# Energy of Conduction and Valence Band in Opposing Directions

• I
• Athenian
This diagram is used to look at the energy levels of an object, in this case an electronic band. The diagram used is the ##E-k## diagram (extended-zone scheme), which shows the highest and lowest occupied energy levels in an object. In this case, the diagram is focusing on the gap between the conduction and valence bands. The reason for this is because in a semiconductor, most of the interesting stuff happens at that point. For example, it is at that point that electron promotion and electron falling happens.f

#### Athenian

TL;DR Summary
In an ##E(k)## diagram where one can think ##k## as being the momentum and ##E## as the energy, why are the diagram's conduction and valence band in opposite directions?
Recently, I have been studying some solid-state physics and I came across this ##E-k## diagram online. Here's an image for reference to what I am referring to: [https://www.google.com/search?sourc...6BAgJEAE&biw=767&bih=712#imgrc=YnRTyhlOuJmRaM].

In short, I was curious why would the conductor band curve upward whereas the valence band curves downward in an electronic band structure (i.e. in the ##E-k## diagram).

In addition, if anybody knows any good solid-state physics sources I can refer to for this question (or similar topics to read and study), I would definitely like to hear about it.

Thanks a lot!

The impression you have is only because to the type of representation used. Energy bands can be represented in the reduced-zone scheme or in the extended-zone scheme. Have a look at Fig. 5 in Tsymbal's
Energy bands - Rutgers Physics

Athenian
Think of a hole as a negative mass

Athenian
I think it doesn't mean that upward or downward direction. It shows the highest occupied energy state of the valance band and lowest unoccupied state of the condiction band

Lord Jestocost
Think of a hole as a negative mass

To my mind, when thinking in terms of electrons and holes, one has to consider the direction of the energy axis.

"Both electrons and holes tend to seek their lowest energy positions. Electrons tend to fall in the energy band diagram. Holes float up like bubbles in water."
From caption of Fig. 1-14 in
Electrons and Holes in Semiconductors

Athenian
1. The E-k diagram is actually extended and complicated, there could be several areas where there are vertical gaps. The diagram you linked is ignoring all of that and focusing on one part, the specific gap where the electronic states below the gap are filled and the states above the gap are empty (at low temps). And again, it is ignoring the whole left-right structure as well, which could have an undulating shape for both the conduction and valence bands, and focusing on the single point of closest approach. So that's the reason it has that >< shape, it's focusing on the point of closest approach.

The reason for focusing on that point is because in a semiconductor, that one point is where most of the interesting stuff happens. The chance to jump the gap reduces exponentially with the size of the gap, so pretty much all of the electron promotion/electron falling happens right there, for those values of ##\Delta E## and k.

2. Notice they're also usually drawn with a sort of parabolic shape. This is because that shape determines the electron and hole effective mass, and it's usually close to parabolic.

Athenian
Thank you everybody for the informative comments! This was incredibly helpful when attempting to understand ##E(k)## diagram.

Lord Jestocost