Question

If the number of electron-hole pairs per cm\(^3\) of an intrinsic Si wafer at temperature 300 K is \(1.1 \times 10^{10}\) and the mobilities of electrons and holes at 300 K are 1500 and 500 cm\(^2\) per volt, second, respectively, then the conductivity of the Si wafer at this temperature (in \(\mu\)mho cm\(^{-1}\)) is nearly:

• A. 352
• B. 35.2
• C. 3.52
• D. 70.4
• E. 17.6

Hint:

The unit of conductivity is Siemens per meter (S/m), but here it is expressed in micro-Siemens per centimeter (\(\mu\)mho cm\(^{-1}\)).

Answer 1

The Correct Option is C

The conductivity \(\sigma\) of the semiconductor can be calculated using the formula: \[ \sigma = e (n \mu_n + p \mu_p) \] where \(e\) is the elementary charge (\(1.6 \times 10^{-19}\) C), \(n\) and \(p\) are the concentrations of electrons and holes, and \(\mu_n\) and \(\mu_p\) are their mobilities. Given \(n = p = 1.1 \times 10^{10}\) cm\(^{-3}\), \(\mu_n = 1500\) cm\(^2\)/Vs, and \(\mu_p = 500\) cm\(^2\)/Vs: \[ \sigma = (1.6 \times 10^{-19}) \times (1.1 \times 10^{10} \times 1500 + 1.1 \times 10^{10} \times 500) \] \[ \sigma = (1.6 \times 10^{-19}) \times (1.1 \times 10^{10} \times 2000) = 3.52 \times 10^{-4} { S/cm} = 3.52 \times 10^{-6} \, \mu{mho cm}^{-1} \]