Unit 1: Solid State Physics - Practice Quiz

1 In the free electron theory of metals, conduction electrons are treated as:

2 Which particles mainly carry electric current in a metal according to free electron theory?

3 Drift current in a semiconductor is produced mainly by:

4 Diffusion current occurs when charge carriers move from a region of:

5 At absolute zero, the Fermi energy is the energy of the:

6 The Fermi-Dirac distribution function gives the probability that an energy state is:

7 At the Fermi energy , the Fermi-Dirac occupation probability is:

8 A range of electron energies that cannot exist in a solid is called a:

9 The highest energy band normally occupied by electrons at in a semiconductor is the:

10 A hole in a semiconductor behaves like a particle with:

11 Effective mass is used to describe how a charge carrier responds to:

12 The Hall effect is the development of a transverse voltage when a current-carrying material is placed in a:

13 For a material with one type of carrier having concentration and charge , the Hall coefficient is:

14 A pure semiconductor without intentionally added impurities is called:

15 Adding a pentavalent impurity to silicon usually produces:

16 In an intrinsic semiconductor, the Fermi level lies approximately:

17 In an n-type semiconductor, the Fermi level shifts closer to the:

18 In a direct band gap semiconductor, an electron can recombine with a hole without requiring a change in:

19 Which material is commonly classified as an indirect band gap semiconductor?

20 A solar cell converts light energy directly into electrical energy through the:

21 In the Drude free-electron model, the conductivity is . If the electron density doubles while the mean collision time becomes half its original value, how does the conductivity change?

22 The electron concentration in a semiconductor increases along the positive -direction. Which electric-field direction is required for the electron drift current to balance the electron diffusion current?

23 For a three-dimensional free-electron gas at , . If the electron density becomes eight times its initial value, the new Fermi energy is:

24 What is the probability that an electronic state at the Fermi energy is occupied at any nonzero temperature?

25 At a certain temperature, an energy state satisfies . What is its Fermi-Dirac occupation probability?

26 When identical and widely separated atoms are brought together to form a crystal, what generally happens to one atomic energy level?

27 Why does a completely filled energy band normally produce no net electrical current under a weak applied field?

28 Near the top of a valence band, the curvature is negative. What is the usual convenient description of charge transport in this region?

29 An electron occupies a band region where its effective mass is negative. If an external force acts in the positive -direction, what is the direction of its acceleration?

30 A material carries current along positive and is placed in a magnetic field along positive . If electrons are the majority carriers, on which side do electrons accumulate?

31 A semiconductor slab has carrier density and thickness . For and , what is the magnitude of the Hall voltage? Use and .

32 The Hall coefficient of a sample is . Assuming one type of carrier, what are the carrier type and approximate concentration?

33 In an intrinsic semiconductor, . If the electron mobility is three times the hole mobility, what fraction of the total conductivity is due to electrons?

34 A silicon crystal is doped with phosphorus atoms. After the donor atoms are ionized, which carriers and fixed ions are produced?

35 Which change most directly explains why the conductivity of an intrinsic semiconductor usually increases strongly with temperature?

36 For an intrinsic semiconductor, . If , where is the intrinsic Fermi level located?

37 At , the electron concentration in a nondegenerate n-type semiconductor increases by a factor of . Approximately how far does the Fermi level move toward the conduction band? Use .

38 Why is a direct band-gap semiconductor generally more efficient for light emission than an indirect band-gap semiconductor?

39 In an illuminated p-n junction solar cell operating under short-circuit conditions, what is the primary role of the depletion-region electric field?

40 A solar cell receives of monochromatic light whose photons each have energy . If of incident photons produce collected electrons, what is the photocurrent? Use .

41 In the Drude free-electron model, metal B has twice the conduction-electron density and three times the effective electron mass of metal A. If both metals have the same electrical conductivity, what must be the relation between their mean collision times?

42 In a nondegenerate semiconductor at thermal equilibrium, the electron concentration varies as . Using the Einstein relation, which electric field makes the total electron current density zero?

43 The excess minority-electron concentration in a -type semiconductor is for . With no applied electric field, what are the directions of electron motion and conventional electron diffusion current?

44 Two three-dimensional free-electron systems are at . System B has electron density and effective mass . What is ?

45 At temperature , a state lies at energy . What are the probabilities that this state is occupied and that a state at is empty?

46 A narrow group of states has a constant density of states symmetric about the chemical potential . Assuming the integration limits are symmetric and much wider than , which statement about thermal excitation is correct?

47 A crystal contains identical atoms, each contributing one electron from a nondegenerate atomic orbital. Neglecting interactions and assuming spin degeneracy, what does band theory predict for the band formed from that orbital?

48 In the nearly-free-electron model, why does an energy gap open at a Brillouin-zone boundary?

49 Near a point in a two-dimensional band, the dispersion is , where . What are the signs of the electron effective-mass components?

50 A nearly full valence band has negative electron curvature near its maximum. Why can its transport be represented by holes with positive effective mass?

51 A rectangular -type sample carries current along and is placed in magnetic field along . Its thickness along is . With the Hall voltage defined as , which result follows from force balance?

52 In a semiconductor containing both electrons and holes, the weak-field Hall coefficient is . Under what condition does the Hall voltage vanish while conductivity remains finite?

53 A compensated semiconductor has fully ionized donors and acceptors with . Assuming thermal equilibrium and nondegenerate statistics, what is the electron concentration?

54 Two intrinsic materials have the same band gap and temperature. Material B has and . Neglecting mobility differences, how does its intrinsic carrier concentration compare with that of material A?

55 An intrinsic semiconductor has parabolic bands with density-of-states masses . Relative to the middle of the band gap, where is the intrinsic Fermi level in the nondegenerate approximation?

56 A fully ionized, nondegenerate -type semiconductor satisfies and has negligible acceptor concentration. If is increased by a factor of at fixed temperature without changing band parameters, how does change?

57 Two semiconductors have equal band gaps, but one is direct and the other indirect. Which statement best explains why the direct-gap material generally emits light more efficiently?

58 An indirect-gap semiconductor has its valence-band maximum at and conduction-band minimum at . What is required for a near-threshold optical absorption event?

59 For an ideal solar cell with diode ideality factor , when . At , by approximately how much does increase when illumination intensity rises by a factor of ?

60 A solar cell has , , and a maximum-power operating point of and . What is its fill factor?