In the first chapter we saw that our present energy economy cannot continue in its current form, because we are in the process of changing the environment in which we live. Mankind and all other forms of life have developed over millions of years by adapting to the conditions around us in a continuous process of evolution. We have good reason to describe changes to these conditions, which are too rapid for life to adapt to, as natural disasters. Life on earth is an extremely complex system, and even today we do not fully understand the interrelations within this system. If we do not wish to risk life as a whole or parts thereof by significant departures from the present equilibrium, we should tolerate only minor changes in the prevailing conditions. Every system reacts linearly to minor changes, even our complex ecosystem. Small changes to the natural processes result in small changes of the properties of the environment. The restriction to minor changes means that we may make use only of processes existing in the natural state of equilibrium. The burning of wood, coal, oil and gas occurs as a natural process as well, resulting in the natural production of CO2, CO and SO2. Burning of wood, coal, oil and gas could thus be tolerated, if their burning by man only caused minor changes to natural processes. However, we are presently proceeding rapidly to violate this condition. The amounts produced by mankind are no longer minor changes. The condition of causing only minor changes is, in any case, violated when processes are used or substances produced which do not exist in nature and it is almost impossible to predict how the environment will react. This is particularly true for many waste products from nuclear energy use. An example which shows what can happen if formerly non-existing substances are introduced into the environment is that of chlorinated fluoro-hydrocarbons (CFC), which do not occur at all in nature. They were regarded as entirely harmless, since they are non-toxic and chemically inert. It came as a great surprise to learn that they in fact destroy the ozone layer and also are, to a large extent, responsible for the greenhouse effect. Many more examples exist, where the violation of the condition of minor changes has led to unpleasant surprises.
No such surprises are to be expected when electricity is generated from solar energy by solar cells. In making use of the processes taking place in a solar cell, we are only linking ourselves into processes which would in any case occur without us. In our absence, solar radiation would be absorbed by the earth and, in part, be reflected back into space. In the course of this process, the earth heats up to just the temperature at which it can re-emit the energy current absorbed from the sun. It is very important that we do not alter this process significantly. Viewed from the standpoint of thermodynamics, the solar heat, very valuable at the sun’s temperature of roughly 6000K, is cooled down to the earth’s temperature, where it is practically worthless and is then emitted into space. What is changed, if the solar radiation is processed by solar cells? Part of the absorbed heat (in fact, most of it in real systems with
efficiencies of 20% or less) is cooled at the site of the solar cells down to the temperature of the environment in the same way as it would be without the solar cells. The electrical power generated by the solar cells is then re-routed through consumers before friction and other dissipative processes finally degrade it to heat at the temperature of the environment, from where it is emitted into space. The energy balance between the absorbed and the emitted energy currents remains unchanged. With the use of solar cells, we simply allow the natural process of cooling the solar heat to take place in ways of greater benefit to us.
The preceding chapters have not only shown that solar cells are well suited for obtaining electrical power from solar energy, they have also shown that there is no better way to do this than with the intelligent utilization of solar cells, e. g., in tandem cell arrangements, because the possible efficiencies of these systems coincide with general efficiency limits predicted by thermodynamics. This has two consequences. On the one hand, there is no need to continue searching for other methods of harnessing solar energy which are fundamentally more efficient. On the other hand, since we cannot hope for future discoveries and technologies with significantly greater efficiencies, there is no reason to wait any longer to begin the serious development of a solar-energy economy.
Our present energy economy consumes oxygen and produces CO2. Because of the fast and extensive spreading of gases in the atmosphere, this is a global, and not simply a local, problem. For heavily populated and industrialized areas such as Germany, where so much oxygen is burnt that none would be left to breathe, this spreading of the gases is very for-
for politicians to decide on radical changes in the
present energy economy, because continuing with the present energy consumption has little consequences locally, or, the other way round, the required very considerable local efforts are not rewarded on a local basis if they are not implemented globally.
A global energy supply by solar energy on the present level must be easily possible, otherwise we would already be suffering from substantial global warming. If our power requirements were not small compared with the solar energy current reaching the earth, their coverage from resources would result in an increase in the temperature of the earth, even without the greenhouse effect in order to allow for the emission of this additional energy into space.
A quick estimate indicates that a solar-based global energy economy could, in principle, be implemented relatively easily. The greater part of the globally consumed 10 x I013 kWh/a, is used to produce low-temperature heat, for heating buildings and for cooking. Even in countries with less than average sunshine like Sweden, most of these requirements can be met using well-insulated solar warm-water collectors. The rest, roughly 5 x 1013 kWh/а, could be generated by solar cells. Most of this would be used for the production of hydrogen, since this is an easily transported and easily stored form of chemical energy. In sunny areas, with incident solar radiation of more than 2000kWh/(a m2), a total efficiency of no more than  themselves, because otherwise the technologies required for use in the deserts would hardly be developed. As an example of an industrialized country, we will assess the situation for solar generation of electrical power in Germany.
In Germany, there are about 80 million people living in an area of 357000km2. This gives a population density of 226 persons per km2, with 4425 m2 available to each person. In Germany, the sun supplies about 1000kWh/(am2), i. e., 115W/m2 averaged over the year. Over the area of 4425 m2 per person, the sun supplies around 500 kW. Compared with this, the current power requirement of 5.7 kW/person, 0.76kW per person of this as electrical power, appear as almost negligibly small. Not all of this area will be used with high efficiency. The Germans allow themselves the “luxury” of using 180000km2, that is half of the total area of Germany, to satisfy an energy requirement of merely 0.1 kW per person. This, however, is our most important energy requirement, our food, produced on agricultural farmland and meadowland.
To satisfy the electrical power requirements with solar cells, assuming an efficiency of 20%, which will become possible in the near future, we would need an area of 33 m2 per person. This is very nearly as much as the average area of 35 m2 living space available per person in Germany. Industrial buildings additionally account for at least the same area. Assuming three-story buildings on average gives a floor space of 23 m2 per person for buildings in Germany. The roof surface areas will be somewhat greater. Only those oriented towards the north are unsuitable for solar cells. Furthermore, especially with multi-storied buildings, the wall areas oriented towards the south are very well suited.
From this estimate, we can see that the areas at and on top of existing buildings are already sufficient for nearly covering our present energy requirements by the use of solar cells, even in a country which does not receive the most sunshine. There is no reason whatever to speak of replacing forests with solar cells. Since there is more sunshine in summer than in winter and more energy is needed in winter than in summer, it is necessary to store energy in the summer for use in winter. This problem remains to be solved, and will certainly entail storage losses. This, of course, makes additional roof surface necessary. At present, though, a large amount of electrical power is wasted in producing low-temperature heat for heating buildings and for hot water. We could, in fact, manage with considerably less electrical power without any loss of comfort. Even for the relatively poor amount of sunshine in Germany, the enormous potential of solar energy for generating power without harm to the environment fully justifies the most intensive efforts to develop a solar-energy economy.
In view of the high population density and high rate of power consumption in industrial – ized countries like Germany, it seems more probable that not all of the power requirements will be met by utilizing only the solar energy captured in these countries. Even in an age of solar energy it is, in fact, more likely that industrialized countries will import energy from sunnier and less heavily populated countries, in very much the same way as today.
W. Shockley, H. J. Queisser, J. Appl. Phys. 32, (1961), 510.
Physics of Solar Cells: From Principles to New Concepts. Peter Wurfel Copyright ©2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-40428-7
^E, earth — , sun + 2 ^E. atm
Since radiation emitted by the earth’s surface is fully absorbed by the atmosphere, the solar energy current incident on the surface of the earth can only be emitted into space by emission from the atmosphere. This leads to the following conditions:
Two particles can be distinguished only if they are in different states. Two states are different when their location x and momentum p differ by more than the minimum of the uncertainty Ax. Ap of one of these states. For one dimension, this Heisenberg Uncertainty Principle has the form
AxApx > h. (2.4)
Particles which cannot be distinguished as a result of the Uncertainty Principle are in the same state. In geometrical and momentum space, a state therefore has the “phase space”
energy current density per solid angle observed from outside the surface j£ & is independent of the angle b at which the emitting surface is viewed. The dependence of the energy current density je on the angle of viewing results from a dependence of the solid angle subtended by
the emitting area. This behaviour precludes the recognition of any further details of a body by
the emitted radiation, except for its contour.
This so-called Lambert behaviour cannot be taken for granted. It applies strictly only
for the surfaces of bodies which absorb all radiation incident upon them, i. e. black bodies. Weakly absorbing bodies such as a sheet of transparent plastic, in which low concentrations
The density of electrons (in the conduction band) is
ne = Nc exp ^-£c k^FC ^ (3.27)
and that of the holes (in the valence band) is
W. Shockley, W. T. Read, Phys. Rev. 87 (1952) 835. R. N. Hall, Phys. Rev. 83 (1951) 228.
For the generation rates of electrons or holes from the impurities into the bands, we know that they must be proportional to the concentration of electrons ne, imp or holes nh, imp = «imp — «e, imp in the impurities. The generation rate of electrons is
Ue. imp ~ Pe«e. imp ■ (3.69)
In the same way, the generation rate of holes is
Uh, imp = Ph«h, imp = Ph(«imp — «e. imp) • (3.70)
Such perfect surface passivation is possible only for Si/Si02 and for the combination of a few III-V compounds having the same lattice constants. In spite of this, contact with another semiconductor in the form of a cover layer usually leads to lower surface recombination velocities than for a free surface or for the contact with a metal. In order for the recombination on the surface of the cover layer to remain insignificant, no electron-hole pairs should be generated within this layer. Semiconductors with a large band gap (Єс > 3 eV) are therefore chosen for passivating cover layers. These are transparent in the visible range and are also known as window layers.
Since Eq. (3.98) does not depend on the energies Єї and £2 explicitly, but only on their difference йсо, each pair of states with energies Zj in the conduction band and £, in the valence band with the same energy difference £; — £,- = h(a contributes to (3.98) in the same way. All possible transitions between valence band and conduction band with the photon energy ЙС0 are accounted for and are contained in (3.98), if а(Йсо) now is the absorption coefficient for all these transitions.
A problem is that the emission rate of the photons cannot be observed. What can be observed and measured is the photon current emitted through a surface. To find the emitted
L. D. Landau, E. M. Lifschitz, Course of Theoretical Physics, Vol. V, Butterworth, Heinemann 1980.
 A. deVos, Proceedings 5. E. C. Photovoltaic Solar Energy Conf, Athens 1983, p. 186.
It then follows that T|e +T|h = eV where V is the voltage between the terminals for the n-region and the p-region.
From the considerations above, it follows that the exponential function in the integrand in Eq. (6.23) is constant over the range of the integration limits. This greatly simplifies the integration of Eq. (6.23), and we obtain the current-voltage characteristic of the pn-junction as
This result requires that a perfect hole membrane at the rear side of the cell prevents the electrons from reaching the back contact where they would otherwise recombine, without contributing to the short-circuit current.
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This result reminds us of the improvement of the efficiency by tandem cells, since here as well, the incident spectrum is divided over different transitions leading to smaller thermaliza – tion losses. Figure 8.13 shows that the occupation of the various states is represented by more than two, namely three, different Fermi energies, a condition for reduced thermalization losses known from the discussion of tandem cells. In fact, since the rate of recombination transitions is determined by the difference between the Fermi energies for the states involved, each transition can be represented by a current-voltage characteristic. This leads to the equivalent circuit shown in Figure 8.13. The solar cell representing the band-band transition is connected in
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 percent over an area of 500 km times 500 km equal to 2.5 x 1011 m2, would be sufficient. Much larger areas are available in the sunny deserts. Nevertheless, covering such an enormous area with solar cells is presently unimaginable. The problems with a future solar-based energy economy would be alleviated, if we could reduce our energy requirements, or at least maintain them at their present level.
This vision of a solar-energy future, at the present time hardly possible for political reasons alone, must not let us lose sight of what solar energy can presently contribute to our energy requirements. Fortunately, there is enormous potential in the industrialized countries