A Slim Chance for Solar Energy?

Such is the explosive growth of the solar power industry that manufacturers of polysilicon, which is moulded into a long ingot and then sliced into thin wafers for solar cells, can't keep up with demand for it. It appears that new supplies are not due to come on stream until 2008, and meanwhile the price of polysilicon has tripled in the past two years and could continue to rise. In the light of this circumstance, it is of interest to look over a few figures and facts about what might be extracted from sunlight, and on what scale this could be achieved. Indeed, is a solar economy possible?
The solar radiation flux (sunlight intensity) at the top of the atmosphere is 1,400 W/m2, but some of this energy is absorbed by the atmosphere as the radiation passes through it. At the equator, at sea level, and at noon on a clear day, the solar flux reaching the earth is attenuated to 1,000 W/m2. If the performance of the solar cell were perfect (i.e. 100% conversion of radiation to electricity) an electrical output of 1,000 W/m2 (i.e. kW/m2) would be obtained. However, the actual output is nearer 100 W, i.e. 10% efficiency. Undoubtedly, the technology will improve, and there are fuel cells in research labs that can generate electricity with an efficiency of more than 30%, but 10% is a reasonable figure for a commercial solar cell at present, so we will work with this. In the U.K., however, an average value for the received solar flux is nearer 150 W/m2, which at 10% efficiency means 15 W/m2.
This is of course during the day only. At night, the power output drops essentially to zero. In the early morning and late day, more of the sun's energy is absorbed by the atmosphere; clouds also reduce the power, and so the actual output is highly dependent on the weather conditions and hence the emphasis on finding ways to "store" the electricity produced by photovoltaic technology.
To get some rough numbers and a scale of what is required, let us consider generating capacities for the U.K., the U.S., China and the world as a whole, and hence the area of photovoltaic solar panels required to meet these outputs.
According to "The World Factbook (2003)", in that year the U.K. generated 360.9 billion kWh of electricity. Dividing by the number of hours in the year, this amounts to a generating capacity of 360.9 x 10*9 kWh/8760 h = 41.2 GW (41,200 MW). Hence, we would need:
41.2 x 10*9 W/ (15 W/m2) = 2.74 x 10*9 m2 of solar panel area to generate it. Since 1 square kilometer (km2) = 1 million m2, this amounts to 2,747 km2, which is only 1.2% of the total land area of the U.K. mainland (230,000 km2).
For the U.S., the total is 3.717 trillion kWh = 3.717 x 10*12 kWh/8760 h = 425 GW.
China generated 1.42 x 10*12 kWh/8760 = 162 GW.
And for the entire world, a grand total of 14.85 trillion kWh was generated, which translates to a generating capacity of 14.85 x 10*12/8760 = 1,695 GW.
The relative solar panel areas appear quite respectable. I leave the reader to work out the percentage of total area required for the U.S. and China, and confine myself to noting that for the whole world, 1,695 x 10*9 W/(15 W/m2) = 113,000 km2 is needed.
This is worked out on the basis of the U.K.'s sunshine and the area could be reduced considerably by placing the panels nearer to the equator, so probably, any solar-powered "local" electricity generating operation would be more efficient in the developing world, e.g. India, Africa, South America - China is more complex in terms of its climate.
Given that 30% of the surface of the Earth is land (i.e. not presently covered by sea - a value that might change if sea levels rise; although they appear to be falling in the Arctic for reasons no one understands), and assuming the planet to be a perfect sphere, we have a land area of:
0.3 x 4(pi) x r*2 = 0.3 x 4 x Pi x (6366)*2 = 153 x 10*6 km2.
This is a rough estimate made on the basis of a circumference of 40,000 km for the Earth, and hence a radius (r) of (40,000/pi)/2 = 6366 km.
Hence, we need "only" cover the earth to the extent of 113,000/153 x 10*6 = 0.07%, which doesn't sound much. Indeed, it corresponds to an area of about 300 kilometers by 380 kilometers, or 235 miles by 300 miles, which is almost exactly half that of the U.K. mainland. Not that I am suggesting we host the whole world's solar production capacity within these shores!
As noted, the sun only shines during the day, and we can expect a sizable output for, say, only 8 hours per day (on average: more in the summer, less in the winter). Therefore, some other means for providing our electrical power is necessary during the dark (night) period. Alternatively and in principle, we might have around three times the area of solar paneling ( 3 x 8 hours = 24 hours) to meet the total demand required, and store the extra in the form of an "energy carrier", either as electrons (batteries) or hydrogen.
If we need this energy in the form of electricity, then "electrons" stored in batteries would be the better bet, as getting electricity "back" from hydrogen via fuel cells would be overall less efficient.
How much silicon would be required to make the required swathe of solar panels? To estimate this, I shall assume that a silicon layer with a thickness of 200 microns (= 0.02 cm) is to be used (this is toward the "thin" end of the 180 - 350 micron range quoted in Wikipedia for solar cells).
The total required solar panel area of 113,000 km2 = 113,000 x 10*6 m2 = 113,000 x 10*6 x 10*4 cm2. This corresponds to a volume of 1.13 x 10*15 x 0.02 = 2.26 x 10*13 cm3 = 2.26 x 10*7 m3.
Assuming an average density of silicon of 2.3 tonnes/m3, this volume corresponds to:
2.26 x 10*7 m3 x 2.3 tonnes/m3 = 51.98 x 10*6 tonnes; i.e. about 52 million tonnes of pure silicon.
The manufacture of one tonne of silicon is reckoned to cause the release of 1.5 tonnes of carbon dioxide (Wikipedia). This, presumably, is reckoned on the basis of an overall mass balance as:

SiO2 (60) + C (12) --> Si (28) + CO2 (44).

From the ratio of molecular/atomic masses for CO2 and Si, 44/28, a value of 1.57 is obtained, in close agreement with the above estimate. However, since the reaction occurs at 1,700 degrees C, a considerable input of energy is required in the form of electricity to make the reaction "go", with an additional amount of CO2 being unleashed skyward. Indeed, it is estimated that 13 MWh of electricity is used to make one tonne of pure silicon. To make the 52 million tonnes of silicon required for our global solar programme would demand 6.76 x 10*11 kWh. We are not of course going to make it all in one year, and perhaps over twenty years would be more realistic. However, that still means making 2.6 million tonnes of silicon every year, a figure to be compared with the current 30,000 tonnes currently produced, and in factories that make up to 10,000 tonnes per year each (some are far smaller than this). Hence, for a start we need something like 100 times the number of silicon factories that we now have!

What about the power requirement for them? To arrive at a per annum estimate we divide the total 6.76 x 10*11 kWh by 20 years, which gives us 3.38 x 10*10 kWh, and is to be compared with the world total electricity production of 14.85 x 10*12 kWh.
Hence, for a twenty year silicon programme, we would need at this rate to increase the world's annual electricity production by just 0.23%.
Nonetheless, building the number of factories necessary to manufacture "pure" silicon on 100 times the scale of current production is simply breathtaking, especially given the difficulty of even meeting the existing demand. Taken with the acquisition of the silica "ore" and the production of charcoal at the necessary grade to make "solar grade silicon", along with the fabrication of the solar panels themselves, the whole enterprise would be a stupendous undertaking.
The message is clear that solar will never become a sole producer of the world's electricity, although it will become increasingly important for stand-alone applications, particularly in the developing world.
I am not anti-renewables - I emphasise this - not in the slightest way! However, as with my earlier calculations on wind-power and biofuels, I am pointing out the sheer scale and energy density of human demand on the planet, which is not readily supplanted by renewable sources of energy. My considerations here are only made over current electricity production. If we try to factor in how much provision, e.g. by solar, would be required to produce electrons or hydrogen to run the world's transport systems at their current and rising size, we could easily multiply the above estimates by a factor of three or four: i.e. Renewables offer us little comfort in the absence of energy efficiency, which must be our leading step forward; then we may be in with a slim chance.

The best option for photovoltaic technology is through the development of thin-film technology, which uses perhaps 1/100th of the amount of semiconductor material, but the task is still monumental on the grand scale, while more localised applications are thus favoured. Other means to capture solar-energy are through roof-based water-heater systems, which use the heat from the Sun's rays to heat water - and of course, good old fashioned photosynthesis!