Semiconductor Fundamentals and Band Theory
What Makes a Semiconductor Different?
Atomic origin of electrical behavior
Semiconductors sit between conductors and insulators because their electrons occupy energy bands with a moderate band gap . At , the valence band is nearly full and the conduction band is nearly empty, but at finite temperature some electrons gain enough energy to cross the gap and create mobile charge carriers.
Core idea
Electrical conductivity in semiconductors is controlled by both the number of carriers and how easily they move, so carrier concentration and mobility matter together.
Band diagrams and carrier creation
The band gap determines how many carriers are thermally generated. Larger means fewer intrinsic carriers at a given temperature. The intrinsic carrier concentration follows , which explains why small changes in temperature can strongly affect conductivity.
Material comparison
| Material | Band gap behavior | Typical role |
|---|---|---|
| Silicon | Moderate indirect band gap | Mainstream electronics |
| Germanium | Smaller band gap | High-speed and historical devices |
| Gallium arsenide | Direct band gap | Optoelectronics and RF |
| Insulator | Very large band gap | Electrical isolation |
Which feature most directly explains why an intrinsic semiconductor becomes more conductive as temperature increases?
Thermal energy excites electrons from the valence band into the conduction band, creating electron-hole pairs.
Correct answer: More electrons gain enough energy to cross the band gap
What are the two mobile carriers created when an electron is excited across the band gap?
Removing an electron from the valence band leaves behind a hole that behaves like a positive carrier.
Correct answer: An electron and a hole
Conductors, semiconductors, and insulators
Conductors
- Bands overlap or are partially filled
- High carrier density even at low temperature
Semiconductors
- Small to moderate band gap
- Carrier density is strongly tunable
How to reason from a band diagram
-
1
Identify the valence and conduction bands and estimate the gap size.
-
2
Check whether the Fermi level lies near the middle, the conduction band, or the valence band.
-
3
Ask whether carriers are generated thermally, by doping, or by optical excitation.
-
4
Connect carrier density to conductivity through .
For an intrinsic semiconductor at equilibrium, how do electron and hole concentrations compare?
In intrinsic material, each thermally generated electron is paired with one hole, so .
Correct answer: They are equal
Write the conductivity formula for a semiconductor using carrier concentrations and mobilities.
This expression shows that both electrons and holes contribute to conductivity.
Correct answer: σ = q(nμ_n + pμ_p)