Energy Bands in Solids — Conductor, Semiconductor, Insulator Band Structure

In an isolated atom, electrons occupy discrete energy levels. When billions of atoms come together in a solid, each level splits into a band of closely spaced levels (due to the Pauli exclusion principle).

Two bands matter most:

• Valence band (VB): The highest energy band that is fully or partially filled with electrons at 0 K
• Conduction band (CB): The next higher band, which may be empty or partially filled
• Band gap ($E_g$): The energy gap between VB and CB

graph TD
    subgraph Conductor
        A1[Conduction Band - partially filled]
        A2[Valence Band]
        A1 --- A2
    end

    subgraph Semiconductor
        B1[Conduction Band - empty at 0K]
        B2["Small gap Eg = 0.1-3 eV"]
        B3[Valence Band - full at 0K]
        B1 --- B2
        B2 --- B3
    end

    subgraph Insulator
        C1[Conduction Band - empty]
        C2["Large gap Eg > 3 eV"]
        C3[Valence Band - full]
        C1 --- C2
        C2 --- C3
    end

At 0 K, a semiconductor’s VB is full and CB is empty — no current flows. When temperature rises, thermal energy ($kT \approx 0.026$ eV at room temperature) gives some electrons enough energy to jump the small band gap into the CB.

Each electron that jumps creates TWO charge carriers: a free electron in the CB and a hole in the VB. Higher temperature = more carriers = higher conductivity.

For insulators, $E_g$ is so large that thermal energy at normal temperatures cannot excite electrons across the gap. For conductors, the bands overlap, so carriers are always available regardless of temperature.