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I am currently studying Physics of Photonic Devices, second edition by Shun Lien Chuang. Chapter 1.3 The Field of Optoelectronics says the following:

The control of the mole fractions of different atoms also makes the band-gap engineering extremely exciting. For optical communication systems, it has been found that minimum attenuation in the silica optical fibers occurs at $1.30 \ \mu\text{m}$ and $1.55 \ \mu\text{m}$ (Fig. 1.8a). The dispersion of light at $1.30 \ \mu\text{m}$ is actually zero (Fig. 1.8b). It is therefore natural to design sources such as light-emitting diodes and laser diodes, semiconductor modulators, and photodetectors operating at these desired wavelengths. In addition, many wavelengths, or the so-called optical channels for dense wavelength-division multiplexing (DWDM) applications, near $1.55 \ \mu\text{m}$ with constant frequency spacing such as $50$, $100$, or $200$ GHz can be used to take advantage of the broad $24$ THz frequency bandwidth near the minimum attenuation. For example, by controlling the mole fraction of gallium and indium in an $\mathrm{In}_{1 - x}\mathrm{Ga}_{x}\mathrm{As}$ material, a wide tunable range of band gap is possible because $\mathrm{InAs}$ has a $0.354 \ \text{eV}$ band gap and $\mathrm{GaAs}$ has a $1.424 \ \text{eV}$ band gap at room temperature.

The presence of the following two statements is what interests me:

  1. The control of the mole fractions of different atoms also makes the band-gap engineering extremely exciting.

  2. by controlling the mole fraction of gallium and indium in an $\mathrm{In}_{1 - x}\mathrm{Ga}_{x}\mathrm{As}$ material, a wide tunable range of band gap is possible because $\mathrm{InAs}$ has a $0.354 \ \text{eV}$ band gap and $\mathrm{GaAs}$ has a $1.424 \ \text{eV}$ band gap at room temperature.

It seems to me that the author is implying that there is some connection between semiconductor laser wavelength and the band gap? Is this correct, or am I misunderstanding this? Otherwise, what else would be the point of statement 2? I would greatly appreciate it if people would please take the time to clarify this.

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  • $\begingroup$ I don't know if the 2nd ed. is very different, but the 1st ed of this book was a great reference text but really not a good choice for self-study. I'd only recommend this book to accompany a course with a good lecturer, or for someone who already knows the material and wants a solid, but terse, reference to it. If you're doing self-study, find another book. $\endgroup$
    – The Photon
    Jul 18, 2020 at 13:35
  • $\begingroup$ @ThePhoton I'm also studying other optoelectronics/photonics books alongside this one. The reason for the multiple textbooks is to ensure that I get a very solid and thorough understanding. The funny thing is that people say the same thing with regards to most textbooks at these levels of study. When I started studying Hecht for optics, people told me that it was not a good introductory textbook and to study something else; and just days ago, I was told to use a different textbook than Principles of Optics by Born and Wolf, because it is not a good introductory textbook. [...] $\endgroup$ Jul 18, 2020 at 13:45
  • $\begingroup$ [...] I think the best option is to just use high quality textbooks, even if they are considered to be "more difficult", and just study diligently to understand the content. $\endgroup$ Jul 18, 2020 at 13:48
  • $\begingroup$ Born and Wolf is about 70 years old, and translated from German. It is definitely not an introductory text. (Mandel & Wolf, on the other hand, is an excellent text for self-study of its material, so this isn't meant to criticize the authors, only to say that some texts are better in one context and other texts in others). $\endgroup$
    – The Photon
    Jul 18, 2020 at 13:49
  • $\begingroup$ In any case, you're asking a question about the introductory chapter of Chuang. Chapter 1 is meant to motivate studying the rest of the book, not to explain everything thoroughly. You can be sure this question will be answered in a later chapter of the book. $\endgroup$
    – The Photon
    Jul 18, 2020 at 13:51

1 Answer 1

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In a direct-gap semiconductor, when an electron and hole recombine in a radiative process, they emit a photon with energy equal to the energy lost by the electron as it recombines with the hole. That is, roughly equal to the band gap energy.

The radiative process could be the spontaneous emission in an LED or below-threshold laser, or the stimulated emission in a laser.

Since the photon energy is directly proportional to the optical frequency or inversely proportional to the wavelength, the connection between bandgap energy of the emitting semiconductor and the LED or laser wavelength is very direct.

In the case of quantum wells or dots, the available energy levels will be slightly above the band gap edges, but the transition energies will still be fairly close (within tenths or hundredths of an eV) to the band gap energy.

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