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Charge Carrier Generation
MCQ questions and answers.
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MCQ Questions
1. An ideal intrinsic insulator has a band gap of 5.0 eV. Assuming its intrinsic carrier concentration varies as n_i ∝ exp(−E_g/2kT), by approximately what factor does n_i increase when the temperature rises from 300 K to 600 K? Take k = 8.6 × 10^−5 eV K^−1.
A.
exp(24.2)
B.
exp(48.4)
C.
exp(96.8)
D.
exp(12.1)
Correct Answer:
exp(48.4)
Explanation:
The ratio is n_i(600)/n_i(300) = exp[(E_g/2k)(1/300 − 1/600)]. Substituting E_g = 5.0 eV and k = 8.6 × 10^−5 eV K^−1 gives an exponent of approximately 48.4. The large factor reflects the strong temperature dependence of thermal electron–hole pair generation in an insulator.
2. A photon is incident on an ideal insulating crystal whose band gap is 3.10 eV. What is the longest wavelength that can generate a free electron–hole pair? Use hc = 1240 eV nm.
A.
200 nm
B.
310 nm
C.
400 nm
D.
620 nm
Correct Answer:
400 nm
Explanation:
Photogeneration begins when photon energy equals or exceeds the band gap. Thus λ_max = hc/E_g = 1240/3.10 nm = 400 nm. Photons with longer wavelengths have insufficient energy to promote an electron across the gap.
3. When thermal energy generates electron–hole pairs in a perfectly pure insulating crystal, which change occurs immediately after generation?
A.
The crystal acquires a net positive charge
B.
The crystal acquires a net negative charge
C.
The number of conduction electrons increases by the same amount as the number of holes
D.
Only holes are generated because electrons remain bound to atoms
Correct Answer:
The number of conduction electrons increases by the same amount as the number of holes
Explanation:
Thermal generation promotes valence-band electrons into the conduction band. Each promoted electron leaves one hole behind, so electron–hole pairs are generated in equal numbers and no net charge is created.
4. A photon of energy 7.5 eV is absorbed by an ideal insulator with a band gap of 6.0 eV. In the simplest single-pair generation model, what is the direct result?
A.
No carriers are generated because the photon energy is not exactly equal to the gap
B.
One conduction electron and one valence-band hole are generated
C.
Two conduction electrons and two holes are necessarily generated
D.
Only one conduction electron is generated, with no hole
Correct Answer:
One conduction electron and one valence-band hole are generated
Explanation:
Since the photon energy exceeds the 6.0 eV band gap, it can promote one valence electron to the conduction band. This necessarily produces one electron–hole pair; the excess photon energy is converted into other forms of energy rather than requiring a second pair.
5. Which photon is least capable of generating free carriers in an insulator with band gap 4.0 eV?
A.
A 300 nm photon
B.
A 250 nm photon
C.
A 400 nm photon
D.
A 200 nm photon
Correct Answer:
A 400 nm photon
Explanation:
The 400 nm photon has energy E = 1240/400 = 3.10 eV, which is below the 4.0 eV band gap and therefore cannot generate a free electron–hole pair. The other photons have energies above the gap.
6. An insulating crystal has a defect level located 1.2 eV below its conduction band. Compared with excitation directly across a 5.0 eV band gap, what is the principal effect of this defect level on electron generation?
A.
It makes electron generation impossible because the defect traps all holes
B.
It permits electrons in the defect level to reach the conduction band using only 1.2 eV
C.
It requires photons of at least 6.2 eV for carrier generation
D.
It generates conduction electrons without leaving any positively charged state
Correct Answer:
It permits electrons in the defect level to reach the conduction band using only 1.2 eV
Explanation:
An occupied defect level 1.2 eV below the conduction band can act as an intermediate source of electrons. Excitation from that level to the conduction band requires only 1.2 eV, although the corresponding defect ionization leaves a positive localized state.
7. A high-energy photon produces electron–hole pairs in an insulating detector. If the average energy required to create one pair is 12 eV, how many pairs can a 1.20 keV photon generate in the idealized limit?
A.
10 pairs
B.
50 pairs
C.
100 pairs
D.
144 pairs
Correct Answer:
100 pairs
Explanation:
The ideal number of generated pairs is the absorbed photon energy divided by the average pair-creation energy: 1200 eV/12 eV = 100 pairs. Each pair consists of one conduction electron and one hole.
8. For an intrinsic insulator, the thermal generation rate is approximately proportional to exp(−E_g/2kT). Which modification most strongly increases thermal carrier generation at a fixed temperature?
A.
Increasing the band gap
B.
Decreasing the band gap
C.
Reducing the number of valence electrons without changing the band gap
D.
Increasing the sample thickness while keeping the illuminated volume unchanged
Correct Answer:
Decreasing the band gap
Explanation:
A smaller band gap makes the exponent −E_g/2kT less negative, increasing the probability that thermal energy generates electron–hole pairs. The other changes do not directly reduce the activation energy for intrinsic generation.
9. A sufficiently strong electric field is applied across a very pure insulator. Which mechanism can generate additional mobile carriers if an initially accelerated electron gains enough energy between collisions?
A.
Impact ionization of bound electrons
B.
Conversion of holes into photons without electronic excitation
C.
Reduction of the band gap to exactly zero in every region
D.
Removal of all valence electrons without creating positive vacancies
Correct Answer:
Impact ionization of bound electrons
Explanation:
A carrier accelerated by a strong field can acquire enough kinetic energy to free another bound electron during a collision. This creates an additional electron–hole pair and is a field-assisted charge-carrier generation mechanism.
10. A 2.5 eV photon illuminates an insulator whose valence-to-conduction band gap is 3.0 eV, but the material contains an occupied impurity level 1.0 eV below the conduction band. Which process is energetically allowed?
A.
Direct valence-to-conduction excitation only
B.
Excitation from the impurity level to the conduction band
C.
Excitation from the conduction band to the valence band
D.
No electronic excitation because the photon energy is below the band gap
Correct Answer:
Excitation from the impurity level to the conduction band
Explanation:
The photon energy of 2.5 eV is insufficient for the 3.0 eV valence-to-conduction transition, but it exceeds the 1.0 eV separation between the occupied impurity level and the conduction band. Therefore, impurity-assisted electron generation is allowed.
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