The resistivity ρ of doped silicon is based on the charge q on an electron, the electron d...

The resistivity ρ of doped silicon is based on the charge q on an electron, the electron density n, and the electron mobility μ. The electron density is given in terms of the doping density N and the intrinsic carrier density ni. The electron mobility is described by the temperature T, the reference temperature T0, and the reference mobility μ0. The equations required to compute the resistivity are

where

Determine N, given T0 = 300 K, T = 1000 K, μ0 = 1360 cm2 (V s)-1, q = 1.7 × 10-19 C, ni = 6.21 × 109 cm-3, and a desired ρ = 6.5 × 106 V s cm/C. Employ initial guesses of N = 0 and 2.5 × 1010. Use (a) bisection and (b) the false position method.