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- Question : Q1 - A silicon sample is uniformly doped with 1016 phosphorus atoms/cm3 and 2 1016 boron atoms/cm3. If all the dopants are fully ionized, the material is: (a) n-type with carrier concentration of 3 1016/cm3 (b) p-type with carrier concentration of 1016/cm3 (c) p-type with carrier concentration of 4 1016/cm3 (d) Intrinsic
- Question : Q2 - n-type semiconductors are: (a) Negatively charged (b) Produced when Indium is added as an impurity to Germanium (c) Produced when phosphorous is added as an impurity to silicon (d) None of the above
- Question : Q3 - The probability that an electron in a metal occupies the Fermi-level, at any temperature ( > 0 K) is: (a) 0 (b) 1 (c) 0.5 (d) None of the above
- Question : Q4 - Measurement of Hall coeffi cient enables the determination of: (a) Mobility of charge carriers (b) Type of conductivity and concentration of charge carriers (c) Temperature coeffi cient and thermal conductivity (d) None of the above
- Question : Q5 - If the energy gap of a semiconductor is 1.1 eV it would be: (a) Opaque to the visible light (b) Transparent to the visible light (c) Transparent to the ultraviolet radiation (d) None of the above
- Question : Q6 - The conductivity of an intrinsic semiconductor is given by (symbols have the usual meanings): (a) ?i eni 2(?n
- Question : Q7 - Consider the following statements: Compared to Silicon, Gallium Ars enide (GaAs) has: 1. Higher signal speed since electron mobility is higher 2. Poorer crystal quality since stoichiometric growth diffi cult 3. Easier to grow crystals since the vapour pressure Arsenic is high 4. Higher optoelectronic conversion effi ciency Of these statements: (a) 1, 2, 3 and 4 are correct (b) 1, 2 and 3 are correct (c) 3 and 4 are correct (d) None of the above
- Question : Q8 - In an intrinsic semiconductor, the mobility of electrons in the conduction band is: (a) Less than the mobility of holes in the valence band (b) Zero (c) Greater than the mobility of holes in the valence band (d) None of the above
- Question : Q9 - The Hall coeffi cient of sample (A) of a semiconductor is measured at room temperature. The Hall coeffi cient of (A) at room temperature is 4 10 4 m3 coulomb 1. The carrier concentration in sample (A) at room temperature is: (a) ~1021 m
- Question : Q10 - In a semiconductor, J, Jp and Jn indicate total diffusion current density hole current density and electron current density respectively, ?_n_ ?x and _?_p_ ?x are the electron and hole concentration gradient respectively in x-direc tion and Dp and Dn are the hole and electron diffusion constants respectively. Which one of the following equations is correct? (e denotes charge of electron). (a) Jn
- Question : Q11 - If the drift velocity of holes under a fi eld gradient of 100 v/m is 5 m/s, the mobility (in the same SI units) is: (a) 0.05 (b) 0.55 (c) 500 (d) None of the above
- Question : Q12 - The Hall effect voltage in intrinsic silicon is: (a) Positive (b) Zero (c) Negative (d) None of the above
- Question : Q13 - The Hall coeffi cient of an intrinsic semiconductor is: (a) Positive under all conditions (b) Negative under all conditions (c) Zero under all conditions (d) None of the above
- Question : Q14 - Consider the following statements: Pure germanium and pure silicon are examples of: 1. Direct band-gap semiconductors 2. Indirect band-gap semiconductors 3. Degenerate semiconductors Of these statements: (a) 1 alone is correct (b) 2 alone is correct (c) 3 alone is correct (d) None of the above
- Question : Q15 - Assume ne and nh are electron and hole densities, and ?e and ?n are the carrier mobilities; the Hall coeffi cient is positive when: (a) nh ?h > ne ?e (b) nh ?h 2 > ne ?e 2 (c) nh ?h < ne ?h (d) None of the above
- Question : Q16 - A long specimen of p-type semiconductor material: (a) Is positively charged (b) Is electrically neutral (c) Has an electric fi eld directed along its length (d) None of the above
- Question : Q17 - The electron and hole concentrations in an intrinsic semiconductor are ni and pi respectively. When doped with a p-type material, these change to n and P respectively. Then: (a) n + p ni + pi (b) n + ni p + pi (c) np ni pi (d) None of the above are applicable
- Question : Q18 - If the temperature of an extrinsic semiconductor is increased so that the intrinsic carrier concentration is doubled, then: (a) The majority carrier density doubles (b) The minority carrier density doubles (c) Both majority and minority carrier densities double (d) None of the above
- Question : Q19 - At room temperature, the current in an intrinsic semiconductor is due to: (a) Holes (b) Electrons (c) Holes and electrons (d) None of the above
- Question : Q20 - A semiconductor is irradiated with light such that carriers are uniformly generated throughout its volume. The semiconductor is n-type with ND 1019 per cm3. If the excess electron concentration in the steady state is ?n 1015 per cm3 and if ?p 10 ?sec. (minority carrier life time) the genera tion rate due to irradiation is:(a) 1022 e-h pairs /cm3 /s (b) 1010 e-h pairs/cm3 /s (c) 1024 e-h pairs/cm3/s (d) None of the above
- Question : Q21 - A small concentration of minority carriers is injected into a homogeneous semiconductor crystal at one point. An electric fi eld of 10 V/cm is applied across the crystal and this moves the minority carriers a distance of 1 cm is 20 ?sec. The mobility (in cm2/volt.sec) is: (a) 1,000 (b) 2,000 (c) 50 (d) None of the above
- Question : Q22 - The mobility is given by: (a) ? _V_0 E0 (b) ? V0 2 _____ E0 (c) ? V__0_ E0 2 (d) None of the above
- Question : Q23 - Hall effect is observed in a specimen when it (metal or a semiconductor) is carrying current and is placed in a magnetic fi eld. The resultant electric fi eld inside the specimen will be in: (a) A direction normal to both current and magnetic fi eld (b) The direction of current (c) A direction anti parallel to magnetic fi eld (d) None of the above
- Question : Q24 - In a p-type semiconductor, the conductivity due to holes (?p) is equal to: (e is the charge of hole, ?p is the hole mobility, p0 is the hole concentration):
- Question : Q25 - The difference between the electron and hole Fermi energies of a semiconductor laser is 1.5 eV and the band gap of the semiconductor is 1.43 eV. The upper and lower frequency limits of the laser will be respectively: (a) 3.3 1015 and 9.9 1013 Hz (b) 3.7 1016 and 3.5 1014 Hz
- Question : Q26 - A sample of n-type semiconductor has electron density of 6.25 1018/cm3 at 300 K. If the intrinsic concentration of carriers in this sample is 2.5 1013/cm3 at this temperature, the hole density becomes: (a) 1016/cm3 (b) 107/cm3 (c) 1017/cm3 (d) None of the above
- Question : Q27 - The intrinsic carrier density at 300K is 1.5 1010/cm3 in silicon. For n-type silicon doped to 2.25 1015 atoms/cm3 the equilibrium electron and hole densities are: (a) n0 1.5 1016/cm3, p0 1.5 1012/cm3 (b) n0 1.5 1010/cm3, p0 2.25 1015/cm3 (c) n0 2.25 1017/cm3, p0 1.0 1014/cm3 (d) None of the above
- Question : Q28 - In a p-type silicon sample, the hole concentration is 2.25 1015/cm3. If the intrinsic carrier concentration 1.5 1010/cm3 the electron concentra tion is: (a) 1021/cm3 (b) 1010/cm3 (c) 1016/cm3 (d) None of the above
- Question : Q29 - A good ohmic contact on a p-type semiconductor chip is formed by intro ducing: (a) Gold as an impurity below the contact (b) A high concentration of acceptors below the contact (c) A high concentration of donors below the contact (d) None of the above
- Question : Q30 - Measurement of Hall coeffi cient in a semiconductor provides information on the: (a) Sign and mass of charge carriers (b) Mass and concentration of charge carriers (c) Sign of charge carriers alone (d) Sign and concentration of charge carriers
- Question : Q1 - Briefl y discuss the basic developments in the study of electronics.
- Question : Q2 - What are crystalline materials?
- Question : Q3 - Give three examples of Group III-V semiconductors.
- Question : Q4 - What do you mean by pure crystals?
- Question : Q5 - Why is Si preferred over Ge?
- Question : Q6 - Why is GaAs preferred over Si?
- Question : Q7 - Give an example of the constituent material of Gunn Diode.
- Question : Q8 - What is Bravais lattice? Discuss briefl y.
- Question : Q9 - What are unit cells and lattice constants?
- Question : Q10 - Explain the differences among simple cubic, body-centred cubic and face-centred cubic lattices respectively
- Question : Q11 - Explain Czochralski growth of the semiconductor crystal in detail.
- Question : Q12 - Explain the wave particle duality principle.
- Question : Q13 - State Pauli exclusion principle.
- Question : Q14 - What is degenerate energy level?
- Question : Q15 - What is energy band gap?
- Question : Q16 - What do you mean by covalent and electrovalent bonds? How these are affected by the temperature?
- Question : Q17 - Explain thermal equilibrium.
- Question : Q18 - What is valence band and conduction band?
- Question : Q19 - What are conduction band carriers?
- Question : Q20 - Explain the existence of hole.
- Question : Q21 - What is momentum effective mass of the carriers? What is its difference with acceleration effective mass?
- Question : Q22 - Explain indistinguishability between the particles. What should be the value of the spin of the particles obeying Fermi
- Question : Q23 - Explain the term
- Question : Q24 - What is bonding model?
- Question : Q25 - Explain the energy band models of semiconductors.
- Question : Q26 - Write the assumptions behind Fermi
- Question : Q27 - Write the fi ve properties of the Fermi
- Question : Q28 - Defi ne Fermi energy. How does Fermi energy vary with temperature?
- Question : Q29 - Write the basic criterion for the classifi cation of metals, semiconductors and insulators.
- Question : Q30 - Draw the model energy band structure diagram of a semiconductor in general.
- Question : Q31 - The split-off hole parabola is more fl attened than the light hole parabola. Justify your answer very briefl y.
- Question : Q32 - What are intrinsic semiconductors?
- Question : Q33 - What are extrinsic semiconductors?
- Question : Q34 - Explain donor ion, acceptor ion, majority carriers, minority carriers, doping and dopants in a semiconductor
- Question : Q35 - What do you mean by the term
- Question : Q36 - What are compound semiconductors? Explain the uses of compound semiconductors.
- Question : Q37 - Explain the difference between metals, insulators and semiconductors with the help of band structure model.
- Question : Q38 - Defi ne the term
- Question : Q39 - Derive an expression of electron concentration in n-type semiconductors. Discuss all the special cases.
- Question : Q40 - Derive an expression of electron concentration in p-type semiconductors. Discuss all the special cases.
- Question : Q41 - What is charge density equation?
- Question : Q42 - Show that:where, the notations mean as usual.
- Question : Q43 - Derive the law of mass action. Is it valid for degenerate semiconductors? Give reasons.
- Question : Q44 - Does the band gap vary with temperature? Give reasons.
- Question : Q45 - How does concentration vary with temperature?
- Question : Q46 - What is mobility?
- Question : Q47 - What is relaxation time?
- Question : Q48 - 48.What is conductivity?
- Question : Q49 - What is Mathiessen
- Question : Q50 - What is diffusion?
- Question : Q51 - What is recombination?
- Question : Q52 - What is generation?
- Question : Q53 - Prove that: _D__n ?n KB___T_ e [F
- Question : Q54 - Write the assumptions of continuity equation and derive continuity equation.
- Question : Q55 - Explain physically the continuity equation.
- Question : Q56 - What is Hall effect?
- Question : Q57 - Derive the relation between mobility and Hall coeffi cient.
- Question : Q58 - What are the applications of Hall effect?
- Question : Q59 - Find out an expression for Hall coeffi cient in a semiconductor when both carriers contribute to the current.
- Question : P1 - The energy spectrum of the conduction electrons of III-V compound semiconductors can be expressed as E[ 1 + (E/ Eg) ] _ _h_2 k_2 2 mc * where the notations have their usual meaning. Find out the momentum effective mass and the acceleration effective mass of the conduction electrons respectively. Draw the plots in two cases on the same graph paper with the independent variable as energy by taking the example of n-GaAs. Interpret the results. Explain the results for Eg ? ?.
- Question : P2 - The dispersion relation of the carriers in a semiconductor is approximately given by E E0
- Question : P3 - (a) Calculate the coordinates of three points on the Fermi
- Question : P4 - In a certain silicon sample at equilibrium, the Fermi level resides at 0.500 eV above the centre of the band gap. (a) Calculate the occupancy probability for a lone isolated state located right at the centre of the band gap. (b) This sample contains donor impurities and no acceptor impurities. The donor states are situated 0.045 eV below the conductionband edge. Find the occu pancy probability of the donor states. (c) Comment on the validity of the assumption of 100 per cent ionization of the donor states in the present situation (d) Derive an approximate form of the Fermi
- Question : P5 - The conduction band can be characterized by a state density (number of states per cm3) of Nc 3.75 1019/cm3, with these states assumed to be situated right at the conduction-band edge. (a) Using this assumption, calculate the conduction- electron density n0 (number of electrons per cm3) for the conditions of Problem 4. (b) The valence band can be characterized by a state density of Nv ? Nc, with these states assumed to be situated right at the valence-band edge. Using this assump tion, calculate the hole density p0. (c) Calculate the p
- Question : P6 - Determine the approximate density of donor states ND (number of donor states per cm3) for the silicon sample of Problems 4 and 5. Provide reasons
- Question : P7 - Derive an expression relating the intrinsic level Ei to the centre of the band gap Eg /2. Calculate the displacement of Ei from Eg /2 for Si at 300 K, assum ing the effective mass values for electrons and holes are 1.1 m0 and 0.56 m0, respectively.
- Question : P8 - (a) Explain why holes are found at the top of the valence band, whereas elec trons are found at the bottom of the conduction band.
- Question : P9 - Calculate the Nc and Nv for the conduction and valence bands of Si and GaAs at 100 K, 200 K and 400 K respectively by assuming the data you require
- Question : P10 - A certain uniformly doped silicon sample at room temperature has n0 106/cm3 and NA 1015/cm3. (a) Find p0. (b) Find ND
- Question : P11 - Using the Boltzmann approximation to the Fermi
- Question : P12 - Given that the majority impurity in the foregoing problem is phosphorus, fi nd the occupancy probability at the donor level. Comment on the assumption of 100 per cent ionization in this case.
- Question : P13 - A silicon sample has NA 1015/cm3 and ND 0. Find the: (a) Majority-carrier density (b) Minority-carrier density (c) Conductivity
- Question : P14 - A certain silicon sample has p0 2.5 l0l0 / cm3. Find the: (a) Electron density n0 (b) Resistivity ?
- Question : P15 - Calculate the position of the intrinsic Fermi level measured from the midgap for InAs.
- Question : P16 - Calculate and plot the position of the intrinsic Fermi level in Si between 80 K and 400 K
- Question : P17 - Calculate the density of electrons in silicon if the Fermi level is 0.45 eV below the conduction bands at 290 K. Compare the results by using the Boltzmann ap proximation and the Fermi
- Question : P18 - In a GaAs sample at 310 K, the Fermi level coincides with the valence band-edge. Calculate the hole density by using the Boltzmann approximation. Also calculate the electron density using the law of mass action.
- Question : P19 - The electron density in a silicon sample at 310 K is 1015 cm
- Question : P20 - A GaAs sample is doped n-type at 4 1018 cm
- Question : P21 - Consider a n-type silicon with a donor energy 60 meV below the con duction band. The sample is doped at 1015 cm
- Question : P22 - Consider a GaAs sample doped at Nd 1015 cm
- Question : P23 - Estimate the intrinsic carrier concentration of diamond at 700 K (you can assume that the carrier masses are similar to those in Si). Compare the results with those for GaAs and Si.
- Question : P24 - A Si device is doped at 2.5 1016 cm
- Question : P25 - Estimate the change in intrinsic carrier concentration per K change in temperature for Ge, Si, and GaAs and InSb at 300 K.
- Question : P26 - A certain silicon sample has ND 5.30 1015/cm3 and NA 4.50 1015/cm3. Find the: (a) Majority-carrier density (b) Minority-carrier density (c) Conductivity ?, using ?n 400 cm2/Vs, and ?p 300 cm2/Vs (d) n0 (e) ? using ?n 500 cm2/V.s and ?p 300 cm2/
- Question : P27 - A silicon samples is doped with 2.5 1015 phosphorus atoms per cubic centimetre and 0.5 1015
- Question : P28 - A silicon sample has ND 1016/cm3 and NA 0. (a) Find ?. (b) What is the conductivity type of the sample in (a)? (c) Another sample has ND 0.5 1014/cm3 and NA 1016/cm3. Find p0. (d) Find n0 in the sample of c. (e) Another sample has ND 1.5 10l5/cm3 and NA 10l5/cm3. Find p0. (f) Find n0 in the sample of (e). (g) Another sample has ND 0.79 1014/cm3 and NA 1015/cm3. Find p0. (h) Find n0 in the sample of (g).
- Question : P29 - A Silicon specimen in the form of circular cylinder (Length L 20 mm, area of cross-section A 2 mm2 and resistivity ? 15 ohm cm is placed in series with an ideal battery of 2 V in a complete circuit. Answer the following questions. (a) Calculate hole current density Jp. (b) Calculate electron current density Jn. (c) How Jn is affected by doubling sample length L and keeping A, ? and applied voltage V the same as in part (a)? (d) How is Jn affected by doubling cross-sectional area A and keeping ?, applied voltage V, and sample length L the same as in part (a)?
- Question : P30 - Ohmic contacts are made to the ends of a silicon resistor having a length L 0.5 cm. The resistor has a cross-sectional area A that is given by the product of its width W and thickness X, where W 1 mm and X 2 ?m. The silicon is uniformly doped with NA 2.5 1015 cm3 and ND 2.5 10l5/cm3. For this dop ing density, ?p 250 cm2/Vs and ?n 400 cm2/Vs. Find the resistance R
- Question : P31 - A silicon sample contains 3.5 1016/cm3 of one impurity type and a negli gible amount of the opposite type. It exhibits a resistivity of 0.22 ?
- Question : P32 - (a) Given an extrinsic but lightly doped n-type silicon resistor R of length L and cross-sectional area A, derive an expression for its net impurity density. (b) For the resistor with, R 1 kilo-ohm, L 5 mm, and A 1.5 mm2. Evaluate the expression derived in a. What is the probable majority impurity in the resistor?
- Question : P33 - Minority carriers in a particular silicon sample drift 1 cm in 100 ?s when E0 15 V/cm. (a) Determine drift velocity V0. (b) Determine minority-carrier diffusivity D. (c) Determine the conductivity type of the sample and explain your reason ing. A sample of heavily doped p-type silicon has a drift-current density of 100 A/cm2. Hole drift velocity is 50 cm/s. Find hole density p0
- Question : P35 - Calculate the intrinsic carrier concentration of Si, Ge and GaAs as a function of temperature from 4 K to 600 K. Assume that the band gap is given by: Eg(T) Eg (0)
- Question : P36 - The resistance of No. 18 copper wire (having a diameter d 1.15 mm) is 6.5 ohm / l000 ft. The density of conduction electrons in copper is n0 8.3 1022/cm3
- Question : P37 - Assume complete ionization. (a) Combine the neutrality equation and the law of mass action to obtain an accurate expression for n0 in near-intrinsic n-type silicon. (b) Use the expression obtained in a. to calculate n0 in a sample having ND 0.9 1014/cm3 and NA 1.0 1014/cm3. (c) Comment on the accuracy of the approximate equation n0 ? ND
- Question : P38 - Given a hole concentration gradient of
- Question : P39 - A lightly doped fi eld-free sample of silicon that is 1 ?m thick in the x direction exhibits a majorityelectron gradient of (dn/dx)
- Question : P40 - In a certain lightly doped silicon sample there exists a hole current-density value due to drift equal to
- Question : P41 - A certain silicon sample has negligible acceptor doping and a donor doping that is linearly graded from 1.5 1015/cm3 at the left surface to 2.5 1014/cm3 at the right surface. The two surfaces are 100 ?m apart. (a) Assuming that n (x) ? ND (x) throughout, calculate diffusion current density due to electrons at the middle of the sample. (b) In a thought experiment, we add 1.5 1016/cm3 of donors uniformly to the sample of (a); recalculate diffusion current density due to electrons. (c) In a second thought experiment we add 1.5 1015/cm3 of acceptors to the sam ple of (a); recalculate diffusion current density due to electrons
- Question : P42 - A thin silicon sample receives steady-state radiation that produces excess carriers uniformly throughout the sample in the amount ?p0 ?n0 l010/cm3. Ex cess-carrier lifetime in the sample is 1 ?s. At t 0, the radiation source is turned off. Calculate the excess-carrier density and recombination rate at (a) t 1 ?s; (b) t 1.5 ?s; (c) t 4 ?s.
- Question : P43 - A thin n-type sample of silicon having an equilibrium minority-carrier density p0 is subjected to penetrating radiation with the radiation source turned on at t 0. At t ?, p p (?). (a) Write the differential equation appropriate to this situation. (b) Find the solution for the differential equation of (a) under the given boundary conditions.
- Question : P44 - Uniform, steady-state ultraviolet radiation impinges on the surface of a semi-infi nite silicon sample in which n0 1015/cm3, producing an excess-carrier density at the surface of ?p0(0) ?n0(0) 101l/cm3. Given further that ? 1 ?s, and that the spatial origin is at the irradiated surface. (a) Calculate diffusion current density due to holes at x 0. (b) Calculate diffusion current density due to electrons at x 0.(c) Calculate diffusion current density due to holesand diffusion current density due to electrons at x Lp. Sketch vectors to scale representing these current-density components. (d) Since the sample is open-circuited, the total current density at x Lp must be zero, J 0. In fact, a tiny electric fi eld accounts for the
- Question : P46 - (a) A Si bar 0.5 cm long and 120 ?m2 in crosssectional area is doped with 1017cm
- Question : P47 - A Si sample is doped with 6.5 1015 cm
- Question : P48 - Find out the expressions of the dens ity-of-state functions for the dispersion relation of the conduction electrons as given in Problem 1 under the conditions (a) E/Eg << 1 and (b) E/Eg >> 1 respectively. Draw the graphs and explain the result physically.
- Question : P49 - Find the expressions for n0 under the conditions as stated in Problem 47. Draw the graphs and explain the result physically.
- Question : P50 - Find the expression of the average energy of electrons in semiconductors having parabolic energy bands for the conditions of both non degenerate and degenerate electron concentrations.
- Question : P51 - Find out a simple expression of photo emitted current density from semiconductors having parabolic energy bands.

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