Question

A potential difference of \(2V\) is applied between the opposite faces of a Ge crystal plate of area \(1\,cm^2\) and thickness \(0.5\,mm\). If the concentration of electrons in Ge is \(2\times 10^{19}\,m^{-3}\) and mobilities of electrons and holes are \(0.36\,m^2V^{-1}s^{-1}\) and \(0.14\,m^2V^{-1}s^{-1}\), then the current flowing through the plate will be

• A. 0.25 A
• B. 0.45 A
• C. 0.56 A
• D. 0.64 A

Hint:

Use \(\sigma=ne(\mu_e+\mu_h)\), \(E=\dfrac{V}{d}\), \(J=\sigma E\), and \(I=JA\). Convert cm\(^2\) into m\(^2\) correctly.

Answer 1

The Correct Option is D

Step 1: Use conductivity of intrinsic semiconductor.
Current density:
\[ J = \sigma E \] where conductivity:
\[ \sigma = ne(\mu_e+\mu_h) \] Step 2: Calculate electric field.
Thickness \(d = 0.5\,mm = 5\times 10^{-4}\,m\).
\[ E = \frac{V}{d} = \frac{2}{5\times 10^{-4}} = 4\times 10^3\,V/m \] Step 3: Calculate conductivity.
Given:
\(n = 2\times 10^{19}\,m^{-3}\), \(e = 1.6\times 10^{-19}\,C\).
\[ \mu_e+\mu_h = 0.36+0.14 = 0.50 \] \[ \sigma = (2\times 10^{19})(1.6\times 10^{-19})(0.5) = (3.2)(0.5)=1.6\ S/m \] Step 4: Find current density.
\[ J = \sigma E = 1.6(4\times 10^3) = 6.4\times 10^3\,A/m^2 \] Step 5: Find current.
Area \(A = 1\,cm^2 = 10^{-4}\,m^2\).
\[ I = JA = 6.4\times 10^3 \times 10^{-4} = 0.64\,A \] Final Answer: \[ \boxed{0.64\ A} \]