Concentrated Solar Photovoltaics

Jeffrey Weisse
November 28, 2010

Submitted as coursework for Physics 240, Stanford University, Fall 2010

Solar Cell Background

Fig. 1: Schematic of solar cell p-n junction.

The Sun supplies the Earth with enough energy to create seasons, affect oceanic and atmospheric currents, and form natural disasters as powerful as hurricanes and tornadoes. Although the Sun is 93 million miles away, it continuously supplies the Earth with 1.2 x 105 terawatts of power. [1] However, meeting the world's annual energy demand (roughly 16.7 terawatts in 2007) without rapidly consuming the world's resources poses a challenge. Amazingly, harvesting just over 1 hour of all the Sun's energy that reaches the earth is enough to meet the world's high annual energy demand. [2] Solar cell technology offers an environmentally friendly opportunity to directly convert sunlight into electricity by exciting electrons within a solar cell. Nevertheless, despite their huge potential, solar cells account for less than 1% of the world energy production, while the much more efficient fossil fuel technologies produce 80%-85% of the world's energy. [1] Fortunately the solar cell industry has been growing at an exponential rate over the past 10 years in efforts to increase efficiency and conserve our natural resources. [3]

Typical solar cells consist of connecting P and N-type semiconducting materials that are capable of absorbing light over the optical spectrum (Fig.1). These cells capture phonons from the light by exciting electrons to travel across the semiconducting material's band gap, from the valance band (VB) to the conduction band (CB), forming electron-hole pairs. The p-n junction provides an electric field which drives the electrons in the conduction band in one direction (to the right in Fig. 1) and the holes in the valance band the other direction (to the left in Fig. 1), forming an external potential difference. [1]

Multiple solar cell technologies have been proposed to increase solar cell efficiency while attempting to decrease material costs. These technologies are organized into three groups: first, second, and third generation solar cells. First-generation solar cells are primarily fabricated from silicon wafers, including both single-crystalline and poly-crystalline silicon. [4] Silicon solar cell technology is the most mature and most used system achieving a best efficiency of 25%. Unfortunately its economics are dominated by the high cost of purifying silicon substrates and therefore has little potential for cost reduction below $1-2/Watt. [3-5] In efforts to move away from high material costs, thin film or second generation solar cells have been developed. The most popular thin film solar cells are CIGS (Cu, In, Ga, Se2), CdTe, and amorphous silicon with best efficiencies of 20.0%, 16.7%, and 12.5% respectively. [3] These solar cells have the potential to break the $1/Watt barrier; however, their efficiencies are still lower than first generation silicon cells, especially at the commercial level, and several second generation cells rely on scarce and toxic materials. [1,4] First and second generation solar cells both suffer from the Shockley-Queisser limit, which states that the maximum thermodynamic efficiency for these solar cells is only 31%. [1] The Shockley-Queisser limit is based on four main assumptions: 1) a single p-n junction, 2) one phonon creates 1 electron-hole pair, 3) thermal relaxation occurs for any electron-hole pairs with energy greater than the band gap, and 4) illumination with unconcentrated sunlight. Recently, third generation solar cells, which violate the Shockley-Queisser limit, have surpassed the 31% efficiency barrier, opening the potential to increase solar cells roll in energy production. [1]

Fig. 2: Schematic of 40% multijunction solar cell. [6]

Multijuction solar cells are one of the most common and successful third generation solar cells. As previously mentioned, in single p-n junction solar cells, any photon with energy lower than the material's band gap will not be absorbed and any photon greater than the band gap will lose energy due to thermal relaxation as show in Fig. 1. [1] Multijunction solar cells contain multiple different tandem p-n junctions. These p-n junctions have semiconducting bandgaps spread out over the spectral distribution of the Sun, arranged in decreasing order (Fig 2). [3] This allows the sunlight to be automatically filtered as it passes though the cell ensuring that the light is absorbed in the most efficient junction. [4] This design is capable of improving solar cell efficiency past the Shockley-Queisser limit by increasing the range of photons absorbed from the solar spectrum while also minimizing their thermalization losses. [4] However, since the junctions are connected in series, it is critical that the junction material's bandgaps are appropriately selected to generate similar currents. [4] So far, multijunction solar cells have been fabricated with efficiencies greater than 40% including the current 41.6% world record. [3] As one would imagine the light absorbance efficiency and thermalization losses could be improved with increasing the number of junctions, further increasing cell efficiency. The theoretical efficiencies for unconcentrated sunlight are 43%, 49%, and 66% for two, three, and infinite junctions respectively. [1] Unfortunately the high production costs of multijunction cells, projected to be $3-5/cm2 by 2015, make them uneconomical to use under unconconcentrated sunlight. [3]

Solar Cell Concentrators

Since the 1970's solar cell concentrators have been used to increase the sunlight supplied to solar cells. Concentrators offer numerous advantages including: superior efficiencies, lower costs, decreased semiconducting material consumption and more. [7] However, concentrators have not attracted much recent interest since they are not suitable for small scale or household power generation but rather for high power generation. [7]

Fig. 3: Effect of concentration on solar cell efficiency. [9]

Solar cell concentrators come in a wide variety of designs that vary in quality and price. Currently common concentrators are made from square flat, linear flat, or linear arched Fresnel lens or reflectors that have a parabolic trough or dish shape. [8] In order to achieve maximum efficiency, solar concentrators must project the sunlight perpendicularly onto the cells. [9] Solar trackers can help align concentrators to increase performance. [7] Tracking systems come in both one and two-axis capabilities. Generally all systems other than the parabolic trough perform best with two axis tracking systems. [8] Tracking systems are typically classified into two categories; close loop and open loop. Close loops trackers use photo-sensors to provide constant feedback, resulting in accurate alignment; however, this constant feedback creates a lot of stress on the motor and can easily be affected by environmental changes or cleanliness of the sensor. [8] Open loop trackers are preprogrammed to follow the sun according to the time, longitude of the sun, declination, local azimuth, elevation, sunrise and sunset. These systems are not affected by the environment or involve constant feedback; however, they do rely on high precision astronomical calculations to predict ideal alignment. [8] Nevertheless, all of these concentrators and trackers function more efficiently in sunny regions with clear skies since diffuse light is not concentrated as efficiently. [3]

Fig. 4: Total system cost as a function of cell efficiency and concentrator cost, assuming solar cell cost of $0.23/Watt at 1100X. [3]

Conveniently, when a solar cell is exposed to concentrated light, the cell is able to extract more current per area, increasing its efficiency. When concentrated light shines on a solar cell the solar cell's photocurrent (IL) typically increases linearly with the solar power intensity (PS). [10] Meanwhile the photovoltage (VOC) increases logarithmically with increasing photocurrent, VOC =VTln(IL/IO), where VT is the thermal voltage and IO is the saturation current. For the most part this means that the efficiency (η) increases logarithmically as the light intensity increase, η = VOC(IL / PS)FF. [8] In this equation FF is the fill factor which also will increase very slowly with the light intensity until, at high currents, it dramatically decreases, therefore also decreasing efficiency (Fig. 3). The FF decrease is due to the ohmic drop in the series resistance at high currents. This means that the series resistance must be very low in high concentration solar cells. [8] Also, as one would imagine, the temperature of the solar cell would also increase with concentrated light from the thermal relaxation, despite best cooling efforts. Typical heat sinks or cooling systems are attached to the solar cell to allow the cells to operate at temperatures less than 80°C. [8] At higher temperatures, the semiconductor bandgaps slightly reduce as well as the VOC. [8] However some solar cells can still be operated properly at concentration ratios at high as 1000X and possibly 5000X. [8]

The cost of a solar cell can be estimated to a first approximation to scale with the area of the cell. [10] Therefore, a concentration of 1000X would decrease the solar cell component cost 1000 times. Recently, Emcore made a $24 million sale to Green and Gold Energy (GGE) for multijuncton solar cells for 105MW facility. [3] This would translate to $0.23/Watt which is significantly less than the both of the first and second generation solar cells. [3] However this price does not include the cost of the land, maintenance, and concentrating and tracking systems that GGE would have to use to obtain their desired concentration ratio of 1100X. Projecting these costs is not a simple task; however, figure 4 shows the total system cost in $/Watt for systems ranging from $100/m2 to $1000/mm2 for land, concentration system, and installation and maintenance costs. [3] As you can see the costs associated with the concentrators play a major role and must be improved to make high efficiency solar cells profitable.


The use of solar concentrators on multijunction solar cells has the ability to harvest sunlight with high efficiencies at a relatively low cost without the need of relying on vast amount of semiconducting materials and land area, which is very appealing to investors. [10] However, the cost of the concentrator system and its maintenance is rather high compared to the actual solar cell cost per area. Despite these issues, concentrated high efficiency solar cells have the potential to enter the energy market at tens or hundreds of megawatts per year and possible even produce a substantial portion of the world's future energy.

© Jeffrey Weisse. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] G. W. Crabtree and N. S. Lewis, "Solar Energy Conversion," Physics Today 60, No. 3, 37 (2007).

[2] "International Energy Outlook 2010,) U.S. Energy Information Administration, DOE/EIA-0484, July 2010.

[3] S. Kurtz, "Opportunities and Challenges for Developing of a Mature Concentrating Photovoltaic Power Industry," NREL Technical Report NREL/TP-520-43208, November 2009.

[4] D. Ginley, "Solar Energy Conversion Toward 1 Terawatt," MRS Bulletin 33, 355 (2008).

[5] M. Green, Third Generation Photovoltaics: Advanced Solar Energy Conversion (Springer, 2005).

[6] R. R. King, "40% Efficient Metamorphic GaInP/GaInAs/Ge Multijunction Solar Cells," Appl. Phys. Lett. 90, 183516 (2007).

[7] R. M. Swanson, "The Promise of Concentrators," Prog. Photovolt. Res. Appl. 8, 93 (2000).

[8] A. Luquei, "Photovoltaic Concentration at the Onset of its Commercial Deployment," Prog. Photovolt. Res. Appl. 14, 413 (2006).

[9] H. Mousazadeh, "A Review of Principle and Sun-Tracking Methods for Maximizing Solar Systems Output," Renewable and Sustainable Energy Reviews 13, 1800 (2009).

[10] S. Kurtz, "Multijunction Solar Cells for Conversion of Concentrated Sunlight to Electricity," Optics Express 18, 73 (2010).