Photovoltaic Conversion
John D. Meakin
Department of Mechanical Engineering & Institute of Energy Conversion, University of Delaware
The photovoltaic effect occurs when light is absorbed by a semiconductor. The energy of the photons is transferred to electrons in the valence band of the semiconductor, promoting them into the conduction band and resulting in the formation of electron-hole pairs. Only photons with energies exceeding the band gap energy of the semiconductor can be effective in this process. If the semiconductor has a small band gap, a large fraction of the incident photons will be able to create electron-hole pairs giving a large current but the voltage generated across the solar cell will be low. With a large band gap semiconductor the voltage generated will be high but the current low. Analysis has shown that to convert sunlight, in which most of the photons have energies between 1 eV and 3 eV, the optimum band gap for maximum power conversion is about 1.5 eV.
In an isolated semiconductor the excited electron would eventually recombine with a hole in the valence band, emitting its excess energy as photons (photoemission) or phonons (heat), and no useful generation of electric energy would take place. To extract the energy of the photo-excited carriers as useable electricity requires the existence of a charge-separating junction such as a p-n homojunction or diode. The passage of the excess charge carriers, known as minority carriers (electrons in the p-region, holes in the n-region), across the junction prevents electron-hole recombination. Thus a photo-generated electron in p-type material has a limited lifetime in the presence of the stable population of holes but an unlimited lifetime after crossing the junction into the n-type material.
In the traditional crystalline silicon solar cell, the charge-separating region is formed by the diffusion of specific impurities, or dopants, into a wafer of silicon, creating regions of opposite conductivity type. Diffusion of carriers across the transition between the n and p regions, i.e., the junction, occurs until an equilibrium is established in which the electric field created prevents further diffusion of charges. This internal electric field constitutes the charge-separating barrier which is key to the operation of the solar cell. Electrons created by light in the p-type material migrate to the junction and are then swept into the n-type region. In an efficient cell this collection occurs before the electrons recombine with the stable population of holes in the p region. The energy absorbed from the light is thus converted into electrical energy which can be fed into an external circuit. (The analogous situation exists for holes created on the n-type side of the junction.)
Figure 1a illustrates a diode under illumination and shows the production of electron-hole pairs which are then separated by the built-in electric field. The I-V behavior of an ideal photo-diode is given by
I = IO (eqV/kT -1) -Isc
where I and V are the external current and voltage respectively, q is the electronic charge and k is Boltzmann's constant, Isc is the short circuit current and IO is the reverse saturation current of the diode. The corresponding I-V curve is given in Figure 1b and is seen to be that of a diode but displaced along the current axis by the ``light-generated current.''
If the external circuit has zero resistance, a maximum current will flow as shown on the current-voltage plot. As the load resistance rises a voltage will be generated across the cell and the external current will eventually fall to zero at the open circuit voltage. In this situation, electrons accumulate on the n-side of the junction (holes on the p-side), biasing the junction in the opposite sense to the built-in field. The maximum voltage the cell can develop corresponds to the forward light-generated current exactly matching the reverse current. The maximum power generation occurs where the current-voltage product, IV, is largest. Under ideal conditions a single-junction solar cell in direct sunlight should convert about 22% of the incident solar energy into electricity. This figure ignores all the losses which inevitably occur in an actual cell, such as reflection from the front surface and various other electrical and optical losses. The theoretical efficiency limit is increased by operating the cell under concentrated illumination, which can be achieved using mirrors or lenses. Efficiencies over 30% are possible but the concentrating system must track the sun as it orbits across the sky.
In 1954 the first practical solar cells, with a structure similar to that shown in Figure 2, were made from single crystal wafers of semiconductor-grade silicon. These cells converted about 6% of the total incident sunlight into electrical power, i.e., they had an efficiency of 6%. Research Si cells have now reached over 20% efficiency under direct sunlight and almost 30% under sunlight concentrated by a factor of a few hundred times. Commercial cells are moving towards 20% efficiency yielding multi-cell modules of about 15% efficiency. Why then are solar cells not being used more extensively to generate electricity? To answer this question we must look more closely at the economics of electricity generation from solar cells.
The most significant costs are the initial capital outlays; operation and maintenance costs are small and there are no fuel costs. A simple analysis reveals the scale of investment that would be economically competitive. A module rated at 1 kW (i.e., able to produce 1 kW of electricity under sunlight of 1 kW/m2) will generate on average about 5 kWh/day or about 5 x 104 kWh of electricity worth $1000 - 3000 over its lifetime of, say, 20 years. About half of the initial investment will be for costs other than the modules, which must therefore be available for a few hundred dollars per kilowatt. More sophisticated analyses taking into account inflation and carrying charges yield similar order of magnitude estimates. Although the first cells produced for space use cost about $1 million/kW, extensive technical and manufacturing progress, coupled with much less stringent specifications for terrestrial use, has brought the present price down to about $3000 - 5000/kW in large quantities. Is it likely that a further order of magnitude reduction can be achieved? To answer this question we must first return to the physics of solar cell operation.
The rate at which sunlight is absorbed by a semiconductor is given by
F = e-µ t
where F is the fraction of radiation absorbed by a thickness t of semiconductor with an absorption coefficient µ . The absorption coefficient, µ , measured in cm-1, varies with the wavelength of the light. It is very low for photon energies below the semiconductor band gap and rises at higher photon energies. Crystalline Si has a relatively low absorption coefficient, between 102 and 104 cm-1, which means that a thickness of about 200 m m is necessary to absorb most of the sunlight. The carriers generated by the photons must then be able to travel about that far in order to reach the charge-separating junction before recombination occurs.
Efficient carrier collection in crystalline Si requires very pure and perfect material, and bringing the price of Si cells down by another factor of ten cannot be assured, although a number of ongoing developments may yield substantial reductions. These include methods to produce large-area thin sheets directly from a silicon melt to avoid the wafering step used with single crystals. Large-grained polycrystalline material, which is less expensive than single crystals, is also in use. Another promising approach is to texture the front and/or rear surface of the cell so that light undergoes multiple reflections within the cell. This lengthens the light path for a given cell thickness without increasing the distance that carriers must travel and may yield efficient cells as thin as 50 m m or less.
There are, however, many semiconducting compounds in addition to the semiconducting elements, Si, Ge, and grey Sn. The essential properties for a material to be a candidate for a low-cost solar cell are an appropriate band gap, say between 1.0 and 1.7 eV, and a very high absorption coefficient. The latter makes it possible to use very thin layers, which in turn relaxes the limitations on purity and perfection as short collection distances (short carrier lifetimes) now apply. Any compound is a potential semiconductor if the ratio of valence electrons to atoms, e/a, is 4, as is the case for the group IV elements.
Among the classes of semiconducting compounds are the II - VI (i.e., a compound AB where A is from group II and B from group VI), III - V, and I - III - VI2 families. Presently, solar cells are being developed based on members of each of these groups with the expectation that an improved combination of higher efficiency and lower cost will result.
Representative of the III - V compounds are GaAs and InP, which in single crystal form have yielded solar cells of about 30% efficiency. As a general rule the III - V's have excellent carrier properties. There is a major effort to develop them for high speed integrated circuits, but their properties are seriously degraded in thin film form and single crystals may have to be used to maintain performance. If this should continue to be the case, a concentrating system may be essential in which an optical assembly is used to focus the energy from a large aperture onto a much smaller solar cell, thus reducing the total area of solar cell needed for a given output. (See Suggested Readings.)
The II - VI compounds are represented by CdTe, which has an ideal band gap of about 1.5 eV and which has yielded solar cells of about 12% efficiency. A number of techniques for forming large areas of thin film are being developed including electroplating, various types of vapor deposition, and a spray pyrolysis process.
The I - III - VI2 material receiving most attention is CuInSe2. This has a rather low band gap of 1.0 eV but, as we shall discuss shortly, that may be an advantage for two junction or tandem cells. A number of research groups have demonstrated efficiencies of well over 10% and recently 14% has been reported. All investigators have confirmed a very high degree of stability for these cells, which is particularly important for thin film cells that in the past have often shown unacceptably short useable lifetimes.
The reason for interest in all of the above compounds is their high absorptivity which means that very thin layers, as little as 1 m m, will completely absorb the useful solar spectrum. The carriers generated by the light need then only travel equally short distances to the junction and relatively impure and imperfect materials, such as polycrystalline thin films, can be used successfully.
In parallel with the development of polycrystalline materials, there has been an explosive growth in the investigation, and application, of amorphous materials based on an alloy of Si and H, conventionally designated a-Si:H. Thin films of this material are deposited by creating a plasma in a gas containing the two elements, most frequently SiH4. The resulting solid contains tetrahedrally bonded Si but in a disordered, not a crystalline array. The hydrogen appears to heal any unsatisfied Si - Si bonds, eliminating energy states that would otherwise essentially eliminate the forbidden energy gap. The hydrogenated a-Si can therefore be doped in contrast to hydrogen-free amorphous silicon.
Progress in the science and technology of amorphous thin films has been remarkable and in about a decade a-Si:H solar cells have gone from a laboratory curiosity to a familiar component in solar-powered calculators. Panels with areas of 1 ft2 and larger are now entering the market for battery charging and other uses.
Scientifically and technically, the field of photovoltaic conversion remains exciting and challenging. New materials are being developed and more efficient configurations reduced to practice. Rather than having one cell to harvest the entire solar spectrum, stacked or tandem structures are appearing. In these systems the top cell removes the high energy photons, allowing the longer wavelengths (lower energy photons) to be efficiently harvested in a second or even third cell, creating the photovoltaic equivalent of a multistage turbine. The compound a-Si:H makes an ideal top cell as its band gap of about 1.6 eV efficiently uses the short wavelength light while transmitting the longer wavelengths into a bottom cell. Polycrystalline CuInSe2 is presently the best available material for the bottom cell as its band gap, 1.0 eV, is close to the ideal value for a two-junction device. A total efficiency of about 16% has been achieved by stacking an a-Si:H cell on a CuInSe2/CdS cell. Multijunction a-Si:H cells are also being developed using amorphous Si alloys containing C, Ge, or Sn to give various band gaps.
The present world market for solar cells, about 30 MW, is modest when compared to the installed electrical generating capacity, over 600 GW (6 x 1011 W) in the United States alone. However, production has doubled each year for some time and 10% market penetration by the year 2000 is quite possible. The economic incentive to develop alternative sources of electricity for use in the developed nations is controlled by the cost of nuclear energy and traditional fossil fuels, such as oil, gas, and coal. However, growing concern about the greenhouse effect and acid rain appear likely to also serve as an incentive for more rapid utilization of photovoltaics and other renewable energy resources.
Solar cells are ideally suited for remote locations and third world areas without grid systems, where the only alternatives are diesel generators or expendable batteries. Under such conditions it is already economical to use solar cells; for example the U.S. Coast Guard is converting all remote buoys to solar cell operation.
In spite of the uncertainty in the future level of solar electricity generation there can be no doubt that solar cells will make a very significant contribution and will continue to attract both scientific and commercial interest.
Suggested Readings
Cook, Earl. Man, Energy, Society, New York, W.H. Freeman, 1976.
Maycock, Paul D. and Edward N. Stirewalt, Photovoltaics, Andover, Mass., 1981.
Green, Martin A., Solar Cells, Englewood Cliffs, Prentice Hall, 1983.
Problems
You should find that the electricity is worth about two orders of magnitude more than the corn. However, one must also address the initial cost of the solar system and compare this to the annual costs of cultivating corn, typically about $180/acre. It is hoped that the total cost of a solar system can be brought down to about $100/m2; what would be the initial cost of a one-acre solar system?
I = IO[eqV/kT - 1] - Isc
where I and V are the current and voltage, respectively, q is the electronic charge and k is Boltzmann's constant, Isc is the short circuit current and IO is the reverse saturation current of the diode.
Figure Legends
Figure 1
Figure 2