43) In a semiconductor device operation, the current continuity equations are:
- A. \( \frac{\partial n}{\partial t} = G_n - U_n + \frac{1}{q} \nabla \cdot J_n \)
- B. \( \frac{\partial p}{\partial t} = G_p - U_p + \frac{1}{q} \nabla \cdot J_p \)
- C. \( \frac{\partial p}{\partial t} = G_p - U_p - \frac{1}{q} \nabla \cdot J_p \)
- D. \( \frac{\partial n}{\partial t} = G_n - U_n + \frac{1}{q} \nabla J_n \)
Choose the correct answer from the options given below:
For Holes (\(p\)):
Holes have a positive charge (\(+q\)). Current density \(J_p\) flows in the same direction as holes. If holes leave a region (positive divergence, \(\nabla \cdot J_p > 0\)), the hole concentration decreases. Therefore, we use a negative sign:
\[ \frac{\partial p}{\partial t} = G_p - U_p - \frac{1}{q} \nabla \cdot J_p \]
(This matches Statement C)
For Electrons (\(n\)):
Electrons have a negative charge (\(-q\)). Because of this negative charge, electron current \(J_n\) flows in the opposite direction to electron motion. If electrons leave a region, the math of the negative charge carrier flips the sign. Thus, for electrons, we use a positive sign:
\[ \frac{\partial n}{\partial t} = G_n - U_n + \frac{1}{q} \nabla \cdot J_n \]