In metals, the outermost conduction electrons (electron plasma) interact with incident photons and according to the classical Drude model, they may resonate and build up longitudinal plasmonic waves either in bulk or surface depending on photons' energy. Similarly, high doped semiconductors and in some cases an intrinsic semiconductor like InSb can support these collective oscillations. But, based on our knowledge, we have both electrons' and holes' plasma in semiconductors which can interact with external perturbations like photons. Hence, why we consider only the electrons share in the plasmonic response of semiconductors?
Dear Aydin,
Holes (in the valence band of a semiconductor) are just missing electrons. Therefore, only electrons can move and make plasma. Simple philosophy ! Right!
ِDear Muhammad Hamza El-Saba
Thanks for your attention.
As you know, the effective mass of holes (Heavy-Hole or Light-Hole) differs from the conduction electron. Therefore, the permittivity and plasma frequency may alter with this parameter.
In metals, the effect of positive ions has been considered as background polarization and taken into account in permittivity of metal. In semiconductors, I think we must consider the valence electron (or holes) beside the conduction electron, too. Therefore, the Drude model can't describe this effect and we've to address it using quantum mechanics. But, in most cases, we ignore these effects and that's why I'm really curious about it!
Mr M H El Saba --your question is essentially " why we consider only the electrons share in the plasmonic response of semiconductors? "
For an appropriate answer the reference below will be very helpful.
http://www.photonics.intec.ugent.be/education/IVPV/res_handbook/v2ch36.pdf
Dear Aydin,
I know you're a smart researcher. This is clear from your question. Therefore, I answered with a few words. We all know, the effective mass of holes differs from the conduction electrons. Of course you know why. Because the motion of electrons in valence band(s) is more or less harder than motion of electrons in the conduction bands (as the acting forces are different). Well, we just talk about different electrons. The plasma of electrons is a collectivist of quasi-free electrons which can oscillate and propagate as quasi-particles (plasmons).
Dear Muhammad Hamza El-Saba
At the end part of your kind response, "we just talk about different electrons", you raise the issue again. That was what I talking about. Different electrons with different quantum properties (like effective mass, angular momentum,...) have been considered alike in the electron plasma, why?
Here you are with a succinct response: https://www.cambridge.org/core/journals/mrs-bulletin/article/reflecting-upon-the-losses-in-plasmonics-and-metamaterials/8A196D2DDC800CEC0F2639DFC1DA96A8# & https://www.google.com/search?sxsrf=ACYBGNRA-sNMyK_HjOT2jv4Lbax27zNvMw:1579500039265&q=why+do+the+holes+not+participatein+a+plasmonic+response+in++a+semi+conductor+while+only+electrons+dowith+photons+in+a+Semi+conductor&tbm=isch&source=univ&safe=active&sa=X&ved=2ahUKEwjQiI2WwJHnAhVHdcAKHbd7CNMQsAR6BAgIEAE&biw=1024&bih=678 & finally https://www.google.com/search?q=why+do+the+holes+not+participatein+a+plasmonic+response+in++a+semi+conductor+while+only+electrons+dowith+photons+in+a+Semi+conductor&safe=active&sxsrf=ACYBGNRA-sNMyK_HjOT2jv4Lbax27zNvMw:1579500039265&tbm=isch&source=iu&ictx=1&fir=9jPxpkOixbyAiM%253A%252C352kfCmyKfV6pM%252C_&vet=1&usg=AI4_-kSTACqbNMB69ud_e7-V8nyt4qlsXg&sa=X&ved=2ahUKEwjQiI2WwJHnAhVHdcAKHbd7CNMQ9QEwD3oECAgQBQ&biw=1024&bih=678#imgrc=9jPxpkOixbyAiM:
Dear Aydin and Ijaz Durrani
The plasma frequency is a direct measure of the square root of the density of valence electrons in a solid. However, considering the fact that holes are missing electrons dose not mean we neglect their effect. This is just a mathematical representation (treating with few number of holes is easier than treating with the whole number of electrons in the valence band). Therefore, we can write the contribution from electrons and holes as follows:
(see the equation in file wp.png)
For more details,You can also refer to Chapter 10 in my book:
Book Transport of Information-Carriers in Semiconductors and Nanodevices
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