Physics · Class 12

Bands and thermal excitation

Allowed bands and gaps restrict electron states. A moderate gap permits thermally generated electron-hole pairs; a large gap suppresses them. A conductor needs available states near occupied ones, not simply a large number of electrons.

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Bands and thermal excitation

அனுமதிக்கப்பட்ட ஆற்றல் பட்டைகளுக்கும் அவற்றின் இடைவெளிக்கும் கடத்துத்திறனில் பங்கு உண்டு. வெப்பம் எலக்ட்ரான்–துளை ஜோடிகளை உருவாக்கலாம்.

Key notes, relationships and model limits

Key relationship

kBT≈8.617×10⁻⁵ T eV; intrinsic carrier factor ∝exp(−Eg/(2kBT)).

Remember

Common trap

The thermal factor alone is not a complete conductivity model.

Model limits

Schematic band classification; Boltzmann thermal factor omits density-of-states prefactors and mobility. Metallic transport is not modelled by the intrinsic formula; zero gap only illustrates overlap.

What you will learn

Interpret energy-band diagrams and gap-dependent excitation.

Try the experiment

Try both scenarios, change one control, and predict the result before checking the graph and readouts.

Think of it this way

Change one input while keeping the others fixed, as you would in a controlled experiment.

Worked example

At300 K,kT≈0.02585 eV; a1.1 eV gap has a very small thermal factor.

Why this matters

The model connects bands and thermal excitation with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

Increasing semiconductor temperature generally changes the intrinsic thermal factor how?

It decreases
It increases
It always becomes zero

Read the explanation

The exponent−Eg/(2kT) becomes less negative.

Course connection: Class XII Chapter 14. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.