# Magneto-spectroscopy of quantum dots

A summary of my key paper, published in October 2006, that looked at the effects of magnetic fields on the electron-phonon interaction in quantum dots.

## Overview and feedback

Briefly, my paper entitled **Intraband magneto-spectroscopy of singly and
doubly charged n-type self-assembled quantum dots** looks at the fundamental
electron phonon interaction in quantum dots for the case where the dots are
populated with one, then two, electrons per dot. The main result is an
observation of an increase in the coupling strength of this interaction with
increasing electron occupancy from one to two per dot, and that this is in
contrast to what is observed in quantum well systems. For a full discussion,
please see below.

Most, if not all, scientific papers appear in one peer-reviewed journal or another. My first paper took my colleagues and I a significant amount of time (OK, it was mostly me that took the time…) to write, but that effort was worthwhile as the referees were pleased with it and suggested only minor corrections. I’m very proud of both of these quotes which are from the anonymous review process. From the first referee:

The authors report on a detailed magnetopolaron spectroscopy study on an InAs quantum dot multilayer sample. The dots are occupied either with one or with two electrons per dot. The main result of these investigations is the fact that an increased electron-LO phonon coupling is observed when the dot occupancy increases from one to two, in contrast to the situation in two-dimensional systems. The authors explain this phenomenon convincingly and quantitatively.

…and from the second referee:

The authors performed intraband spectroscopy on InAs/GaAs quantum dots, in magnetic fields up to 28T. For these quantum dots, they find a dependence of the electron-phonon coupling on the carrier concentration which is opposite to the case in 2-dimensional systems. The experimental observation is clearly explained with the used Fröhlich Hamiltonian. Furthermore, the polarization dependence of the ground to first-excited state transition as a function of magnetic field is shown. The polarization change from linear to circular polarization is ascribed to the Zeeman splitting which becomes larger than the zero-field excited state splitting energy at high fields. Both observations presented in this paper are interesting. The style of the presentation and the length of the manuscript are very good […]

Many thanks are due to all the authors on the paper for putting up with my countless revisions and persistence in getting this paper written, but especially to my supervisor Luke Wilson; Marcin Sadowski and Evgeny Zibik for experimental; and David Whittaker for theoretical support. Cheers guys, without your help this would never have been possible…

## Intraband magneto-spectroscopy of singly and doubly charged n-type self-assembled quantum dots

A scientific paper, by its very nature, makes quite terse reading for anyone who doesn’t work in the field for which it was written. I have had much interest in a ‘friendly’ version of the paper, and hence have put together this version specifically for the non-physicist reader. The more technical topics have links to other online articles such as those provided by Wikipedia, as this article focuses on the results rather than the elsewhere well documented processes that were used to gain those results.

The physicist reader may find it helpful to skip past topics that are familiar; this article is intentionally written at a fairly basic level. I have no desire to re-write the paper here though, so the many points are left for the interested reader to look up in the paper itself. Enough details will be provided here to understand the concepts involved and the key result, but there are no equations and very few numbers to make for easier reading. If you’re a non-physicist reader, you may find it helpful to read my simple guide which provides most of the background material that is then built on in this article. Done? Good. Let’s carry on then…

### Quantum dots and the experiments

The semiconductor wafers used for the work in this paper were grown by Molecular Beam Epitaxy at the EPSRC National Centre for III-V Semiconductors. Briefly, the semiconductor materials are deposited in layers on a smooth semiconductor surface known as the substrate. The fundamental properties of the materials are used to generate the quantum dots by a process known as Stranski-Krastanow self-assembly: After a critical thickness of a given layer of material has been passed, the material ruptures from a smooth surface into one of numerous randomly distributed ‘islands’. These are the quantum dots and the wafers used here contain 80 layers of quantum dots when they’re finished.

The most interesting results in this paper arise from the difference in behaviour between quantum dots that contain one electron each over those that contain two electrons each. Samples in which the quantum dots contain one or more electrons are known as ‘doped’ quantum dots. To measure the effect of having the extra electrons, the results are always compared with otherwise identical but ‘undoped’ samples, i.e. samples with no additional electrons per dot.

Everything here is obtained from ‘transmission’ measurements: A source of light at mid-infrared wavelengths is shone through the semiconductor wafers and we study the difference between the amount of light that gets through at a given wavelength for the doped vs. the undoped samples. The transmission measurements are made within a large magnet and at just a few degrees above absolute zero.

### A bit more basic physics… Phonons

The key results in the paper come from the interactions between electrons and the vibrations of the crystal in which those electrons sit. An easy way to visualise this is the effect of taking a soft cushion and placing a marble on it. The presence of the marble causes a distortion in the surface of the pillow and when the marble moves across the surface of the pillow the distortion moves with it. Swap the cushion for a semiconductor crystal lattice and swap the marble for an electron, put everything in three dimensions rather than two and we have an analogy for our electron in the quantum dot. Distortions in a crystal lattice are known as phonons and there is an effective interaction between any given electron and the phonons, which you can think of as analogous to the ‘depth’ of the depression the marble makes in the cushion.

### Key result

The main result focuses on the relative strength of the electron-phonon interaction in quantum dots doped with one electron vs. quantum dots doped with two electrons. There are two semiconductor wafers (samples) studied here: One is doped with one electron per dot and is known as a one electron system; the other is doped with two electrons per dot and is known as a two electron system. We have shown that the electron-phonon interaction is stronger for the latter case; there is an increase by a factor of a bit less than 1.5 in the interaction strength from a one electron system to a two electron system.

### Brief discussion

This is interesting because it is the opposite of what occurs in a quantum well system. As presented in the simple guide an electron in a quantum well is only confined in one dimension and is free to move in the other two. As more electrons are added to a quantum well system, the effective electron-phonon interaction that a given electron is subjected to reduces, because the other electrons get in the way. In a quantum dot, clearly as the electrons are not free to move the same does not happen, hence the observed interaction strength increase.

An increase in the interaction strength in good agreement with what we have seen was predicted theoretically in a short section of a PhD thesis from the University of Paris VI. This theoretical work arrives at the conclusion we have seen experimentally purely by considering the fundamental properties of electrons in quantum dots, especially for the case where each quantum dot contains two electrons.

We explain much of the observed behaviour using a computer model I wrote in which all the relevant energy states of the system of electrons and phonons are considered with a small number of interactions between those states. The data for the one electron system are fitted first with this model. With minimal adjustments to the parameters, the model fits the data for the two electron system very well only once the increase in the interaction strength is taken into account.

### Further reading

Of course, now you’ve read the qualitative description you’ll be better informed to extract the bits of detail that interest you from the paper itself.

With permission from the American Physical Society, I can distribute from this page a copy of my paper: Intraband magneto-spectroscopy of singly and doubly charged n-type self-assembled quantum dots (PDF)

The official page on the Physical Review B website can be accessed at the following address: http://link.aps.org/abstract/PRB/v74/e161302