A silicon (Si) specimen is doped with aluminium (Al). The concentration of acceptor atoms is \(10^{18}\text{ m}^{-3}\). Given that the intrinsic carrier concentration is \(10^{16}\text{ m}^{-3}\), the concentration of electrons in the specimen is
1. 10^{14} m^{-3}
2. 10^{16} m^{-3}
3. 10^{18} m^{-3}
4. 10^{12} m^{-3}
View Answer
Formula: \(n_e n_h = n_i^2\). Since the semiconductor is heavily p-doped, \(n_h approx N_a = 10^{18}\text{ m}^{-3}\). Therefore, \(n_e = frac{n_i^2}{n_h} = frac{(10^{16})^2}{10^{18}} = 10^{14}\text{ m}^{-3}\).
Consider the following statements:
(a) At 0 K, semiconductor behaves as perfect conductor.
(b) Semiconductors have negative temperature coefficient of resistance.
Choose the correct statement.
1. Only (a)
2. Only (b)
3. Both (a) & (b)
4. Neither (a) nor (b)
View Answer
At 0 K, semiconductors behave as insulators since no electrons are in the conduction band. The resistance of a semiconductor decreases with increasing temperature, meaning it has a negative temperature coefficient of resistance. Thus, only statement (b) is correct.
Consider the following statements
(i) An intrinsic semiconductor will behave as insulator at \(T = 0text{ K}\).
(ii) Doping pure silicon with trivalent impurities gives p-type semiconductors.
(iii) The majority carriers in n-type semiconductors are electrons.
(iv) Solar cell works when it is in forward bias.
The correct statements(s) is/are
1. Only (i) and (ii)
2. Only (i) and (iii)
3. Only (i), (ii) and (iii)
4. Only (i), (ii) and (iv)
View Answer
At \(T = 0text{ K}\), all electrons are in the valence band, so an intrinsic semiconductor acts as an insulator. Trivalent doping creates p-type, and n-type has majority electron carriers. Solar cells do not require external bias to operate. Thus, statements (i), (ii), and (iii) are correct.
Assertion (A): The conductivity of an intrinsic semiconductor depends on its temperature.
Reason (R): No important electronic device can be developed using intrinsic semi conductor.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
In an intrinsic semiconductor, conductivity increases with temperature due to increased generation of electron-hole pairs. So Assertion (A) is true. Intrinsic semiconductors have limited practical use due to low conductivity, making Reason (R) true in terms of 'important' devices. However, (R) does not explain (A).
Assertion (A): The number of electrons in n-type semiconductor is higher than the number of electrons in a pure silicon semiconductor.
Reason (R): The law of mass action is applicable only to n-type semiconductors.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
In n-type semiconductors, donor impurities increase the number of free electrons, making Assertion (A) true. The law of mass action (\(n_e n_h = n_i^2\)) is a fundamental principle applicable to all types of semiconductors (intrinsic, n-type, p-type), so Reason (R) is false.
Assertion (A): Electron hole recombination takes place in P-region and N-region of PN Junction diode except in depletion region.
Reason (R): Electric field in depletion region oppose the diffusion.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is generally true in simplified models, where most recombination occurs in the quasi-neutral P and N regions. While some recombination does occur in the depletion region, its contribution to the overall current is often considered secondary for typical forward-biased diodes.
Reason (R) is true; the electric field in the depletion region acts as a barrier, opposing the diffusion of majority carriers across the junction. (R) does not explain the spatial distribution of recombination described in (A).
Assertion (A): Width of depletion region is reduced in forward bias.
Reason (R): In n-type semiconductor majority charge carriers are free electrons while in p-type they are holes.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
When a p-n junction is forward biased, the applied voltage counteracts the internal electric field, causing majority carriers to move towards the junction and reducing the depletion region's width. Thus, Assertion (A) is true.
Reason (R) correctly states the majority carriers in n-type (electrons) and p-type (holes) semiconductors, which is also true. However, Reason (R) does not explain why the depletion region width reduces under forward bias. Hence, both are true, but R is not the correct explanation for A.
Assertion (A): The drift current in a p-n junction is from n-side to p-side.
Reason (R): The diffusion current in a p-n junction is from p-side to n-side.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
In a p-n junction, the built-in electric field points from the n-side to the p-side, causing drift current to flow from n-side to p-side. Thus, Assertion (A) is true. Due to concentration gradients, diffusion current arises from the movement of majority carriers, resulting in a net diffusion current from p-side to n-side. Thus, Reason (R) is also true.
These are two distinct current mechanisms, and R does not explain A.
Assertion (A): P-type semiconductor has high density of holes in valence band while N-type semiconductor has high density of electrons in conduction band.
Reason (R): In N-type semiconductor, as the density of donor atoms (N_D) is increased, the fermi energy level shifts towards the valence band.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
P-type semiconductors have a high concentration of holes in the valence band, and N-type semiconductors have a high concentration of electrons in the conduction band. Thus, Assertion (A) is true.
In an N-type semiconductor, increasing the donor atom density (N_D) increases the electron concentration, causing the Fermi energy level to shift closer to the conduction band, not the valence band. Hence, Reason (R) is false.