The maximum wavelength of light that a certain silicon photocell can detect is 1.11 mm. (b) Explain why pure silicon is opaque.

Verified step by step guidance

To understand why pure silicon is opaque, we need to consider its electronic structure and band gap. Silicon is a semiconductor with a specific energy band gap.

In a semiconductor, the band gap is the energy difference between the valence band (where electrons are normally present) and the conduction band (where electrons can move freely and conduct electricity).

For silicon, the band gap is about 1.1 eV. This means that photons with energy less than 1.1 eV cannot excite electrons from the valence band to the conduction band.

Light with a wavelength of 1.11 mm corresponds to a photon energy that is much lower than 1.1 eV. Therefore, such light does not have enough energy to bridge the band gap in silicon.

As a result, pure silicon does not absorb this light and is opaque to it, because the photons do not have sufficient energy to excite electrons across the band gap.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Band Gap Energy

The band gap energy is the energy difference between the valence band and the conduction band in a semiconductor. For silicon, this gap determines the range of photon energies it can absorb. Photons with energy less than the band gap cannot excite electrons to the conduction band, making pure silicon opaque to certain wavelengths.

Photon Absorption

Photon absorption in semiconductors occurs when photons have enough energy to move electrons from the valence band to the conduction band. Silicon's band gap requires photons with energies corresponding to wavelengths shorter than its maximum detectable wavelength. Longer wavelengths, like 1.11 mm, lack sufficient energy for absorption, contributing to opacity.

Material Transparency

Material transparency is determined by its ability to transmit light without significant absorption. In pure silicon, the absence of free charge carriers and the specific band gap result in limited absorption of longer wavelengths, rendering it opaque. Doping or altering the material can change its transparency by modifying the band structure.

Recommended video:

06:37

Ray Diagrams for Converging Lenses

Related Practice

Textbook Question

A forward-bias voltage of $15.0$ mV produces a positive current of $9.25$ mA through a $p - n$ junction at $300$ K. What does the positive current become if the forward-bias voltage is reduced to $10.0$ mV?

views

Textbook Question

Suppose a piece of very pure germanium is to be used as a light detector by observing, through the absorption of photons, the increase in conductivity resulting from generation of electron–hole pairs. If each pair requires $0.67$ eV of energy, what is the maximum wavelength that can be detected? In what portion of the spectrum does it lie?

views

Textbook Question

At a temperature of $290$ K, a certain $p - n$ junction has a saturation current $I sub S equals 0.500$ mA. Find the current at this temperature when the voltage is (i) $1.00$ mV, (ii) $negative 1.00$ mV, (iii) $100$ mV, and (iv) $negative 100$ mV.

views