Category Physics of Solar Cells

Thin-film solar cells

Silicon has so many advantages for solar cells that other materials can compete only when they do not share its disadvantage, the poor absorption of light. In materials competing with silicon, the transitions between the valence and conduction bands must be direct. The absorp­tion coefficient then has a large value. For the absorption of that part of the solar spectrum which can be absorbed, a thickness of only a few jum is sufficient for thin-film solar cells. For the same number of recombination centers as in a thick silicon cell, a higher impurity con – centration and the presence of grain boundaries in the film can be tolerated. Because of the smaller distances to the membranes at the surfaces, the diffusion lengths can also be smaller...

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Light trapping

The absorptivity of a body increases as the reflectivity is reduced and the path of the photons within the body becomes longer. This triviality enables us to consider still another way to im­prove the absorptivity than by an anti-reflection coating and a large thickness. The reflectivity of a body decreases when the reflected photons are deflected in such a way that they impinge on the body a second time. The pyramid-shaped structure of Figure 7.6 makes this possible.

image396

For light reflected twice, the total reflectivity is given by

^total — >?n.

A surface with 10% reflection as a planar surface reflects only 1% in a structure, where each reflected photon hits the surface a second time.

In addition, as a result of the textured surface, together with a reflecting rear surface, the li...

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The optimal silicon solar cell

Silicon has many advantages. It is the second most abundant element in the earth’s crust and is thus available in practically unlimited amounts. Silicon is not toxic, On exposure to air, silicon forms an oxide surface layer which fully protects it and prevents any further corrosion. The interface between Si and Si02 when grown under clean-room conditions has a very low density of surface states, with a very low surface recombination velocity. With Єс — 1.12eV, silicon has a favourable energy gap for the conversion of solar energy, Besides all these advantages, silicon with its indirect optical transitions has the serious disadvantage of weak absorption. Consequently, silicon must be much thicker than a semiconductor with direct transitions...

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Efficiency of solar cells as a function of their energy gap

The short-circuit current of a solar cell depends on the absorbed photon current. It is a max­imum for a semiconductor with an energy gap £g = 0 and decreases with increasing £q. The open-circuit voltage Уос is, however, zero for 8g = 0 and increases with increasing energy gap. The efficiency ц is therefore zero at £g = 0 and at 8q —► Somewhere in between is its maximum. From Eq. (7.10) and Eq. (7.11) we can calculate the efficiency л as a function of the energy gap 8g when only radiative recombination takes place for the case of thick cells, in which a(h(0 < 8g) = 0 and a(Hc0 > 8g) = 1.

Figure 7.2 gives the result for the AMO spectrum outside the atmosphere, and Figure 7.3 for the AM 1.5 spectrum on the surface of the earth...

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Maximum open-circuit voltage

The open-circuit voltage Voc defines the separation Epc — Єру of the Fermi energies at which recombination is in equilibrium with electron-hole generation throughout the entire cell. Due to the exponential decay of the photon current density within the semiconductor, the rate of generation (per volume) is greatest at the surface. The electrons and holes produced are distributed by diffusion more or less uniformly over the thickness, depending on the diffusion length. The recombination rate is then everywhere equal to the averaged generation rate. When the thickness of the solar cell is reduced and surface recombination is prevented, the recombination rate (per volume) and with it Epc — Єру must increase, because the averaged generation rate increases with decreasing cell thickness...

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Maximum short-circuit current

A large short-circuit current requires a solar cell as thick as possible to maximize its absorp­tivity. With anti-reflection coatings, we can theoretically reduce the reflection to r = 0. For a cell with large thickness and at the same time a large diffusion length, the absorptivity over the diffusion length is given by a(hd> > Eg) ~ 1. The short-circuit current produced by the absorbed photon current is then

лею poo

Ac = – e a(ho)) djy, Sun(йю) = – e J^ djlifiun(h(o) . (7.6)

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Maximum efficiency of solar cells

The maximum energy current delivered by a solar cell is given by the largest rectangle fitting under the current-voltage characteristic, as shown in Figure 4.1. It defines the “maximum power point” for the charge current density jmp and the voltage Vmp. For a given current – voltage characteristic, it is therefore important to have an algorithm in order to find the maxi­mum power point.

Independently of the form of the characteristic, the functional relationship between jq and V, the condition for maximum power yields

d{jQV) = djQV + jQ dV = 0,

and thus—————————————————————————————————

image381Подпись: (7.1)Л! іЛ =.

V / mp ‘ / mp This relationship is illustrated geometrically in Figure 7.1...

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Limitations on Energy Conversion in Solar Cells

In connection with the derivation of the current-voltage characteristic, we have neglected a voltage drop over the transport resistances as being negligibly small. With this approximation, the voltage V at the contacts of a sufficiently doped solar cell is given by the separation of the Fermi energies, eV = Єре — Єру* In addition, we did not consider currents of minority carriers flowing in the wrong direction, in spite of the large gradients of their Fermi energies, because of the small conductivity of the minority carriers in regions which function as semi-permeable membranes for the majority carriers.

With this approximation, all electrons and holes produced by the illumination, which do not recombine, contribute to the charge current...

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