The resistivity (\(\rho\)) of silicon doped with phosphorus can be estimated using the formula:
\[
\rho = \frac{1}{q \mu_n N_D}
\]
where \(q\) is the charge of an electron (\(1.6 \times 10^{-19}\) Coulombs), \(\mu_n\) is the mobility of electrons in
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