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Carbon, silicon, germanium and tin sit in the same group of the periodic table, and the first three share the same diamond-like crystal structure. Yet diamond insulates, silicon and germanium conduct a little, and tin is a metal. One number explains the difference: the energy gap between two bands. This post explains the band picture in plain terms, works three calculations with that number and lists the mistakes that cost marks.
Where is this in the syllabus?
The CBSE Physics curriculum for 2026-27 lists "Energy bands in conductors, semiconductors and insulators (qualitative ideas only)" in Chapter 14. The current NCERT chapter Semiconductor Electronics: Materials, Devices and Simple Circuits covers it in its section on classifying solids. The JEE (Main) 2026 syllabus and the NEET (UG) 2026 syllabus open their Electronic Devices unit with "Semiconductors". The JEE (Advanced) 2026 brochure has no semiconductor topic in its physics syllabus. Check the documents for your own exam year.
Our guide to diodes, Zener regulators and logic gates covers the devices. This post stays with the bands underneath them.
What is an energy band?
In a single atom, electrons occupy sharp energy levels. NCERT explains that in a crystal the atoms are so close that the outer levels of neighbouring atoms interact and spread into bands of very closely spaced levels. The valence band holds the valence electrons. The conduction band lies above it. The gap between the top of the valence band and the bottom of the conduction band is the band gap, Eg.
How does the band gap sort materials?
NCERT describes three cases:
Metals: the conduction band is partly filled, or the two bands overlap, so electrons can move into empty levels with almost no extra energy. Tin's gap is 0 eV.
Insulators: a large gap, Eg > 3 eV. Diamond's is 5.4 eV.
Semiconductors: a small gap, Eg < 3 eV. Silicon's is 1.1 eV and germanium's 0.7 eV.
NCERT also gives indicative resistivity ranges: about 10⁻⁸ to 10⁻² Ω m for metals, 10⁻⁵ to 10⁶ Ω m for semiconductors and 10¹¹ to 10¹⁹ Ω m for insulators. It warns that resistivity alone does not decide the class.
Worked example 1: which light can cross the gap?
A photon can lift an electron from the valence band to the conduction band only if its energy is at least Eg. The longest such wavelength is λ = hc/Eg, with hc ≈ 1240 eV nm.
Diamond: 1240 ÷ 5.4 ≈ 230 nm, in the ultraviolet.
Silicon: 1240 ÷ 1.1 ≈ 1130 nm, in the infrared.
Germanium: 1240 ÷ 0.7 ≈ 1770 nm.
Visible light runs from about 400 to 700 nm, so its photons carry roughly 3.1 to 1.8 eV. None of them has 5.4 eV, so visible light cannot lift electrons across diamond's gap, which is why pure diamond is transparent. All of them have more than 1.1 eV, so silicon absorbs visible light. NCERT's 3 eV dividing line works out to about 413 nm, close to the violet end of the visible range. For more photon-energy practice, see our photoelectric effect problems.
Worked example 2: why does temperature matter so much?
At 300 K, the thermal energy scale kT is about 0.026 eV. Silicon's gap is about 43 times that, and diamond's about 209 times, so only a tiny fraction of electrons is thermally excited across. NCERT's own numbers show how tiny: pure silicon has about 5 × 10²⁸ atoms per m³ and an intrinsic carrier density of 1.5 × 10¹⁶ m⁻³, roughly one free electron for every 3 × 10¹² atoms.
Compare a donor electron from a pentavalent dopant. NCERT says it needs only about 0.05 eV in silicon, about twice kT, so almost every donor is ionised at room temperature.
This also explains the temperature trend. NCERT's Current Electricity chapter notes that in a metal the number of free electrons hardly changes with temperature, so more frequent collisions make resistivity rise. In semiconductors and insulators the carrier number rises with temperature, more than making up for the collisions, so resistivity falls.
Worked example 3: carriers in a doped crystal
Sample numbers: silicon with 5 × 10²⁸ atoms m⁻³ is doped with boron at 0.1 parts per million.
Acceptor density: N_A = 5 × 10²⁸ × 10⁻⁷ = 5 × 10²¹ m⁻³, so holes n_h ≈ 5 × 10²¹ m⁻³.
Use n_e n_h = n_i²: n_e = (1.5 × 10¹⁶)² ÷ (5 × 10²¹) = 2.25 × 10³² ÷ 5 × 10²¹ = 4.5 × 10¹⁰ m⁻³.
Holes outnumber electrons by about 10¹¹ to one, so the crystal is p-type. NCERT's Example 14.2 does the n-type version with arsenic at 1 ppm.
Which mistakes cost marks?
Saying insulators "have no electrons". Their valence band is full; the problem is the large gap above it.
Saying metals conduct because their gap is small. There is no gap, or the band is only partly filled.
Claiming every material's resistivity rises with temperature.
Mixing up the band gap of silicon (1.1 eV) with the donor ionisation energy (about 0.05 eV).
Treating 3 eV as an exact law. NCERT calls its ranges indicative.
A practice routine
Draw the three band diagrams from memory, label the valence band, conduction band and Eg, and write one sentence under each.
Repeat example 1 for sample gaps of 1.4, 2.3 and 3.4 eV, and name the part of the spectrum each wavelength falls in.
Redo example 3 with 1 ppm and then 0.01 ppm of boron.
In four sentences, explain why copper's resistivity rises and silicon's falls as both are heated.
If the step from atomic levels to bands still feels abstract, the Fermi Concept Library has every concept in physics, chemistry, biology, mathematics and computing, each with its own lesson and its place in the map.
Today, write NCERT's three band gaps on a card and turn each into a wavelength without a calculator.
