Energy band gap when there is an electric field

In summary, the conversation discussed the topic of electric fields and their effects on electrons and holes in conducting bands and valence bands. The question of how the equation for loss/gain of energy of the electron is derived was brought up, with the possibility of it being proven by working backwards. The topic of energy band diagrams, specifically in relation to the effects of electric fields, was also discussed with questions about changes in the diagram and how it can represent increased electrical conductivity. The discussion also touched on the topics of valence bands, conduction bands, and holes, and their relation to semiconductors and metals. The use of blocks and lines in energy band diagrams was also mentioned.
  • #1
jisbon
476
30
Homework Statement
A constant electric field is applied between two ends of a piece of metal. Show that the electric field is given by
##\xi =\dfrac {1}{e}\dfrac {dE}{dx}##
Where E is the electron energy and x is the distance on the sample.
Also, draw the energy band of diagram of the metal with and Without the electric field
Relevant Equations
-
So I have just been taught this topic but this question seems to be one of a kind and I can't seem to figure it out.

What I've learnt:

When there is a positive electric field applied to the right, for example, the electrons that are free moving in a crystal (aka conducting band) will oppose the direction and move to the left. On the other hand, the holes in the valence band will move with the direction of the electric field.
However, I was not taught anything about how the above equation works.

Working backwards (I know I'm not supposed to do that but I'm really stuck), I can find that dE/dx is actually the loss/gain of energy of the electron that varies with distance. But why will there be a 1/e infront? I'm not really sure how to even start to prove this equation.

As for part 2, regarding the energy band diagram:

1579786136238.png

This is what a normal energy band diagram will look like for maybe a 2s band aka Li atom. With the electric field, what would actually change? Since the electrons now create a net displacement, does this mean increased electrical conductivity? If so, how can I represent it on the band diagram? By overlapping or sorts?

Thank you so much.
 
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  • #2
Did the discussion of valence bands/conduction bands/holes come up during a section on semiconductors or metals? What topics were discussed during the metals section?

As for the band diagram, were you only taught with these blocks or did you see diagrams with lines? Is that an x on your horizontal axis?
 

Related to Energy band gap when there is an electric field

1. What is an energy band gap?

The energy band gap is the difference in energy levels between the valence band (the highest occupied energy level) and the conduction band (the lowest unoccupied energy level) in a material.

2. How does the presence of an electric field affect the energy band gap?

An electric field can cause the energy bands to shift, resulting in a change in the energy band gap. This is known as the Stark effect.

3. Can an electric field change the conductivity of a material?

Yes, the presence of an electric field can increase the conductivity of a material by moving electrons from the valence band to the conduction band, allowing them to flow more freely.

4. Is the energy band gap a fixed value for all materials?

No, the energy band gap varies for different materials and can also be altered by factors such as temperature and applied pressure.

5. How is the energy band gap measured?

The energy band gap can be measured using various methods, such as optical absorption spectroscopy or electrical conductivity measurements.

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