Why Solar Panels Can’t Get Much More Efficient (And That’s Okay!): Shockley-Queisser and the limits to converting sunlight into electricity

Commercially available solar panels now routinely convert 20% of the energy contained in sunlight into electricity, a truly remarkable feat of science and engineering, considering that it is theoretically impossible for silicon-based solar cells to be more than 32% efficient. This upper bound, known as the Shockley-Queisser Limit, was first calculated by the eponymous scientists (who actually gave 30% as their original limit) in the Journal of Applied Physics in 1961 [1] (see also updates by Rühle [2]).

Now, if we can answer why solar panels are thus limited, we can understand the essentials of photovoltaics (PV), which have their basis in the photoelectric effect, and p-n semiconductor junctions. While many have never heard of it, the photoelectric effect is of monumental importance, and when Albert Einstein received the 1921 Nobel Prize in physics, it was “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect,” while p-n junctions lie at the foundations of modern electronics, including transistors and LEDs. Indeed, a solar cell is essentially an LED in reverse: Instead of an electric current generating light, light generates electric current!

LEDs and solar cells are just the inverses of each other!

The goal of the remainder of this post is to introduce the very basic physics of solar cells, so that as a reader you come away with a basic understanding of the function and limits to solar PV technology. To start, let us outline how crystalline silicon (the basis for virtually all solar cells) can be formed into a p-n junction that generates a useful current, but for this, gentle reader, we must recall some basic chemistry, and turn to our oft-memorized but seldom understood periodic table of elements (and zoom in to the top three rows), with carbon(C) and silicon (Si) highlighted:


eriodic table of elements and the first few rows highlighted: As we move across columns from left to right, we add electrons to the element’s outermost shell, until a stable, full valence is reached on the right. By virtue of their position in a common column, carbon and silicon have similar chemistries. Periodic table adapted from https://pubchem.ncbi.nlm.nih.gov/periodic-table/ (US government); overall figure by the author. All remaining figures by the author.

Now that we have a crystal silicon lattice, let’s introduce the photoelectric effect, wherein sunlight falling upon this lattice may strike an electron, knocking it out of its covalent bond (the electron is then said to enter the conduction band), allowing it to migrate freely (and randomly) through the lattice. When such a negatively charged “free electron” begins wondering, it necessarily leaves behind an unpaired electron and a positively charged “hole.” Like the free electron, as electrons un-pair and re-pair, the hole can also migrate randomly through the lattice. In a pure Si lattice, light and the attendant photoelectric effect does nothing more than create electron-hole pairs that diffuse randomly until recombining, generating no useful current (remember that current is the ordered flow of charge):

If we stack n-doped silicon on p-doped silicon, un-paired electrons from the n-side fill holes on the p-side, and thus the n-side develops a permanent net positive charge (as it has lost electrons), while the p-side becomes permanently negative. With this charge separation, we can create a useful current loop: When we shine a light on the p-n junction, excited electrons flow unidirectionally to the positively charged n-type silicon. We then place wires on the silicon surface to collect up electrons, connect to an external load, and back to the p-type silicon, and thus electrons are driven in a closed loop, generating electrical current. Voila! A solar cell is born!

The left-hand figure gives the solar spectrum in terms of wavelengths hitting the surface of the Earth (as well as the “top of the atmosphere”). On the right side, the energy of a photon with any given wavelength is indicated by the blue curve: Any electron with a wavelength above about 1,150 nm carries less than 1.1 eV, and so its energy is lost. For electrons with shorter wavelengths, only 1.1 eV is used for photoexcitation, and so the energy gap between 1.1 eV and whatever the photon carries is wasted. The inscribed spectrum is simply for reference (not to scale).

Energy losses and “spectral efficiency” based on a standard solar spectrum and a band gap energy of 1.1 eV.

To see what band gap best balances the two forms of energy loss, we systematically change the band gap energy and make another version of the above figure, tabulating the results (obviously we make a computer do the details!), for example:

Thus, spectral efficiency indeed peaks at very nearly the 1.1 eV band gap of silicon. Finally, by adding in our energy losses from radiative recombination and circuit resistance, we can determine theoretical maximum efficiency as a function of a solar cell’s material band gap:

Key Points


See also the medium.com version

Leave a Reply

Your email address will not be published.