Bandgap

The bandgap $E_g$ is the energy difference between the top of the valence band and the bottom of the conduction band — the size of the forbidden zone an electron must jump to become a free charge carrier. It is the single number that sorts materials into conductors, insulators, and semiconductors.

$E_g=E_c-E_v$

where $E_c$ is the energy of the conduction-band edge and $E_v$ that of the valence-band edge. It is quoted in electron-volts (eV): one eV is the energy an electron gains falling through one volt, $1\text{eV}=1.602\times 10^{-19}\text{J}$.

What the value tells you

The bandgap directly classifies the material via band theory:

• Zero (or overlapping bands) → conductor.
• A few eV → insulator; thermal energy can never lift electrons across, so no carriers.
• Moderate → semiconductor. For silicon, $E_g\approx 1.1\text{eV}$ (often quoted as $1.12\text{eV}$ at room temperature).

The reason $1.1\text{eV}$ is “moderate” is the comparison with thermal energy. At room temperature the characteristic thermal energy is $kT\approx 0.025\text{eV}$ (Boltzmann constant $k$ times absolute temperature $T$). Silicon’s gap is about 45 times that — far too big for most electrons to cross, but small enough that the exponential tail of the thermal distribution promotes a few. That balance is exactly what makes a semiconductor weakly conducting on its own and dramatically tunable by Doping.

Why the gap controls carrier generation

The probability that thermal energy promotes an electron across the gap goes as the Boltzmann factor $\exp (-E_g/2kT)$. This appears directly in the Intrinsic carrier concentration formula

$n_i=B{T}^{3/2}\exp (-\frac{E_g}{2kT})$

so a larger $E_g$ means exponentially fewer intrinsic carriers, and the count is extremely temperature-sensitive through the same factor. The exponent carries $E_g/2$ rather than $E_g$ because each excitation produces a pair (an electron and a hole), so the energy effectively splits between the two carriers in the statistics.

It sets photon energies later

The bandgap is also the energy released or absorbed when an electron crosses it by emitting or absorbing light. An electron dropping from the conduction band back to the valence band gives up roughly $E_g$ as a photon, so $E_g$ fixes the colour of light a Light-emitting diode emits ($E_{photon}=hf\approx E_g$), and conversely the minimum photon energy a material can absorb in a photodetector or solar cell. Whether that light emission is efficient depends on the direct vs indirect nature of the gap — silicon’s indirect gap is why silicon makes good transistors but poor LEDs.