at 300 K. What is the diffusion length?

83

21. A specimen of Germanium at 300 K for which the density of carriers is

2.5 x 1013 per cm3, is doped with impurity atoms such that there is one impurity atom for 106 germanium atoms. All the impurity atoms may be assumed ionized. The resistivity of doped material is 0.039 cm . Carrier mobility for germanium at 300 K is 3600 cm2/V-s. For the doped material, find the electron and hole densities. e= 1.602 x 10-19 C.

22. The intrinsic resistivity of germanium at 300 K is 0.47 m . The electron mobility is 0.39 m2/V-s and hole mobility is 0.19 m2/V-s. Calculate the density of electrons in the intrinsic material. Also calculate the drift velocities of holes and electrons for an electric field E= 104 V/m.

84

23. The conductivity of n-type Germanium semiconductor is 39 1 1m . If the mobility of electrons in Ge is 0.39 m2/V-s. Find the concentration of donor atoms

24. Find the resistance of an intrinsic Germanium rod 1 cm long, 1 mm wide, 1 mm thick at 300 K. for Ge, ni = 2.5 x 1019 /m3. The mobilities of e-s and holes are 0.39 m2/v-s and 0.19 m2/V-s.

85

25. Explain the formation, working and significance of a p-n junction.

86

26. Explain the formation, working and significance of a Schottky Junction in detail. Give at least two main difference of Schottky Junction with Ohmic Junction.

87

88

Summary for Module 3

89

Module 4

Measurements

1. How is the resistivity measured dependent on probe spacing for a bulk sample?

90

2. Show that for a thin film sample, the resistivity is independent of probe spacing.

91

3. What is the basic principle of Hot Probe Method? Why is it used? Explain the whole process for n type semiconductor.

92

4. For a thin film having thickness t=100nm, and the slope of V-I characteristic is 1.025. Calculate the resistivity of the material.

5. Calculate the resistivity of the same material taken in bulk form. It is given that the probe spacing is 1mm.

93

6. How does the hall coefficient give information about the majority charge carriers?

7. Why the hall coefficient of metals is always less than that of semiconductors?

94

8. The measurement of large magnetic fields on the order of a Tesla is often done by using Hall Effect. Explain the Process

95

9. For a given hall probe of thickness 2µm, the current applied to the probe is 1mA shows the hall voltage on voltmeter to be 73.7µV. If the number density of the material is 8.47X1028 /m3. Find the value of external magnetic field.

10. How do we identify the nature of the semiconductor using Hall Voltage?

96

11. The hall coefficient of a sample A of a semiconductor is measured at room temperature. The hall coefficient of A at room temperature is 4 X104 C-1. What is the charge carrier concentration of A?

12. An electric field of 100 V/m is applied to a sample of n type semiconductor whose Hall coefficient is -0.0125 m3/C. Determine the current density in the sample assuming mobility of electron to be 0.36 m2V-1s-1

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13. The hall coefficient of a certain specimen of silicon is found to be -7.35 X 10-5m3/C from 100 to 400K. Is this semiconductor extrinsic or intrinsic at room temperature, and is it n type or p type? The electrical conductivity at room temperature was found to be 200 Ὤ-1-m-1. Calculate the density and mobility of charge carriers at room temperature.

14. The resistivity of a doped silicon sample is 8.9 X 10-3 ohm-m. The hall coefficient was measured to be 3.6 X 10-4 m3/C. Assuming single charge carrier conduction, find the mobility and density of charge carriers.

98

15. We have a bar of silicon which is 2cm long and has a cross section of 1cm2. The crystal is n type with a donor concentration of 1023 /m3. The resistance of the sample is 10 ohms. Estimate the electron mobility.

99

Objective type Questions 1. Hall effect can be used to measure a) Magnetic field intensity b) Electric field intensity c) Carrier concentration d) None of the above

2. In Hall Effect, the output voltage produced across the crystal is due to

a) Drop across the crystal is due to the current passed through it b) Induced voltage by the applied magnetic field c) Movement of charge carriers towards one end d) All of the above

3. In any specimen, the Hall voltage is proportional to a) (Current through specimen)2 b) B. Current through specimen c) C. None of the above

4. Electric field strength related to hall voltage is given by

a) VH .d b) VH ⁄d c) VHE d) Ed

5. Hall probe is made up of

a) metals b) non metals c) semiconductor d) radioactive material 6. Hot Point Probe method is used for measuring a) charge carrier concentration b) Resistivity c) Mobility d) type of doping 7. The current flow in the semiconductor in Hot Probe method is due to a) Potential applied b) Electrodes c) Temperature gradient d) Diffusion

8. The force experienced by charge carried in Hall Effect set up is due to a) Electric field

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b) Magnetic field c) Both d) None 9. Suppose a metal bar is placed in positive x direction, the magnetic field

is applied in the positive z direction and the direction of current is parallel to x axis. Where will be the direction of force due to magnetic field?

a) Negative y axis b) Positive y axis c) Negative x axis d) Positive x axis 10. If the hall coefficient is coming out to be negative, what can you say

about the semiconductor specimen? a) p-type b) n-type c) extrinsic d) intrinsic 11. How is mobility of charge carriers (µ) related to hall coefficient(R),

where σ is the conductivity? a) µ=σ/R b) µ=-σ/R c) µ=σ.R d) µ=σ(-R) 12. The hall coefficient for p type semiconductor (n ~ 1022/m3) is a) 6.25 X10-3 m3C-1

b) -6.25 X10-3 m3C-1

c) 6.25 X10-4 m3C-1

d) -6.25 X10-4 m3C-1

13. When the hot probes are applied to a semiconductor, the sensitive ammeter shows a negative value of current. What can be concluded from this about the type of semiconductor specimen?

a) n-type b) p-type c) intrinsic d) could be any 14. In Four Probe Method, the outer probes are connected to a) Voltage source b) Current source c) Oven

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d) None of the above

15. One of the main application of hall voltage is a) To measure magnetic field b) To measure electric field c) To measure both the fields d) To measure current

16. In Hot Probe experiment , the charge carriers in semiconductor move

from a) Cold probe to hot probe b) Hot probe to cold probe c) The movement depends upon the type of semiconductor d) None of the above 17. The probe spacing is kept constant in a four probe experiment to ensure a) Uniform heating b) Uniform temperature gradient c) Uniform resistivity d) For good conductivity 18. The middle two probes in four probe method are connected to a) Voltage source b) Current source c) Oven d) None of the above

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Summary for Module 4

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Module 5

Lasers

1. Write down the full form of LASER.

2. What is stimulated emission in the full form of LASER?

3. State the differences between normal light and laser light.

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4. Describe the energy level diagram, the phenomena of spontaneous emission, stimulated emission and stimulated absorption in a two level system.

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5. Obtain the relations between the Einstein’s A and B coefficients.

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6. What are the necessary conditions for lasing action?

7. Why do we need population inversion in a laser? How is it achieved?

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8. When the electron jumps from an energy level 5.44 X10-19 J to an energy level of 2.42X10-19J, find the wavelength and colour of the photon.

9. Find the ratio of stimulated to spontaneous emission rate at temperature of 240ºC for sodium D lines.

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10. Find the ratio of rate of spontaneous emission to that of stimulated emission at T= 103K for visible light of wavelength 5X1014 Hz and microwave of frequency 109Hz. Compare both the results.

11. A 10mW laser has aperture of diameter 1.6mm. Find the intensity of the light, assuming it as uniform across the beam.

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12. If the population of the two states in thermal equilibrium at room temperature 300K is 1/e. find the wavelength of the laser light emitted.

13. A two level laser emits a light of wavelength 5500 Ȧ. What will be the ratio of population of upper level (E2) to the lower energy level (E1) if the optical pumping mechanism is shut off (Assume T = 300 K). At what temperature for the condition of above would the ration of population be ½?

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14. Calculate the power per unit area delivered by a laser pulse of energy 4.0 x 10-3 Joule and the pulse length in time as 10-9 sec. when the pulse is focused on target to a very small spot of radius 1.5 x 10-5 m.

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15. What are the some applications of lasers?

16. Explain the working of He-Ne laser using a neat energy level diagram.

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17. Explain the working of Ruby laser using a neat energy level diagram.

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Objective type questions

1. LASER is a short form of (a) Light Amplification Stimulated Emission Radiation (b) Light Amplification by Stimulated Emission of Radiation (c) Light Absorption by Stimulated Emission of Radiation (d) Light Absorption by Spontaneous Emission of Radiation

2. What is the life time of electron in metastable state (a) 10-3 s (b) 10-5 s (c) 10-8 s (d) 10-7 s

3. In the population inversion (a) The number of electrons in higher energy state is more than the

ground state (b) The number of electrons in lower energy state is more than higher

energy state (c) The number of electrons in higher and lower energy states are same (d) None of the above

4. The relation between Einstein’s coefficients A and B is

(a) 3

3

8 hc

(b) 2 3 3

3

8 hc

(c) 32 h

c

(d) 8 hc

5. Laser beam is made of (a) Electrons (b) Highly coherent photons (c) Very light and elastic particles (d) None of the above

6. In ruby laser which ions give rise to the laser action? (a) 2 3Al O (b) 3Al (c) 3Cr (d) None of the above

7. Which one of the following laser have highest efficiency, ruby, He-Ne, and semiconductor and carbon dioxide (a) Ruby (b) Semiconductor (c) He-Ne

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(d) Carbon-dioxide 8. The method of population inversion to the laser action in He-Ne laser is

(a) Molecular collision (b) Direction conversion (c) Electric discharge (d) Electron impact

9. Ruby laser produces the laser beam of wavelength (a) 6943 Ȧ (b) 6328 Ȧ (c) 6320 Ȧ (d) 6940 Ȧ

10. Characteristic of laser are (a) Highly directional (b) Highly intense (c) Highly monochromatic

All of them

Summary for Module 5

Answer

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