Quantum confinement effects in nanocrystals of SnO$_{2}$ in MgO matrix

We have studied the nanocrystal formations of SnO$_{2 }$in$_{ }x$SnO$_{2}$-(1-$x)$MgO composite thin films ($x$ =0 to 1 and thickness 0.5 to 1 $\mu $m) prepared by metal-organic decomposition method. We find a direct relationship between the size of SnO$_{2}$ nanocrystals and the annealing temperature. Similarly, higher concentration of Mg in $x$SnO$_{2}$-(1-$x)$MgO leads to smaller size nanocrystals of SnO$_{2}$. Under the controlled choice of composition and annealing conditions, the bandgap of SnO$_{2}$ can be continuously increased from 3.89 eV to 4.5 eV thus providing a generic approach for tuning the bandgap in nanocomposite systems over a wide range of energy. We discuss this behavior in terms of the quantum confinement effect arising from particle size being comparable to the order of Bohr radius of the material.