101. When a small amount of phosphorus is added to pure silicon, the resulting semiconductor is generally:
ⓐ. \(n\)-type because phosphorus donates an extra electron
ⓑ. \(p\)-type because phosphorus is trivalent and creates holes
ⓒ. intrinsic because any impurity keeps \(n_e=n_h\)
ⓓ. insulating because all covalent bonds disappear
Correct Answer: \(n\)-type because phosphorus donates an extra electron
Explanation: Phosphorus has five valence electrons, while silicon effectively uses four valence electrons for covalent bonding. When phosphorus replaces a silicon atom, four of its electrons take part in bonds with neighbouring silicon atoms. The fifth electron is only weakly bound and can become available for conduction. Such an impurity is called a donor impurity. Since it increases the electron concentration, the doped material becomes \(n\)-type rather than intrinsic or \(p\)-type.
102. In a silicon crystal doped with a pentavalent impurity, the fifth valence electron of the impurity atom is important because it:
ⓐ. forms a fifth strong covalent bond with silicon
ⓑ. can become a conduction electron
ⓒ. becomes a hole of charge \(+e\)
ⓓ. changes the impurity atom into a moving negative ion
Correct Answer: can become a conduction electron
Explanation: A pentavalent impurity atom has one more valence electron than the four needed for covalent bonding in silicon. Four electrons are used to complete bonds with surrounding silicon atoms. The fifth electron is not strongly tied to a covalent bond, so a small amount of energy can free it. Once free, it contributes to conduction as an electron. The impurity atom left behind becomes an ionised donor, but it remains fixed in the crystal lattice.
103. In the band picture of an \(n\)-type semiconductor, the donor level is usually located:
ⓐ. just above the valence band
ⓑ. just below the conduction band
ⓒ. exactly at the external anode terminal
ⓓ. below the nucleus of every atom
Correct Answer: just below the conduction band
Explanation: Donor impurity atoms provide extra electrons that need only a small amount of energy to reach the conduction band. This is represented by a donor energy level close to the conduction band. Because the donor level is near the conduction band, electrons can be easily promoted into conducting states. This explains why donor doping greatly increases electron concentration. An acceptor level, by contrast, is placed near the valence band in a \(p\)-type semiconductor.
104. In an \(n\)-type semiconductor, the majority and minority carriers are respectively:
ⓐ. electrons and holes
ⓑ. holes and electrons
ⓒ. protons and electrons
ⓓ. donor ions and acceptor ions
Correct Answer: electrons and holes
Explanation: An \(n\)-type semiconductor is formed by adding donor impurities to a pure semiconductor. Donor atoms provide extra electrons, so electrons become the majority carriers. Holes are still present due to thermal generation, but their concentration is much smaller than the electron concentration. The material can contain fixed ionised donor atoms, but these ions are not the mobile majority carriers. The letter \(n\) refers to negative mobile electrons being dominant.
105. A silicon sample is doped with arsenic atoms and has \(n_e\gg n_h\). The sample is still electrically neutral overall because:
ⓐ. extra electrons balance fixed donor ions
ⓑ. electrons have no charge inside a semiconductor
ⓒ. holes become protons and cancel all charge
ⓓ. the crystal loses all nuclei after doping
Correct Answer: extra electrons balance fixed donor ions
Explanation: In an \(n\)-type semiconductor, donor atoms can release extra electrons into the crystal. After donating an electron, each donor atom becomes a fixed positive ion in the lattice. The mobile negative charge of the extra electrons is balanced by the positive charge of these ionised donor atoms. Therefore, the semiconductor is not negatively charged as a whole. Majority carrier type and overall electrical neutrality are two different ideas.
106. When a donor atom in silicon gives up its extra electron, the donor atom becomes:
ⓐ. a mobile negative ion carrying current
ⓑ. a hole moving through the valence band
ⓒ. an acceptor atom with three valence electrons
ⓓ. a fixed positive ion in the lattice
Correct Answer: a fixed positive ion in the lattice
Explanation: A donor impurity atom is located at a lattice site inside the semiconductor crystal. When it donates its loosely bound electron, it loses a negative charge. The remaining impurity atom is therefore positively ionised. However, it is still part of the crystal lattice and cannot move freely like a mobile carrier. Current in \(n\)-type material is carried mainly by electrons, while the positive donor ions provide fixed charge balance.
107. Read the situation below.
A pure silicon crystal is doped with a very small amount of antimony. Each antimony atom forms four covalent bonds with neighbouring silicon atoms and has one extra electron that is weakly held.
The semiconductor formed is best described as:
ⓐ. \(p\)-type with holes as majority carriers
ⓑ. intrinsic with \(n_e=n_h\) only
ⓒ. \(n\)-type with electrons as majority carriers
ⓓ. an insulator with no mobile carriers at room temperature
Correct Answer: \(n\)-type with electrons as majority carriers
Explanation: Antimony is a pentavalent impurity, so it acts as a donor when added to silicon. Four of its valence electrons form covalent bonds with neighbouring silicon atoms. The fifth electron can be freed easily and becomes a mobile conduction electron. This makes electrons the majority carriers in the doped semiconductor. The material is \(n\)-type because conduction is dominated by negative charge carriers.
108. Study the table about donor-doped silicon.
| Row | Feature | Suitable description |
|---|
| P | Impurity valency | Pentavalent |
| Q | Energy level introduced | Donor level near conduction band |
| R | Majority carrier | Electron |
| S | Overall material charge | Strongly negative |
The row that is not suitable is:
ⓐ. Row P
ⓑ. Row Q
ⓒ. Row R
ⓓ. Row S
Correct Answer: Row S
Explanation: Donor-doped silicon is \(n\)-type, so rows P, Q, and R are suitable. The impurity is pentavalent, the donor level lies close to the conduction band, and electrons are the majority carriers. Row S is not suitable because an \(n\)-type semiconductor remains electrically neutral overall. The mobile electrons are balanced by fixed positive donor ions. A material can have electrons as majority carriers without carrying a net negative charge.
109. Assertion: Donor impurities make electron conduction easier in silicon.
Reason: Donor levels lie close to the conduction band, so electrons need only small energy to reach conducting states.
ⓐ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓑ. Assertion is true, but Reason is false
ⓒ. Assertion is false, but Reason is true
ⓓ. Both Assertion and Reason are true, and Reason explains Assertion
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: The Assertion is true because donor impurities increase the number of electrons available for conduction. The Reason is also true because donor energy levels are close to the conduction band. Since the energy separation is small, donor electrons can be excited easily into conduction states. This makes \(n\)-type material much more conducting than the corresponding pure semiconductor. The donor level position gives the band-based reason for the increased electron concentration.
110. A silicon sample contains \(4.0\times10^{21}\,\text{m}^{-3}\) donor atoms, and all donor atoms are ionised. If intrinsic carriers are neglected, the majority carrier concentration is approximately:
ⓐ. \(1.0\times10^{21}\,\text{m}^{-3}\)
ⓑ. \(2.0\times10^{21}\,\text{m}^{-3}\)
ⓒ. \(4.0\times10^{21}\,\text{m}^{-3}\)
ⓓ. \(8.0\times10^{21}\,\text{m}^{-3}\)
Correct Answer: \(4.0\times10^{21}\,\text{m}^{-3}\)
Explanation: \( \textbf{Given donor concentration:} \) \(N_D=4.0\times10^{21}\,\text{m}^{-3}\).
\( \textbf{Ionisation condition:} \) All donor atoms are ionised.
\( \textbf{Intrinsic carriers:} \) Neglected, so donor electrons dominate.
\( \textbf{Carrier type:} \) Donor atoms supply electrons, so electrons are majority carriers.
\( \textbf{Electron contribution per donor:} \) One ionised donor contributes approximately one electron.
\( \textbf{Approximate relation:} \)
\[
n_e\approx N_D
\]
\( \textbf{Substitution:} \)
\[
n_e\approx 4.0\times10^{21}\,\text{m}^{-3}
\]
\( \textbf{Minority carrier note:} \) Holes are not counted as majority carriers in this approximation.
\( \textbf{Final answer:} \) The majority carrier concentration is approximately \(4.0\times10^{21}\,\text{m}^{-3}\).
111. A claim says: “An \(n\)-type semiconductor is formed by adding electrons directly from a battery into pure silicon.” The better interpretation is:
ⓐ. the claim is suitable because a battery converts every silicon atom into phosphorus
ⓑ. \(n\)-type material is formed by donor doping, not battery charging
ⓒ. the claim is suitable only when holes become majority carriers
ⓓ. \(n\)-type material cannot contain any impurity atom
Correct Answer: \(n\)-type material is formed by donor doping, not battery charging
Explanation: An \(n\)-type semiconductor is a material prepared by adding donor impurity atoms such as phosphorus, arsenic, or antimony. These atoms become part of the crystal and provide loosely bound electrons. Connecting a battery can drive current through a device, but it does not by itself create the doped material structure. Doping changes carrier concentration inside the semiconductor in a controlled way. The distinction is between material preparation and external circuit operation.
112. A \(p\)-type semiconductor is formed when silicon is doped with:
ⓐ. a trivalent impurity such as boron
ⓑ. a pentavalent impurity such as phosphorus
ⓒ. a divalent metal that removes the band gap completely
ⓓ. only extra free electrons from a battery
Correct Answer: a trivalent impurity such as boron
Explanation: A \(p\)-type semiconductor is produced by adding a trivalent impurity to silicon or germanium. Boron, aluminium, gallium, and indium are common examples of trivalent acceptor impurities. Since they have only three valence electrons, they leave one covalent bond incomplete. This incomplete bond can accept an electron from a neighbouring bond, producing a hole. The \(p\)-type name reflects holes as the dominant positive mobile carriers.
113. In a silicon crystal doped with boron, one covalent bond around each boron atom is incomplete because boron:
ⓐ. has five valence electrons
ⓑ. has no nucleus
ⓒ. has an overlapping conduction band like a metal
ⓓ. has three valence electrons
Correct Answer: has three valence electrons
Explanation: Silicon needs four valence electrons for four covalent bonds in the crystal structure. Boron has only three valence electrons, so it can complete only three bonds directly. One bond remains deficient in one electron. This deficiency can be filled by an electron from a neighbouring bond, leaving a hole there. The three-valence-electron property is what makes boron an acceptor impurity.
114. In a \(p\)-type semiconductor, the majority and minority carriers are respectively:
ⓐ. electrons and holes
ⓑ. donor ions and protons
ⓒ. neutrons and electrons
ⓓ. holes and electrons
Correct Answer: holes and electrons
Explanation: A \(p\)-type semiconductor is formed by acceptor doping. Acceptor atoms create holes by accepting electrons from neighbouring bonds. These holes become the majority carriers and dominate conduction. Electrons are still present because of thermal generation, but they are minority carriers. The letter \(p\) refers to positive mobile holes, not to mobile protons.
115. The acceptor energy level in a \(p\)-type semiconductor is generally shown:
ⓐ. just below the conduction band
ⓑ. just above the valence band
ⓒ. outside the crystal as a battery terminal
ⓓ. exactly equal to the resistance of the sample
Correct Answer: just above the valence band
Explanation: Acceptor impurities create energy levels close to the valence band. An electron from the valence band can easily move into the acceptor level, leaving behind a hole in the valence band. This is why acceptor doping increases hole concentration. Donor levels are instead found near the conduction band in \(n\)-type semiconductors. The acceptor level position explains hole formation using the band model.
116. When an acceptor atom accepts an electron in a silicon crystal, the acceptor atom becomes:
ⓐ. a mobile positive hole
ⓑ. a free conduction electron
ⓒ. a fixed negative ion
ⓓ. a donor atom with five valence electrons
Correct Answer: a fixed negative ion
Explanation: A trivalent acceptor atom has one incomplete bond when placed in the silicon lattice. It can accept an electron from a neighbouring covalent bond. After accepting this electron, the acceptor atom has gained negative charge and becomes a negative ion. It remains fixed at its lattice site and does not move through the crystal as a carrier. The mobile carrier created by this process is the hole left in the valence band.
117. A doped semiconductor has \(n_h\gg n_e\), but the sample is electrically neutral overall. The best reason is:
ⓐ. holes are balanced by fixed negative acceptor ions
ⓑ. holes have no effective charge
ⓒ. electrons and protons are both absent from the material
ⓓ. the semiconductor contains no impurity atoms
Correct Answer: holes are balanced by fixed negative acceptor ions
Explanation: In a \(p\)-type semiconductor, holes are the majority carriers. These holes are created when acceptor atoms accept electrons from nearby bonds. The acceptor atoms then become fixed negative ions in the lattice. The positive charge of the mobile holes is balanced by the negative charge of these fixed acceptor ions. Hence, a \(p\)-type semiconductor is neutral overall even though holes dominate its conduction.
118. Match the doped-semiconductor descriptions.
| Column I | Column II |
|---|
| P. \(n\)-type semiconductor | 1. Holes are majority carriers |
| Q. \(p\)-type semiconductor | 2. Electrons are majority carriers |
| R. Ionised donor atom | 3. Fixed positive ion |
| S. Ionised acceptor atom | 4. Fixed negative ion |
The suitable matching is:
ⓐ. P-1, Q-2, R-4, S-3
ⓑ. P-2, Q-1, R-3, S-4
ⓒ. P-2, Q-3, R-1, S-4
ⓓ. P-4, Q-1, R-3, S-2
Correct Answer: P-2, Q-1, R-3, S-4
Explanation: In an \(n\)-type semiconductor, donor impurities supply electrons, so electrons are majority carriers. In a \(p\)-type semiconductor, acceptor impurities create holes, so holes are majority carriers. After donating an electron, a donor atom becomes a fixed positive ion. After accepting an electron, an acceptor atom becomes a fixed negative ion. The fixed ions maintain charge balance but are not the mobile carriers that mainly conduct current.
119. A passage describes a doped crystal.
A small amount of gallium is introduced into pure silicon. Each gallium atom forms only three covalent bonds directly. An electron from a neighbouring bond can move into the incomplete bond, leaving a hole behind.
The impurity action described in the passage is:
ⓐ. donor action producing \(n\)-type material
ⓑ. intrinsic pair generation with no impurity effect
ⓒ. acceptor action producing \(p\)-type material
ⓓ. metallic band overlap producing a conductor
Correct Answer: acceptor action producing \(p\)-type material
Explanation: Gallium is trivalent, so it has only three valence electrons available for bonding. When it replaces a silicon atom, one bond is incomplete. The impurity can accept an electron from a neighbouring bond, and that movement leaves a hole. This is acceptor action and it produces \(p\)-type material. The passage describes impurity-controlled hole creation, not donor electron supply.
120. Consider the following statements about \(n\)-type and \(p\)-type semiconductors.
I. \(n\)-type semiconductors are produced using donor impurities.
II. \(p\)-type semiconductors are produced using acceptor impurities.
III. A doped semiconductor must be electrically charged overall.
The valid statements are:
ⓐ. II and III only
ⓑ. I and III only
ⓒ. I and II only
ⓓ. I, II, and III
Correct Answer: I and II only
Explanation: Statement I is valid because \(n\)-type material is formed using pentavalent donor impurities. Statement II is valid because \(p\)-type material is formed using trivalent acceptor impurities. Statement III is not valid because doped semiconductors are electrically neutral overall. In \(n\)-type material, mobile electrons are balanced by fixed positive donor ions, while in \(p\)-type material, mobile holes are balanced by fixed negative acceptor ions. The carrier imbalance determines majority and minority carriers, not the total charge of the sample.
