Dear Anjani
If you consider a single atom of a material (i.e. semiconductor) you have a bandgap equal to the distance between ground state and first excited state, while in the bulk both levels are broadened. This broadening leads to narrowing of the bandgap.
In a nanoparticle broadening must be less than in the bulk, and narrower bandgap is expected. As we shrink the semiconducting nanoparticle (such as quantum dots), the size of the particle approaches the size of the electron-hole distance known as the Bohr radius. For a 3D spherical particle, we consider the energy of a particle in a "infinite potential well" to describe the band gap energy.
E_n=(h^2 n^2)/(8 m_c R^2)
This is the band gap energy for a spherical box (same lengths in all 3 dimensions), n is energy level, h is planck's constant, m_c is the effective mass of a point charge, and R is the radius of our box (or the size of the particle). We see from this that as our particle increases in size, the band gap energy decreases. Therefore, as size varies in QDs, the energy changes because the exciton in the QDs behaves like a "particle in a box."
Electronic states of an atom are typically characterized by discrete energy levels that are often separated by electron volts. The spatial distribution of these states is highly localized. At the nanoscale, the dimension of energy states resides between these limits. An electron confined within a one-dimension (1-D) box of size ‘L’ is considered. The lowest energy level of this system is given by , E= h.h/ 8 m L. L, where ‘h’ is the Planck’s constant and ‘m’ is the mass of the particle (electron). Since, , if size of the box (particle diameter) is reduced, then E increases, hence a drastic variation of its bulk properties. In the nanoscale phenomena, the energy level spacing of electronic states of atom increases with reduction in dimensionality of particle and is called Quantum Confinement (QC). The QC phenomena can be readily understood from the well-known Heisenberg’s uncertainty principle. Considering the energy of a free electron with momentum P . Since the uncertainty in momentum cannot exceed the momentum itself P, . If one tries to localize the position of an electron by reducing the box size (L), its energy must increases and diverges as the confining region vanishes. Hence, depending on the dimensions in which the length scale is nanometers, they can be classified into: (a) nanoparticles (0-D), (b) lamellar structure (1-D), (c) filamentary structure (2-D), and (d) bulk nanostructured (3-D) materials.
Let us Consider a bulk material, it's particle size is very large such that more number of electrons can pass from one partilcle to another. hence the band gap is lesser.
if we go on reducing the size of the bulk particle, there will be lesser amount of electrons corresponding to each particles. thus the amount of transfer of electrons from one particle to another will surely decrease. this causes a increase in the band gap while reducing the particle size
this property is called as red shift
I agree with this statement that " In a nanoparticle broadening must be less than in the bulk, and narrower bandgap is expected". My observation is that the nano range (1-100 nm), the band gap is increases as decreasing particle sizes.
The width of energy band decreases in nanometer due to reduction of atoms in nanometer range causing incrrase in band gap
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