Example: Determine if a material with a band gap of 1.1 eV behaves as a metal, semiconductor, or insulator at room temperature (300 K). Step 1: Recall typical band gap ranges: - Metal: 0 eV (overlapping bands) - Semiconductor: 0.5 – 3 eV - Insulator: > 3 eV Step 2: Compare the given gap (1.1 eV) with the ranges. Step 3: 1.1 eV lies between 0.5 eV and 3 eV, so the material is a semiconductor. Step 4 (optional): Estimate intrinsic carrier concentration using n_i ≈ N_c exp(-Eg/2kT). Take N_c ≈ 10^19 cm⁻³, k = 8.617×10⁻5 eV/K. Calculate exponent: -Eg/(2kT) = -1.1/(2×8.617×10⁻5×300) ≈ -21.3. Thus n_i ≈ 10^19 × e^(‑21.3) ≈ 10^19 × 5.9×10⁻10 ≈ 5.9×10⁹ cm⁻³, a low but non‑zero carrier density, confirming semiconductor behavior.