Dear Mr. Yadav,

you can find a short explanation on

http://www.chm.bris.ac.uk/webprojects2002/etan/Webpages/theory.htm

I hope, that could help.

Dear Manoj,

The colleagues above gave an answer to your question above. i want to elaborate on the similarity and differences between atomic energy level diagram and the quantum dot energy level diagram.

The quantum dot is a an assembly of atoms of specific material that has few nanometer dimensions. It is termed as a virtual atom.

Because of this microscopic size the electrons are confined inside the dot. This is the same for the electrons in an atom they are confined and localized in the atomic space.

In order to obtain the possible energy levels in the atom or in the dot because of the space confinement one has to use quantum mechanical laws. That is one has to solve the Schrodinger equation  with relevant boundary condition. 

The motion of electrons in the confined space can be modeled by the motion of a particle in a potential well with infinite walls. 

While the atom is modeled by one well with infinite wall with size of the atom, the electrons in the quantum dot can be modeled by a potential well with infinite walls with the minimum energy level is that of the conduction band. Since we are interested in the confinement in the conduction band. Like wise we are interested in the holes in the valence band therefore, there will be an inverted well for the holes in the valence band. 

So, the picture is now is that we have electrons confined in the conduction band and holes in the valence band.

If there is no confinement as in big crystal, there will be no confinement and the electrons in the conduction band will occupy the bottom of the conduction band and the holes will reside at the top of the valence band.

When we solve Schrodinger equation in potential well with infinite wall we find that the electrons will have only discrete energy levels in the valence band and so doe the holes in the valence band.

The energy level diagram in the conduction band will be similar to that of an atom and so the energy levels of the holes in the valence band will have also discrete energy levels as the shown in the energy level diagram  given in the attached link: archive.cnx.org/.../optical-properties-of-group-12-16-ii-vi-semiconductor-nanoparticl

The energy levels above the conduction band has an energy measured from the conduction band edge Ene = h^2 n^2/ 8 pi^2 me d^2,

where h is the Planck constant, n the order of the level, me is the effective mass of electrons in the quantum dot and d is the length of the dot.

The same equation holds for the holes energy Enh in the valence band with mh the hole effective mass instead of  of me.

So, the energy gap for the quantum dot becomes Egqd= Eg + E1e + E1h,

with E1e is the excess energy of the first level in the quantum dot E1e and E1h is that corresponding level for the holes.

It is clear that one can tune the effective energy gap in the quantum dot by changing its size d.

Best wishes