Unit 1 - Practice Quiz

1 Which of the following materials has the largest energy band gap?

2 In which type of material do the valence and conduction bands overlap?

3 At absolute zero temperature (), a pure semiconductor behaves like a/an:

4 What is the relationship between the number of electrons () and holes () in an intrinsic semiconductor?

5 An intrinsic semiconductor is one that is:

6 Adding pentavalent impurities to a pure semiconductor creates what type of material?

7 Which of the following is an example of an acceptor impurity?

8 What are the majority charge carriers in a P-type semiconductor?

9 An impurity that donates a free electron to the conduction band is known as a:

10 In an N-type semiconductor, where is the Fermi level located?

11 In a P-type semiconductor, the Fermi level shifts towards the:

12 As the temperature of an extrinsic semiconductor increases significantly, the Fermi level shifts towards:

13 What does the Law of Mass Action state for a semiconductor in thermal equilibrium?

14 What is the net electrical charge of an N-type semiconductor?

15 How is the mobility () of a charge carrier defined?

16 Which charge carrier generally has higher mobility in a silicon semiconductor?

17 What happens to the conductivity of a pure semiconductor as temperature increases?

18 The total conductivity () of an intrinsic semiconductor is given by the formula:

19 What is the primary cause of diffusion current in a semiconductor?

20 The average time an electron-hole pair exists before recombination is called the:

21 How does the electrical resistivity of a typical metal and an intrinsic semiconductor behave as the temperature increases from room temperature?

22 A solid material has an energy band gap () of approximately . How is this material classified at room temperature?

23 The square of the intrinsic carrier concentration () in a semiconductor is proportional to which of the following expressions regarding temperature and bandgap energy ?

24 At absolute zero (), what is the probability of finding an electron in the conduction band of an intrinsic semiconductor?

25 In the energy band diagram of an n-type semiconductor, where is the discrete donor energy level () introduced by the dopant atoms located?

26 If a pure Silicon crystal is doped with Boron atoms, what type of impurity is introduced, and what type of extrinsic semiconductor is formed?

27 Why is the ionization energy of shallow donor impurities generally lower in Germanium than in Silicon?

28 A silicon sample at has an intrinsic carrier concentration of . If it is doped with phosphorus atoms, what is the approximate minority carrier (hole) concentration?

29 Which of the following equations correctly represents the exact charge neutrality condition in a semiconductor uniformly doped with both donor () and acceptor () impurities?

30 A semiconductor is doped with a donor concentration and an acceptor concentration . Assuming complete ionization, what is the approximate majority carrier concentration at room temperature?

31 As the concentration of donor impurities in an n-type semiconductor increases at a constant temperature, how does the position of the Fermi level () change?

32 What happens to the Fermi level of a moderately doped n-type semiconductor as the temperature increases to very high values (approaching intrinsic behavior)?

33 In a p-type semiconductor at room temperature, the Fermi level is located above the valence band. If the acceptor doping concentration is increased while keeping the temperature constant, what happens to this distance?

34 At high temperatures, the mobility of charge carriers in a moderately doped semiconductor is predominantly limited by which scattering mechanism?

35 When a very high electric field is applied to a semiconductor, how does the drift velocity of the charge carriers behave?

36 For a semiconductor with an intrinsic carrier concentration , electron mobility , and hole mobility , at what electron concentration does the minimum conductivity occur?

37 Calculate the approximate conductivity of an n-type Silicon sample doped with , given electron mobility and elemental charge . (Assume complete ionization and neglect intrinsic carriers).

38 An intrinsic semiconductor block has length , cross-sectional area , and conductivity . If the physical length of the block is doubled while maintaining the same temperature and material, what happens to its conductivity?

39 According to the Einstein relation for a semiconductor at thermal equilibrium, what is the value of the ratio of the electron diffusion constant () to the electron mobility ()?

40 In an n-type semiconductor, the minority carrier lifetime for holes is and their diffusion coefficient is . The average distance a hole diffuses before recombining (diffusion length ) is given by:

41 How does the Varshni empirical relation model the temperature dependence of the bandgap in semiconductors, and what is the dominant physical cause for this variation at high temperatures?

42 In a solid where the conduction band minimum is highly anisotropic, forming ellipsoidal constant energy surfaces (e.g., Silicon), how is the conductivity effective mass related to the longitudinal () and transverse () effective masses?

43 The intrinsic carrier concentration of a semiconductor depends heavily on temperature . If the term is plotted as a function of , what does the slope of the resulting linear plot theoretically represent?

44 In an intrinsic semiconductor at a temperature K, if the effective density of states in the conduction band is exactly four times the effective density of states in the valence band , where does the intrinsic Fermi level lie relative to the geometric mid-gap energy ?

45 At absolute zero temperature ( K), an n-type semiconductor is doped with both donor () and acceptor () impurities such that it is partially compensated (). Where is the Fermi level precisely located?

46 As a semiconductor becomes degenerately doped with donor impurities (e.g., ), how does the Burstein-Moss shift affect its optical properties?

47 A semiconductor is doped with shallow donors and deep acceptors located at an energy level . Under thermal equilibrium, assuming complete ionization of shallow donors but partial ionization of deep acceptors (with ground state degeneracy factor ), what is the exact charge neutrality equation?

48 A silicon sample at 300 K () is doped with shallow donors and shallow acceptors . Assuming complete ionization, what is the equilibrium electron concentration ?

49 An n-type semiconductor () is subjected to high-level optical excitation such that the excess carrier concentration is immense (). How do the electron () and hole () quasi-Fermi levels behave relative to the intrinsic Fermi level ?

50 In a moderately doped n-type semiconductor, as the temperature strictly increases from the freeze-out regime (near absolute zero) through the extrinsic regime and into the intrinsic regime, how does the position of the Fermi level shift over the entire range?

51 For a degenerately doped semiconductor where the Fermi level penetrates the conduction band (), the standard Boltzmann approximation significantly overestimates the electron concentration. Which mathematical formulation must be strictly used to calculate the exact electron concentration ?

52 A semiconductor at a low temperature () is doped with deep donors (at energy ) and shallow acceptors , where . Assuming the degeneracy factor is 1, what is the approximate position of the Fermi level ?

53 The electron mobility in a doped semiconductor is restricted by both lattice scattering () and ionized impurity scattering (). Assuming Matthiessen's rule applies, at what temperature does the maximum overall mobility occur?

54 In a mixed-conduction semiconductor where both electrons () and holes () actively transport charge, what is the exact expression for the Hall coefficient under a weak magnetic field?

55 At highly elevated electric fields, the drift velocity of carriers ceases to increase linearly and instead saturates (). What is the primary quantum-mechanical scattering mechanism responsible for this velocity saturation?

56 For a semiconductor maintained at a constant temperature with intrinsic concentration , electron mobility , and hole mobility , what is the absolute minimum possible theoretical conductivity (assuming holds)?

57 In the extrinsic temperature region (where impurities are completely ionized but thermal generation of intrinsic carriers is negligible), an n-type semiconductor's conductivity exhibits a slight decrease as temperature increases. What primary physical effect dictates this specific behavior?

58 The steady-state 1D continuity equation for excess holes in an n-type semiconductor under a constant applied electric field and optical generation is . If diffusion is negligible, what is the spatial profile for when continuously injected at with ?

59 In a Haynes-Shockley experiment, a pulse of minority holes drifts under an electric field over a distance in time . The pulse broadens spatially over time, exhibiting a Gaussian spatial variance . How can the minority diffusion length be directly extracted from these experimental observables?

60 At extreme high carrier injection levels (), the effective minority carrier lifetime in a semiconductor becomes heavily dominated by Auger recombination. How does fundamentally scale with the excess carrier concentration in this specific regime?