Question

After adding an impurity atom that donates an extra electron to the conduction band of silicon (μ_n = 0.13 m²/Vs), the conductivity of the doped silicon is measured as 1.08 (Ωm⁻¹). Determine the doped ratio (density of silicon is 2,420 kg/m³).

Answer 1

The number of silicon atoms/m³

Let x be the fraction of impurity atom (donor). The general expression for the conductivity is

where n_n and n_p are the densities of the negative and positive charge carriers. Because n_n >> n_p,

Note that in normal silicon the conductivity is of the order of 10⁻⁴(Ω− m)⁻¹. A small fraction of doping (10⁻⁹) has dramatically increased the value by four orders of magnitude.