Efficient Multiterminal Spectrum Splitting via a Nanowire Array Solar Cell.

Nanowire-based solar cells opened a new avenue for increasing conversion efficiency and rationalizing material use by growing different III-V materials on silicon substrates. Here, we propose a multiterminal nanowire solar cell design with a theoretical conversion efficiency of 48.3% utilizing an efficient lateral spectrum splitting between three different III-V material nanowire arrays grown on a flat silicon substrate. This allows choosing an ideal material combination to achieve the proper spectrum splitting as well as fabrication feasibility. The high efficiency is possible due to an enhanced absorption cross-section of standing nanowires and optimization of the geometric parameters. Furthermore, we propose a multiterminal contacting scheme that can be fabricated with a technology close to standard CMOS. As an alternative we also consider a single power source with a module level voltage matching. These new concepts open avenues for next-generation solar cells for terrestrial and space applications.

Introducing multiple band gap concepts into nanowire solar cell designs has high promise for maximum solar conversion efficiency while keeping the unique advantages of the nanowires. Nanowire-based solar cells are increasingly attracting attention due to their enhanced absorption properties and the possibility to combine a wide selection of different materials.[1−8] The nanowire geometry allows them to be used in various ways from vertical[9] or horizontal[10] arrangements to hybrid cells comprising organic materials.[11−14] The diameter of a nanowire is much smaller than its length, so that defect-free nanowires can be grown on substrates with lattice constants considerably different from their own.[15−17] As a result, silicon and III–V materials can be combined in a double-junction cell.[18,19] The geometry of nanowires also allows engineering light–matter interactions to obtain enhanced absorption combined with antireflection properties.[20−23] Various nanowire-based solar cell designs have been proposed. The profound understanding of the photonic properties of standing nanowires resulted in an experimental realization of a single-junction InP nanowire cell reaching 13.8% efficiency.[4] Various designs suggest that the cells can be improved by using dual-junction nanowires with axial or radial junctions,[24−26] by an additional junction in the substrate,[26,27] by heterojunction with organic semiconductors,[11−13] etc. It was also predicted that efficiencies above 39% for double-junction nanowire designs should be feasible.[24] With all the work done however the pool of possibilities and concepts leading to principally new efficient solar cell designs that utilize nanowires is far from being depleted. For example, the spectrum splitting, a natural way to increase a photovoltaic conversion system efficiency,[28,29] has found yet a very limited application in nanowire solar cell concepts. Spectrum splitting allows reducing the carrier thermalization loss and thereby greatly improving the conversion efficiency of each photon.[30,31] The efficiency of classical multijunction cells (the most common cells utilizing the spectrum splitting) has recently reached 44.7%.[32] For the nanowires it was suggested to use core–shell[24] or axial[26] tandem structures. The issue however is that such designs require a fabrication of tunnel junctions in dissimilar materials, which has proven to be extremely challenging.[33,34] In addition, the performance of these cells is limited by the current-matching condition.

The questions we address in this work are the following: Should one be bound to the classical multijunction design[32] and replicate it directly on each nanowire?[24,26] Is it possible to think outside the box and to lay out new arrangements of nanowires that act effectively like a multijunction device, just by considering their special photonic properties?

Multiterminal Nanowire Array

In this paper we present a novel nanowire-based triple band gap design with a two-dimensional spatial arrangement of three independently contacted nanowire subarrays grown on a single flat substrate. The design combines all the advantages of the spectrum splitting with independent subcell contacting and fabrication on a silicon substrate. Nanowires allow one to combine a wide range of materials such as growing III–V nanowires on a silicon substrate[3,15,17,35] and to simultaneously grow different nanowires on the same substrate.[35,36] From the detailed balance consideration we chose Al0.54Ga0.46As, GaAs, and In0.37Ga0.63As so that they form an ideal band gap combination (2.01, 1.42, and 0.93 eV, correspondingly). These materials can be grown in the same epitaxial system, which is important for the fabrication process. The nanowires of different materials are physically separated, so that the complexity of each wire is not greater than that in a single-junction nanowire design. This makes the fabrication of such nanowires much easier than, for example, double-junction nanowires, which additionally require a tunnel junction.[24,26] The spectrum splitting and the independent electrical connection of the subarrays bring a high conversion efficiency and great spectrum change tolerance (due to the absence of current and voltage matching limitations; see Supporting Information section 1). To allow independent connections, the substrate must have three independent contact grids, one for each nanowire subarray. The latter can be realized by a layered structure of highly doped silicon conduction lines within an insulating silicon dioxide substrate fabricated with a CMOS-like technology (see Figure ). We should note here that we suggest using radial junction nanowires so that the silicon conduction lines will be contacting the cores of the corresponding nanowires while the shells will be connected by transparent contacts (see Supporting Information section 3 for a detailed description).

Figure 1

Design concept. (a) Schematic illustration of the triple-junction nanowire array on a Si substrate. Each unit cell contains high, low, and two medium band gap nanowires (the higher the band gap value, the higher the wires). (b) Working principle of the design. (c) Contacting scheme of the multiterminal device. Photoelectrical power is extracted separately from nanowires of different band gaps (lengths), so that the generated power is directly added.

Figure shows the general scheme, working principle, and contacting scheme for the triple-junction nanowire array proposed in this work. Nanowires made of materials with different band gaps are arranged on the substrate in a two-dimensional periodic array such that the incoming light is absorbed selectively within the wires according to the band gap. As a general rule, the larger the band gap, the taller the nanowires should be. The idea here is that high-energy photons will be completely absorbed before they reach the height of nanowires with a lower band gap (see Figure b). This is due to the advantage of the increased absorption cross-section in standing nanowires. As a result, the solar spectrum is divided into three absorption spectral ranges. The periodic array has a rectangular unit cell, where the higher and lower band gap nanowires are disposed on one side of the cell, while the nanowires with a medium band gap are arranged on the other side (see Figure a). Simulations indicate that the best performance is achieved with two medium band gap nanowires per unit cell. This configuration was chosen over others because it has a similar or superior performance with a simpler geometry and fewer parameters. In particular we performed a short set of comparisons for several hexagonal arrangements and rectangular unit cells. Similar results were obtained for most of the configurations. Thus, we focus on the simplest rectangular unit cell with a rectangular arrangement of nanowires inside. For this arrangement it is natural that one of the nanowire types is duplicated within the cell in order to achieve an efficient space utilization. The GaAs nanowires were chosen to be doubled because they provide the highest contribution to the efficiency, arising from light absorption closest to the maximum of the solar spectrum. A more detailed study of different nanowire arrangements is very time-consuming and will be performed in future works.

The optimized structure has the following parameters: Al0.54Ga0.46As, GaAs, In0.37Ga0.63As nanowire radii (lengths) of 51 nm (12 μm), 73 nm (6.6 μm), and 114 nm (3.3 μm), respectively, array periods of 580 × 500 nm, and center-to-center spacing between GaAs–GaAs (GaAs–InGaAs) nanowires of 290 nm (250 nm). The equivalent bulk thicknesses of AlGaAs, GaAs, and InGaAs layers are 340, 760, and 460 nm, correspondingly. The lengths, diameters, and positions of the nanowires are calculated and optimized using a Fourier modal method (FMM)[37] combined with an evolution strategy (ES)[38] and Nelder–Mead[39] optimizers (see Supporting Information section 2 for more details). We present here the calculations for a triple band gap solar cell, but the principle can be employed for a higher number of junctions.

Figure c depicts a contacting scheme of the three solar subcells. The junctions are designed in a core–shell fashion. The core–shell structures offer more robustness in terms of surface recombination losses. Still, axial junctions would also be possible if adequate surface passivation is provided. The photogenerated power is collected separately for each of the three different kinds of nanowires. Nanowires are grown on sub-micrometer-scale platforms insulated electrically from the neighboring ones. Such a scheme could be achieved by subsequently growing three nanowire subarrays on a patterned (highly doped) silicon-on-insulator substrate (SOI). The highly doped silicon platforms would directly contact nanowire cores, while nanowire shells would be contacted via transparent top-contacts. The process would involve the insulation (passivation) of the nanowires and selective etch of each of the nanowire tips, as shown in prior works.[40] A transparent polymer layer would ensure the mechanical stability of the nanowire/contacts ensemble (see Supporting Information section 3 for the detailed fabrication steps description).

A natural way to collect the generated power of the multiterminal contacting scheme is to use three independent external converters supplying energy to the grid. Such schemes have a high spectrum change stability. An alternative with only one converter is a voltage matching scheme on the module level leading to a single power source. One example of such scheme with still high efficiency is presented in the Supporting Information section 4. As an advantage of such a scheme, we do not have to include tunnel junctions for current matching as in standard multijunction cells, which would make fabrication more demanding.[33,34] Although the voltage-matched scheme is less tolerant to the spectrum changes, the module interconnection scheme is very flexible. One can imagine that it could even have electronic controls that adapt to the spectrum during operation.

Results and Discussion

In Figure a the spectral distribution of light absorption within the nanowires and detailed balance current–voltage dependences for the optimal structure are shown. The detailed balance limit efficiency estimation[41] of the optimized structure is 48.3% for an AM1.5 direct solar spectrum (see Figure a). This value is close to the maximum conversion efficiency for a triple band gap design under ideal sunlight splitting, which is 51.3% (for the same spectrum, see the Supporting Information section 5). One can see that the GaAs subcell gives the highest contribution to the overall conversion efficiency (see Figure b) and is closest to the maximum absorption within the corresponding spectral range (see Figure a). Such a result is to be expected due to the doubled number of GaAs nanowires compared to Al(In)GaAs. It is also beneficial from the fabrication point of view because the GaAs is a simple compound material and the least demanding in the growth process. Furthermore, the GaAs single-junction cell showed 28.8% efficiency,[42] which is close to the detailed balance conversion efficiency. The highest yield subcell in the design is therefore also the most promising from the fabrication point of view. Another observation one can make from Figure a is that the majority of the absorption losses are happening at the beginning and at the end of the absorption range. The loss at the beginning (low frequencies) happens due to the low absorptivity of InGaAs close to its band gap. That could be compensated by increasing the lengths of the corresponding nanowires or a choice of material with a steeper absorption growth near the band gap. The loss at the end (high frequencies) happens due to the cross-section of AlGaAs nanowires reaching its limits. At high frequencies the wavelength of the light becomes smaller than the internanowire distance and some photons are passing through without feeling the nanowires’ presence. Both of the issues listed above will become a subject of further research on improved material combinations and nanowire array geometries.

Figure 2

Performance calculation. (a) Absorption distribution between the different band gaps. (b) Current–voltage dependences of the optimal nanowires’ structure. Calculations are made using detailed balance limit and AM1.5 direct solar spectrum. Overall efficiency limit of the nanowire array is 48.3%. Current/voltage (in mA/cm2 and V) in the optimal points for Al0.54Ga0.46As is 10.1/1.64, for GaAs, 17.5/1.03, and for In0.37Ga0.63As, 14.7/0.60.

The obtained result (48.3% out of a maximal 51.3% detailed balance efficiency) shows a high potential of the optical design due to the nanowire concentration effect. It is evident though that a more realistic conversion efficiency could be obtained with a more detailed consideration of factors such as nonradiative losses, resistive losses, and additional losses introduced by transparent contacts. To get a hint about the fabrication demands and resistive losses of the designed cell, one can consult the band profile estimations for nanowires performed in ref (43). We will take the AlGaAs wires as an example. Due to these nanowires being the thinnest and longest, the corresponding subcell will certainly exhibit the highest series resistance and voltage reduction. We assume core and shell doping levels of n = 1019 cm–3 and a surface-state density below 1011 cm–2 eV–1. For the nanowires with a diameter of around 100 nm we can estimate from ref (43) that it is possible to have a partially nondepleted core and shell, which is essential for the conductivity. Due to the smaller mobility of free holes, we address here the voltage drop given in the p-type core of the AlGaAs nanowires. For 54% of aluminum the hole mobility is expected to be around μh = 54 cm2/V/s. The nondepleted (conductive) section roughly corresponds to half of the nanowire cross-section, S = 0.5πr2 = 3.93 × 10–11 cm2. Thus, the resistance at the nanowire core will be R = l/(nμheS) = 353 kΩ, where l = 12 μm is the nanowire length. Under the one sun operation conditions, the current flowing through the AlGaAs nanowire will be I = 2.93 × 10–11 A. Thus, the voltage drop due to the core resistance will be dV = IR = 3 × 10–5 V. In conclusion, the series resistance for a realistic device should not degrade too much the theoretical values, provided that there is an impeccable fabrication protocol. It is also worth mentioning that the surface recombination is less critical for radial junctions.[44]

The actual efficiency that would be obtained experimentally depends on multiple parameters, some of which depend strongly on the fabrication process (such as defect densities). However, a rough estimation of efficiency can be given based on the known technological achievements. As described in ref (45), we can assume that recombination in GaAs-based III–V materials is around 150 times stronger than its radiative values, and therefore the actual efficiency would be around 42% rather than 48%.

To further illustrate the working principle of our design, we show how the light is spatially distributed and selectively absorbed in the nanowire array. In Figure we depict the Poynting vector flow-lines near the nanowires for photon energies of 1.2, 1.7, and 2.2 eV. The Poynting vector is a direct illustration of the electromagnetic energy flow. Calculations shown in Figure a indicate that for all of the absorbed photon energies not only does light enter the nanowire through the top surface, but the Poynting vector gradually leads in through the side walls. This is a consequence of the nanowire light concentration. The pattern of energy flow is key to the efficient spectral light splitting within the nanowire array. In this way high-frequency photons (above the AlGaAs band gap) are being mostly absorbed before reaching the GaAs nanowires, and in the same way medium-frequency photons (above the GaAs and below the AlGaAs band gap) are being absorbed by GaAs nanowires before reaching InGaAs.

Figure 3

Poynting vector flow-lines for frequencies of 1.2, 1.7, and 2.2 eV. Each distribution is shown near a nanowire with an appropriate band gap. The nanowire array structure shown here is the optimal design found from the optimization.

Conclusion

In conclusion, a new strategy for the design of highly efficient nanowire-based solar cells is outlined. We propose splitting the incoming solar spectrum spatially so that nanowires with different band gaps separately photoconvert it into electrical power. This opens new possibilities for multijunction cells, where materials with different band gaps and lattice constants are combined on a single substrate. The physically separated junctions based on nanowires guarantee spatial solar spectrum splitting while avoiding the need to fabricate complicated nanowires with tunnel junctions. The absence of the current/voltage matching limitations results in an extremely high theoretical conversion efficiency, namely, 48.3% without light concentration. The design ensures a significantly reduced material consumption compared to standard bulk structures due to the low nanowire volume and the fabrication on a silicon substrate. Although the fabrication and contacting scheme are challenging, we propose that current CMOS technology processes could be transferred to this kind of device. Finally, independent contacting of different junctions grants improved spectrum stability, compared to current matched schemes. This novel nanowire-based multi-band-gap solar cell scheme opens the path toward a new generation of devices that fully exploit the potential of nanowires.