The table below gives the resistivity (at 20 °C), free electron density (at 20 °C), and the temperature coefficient of n-type silicon, a common semiconductor.
Material | Resistivity (ρ) at 20°C | Free Electron Density (n) at 20°C | Temperature Coefficient (α)
Silicon | 2.72 × 10⁻² Ωm | 4.60 × 10²² m⁻³ | – 0.075 °C⁻¹
(i) Use the Drude model, ρ = m_e / (nq²τ), to calculate the mean free time between collisions, τ, of the free electrons in this material at 20°C (assume m_e = 9.11 × 10⁻³¹ kg).
(ii) Use the Drude model to explain why the resistivity of silicon decreases with temperature.