Solar Cells: Optical and Recombination Losses
4.1 Optical Losses
4.1.1 Preliminary Remarks: Reflection, Refraction, Absorption and Transmission
In Chap.3, we learned that electricity is generated when a photon is absorbed by a solar cell. The basic materials for solar cells are semiconductors. Semiconductors are characterized by having an energetic bandgap (forbidden band or forbidden zone) between the valence band and the conduction band. By absorbing photons, electrons can be lifted from the valence band into the conduction band. The condition for this is that the photon energy is equal to or greater than the bandgap energy of the semiconductor.1If this condition is fulfilled, positively and negatively charged electric charge carriers can be generated by the incoming sunlight. The conductivity of the semiconductor plays an important role in the separation of the charge carriers and letting them flow out of the solar cell. Doping can increase the conductivity. In this Sect.4.1we want to learn how we can absorb as many photons as possible.
Light that strikes the surface of a material will partly be reflected; the rest of the light will penetrate into the material. The light, which penetrates into the material, is refracted. By “refraction” one designates the bending of the light rays when they enter into a material. Light rays are refracted at each interface as they transit from one material, to another material that has different optical properties. In photovoltaics, one has very many interfaces, between regions, which have different optical prop-erties—either because they are doped in a different way or because their chemical composition is different.
These are the 4 basic phenomena in Optics:reflection, refraction, absorption and transmission. Newton already thought about the phenomenon of partial reflec-tion. Indeed, at the boundary (interface) between two different materials, it is not clear how a photon can “decide” whether to penetrate into the second material or to be reflected back into the first material. Quantum Physics give us the answer: it tells us that we can only state the probability with which photons are reflected. We do not know which photon will be reflected and which one will be transmitted. But we know that always the same proportion of photons is reflected; we also have precise data on the optical properties of different materials.
Another interesting phenomenon of optics, which is important to us, was found by Pierre de Fermat: When light is refracted at a boundary layer or “interface”, it will always take the fastest path, not the shortest path. This property also gives rise to puzzles: How can the light at the boundary layer “know” which path is the fastest one? And how can the photons “know” which one of them should be reflected and which one may penetrate into the next material, so that always the same proportion of photons are reflected? Quantum Physics provides the following explanation: the light simply “tries out” all possible ways at the same time. All alternative paths (i.e.
all paths except the one that is selected) are cancelled out by destructive overlapping.
1The bandgap of a silicon crystal is 1.12 eV.
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Fig. 4.1 Illustration of the photo-generation of an electron-hole pair according to Sect.3.2.1
The above questions led to the refraction laws, which were published mainly by Willebrord van Roijen Snell, in 1621. Augustin Jean Fresnel (1788–1827) con-tributed essential insights into the wave character of light. Both of these distinguished researchers of “past times” will assist us with the question of light trapping within solar cells.
Per m2and second, 1021photons hit the Earth from space with an energy between 1 and 5 eV. It is now important to absorb as many of these photons as possible; and to convert a large part of them into electrical energy. This is described in the following sections.
4.1.2 Absorption
Absorption of light in a solar cell means that a photon is absorbed in the semiconduc-tor and gives off its energy to create an electron-hole pair. Thanks to the energy of the photon, a bound electron, which is closely attached to a silicon atom, is released and becomes a “free electron”. In semiconductor physics, one says that the electron has been moved from the valence band to the conduction band (see Fig.4.1). Thereby a
“free hole2” is left behind in the valence band. Thus, a pair of one “free electron” and one “free hole” is created. This only happens if the energy of the photon is greater than the bandgap energyEg. If the photon energy is too small, the photons pass unim-peded through the silicon crystal and the energy of the photon is lost for the solar cell. This happens because photons with lower energy cannot produce electron-hole pairs. For such photons, the semiconductor is virtually transparent.
Even with photon energies higher than the bandgap energy Eg, not all photons are immediately absorbed near the surface; in fact, most of them penetrate deeper into the solar cell. The absorption coefficientαdetermines the penetration of light within the silicon crystal. Here,αis a function of the wavelengthλof the light. As
2A “hole” is simply the absence of an electron, where originally there was one. According to semiconductor physics, holes behave just as if they were elementary particles themselves.
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Fig. 4.2 Illustration of the absorption of light within a silicon crystal
illustrated in Fig.4.2, the light intensityIE(x) decreases exponentially within the material at the positionx. One has the following function for the light intensityIE:
IE(x)=IE0e−αx (4.1)
The absorption depth dα indicates how deep light of a specific wavelength λ penetrates into the material, before its intensity has fallen to 1/e, e.g.≈36% of its original intensity.3In silicon (and in most other semiconductors used for solar cells), dαincreases for increasing wavelengthsλ. For light with a wavelengthλ=575 nm, the absorption depthdαis 1μm and forλ=980 nm dαis already 100μm. At longer wavelengths there is, thus, the danger that some of the photons leak out from the back side of the solar cell.
For semiconductors with direct transitions (like GaAs, CdTe, etc.), an electron, which absorbs the energy of a photon, does not need to change its momentum.4 The crystal structure is formed in such a way that in the diagram of Energy versus
3e≈2.71828… is a mathematical constant called “Euler’s number”—it is the base of the natural logarithm.
4In contrast to energy, the momentum has an amount and a direction. In quantum physics, light, electrical current and mechanical vibration are all represented by “quanta” or “elementary particles”.
• for light: photons
• for electrical current: electrons
• for mechanical vibration: phonons.
These particles are not only characterized by their energyEbut also by their momentumP.
For a transition, i.e. from valence band to conduction band, it is necessary to consider not only energy but also momentum. In a rough approximation one can say: electrons have both energy and momentum; photons have energy but zero momentum; phonons have very little energy, but considerable momentum.
Since the momentum of a photon is zero it cannot change the momentum of an electron-hole-pair. This requires the additional vibrational energy of the crystal lattice, which is transmitted by a phonon.
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Fig. 4.3 Diagram of Energy versus Momentum for electrons ina semiconductors with direct transitions andbsemiconductors with indirect transitions: the energy levelEis plotted on the y-axis and the momentumPeis shown on the x-axis.ECstands for the lowest energy level of the conduction band andEVfor the highest energy level of the valence band
Momentum, the minimum of the conduction band lies directly above the maximum of the valence band. This is illustrated in Fig.4.3a.
On the other hand, in semiconductors with indirect transitions (like silicon), the crystal structure is formed in such a way that in the diagram of Energy versus Momen-tum, the minimum of the conduction band does not lie above the maximum of the valence band. In a semiconductor with an indirect transition, the electron must change its momentum (Fig.4.3b). This is only possible with the help of a phonon5[1].
Thus, it is also understandable that in a direct semiconductor the absorption coef-ficient αincreases very steeply in function of the wavelength as soon as the band energyEgis reached. In contrast, in an indirect semiconductor, the absorption coef-ficient does not increase so steeply. This is because, for the absorption of a photon, a “detour” via third particles, namely phonons, must be carried out. The situation is shown in Fig.4.4.
In order for a photon to be able to produce an electron-hole pair with high prob-ability, the optical path through the silicon wafer must be long enough. This can
5A “phonon” is in quantum physics the elementary particle describing a mechanical vibration.
(Here, the mechanical vibration within the semiconductor crystal we are looking at—for example, silicon.) In a similar way, a “photon” is the elementary particle describing light, and an “electron”
is the elementary particle describing electric current.
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Fig. 4.4 Absorption curve for a direct semiconductor (here: GaAs) compared to the absorption curve for an indirect semiconductor (here: silicon). It can be seen that the curves start exactly at the point where the bandgap energyEgis reached. This is 1.44 eV for GaAs and 1.12 eV for silicon
be achieved by making the solar cell very thick. At a thickness of 10 mm (almost) all the light would be absorbed. However, material costs are a constraining factor and so the aim is to make the solar cell as thin as possible. Today’s solar cells have thicknesses of 160–180μm with a wafer size between M2 (156×156 mm2) and M6 (166×166 mm2); the thinner the solar cell becomes, the more important it is to increase the absorption of sunlight in ways other than thickness. There are basically three possibilities:
1. Front side: reducing reflection with optimized surface coating 2. Texturing of the front surface
3. Passivation of the back surface; mirror formation at the back.