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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:

One can grow a few atomic layers of $\rm AlAs$ on top of a $\rm GaAs$ substrate, then grow alternate layers of $\rm GaAs$ and $\rm AlAs$. One can also grow a ternary compound such as Al$_x$Ga$_{1 - x}$As (where the aluminum mole fraction $x$ can be between $0$ and $1$) on a GaAs substrate and form a heterojunction, Fig. 1.6a. Interesting applications have been found using heterojunction struc- tures. For example, when the wide band-gap Al$_x$Ga$_{1 - x}$As is doped by donors, the free electrons from the ionized donors tend to fall to the conduction band of the GaAs region because of the lower potential energy on that side, as shown by the band diagram in Fig. 1.6b. enter image description here

Why does the conduction band of the GaAs region have lower potential energy than the valence band? I would greatly appreciate it if people would please take the time to explain this.

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Those diagrams don't show the conduction band being at lower energy than the valence band anywhere. They show the conduction band being at lower energy in one material than the conduction band in another material nearby.

It is possible, by applying an external voltage, to arrange that the conduction band edge on the n-side of the junction to be at a lower energy than the valence band edge on the p-side. In that case, the reason for it is the applied external voltage.

Remember that if there's no applied voltage, then the Fermi level equalizes across the junction. So to have the conduction band edge on one side fall below the valence band edge on the other, you'd essentially need to have degenerate doping on both sides --- putting the valence band edge on the p-side above the Fermi level and the conduction band edge on the n-side below the Fermi level. In that case, the cause of the situation would be the extremely heavy doping on both sides of the junction.

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  • $\begingroup$ Ohhh, I misinterpreted "tend to fall to the conduction band of the $\rm{GaAs}$ region"; it's actually referring to the conduction bands of the two materials, rather than conduction band vs valence band. $\endgroup$ Jul 18, 2020 at 6:02
  • $\begingroup$ In that case, can you please explain why the $\rm{GaAs}$ region has lower potential energy? $\endgroup$ Jul 18, 2020 at 6:08
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    $\begingroup$ @ThePointer, it's shown in your diagram (a), the band gap of GaAs is less than the band gap of AlGaAs. But notice how much the c.b. edge shifts and how much the v.b. edge shifts at the material boundary are not equal. To work out how much of the gap energy difference comes from one edge or the other you need to know the work functions of the two materials. $\endgroup$
    – The Photon
    Jul 18, 2020 at 6:15
  • $\begingroup$ Ohh, I see: It's because $\Delta E_c$ is positive. Ok, now it's clear to me. $\endgroup$ Jul 18, 2020 at 6:23
  • $\begingroup$ Some nice images for future reference: upload.wikimedia.org/wikipedia/commons/thumb/f/fa/… from en.wikipedia.org/wiki/P–n_junction $\endgroup$ Jul 18, 2020 at 6:52

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