**1. Introduction**

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In recent years there has been intense research work into the development of high efficiency solar cells relying on emerging novel materials and structures. All this has lead to a continuous record breaking of highest achievable efficiencies using different technologies. Since the first photovoltaic devices were developed the most prevalent concern is to hem in all sorts of efficiency losses preventing from reaching the physical limits [1-3]. To overcome this impedi‐ ment, thorough investigations have been carried out to control and unearth their origins in order to identify potential efficiency advantages. Numerous thermodynamic approaches were employed to calculate solar cell efficiency limit, starting from the ideal Carnot engine to the latest detailed balance with its improved approach.

The aim of this chapter is to present a review of the techniques used to calculate the energy conversion efficiency limit for solar cells with detailed calculation using a number of numerical techniques. The study consists of analyzing the solar cell intrinsic losses; it is these intrinsic losses that set the limit of the efficiency for a solar energy converter. Several theoretical approaches were used in order to obtain the thermodynamic limit for energy conversion.

In the first place a solar cell could be considered as a simple energy converter (engine) able to produce an electrical work after the absorption of heat from the sun. In this fundamental vision the solar cell is represented by an ideally reversible Carnot heat engine in perfect contact with high temperature reservoir (the sun) and low temperature reservoir representing the ambient atmosphere. If the sun is at a temperature of *6000K* and the ambient temperature is *300K*, the maximum Carnot efficiency is about *95*% this value constitutes an upper limit for all kind of solar converters.

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

When the solar cell is supposed a blackbody converter absorbing radiation from the sun itself a blackbody, without creating entropy, we obtain an efficiency of about 93 % known as the Landsberg efficiency limit, which is slightly lower than Carnot efficiency.

Whilst a solar cell is assumed as an endoreversible system [4], the energy conversion efficiency is limited to 85.7% this figure is obtained where the sun is assumed fully surrounding the cell (maximum concentration). If we bear in mind that in a real situation the solar cell does not operate always in maximum concentration and the solid angle under which the cell sees the sun is in fact only a minute fraction of a hemisphere, the maximum efficiency is not larger than 12.79%, which is actually lower than most recently fabricated solar cells. However, we can conclude that solar cell is a quantum converter and cannot be treated as a simple solar radiation converter [5].

Semiconductor *pn* junction solar cell is a quantum converter where the energy band-gap of semiconductor material is the most important and critical factor controlling efficiency. Incident photons with energy higher than the energy gap can be absorbed, creating electron-hole pairs, while those with lower energy are not absorbed, either reflected or transmitted.

In the ideal model of a monochromatic cell incident photons are within a narrow interval of energy, while the cell luminescence outside this range is prevented. The overall resulting efficiency upper limit for an infinite number of monochromatic cells is 86.81% for fully concentrated sun radiation.

The ultimate efficiency of a single band gap *pn* junction for an AM1.5 G solar spectrum gives a value of 49%, this maximum efficiency, if compared to Carnot efficiency limit, is substantially lower. Therefore in quantum converters it is obvious that more than 50% of the solar radiation is lost because of spectral mismatch.

To represent a more realistic picture of a solar cell, three other fundamental factors should be taken into account, namely; the view factor of the sun seen from the solar cell position, the background radiation which could be represented as a blackbody at ambient temperature, and losses due to recombination, radiative and non-radiative.

In the detailed balance efficiency limit calculation first suggested in 1961 by Shockley and Queisser (SQ) in their seminal paper [6]. It is assumed that illumination of semiconductor *pn* junction by a blackbody source creates electron-hole pairs due to the fundamental absorption of photons with energies greater than the band-gap. These pairs either recombine locally if they are not separated and extracted along different paths to perform work in an external circuit. They assumed that recombination in the semiconductor is partly radiative and the maximum efficiency is attained when radiative recombination in dominant. The Shockley-Queisser model has been extended and completed to account for more physical phenomena [7-13]. For instance, the generalised Planck radiation law introduced by Würfel [7], the effect of background radiation has been included and elaborate numerical techniques has been used in order avoid mathematical approximations which would yield erroneous results.

The currently achieved short-circuit current densities for some solar cells are very close to predicted limits [14]. Nevertheless, further gain in short-circuit current can therefore still be obtained, mainly by minimising the cell surface reflectivity, while increasing the thickness, so as to maximize the photons absorption. For thin film solar cells gain in photocurrent can be obtained by improving light trapping techniques to enhance the cell absorption.

Radiative recombination and the external fluorescence efficiency have a critical role to play, if the created photons are re-emitted out of the cell efficiently, which corresponds to low optical losses, the open circuit voltage and consequently the cell efficiency approach their limits [15]. Concentrating solar radiation onto a solar cell improves remarkably its performance. Compa‐ rable effect could be obtained if the solar cell emission and acceptance angles were made equal.
