Classification by Conductivity
The first and most observable way to sort solids, given in NCERT §14.2, is by the relative values of their electrical conductivity $\sigma$ or its reciprocal, the resistivity $\rho = 1/\sigma$. On this scale solids fall into three broad classes. Metals have very low resistivity, in the range $\rho \sim 10^{-2}$ to $10^{-8}\ \Omega\,\text{m}$, with conductivity $\sigma \sim 10^{2}$ to $10^{8}\ \text{S m}^{-1}$. Insulators sit at the opposite extreme, with $\rho \sim 10^{11}$ to $10^{19}\ \Omega\,\text{m}$. Semiconductors occupy the intermediate territory, with $\rho \sim 10^{-5}$ to $10^{6}\ \Omega\,\text{m}$.
NCERT is careful to caution that these numbers are indicative of magnitude and could well fall outside the quoted ranges. Resistivity alone is not the only criterion that separates the three classes — there are other differences, the deepest of which is exposed only when we look at how electron energy levels are arranged inside the solid. That deeper description is the band theory of solids, and it is the part the NEET examiner tests most.
| Class | Resistivity $\rho$ ($\Omega\,\text{m}$) | Conductivity $\sigma$ ($\text{S m}^{-1}$) |
|---|---|---|
| Metals (conductors) | 10⁻² – 10⁻⁸ | 10² – 10⁸ |
| Semiconductors | 10⁻⁵ – 10⁶ | 10⁵ – 10⁻⁶ |
| Insulators | 10¹¹ – 10¹⁹ | 10⁻¹¹ – 10⁻¹⁹ |
Energy Bands in Solids
According to the Bohr model, an electron in an isolated atom occupies one of a set of sharp, discrete energy levels fixed by its orbit. When atoms are brought together to build a solid, NCERT explains, they sit so close that the outer orbits of neighbouring atoms come very near or even overlap, and the motion of the electrons becomes quite different from that in an isolated atom. Inside the crystal every electron sees a slightly different pattern of surrounding charges, so no two electrons have exactly the same energy. The result is that the single sharp level of the free atom spreads into a near-continuous range of closely spaced levels called an energy band.
Two of these bands matter for conduction. The band that contains the energy levels of the valence electrons is the valence band; the band lying immediately above it is the conduction band. With no external energy supplied, all the valence electrons reside in the valence band and the conduction band is normally empty. NIOS §28.1 reaches the same picture from the Pauli exclusion principle: when $N$ atoms interact, each atomic state splits into $2N$ states so finely spaced (about $10^{-23}\ \text{eV}$ apart) that they form a quasi-continuous band.
NCERT works the count explicitly for silicon and germanium. Each atom has four outer electrons (the $2s$ and $2p$ type levels of the outermost shell — the third orbit for Si, the fourth for Ge), so a crystal of $N$ atoms holds $4N$ valence electrons. The outer shell can hold a maximum of eight electrons, giving $8N$ available states. At the lattice spacing of Si and Ge these $8N$ states split into two bands separated by an energy gap $E_g$: a lower valence band fully occupied by the $4N$ valence electrons at absolute zero, and an upper conduction band of $4N$ states that is completely empty at absolute zero.
At absolute zero the valence band is full, the conduction band is empty, and they are separated by the energy gap $E_g$ between $E_V$ and $E_C$.
The Energy Gap Eg
The lowest energy level of the conduction band is written $E_C$ and the highest level of the valence band is written $E_V$. The separation between the top of the valence band and the bottom of the conduction band is the energy band gap, $E_g = E_C - E_V$. This single quantity is the master variable of the whole subtopic. NCERT states plainly that $E_g$ may be large, small, or zero depending on the material, and it is exactly this difference that produces the three classes of solids.
The physical meaning is straightforward. An electron sitting in the valence band can contribute to electrical conduction only if it is promoted across the gap into the conduction band, where empty states are available for it to move through. If the gap is small, modest thermal energy at room temperature is enough to lift a few electrons across; if the gap is large, even thermal excitation cannot manage it; and if there is no gap at all — or the bands overlap — electrons move into conduction states with no barrier whatsoever.
Three Cases of Band Structure
NCERT Fig. 14.2 distinguishes the three classes through three distinct band pictures, summarised below.
Metal: bands overlap, $E_g \approx 0$. Semiconductor: small gap, $E_g < 3\ \text{eV}$. Insulator: large gap, $E_g > 3\ \text{eV}$.
Case I — Metals. A metal arises either when the conduction band is partially filled and the valence band partially empty, or when the conduction and valence bands overlap. Where there is overlap, electrons from the valence band move into the conduction band with no barrier, making a large number of electrons available for conduction. The resistance is therefore low and the conductivity high.
Case II — Insulators. Here a large band gap exists, $E_g > 3\ \text{eV}$. There are no electrons in the conduction band and no conduction is possible. The gap is so large that thermal excitation cannot lift electrons from the valence band into the conduction band.
Case III — Semiconductors. A finite but small band gap, $E_g < 3\ \text{eV}$, separates the bands. Because the gap is small, at room temperature some valence electrons acquire enough energy to cross it and enter the conduction band. These carriers, though few in number, allow conduction, so the resistance of a semiconductor is not as high as that of an insulator. The chapter summary fixes the working bands as $E_g > 3\ \text{eV}$ for insulators, $E_g$ from $0.2\ \text{eV}$ to $3\ \text{eV}$ for semiconductors, and $E_g \approx 0$ for metals.
Once a few electrons cross the gap they leave behind mobile vacancies. See how this generates electron–hole pairs in Intrinsic Semiconductors.
Comparison Table
The table below consolidates the band-gap, conductivity and resistivity criteria with NCERT's own example materials, so the three classes can be told apart at a glance.
| Property | Conductor (metal) | Semiconductor | Insulator |
|---|---|---|---|
| Energy gap $E_g$ | $\approx 0$ (bands overlap) | small, $< 3\ \text{eV}$ (about $0.2$–$3\ \text{eV}$) | large, $> 3\ \text{eV}$ |
| Conduction band at 0 K | partially filled / overlapping | empty | empty |
| Conductivity $\sigma$ ($\text{S m}^{-1}$) | 10² – 10⁸ | 10⁵ – 10⁻⁶ | 10⁻¹¹ – 10⁻¹⁹ |
| Resistivity $\rho$ ($\Omega\,\text{m}$) | 10⁻² – 10⁻⁸ | 10⁻⁵ – 10⁶ | 10¹¹ – 10¹⁹ |
| Examples | Cu, Sn ($E_g = 0$) | Si ($1.1\ \text{eV}$), Ge ($0.7\ \text{eV}$) | diamond / C ($5.4\ \text{eV}$) |
Why C, Si and Ge Differ
Carbon (diamond), silicon and germanium all sit in group IV with four valence electrons and share the same diamond-like crystal structure, yet diamond is an insulator while Si and Ge are semiconductors. NCERT resolves this with the band gaps: for C, Si and Ge the energy gaps are $5.4\ \text{eV}$, $1.1\ \text{eV}$ and $0.7\ \text{eV}$ respectively. Tin (Sn) is also a group IV element, but it is a metal because its energy gap is $0\ \text{eV}$.
The reason the gaps differ lies in which orbit holds the bonding electrons. In carbon they lie in the second orbit, in silicon the third, and in germanium the fourth. The energy needed to remove an electron is greatest for carbon and least for germanium, so the number of electrons free for conduction is significant in Ge and Si but negligibly small in C. The ordering $(E_g)_C > (E_g)_{Si} > (E_g)_{Ge}$ is a frequently tested relation.
C, Si and Ge have the same lattice structure. Why is C an insulator while Si and Ge are intrinsic semiconductors?
The four bonding electrons of C, Si and Ge lie in the second, third and fourth orbits respectively. The energy required to remove an electron (the gap $E_g$) is therefore least for Ge, more for Si, and highest for C. Hence the number of free electrons available for conduction is significant in Ge and Si but negligibly small in C, making C an insulator and Si and Ge semiconductors.
Temperature Dependence
A defining and heavily tested feature of semiconductors is how their conduction responds to heat. In a semiconductor the band gap is small, so raising the temperature gives more valence electrons enough thermal energy to cross into the conduction band. This increases the number of charge carriers, so the conductivity rises and the resistivity falls as the temperature is raised. NIOS adds the limiting case: at absolute zero a semiconductor has no electrons in the conduction band and behaves like a perfect insulator.
A metal behaves in the opposite manner. Its conduction band is already richly populated and the carrier count is essentially fixed, so heating does not add carriers. Instead it intensifies the lattice vibrations that scatter the moving electrons, which raises resistivity and lowers conductivity. This contrast — conductivity rising with temperature for a semiconductor but falling for a metal — is one of the cleanest fingerprints distinguishing the two.
Same direction of heating, opposite response
Students routinely mix up the temperature behaviour and the band-gap values. Heating a semiconductor pushes more electrons across the small gap, so conductivity increases; heating a metal increases scattering, so conductivity decreases. Equally, the gap thresholds are easy to invert: insulators have the large gap ($> 3\ \text{eV}$), semiconductors the small gap ($< 3\ \text{eV}$, around $1\ \text{eV}$). Remember Si $= 1.1\ \text{eV}$ and Ge $= 0.7\ \text{eV}$ are semiconductor values, not insulator values.
Semiconductor: small $E_g$, $\sigma$ rises with $T$. Metal: $E_g \approx 0$, $\sigma$ falls with $T$. Insulator: large $E_g > 3\ \text{eV}$, effectively no conduction.
Band theory classification at a glance
- Solids classify by resistivity: metals $\rho \sim 10^{-2}$–$10^{-8}\ \Omega\,\text{m}$, semiconductors $\sim 10^{-5}$–$10^{6}$, insulators $\sim 10^{11}$–$10^{19}$.
- Energy bands form when atomic levels split and spread; the valence band holds valence electrons, the conduction band lies above it.
- The energy gap $E_g = E_C - E_V$ is the master variable: metal $E_g \approx 0$ (overlap), semiconductor $E_g < 3\ \text{eV}$, insulator $E_g > 3\ \text{eV}$.
- NCERT values: C $= 5.4\ \text{eV}$ (insulator), Si $= 1.1\ \text{eV}$, Ge $= 0.7\ \text{eV}$, Sn $= 0\ \text{eV}$ (metal); ordering $(E_g)_C > (E_g)_{Si} > (E_g)_{Ge}$.
- Conductivity of a semiconductor rises with temperature; that of a metal falls — the carrier mechanisms are opposite.