Semiconductor Materials: Properties, Carriers & Doping: 17 MCQs with answers

$10^{-6}$ to $10^3$ S/cm

Semiconductors sit between conductors ($10^4$ to $10^7$ S/cm) and insulators ($10^{-12}$ to $10^{-18}$ S/cm), in the range $10^{-6}$ to $10^3$ S/cm.

It behaves as an insulator

At absolute zero, all valence electrons are locked in covalent bonds, so no free carriers exist and the crystal behaves as an insulator.

The hole

Thermal breaking of a covalent bond frees an electron and leaves a hole, which behaves as a positive carrier and contributes to current.

Phosphorus (P)

Phosphorus is pentavalent (Group V) and acts as a donor. Boron, aluminium, and gallium are trivalent acceptors.

Electrons

Donor atoms contribute free electrons, so electrons outnumber holes and are the majority carriers in n-type material.

True

Semiconductors have a negative temperature coefficient of resistivity, meaning resistivity decreases as temperature rises — the opposite of metals.

A hole is the absence of an electron at a bond site, so no positive particle actually moves

A hole is a vacancy left by a freed electron. Because an electron is negative, its absence looks positive, but no real positive particle is moving — bound electrons hop between bonds instead.

It decreases, because more covalent bonds break and free more carriers

Semiconductors have a negative temperature coefficient of resistivity. Heating breaks more covalent bonds, creating more electron-hole pairs and lowering resistivity.

Boron, because it is trivalent and accepts an electron

Trivalent dopants such as boron, indium, aluminium, and gallium act as acceptors and produce p-type material. Arsenic, antimony, and phosphorus are donors.

Both A and R are true, and R correctly explains A

The acceptor level sits just above $E_v$ precisely because the hole it creates is only weakly bound and easily released into the valence band, so R is the correct reason for A.

Hole motion is opposite in direction to the bound electron motion that creates it

When a bound electron fills a neighbouring hole, a new hole appears where that electron came from. The hole therefore appears to move opposite to the electron that filled it.

They obey Ohm's law exactly at all voltages

Semiconductors are nonlinear conductors and do not obey Ohm's law. The other three statements are all standard semiconductor properties.

A donor level $E_d$ appears just below the conduction band $E_c$

Arsenic is pentavalent and acts as a donor. Its loosely held fifth electron creates a donor level $E_d$ just below the conduction band $E_c$, giving n-type behaviour.

Doping changes the dominant carrier type but leaves the crystal electrically neutral overall

Each dopant atom substitutes for a silicon atom and contributes the same number of nuclear charges as the atom it replaces, so the crystal remains neutral. Only the balance of carrier types changes.

III-V semiconductors combine one Group III element with one Group V element

III-V compounds pair a Group III element with a Group V element, while II-VI compounds pair a Group II element with a Group VI element.

Replace a pentavalent dopant with a trivalent dopant

Pentavalent donors give electron-majority n-type material; trivalent acceptors give hole-majority p-type material. Switching the dopant type switches the dominant carrier.

$1.5 \times 10^{2} \text{ cm}^{-3}$

Using the mass action law, we have \( n \cdot p = n_i^2 \). Given \( p = 1.5 \times 10^{16} \text{ cm}^{-3} \) and \( n_i = 1.5 \times 10^{10} \text{ cm}^{-3} \), we can calculate \( n \):…