Question

Pure silicon crystal at \(300\)K has equal electron and hole concentration \(2\times 10^{16}\) per m\({}^{3}\). Doping by indium increases hole concentration to \(4\times 10^{22}\) per m\({}^{3}\). Electron concentration in doped silicon is

• A. \(5\times 10^{9}/m^{3}\)
• B. \(10^{10}/m^{3}\)
• C. \(8\times 10^{10}/m^{3}\)
• D. \(10^{9}/m^{3}\)

Hint:

Use the law of mass action, where the product of electron and hole concentrations stays equal to the square of the intrinsic concentration.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In a doped semiconductor at a fixed temperature, \(n_e\,n_h=n_i^2\).

Step 2: Data
\(n_i=2\times10^{16}\,\text{m}^{-3}\) and \(n_h=4\times10^{22}\,\text{m}^{-3}\).

Step 3: Calculation
\(n_e=\dfrac{n_i^2}{n_h}=\dfrac{(2\times10^{16})^2}{4\times10^{22}}=\dfrac{4\times10^{32}}{4\times10^{22}}\)
\(n_e=10^{10}\,\text{m}^{-3}\)

Step 4: Compare the options
This matches option (B).

Final Answer:
The electron concentration is \(10^{10}\,/\text{m}^3\). \[ \boxed{\text{(B) }10^{10}/m^{3}} \]