1. Introduction

The photovoltaic technology has achieved significant results in recent years [1]. The market-dominating silicon solar cell provides a maximum achievable efficiency of 25%, and features mature production technologies. Meanwhile, by applying thin-film technology, different material layers are grown on top of each other to form multi-junction cells, and the world record cells using highly absorptive III–V materials have been reported to reach efficiencies around 43%. However, high efficiency multi-junction solar cells are not widely applied in civilian industry due to their relatively expensive fabrication and material cost. Up to now, the cell efficiency has become the crucial factor for the entire photovoltaic industry [2], which still has a room for improvement. The aim is that the industrialized production and application of solar cell can be cost effective when compared with conventional electricity generation methods.

A semiconductor solar cell of high unit cell efficiency needs to satisfy two major requirements. One is to have superior optical properties, meaning the cell should have high cell absorption over a broad-band solar spectrum. The other one is to reduce the thermalization loss during the energy conversion, for which the multi-junction cell is often used [3]. Both points can benefit from the employment of nanowire array solar cells [4, 5]. It has been demonstrated that due to an optical concentration effect, the cell optical absorptivity of nanowires can reach or even surpass that of a thin film solar cell [6–9], yet with much less material consumption. The nanowire structure also allows lateral relaxation of built-in strain, thus for a nanowire multi-junction structure, the material selection is much more flexible [10, 11]. Furthermore, innovative structures that can only be realised in nanowire solar cells can bring new possibilities into solar cell development [12–15].

The dual-diameter nanowire is a new nanowire structure. It has been shown that by forming a nanowire from two cylinders with different diameters, the optical absorptivity was enhanced over the visible spectrum [16]. According to previous work, the nature of optical concentration effect, which is the major factor for optical absorption enhancement in single-diameter nanowire array, can be explained as the superposition of dispersive optical modes. Their dispersion and overlap factor strongly depend on the geometry [6, 17]. In the concept presented here, (see Fig. 1) by applying the internal-device physics regarding the optical concentration effect on a dual-diameter nanowire array, we are able to tailor the nanowire array solar cell to provide high optical absorptivity, with the short wavelength spectrum and long wavelength spectrum concentrating within different nano-cylinders. By employing a dual-junction structure to spatially and spectrally accommodate the separated absorption spectrum, we aim at designing an innovative dual-junction solar cell whose performance is comparable to an ideal case.

 

Fig. 1 Dual-diameter nanowire array solar cell structure. Geometrical parameters are noted in the picture: a is the array pitch, d and D are the respective diameters of core and shell nanowire, h and H are the respective heights of core and shell nanowire. (a): Dual-diameter nanowire array. (b): Single wire structure: blue region is the core nanowire with a small diameter and a large bandgap (E_g_c), red region is the shell nanowire with a large diameter and a small band gap (E_g_s), yellow region is the substrate (E_g_sub). (c) Radially arranged dual-junction structure, the contacts for core and shell junctions are noted.

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The optical absorptivity of the dual-diameter nanowire array is evaluated by solving Maxwell’s equations using a three-dimensional microscopic model. The Shockley-Queisser method is employed to calculate the thermal efficiency limit of the device as a dual-junction solar cell [18]. A brief introduction of our simulation model is given in Section 2, and the device design is given in Section 3, in the end, the simulation results are presented and discussed in Section 4.

2. Simulation methods

2.1. Optical properties

By solving Maxwell’s equations, the spatial electromagnetic (EM) field distribution can be evaluated for each optical wavelength. This is done by a three-dimnesional finite-element implementation of the vectorial Helmholtz equation in frequency domain. Material dispersion as well as the substrate is included in the calculation. The optical properties of the investigated structure are then deduced from the EM field solution. The optical absorptivity can be expressed as follows [6]:

2.2. Detailed balance calculation

The detailed balance limit (Shockley-Queisser limit) calculation gives a theoretical limit of solar cell efficiency [19]. In this method, the output current is composed of the sum of photocurrent and diode current, and only radiative recombination is considered as recombination mechanism. The current-voltage relationship is given by:

3. Device design

The prototype of the dual-diameter nanowire array solar cell is depicted in Fig. 1. Being arranged in a square array, each dual-diameter nanowire is composed of a core wire with a small diameter and a shell wire with a large diameter. As shown in previous work, the optical absorptivity of nanowire is strongly affected by the nanowire geometry [6]. Assuming that the space fill factor is kept constant, and the material band gap is sufficiently small to absorb the entire solar spectrum, the optical absorptivity of the long wavelength spectrum increases with the diameter of the nanowire. This is due to the waveguide modal dispersion of the wire array; a thinner wire carries less higher order modes, which are responsible for the absorption process [6]. Hence, the basic idea of the dual-diameter nanowire structure is to have the short wavelength spectrum being absorbed by the thinner wire and the large wavelength part by the thicker wire.

As shown in Fig. 1(b), the core wire is much longer than the shell wire, so the solar power of short wavelength spectrum can be sufficiently absorbed within the core. This principle enhances the wavelength separation, as most of the short wavelength spectrum is absorbed in the top section. A large bandgap material is assigned to the core wire to suppress the thermalization loss, and the shell wire is assigned with a small bandgap material. The dual-diameter structure is viewed as a radially arranged dual-junction cell, as depicted in Fig. 1(c).

The optical absorption property of the dual-diameter nanowire array is sensitive to both the geometry and the constituent material. Here an optimized structure has been designed with140 nm diameter (d) and 4.5 μm long (h) core wire and 250 nm diameter (D) and 2.5 μm long (H) shell wire, the array pitch (a) is 360 nm. The materials for core and shell wire are GaInP and InAsP, respectively [20]. Other material combinations can be envisioned employing the same principle. A technological implementation of this geometry requires arranging the double p-n-junctions and the tunnel junction within the radial dimension of 250nm, as shown in Fig. 1(c). To prevent the short circuit condition, the substrate should be insulating. This is a challenging task, which requires tight control of the involved process, and is left for future work.

4. Results and discussion

The spectral optical absorptivity of the dual-diameter nanowire array solar cell is shown in Fig. 2. The result shows a clear spectral split between the core and the shell wire, with near perfect optical absorption of short wavelength range in the core wire, and an average above 90% absorptivity of large wavelength spectrum in shell wire. The absorptive property of dual-diameter nanowire array is close to an ideal absorber for a dual-junction solar cell.

 

Fig. 2 Normalized optical absorptivity of dual-diameter nanowire array solar cell. The short wavelength spectrum (λ <= 800 nm) is absorbed in the core nanowire with absorptivity above 90%. The long wavelength spectrum is absorbed in the shell nanowire. The band gap positions are noted with arrows in the figure.

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Due to the optical micro-concentration effect, the absorption spectrum in a dual-diameter nanowire array is spatially separated perpendicular to the propagation direction of the optical modes. As an example, the optical generation rates of dual-diameter nanowire under illumination of 500 nm wavelength and 1040 nm wavelength are depicted in Fig. 3. The spatial separation of the solar spectrum is shown in the picture: at 500 nm wavelength, the optical generation concentrates in the core nanowire, while under 1040 nm wavelength illumination, the optical generation is localized in the shell wire. In [21] it has been pointed out that leaky modes have an influence on the absorptivity of core-shell structures composed of different materials. In our case, the refractive index difference between the core and the shell is small, therefore they do not play a major role (except for a minor optical effect as discussed before).

 

Fig. 3 Optical generation localization under different wavelength illumination. (a): 500 nm wavelength, the optical generation is localized in core nanowire. (b): 1040 nm wavelength, the optical generation is localized in shell nanowire. (c): Radial distribution of optical generation at 500 nm wavelength, generation localized in core nanowire. (d): Radial distribution of optical generation at 1040 nm wavelength, generation localized in shell nanowire.

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By tuning the geometrical and material parameters, we are able to tailor our structure to approach an ideal absorber. Applying the detailed balance limit calculation for a dual-junction solar cell in each case, we select the optimum structure with the band gap of core wire being 1.52 eV, and the band gap of the shell wire being 0.94 eV. The normalized short circuit current density J_sc is 229.2 A/m², and the open circuit voltage V_oc is 1.92 V, the current-voltage relationship is shown in Fig. 4. The maximum cell efficiency is 39.1%.

 

Fig. 4 Current-voltage relationship of dual-diameter nanowire array solar cell evaluated by detailed balance limit calculation. For the output of dual-junction solar cell, J_sc is 229.2 A/m², and V_oc is 1.92 V. The maximum cell efficiency is 39.1%

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The Shockley-Queisser limit of an ideal dual-junction absorber is around 44%, which means some improvement space is still left for this structure. This is due to the non-perfect optical absorption in the long wavelength part of the solar spectrum in the shell wire, and the decline of absorptivity near the bandgap in the short wavelength range within the core wire, which leads to a small part of short wavelength optical power leaking into the shell. Fine adjustments of geometrical parameters and material selection provide the possibility to enhance the device performance even further.

5. Conclusion

By adjusting the geometrical parameters, a dual-diameter nanowire array can be tailored to divide the optical absorption spectrum. Generally speaking, the small wavelength spectrum is absorbed in the core wire, which has a small diameter and large bandgap, and the long wavelength spectrum is absorbed in the shell wire, which has a large diameter and small bandgap. This is due to a combination of waveguide mode dispersion and top exposure of the large band gap material. The dual-diameter nanowire array is highly absorptive for both parts of the solar spectrum with an average optical absorptivity over 90%.

By optimizing the respective band profile, the optimum dual-junction solar cell structure is found to have J_sc of 229.2 A/m², and V_oc of 1.92 V, and provides a maximum efficiency of 39.1%. This structure can be further developed to a multi-diameter nanowire array. By shaping the structure to spatially and spectrally accommodate different requirements of absorption spectrum separation, it can be applied in the design of the multi-junction solar cell.