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Question #43115

Difficulty: 8/10 | 🟢 Free

The Question

A plane electromagnetic wave of angular frequency $\omega$ is incident normally from vacuum onto the flat surface of a semiconductor device. The semiconductor lattice has a static relative permittivity $\epsilon_r = 4$ and relative permeability $\mu_r = 1$ . When the device is operated in reverse bias (as a photo-diode), the active region is fully depleted of free charge carriers. When operated in forward bias (as an LED), charge carriers are injected into the active region, giving it a uniform conductivity $\sigma = 3 \epsilon_0 \omega$ . Assuming the Drude-Lorentz model for the complex permittivity $\tilde{\epsilon} = \epsilon_0 \epsilon_r + i \frac{\sigma}{\omega}$ , what is the ratio of the power reflection coefficient under forward bias ( $R_F$ ) to that under reverse bias ( $R_R$ )?

Options

A.
$27 - 18\sqrt{2}$
B.
$3 - 2\sqrt{2}$
C.
$\frac{63 - 27\sqrt{5}}{2}$
D.
$23 - 8\sqrt{7}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Medium Dependency|Boundary Condition Reflection|Photo-diode vs LED Bias

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of electromagnetic wave reflection at the boundary of a lossy medium, specifically bridging solid-state device physics (bias-dependent carrier injection) with wave optics.

The lethal trap occurs when students treat the forward-biased semiconductor as a simple dielectric.

Instead of correctly calculating the complex refractive index $\tilde{n} = n + ik$ from the complex permittivity, students often incorrectly calculate an 'effective' real refractive index using the magnitude of the complex permittivity ( $|\tilde{\epsilon}/\epsilon_0| = \sqrt{4^2 + 3^2} = 5 \implies n_{eff} = \sqrt{5}$ ).

This misapplication of the Fresnel equations ignores the phase shift induced by the conductivity of the injected charge carriers, leading directly to the trap option C.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Waves - Class 12
Concept	Medium Dependency
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free