Trapped single states

Figure 1: Sample structure: Different
semiconductor materials stacked.

Today I have been working on a lab report all day ... Only after some time I realised how awesome the physics is that is behind the experiment! (At least I think it is awesome. :) ) We trapped single electrons in a quantum well! I mean really single electrons, not the assumed single electrons or only few single electrons. So as I am working on this anyway I thought I should share parts of it in a very high-level (that means not too much crazy science, only a little ;) ) way. I hope it is understandable. :)

The setup consists of a stacked semiconductor structure as shown in figure 1. The gallium arsenide and and the aluminium gallium arsenide have different band gaps which the electrons in the device see as a well in energy. This is like if you jump into a well in the ground - you see the walls around you once you are in the well. (See figure 2 for the wells.)

Figure 2: Two bands resulting from
the different band gaps in the structure
from figure 1 and possible ways
to excite an electron from the bottom
to the top. Laser!

The next prerequisite is to know that physicists assume that there are differen bands in semiconductors that define the energies that electrons can have. (In which they can move if you want.) Now there are not only bands for electrons but also for holes which are the conception of missing electrons. Just like if you take a chocolate marshmallow out of its box leaving a blank space. These holes can move as well just like electrons.

So if there is an electron in one of the bands (the valence band to be precise) it can be moved to another band (the conduction band) by giving energy to it. (For example by shooting at it with a laser - pew, pew!) From before now it is known that this will leave a hole behind.

Figure 3: Spectrum recorded
during the experiment.

After some time the excited electron (the one that was shot to the other band) and the hole recombine because it is more suitable for them. (Particles always want to reach the lowest possible energy state.) If they recombine they emit the energy that the electron got from the laser before. This is visible as light so it can be detected. By a detector ...

Because we are not sure (unless we calculate it before, as I just had to for the lab report ...) which energy this light will have we let the detector detect a lot of possible energies. For some of the detected energies there will be nothing special but for some other energies there will be peaks which means that at these energies there is something going on. For example recombination of electrons and holes. This measurement of different energies is called a spectrum. Figure 3 shows an original spectrum from our experiment. :)

But how do we know that we trapped only one single electron in our well? That we know from the calculations. The movement of particles can be described by the Schrödinger equation. The setup with the quantum well gives boundary conditions to this equation so we get discrete solutions for it. As the semiconductor setup used is a little more complicated than a "normal" quantum well (whatever a >normal >quantum well may be ... <.< ) the solutions for the Schrödinger equation could not be obtained analytically. Instead we used a graphical method. The clue behind this is to plot the graph of the equation. Only at points where the graphs intersect a bound (trapped) state can exist. If you look at figure 4 you see yourself that there is only one intersection point. So one single trapped electron.! BÄM, science! ;)

Figure 4: Graphical solution of the Schrödinger equation. There is only
one intersection point (blue and red) so there is only one(!) single(!) electron
trapped in the quantum well!

So this was a very much broken down overview of what happened. I hope you could understand something. I am still fascinated that something like this is possible and that we did it. O.O

Last thing: Why do we do stuff like this? Well if the behaviour of the electrons in the well is better understood one can build some fancy devices out of this! Maybe new transistors which result in faster computers? Maybe quantum computers? Maybe better solar cells? (Actually I participated in another project where we measured nanowire solar cell arrays! I hope that I will tell something about this as well.)

If I am that fascinated this seems to be the right stuff to study! :)