The most popular term in the nano world is quantum confinement effect which is essentially due to changes in the atomic structure as a result of direct influence of ultra-small length scale on the energy band structure. The length scale corresponds to the regime of quantum confinement ranges from 1 to 25 nm for typical semiconductor groups of IV, III-V and II-VI. In which the spatial extent of the electronic wave function is comparable with the particle size. As a result of these "geometrical" constraints, electrons "feel" the presence of the particle boundaries and respond to changes in particle size by adjusting their energy. This phenomenon is known as the quantum-size effect. Quantization effects become most important when the particle dimension of a semiconductor near to and below the bulk semiconductor Bohr exciton radius which makes materials properties size dependent.
Firstly, from reading Feynman's PhD thesis (see reference, Feynman and
Wheeler, 1945) he was aware of Feynman's conception of charged particles
which 'somehow' generated Spherical Electromagnetic In and Out Waves (Feynman
called them advanced and retarded waves), but Wolff realised that there
are no solutions for spherical vector electromagnetic waves (which are
mathematical waves which require both a quantity of force and a direction
of force, . vector). Wolff had the foresight to try using real waves,
which are Scalar (defined by their Wave-Amplitude only).
And this then led to a series of remarkable discoveries.