A multi-junction photovoltaic cell is a solar cell with multiple pn junctions of different semiconductor materials. Each pn junction of each material produces electrical current in response to a different wavelength of light. A simple cell produces electrical current of a single wavelength in the spectrum of sunlight. A multi-junction cell solar cell will produce an electric current at multiple wavelengths of light, which increases the energy conversion efficiency of sunlight to usable electrical energy.

Traditional single-union cells have a maximum theoretical efficacy of 33.16%. Theoretically, an infinite number of joints would have a limit efficiency of 86.8% under highly concentrated sunlight.

Currently, the best laboratory examples of traditional crystalline silicon solar cells have efficiencies between 20% and 25%, while laboratory examples of multiple-junctional cells have shown a yield greater than 46% under concentrated sunlight. Commercial examples of tandem cells are widely available to 30% under illumination with one sun, and improve to around 40% with concentrated sunlight. However, this efficiency is obtained at the expense of greater complexity and manufacturing price. To date, its higher price and its higher price / performance ratio have limited its use to special functions, especially in the aerospace sector, where its high power / weight ratio is desirable. In terrestrial applications, these solar cells are emerging in photovoltaic concentrators (CPV), with an increasing number of installations around the world.

Tandem manufacturing techniques have been used to improve the performance of existing designs. In particular, the technique can be applied to low-cost thin-film solar cells that use amorphous silicon, unlike conventional crystalline silicon, to produce a cell with an efficiency of about 10% that is light and flexible. This approach has been used by several commercial suppliers, but these products are currently limited to certain niche roles, such as roofing materials.

Traditional single-union cells have a maximum theoretical efficiency of 34%. In a theoretically infinite number of joints, the efficiency of multi-junction cells would be 87% under highly concentrated sunlight.

Currently, the best laboratory examples of traditional silicon solar cells have an efficiency of around 25%, while laboratory examples of multi-junction cells have shown a performance above 43%.

Description

Multi-junction cells

Cells made from multiple materials layers can have multiple bandgaps and will therefore respond to multiple light wavelengths, capturing and converting some of the energy that would otherwise be lost to relaxation as described above.

For instance, if one had a cell with two bandgaps in it, one tuned to red light and the other to green, then the extra energy in green, cyan and blue light would be lost only to the bandgap of the green-sensitive material, while the energy of the red, yellow and orange would be lost only to the bandgap of the red-sensitive material. Following analysis similar to those performed for single-bandgap devices, it can be demonstrated that the perfect bandgaps for a two-gap device are at 1.1 eV and 1.8 eV.

Conveniently, light of a particular wavelength does not interact strongly with materials that are of bigger bandgap. This means that you can make a multi-junction cell by layering the different materials on top of each other, shortest wavelengths (biggest bandgap) on the “top” and increasing through the body of the cell. As the photons have to pass through the cell to reach the proper layer to be absorbed, transparent conductors need to be used to collect the electrons being generated at each layer.

Producing a tandem cell is not an easy task, largely due to the thinness of the materials and the difficulties extracting the current between the layers. The easy solution is to use two mechanically separate thin film solar cells and then wire them together separately outside the cell. This technique is widely used by amorphous silicon solar cells, Uni-Solar’s products use three such layers to reach efficiencies around 9%. Lab examples using more exotic thin-film materials have demonstrated efficiencies over 30%.

The more difficult solution is the “monolithically integrated” cell, where the cell consists of a number of layers that are mechanically and electrically connected. These cells are much more difficult to produce because the electrical characteristics of each layer have to be carefully matched. In particular, the photocurrent generated in each layer needs to be matched, otherwise electrons will be absorbed between layers. This limits their construction to certain materials, best met by the III-V semiconductors.

Material choice

The choice of materials for each sub-cell is determined by the requirements for lattice-matching, current-matching, and high performance opto-electronic properties.

For optimal growth and resulting crystal quality, the crystal lattice constant *a* of each material must be closely matched, resulting in lattice-matched devices. This constraint has been relaxed somewhat in recently developed metamorphic solar cells which contain a small degree of lattice mismatch. However, a greater degree of mismatch or other growth imperfections can lead to crystal defects causing a degradation in electronic properties.

Since each sub-cell is connected electrically in series, the same current flows through each junction. The materials are ordered with decreasing bandgaps, E_{g}, allowing sub-bandgap light (*hc/λ < e•E _{g}*) to transmit to the lower sub-cells. Therefore, suitable bandgaps must be chosen such that the design spectrum will balance the current generation in each of the sub-cells, achieving current matching. Figure C(b) plots spectral irradiance

*E*(λ), which is the source power density at a given wavelength λ. It is plotted together with the maximum conversion efficiency for every junction as a function of the wavelength, which is directly related to the number of photons available for conversion into photocurrent.

Finally, the layers must be electrically optimal for high performance. This necessitates usage of materials with strong absorption coefficients α(λ), high minority carrier lifetimes τ_{minority}, and high mobilities µ.

The favorable values in the table below justify the choice of materials typically used for multi-junction solar cells: InGaP for the top sub-cell (E_{g} = 1.8 − 1.9 eV), InGaAs for the middle sub-cell (E_{g} = 1.4 eV), and Germanium for the bottom sub-cell (E_{g} = 0.67 eV). The use of Ge is mainly due to its lattice constant, robustness, low cost, abundance, and ease of production.

Because the different layers are closely lattice-matched, the fabrication of the device typically employs metal-organic chemical vapor deposition (MOCVD). This technique is preferable to the molecular beam epitaxy (MBE) because it ensures high crystal quality and large scale production.

Material | E_{g}, eV |
a, nm |
absorption (λ = 0.8 μm), 1/µm |
µ_{n}, cm²/(V•s) |
τ_{p}, µs |
Hardness (Mohs) |
α, µm/K | S, m/s |
---|---|---|---|---|---|---|---|---|

c-Si | 1.12 | 0.5431 | 0.102 | 1400 | 1 | 7 | 2.6 | 0.1–60 |

InGaP | 1.86 | 0.5451 | 2 | 500 | – | 5 | 5.3 | 50 |

GaAs | 1.4 | 0.5653 | 0.9 | 8500 | 3 | 4–5 | 6 | 50 |

Ge | 0.65 | 0.5657 | 3 | 3900 | 1000 | 6 | 7 | 1000 |

InGaAs | 1.2 | 0.5868 | 30 | 1200 | – | – | 5.66 | 100–1000 |

Structural elements

Metallic contacts

The metallic contacts are low-resistivity electrodes that make contact with the semiconductor layers. They are often aluminum. This provides an electrical connection to a load or other parts of a solar cell array. They are usually on two sides of the cell. And are important to be on the back face so that shadowing on the lighting surface is reduced.

Anti-reflective coating

Anti-reflective (AR) coating is generally composed of several layers in the case of MJ solar cells. The top AR layer has usually a NaOH surface texturation with several pyramids in order to increase the transmission coefficient *T*, the trapping of the light in the material (because photons cannot easily get out the MJ structure due to pyramids) and therefore, the path length of photons in the material.^{R decreases to 1%. In the case of two AR layers L1 (the top layer, usually SiO
2) and L2 (usually TiO
2), there must be to have the same amplitudes for reflected fields and nL1dL1 = 4λmin,nL2dL2 = λmin/4 to have opposite phase for reflected fields. On the other hand, the thickness of each AR layer is also chosen to minimize the reflectance at wavelengths for which the photocurrent is the lowest. Consequently, this maximizes JSC by matching currents of the three subcells. As example, because the current generated by the bottom cell is greater than the currents generated by the other cells, the thickness of AR layers is adjusted so that the infrared (IR) transmission (which corresponds to the bottom cell) is degraded while the ultraviolet transmission (which corresponds to the top cell) is upgraded. Particularly, an AR coating is very important at low wavelengths because, without it, T would be strongly reduced to 70%.}

Tunnel junctions

The main goal of tunnel junctions is to provide a low electrical resistance and optically low-loss connection between two subcells.

Hence, electrons can easily tunnel through the depletion region. The J-V characteristic of the tunnel junction is very important because it explains why tunnel junctions can be used to have a low electrical resistance connection between two pn junctions. Figure D shows three different regions: the tunneling region, the negative differential resistance region and the thermal diffusion region. The region where electrons can tunnel through the barrier is called the tunneling region. There, the voltage must be low enough so that energy of some electrons who are tunneling is equal to energy states available on the other side of the barrier. Consequently, current density through the tunnel junction is high (with maximum value of , the peak current density) and the slope near the origin is therefore steep. Then, the resistance is extremely low and consequently, the voltage too. This is why tunnel junctions are ideal for connecting two pn junctions without having a voltage drop. When voltage is higher, electrons cannot cross the barrier because energy states are no longer available for electrons. Therefore, the current density decreases and the differential resistance is negative. The last region, called thermal diffusion region, corresponds to the J-V characteristic of the usual diode:

In order to avoid the reduction of the MJ solar cell performances, tunnel junctions must be transparent to wavelengths absorbed by the next photovoltaic cell, the middle cell, i.e. E_{gTunnel} > E_{gMiddleCell}.

Window layer and back-surface field

A window layer is used in order to reduce the surface recombination velocity *S*. Similarly, a back-surface field (BSF) layer reduces the scattering of carriers towards the tunnel junction. The structure of these two layers is the same: it is a heterojunction which catches electrons (holes). Indeed, despite the electric field *E _{d}*, these cannot jump above the barrier formed by the heterojunction because they don’t have enough energy, as illustrated in figure E. Hence, electrons (holes) cannot recombine with holes (electrons) and cannot diffuse through the barrier. By the way, window and BSF layers must be transparent to wavelengths absorbed by the next pn junction i.e. E

_{gWindow}> E

_{gEmitter}and E

_{gBSF}> E

_{gEmitter}. Furthermore, the lattice constant must be close to the one of InGaP and the layer must be highly doped (

*n*≥ 10

^{18}cm

^{−3}).

J-V characteristic

For maximum efficiency, each subcell should be operated at its optimal J-V parameters, which are not necessarily equal for each subcell. If they are different, the total current through the solar cell is the lowest of the three. By approximation, it results in the same relationship for the short-circuit current of the MJ solar cell: *J _{SC} = min (J_{SC1}, J_{SC2}, J_{SC3})* where

*J*(λ) is the short-circuit current density at a given wavelength λ for the subcell

_{SCi}*i*.

Because of the impossibility to obtain *J _{SC1}, J_{SC2}, J_{SC3}* directly from the total J-V characteristic, the quantum efficiency

*QE*(λ) is utilized. It measures the ratio between the amount of electron-hole pairs created and the incident photons at a given wavelength λ. Let φ

_{i}(λ) be the photon flux of corresponding incident light in subcell

*i*and

*QE*

_{i}(λ) be the quantum efficiency of the subcell

*i*. By definition, this equates to:

The value of is obtained by linking it with the absorption coefficient , i.e. the number of photons absorbed per unit of length by a material. If it is assumed that each photon absorbed by a subcell creates an electron/hole pair (which is a good approximation), this leads to:

where *d _{i}* is the thickness of the subcell

*i*and is the percentage of incident light which is not absorbed by the subcell

*i*.

Similarly, because, the following approximation can be used: .

The values of {\displaystyle V_{OCi}} are then given by the J-V diode equation:

Theoretical limiting efficiency

We can estimate the limiting efficiency of ideal infinite multi-junction solar cells using the graphical quantum-efficiency (QE) analysis invented by C. H. Henry. To fully take advantage of Henry’s method, the unit of the AM1.5 spectral irradiance should be converted to that of photon flux (i.e., number of photons/m^{2}/s). To do that, it is necessary to carry out an intermediate unit conversion from the power of electromagnetic radiation incident per unit area per photon energy to the photon flux per photon energy (i.e., from [W/m^{2}/eV] to [number of photons/m2/s/eV]). For this intermediate unit conversion, the following points have to be considered: A photon has a distinct energy which is defined as follows.

(1): E_{ph} = h∙f = h∙(c/λ)

where E_{ph} is photon energy, h is Planck’s constant (h = 6.626*10^{−34} [J∙s]), c is speed of light (c = 2.998*10^{8} [m/s]), f is frequency [1/s], and λ is wavelength .

Then the photon flux per photon energy, dn_{ph}/dhν, with respect to certain irradiance E [W/m^{2}/eV] can be calculated as follows.

(2): = E/{h∙(c/λ)} = E[W/(m^{2}∙eV)]∙λ∙(10^{−9} )/(1.998∙10^{−25} [J∙s∙m/s]) = E∙λ∙5.03∙10^{15} [(# of photons)/(m^{2}∙s∙eV)]

As a result of this intermediate unit conversion, the AM1.5 spectral irradiance is given in unit of the photon flux per photon energy, [number of photons/m^{2}/s/eV]

Based on the above result from the intermediate unit conversion, we can derive the photon flux by numerically integrating the photon flux per photon energy with respect to photon energy. The numerically integrated photon flux is calculated using the Trapezoidal rule, as follows.

(3):

As a result of this numerical integration, the AM1.5 spectral irradiance is given in unit of the photon flux, [number of photons/m2/s].

It is should be noted that there are no photon flux data in the small photon energy range from 0 eV to 0.3096 eV because the standard (AM1.5) solar energy spectrum for hν < 0.31 eV are not available. Regardless of this data unavailability, however, the graphical QE analysis can be done using the only available data with a reasonable assumption that semiconductors are opaque for photon energies greater than their bandgap energy, but transparent for photon energies less than their bandgap energy. This assumption accounts for the first intrinsic loss in the efficiency of solar cells, which is caused by the inability of single-junction solar cells to properly match the broad solar energy spectrum. However, the current graphical QE analysis still cannot reflect the second intrinsic loss in the efficiency of solar cells, radiative recombination. To take the radiative recombination into account, we need to evaluate the radiative current density, J_{rad}, first. According to Shockley and Queisser method, J_{rad} can be approximated as follows.

(4):

(5):

where E_{g} is in electron volts and n is evaluated to be 3.6, the value for GaAs. The incident absorbed thermal radiation J_{th} is given by J_{rad} with V = 0.

(6):

The current density delivered to the load is the difference of the current densities due to absorbed solar and thermal radiation and the current density of radiation emitted from the top surface or absorbed in the substrate. Defining J_{ph} = en_{ph}, we have

(7): J = J_{ph} + J_{th} − J_{rad}

The second term, J_{th}, is negligible compared to J_{ph} for all semiconductors with E_{g}. ≥ 0.3 eV, as can be shown by evaluation of the above J_{th} equation. Thus, we will neglect this term to simplify the following discussion. Then we can express J as follows.

(8):

The open-circuit voltage is found by setting J = 0.

(9):

The maximum power point (J_{m}, V_{m}) is found by stetting the derivative . The familiar result of this calculation is

(10):

(11):

Finally, the maximum work (W_{m}) done per absorbed photon, Wm is given by

(12):

Combining the last three equations, we have

(13):

Using the above equation, W_{m} (red line) is plotted for different values of E_{g} (or n_{ph}).

Now, we can fully use Henry’s graphical QE analysis, taking into account the two major intrinsic losses in the efficiency of solar cells. The two main intrinsic losses are radiative recombination, and the inability of single junction solar cells to properly match the broad solar energy spectrum. The shaded area under the red line represents the maximum work done by ideal infinite multi-junction solar cells. Hence, the limiting efficiency of ideal infinite multi-junction solar cells is evaluated to be 68.8% by comparing the shaded area defined by the red line with the total photon-flux area determined by the black line. (This is why this method is called “graphical” QE analysis.) Although this limiting efficiency value is consistent with the values published by Parrott and Vos in 1979: 64% and 68.2% respectively, there is a small gap between the estimated value in this report and literature values. This minor difference is most likely due to the different ways how to approximate the photon flux from 0 eV to 0.3096 eV. Here, we approximated the photon flux from 0 eV to 0.3096 eV as the same as the photon flux at 0.31 eV.

Source from Wikipedia