If however,‭ ‬the Exciton Bohr Radius is approximately the size of a particular quantum dot or even smaller,‭ ‬the exciton will not be able to travel throughout the crystal.  This condition is considered quantum confinement,‭ ‬which relates to the fact that quantum dots by nature have discrete energy levels.

This quantum functionality is determined by the quantum confinement,‎ ‏which in turn is dependent on the material’s size,‭ ‬not its composition.  An analogy would be if one was to chip at a red stone and yet the flecks that broke off were blue.   Observing this phenomena can be accomplished by regarding the confinement in different dimensions.  Three dimensions and the phenomena is referred to as a quantum dot.  Two dimensions and now the phenomena is called a quantum wire.  Lastly,‭ ‬one dimension and the phenomena is a quantum well.  To determine the quantum confinement,‭ ‬the Exciton Bohr Radius‭ ‬(aB‭) ‬is used.  This measurement is compared to the diameter of the nanocrystal‭ (‬D‭)‬.

In quantum dots,‎ ‏the optical properties are affected when the diameter of the nanocrystal is less than two times the Exciton Bohr Radius.  In a CdSe system,‭ ‬if the dimensions of the nanocrystal are below the Exciton Bohr Radius‭ (‬approximately‭ ‬5‭ ‬to‭ ‬5.5‭ ‬nm‭) ‬the result will be a shift towards the blue spectrum‭ (‬i.e. higher energy.‭)‬

Earlier it was mentioned that by altering the size of the quantum dot,‎ ‏different properties for the particle could be obtained.  This is due once again to the relationship between the diameter of the nanocrystal to its Exciton Bohr Radius.  The next question to ask oneself is how to alter the size of this particle.  This can be accomplished by the addition or the removal of electrons.


Dots can be connected via potential barriers to a source and drain contacts.  If a barrier can be used that prevents the movement of electrons,‭ ‬the number of electrons on the dot‭ (‬N‭) ‬will be an integer.  This number can and will change as electrons move‭ (‬tunnel‭) ‬towards and away from the dot.  Another factor to consider at this point is the repulsion of the electrons,‭ ‬Coulomb repulsion.  Because of this,‭ ‬a dot with N+1‭ ‬electrons will have a higher value of energy,‭ ‬which consequently will mean that to add additional electrons,‭ ‬more energy will be required.  A Coulomb blockade can be created when no current can flow.  This can be bypassed via a gate contact.

The addition of an electron is referred to as the charging energy and is notated by‎ ‏e2/C.  for an electron to tunnel,‭ ‬there cannot be any net energy difference.  This means that the dot and electron can experience tunneling only when the dot’s size allows the charge to be neutral.  This neutrality occurs when the dot has N and half an electron.  However,‭ ‬since it is only possible for the value to be an integer,‭ ‬the net charge must be‭ ‬±e/2,‭ ‬depending on whether there are‭ ‬N or‭ ‬N+1‭ ‬electrons in the‭ ‬dot.