So it is clear we must tread lightly, leaving the great body of 20th century quantum theory undisturbed. Yet not entirely, for it contains precious nuggets relating to the nature of sunlight and imposes fundamental limits on the efficiency of solar cells.
Certain eminent physicists, from Isaac Newton in the 17th century to Albert Einstein in the 20th, viewed light as a stream of minute particles carrying discrete packets of energy. And we stated – without explanation – that a light quantum or photon needs a certain minimum energy, known as the bandgap, if it is to have any chance of creating an electron – hole pair in a silicon crystal lattice. It is now time to bring these ideas together with the help of a little quantum theory.
The human eye is sensitive to visible light – all the colours of the rainbow from violet to red. The corresponding range of wavelengths is about 0.4 to 0.8 μm. The complete solar spectrum, previously shown in Figure 1.4 , also contains signifi cant energy at ultraviolet (UV) and especially infrared (IR) wavelengths. A key concept of quantum theory is that the energy content of a photon is related to wavelength by a surprisingly simple equation:
Where E is the photon energy, his Planck ’ s constant, cis the velocity of light, and λ is the wavelength. This means that the packet of energy or quantum is about twice as large for a violet photon as for a red photon. And as Einstein proposed in 1905, quanta can only be generated or absorbed as complete units.
A second key point is that solar cells based on semiconductors are essentially quantum devices. An individual solar photon can only generate an electron – hole pair if its quantum of energy exceeds the bandgap of the semiconductor material, also known as its forbidden energy gap. This is illustrated by Figure 2.13.
You may recall that the creation of an electron – hole pair involves jolting a valence electron to produce a broken bond in the crystal lattice. The electron moves from the valence bandto the conduction band, leaving behind an equal, but oppositely charged hole. However the energy levels of an electron in the two bands are separated by a discrete energy gap. Moving from one band to another requires a ‘ quantum leap ’ – it is all or nothing, and intermediate levels are forbidden. Long - wavelength infrared and red photons do not generally have the necessary amount of energy. Conversely most photons towards the violet end of the spectrum have more than enough and the excess must be dissipated as heat. These fundamental considerations, taken in conjunction with the Sun’s spectral distribution, reduce the theoretical maximum effi ciency of a silicon solar cell at an insolation of 1000 W/m2 to about 45%. The fi gure does not take account of various other loss mechanisms and practical design considerations, some of which were illustrated by Figure 2.8 . So it is not hard to appreciate why cells made in research laboratories do well to reach 30% and why current commercial, mass - produced, cells achieve less than 20%.
We can now appreciate why the size of the bandgap is a very important influence on solar cell efficiency. If the bandgap is too large many photons possess insuffi cient energy to create electron – hole pairs. But if it is too small, many have a lot of excess energy that must be dissipated as heat. It is found that efficient harvesting of the Sun ’ s energy requires bandgaps in the range 1.0 – 1.6 electron volts (eV). Silicon’s bandgap of 1.1 eV is fairly good in this respect. Certain other semiconductor materials have bandgaps closer to the middle of the range, and we will discuss them later.
Unfortunately not all photons with the necessary energy are readily absorbed. Most solar cell materials, the direct - bandgap semiconductors, act as good light absorbers within layers just a few micrometres thick. But crystalline silicon, an indirect - bandgapmaterial, is not so effective. It absorbs high - energy blue photons quite easily, close to the cell ’ s top surface, but low - energy red photons generally travel much further before absorption and may exit the cell altogether. The basic problem is that successful generation of conduction electrons in silicon requires additional quantum lattice vibrations that complicate the process, so that layers less than about 1 mm thick are not good light absorbers. Special light - trapping techniques may be used to increase the pathlength of light inside the cell and give a better chance of electron – hole generation.
To summarize, it would be helpful if every photon entering a solar cell produced an electron – hole pair and contributed to power generation, in other words if the quantum effi ciencywas 100%. But quantum theory tells us this is impossible. Photons are all - or - nothing packets of energy that can only be used in their entirety. Some are too feeble in their energy content while others are unnecessarily strong, placing fundamental limits on solar cell efficiency. Disappointing though this may seem, we should always remember that sunlight is ‘ free ’ energy, to be used or not as we wish. Photons are not wasted if untapped – at least not in the sense of an old -fashioned power station burning fossil fuel that effectively discards around 60% of its precious fuel as waste heat.
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