#### LESSONS OF EASTER ISLAND

March 17th, 2016

In Chapter 2 we considered how strongly we can focus the incident solar radiation. For concentrated radiation, the same power is delivered by a solar cell with smaller area than for non – concentrated radiation. Another advantage is that concentrated radiation can be processed with greater efficiency, as discussed in Chapter 7.

In areas with much more direct, unscattered solar radiation, the additional expense for concentration is rewarded by a better efficiency from a smaller solar cell. When the radiation is concentrated with lenses or mirrors, the solar cell sees only a part of the hemisphere and, in the limiting case of maximum concentration, only the sun. The greater the concentration, the more carefully the concentrating system must track the path of the sun...

Read MoreThe reduction of thermalization losses and the improvement in the absorption efficiency can be simultaneously achieved by offering the solar cell only photons within the narrow energy interval Єс < Ясо < Eg + de and processing the other photons by solar cells with a different band gap. Cells operated in this way are known as tandem cells.

Qs 4n3h3c2 |

For a black-body solar spectrum, a solar cell with the energy gap £g and the idealized absorptivity а(йсо < Eg) = 0, д(Йсо > Eg) = 1, has the short-circuit current

Figure 8.1 gives the short-circuit current jsc as a function of the energy gap Eg/є. Following thermalization, the energy current flowing into the electron-hole pairs is

jE. eh — JscEg/c — 7y, abs■ (8.2)

Using (Ее + £h) — £g in...

Read MoreAs was shown in the previous chapter, even avoiding all non-radiative recombination processes leaves us with a solar cell efficiency well below the theoretical maximum value of t| = 0.86, derived in Chapter 2 as the upper limit for solar energy conversion. The main reasons were identified as losses by thermalization and the non-absorption of low-energy photons. In order to improve the efficiency, we must focus primarily on reducing these losses. We will now discuss different methods by which this can be accomplished, in principle. The underlying conditions are idealized, often to such an extent that it is difficult to imagine how they can be met, in practice. Nevertheless, it is still important to examine these methods in order to recognize the principles for possible improvements...

Read MoreWith a theoretical limit for the efficiency of r = 0.3 for the AMO spectrum, energy conversion with a solar cell is still well away from the theoretical limit of T|max =0.85 for the solar heat engine of Section 2.1.1. It is very instructive once again to examine the processes in a solar cell individually and break down the overall efficiency into the efficiencies of the individual processes in order to recognize where the greatest losses occur. Figure 7.12 shows the individual processes schematically.

The first process is the absorption of the incident energy current. Its efficiency has to account for the photons with energy йсо < Єс, which are not absorbed by the solar cell...

We know from earlier discussions that maximum efficiencies are obtained for maximum concentration of the incident radiation. Since concentration means that a smaller area is required for a given energy current, it is an option for expensive solar cell materials. That an increase of the efficiency can be expected is all the better.

The short-circuit current jsc is simply given by the absorbed photon current and increases, as expressed by Eq. (7.6), proportional to the intensity.

jsc — &jy:abs (7.17)

The open-circuit voltage Voc defines the difference between the Fermi energies at which the total recombination rate in the cell is equal to the total generation rate given by the absorbed photon current. With /у emit — jy, abs we find from Eq. (7.8)

(7.18)

where js is the reverse saturat...

Read MoreSolar cells deliver only a small part of the absorbed energy current as electrical energy to a load. The remainder is dissipated as heat and the solar cell must therefore have a higher temperature than the environment. For solar irradiation of 1 kW/m2 the temperature difference to the environment may be some 10 K.

Heating reduces the size of the energy gap. The absorbed photon current increases, leading to a slight increase in the short-circuit current jsc. The heating has a detrimental effect on the open-circuit voltage. From

Voc = -(Пе+Ль) = — Іп^^уЛ, (7.14)

e e Щ J

we find for the temperature dependence

dVoc _k fnenh кТ 1 dne 1 dnh 1 d(n?)

dT ~ e ІП V n ) + e nc dT + nh dT n dT

Here and

d(ni) eg 2

dT кТ2 1 ‘

It follows that

dVoc _ Voc – eG/e кТ / 1 dne 1 dnh dT ~~ T + ...

In the current-voltage characteristic for the solar cell in Eq. (6.35) we can regard the current Iq as the sum of the current through the pn-junction in the dark and the current /sc from a current source, connected in parallel for the currents to add.

Figure 7.10 shows the equivalent circuit diagram, extended by two additional elements. The resistance Rp, in parallel with the two diodes of the two-diode model, represents the shunts which can occur in real solar cells across the surfaces, at pin holes in the pn-junction or at grain boundaries. The series resistance Rs accounts for all voltage drops across the transport resistances of the solar cell and its connections to a load. The current-voltage characteristic then takes the form

Figure 7...

Read MoreThe thickness of a solar cell is an important issue. It is not only that a larger amount of precious material is needed for a thicker cell, a thinner cell could tolerate less optimal material properties. Organic materials could be very useful for solar cells because of their good absorption properties and of good luminescent quantum yields, indicating dominant radiative

P+

(a) (b)

Figure 7.9: (a) In the plane arrangement of an absorber between electron and hole membranes, the diffusion lengths Le>h must be larger than the thickness of the absorber and the thickness must be larger than the penetration depth 1/a of the photons, (b) Many absorbing layers in a meander-like structure combine good absorption with a small distance between the membranes.

recombination...

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