A considerable loss of energy in a solar cell is due to the photons with energy hCO < 8g which are not absorbed. It would be very convenient if two or more of these useless photons could be converted into one photon with energy h(& > 8g, which could then be absorbed by the solar cell. In the following discussion, Єо defines the band gap of the solar cell for which small-energy photons will be up-converted. That such an up-conversion of the photon energy is not forbidden by thermodynamics is demonstrated by Figure 8.14, which shows a device consisting of a tandem of two small band gap solar cells connected to an LED. These solar cells absorb small-energy photons, and due to their series connection, deliver a voltage which is large enough to drive the LED with a large band gap to emit photons with energy ft(0 > £g which can be absorbed by the solar cell we have in mind. There is no doubt that this type of up-conversion will work. One may, however, ask why we do not use the electrical energy from the small-gap solar cells directly instead of investing it into an LED. We remember that the arrangement of two solar cells and an LED in Figure 8.14 is identical to the equivalent circuit of a three-level system represented by two bands and an impurity level in Figure 8.13 in the previous section.
Figure 8.14; Two solar cells with small band gaps drive a LED with a large band gap, to emit photons useful for a large band gap solar cell, thereby up-converting two small energy photons into one higher energy photon.
A three-level system placed behind a solar cell could be used to convert small-energy photons transmitted by the solar cell into higher-energy photons supplied to the solar cell, in addition to the photons absorbed directly from the sun as shown in Figure 8.15. A mirror behind the up-converter ensures that all emitted photons are directed towards the solar cell. A closer inspection of the impractical but functioning up-converter in Figure 8.14 reveals that it is better represented by a four-level system than by a three-level system. The sum of the band gaps of the two solar cells is larger than the band gap of the LED. In fact, detailed calculations along the line outlined in the last section show that an energy loss, indicated in Figure 8.15 at the upper level, is necessary to prevent the recombination of the electron-hole pairs via the intermediate level with the re-emission of two small-energy photons.
Figure 8.16 shows a substantial improvement in the efficiency of a solar cell for an incident 6000 К black-body spectrum. As always, the efficiency is larger for maximum concentration than for non-concentrated radiation. The possible efficiencies of a solar cell with
Figure 8,17: Efficiency of a solar cell as a function of its band gap Eq operating with directly absorbed and with down-converted photons from a non-concentrated 6000 К black-body spectrum for a down – converter placed on the rear side of the solar cell (thin line). The efficiency for operation only with photons from the down-converter when it is placed on the front side is smaller (thick line).
up-conversion and of the impurity photovoltaic effect are very similar. Both use two-step ex- citations to absorb otherwise non-absorbed photons. The up-conversion, however, has distinct advantages. First, the up-converter is a purely optical device and can consist of a material such as an organic dye, in which electrons and holes are virtually immobile, but which has a high quantum efficiency. Second, the up-converter is a separate device which can be applied to existing well developed bifacial solar cells. Third, since the up-converter is separated from the solar cell, it would very little interfere with the recombination processes in the solar cell. Applying an up-converter to a solar cell would not do any harm, it could only improve the solar cell’s efficiency, even if it is not working quite as well as theoretically predicted.
Since in a three-level system, the recombination from the upper level is more probable via the intermediate level instead of directly to the lowest level, a three-level system can be used for down-conversion. In this process, a high-energy photon is absorbed in a transition from the lowest level to the upper level. By the back transition, via the intermediate level, two small-energy photons are emitted. Applied to a solar cell, a down-converter reduces the ther – malization loss incurred by the absorption of photons with hd > 2 Eg by splitting these photons into two photons with Й0) > £q. Since high-energy photons are not transmitted by the solar cell, the high-energy part of the spectrum must be diverted by a dichroic mirror or other means to the rear side of the cell, where the down-converter is placed. In addition, another dichroic mirror transmitting high-energy photons but reflecting small energy photons is applied to the back of the down-converter, where it prevents the loss of small-energy photons produced in the down-converter. The efficiency for a solar cell combined with a down-converter on its backside is shown in Figure 8.17 by the thin line as a function of the band gap of the solar cell.
A much simpler and more elegant method would be to place the down-converter on the front side of the solar cell. In this arrangement, all the incident solar photons, which the solar cell could absorb, are absorbed by the down-converter. Photons with < ЙС0 < 2£q are absorbed in transitions involving the intermediate level and larger energy photons cause direct transitions from the lower to the upper level. Nearly all photons emitted by the down-converter have an energy ЙС0 > Eq and could be absorbed by the solar cell. However, being on the front side of the solar cell, no mirror directing all the emitted photons into the solar cell can be applied and one might think that this deficiency leads to the loss of one-half of the photons being emitted through the front surface towards the sun. This is not necessarily the case. We remember that the probability for emission is proportional to the density of photon states. This makes the emitted photon currents proportional to the square of the index of refraction. If a material for the down-converter is chosen which has the same large index of refraction as the solar cell, all the photons emitted towards the solar cell enter the solar cell without reflection, whereas most of the photons emitted towards the front surface are totally reflected.
For the down-converter on the rear side of the solar cell, a maximum efficiency of almost 40% is found. A smaller efficiency of 36% is found, caused by the loss of down-converted photons, when the down-converter is placed on the front side of the solar cell. An index of refraction of n = 3.6 was used for the down-converter and the solar cell, which prevents the loss by total internal reflection of most down-converted photons.
Small band gap solar cells are advantageous in combination with a down-converter, whereas higher band gap solar cells are favourable with an up-converter. For both systems. the calculations consider only radiative transitions, which may, however, be closer to reality in materials which do not require good transport properties for electrons or holes.