# Formal definition of quantum dot

1. Jun 25, 2013

### cryptist

Is there a definition of quantum dot that everybody agrees? I searched intensively both from google and from web of science, but I couldn't find a formal definition.

e.g (wiki says)
A quantum dot is a semiconductor whose excitons are confined in all three spatial dimensions.

confined but how much confined? Is there a consensus on that, like; "when domain size is smaller than most probable de broglie wavelength, than it is quantum dot" or is it about excitations like "if there is no excitation, then it is quantum dot?" But this cannot be since we can make qdots with thousands of particles..

2. Jun 25, 2013

### moj20062001

i think,a quantum dot is one that have the properties between bulk semiconductor and molecules.its the defining charectristics of them.
now you can have diffrent size of them,and different types,but the behaviour should be included in those properties(something between bulk semiconductor and molecules)-so it depends somehow on the matter you work on.

3. Jun 25, 2013

### Cthugha

Confinement leads to quantization. Momentum/kinetic energy in a confined direction are not continuous anymore. So, the appearance of bound states marks confinement. This also reflects in the density of states, when you have confinement in one or more dimensions. In 3D, the density of states (in terms of energy) follows (E-E0)^1/2, in 2D, it follows a Heaviseide step function of E-E0, in 1D it follows (E-E0)^-1/2 and in 0D you just get delta distributions which means you just have a single discrete energy per state.

So if discrete energy states form for a single dot, you have a quantum dot.

4. Jun 27, 2013

### moj20062001

you know,we always have discrete set of energy levels.but as the dimention of the box get larger we see this discreteness harder.
there is no strict limitation on the realm of quantum and classic justification.

if you want certain number,i think you would find nothing.

we say when the debroglie wave of particles(constituents) is about the interparticle spacing,we use quantum mechanical way and if it is much much smaller than the interparticle spacing we use classicall way.and also we consider the temperature.the temperature should be high in classicall way while it is down in Q.Ms.
thats what i know about it. :)

Last edited: Jun 27, 2013
5. Nov 11, 2016

### bluejay27

When you say delta function, you are meaning dirac delta function right?