Dear Aditi,

Any semiconductor material can be considered of having a geometrical shape. the shape has a bulk and a surface. It is found that the energy band structure will be affected by the boundaries of the materials. As the size decreases, the the electrons will be more confined in the material leading to to the so called quantum confinement resulting in increase of the energy gap of the bulk extended material.

There will be also an increase of the surface to the volume states.

Also there is is an effect of dimentionality of the material on the energy band band structure.There is one dimensional structures such as rods, two dimensional and three dimensional shapes. They affect the energy band structure because of the quantum mechanical confinement.

It is so that such dependence has been used for producing specific effects in electronic devices.

@ Mr. Zekry:

So what we mean when we say this particular material having that particular value for the band gap??? (like 1.14 fo Si or 1.5 for Zn3P2 and so on!!)

Is it so that after a particular size, these effects get stabilized?? quantum confinement that you mentioned about, is an effect of quantum realm! atomic order if I'm not wrong... so just by changing the shape (macro scopically) microscopic properties can be tailored??

or its just that the question itself is dealing with the quantum realm (as not so clear by the language)

The band gap energy of 1.11 eV for Si (at 300K) reflect the band theory application assuming; (I) having an infinite-size system, (II) the system is homogeneous, and (III) it is non-interactive (i.e., the band structure describing single electron states with no interaction with lattice vibrations, other electrons, or photons, etc.). However, for low-dimensional systems such as superlattices, quantum well structures, nanorods, and nanoparticles, we are dealing with small systems where energy band diagrams and bandgaps that are different from that for the bulk materials (e.g., see: http://mingli.weebly.com/uploads/1/0/4/8/10483702/ijmpb101.pdf) or https://www.researchgate.net/publication/13286698_Band_gap_of_strain-symmetrized_short-period_SiGe_superlattices

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@ Abdelhalim Zekry

Thank you for your answer.

Like if my nano-particles are of same size but they are having different shapes one is having square plates and other is assembled particles in shape of porous sphere , then how quantum mechanical confinement affect the band gap?

The presence of the porous spheres (as compared with a solid materials even when samples are the same size) we should expect the impact of the porous spheres on properties such as binding energies, quantum confinement, optical properties, absorptions, etc. For example you may review online sources for additional or specific relevant information, such as:

Article Physical confinement and chemical adsorption of porous C/CNT...

https://www.mdpi.com/2079-4991/9/2/132/htm

You may also look at the review articles on porous semiconductors such as:

https://www.cambridge.org/core/journals/mrs-online-proceedings-library-archive/article/porous-semiconductors-a-tutorial-review/3DA894B39686E75CAD01A6EC5C8157E9

Dear Adity,

If you change the shape of the material with out any distrubing any dimension and size then band gap must be same . but if you reduce or increase the size of the material then there must be change of band gap.in case of semiconductor you can play with the band gap via changing the temperature with out any changing the dimension or size.

Hi

It is better to define the dimensions, since such effects become more pronounced at lower dimensions.

These two articles may help you

Size and shape effects on the band gap of semiconductor compound nanomaterials

Madan Singh, Monika Goyal &Kamal Devlal.

Journal of Taibah University for Science , 12(4), (2018), Pages 470-475

https://www.tandfonline.com/doi/full/10.1080/16583655.2018.1473946

Size-dependent band gap of colloidal quantum dots

Sotirios Baskoutas & Andreas F. Terzis

Journal of Applied Physics 99, 013708 (2006);

https://doi.org/10.1063/1.2158502

Book Chapter

Band Structure, Morphology, Functionality, and Size Dependent Properties of Metal Nanoparticles

Joseph Adeyemi Adekoya etal,

https://covenantuniversity.edu.ng/content/download/58400/395274/file/Size+dependent+property_Intech.pdfhttp://dx.doi.org/10.5772/intechopen.72761

Dear Maya, Dear Aditi

welcome,

Sorry for coming late. It is so that i noticed your rebuttal after recommending my answer by a colleague from the RG. Irrespective of the shape If any dimension of the material gets small that quantum mechanical effects becomes measurable then one has to take it into consideration. You can estimate the shift of the conduction band edge due to quantum mechanical confinement using the energy well with infinite walls.

To quantify the effect please refer to the paper in the link: https://www.tandfonline.com/doi/full/10.1080/16583655.2018.1473946

Best wishes

Certainl, optical band gap changes with crystallite size, which is called quantum size effect...But it depends on deposition technique. Sometimes, we also see that band gap transmutes with several structural defects such as lattice strain, stress, dislocation density and stacking fault probability.

You can also my research article.

Thank you for asking tremendous question.