Change of ε with pressure for Semiconductors

In summary: However, it is commonly observed that ε∞ increases with pressure.In summary, In "Sado Adachi" book "Properties of Group-IV, III–V and II–VI Semiconductors" page 222, the author reports that the dielectric constants (εs and ε∞) of materials InAs, InP, and InSb decrease almost linearly with increasing pressure. However, there is no empirical formula available to describe this relationship. The effect of material-dependent pressure on optical properties can be computed through first principles using Density Functional Theory or through experimental measurements. The effect of pressure may also result in a transient state of matter. The dielectric constant εs varies with the zone center phonon mode frequency
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In "Sado Adachi" book "Properties of Group-IV, III–V
and II–VI Semiconductors" page 222, he reported that "both εs and ε decrease almost linearly with increasing pressure", however i was not able to find any empirical formula to describe these relationship for materials InAs, InP, InSb, where can i find these relations?
 
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In general, I would find the effect of material-dependent pressure on the optical properties of materials by two ways.
(i) It can be computed from first principles using Density Functional Theory.
(ii) There are also some experimental measurements which propose some fitted functions for a description at equilibrium, let's say.
In general, the effect of pressure may be a transient effect, which means that non-equilibrium can make you reach a state of matter which was not observed experimentally so far.
Would you have access to scientific literature, maybe? http://scholar.google.com would help here.
 
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εs varies with 1/ω2 , where ω is the zone center phonon mode frequency as you can find in the classic by Born and Huang. Also as you increase the pressure, ω increases because the ions get closer, the bonds get stronger, and the vibrations become faster. I do not think there is a clear-cut formula to describe pressure (p) vs. ω, but according to your statement , it should be something like √p α ω.

I do not fully understand the variation of ε∞ with external thermodynamic forces such as pressure.
 
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1. How does the bandgap energy change with pressure in semiconductors?

The bandgap energy in semiconductors generally decreases with increasing pressure. This is due to the compression of the crystal lattice, which brings the valence and conduction bands closer together, reducing the energy gap between them.

2. Does the change in bandgap energy with pressure vary among different semiconductors?

Yes, the exact change in bandgap energy with pressure can vary among different semiconductors. This is because it depends on the specific crystal structure and composition of the semiconductor material.

3. How does the pressure coefficient of the bandgap energy compare between semiconductors and insulators?

The pressure coefficient, which measures the change in bandgap energy per unit of pressure, is generally larger for semiconductors compared to insulators. This is due to the smaller bandgap energy in semiconductors, making them more sensitive to changes in pressure.

4. Can the change in bandgap energy with pressure be reversed?

Yes, the change in bandgap energy with pressure can be reversed if the pressure is released. The bandgap energy will return to its original value as the crystal lattice expands back to its normal state.

5. How does the change in bandgap energy with pressure affect the electrical conductivity of semiconductors?

The change in bandgap energy with pressure can affect the electrical conductivity of semiconductors by altering the number of available charge carriers. As the bandgap energy decreases, more charge carriers are able to move through the material, resulting in an increase in conductivity.

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