Conductors, Insulators, Semiconductors — Revision Notes

⚡ 30-Second Revision

Conductors — $E_g \approx 0$ (overlapping bands or partially filled CB). High conductivity. Conductivity decreases with T.
Insulators — $E_g > 3 \text{ eV}$. Very low conductivity. Conductivity almost constant with T.
Semiconductors — $0.5 \text{ eV} < E_g < 3 \text{ eV}$. Moderate conductivity. Conductivity increases with T.
Valence Band (VB) — Filled with bonding electrons.
Conduction Band (CB) — Contains free electrons.
Forbidden Energy Gap ($E_g$) — Energy barrier between VB and CB.
Charge Carriers (Semiconductors) — Electrons (in CB) and Holes (in VB).

2-Minute Revision

The electrical properties of materials are determined by their energy band structure, specifically the valence band (VB), conduction band (CB), and the forbidden energy gap ($E_g$) between them. Conductors, like metals, have overlapping VB and CB or a partially filled CB, meaning $E_g \approx 0$.

This allows electrons to move freely, resulting in high conductivity that decreases with increasing temperature due to increased lattice scattering. Insulators, such as glass, have a large $E_g$ (typically $>3 \text{ eV}$) between a filled VB and an empty CB.

This large barrier prevents electron movement, leading to very low conductivity, largely unaffected by temperature. Semiconductors, like silicon, have a small to moderate $E_g$ (typically $0.5 \text{ eV}$ to $3 \text{ eV}$).

At room temperature, some electrons gain enough thermal energy to jump the gap, creating electron-hole pairs that act as charge carriers. Consequently, semiconductor conductivity is moderate and significantly increases with rising temperature.

Understanding these band structures and their temperature dependence is crucial for NEET.

5-Minute Revision

To master conductors, insulators, and semiconductors for NEET, focus on their defining characteristics based on the energy band theory. Every solid material possesses energy bands: the valence band (VB), which contains electrons involved in bonding, and the conduction band (CB), where electrons are free to move and conduct electricity. The **forbidden energy gap ($E_g$)** is the energy difference an electron must overcome to jump from the VB to the CB.

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Conductors — Characterized by overlapping VB and CB, or a partially filled CB. This means $E_g \approx 0$. Electrons are readily available for conduction. Their conductivity is very high (resistivity is very low, e.g., $10^{-8} \text{ \Omega m}$). As temperature increases, lattice vibrations increase, scattering electrons more, thus conductivity decreases.

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Insulators — Have a completely filled VB and a completely empty CB, separated by a **large $E_g$ (typically $>3 \text{ eV}$)**. Examples: Diamond ($E_g \approx 5.5 \text{ eV}$), glass ($E_g \approx 9 \text{ eV}$). The large gap prevents electrons from gaining enough thermal energy to jump to the CB. Their conductivity is extremely low (resistivity is very high, e.g., $10^{10} \text{ \Omega m}$). Conductivity is largely unaffected by temperature until dielectric breakdown occurs at very high fields/temperatures.

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Semiconductors — Possess a filled VB and an empty CB at 0 K, separated by a **small to moderate $E_g$ (typically $0.5 \text{ eV}$ to $3 \text{ eV}$)**. Examples: Silicon ($E_g \approx 1.12 \text{ eV}$), Germanium ($E_g \approx 0.67 \text{ eV}$). At 0 K, they behave as insulators. At room temperature, some electrons gain enough thermal energy to jump the gap, creating electron-hole pairs. Both electrons (in CB) and holes (in VB) act as charge carriers. Their conductivity is intermediate (resistivity e.g., $10^{-5} \text{ \Omega m}$) and increases significantly with increasing temperature due to more electron-hole pair generation.

Key takeaway: The magnitude of $E_g$ and the temperature dependence of conductivity are the most testable aspects. Always relate the material's behavior back to its band structure.

Prelims Revision Notes

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Energy Bands — In solids, discrete atomic energy levels broaden into continuous bands: Valence Band (VB) and Conduction Band (CB).
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Valence Band (VB) — Highest energy band occupied by electrons at 0 K. Electrons here are typically bound.
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Conduction Band (CB) — Lowest energy band that can accept free electrons. Electrons here contribute to current.
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Forbidden Energy Gap ($E_g$) — Energy difference between the top of VB and bottom of CB. No electron states exist here.
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Conductors (e.g., Metals)

* Band Structure: VB and CB overlap, or CB is partially filled. $E_g \approx 0$. * Conductivity: Very high. Abundant free electrons. * Temperature Effect: Conductivity decreases with increasing temperature (due to increased lattice vibrations scattering electrons). * Resistivity: Very low ($10^{-8} \text{ \Omega m}$ range).

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Insulators (e.g., Glass, Diamond)

* Band Structure: Filled VB, empty CB. Large $E_g > 3 \text{ eV}$. (e.g., Diamond $E_g \approx 5.5 \text{ eV}$). * Conductivity: Extremely low. Electrons cannot easily jump the large gap. * Temperature Effect: Conductivity remains almost constant, very low (until breakdown). * Resistivity: Very high ($10^{10} \text{ \Omega m}$ to $10^{18} \text{ \Omega m}$ range).

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Semiconductors (e.g., Silicon, Germanium)

* Band Structure: Filled VB, empty CB at 0 K. Small to moderate $E_g$ ($0.5 \text{ eV} < E_g < 3 \text{ eV}$). (e.g., Si $E_g \approx 1.12 \text{ eV}$, Ge $E_g \approx 0.67 \text{ eV}$). * Conductivity: Intermediate.

At 0 K, acts as insulator. At room temp, some electrons jump to CB. * Charge Carriers: Electrons (in CB) and Holes (in VB, behave as positive charge). * Temperature Effect: Conductivity increases significantly with increasing temperature (due to more electron-hole pair generation).

* Resistivity: Moderate ($10^{-5} \text{ \Omega m}$ to $10^5 \text{ \Omega m}$ range).

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Key Concept — The magnitude of $E_g$ is the primary determinant of a material's electrical classification.

Vyyuha Quick Recall

To remember the band gap sizes: Conductors In Small Gaps.

Conductors: Invisible Gap (overlapping/zero $E_g$)
Insulators: Super Gap (large $E_g$)
Semiconductors: Moderate Gap (small $E_g$)