Unit 5: Solid State Physics - Practice Quiz

1 According to the free electron theory, conduction electrons in a metal are treated mainly as:

2 What primarily limits the motion of free electrons in a real metal?

3 Drift current in a semiconductor is produced by:

4 Diffusion current occurs when charge carriers move from:

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

6 At , electron states with energy below the Fermi energy are:

7 Which expression represents the Fermi-Dirac distribution function?

8 For any temperature, the occupation probability at is:

9 The density of states describes the number of:

10 For free electrons in a three-dimensional solid, the density of states generally varies with energy as:

11 The energy range between the valence band and conduction band containing no allowed electron states is called the:

12 A solid usually behaves as a conductor when its:

13 Compared with an insulator, a semiconductor generally has:

14 In an ideal intrinsic semiconductor, the Fermi level lies approximately:

15 In an n-type semiconductor, the Fermi level shifts toward the:

16 In a p-type semiconductor, the Fermi level shifts toward the:

17 In a direct band-gap semiconductor, the conduction-band minimum and valence-band maximum occur at:

18 An electron transition across an indirect band gap usually requires the participation of a:

19 A hole in the valence band is commonly treated as a particle with:

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

21 According to the Drude free-electron theory, what happens to the electrical conductivity of a metal if the mean relaxation time doubles while the electron density remains constant?

22 Electron concentration is higher at the left end of a semiconductor than at the right end. An electric field is applied from left to right. How are the conventional electron diffusion and drift currents directed?

23 For a three-dimensional free-electron gas at , . If the electron concentration becomes eight times its original value, the Fermi energy becomes:

24 At , which statement correctly describes electron occupation in a metal relative to its Fermi energy ?

25 What is the probability that an available state at is occupied by an electron at any nonzero temperature?

26 If at a particular temperature, what is at the same temperature?

27 Near the bottom of a three-dimensional parabolic conduction band, the density of states varies as . What is the ratio ?

28 Two conduction bands have the same band-edge energy, but band X has a larger electron effective mass than band Y. Near the band edge, which band generally has the larger three-dimensional density of states?

29 A solid has a completely filled valence band and a partially filled conduction band at . How should it be classified using band theory?

30 Why does a completely filled energy band normally make no net contribution to electrical conduction?

31 Two pure solids have full valence bands at . Solid P has a band gap of , while solid Q has a band gap of . At room temperature, which behavior is most likely?

32 An intrinsic semiconductor has , where and are the effective densities of states. Relative to the exact middle of the band gap, where is its intrinsic Fermi level?

33 A silicon sample is doped with donor atoms, and the donors are almost fully ionized. Compared with intrinsic silicon at the same temperature, the Fermi level moves:

34 A semiconductor initially contains equal concentrations of donors and acceptors. Additional acceptors are then introduced so that acceptors dominate. What is the expected Fermi-level shift?

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

36 During an optical transition across the fundamental gap of an indirect semiconductor, which additional participant is generally required to conserve crystal momentum?

37 For a band described by , how does stronger positive curvature of the - relation affect the electron effective mass?

38 Near the maximum of a valence band, the band curvature is negative. Why is transport commonly described using holes with positive effective mass?

39 A material has one dominant type of carrier and a measured Hall coefficient . Using , what are the carrier type and concentration?

40 A rectangular n-type sample carries in a magnetic field . Its carrier concentration is , and its thickness along the magnetic field is . What is the magnitude of its Hall voltage? Use .

41 In a three-dimensional Drude-Sommerfeld metal, the electron density changes from to while the relaxation time changes from to . The electron mass remains constant. By what factors do the conductivity , Fermi energy , and mean free path change, respectively?

42 A nondegenerate electron gas at is in equilibrium in an electrostatic potential satisfying . Using the Einstein relation and zero net electron current, what is ?

43 For a three-dimensional degenerate electron gas with parabolic dispersion, the carrier density increases by a factor of while its effective mass increases by a factor of . What is the resulting factor of change in measured from the band minimum?

44 Let be the chemical potential and . Which relation is exactly satisfied by the Fermi-Dirac function at every nonzero temperature?

45 At , a state has Fermi-Dirac occupation probability . Approximately how far above the chemical potential is that state?

46 A semiconductor has six equivalent ellipsoidal conduction-band valleys. Each valley has density-of-states mass . If the total density of states is represented by one equivalent parabolic valley of mass , what is ?

47 For parabolic bands, which statement correctly compares the density of states immediately above a band edge in one, two, and three dimensions?

48 Why does a completely filled, isolated energy band carry no net current under the usual semiclassical band description?

49 A one-dimensional tight-binding band is with . If increased orbital overlap doubles without changing , how do the bandwidth and effective mass at change?

50 Two intrinsic solids have identical effective densities of states and carrier mobilities, but their band gaps are and . At , approximately how many times larger is the conductivity of the smaller-gap solid?

51 An intrinsic semiconductor has parabolic bands with . Ignoring additional valley degeneracy, where is its intrinsic Fermi level relative to the middle of the band gap?

52 At , an -type semiconductor has , , and . Assuming complete ionization, negligible holes, and nondegenerate statistics, where is ?

53 In a nondegenerate semiconductor at , doping moves the Fermi level above the intrinsic level. What is the approximate ratio ?

54 Which statement best explains why radiative recombination is generally much faster in a direct-gap semiconductor than in an indirect-gap semiconductor?

55 For an indirect semiconductor with band gap and a relevant phonon energy , what are the ideal absorption thresholds for a phonon-absorption process and a phonon-emission process, respectively?

56 Near a valence-band maximum, the electron energy is with . Which effective-mass interpretation is correct?

57 An anisotropic parabolic band has . For a quasiparticle of charge in a field , which pair correctly gives its acceleration and density-of-states mass?

58 A single-carrier -type slab carries conventional current density in a magnetic field . Taking as the transverse direction, what are the Hall field and Hall coefficient?

59 An intrinsic semiconductor has and electron mobility . In the weak-field limit, what is its Hall coefficient?

60 A single-carrier sample has Hall coefficient and conductivity . What are its carrier density and mobility?