# Physical Limitations of Photovoltaic Conversion

Laurentiu Fara (Polytechnic University of Bucharest, Romania & Academy of Romanian Scientists, Romania) and Masafumi Yamaguchi (Toyota Technological Institute (TTI), Japan)
DOI: 10.4018/978-1-4666-1927-2.ch002
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## Abstract

This chapter presents the factors that are included in the expression of the conversion efficiency of a solar cell. These factors are upper limited, and that is why the conversion efficiency could not exceed certain critical values. The chapter analyzes thermodynamic limitations, correction introduced by the atmosphere, Shockley-Quiesser limitations (based on the detailed energy balance), as well as additional limitations. Then it discusses ways to improve the conversion efficiency and future research directions.
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## Thermodynamic Limitations

One factor limiting the conversion efficiency is the thermodynamic efficiency. A solar cell converts the sun’s thermal radiation into electricity. Therefore, thermodynamic laws may restrict the efficiency to lower values of Carnot efficiency:

(1) where TS is the sun’s temperature and Tc is the cell’s temperature. The sun is usually considered as a blackbody with temperature of 6000 K and the solar cell is considered to be in thermal equilibrium with the environmental temperature, so that . In reality, the sun is composed of plasma, so its behavior is closer to the thermal one of a metal, resulting in TS≈ 5800 K. On the other hand, the solar cell is warmer than the environment (due to processes that are occurring in it), so that we can take TC ≈ 320 K and the yield falls to 94.5%. However, such a value is very high.

A closer analysis of the thermodynamic efficiency must take into account the thermal radiation laws. If we use the blackbody model, both for the Sun, and for the cell, and consider the cell in thermal equilibrium with the environment, we obtain the Landsberg yield (Markvart & Castañer, 2003; Landsberg & Badescu, 1998):

(2)

A more precise calculation requires the cell’s temperature evaluation when the Sun and the environment are in a thermodynamic equilibrium. Considering the heat exchange between the Sun and solar cell using the blackbody’s laws, and the one between the environment and the cell corresponding to thermal contact, Müser obtained the heat balance equation,

(3) and the yield value of 85.6% (Markvart & Castañer, 2003; Badescu & Landsberg, 1998). The heat radiation corrections of metals reduce this value down to about 85.2%.

A particular problem which will be discussed again in the next paragraph refers to the Earth's atmosphere selective absorption . This moves the solar spectrum, giving the appearance of lower temperatures (the blackbody model, this apparent temperature is leading to (the metal heat radiation corrections reduce these values by about 0.4%).

When it comes to space applications, the situation changes. Here the environmental temperature is almost 0 K, and the cell losses appear only by thermal radiation. Even if we consider the cell isothermal and the circuit open, the cell temperature is:

(4) (Ω = 6,8·10-5 Sr is the solid angle under the Sun is seen from Earth, RS = 696·103 km is the Sun’s radius and DSP = 149,6·106 km is the Sun – Earth distance), so that the previously calculated yield decreases by about 0.1% . A more accurate calculation leads to a decrease of 0.2%. It can be seen that these corrections are insignificant.

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