#### LESSONS OF EASTER ISLAND

March 17th, 2016

In the radiative limit, the total number of electrons flowing between any two bands is equal to the difference between the total absorption of photons exciting electrons between the bands throughout the device volume minus the total emission of photons by radiative relaxation of an electron back to the originating band. If only one absorption process is possible for any given photon energy, efficient photon recycling is possible. Emission and absorption are balanced through most of the cell volume, apart from the imbalance needed to absorb the solar photons and to provide for the enhanced thermal emission from the cell.

If competing absorption processes are present, there need no longer be this delicate balance between absorption and emission...

Read MoreThe diversion of photons to non-optimal absorption processes results in a performance loss that has recently been analysed (Luque et al. 2000) and is related to the free-carrier absorption loss discussed in Sect. 4.6. Our starting point will be Eq. (4.36) where competition between two absorption processes has already been analysed. The obvious extension of this equation to the three level case becomes (Luque and Marti 1997; Luque et al. 2000):

u – V/pt = a31[ f. BE( №31 ) – fpt] + a32[ fBE( №32 ) – fpt] + a21[ fBE( №21 ) – fpt ]

(8.3)

If the case is examined where we follow a light ray propagating in the direction u, the left hand side reduces to dfp/du and the solution for fpt along the path of the ray becomes:

where fpt(0) is the value at the surface, as discussed in Sect. 4...

Read MoreA third approach to photon selectivity is based on spatial partitioning of the absorption processes (Green 1999). By designing the cell so that the incoming light is exposed first to a region only able to absorb high energy photons, these high energy photons can be filtered from the incoming light. The light then passes to a region only able to absorb high and intermediate energy photons, and finally to a region able to absorb these and low energy photons. Three examples are shown in Fig. 8.7. This spatial approach ensures optimal use is made of incoming light but does not necessarily guarantee this for recycled photons.

The scheme in Fig. 8.7(a) relies on an impurity band to form the intermediate band, although this band is not continuous through the whole device (Green 1999)...

Read MoreA second approach to ensuring photon selectivity is to have a gradation in absorption properties so that the highest energy processes are the most strongly absorbing and the lowest energy, the most weakly absorbing. This will ensure that high energy photons are preferentially absorbed in those processes able to utilise them (Green 1999).

A recent analysis of this strategy (Cuadra et al. 2000) shows that a grading ratio of absorption coefficients above 2 will produce better limiting cell performance than for a single junction cell (40.8%), while values in the 10-100 range produce efficiencies quite close to the limiting efficiency (63.2%).

Read MoreTo reach the limiting performance of Fig. 8.5, high energy photons cannot be wasted on low energy processes. Any such misappropriation or leakage represents an energy loss that obviously will detract from overall efficiency. Approaches for avoiding this loss are outlined in the following sections.

8.3.1 Finite Bandwidths

One way of ensuring the required photon selectivity is if the width of all the bands involved in the cell are finite and reasonably small. This means there would automatically be an upper and lower limit on the energy of the photons eligible for each of the possible excitation processes (Green 1999, 2000).

For example, for the 3-band cell, the optimal design (Fig. 8.6) is to have the middle band quite narrow, as would be the case if it were an impurity band...

Read MoreA central assumption of the analysis is that high energy photons do not waste their energy on excitations possible with lower photon energy (e. g., in Fig. 8.3, photons with sufficient energy for process 31 are not involved in lower energy excitations such as process 21). Approaches to achieving this are discussed in Sect. 8.3. If such photon absorption selectivity can be ensured, it is possible to write down the by now familiar particle balance for each transition:

Ihl = qA[ fsN(EhEh0,Ts ) + (fc – fs )N(EhEh0,TA )- fclN(El, Eh,^hl, Tc )]

(8.1)

where Ihl is the current flowing between the two bands being considered, El and Eh are the lower and upper photon energies involved in the corresponding transition, and 0hl is the chemical potential or quasi-Fermi energy difference between these ban...

Read MoreOther processes apart from impact ionisation offer additional prospects for implementing multiple pair generation. One such process is Raman luminescence as shown in Fig. 7.5(a). Here an incoming energetic photon creates an electron-

(a)

hole pair, with any additional energy emitted as a second photon. (This process is similar to the Raman scattering processes used in material characterisation, where the second photon differs in energy from the first by the energy of a phonon involved in the scattering processes).

The likely strength of such processes can be investigated by comparing with the virtual excitation processes that determine the high refractive index of semiconductors at sub-bandgap wavelengths (Fig. 7.5(b))...

Read MoreA more general, less idealised analysis of multiple electron-hole pair creation is possible by defining absorption coefficients, am, for processes involving the generation of m electron-hole pairs. For m = 0, this would be the free carrier absorption coefficient. For m = 1, this corresponds to the usual band-to-band absorption processes, with a1 having reasonably large values for energies larger than the semiconductor bandgap but finite values even below the bandgap due to

phonon assisted processes (Green 1995). The case of m = 2 corresponds to absorption creating two electron pairs and would not be expected to be significant except for energies larger than twice the semiconductor bandgap...

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