(3D Periodic Table. Michael Aldersley)

  I had noticed about this fantastic Scientific Delirium Madness Residence on the Yasmin list, which by the way is having days of struggle these last months. Quickly I sent my proposal, including two projects related to nanotechnology. Here I would like to present the preliminary results that I´ve developed on one of these projects during the residence, which I called the “Nano Table”. In my scientific research I study the emission from single semiconductor quantum dots. These nanostrusctures are fascinating, as in many ways behave as single atoms. They are called “artificial atoms”, because we can control its properties by changing the size, shape, chemical composition, crystal structure, lattice parameter, … This made me think about the possibility to arrange a particular “periodic table” for these artificial atoms. I came here with the idea to develop some interaction with the artists and scientists to answer to these questions: Is there any possibility to think about a periodic table for these artificial atoms?  Would it make sense any possible periodic table for nanostructured elements? My starting point was that periodicity with semiconductor quantum dots may be has no sense, as any change in shape or size for quantum dots is translated into different electronic configuration. So, we can say that there is a continuous “artificial atom” evolution, instead of this discrete configuration of the periodic table. However, may be it is possible to find some periodicity, even if it is not composed by discrete arrangements. In my presentation talk I’ve just presented the problem, circulating around one idea: thinking about a third dimension for the periodic table. Nanotechnology could be thought as a kind of this third dimension. For example, nanoparticles could be arranged as a third dimension along a vertical axes of the Silicon position in the periodic table. However, with this approximation it was only possible to arrange a small amount of elements, since semiconductor nanoparticles are most of the times binary or ternary alloys, even more complicated. Returning from the dinner, Luca and me were speaking about the possibilities, and he just asked me – why are you thinking in three dimensions?, why not four?, or even more? –. I was answering him, trying to imagine in which way I could represent more than three dimensions, when I understood his question. Yes, I just needed another parameter, and before to enter to my studio I visualized that this fourth parameter would be the frequency from the quantization energy for each nanoparticle. Yes !! Each nanoparticle has its own confinement range, and this is just the range where nanotechnology is important for semiconductors: the area where the exciton (electron bonded by a hole in the semiconductor crystal) is confined by the size of the nanoparticle. The next day I selected the mathematical expression to relate semiconductor materials with nanoparticle diameter and, finally, excitonic energy. I used the easiest model, just considering effective mass approximation and spherical nanoparticles. This model is too far from any realistic approach, but it is the starting point to make some calculus and pictures. I just arranged some information from different binary semiconductors (effective masses for electron and holes, and their dielectric constants). With this information I calculated the excitonic radius, and then the excitonic energy, following these expressions:

 Next step was to plot these results, and I did it arranging different materials with increasing energy gap. So, this was an important decision. In this step I forgot any input from the periodic table of elements, and began a new arrangement basing the classification on the energy gap of the semiconductor. Here you can see the first result using a double log plot:

 As you can see, for each material, as nanoparticle diameter increases, the excitonic energy decreases until reaching a stable value (energy gap). It is very important that semiconductor nanoparticles with lower energy gaps have large confinement range. However, this is not completely true, as it must be taken into account in more realistic phenomena (related to atomic size, crystal structure, growth process, …). But, the figure could be used to visualize the area where nanotechnology is important for semiconductor nanoparticles. In order to get a clearer picture of this region, I plotted a 2D image: Here it is shown in a clearer way the evolution of the excitonic energy for each material as particle sizes increase. All lines tend to the large particle limit, where nanotechnology effects (quantum confinement, in this case) don’t apply. In my imagination, the area between the top line (corresponding to the small particles) and the limit case (bulk limit), corresponds to a visualization of the quantum confinement for semiconductor nanoparticles. It seemed to me a triangle, and I just plotted the following arrangement:

As we go upwards in this triangle, material energy gap increases, excitonic bohr radius decreases, and the theoretical range for quantum confinement decreases in a first approximation of the effective mass approach. This visualization doesn´t make sense to describe any realistic system, since many simplifications have been made. However, it could be understood as an example of how scientific imagination could be engaged by the artistic community. In this case, trying to understand how to visualize a nanotechnological arrangement of semiconductor materials. For sure, the more interactions with artists, the more esthetical and sophisticated final graphics and ideas would be developed.   Note: I used only a small group of the possible binary semiconductors, as here I don´t have access to all the parameter information for all materials.