Theoretical performance of multi-junction solar cells combining III-V and Si materials

A route to improving the overall efficiency of multi-junction solar cells employing conventional III-V and Si photovoltaic junctions is presented here. A simulation model was developed to consider the performance of several multi-junction solar cell structures in various multiterminal configurations. For series connected, 2-terminal triple-junction solar cells, incorporating an AlGaAs top junction, a GaAs middle junction and either a Si or InGaAs bottom junction, it was found that the configuration with a Si bottom junction yielded a marginally higher one sun efficiency of 41.5% versus 41.3% for an InGaAs bottom junction. A significant efficiency gain of 1.8% over the two-terminal device can be achieved by providing an additional terminal to the Si bottom junction in a 3-junction mechanically stacked configuration. It is shown that the optimum performance can be achieved by employing a four-junction series-connected mechanically stacked device incorporating a Si subcell between top AlGaAs/GaAs and bottom In0.53Ga0.47As cells. © 2012 Optical Society of America OCIS Codes: (230.0230) Optical devices; (350.6050) Solar energy; (040.5350) Photovoltaic. References and links 1. M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl. 20(1), 12–20 (2012). 2. D. J. Friedman, “Progress and challenges for next-generation high-efficiency multijunction solar cells,” Curr. Opin. Solid St. M. 14(6), 131–138 (2010). 3. D. C. Law, R. R. King, H. Yoon, M. J. Archer, A. Boca, C. M. Fetzer, S. Mesropian, T. Isshiki, M. Haddad, and K. M. Edmondson, “Future technology pathways of terrestrial III–V multijunction solar cells for concentrator photovoltaic systems,” Sol. Energy Mater. Sol. Cells 94(8), 1314–1318 (2010). 4. J. F. Geisz, J. M. 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Introduction
Triple-junction solar cells based on the III-V material system are the current state of the art photovoltaic devices with conversion efficiencies of over 40% under solar concentration [1].The performance of triple-junction solar cells is steadily improving but alternative multijunction materials and technologies are required to significantly advance device performance towards efficiencies of 50% [2] and further reduce the cost of concentrating photovoltaic (CPV) systems.The integration of III-V materials with Si is of interest as its 1.1 eV bandgap is close to the desired 1 eV value for the bottom and second from bottom junction in triple and four junction solar cells, respectively [3].Furthermore, if Si can be used as the principle substrate it provides additional benefits over conventional Ge-based multi-junction solar cells or indeed other candidate materials such as InP or GaAs since Si wafers are available in larger sizes which provide economies of scale and will increase the cell yield per epitaxial growth run.
There are a number of drawbacks which make the integration of Si with III-V materials in multi-junction devices difficult.Direct epitaxial growth is inhibited by the lattice mismatch, difference in thermal expansion co-efficient and polar/non-polar interface between Si and III-V materials.GaP nucleation layers provide a route to direct growth of III-V materials on Si as this high bandgap material is closely lattice matched to Si [4][5][6].Tandem solar cells incorporating an active GaAsP junction grown directly on an active Si substrate have also been demonstrated with a 2-terminal efficiency of 9.2% [7].
III-V templates formed using Ge buffer layers or by III-V layer transfer and wafer bonding to Si have also been used to grow solar cells [8,9].However, such epitaxial templates must have low threading dislocation densities in order to act as suitable solar cell growth templates, which is difficult in the case of materials with a large mismatch in thermal expansion coefficient.
These constraints on III-V epitaxial growth on Si substrates are removed by mechanically stacking individual solar cells.To date, the highest performing multi-junction solar cell incorporating III-V and Si solar cells is a spectrum splitting system built at the Fraunhofer ISE which achieved an outdoor photovoltaic conversion efficiency of 34.3% under one-sun conditions [10].
Up to now, research has focussed on overcoming the difficult challenges faced when integrating Si successfully in multi-junction solar cells.When considered, the potential photovoltaic conversion efficiency of these novel bandgap combinations has been modelled using the detailed balance limit of efficiency method [11].This method assumes each junction in the device is made of a direct bandgap material where each photon with energy greater than that bandgap is absorbed and contributes one carrier pair to the external circuit.This assumption does not hold when investigating the potential performance of combinations incorporating indirect bandgap materials such as Si where thickness is an important parameter in the final cost of the device.In order to investigate the potential photovoltaic conversion efficiency of multi-junction solar cells incorporating Si, a one-dimensional electrical and optical model was developed.The model was adapted from those already used to investigate the effect of cell thickness on power output from monolithic multi-junction solar cells [12,13].The power output of various multi-junction technologies incorporating Al 0.3 Ga 0.7 As, GaAs, Si and In 0.53 Ga 0.47 As was evaluated.For this modelling exercise Al 0.3 Ga 0.7 As was chosen as the material for the high bandgap top junction as opposed to the more widely used Ga 0.5 In 0.5 P as its electrical parameters are more readily available.The efficiency of the industry standard lattice-matched GaInP/Ga 0.99 In 0.01 As/Ge multijunction solar cell is limited by the choice of Ge as the bottom junction as the low E g material contributes a low voltage while the non-optimal bandgap combination leads to an excess short-circuit current in the Ge junction.The bandgap of Si (1.1 eV) is close to the desired 1 eV for better spectral splitting with the lattice matched GaInP/GaAs material system.Here the performance of a 2-terminal device incorporating an active Si bottom junction, as shown in Fig. 1(a), is compared to a triple-junction solar cell with an In 0.53 Ga 0.47 As bottom junction i.e. a device consisting of a bandgap combination close to the GaInP/GaAs/Ge material system.The benefit of inserting a fourth junction is also considered and a Si junction is placed between the high-bandgap AlGaAs/GaAs and low-bandgap InGaAs junctions to provide better current matching in a series connected 2-terminal configuration as shown in Fig. 1(c).

Mechanically stacked solar cells
Improving the performance of monolithic multi-junction solar cells is constrained by the drawbacks of current matching, crystal lattice mismatch between optimum cell materials and tunnel junction reliability [14].Mechanically stacked solar cells (MSSCs) can overcome these drawbacks and offer an alternative route to the integration of Si with III-V solar cells.The constraint of current-matching can be eliminated by providing more than two electrical contacts so the total current produced by a junction can be utilised as outlined in Fig. 2. Si is considered as the bottom junction under a dual junction Al 0.3 Ga 0.7 As/GaAs solar cell.The performance of an MSSC with an In 0.53 Ga 0.47 As bottom junction is also analysed to compare the performance of the 1.1 eV and 0.75 eV devices.A significant drawback of mechanically stacked solar cells is the cost of producing and stacking the individual solar cells.An important parameter for reducing this cost is the thickness of each material used and the performance of these solar cells is evaluated as a function of the thickness of the bottom junction.A four-junction MSSC is also considered which integrates both a Si and In 0.53 Ga 0.47 As solar cell under a dual junction top cell in a 6-terminal configuration (Fig. 2(c)).The Si cell thickness is varied to find the optimum value to split the spectrum between the two cells and give the maximum power output from these two cells combined.

Theoretical model
The ideal diode equations for photovoltaics were used to determine the electrical performance of solar cells.The model is based on the semiconductor transport properties of each material and its absorption profile.It was assumed the junction behaves according to the one-diode model where each absorbed photon creates one electron-hole pair and radiative recombination is the only loss mechanism i.e. no ohmic, optical or non-radiative recombination losses are considered.While these assumptions will result in an overestimation of the performance of the multi-junction solar cells, since in practical applications these losses are non-zero, the model can be used to assess the relative performance of each technology.The light generated current per unit area, J L (mA/cm 2 ), in a cell was determined using the AM1.5 Direct Solar Spectrum from the ASTM G-173-03 reference standard [15] as used in terrestrial concentrating PV systems.The photon flux (PF(λ), # photons m −2 s −1 ) incident on a solar cell was determined using Eq. ( 1) where I o is the power (W m −2 nm −1 ) of the AM1.5 Direct Solar spectrum at wavelength λ (nm).
The absorption profile and thickness of each material in a solar cell have been used to determine J L .The absorption profiles given in Fig. 3 were taken from the literature [16,17].The light generated current per unit area, J L , was taken as the number of photons absorbed across the entire thickness of the solar cell as in Eq. (2). .
(3) In the case of a multi-junction solar cell the spectrum incident on the n th material junction, I n , was adjusted for absorption in the preceding materials as in Eq. ( 4) where d n-1 (cm) is the thickness of the preceding material and I n-1 is the illumination intensity incident on the previous junction (I n = I o for the top junction).
The reverse saturation current per unit area (5), J o , was calculated as the sum of the contribution of the n-and p-type layers assuming uniform doping in each.
The intrinsic carrier concentration (n i ), the minority carrier diffusion constants (D e , D h ) and the electron and hole minority carrier diffusion lengths (L e , L h ) are calculated in the usual manner.The minority carrier mobilities (µ e , µ h ) and minority carrier lifetimes (τ e , τ h ) are taken from the literature and are given in Table 1.
When a number of junctions are considered as series-connected, the current matching condition was first found using an iterative process by varying the thickness of each junction so the contribution from each was equal and maximised.It should be noted that this optimisation should be carried out while considering the operating current of the device, J MPP , but in this case the light-generated current density, J L , was used as it was deemed to be sufficiently similar to not greatly reduce the accuracy of the model.The LIV characteristics of a series-connected multi-junction solar cell with n integer junctions were found by adding the voltages of each junction when this matched current was present in each (Eq.( 6).  1) .
The maximum power output per unit area of a solar cell is found by differentiating the power output function of a solar cell and setting it to zero as in Eq. (7).
Individual solar cells in a mechanical stack configuration are connected in parallel allowing separate load control of each cell.Therefore, the maximum power output per unit area of the stack is the sum of the maximum power output per unit area of the individual solar cells.
The model considers solar cells connected in series and parallel, as required, and the photovoltaic conversion efficiency for each system is derived by finding the power output of the combined solar cells and dividing by the incident power.The photovoltaic conversion efficiency, η, is equal to P out /P in where the incident power of the AM1.5d spectrum is 887 W/m 2 .

Model limitations
This work does not consider optical losses due to grid shading, reflection at the surface of solar cells or the interfaces between dissimilar materials or absorption in III-V epitaxial substrates.Each of the multi-junction solar cell configurations presented in this study can be optimised through various methods which can minimise these losses, e.g. the use of multilayer anti-reflection coatings and index-matching interface bonding layers [24].Furthermore, the effect of surface recombination has been ignored as it is dependent on the passivation used in the cell design which will vary greatly for each multi-junction device considered here.

2-terminal devices
The first devices considered are monolithic 2-and 3-junction solar cells with only a 2 terminal connection, thus the individual subcells are connected in series and the photocurrent is limited accordingly.The photocurrent in the dual junction Al 0.3 Ga 0.7 As /GaAs solar cell was matched and maximised at 14.4 mA/cm 2 for material thicknesses of 0.56 µm of and 3 µm, respectively.
Subsequently, an open-circuit voltage of 2.51 V and a photovoltaic conversion efficiency of 36.7% were determined for this cell combination, which was used as the top cell in a number of mechanically stacked solar cell configurations; the results of which are presented in the following sections.
A 200 µm Si substrate was considered as the bottom junction in a series connected triplejunction solar cell.The current of the device is limited by the Si junction as the 200 µm thick layer absorbs 97.1% of the transmitted photons below 1120 nm.The current matching for the AlGaAs, GaAs and Si junctions was found with a top junction thickness of 0.38 µm and a middle junction thickness of 1.02 µm giving a light-generated current density of 13.1 mA/cm 2 in the device.This series-connected device has a relatively high open-circuit voltage of 2.89 V and an efficiency of 41.5%.
This device was compared to a triple-junction AlGaAs/GaAs/InGaAs solar cell.The lower bandgap material (~0.75 eV) absorbs a much higher portion of the spectrum transmitted by the AlGaAs and GaAs material layers (97.2% of photons below 1680 nm with an InGaAs thickness of 3.5 µm) and produces a higher current than a Si bottom junction allowing thicker top and middle junctions to be used in the device.The current through the device is limited by the matching of the top two junctions with the limiting current being 14.4 mA/cm 2 .A combined InGaAs emitter and base thickness of 0.48 µm is required to match this current.This device has an open-circuit voltage of 2.63 V under illumination and an efficiency of 41.3% which is marginally less than the Si-based series-connected triple-junction solar cell.It is clear that higher voltage Si-based triple-junction solar cells could achieve similar performance to current triple junction devices if the manufacturing challenges can be overcome.The performance of a four-junction device which utilises Si as the ~1 eV bandgap between the higher bandgap AlGaAs/GaAs materials and InGaAs was also modelled.The same current matching condition was found to exist for the 4J cell as the Si-based 3J cell since InGaAs strongly absorbs the spectrum transmitted by an AlGaAs/GaAs/Si device.The device produces a photocurrent of 13.1 mA/cm 2 with a combined InGaAs emitter and base thickness of 1.53 µm and gives a four-junction solar cell with an open-circuit voltage of 3.55 V.The overall efficiency is 45.7% or an increase of approximately 4% above the triple-junction cells due to the added voltage of the Si junction.A summary of the performance of these 2-terminal devices is given in Table 2.

Mechanically stacked solar cells
At this point we consider the performance of mechanically stacked solar cells where some or all of the current-limitations imposed by series connection are removed.Assuming no free-carrier absorption in the GaAs substrate, it was found that an AlGaAs/GaAs to Si mechanically stacked solar cell with Si thickness of 200 µm has an efficiency of 43.1% under 1-sun illumination.This is a 1.8% improvement over an ideal series connected AlGaAs/GaAs/Si triple-junction solar cell and results from complete utilisation of the current from the Si junction.The Si junction produces a short-circuit current density of 10.4 mA/cm 2 .Figure 4 shows that mechanically stacked thin-film Si solar cells will result in a significant efficiency boost even for thicknesses below 100 µm.Lower bandgap materials are more suited for use in MSSCs where the full current absorbed in the bottom junction can be used if the solar cell is provided with parallel electrical contacts.It was found that an InGaAs solar cell with a combined emitter and base thickness of 3.5 µm resulted in a short-circuit current density of 27.6 mA/cm 2 when stacked under an AlGaAs/GaAs dual junction top cell.Providing separate electrical connections to this junction as in a mechanical stack results in an efficiency of 46.4%.This is approximately an absolute increase of 5% in efficiency over a monolithic triple-junction solar cell of the same material system.It is also a 0.7% absolute increase over the four-junction, 2-terminal device, described in Section 3.1.The performance of the bottom cell in the AlGaAs/GaAs-InGaAs configuration is given in Fig. 5 as a function of combined emitter and base thickness.Most of the benefit provided by this junction is achieved with a material thickness of 2 µm.While a higher photocurrent density can be achieved with greater thicknesses, the cost of growing the extra III-V materials would need to be considered against the performance increase.For the four-junction configuration described in the following section, an InGaAs active absorption thickness of 3.5 µm was chosen as a suitable balance of cost and performance.The final cell configuration considered is that of an AlGaAs/GaAs-Si-InGaAs structure with a 4-terminal connection.It is clear from Fig. 6 that most of the efficiency boost provided to the stack is due to the InGaAs junction.A combined efficiency of 11.5% is found for the stacked Si and InGaAs cells using only 10 µm of Si with 5 µm of InGaAs while the same InGaAs thickness with 500 µm of Si yields a boost of 13%.The overall device efficiency using a more realistic 200 µm Si solar cell and an InGaAs active layer thickness of 3.5 µm is 49% or a boost of 12.3% to the dual junction top cell.A summary of performance of the various multijunction configurations is presented in Table 3 below, indicating that the 4-junction 4-terminal structure gives the highest overall efficiency of the devices considered.

Efficiency versus illumination intensity
In order to justify the cost of using III-V materials, the configurations modelled are most suited to concentrating photovoltaic (CPV) systems.An analysis on the effect of concentration on photovoltaic conversion efficiency was carried out by increasing the illumination intensity of the AM1.5d spectrum while assuming that the junction temperature remained at 300 K.As this treatment of increased illumination intensity ignores the effect increasing temperature has on resistance, E g narrowing and stresses and strains caused by the different thermal expansion coefficients of the materials used the results presented are an upper limit to performance when considering the measured absorption coefficients of each material.Figure 7 shows the efficiency versus concentration for each of the modelled solar cells.At a concentration of 500 Suns a four-junction monolithic device has an efficiency of 55.9% versus 49.8% for the AlGaAs/GaAs/InGaAs material system.While theoretically both a 4terminal and triple-junction MSSC with an InGaAs bottom junction or a 6-terminal and fourjunction MSSC outperform the best 2-terminal device at high concentration levels they are currently not used in commercial terrestrial concentrating photovoltaic systems.A number of challenges to producing mechanically stacked solar cells make the expected efficiency gains difficult to realise.Optical losses due to reflection at the interfaces between stacked solar cells and light absorption in the stacking system or material substrates reduce the photocurrent of the bottom junctions.The complex stacking scheme associated with mechanical stacking potentially increases the thermal resistance of the multi-layer configuration resulting in an increase in junction temperature that would inevitably lead to a drop in efficiency without adequate cooling mechanisms [25].Furthermore the resistance of any contacting scheme must be kept low due to the high currents seen under concentration.This is difficult when additional contacts are required which introduce extra resistive elements such as lateral conduction layers.Finally the cost of these cells must be justified as a number of individual solar cells are required as well as a complex fabrication process.These are the drawbacks which must be overcome for the efficiencies predicted by theory to be achieved and mechanically stacked solar cells to be utilised in commercial CPV systems.the bottom junction in a series connected 2-terminal triple-junction (AlGaAs/GaAs/Si) solar cell results in a performance similar to devices utilising lower bandgap materials, e.g.AlGaAs/GaAs/InGaAs.
Providing separate terminals to the Si junction to create a 4-terminal mechanically stacked solar cell provides an efficiency gain of 1.8% over the two-terminal device.It was shown that a 3J (AlGaAs/GaAs-InGaAs) mechanically stacked solar cell has a theoretical efficiency of 46.4% when a 4-terminal configuration is used to separately contact the bottom InGaAs cell.This device outperforms a four-junction series connected device which incorporates Si between the AlGaAs/GaAs and InGaAs Finally, four-junction mechanically stacked solar cells, incorporating a 4-terminal AlGaAs/GaAs-Si-InGaAs structure, were shown to be the highest performing III-V/Si solar cells under the AM1.5d spectrum with an overall efficiency of 49% under 1-Sun illumination.This can be further increased to in excess of 55% efficiency under x500 concentration.
Since the impact of resistive and optical losses is not considered in this study, the results present a theoretical upper limit to the improved efficiencies that could be achieved from optimised stacking and connection configurations.Nevertheless, it does provide a relatively simple route to improving the performance of multi-junction devices using widely available solar cell materials thus avoiding the need for further complex bandgap engineering or advanced device epitaxy capability.The main challenge remains to develop stacking and electrical connection configurations and strategies that minimise the above mentioned losses.

Fig. 1 .
Fig. 1.Triple-junction (a, b) and four-junction (c) series-connected multi-junction solar cell configurations modelled where the interface between Si and InGaAs and the other semiconductor materials is considered as a completely transparent and ideal ohmic contact.

Fig. 2 .
Fig. 2. Triple-junction mechanically stacked solar cells formed using Si (a) and InGaAs (b) bottom solar cells and a four-junction configuration (c).

Fig. 3 .
Fig. 3.The absorption co-efficients of the materials considered for multi-junction solar cells.The AM1.5d ASTM G173-03 spectrum is shown for comparison.
ideal diode equation (Eq.(3) was used to determine the Light Current-Voltage (LIV) characteristics of a solar cell./ ( )

Fig. 4 .
Fig. 4. The modelled electrical performance of a Si solar cell mechanically stacked under a dual junction AlGaAs/GaAs solar cell as a function of Si thickness.

Fig. 5 .
Fig. 5.The modelled electrical performance of an InGaAs solar cell mechanically stacked under a dual junction AlGaAs/GaAs solar cell as a function of InGaAs combined emitter and base thickness.

Fig. 7 .
Fig. 7. Efficiency versus solar intensity for each technology Electronic charge h Planck's constant c Speed of light k Boltzmann's constant T Temperature α(λ) Absorption co-efficient of material (wavelength dependent) E g Semiconductor Bandgap