Mind the gap!

Article Mind the gap!

This would help you.

Hi M. A. Hadi ,

this is a very general question. What optical properties are you interested in specifically?

Hi Robert Karsthof

Specifically, optical absorption, dielectric function, reflectivity and energy loss function.

Thanks Dr. Krishnamoorthy Arumugam for providing a useful article.

Hi M. A. Hadi

it is difficult to answer that shortly -- in general I would say there is a vast amount of ways we make correlations of optical properties with the electronic structure of a solid. After all, electrons are, apart from ions, a large part of what the solid consists of.

The document Krishnamoorthy Arumugam has shared seems to deal with semiconductors and insulators, where you have a band gap. For metals, however, things can be totally different (not really my specialty, tbh). A good reference for semiconductors is the book "Semiconductor Optics" by Claus Klingshirn. "Fundamentals of Semiconductors" by Yu&Cardona is also a really good book that deals with many different aspects of absorption by electronic excitations, amongst others.

Hope that helps.

R

Hi M.A. Hadi

Yes indeed, optical properties of a given semiconductor (or solid) are tightly related to its electronic structure and more particularly to its energy band structure in several ways I try to summarize hereafter:

- The energy separation between valence and conduction bands, i.e. various energy gaps: the fundamental one (smallest one) and higher order ones (with larger energy values) occuring at different points of the Brillouin zone,

- The nature of the energy bandgaps : direct gaps (with momentem P and k-vector conservations as in GaAs) or indirect gaps (with change in momentum P and k-wave vector as in Silicon), higher order ones (saddle points, ...),

- The exact symmetry of valence states and conduction band states which depend on the nature of the semiconductor and its crystal phase,

- The shape (E=f(k)) of energy bands (directly related to particle effective masses and to density of states which is crucial parameter for optical transitions,

- Possible coupling or interaction between valence and conduction bands leading to energy and symmetry liftings or changes, ...

All these effects determine several factors of the optical properties:

1. is the optical transition allowed or not (on the basis of selection rules depending on the symmetry of initial and final states)?

2. what is the strength (intensity) of this optical transition which depends on the density of states of initial and final states and their energy separation within a crucial parameter called the harmonic oscillator strength of the optical transition

I Hope this will help you.

Yes indeed, optical properties of a given semiconductor (or solid) are tightly related to its electronic structure and more particularly to its energy band structure in several ways I try to summarize hereafter:

- The energy separation between valence and conduction bands, i.e. various energy gaps: the fundamental one (smallest one) and higher order ones (with larger energy values) occuring at different points of the Brillouin zone,

- The nature of the energy bandgaps : direct gaps (with momentem P and k-vector conservations as in GaAs) or indirect gaps (with change in momentum P and k-wave vector as in Silicon), higher order ones (saddle points, ...),

- The exact symmetry of valence states and conduction band states which depend on the nature of the semiconductor and its crystal phase,

- The shape (E=f(k)) of energy bands (directly related to particle effective masses and to density of states which is crucial parameter for optical transitions,

- Possible coupling or interaction between valence and conduction bands leading to energy and symmetry liftings or changes, ...

All these effects determine several factors of the optical properties:

1. is the optical transition allowed or not (on the basis of selection rules depending on the symmetry of initial and final states)?

2. what is the strength (intensity) of this optical transition which depends on the density of states of initial and final states and their energy separation within a crucial parameter called the harmonic oscillator strength of the optical transitionI got at least 2 very good reference books for this topics:

1. Handbook on semiconductors : optical properties of semiconductors by Minko Balkanski editor (In North-Holland Publishing Co; 2nd ed. edition (19 Dec. 1994))

2. Electronic structure and optical properties of semiconductors by Marvin L. Cohen and James R. Chelikowski (In Springer series in solid state physics 75)

Thanks a lot Dr. Abderrahmane Kadri for details discussions and providing two reference books.

Best regards,

you are welcome

Thank you Md. Atikur Rahman for explain the relation between optical properties and electronic structures of crystalline solids.

Thanks again Md. Atikur Rahman for adding the explanation.

Best wishes,

M.A. Hadi

Dear Dr M.A.Hadi,

@ Md. Atikur Rahman is unfairly trolling my answer.

be aware of this.

Dear Prof. M. A. Hadi, in addition to all the interesting answer of this thread, I will add some worlds for the case of normal metals, the high-frequency properties (called also optical properties) are separate from the low-frequency properties of the light-metal interaction. In the end, I will refer to the relation to the electronic structure.

I elaborate further, for frequencies below the plasma frequency, the refractive index - n is complex, so the wave is attenuated and does not propagate far into the metal.

For high frequencies above the plasma frequency, the refractive index n is real, hereby, the metal becomes transparent and behaves like a non-absorbing dielectric medium.

In addition, I guess, that the optical properties of a normal metal are two (mainly) the reflectivity and the skin depth.

The skin depth in normal metals also can be separated into two regimes, the normal and the anomalous skin effect. The experimental and theoretical work on the study of the Fermi surface of pure metals by the aid of high-frequency size effects relates their electronic structure and the optical properties.

Article The theory and history of the anomalous skin effect in normal metals

Article High frequency size effect study of the Fermi surface of metals

Thank you Prof. Dr. Pedro L. Contreras E. for adding a nice answer and providing two useful articles.

Best regards,

M.A. Hadi

My pleasure, Dear Prof. M. A. Hadi. I see many fellows discussing semiconductors and more exotic materials in RG threads. But the questions concerning normal metals are quite ignored, despite the period table have more metallic elements than semiconductors, and also that the metallic behaviour it is not easy to understand.