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Question #43376

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The Question

A closed isothermal circuit is maintained at a uniform temperature of $T = 300 \text{ K}$ . It consists of a Silicon PN-junction diode with a built-in potential $V_{bi,Si} = 0.7 \text{ V}$ , a Germanium PN-junction diode with a built-in potential $V_{bi,Ge} = 0.3 \text{ V}$ , and a resistor $R = 100 \ \Omega$ . The components are connected in series via ideal copper wires. The P-regions of both diodes are connected to each other via a copper wire, while their N-regions are connected to the opposite ends of the resistor via copper wires. Let $I$ be the steady-state macroscopic current flowing through the resistor $R$ . Let $k$ be the ratio of the magnitude of the drift current to the diffusion current ( $I_{drift}/I_{diff}$ ) across the depletion region of the Silicon diode. Which of the following gives the correct values of $(I, k)$ ?

Options

A.
$4 \text{ mA}, \ e^{16}$
B.
$0 \text{ mA}, \ 1$
C.
$10 \text{ mA}, \ 1$
D.
$4 \text{ mA}, \ 0$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Equivalent EMF for Cells|Drift vs Diffusion Current|Kirchhoff’s Junction Rule

Why This Question Is Tricky

Common Mistakes

This question tests a fundamental misconception regarding the physical nature of the built-in potential ( $V_{bi}$ ) in semiconductor junctions.

Students frequently misapply Kirchhoff's Voltage Law by treating $V_{bi}$ as an active electromotive force (EMF) capable of driving a steady current, leading them to calculate a net voltage of $0.7 \text{ V} - 0.3 \text{ V} = 0.4 \text{ V}$ and a spurious current of $4 \text{ mA}$ .

The trap exploits the failure to account for the contact potentials at the metal-semiconductor interfaces, which perfectly cancel the built-in potentials in any isothermal closed loop to maintain a uniform Fermi level.

Furthermore, it tests the principle of detailed balance, ensuring students understand that thermal equilibrium in a depletion region is a dynamic state where drift and diffusion currents are equal and opposite, not zero.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Current Electricity - Class 12
Concept	Equivalent EMF for Cells
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free