Answer:
The necessary number of electron charge carriers required is:
8.1019 × 10¹⁹ electrons/m³
Explanation:
The necessary number of charge carriers required can be determined from the resistivity. Given that, the phosphorus make an n-type of silicon semiconductor;
Resistivity [tex]\rho = \dfrac{1}{\sigma}[/tex]
[tex]\rho = \dfrac{1}{q \mu _n n_n}[/tex]
where;
The number of electron on the charge carriers [tex]n_n[/tex] is unknown??
The charge of the electron q = [tex]1.6 \times 10^{-19} \ C[/tex]
The electron mobility [tex]\mu_n[/tex] = 0.135 m²/V.s
The electrical conductivity [tex]\sigma[/tex] = 1.75 (Ωm)⁻¹
Making [tex]n_n[/tex] the subject from the above equation:
Then;
[tex]n_n = \dfrac{\sigma }{q \mu_n}[/tex]
[tex]n_n = \dfrac{1.75 \ \Omega .m^{-1} }{1.6 \times 10^{-19} \times 0.135 \ m^2/V.s}[/tex]
[tex]n_n =8.1019 \times 10^{19}[/tex] electrons/m³
Thus; the necessary number of electron charge carriers required is:
8.1019 × 10¹⁹ electrons/m³