# Contents

## Idea

Photovoltaic solar power or PV is a form of solar power in which solar radiation is converted into direct current electricity using semiconductors that exhibit the photovoltaic effect. Photovoltaic power generation employs solar panels with ‘cells’ containing these semiconductors.

As of 2011, photovoltaic solar power had a capacity of 70 gigawatts. Only a fraction of this capacity is actually used, thanks to clouds and night. However, between 2004 and 2009, the capacity increased at an annual average rate of 60%. From 2009 to 2010 the capacity rose from 23 to 40 gigawatts, an increase of 74%. From 2010 to 2011 it rose from 40 to 70 gigawatts, an increase of 75%.

The following chart shows the rapid growth:

This chart is from the 2010 report here:

• REN21, Renewables 2010 Global Status Report, page 19.

and the more recent figures are from:

• REN21, Renewables 2012 Global Status Report, page 17.

Quoting from the 2010 report:

Cumulative global PV installations are now nearly six times what they were at the end of 2004. Analysts expect even higher growth in the next four to five years. Thin film’s share of the global market increased from 14 percent in 2008 to 19 percent in 2009 for cells, and from 16 to 22 percent for modules.

Germany again became the primary driver of PV installations, more than making up for the Spanish gap with 3.8 GW added — about 54 percent of the global market. This was far above Spain’s prior record-breaking addition of 2.4 GW in 2008, and brought Germany’s capacity to 9.8 GW by the end of 2009, amounting to 47 percent of existing global solar PV capacity. While Germany has played a major role in advancing PV and driving down costs, its importance will decline as other countries step up their demand and reduce the industry’s reliance on a single market.

After its record-breaking year in 2008, the Spanish PV market plummeted to an estimated 70 MW added in 2009, due to a cap on subsidies after the national solar target was exceeded. But there were other sunny spots in Europe. Italy came in a distant second after Germany, installing 710 MW and more than doubling its 2008 additions due to high feed-in tariffs and a good national solar resource; such strong growth is expected to continue. Japan reemerged as a serious player, coming in third with 485 MW installed after reinstating residential rebates and introducing a buyback program for residential rooftop systems.

The United States added an estimated 470 MW of solar PV in 2009, including 40 MW of off-grid PV, bringing cumulative capacity above the 1 GW mark. California accounted for about half of the total, followed by New Jersey with 57 MW added; several other states are expected to pass the 50 MW per year mark in the near future. Residential installations came to 156 MW, a doubling from 2008 thanks in part to removal of the \$2,000 cap on the federal Investment Tax Credit and to a 10 percent drop in installed costs relative to 2008.

## Efficiency

In Without the Hot Air, David MacKay writes (pp. 39ff) that typical efficiency of solar power cells is 10% and double that for expensive ones on which he bases his UK calculations on. There is a theoretical upper bound on efficiency of 68%.

Here is an NREL chart of the efficiency of various experimental solar cells - click to enlarge:

The book

has a photovoltaics chapter which is written by Michael Graetzel, a PV researcher and advocate. This includes diagrams on total global production of photovoltaic cells up to 2003 (744 MW that year). Laboratory model PV-cells have around 35% efficiency (see Fig 8.3), but you lose 0.5% efficiency per °C in commercial installations (p.124). Graetzel then talks about geneneration-1 thin film, single crystal silicon, generation 2 (low cost), and generation 3 (>33% efficiency) e.g. multi gap tandem cell, quantum dot cells, hot electron converters. Generation 2 PV-cells would have a payback time of < 1 year compared to >4 years for generation 1 PV. DSC—dye sensitive solar cells—are generation with 11% efficiency today, but they also can produced cheaply, and they allow conversion of the power to hydrogen (using solar photolysis).

The efficiency and cost tradeoffs are illustrated in the following diagram which comes from the book

## The physics of photovoltaics

Harry Atwater of Caltech gave a talk on photovoltaic solar power at this conference:

What follows are some notes on that, taken by John Baez as part of week293 of This Week’s Finds:

The efficiency of silicon crystal solar cells peaked out at 24% in 2000. Fancy "multijunctions" get up to 40% and are still improving. But they use fancy materials like gallium arsenide, gallium indium phosphide, and rare earth metals like tellurium. The world currently uses 13 terawatts of power. The US uses 3. But building just 1 terawatt of these fancy photovoltaics would use up more rare substances than we can get our hands on:

For more details, see Mineral resources.

So, if we want solar power, we need to keep thinking about silicon and use as many tricks as possible to boost its efficiency.

There are some limits. In 1961, Shockley and Quiesser wrote a paper on the limiting efficiency of a solar cell. It’s limited by thermodynamical reasons! Since anything that can absorb energy can also emit it, any solar cell also acts as a light-emitting diode, turning electric power back into light:

• W. Shockley and H. J. Queisser, Detailed balance limit of efficiency of p-n junction solar cells, J. Appl. Phys. 32 (1961) 510-519.

• Schockley-Quiesser limit, Wikipedia.

What are the tricks used to approach this theoretical efficiency? Multijunctions use layers of different materials to catch photons of different frequencies. The materials are expensive, so people use a lens to focus more sunlight on the photovoltaic cell. The same is true even for silicon - see the Umuwa Solar Power Station in Australia. But then the cells get hot and need to be cooled.

Roughening the surface of a solar cell promotes light trapping, by a large factor. Light bounces around ergodically and has more chances to get absorbed and turned into useful power. There are theoretical limits on how well this trick works. But those limits were derived using ray optics, where we assume light moves in straight lines. So, we can beat those limits by leaving the regime where the ray-optics approximation holds good. In other words, make the surface complicated at length scales comparable to the wavelength at light.

For example: we can grow silicon wires from vapor. They can form densely packed structures that absorb more light:

• B. M. Kayes, H. A. Atwater, and N. S. Lewis, Comparison of the device physics principles of planar and radial p-n junction nanorod solar cells, J. Appl. Phys. 97 (2005), 114302.

• James R. Maiolo III, Brendan M. Kayes, Michael A. Filler, Morgan C. Putnam, Michael D. Kelzenberg, Harry A. Atwater and Nathan S. Lewis, High aspect ratio silicon wire array photoelectrochemical cells, J. Am. Chem. Soc. 129 (2007), 12346-12347.

Also, with such structures the charge carriers don’t need to travel so far to get from the n-type material to the p-type material. This also boosts efficiency.

There are other tricks, still just under development. Using quasiparticles called "surface plasmons" we can adjust the dispersion relations to create materials with really low group velocity. Slow light has more time to get absorbed! We can also create "meta-materials" whose refractive index is really strange - like $n = -5$!

Recall that the refractive index of a substance is the inverse of the speed of light in that substance - in units where the speed of light in vacuum equals 1. When light passes from material 1 to material 2, it takes the path of least time - at least in the ray-optics approximation. Using this you can show Snell’s law:

$\frac{sin(\theta_1)}{sin(\theta_2)} = \frac{n_2}{n_1}$

where $n_i$ is the index of refraction in the $i$th material and $\theta_i$ is the angle between the light’s path and the line normal to the interface between materials:

Air has an index of refraction close to 1. Glass has an index of refraction greater than 1. So, when light passes from air to glass, it "straightens out": its path becomes closer to perpendicular to the air-glass interface. When light passes from glass to air, the reverse happens: the light bends more. But the sine of an angle can never exceed 1 - so sometimes Snell’s law has no solution. Then the light gets stuck! More precisely, it’s forced to bounce back into the glass. This is called “total internal reflection”, and the easiest way to see it is not with glass, but water. Dive into a swimming pool and look up from below. You’ll only see the sky in a limited disk. Outside that, you’ll see total internal reflection.

But negative indices of refraction are much weirder! The light entering such a material will bend backward:

Materials with a negative index of refraction also exhibit a reversed version of the ordinary Goos-Hänchen effect. In the ordinary version, light "slips" a little before reflecting during total internal reflection. The "slip" is actually a slight displacement of the light’s wave crests from their expected location — a "phase slip". But for a material of negative refractive index, the light slips backwards. This allows for resonant states where light gets trapped in thin films. Maybe this can be used to make better solar cells.

## California

The First Solar Agua Caliente photovoltaic power plant, with an 290 megawatt alternating current rating, is slated to be the single largest solar generating plant in the world when it starts up in 2013.

Located 65 miles east of the city of Yuma on the former White Wing Ranch, this plant will produce sufficient electricity to power about 100,000 average homes per year, displacing approximately 220,000 metric tons of carbon dioxide per year — the equivalent of taking about 40,000 cars off the road.

category: energy