Band Theory & Electrical Properties

The Bandgap

Direct vs indirect bandgaps, temperature effects, and bandgap engineering

Direct vs Indirect Bandgaps

Direct vs Indirect Bandgaps

Bandgaps come in two varieties based on the crystal's momentum-energy relationship:

  • Direct bandgap: An electron can transition between bands by absorbing/emitting a photon directly. Materials: GaAs, GaN, InP. These are excellent for LEDs and lasers.
  • Indirect bandgap: The transition requires both a photon and a phonon (lattice vibration) to conserve momentum. Materials: Si, Ge. This makes silicon a poor light emitter but fine for electronics.

Key Concept: Why Silicon LEDs Don't Work

Silicon's indirect bandgap means it can't efficiently convert electrical energy to light. This is why LEDs use direct-bandgap materials like GaN (blue/white) and GaAs/InGaP (red). However, silicon's indirect bandgap is perfectly fine for transistors and logic circuits.

Temperature Effects on Bandgap

Temperature Effects on Bandgap

The bandgap decreases with increasing temperature. For silicon:

  • At 0 K: Eg = 1.17 eV
  • At 300 K (room temp): Eg = 1.12 eV
  • At 400 K: Eg = 1.09 eV

This happens because thermal expansion weakens atomic bonds and lattice vibrations perturb the periodic potential.

The practical consequence: at higher temperatures, more electrons are thermally excited across the bandgap, increasing leakage current. This is why hot chips leak more power and why cooling is critical in modern processors.

Analogy: A Lower Fence

As temperature rises, the bandgap "fence" between the valence and conduction bands gets shorter. More electrons can jump over a shorter fence, leading to more leakage — electrons going where you don't want them.

Knowledge Check

Knowledge Check

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Why can't silicon be used efficiently in LEDs?