According to the theory,‭ ‬once nature is observed at a level that is small enough,‭ ‬matter and radiation can be thought of as discrete or discontinuous.  Also,‭ ‬according to the theory,‭ ‬an object is permitted to exist at an allowed energy level only by absorbing or emitting the energy required to exist at an allowed level.

Next to be investigated are how bandgap,‎ ‏conduction and valence bands,‭ ‬exciton,‭ ‬and Bohr radius holes relate to quantum dots.  A bandgap in a quantum dot has the same basic function as that of a semiconductor.  It separates the valence from the conduction bands.  The main difference is that in a quantum dot crystal,‭ ‬the size of the bandgap can be altered,‭ ‬whereas in a traditional semiconductor,‭ ‬the bandgap is fixed,‭ ‬due to continuous energy states‭ (‬i.e. at a large scale,‭ ‬the semiconductor does not behave in regards to quantum mechanics‭)‬.  ‭ ‬The bandgap can be altered by changing the size of the quantum dot and therefore produce a range of energies.

‏In a quantum dot,‭ ‬the conduction band can be thought of as a band that possesses energy levels above the value of the bandgap.  Due to the nature of a bandgap,‭ ‬its distance will be greater than that of the distances between energy levels.  This distance provides a barrier to electrons and therefore not many electrons can jump from the valence band.  However,‭ ‬electrons can cross the bandgap if the electron is able to absorb energy in the form of radiation greater or equal to the bandgap energy.  As electrons drop back to the valence band,‭ ‬the radiation emitted,‭ ‬and what is identified as a qualifying feature of a quantum dot. 

The valence band contains electrons with the lowest energy as well as electrons that are just below the threshold of the lower values of the bandgap.‎  ‏In nature,‭ ‬electrons occupy energry states with the lowest energy values,‭ ‬so this band’s energy levels are generally complete.

When there is an absence of an electron in the valence band,‎ ‏it is referred to as a‭ ‘‬hole‭’‬.  Convention treats holes with a positive charge,‭ ‬since they‭ “‬appear‭” ‬after the electron,‭ ‬which is negatively charged jumps across the bandgap to the conduction band.  The next concept is that of exciton,‭ ‬which by definition is both the electron and the hole that is created as the electron crosses the bandgap.  The separation between the electron and the hole also has a name and is called Exciton Bohr Radius.  This can vary between different substances and because of it,‭ ‬is an average distance.  The importance of the Exciton Bohr Radius is that it is used to differentiate between whether a crystal is a quantum dot or a semiconductor.  If the Exciton Bohr Radius is small compared to the crystal in question,‭ ‬the exciton can easily move throughout the crystal,‭ ‬and this crystal would be considered that of a bulk semiconductor‭ (‬i.e. large‭)‬.