Question

Answer the following questions about resistivity of Silicon at T=300 K. Assume, electron mobility, μn =1000 cm² /Vs and hole mobility, μp =500 cm² /Vs. Assume ni = 10¹⁰ /cm³ at room temperature.

Compute the resistivity of intrinsic Si at T=300 K.

Answer 1

To calculate the resistivity of intrinsic silicon at 300 K, we apply the resistivity formula considering the intrinsic charge carrier concentration and the given electron and hole mobilities to first find total conductivity and then take its reciprocal.

Step-by-step explanation:

To compute the resistivity of intrinsic silicon at 300 K, we use the formula ρ = 1 / (σ_n + σ_p), where ρ is the resistivity, and σ_n and σ_p are the conductivities for electrons and holes, respectively.

The conductivities are given by the product of charge carrier mobility, charge carrier concentration, and the charge of an electron (σ = q·n·μ). In this case, for intrinsic silicon, electron concentration (n) and hole concentration (p) are equal to the intrinsic carrier concentration (n_i). Therefore, the conductivity for electrons (σ_n) and for holes (σ_p) can be calculated by substituting the given values into σ_n = q·n_i·μ_n and σ_p = q·n_i·μ_p, where μ_n and μ_p are the electron and hole mobilities, respectively, and q is the charge of an electron (1.602 x 10^-19 C).

After determining σ_n and σ_p, we sum them to find the total conductivity, then take the reciprocal to get the resistivity. Given that μ_n = 1000 cm²/Vs, μ_p = 500 cm²/Vs, and n_i = 10¹° /cm³, we can compute the resistivity of intrinsic silicon at 300 K.