Question
Explain band theory. How does the band gap differ in conductors, insulators, and semiconductors? What are n-type and p-type semiconductors?
(JEE Main and CBSE 12 — tested as conceptual MCQs and assertion-reason)
Solution — Step by Step
In an isolated atom, electrons occupy discrete energy levels. When atoms come together in a solid, each energy level splits into closely spaced levels, forming a continuous energy band.
Two bands matter most:
- Valence band: The highest energy band that is occupied by electrons at 0 K
- Conduction band: The next higher energy band (empty or partially filled)
- Band gap (): The energy difference between the top of the valence band and bottom of the conduction band
| Material | Band Gap | Conductivity | Example |
|---|---|---|---|
| Conductor | Zero (bands overlap) | Very high | Cu, Ag, Au, Fe |
| Insulator | Large (> 3 eV) | Negligible | Diamond ( = 5.5 eV), rubber |
| Semiconductor | Small (0.1-3 eV) | Moderate, increases with temperature | Si ( = 1.1 eV), Ge ( = 0.7 eV) |
In conductors, the valence and conduction bands overlap — electrons move freely. In insulators, the gap is so large that electrons cannot jump across at normal temperatures. Semiconductors sit in between.
n-type semiconductor: Silicon doped with a Group 15 element (P, As). The dopant has 5 valence electrons — 4 bond with Si, 1 is free (extra electron = negative carrier). Majority carriers: electrons.
p-type semiconductor: Silicon doped with a Group 13 element (B, Al, Ga). The dopant has 3 valence electrons — creates a hole (missing electron = positive carrier). Majority carriers: holes.
A p-n junction (combining p-type and n-type) forms the basis of diodes, transistors, and solar cells.
graph TD
A["Band Theory"] --> B["Conductor"]
A --> C["Semiconductor"]
A --> D["Insulator"]
B --> E["No band gap - Bands overlap"]
C --> F["Small band gap 0.1-3 eV"]
D --> G["Large band gap > 3 eV"]
C --> H["Doping"]
H --> I["n-type: Group 15 dopant"]
H --> J["p-type: Group 13 dopant"]
I --> K["Majority carrier: electrons"]
J --> L["Majority carrier: holes"]Why This Works
Band theory explains why electrical conductivity varies so dramatically across materials. Metals conduct because their electrons can move freely (overlapping bands). Diamond insulates because its electrons are locked in the valence band with no way to reach the conduction band (5.5 eV gap). Silicon semiconducts because a small energy input (heat, light) can push electrons across the narrow gap.
Doping works because it introduces energy levels within the band gap. In n-type Si, the extra electron from phosphorus sits just below the conduction band — it needs very little energy to jump in. In p-type Si, the hole (from boron) sits just above the valence band — electrons from the valence band can easily fill it, creating mobile holes.
Alternative Method
For JEE, remember this trend: semiconductor conductivity increases with temperature (more electrons gain enough energy to cross the gap), while metal conductivity decreases with temperature (increased lattice vibrations scatter electrons). If a question asks “which material’s conductivity increases with temperature?” — the answer is semiconductor.
Common Mistake
Students often confuse intrinsic and extrinsic semiconductors. An intrinsic semiconductor (pure Si) has equal numbers of electrons and holes. An extrinsic semiconductor (doped Si) has unequal carriers — n-type has more electrons, p-type has more holes. When a JEE question says “pure silicon at room temperature,” it is intrinsic — do not apply doping concepts.
Also, adding a Group 15 element creates an n-type (not p-type) semiconductor. The extra electron makes it n-type. Students sometimes reverse this, thinking “extra electron fills a hole, so it is p-type.” No — the extra electron is a free carrier, making it n-type (negative).