The title of this post deserves some clarification. Isn’t the answer obvious? You need to understand how solar cells work in order to improve them and physics are the foundation of that understanding, right? We suspect that most people would not deny the importance of physics in the field of solar cells, so you might wonder what there is to discuss about this subject.
So let’s examine a little closer what we mean by “solar cell physics”. First of all there is the whole body of theory and equations that has already been discovered and tested. There exist several sophisticated software packages that have implemented detailed mathematical models based on this existing theory and these programs are capable of accurately predicting the efficiencies of complex cell designs. At first glance, the physics of solar cells might appear to be a closed chapter for the most part; a finished work we can just hand over to the engineers to play with. Obviously there are still some gaps left in this theory: new solar cell designs based on new materials will continuously put a demand on physicists to come up with models that can describe these cells and existing models (for, e.g., recombination mechanisms) can almost always be improved. These seem like good reasons to think that physics continues to make important contributions to the field of solar cells.
However, let’s go back one step and examine what exactly we mean when we say that “physics helps us understand how solar cells work”. Naturally, when we talk about understanding solar cells, we talk about improving them since photovoltaics (PV) is not a purely academic subject that we study just for the science of it. The question then rises what the role of physics is (or should be) in the design of solar cells, since this seems ultimately more of an engineering problem. The ideal we normally have of science and physics is that we study a subject to learn about it and then hand over that knowledge to engineers to use this knowledge to improve what whatever it is that needs improving. However, this ideal is not as straightforward to realise as we would often like and the step from knowledge to improvement is not always trivial (as is often assumed, unfortunately). We can ask a computer to calculate the efficiency of a certain cell design and we would get a very accurate answer, but what we would much rather do is ask the computer to calculate a cell design that achieves, e.g., a 26% efficiency given certain practical constraints.
So by the looks of it (see also fig. 1), the role of physics is to improve the mathematical model that describes a cell, while it’s up to the engineers to improve the design of the cell. Or, in other words, physics is about predicting the response of particular solar cell design, while engineering is more or less the inverse problem: coming up with a design that gives a certain response (in this case: an efficiency as high as possible).
The question then rises if there is anything in physics that can contribute to this inverse problem. The answer to that question is, of course, thermodynamics. Thermodynamics is from its very roots a cross-over field between physics and engineering. After all, it’s foundations were laid by Carnot; an engineer who was very much interested in solving practical problems. To this day, thermodynamics is of great importance in many engineering disciplines where there is need to optimise energy conversion processes. However, when reviewing the field of solar cell development, it almost seems like thermodynamics is a purely academic subject about the upper efficiency limit of hypothetical devices. Meanwhile, engineers who are busy finding the best doping profile for their silicon cell generally seem unconcerned about thermodynamics.
Figure 1. The contrast between learning about solar cells and improving them. Both disciplines are rooted in experiment and observation, but for science the ultimate goal is to improve the mathematical models of solar cells while engineering is concerned with improving the cell itself. Of course, the two are not mutually exclusive: engineering can lead to interesting new questions science can investigate (top red arrow) while the scientific models can help to find new solutions to engineering problems (bottom red arrow).
The fact that thermodynamics isn’t used more commonly in the engineering of solar cells is rather unfortunate, since most of the solar cell physics that is widespread in the field is actually thermodynamics in disguise. It’s just that because we generally teach “semiconductor physics” that this link to thermodynamics (or actually: non-equilibrium thermodynamics) is obfuscated and important thermodynamic concepts like entropy are ignored. It also turns out that the thermodynamic view of semiconductor physics leads quite naturally to a concept of solar cells in terms of electron- and hole-selective membranes, thus giving a solid underpinning for the development of passivating contacts (see also fig. 2).
To demonstrate this link between semiconductor physics and thermodynamics and explain how this link can be used to gain a better understanding of the selective membrane model of solar cells, we encourage the interested reader to read some chapters (in particular Chapter 2 and 3) of my PhD thesis, which have been provided here in PDF form. I would also like refer to this paper.
Figure 2. Two competing pictures of solar cell junctions. The left picture is a rather naive visualisation of the operation of a solar cell for several reasons. First of all, it puts great emphasis on the build-in voltage, the space charge region (SCR) and the forces the electric field exert on the carriers, giving the incorrect impression that the electric field drives the current even though an electric field cannot perform net work since it is a conservative force. The left picture also depicts the thermalisation of the energy of an electron-hole pair after excitation. This is also slightly naive, since the (total) energy of an electron-hole pair is, thermodynamically speaking, rather inconsequential: the total energy is not necessarily the amount of energy one can convert into work. In fact, the diagram shown on the left is in equilibrium; in this situation none of the energy of the excited pair can be extracted as work in the same way one cannot extract thermal energy from a silicon wafer and use that to power a machine. The right picture (by Peter Würfel) is a thermodynamically less naive presentation of a solar cell and it puts the emphasis on the quasi Fermi levels that represent the free energy of the ensembles of electrons and holes. These averaged particles do not feel electrostatic forces but electrochemical forces (the gradients of the quasi Fermi levels). Because the Fermi levels come together in the metal, there will always be electrons flowing towards the hole-collecting contact and the only way to do something about that is by making sure that the electrons encounter much more resistance (represented by rectangular resistor symbols) than the holes on their way from the bulk to the contact. This asymmetry between electron and hole resistance is what we call selectivity. The free energy picture also allows us to provide a new, more insightful, view of thermalisation losses associated with photon absorption, because the free energy is the maximum energy one can hope to extract as useful work from the system. For example, by considering free energy thermalisation rather than energy thermalisation it suddenly becomes obvious why photon absorption in selective membranes is less effective than in the bulk of the cell: in the membranes the Fermi level splitting is less and the free energy thermalisation losses are larger. In practise, these thermalisation losses manifest themselves as parasitic absorption; a well-known problem in solar cells.
Leave a Reply