The Relationship Between Dielectric Function and Joint Density of States

In summary, the imaginary part of the dielectric function, Epsilon_2, is *almost* directly proportional to the joint density of states (JDoS). However, this proportionality is exact only when the matrix element for the transition is independent of the position in k-space on the surface that defines the energetically allowed transition. In most cases, the matrix element is only weakly dependent and can be replaced with an averaged matrix element. Additionally, for anisotropic materials, the coupling between the conduction and valence band will also be anisotropic and must be taken into account. The formula for Epsilon in books is normally given for isotropic materials, but for anisotropic materials, the polarisation vector e
  • #1
jet10
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Hi. I have been looking at some lecture notes. What is not so clear for me is, how the imaginary part of the dielectric function is related to the joint density of states. Is the "amplitude" of the epsilon2 directly proportional to JDOS? or is JDOS some kind of derivative of epsilon2?

Thanks
 
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  • #2
Epsilon_2 is *almost* directly proportional to the JDoS. It is exactly proportional if the matrix element for the transition is independent of the position in k-space on the surface that defines the energetically allowed transition. For most purposes in crystals, the matrix element is only weakly dependent, and people like to just move it outside of the integral and replace it with an averaged matrix element.
 
  • #3
Thanks for your clear answer. Just one more question. I see that the formula for Epsilon in books are normally given for isotropic material. What changes in the integral of the formula if we want to know Epsilon in a certain direction for anisotropic material? There is a polarisation vector e in the matrix element for the transition <c|e.p|v>. I guess that for anisotropic material, the matrix element will depend on which e or which direction I take, whereas for isotropic material, it doesn't matter. Is this right?
 
  • #4
Yes, the coupling between the conduction and valence band will be anisotropic. You also have to include the coupling between the valence band states.
 
  • #5
Ok. Thanks very much for the help!
 
  • #6
genneth said:
Epsilon_2 is *almost* directly proportional to the JDoS. It is exactly proportional if the matrix element for the transition is independent of the position in k-space on the surface that defines the energetically allowed transition. For most purposes in crystals, the matrix element is only weakly dependent, and people like to just move it outside of the integral and replace it with an averaged matrix element.

I noticed that there is a factor of 1/E^2 in the [tex]\varepsilon_2[/tex] equation. Since [tex]\varepsilon_2[/tex] is dependent on E, isn't the JDOS rather *almost* proportional to [tex]E^2\varepsilon_2[/tex]?
 

1. What is the dielectric function?

The dielectric function, also known as the electric susceptibility or permittivity, is a material property that describes how it responds to an external electric field. It is defined as the ratio of the induced polarization to the applied electric field.

2. How is the dielectric function related to the optical properties of a material?

The dielectric function is related to the optical properties of a material through the refractive index. The refractive index is the square root of the dielectric function, and it determines how light propagates through the material. Higher refractive indices indicate a slower speed of light and stronger light-matter interactions.

3. What is the physical significance of the imaginary part of the dielectric function?

The imaginary part of the dielectric function represents the absorption of light by a material. It is related to the energy loss of an external electric field due to the excitation of electrons in the material. Materials with higher imaginary parts of the dielectric function are better absorbers of light.

4. How is the joint density of states (JDOS) related to the dielectric function?

The JDOS is a spectroscopic quantity that describes the density of energy states available for an electron to occupy at a given energy. It is directly related to the imaginary part of the dielectric function through the Kramers-Kronig relation. The JDOS can provide valuable information about the electronic structure of a material and its optical properties.

5. Why is the study of dielectric function and JDOS important in materials science?

The dielectric function and JDOS are crucial for understanding the optical and electronic properties of materials. They can provide insights into the band structure, excitations, and energy levels of a material, which are essential for designing and optimizing materials for various applications, such as solar cells, LEDs, and photodetectors. Additionally, studying these properties can help identify and characterize defects and impurities in materials, which can affect their overall performance.

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