Quantum confinement effect plays an important role on band-gap of quantum dots. but in some conditions, even though the size of the particle is reduced due to doping the optical band gap not widened. i expect detailed description from the experts.
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These articles helped me to understand this fact. Hope it would help you too.
1.Article Determination of the Quantum Dot Band Gap Dependence on Part...
2.https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=1191&context=studentpub
3. https://aip.scitation.org/doi/abs/10.1063/1.2158502?journalCode=jap
You could expect a variation in bandgap only at certain size ranges and those will not happen beyond that range of size for e.g. 2-10 nm
These papers may help you
Recent progress in the fields of tuning the band gap of quantum dots
Sci. China Technol. Sci. (2012) 55: 903.
@ https://doi.org/10.1007/s11431-011-4717-1
Tuning the band gap of PbSe quantum dots in glasses by TiO doping
Journal of Materials Science Materials in Electronics 28(10): May 201; 7013
@ DOI: 10.1007/s10854-016-6023-y
Factors determining the photovoltaic performance of a CdSe quantum dot sensitized solar cell: the role of the linker molecule and of the counter electrode
@ Article Factors determining the photovoltaic performance of a CdSe q...
Band Gap Energy of Gradient Core–Shell Quantum Dots
J. Phys. Chem. C, 2017, 121 (25), pp 13655–13659
@ Article Band Gap Energy of Gradient Core-Shell Quantum Dots
Attached are the files of quantum dots and their optical poperties [1] http://www.issp.ac.ru/ebooks/books/open/Quantum_Dots_-_A_Variety_of_New_Applications.pdf
[2] http://www.inam.uji.es/sites/default/files/paper/paper51.pdf
Another Add from Researchgate
https://www.sigmaaldrich.com/technical-documents/articles/materials-science/nanomaterials/quantum-dots.html?utm_source=researchgate&utm_medium=social-media-ad&utm_campaign=Fetch%20Mat%20Sci%20Tech%20Articles#applications
Very simple. First of all if you consider it as a spherical shape then from simple 3d spherical well solution you could find its band gap inversly proportion to the square of the particle size. Second very important thing is dielectric constant of the dot because coulomb force inversly proportional to the dielectric constant of the material. If dielectric constant is too high then it could lead to pretty loosely bound exiton which could lead to low dependence of band gap to length. 3rd point is if Qd energy separation is below thermal energy then because of thermal broadening you might not able to detect any quantum level.
In some cases, even though the size is reduced, band gap not increased. Then Quantum confinement effect?
That is what i'm talking about. Then other two factors that i discussed come to play
Size, geometry and composition. FYI Doing changes the composition ( dielectric constany) not size.
Intensity of the diffraction planes of that particular materials and its annealing temperatures are also the deciding factors for the variation of band gap of individual materials
Dear Sakthivel, other than some of the factors raised in earlier answers, you also need to consider the role of coupled electron-hole pairs or excitons which are bound by the Coulombic force in quantum dots. Infact in some material systems, the binding energies of excitons become significantly large (about 0.5 to 0.9 eV in MoS2, MoSe2) that there is a large difference between the electrical band gap and optical band gap. This difference yields the binding energy of the exciton.
Size and shape is important to tune the band gap of the quantum dot. You may anneal it to increase/decrease the band gap. Also change the process of the fabrication help full. You can simulate the quantum dot for particular size. After simulation fabrication is easy.
What is the size of the QD you are interested in? In the nanoscale region, charge screening is poor or vanishes and then Coulomb repulsion becomes relevant.
There are three factors controlling the widening of the energy gap in the QDs; the size of the quantum dot the effective mass and the dielectric constant of the material. For energy gap of the QD expression please follow the link: https://archive.cnx.org/contents/8e8a1e1b-0d9f-453b-95e1-bc95782973da@2/band-gap-measurements-of-quantum-dots
Best wishes
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