What Does 'Quantum Dot Exciton' Mean?

[Barth]

Why do we talk about " quantum dot excitons" ? For me, excitons and quantum dots are two distincts objects

For me, excitons (at least in a bulk) are a bound state of an electron and a hole, bound by the attractive coulomb potential, and their binding energy and wavefunctions are the one of a hydrogen-like system. In a quantum dot, instead, electrons and holes are localised by crystal potential barrers, and not by mutual attraction, and the energy levels and wavefunctions are determined by the size and shape of the dot.

Does "quantum dot exciton" simply means "one electron and one hole in a quantum dot", or something less trivial ?


Second question: when we calculate the energy levels of a quantum dot, we find a serie of discrete levels. Is it possible to calculate the degeneracy of such levels ?


Barth

 

[Gokul43201]

Why do we talk about " quantum dot excitons" ? For me, excitons and quantum dots are two distincts objects

That is true. However, the exciton radius (sometimes called the "bohr" radius of the exciton) is a natural number to use for quantifying length scales in a semiconductor. There are two distict regimes in the context of this length scale. One, where the spacing between electronic states (within a band)
is small compared to excitonic level spacings (which are tiny, due to the dielectric constant). And the other regime, where they are comparable.

For me, excitons (at least in a bulk) are a bound state of an electron and a hole, bound by the attractive coulomb potential, and their binding energy and wavefunctions are the one of a hydrogen-like system. In a quantum dot, instead, electrons and holes are localised by crystal potential barrers, and not by mutual attraction, and the energy levels and wavefunctions are determined by the size and shape of the dot.

Exactly. However, when you have a quantum dot exciton, the excitonic states get significantly modified by the boundary conditions imposed by the dot.

It is when this significant change occurs that we say that "confinement" is achieved.

Second question: when we calculate the energy levels of a quantum dot, we find a serie of discrete levels. Is it possible to calculate the degeneracy of such levels ? Barth

In the absence of a magnetic field - unless I've misunderstood you - all levels are doubly degenerate (due to Pauli).

 

[Barth]

So if i understood well, in a quantum dot, there is two type of states:
the discrete "particule in a box", one electron states, equivalents in the confined object of the (kx,ky,kz,n) states of the bulk, and excitonic states, equivalents of the excitonics states of the bulk. And the only difference between bulk states and quantum dots states take their origin in the boundary conditions.

Is that right ?

 

[noura]

can u help me to get more information about the quantum dot and kondo effect it my project in Msc,

 

[Gokul43201]

So if i understood well, in a quantum dot, there is two type of states:
the discrete "particule in a box", one electron states, equivalents in the confined object of the (kx,ky,kz,n) states of the bulk, and excitonic states, equivalents of the excitonics states of the bulk. And the only difference between bulk states and quantum dots states take their origin in the boundary conditions.

Is that right ?

I believe this is correct, but you shouldn't take my word for it. The excitonic states are "intrinsic" to the quantum dot just as they are intrinsic to a bulk semiconductor - however, their dispersion is different from bulk excitons (due to difference in V(r)). The single particle states are the spectrum of electrons/holes that are made to populate the well (by doping, or heating for instance). The well/box itself, is nothing but the local structure in the conduction (or valence, in the case of holes) band.