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1.16. EXERCISES

1.16.1. Questions for Practice

  1. Give examples of good conductors. What is an insulator? What is the mechanism by which conduction takes place inside the semiconductor? What is the importance of valance shells and valance electrons? What is energy gap? Differentiate between semiconductors, conductors, and insulators on the basis of band gap.

  2. What is covalent bond? Under what condition do atoms form covalent bonds? What are intrinsic semiconductors? What is doping? What is the name of the impurity that makes semiconductor n-type? What are minority carriers in n-type and in p-type? Why? What are the impurities that make a semiconductor p-type? What are majority and minority charge carriers in p-type material?

  3. What are the two conduction processes in semiconductor? What are the approximate voltages required to break open the covalent bonds in Ge and Si? What are majority and minority carriers in n-type and p-type materials? Name three elements that are used as n-type and p-type impurities. What is the main factor for controlling the thermal generation and recombination?

  4. What is the meaning of intrinsically neutral? What is the forbidden energy gap? How does it come in? How much is its magnitude in Ge and Si?

  5. What happens to the conductivity of the semiconductor with the rise in the temperature? Do metals also exhibit the same behaviour?

  6. Which of the two semiconductor materials Si or Ge has larger conductivity/resistivity at room temperature? How does the conductivity or resistivity of the semiconductor materials vary with temperature? In which bands the movement of electrons and holes take place?

  7. Can both types of current flow, i.e due to holes and electrons, take place in one particular type of semiconductor? What is the ratio of majority and minority charge carriers in intrinsic and extrinsic semiconductors?

  8. Why does the fifth valent element not liberate as many holes in the valence band as electrons in the conduction band? Are n-type and p-type materials neutral? How does a semiconductor differ from a conductor? What is meant by doping?

  9. What are donor and acceptor impurities? What proportion of impurity should be mixed in an intrinsic Si or Ge for manufacturing junction diode or BJT?

  10. What is meant by Fermi level in semiconductor? Where does the Fermi level lie in an intrinsic semiconductor? Prove that the Fermi level in an n-type material is much closer to the conduction band. Prove that the Fermi level in a p-type material is much closer to the valence band.

  11. Show the donor and acceptor levels on the band diagram of n-and p-type materials. Define diffusion constant of electrons and holes. Define mean life-time of a carrier.

  12. Define mobility of a carrier. Show that mobility constant of electron is larger than that of a hole? The Fermi level of intrinsic semiconductor lies in the middle of the band gap but in an n-type semiconductor it is nearer to the conduction band. What is the effect of temperature on the position of Fermi level of a semiconductor?

  13. In an n-type Si the donor concentration is 1 atom per 2 × 108 silicon atoms. Assuming that the effective mass of electron is equal to the mass of electron at rest. Find the value of temperature at which the Fermi level will coincide with the edge of the conduction band.

  14. The current of p-n junction is expressed as


    rent is 0.5 mA at V = 0.34 V and 15 mA at 0.44 V. Calculate the value of η assuming KT/q = 25 mV.

  15. Calculate the conductivity of an n-type semiconductor having electron density 1021/m3 and mobility 1200 cm2/Vs. (IETE June, 1996)


  16. The resistivity of intrinsic Ge at 300 K is 0.47 Ω. The electron and hole mobilities are 0.38 and 0.18 m2/Vs, calculate the intrinsic carrier density at 200 K. (IETE Dec., 1996)


  17. If the carrier mobility in a sample is 3 m2/V sec at 0°C, what is the diffusion constant of carrier at that temperature given that Boltzmann constant is 1.38 × 10−21J/K.


1.16.2. Multiple Choice Questions

  1. A Ge atom contains

    (a) four orbits

    (b) two orbits

    (c) five valence holes

    (d) four valence electrons.

  2. Two atoms of the semiconductor are held together by

    (a) valance bond

    (b) ionic bond

    (c) metallic bond

  3. Intrinsic semiconductor at absolute zero behaves as

    (a) insulator

    (b) metal

    (c) semiconductor

  4. An electron in conduction band has

    (a) no charge

    (b) higher energy than electron in the valance band

    (c) lower energy than the electron in the valance band

  5. At room temperature when voltage is applied to the intrinsic semiconductor

    (a) electrons move towards the positive terminal and holes move towards the negative terminal

    (b) both holes and electrons move towards the positive terminal

    (c) booth holes and electrons move towards the negative terminal

  6. With the increase in the temperature of the intrinsic semiconductor

    (a) energy of atom increases

    (b) holes are generated in the conduction band

    (c) resistance of the semiconductor increases

    (d) atomic radius decreases

  7. Fifth group elements are called

    (a) donor impurity

    (b) acceptor impurity

    (c) none

  8. The p-type impurities create

    (a) excess number of electrons

    (b) excess number of holes

    (c) excess number of ionized positive charges

  9. If small amount of antimony is added to silicon

    (a) its resistance increases

    (b) the silicon will become p-type

    (c) it contains more free electrons than holes

  10. If small amount of gallium is added to germanium

    (a) it becomes p-type material

    (b) it has more number of electrons

    (c) it becomes an insulator

  11. Conduction band is

    (a) the same as valance band

    (b) always located at the top of the crystal

    (c) is called forbidden band

    (d) the energy band above forbidden band

  12. Forbidden band is

    (a) above conduction band

    (b) below valance band

    (c) between valance and conduction band

  13. The concentration of minority carriers in the n-type semiconductor depends on

    (a) doping technique

    (b) temperature of the material

    (c) quality of intrinsic Ge or Si

    (d) number of donor atoms

  14. A neutral semiconductor

    (a) has no free charge carrier

    (b) has equal number of electrons and holes

    (c) has no minority carrier

    (d) has no majority carrier

  15. A p-type material is

    (a) neutral

    (b) negatively charged

    (c) positively charged

    (d) insulator

  16. A n-type material has

    (a) electrons as majority carriers

    (b) holes as majority carriers

    (c) both positive and negative charge carriers are equal in number

  17. When an atom is ionized, it releases

    (a) negative charge carrier

    (b) positive charge carrier

    (c) negative ion

    (d) positive ion

  18. When an atom loses an electron it becomes

    (a) positively charged

    (b) negatively charged ion

    (c) electrically neutral

    (d) positive charge carrier

  19. Resistivity of semiconductor depends upon

    (a) shape and its length

    (b) its carrier concentration

    (c) neither shape nor carrier concentration

  20. A n-type material induces an impurity energy level in

    (a) the energy gap

    (b) conduction band

    (c) valance band

    (d) none of these

  21. The process of doping

    (a) increases conductivity

    (b) decreases conductivity

    (c) neither increases nor decreases conductivity

  22. Resistivity of a good conductor is

    (a) 10−8 Ωm

    (b) 108 Ωm

    (c) 106 Ωm

    (d) 1012 Ωm

  23. Resistivity of a good insulator is

    (a) 10−8 Ωm

    (b) 108 Ωm

    (c) 1010 or 1012 Ωm

    (d) 10−10 or 10−12 Ωm

  24. Semiconductor material includes

    (a) only elements

    (b) only intermetallic compounds

    (c) both elements and intermetallic compounds

  25. Every time a covalent bond is broken it results in

    (a) free electron

    (b) free hole

    (c) electron hole pair

  26. Intrinsic semiconductor contains

    (a) more number of electrons

    (b) more number of holes

    (c) equal number of electrons and holes

    (d) equal number of negative and positive immobile charges

  27. On an average at 25°C × in a Si crystal, out of 1019 bonds

    (a) one is broken

    (b) no bond is broken

    (c) infinite bonds are broken

  28. At room temperature in silicon, out of 1010 bonds

    (a) one bond is broken

    (b) infinite bonds are broken

    (c) no bonds are broken

  29. Normally used semiconductor materials are

    (a) C, Na

    (b) Si, Ge

    (c) GaAsP

  30. Good conductors are

    (a) silver, aluminium, copper etc.

    (b) glass, quartz

    (c) Ge, Si

  31. With the increase in temperature resistivity of a conductor

    (a) increases

    (b) decreases

    (c) remains constant

  32. With the increase in temperature the resistivity of the semiconductor

    (a) increases

    (b) decreases

    (c) neither increases nor decreases

  33. At higher temperature conductivity is better in

    (a) semiconductor

    (b) metal

    (c) insulator

  34. Temperature coefficient of semiconductor is

    (a) positive

    (b) negative

    (c) neither positive nor negative

    (d) zero

  35. Extrinsic semiconductor is

    (a) pure semiconductor

    (b) impure semiconductor

    (c) neither pure nor impure

  36. Conductivity of a semiconductor can be controlled by

    (a) adding impurity

    (b) increasing size

    (c) changing temperature

  37. A semiconductor is called intrinsic even if impurity is

    (a) one part in hundred million parts of semiconductor

    (b) 100 in 100 million parts of semiconductor

    (c) 1000 in 100 million parts of semiconductor

  38. In an intrinsic silicon the band gap is

    (a) 1.12 eV

    (b) 0.7 eV

    (c) 2 eV

    (d) 0.2 eV

  39. In an intrinsic Ge the band gap is

    (a) 1.12 eV

    (b) 0.7 eV

    (c) 0.2 eV

    (d) 0.6 eV

  40. Conductivity of pure Ge is approximately

    (a) 2.2 S/m

    (b) 5 × 10−4S/m

    (c) 5 × 104S/m

  41. Conductivity of pure Si is nearly

    (a) 2.3 × 109 S/m

    (b) 5 × 10−4 S/m

    (c) 3.85 × 107 S/m

  42. Conductivity of Al is

    (a) 3.85 × 107 S/m

    (b) 6.25 × 10−7 S/m

    (c) 5 × 10−4 S/m

  43. Conductivity of glass is

    (a) 1.54 S/m

    (b) 5.88 × 10−12 S/m

    (c) 110−16 S/m

  44. Conductivity of hard rubber is

    (a) 5 × 10−4 S/m

    (b) 5.88 × 10−12 S/m

    (c) 10−16 S/m

  45. Mobility of holes in intrinsic Si is

    (a) 0.048 m2/Vs

    (b) 0.135 m2/Vs

    (c) 1350 m2/Vs

    (d) 480 m2/Vs

  46. Mobility of electrons in intrinsic Si is

    (a) 0.135 m2/Vs

    (b) 0.048 m2/Vs

    (c) 480 m2/Vs

    (d) 13.5 m2/Vs

  47. Mobility of electrons in intrinsic Ge is

    (a) 0.39 m2/Vs

    (b) 0.19 m2/Vs

    (c) 390 m2/Vs

    (d) 190 m2/Vs

  48. Mobility of holes in intrinsic Ge is

    (a) 0.39 m2/Vs

    (b) 0.19 m2/Vs

    (c) 3900 m2/Vs

    (d) 1900 m2/Vs

  49. Carrier density in intrinsic Si is

    (a) 1.5 × 1016/m3

    (b) 15 × 1016/m3

    (c) 150 × 1016/m3

  50. Electron hole pair in intrinsic Ge crystal at 300K is nearly

    (a) 2.5 × 1019/m3

    (b) 240 × 1019/m3

    (c) 2400 × 1019/m3

  51. Resistivity of intrinsic Si is nearly

    (a) 2300 Ωm

    (b) 23 Ωm

    (c) 0.23 Ωm

  52. Resistivity of intrinsic Ge is nearly

    (a) 0.46 Ωm

    (b) 46 Ωm

    (c) 460 Ωm

    (d) 1000 Ωm

  53. The value of q/KT at room temperature is approximately

    (a) 40/V

    (b) 400/V

    (c) 0.40/V

  54. The conduction band in intrinsic semiconductor is

    (a) above the valence band

    (b) below the valence band

    (c) in the valance band

  55. Mobile electrons are found in

    (a) conduction band

    (b) valence band

    (c) below the valence band

    (d) in the band gap

  56. Mobile hole are found in

    (a) conduction band

    (b) valence band

    (c) below the valence band

    (d) in the band gap

  57. Fermi level in the intrinsic Si/Ge is

    (a) in the middle of the band gap

    (b) near the valance band

    (c) near the conduction band

  58. The energy required to dislodge electrons from n-type Si is

    (a) 0.05 eV

    (b) 5 eV

    (c) 50 eV

  59. The donor energy band is available in n-type material in the

    (a) conduction band

    (b) valance band

    (c) in the band gap

  60. The acceptor energy band is available in p-type material in the

    (a) band gap

    (b) conduction band

    (c) in the valance band

  61. The diffusion constant of electron in Si is

    (a) 35 × 10−4 m2/s

    (b) 0.34 × 10−4 m2/s

    (c) 3400 × 10−4 m2/s

  62. The diffusion constant of holes in Si is

    (a) 12 × 10−4 m2/s

    (b) 0.13 × 10−4 m2/s

    (c) 1300 × 10−4 m2/s

  63. The diffusion constant of electrons in Ge is

    (a) 100 × 10−4 m2/s

    (b) 99 × 10−4 m2/s

    (c) 9900 × 10−4 m2/s

  64. The diffusion constant of holes in Ge is

    (a) 49 × 10−4 m2/s

    (b) 0.47 × 10−4 m2/s

    (c) 4700 × 10−4 m2/s

  65. The density of Ge at 25°C is

    (a) 5.3 × 109 kg/m3

    (b) 533 × 109 kg/m3

    (c) 0.53 × 109 kg/m3

  66. The density of Si at 25°C is

    (a) 2.33 × 109 kg/m3

    (b) 233 × 109 kg/m3

    (c) 0.0233 × 109 kg/m3

  67. The intrinsic carrier concentration of electron in Ge at 25°C is

    (a) 2.5 × 1010 atoms/m3,

    (b) 0.025 × 1019 atoms/m3

    (c) 250 × 1019 atoms/m3

  68. The majority carrier in n-type material are

    (a) electrons

    (b) holes

    (c) ionized positive charge

  69. The minority carrier in n-type material are

    (a) electrons

    (b) holes

    (c) ionized negative charge

  70. The majority carriers in p-type material are

    (a) holes

    (b) electrons

    (c) immobile positive charge

  71. In order to get excess electrons from the intrinsic semiconductor one can add to tetravalent element

    (a) pentavalent element

    (b) trivalent element

    (c) tetravalent element

  72. In order to get excess holes from the intrinsic semiconductor one can add to tetra valent element

    (a) pentavalent element

    (b) trivalent element

    (c) tetravalent element

  73. Electrons in the outermost orbit are called

    (a) valence electrons

    (b) conduction electrons

    (c) donor electrons

  74. Energy of electrons in bigger orbit is

    (a) higher

    (b) lower

    (c) constant

  75. The forces holding the Si/Ge atoms together in a crystal are called

    (a) valance bond

    (b) ionic bond

    (c) metallic bond

  76. Doped crystal is called

    (a) intrinsic

    (b) extrinsic

    (c) both

  77. Velocity of electron is

    (a) proportional to its mobility

    (b) inversely proportional to its mobility

    (c) constant

  78. Velocity of holes/electrons are proportional to

    (a) electric filled

    (b) magnetic field

    (c) inverse of magnetic field

  79. Ionization energy of As, P and Sb in Ge are arranged in sequence as

    (a) 0.045 eV, 0.049 eV, 0.039 eV

    (b) 0.049 eV, 0.039 eV, 0.045 eV

    (c) 0.039 eV, 0.045 eV, 0.049 eV

  80. Ionization energy of As, P and Sb elements in Si crystal are

    (a) higher than that in Ge

    (b) lower than that in Ge

    (c) equal to Ge

  81. Ionization energy decreases slightly with

    (a) increasing impurity contents

    (b) decreasing impurity contents

    (c) remains constant

  82. An intrinsic semiconductor is

    (a) pure

    (b) impure

    (c) free from impurity

  83. The intrinsic semiconductor has

    (a) more electrons

    (b) more holes

    (c) none of the two

  84. At room temperature the intrinsic semiconductor behaves as

    (a) metal

    (b) semiconductor

    (c) insulator

  85. The extrinsic semiconductor at room temperature has

    (a) free charge carriers

    (b) no free charge carriers

    (c) qA = (n + p)

  86. An n-type material has more numbers of

    (a) free electrons

    (b) free holes

    (c) none of the above.

  87. An p-type material has more numbers of

    (a) free electrons

    (b) free holes

    (c) none of the above

  88. The resistance of a material is expressed as

    (a) LqA(n + p)

    (b) qA(n + p)/L

    (c) AL/qA(n + p)

    (d) qA(n + p)/L

  89. The resistivity of a material is expressed as

    (a) L/qA(n + p)

    (b) qA(n + p)/L

    (c) 1/qA(n + p)

  90. The conductivity of a material is expressed as

    (a) q(n + p)

    (b) qA/(n + p)

    (c) 1/q(n + p)

  91. The Fermi level of an intrinsic semiconductor lies

    (a) near conduction band

    (b) near valence band

    (c) in the middle of the valence and conduction band

  92. The Fermi function is expressed as


  93. The primary bonds are

    (a) ionic, metallic, and vander Waal bonds

    (b) ionic, covalent, and vander Waal bonds

    (c) ionic, covalent, and metallic

  94. The mean free path in an ideal crystal without imperfections and impurities is

    (a) infinite at 0 K

    (b) zero at 0 K

    (c) infinite at all temperatures

    (d) zero at all temperatures

  95. Glass and Bakelite are

    (a) crystalline

    (b) amorphous

    (c) solid solution

  96. With increase in temperature, average velocity of atom

    (a) increases

    (b) decreases

    (c) remains constant

  97. The Fermi level in a n-type material is expressed as

    (a) EC − KTln(NC/nn)

    (b) EC − KTln(NC/nn)

    (c) EC − KTln(ND/nn)

  98. The Fermi-level in a p-type material is expressed as

    (a) EV − KTln(NV/pp)

    (b) EV − KTln(NV/pp)

    (c) EV − KTln(ND/pp)

  99. The VT is expressed as

    (a) KT/q

    (b) q/KT

    (c) KTq

    (d) nKTq

  100. The diffusion constant and the mobility of electron are related as

    (a) Dn/μn = KT/q

    (b) Dn/μn = q/KT

    (c) Dn/μn = KT/q

  101. The diffusion constant and the mobility of electron and hole are related as

    (a) Dn/μn = KT/q

    (b) Dn/μn = q/KT = μp/Dp

    (c) Dn/μn = KTq = μp/Dp

  102. The diffusion current is influenced by

    (a) concentration gradient

    (b) electric field

    (c) electrostatic field

  103. The drift plus diffusion current density of electron in amp/m2 is expressed as

    (a) Jn = {qnμnE + qDn(dn/dx)}

    (b) Jn = {qnμnE + qDn(dn/dx)}

    (c) Jn = {qnμnE + AqDn(dn/dx)}

  104. The drift plus diffusion current density of holes in amp/m2 is expressed as

    (a) Jp = qnμpE + qDp(dp/dx)

    (b) Jp = qnμpE + qDp(dp/dx)

    (c) Jp = qnμpE + qDpA(dp/dx)

  105. Electron population in silicon is not

    (a) zero in the forbidden band

    (b) zero in the conduction band at 0 K

    (c) zero at the conduction band edge EC

    (d) zero in the conduction band at room temperature.

    Explanation:(d) The carrier concentration is zero in the forbidden band. At 0 K, electrons are filled in the available states only upto the Fermi level, which lies below the conduction band edge (EC) and hence, the concentration is zero in the conduction band. Also from density-of-state function, the number of available states at the band edges is always zero. Hence, conduction electrons in the conduction band due to thermal generation from the valence band as well as due to dopants are present in the silicon at all temperatures.

  106. The density of states function for holes is

    (a) zero in the valence band edge (EV)

    (b) zero in the forbidden band edge

    (c) zero in the complete conduction band

    (d) zero in all bands other than the valence band. Explanation is presented in Q.105.

  107. The Fermi-Dirac statistics is based on

    (a) electron and photons

    (b) photons and protons

    (c) electrons and holes

    (d) Gas molecules

    Explanation: Fermi-Dirac statistics are valid for particles which obey the Pauli exclusion principle, i.e. the concept of finite limited occupancy of state applies.

1.16.3. Answers to Multiple Choice Questions

  1. (d)

  2. (a)

  3. (a)

  4. (b)

  5. (a)

  6. (a)

  7. (a)

  8. (b)

  9. (c)

  10. (a)

  11. (d)

  12. (c)

  13. (b)

  14. (b)

  15. (a)

  16. (c)

  17. (a)

  18. (a)

  19. (b)

  20. (a)

  21. (a)

  22. (a)

  23. (c)

  24. (c)

  25. (c)

  26. (c)

  27. (b)

  28. (a)

  29. (b)

  30. (a)

  31. (a)

  32. (b)

  33. (a)

  34. (b)

  35. (b)

  36. (a)

  37. (a)

  38. (a)

  39. (b)

  40. (a)

  41. (b)

  42. (a)

  43. (b)

  44. (b)

  45. (a)

  46. (a)

  47. (a)

  48. (b)

  49. (a)

  50. (a)

  51. (a)

  52. (a)

  53. (a)

  54. (a)

  55. (a)

  56. (b)

  57. (a)

  58. (a)

  59. (c)

  60. (a)

  61. (a)

  62. (a)

  63. (a)

  64. (a)

  65. (a)

  66. (a)

  67. (a)

  68. (a)

  69. (b)

  70. (a)

  71. (a)

  72. (b)

  73. (a)

  74. (a)

  75. (a)

  76. (b)

  77. (a)

  78. (a)

  79. (a)

  80. (a)

  81. (a)

  82. (a)

  83. (c)

  84. (c)

  85. (b)

  86. (a)

  87. (b)

  88. (a)

  89. (c)

  90. (a)

  91. (c)

  92. (a)

  93. (c)

  94. (a)

  95. (b)

  96. (a)

  97. (a)

  98. (b)

  99. (a)

  100. (a)

  101. (a)

  102. (a)

  103. (a)

  104. (b)

  105. (d)

  106. (a) and (b)

  107. (c)

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