The free electron concentration profile \(n(x)\) in a doped semiconductor at equilibrium is shown in the figure, where the points A, B, and C mark three different positions. Which of the following statements is/are true?
The free electron concentration profile \(n(x)\) in a doped semiconductor at equilibrium is shown in the figure, where the points A, B, and C mark three different positions. Which of the following statements is/are true?
For x between B and C, the electron diffusion current is directed from C to B.
For x between B and A, the electron drift current is directed from B to A.
For x between B and C, the electric field is directed from B to C.
For x between B and A, the electric field is directed from A to B.
The Correct Option is A, B, C
Solution and Explanation
The problem involves understanding the behavior of free electron concentration and analyzing the directions of diffusion and drift currents along with the electric field in a doped semiconductor.
- Electron Diffusion Current:
- The diffusion current occurs due to the gradient in electron concentration. It flows from a region of higher concentration to a lower concentration.
- In the figure, the concentration at C is lower than at B, indicating a negative gradient from B to C. Therefore, the electron diffusion current is directed from C to B.
- Thus, the statement "For x between B and C, the electron diffusion current is directed from C to B" is true.
- Electron Drift Current:
- The drift current is due to the electric field affecting the movement of charged particles. If the field is pointing in a particular direction, electrons (negative charge) move opposite to it.
- Between B and A, assuming an electric field is directed as described later, the drift current would be influenced by this field direction.
- This affirms the statement "For x between B and A, the electron drift current is directed from B to A" is true.
- Electric Field Direction:
- The electric field direction can be deduced based on the potential and charge carrier movement.
- If the electron concentration decreases (from B to C), an electric field develops pointing from B to C to balance the diffusion.
- Therefore, the statement "For x between B and C, the electric field is directed from B to C" is confirmed to be true.
- Electric Field between B and A:
- Given the concentration gradient, an opposite electric field from A to B counteracts diffusion.
- However, our analysis shows this is consistent with the given diffusion directions and current behaviors.
- The statement is misleading concerning known electric field effects derived from potential variations.
Based on the analysis above, the correct statements are the diffusion and drift current directions and the electric field between B and C.
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