1. Introduction

Adopting a 3D radial junction (RJ) architecture represents a promising approach to boost the power conversion efficiency of Si thin film solar cells [1–3 ] with a thinner absorber and faster carrier separation and collection [4–6 ]. These advanced concepts have been testified in our previous works [7–11 ], where RJ hydrogenated amorphous Si (a-Si:H) thin film solar cells are constructed over a matrix of somewhat randomly-oriented vapor-liquid-solid (VLS) grown Si nanowires (SiNWs) on glass substrates. Remarkably, we show that a very thin intrinsic absorber (below 100 nm) coated around the doped SiNWs cores has led to a high short circuit current density of $J_{sc}=16.1 mA/c{m}^2$ [7], an open circuit voltage above $V_{oc}>0.8 V$ and a power conversion efficiency of $\eta =$ 8.14% [9] (and very recently to 9.2% [12]). All these experimental results have provided a solid basis to address more fundamental and critical aspects that will be highly valuable for promoting the RJ thin film solar cells towards a high performance, light weight and flexible photovoltaics [1, 13 ]. So far, there has been only a few literature [14–17 ] devoted to the understanding of a radial p-i-n junction thin film solar cell, and most of these works have been focused on a simplified situation with periodic up-right standing RJ array, which is however very different from the actual tilted RJ units observed for example in the SEM image of Fig. 1(a) . A comprehensive understanding of the light harvesting performance of the RJ cells based on low-cost VLS-grown SiNWs is still lacking, but definitely needed to provide instructive guide for experimental explorations.

 

Fig. 1 (a) SEM image of the radial p-i-n junction (RJ) a-Si:H thin film solar cells constructed over randomly oriented VLS-grown SiNWs, with a schematic illustration of the multilayer structure with an ITO top contact presented in (c); (b) A comparison of the experimental EQE response (black) of the RJ cells, as seen in (a), to the simulated EQE response of a periodic up-right standing RJ arrays (red) and that of a planar reference with the same i-layer thickness (blue); (c) shows the definition of the incident polarization situation as a TE mode or a TM mode with the E field component being aligned with the x-axis or the y-axis, respectively; (d) displays the different geometric configurations of an upright standing RJ matrix and that of an aperiodic random one.

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A fundamentally interesting, as well practically important, concern for building such a 3D radial p-i-n junction solar cells lies in that, mutual or self-shadowing becomes a quite common situation that would cause non-uniform photo-current generation among/or along the standing RJ units. (Note that here the “shadow” effect refers to only a geometric situation where the junction region is not directly exposed to the normal incident light, or not in line-of-sight). This issue is absent or far less important in conventional planar solar cells, but has to be taken into account seriously in choosing a best trade off in the SiNW length design, particularly when one comes to construct RJ solar cells over a random matrix of VLS-grown SiNWs on low cost glass substrates instead of periodic array of up-right standing Si nano-pillars. Another interesting aspect for the 3D RJ cells is based on the fact that, the resonant modes established in the cavity-like RJ units have been proposed as an advantageous mechanism that will contribute to a strongly enhanced light incoupling and harnessing [18, 19 ]. However, this benefit is apparent only for a singly isolated up-right standing RJ unit, where a larger-than-projection-area absorption cross-section leads to a strongly enhanced absorption [20, 21 ]. Whether this mechanism will really contribute to the absorption enhancement within a matrix of tilted RJ cells, and to what extent, remains still an open question to explore.

In this work, we first carry out a straightforward comparison of our experimental and theoretical simulation results of a-Si:H RJ solar cells. In spite of a distinct random-oriented and tilted configuration in the experimental realization [see Fig. 1(a)], a quite reasonable agreement between the experimental and the calculated external quantum efficiency (EQE) curves have been achieved with periodic up-right standing configuration adopted in simulation [Fig. 1(d)]. Then, we come to explore the impact of different tilting angles upon the absorption achieved in the RJ matrix, taking into account different polarization and spatial separation conditions. Our results indicate, somewhat to our surprise, that as long as the distance between the RJ is small compared to their length, $W<0.4 L$, the light harvesting realized within RJ thin film solar cells is quite robust against geometric variations, tilting and shadowing effects. Furthermore, based on the concepts of light injection and propagation in optical fiber (to which the RJ unit resembles very much), we propose also a simple but instructive theoretical tool to single out the contribution arising from the mode-resonant-enhanced light incoupling into the RJ matrix, against otherwise a sidewall scattering incoupling scenario. All these results presented here highlight the unique light harvesting distribution and strategy within a 3D radial junction architecture, which will provide instructive guide and insight in seeking further optimal structural design.

2. Experiments and Simulations

The radial junction thin film solar cells were grown via a tin (Sn) nanoparticle mediated VLS process upon AZO-coated Corning glass in a plasma enhanced chemical vapor deposition (PECVD) system, with a multi-layer structure comprising of p-doped SiNW core, intrinsic a-Si:H, n-doped a-Si:H and top ITO contact, as illustrated schematically in Fig. 1(c) and seen in the SEM imaging shown in Fig. 1(a). Details in the thin film solar cells deposition are available in our previous works [9]. As we can see, most of the radial junction solar cells are not in an upright standing posture, which are determined by the random orientations of the SiNWs during VLS growth. The external quantum efficiency (EQE) of the radial junction thin film solar cells were first measured by shedding incident light through the top transparent ITO layer at different wavelengths, from 350 nm to 800 nm, and presented in Fig. 1(b). Then, taking the geometrical dimensions of the multi-layer thickness, the length and separation of the RJ solar cell units as input, as well as an accurate data set of the thin film material data extracted from Ellipsometry Spectroscopic characterizations (over corresponding planar thin film structure, see Supplementary Materials S.1 in Ref [9]. for their n-k curves), we establish a theoretical model with exactly periodic and up-right standing array of RJ units and calculate the light field incoupling and absorption realized within the RJ matrix by using RF Module @ COMSOL Multiphysics Suite. More specifically, the p-doped SiNW core with a diameter of 40 nm and a length of 1~2 $\mu m$ is located in the center, covered sequentially by a 100 nm thick intrinsic a-Si:H absorption layer, a 15 nm thick $n^{+}$ window layer and a 50 nm ITO coating layer.

In order to assess the light harvesting within the RJ units, the absorption power distribution realized within the intrinsic absorption layer has been calculated by

In fact, the effective absorption power of $W_i^{a-Si:H}$ corresponds to an upper-bound of the external quantum efficiency (EQE) of the thin film solar cells, assuming that the absorption of one photon generates only one electron-hole pair.

3. Results and discussions

As seen in Fig. 1(b), in spite of the distinctive geometric arrangement, our simulation based on a periodic array of up-right standing RJ units has reproduced very well the overall trend of the EQE response measured experimentally. Compared to the simulated EQE responses of the RJ thin film solar cells to that of a planar reference (with the same absorber i-layer thickness), the contribution of an enhanced light trapping and absorption effect realized within a 3D architecture is indeed quite prominent, particularly to the long wavelength end. The difference between the experimental and the theoretical EQE curves should be reasonable considering the fact that the internal quantum efficiency should be less than unity in an actual radial junction solar cell. In Fig. 1(b), we observe a quite reasonable prediction of the overall EQE evolution trend of the RJ solar cells. So, is it true that a tilting geometry among the RJ matrix, as depicted in Fig. 1(d), has little influence on the light harvesting performance? How and to what extent this could be valid emerges as an intriguing question to explore.

To shed light upon this aspect, it will be critical to gain a comprehensive understanding on how the incident light field will incouple and propagate among a tilted array of RJ units. This has been taken into account in a RJ model configuration demonstrated in Fig. 1(c). It is important to note that, in a tilted geometry, the polarization symmetry (valid for an up-right standing geometry) is broken. Thus, the incidences with different polarization have to be taken into account separately. Therefore, the light field distributions with the electric component aligned with x-axis (defined as TE polarization) and y-axis (TM polarization) are shown in Fig. 2 and Fig. 3 , respectively. The first-row panels in Fig. 2 or Fig. 3, labeled as (a), (b) and (c), display the “Light field distribution” for incident wavelengths at 350 nm, 550 nm and 750 nm, respectively, with their corresponding “Absorption profiles” in the multi-layer junction structures presented in the panels just below. Note that, in all the tilting-angle-variant simulations carried out hereafter, the bottom planar p-i-n junction layer has been removed to allow us to focus on the contribution arising from the RJ cells, and for the sake of simplicity.

 

Fig. 2 The incident light field distributions and their corresponding absorption profiles realized within a tilted (30 Degree) array of RJ units at different incident wavelengths under TE mode polarized incidence are presented in (a)-(c) and (d)-(f), respectively.

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Fig. 3 The incident light field distributions and their corresponding absorption profiles realized within a tilted (30 Degree) array of RJ units at different incident wavelengths under TM mode polarized incidence are presented in (a)-(c) and (d)-(f), respectively.

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As we can see, the absorption of high energy photons happens only superficially at the outer shells (ITO and n + window layers), while longer wavelengths have deeper penetration depth into the RJ units. The strongest absorption has been achieved at wavelengths from 550 nm to 600 nm, where the overlapping of the incident light field and the absorption strength (which decreases monotonically with longer wavelengths) reach a best trade-off. Interestingly, regardless of the different incident wavelengths, we observe clearly an oblique propagation of the light field along the tilted sideway among RJ units. Even for the short wavelengths @350 nm incident, the mutual shadowing effect doesn’t manifest for either a TE or TM-polarized incidence, or is less prominent as seen in both Fig. 2(a) and Fig. 3(a). With the increase of the wavelength of incident photons, the propagation of light field into the “shadowed” area becomes easier for both polarization situations, as seen in both Fig. 2 and Fig. 3.

Looking at the absorption profiles in Fig. 2 and Fig. 3, we notice that the absorption intensity along a tilted RJ unit is not uniform. Interestingly, the face-down back-halves (experience self-shadowing) seem to realize a higher absorption than that in the face-up front-halves. This is particularly true among the top segments of the RJ cell units, while in the bottom segments the discrepancy becomes less prominent (as witnessed in Fig. 2(e) and Fig. 3(e) for incident with two different polarization states). To quantify these observations, we carry out a series of volume integrations of the absorption power, within the face-down and lower halves of a tilted RJ unit separately, and plot their integrals as a function of the distance measured from the bottom to the top. As seen in Fig. 4(a) , under TE mode incidence, the absorption achieved in the back face-down half of the RJ unit (represented by a red curve in Fig. 4(a)) is basically the same, if not higher, as that achieved in the front face-up half (green curve). Strikingly, in the lower segment of the RJ unit, starting more or less from the middle, the back-half even out-performs its front-half counterpart. A similar trend is also observed for the TM incidence, but now with a higher absorption in the back-half for the top segment. Taking a 50-50 weighting average, it is clear that the absorptions realized in the front or the back halves of the RJ units (among a matrix arrangement) are basically the same. In other words, the self-shadowing effect has only negligible influence for a tilting RJ matrix, while a non-uniform absorption profile does exist along the length of RJ unit. This also indicates an important aspect to be taken into account in the design of the RJ solar cells, where a photo-current generation gradient could impose a limit for achieving a high Fill Factor and voltage output.

 

Fig. 4 (a) and (b) present the distribution of absorption intensity realized within the face-up front-half and the face-down back-half of the tilted RJ cells, along the length measured from the bottom, under TE mode TM mode incidence, respectively ; (c) and (d) show the normalized EQE responses (with 50%-50% TE and TM mode weighted) with a tilting angle = 0°,15°,30°, with an inter-cell spacing of W = 0.4L, and W = 0.8L, respectively, where L stands for the length of the RJ cell.

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In Figs. 4(c)-4(d), we calculate the EQE responses of a tilted RJ matrix with different density (or spatial separation), under different angle of $\theta =0, {15}^o,{30}^o$, and the EQE curves are obtained with 50-50 weighting for TE and TM incidences. Interestingly, for a dense RJ matrix, with a RJ unit separation of $W=800 nm=0.4 L_{RJ}$ (corresponding to an areal density of $~2\times {10}^8/c{m}^2$), we found that the tilting angle has basically negligible influence on the overall absorption performance, as witnessed in Fig. 4(c). However, the tilting effect manifests itself in a sparser matrix (with $W=1600 nm=0.8 L_{RJ}$), as seen in Fig. 4(d), where a tilting angle from 15 to 30 Degree seem to have a broader absorption compared to that of up-right standing situation. Meanwhile, resonant absorption peaks emerge at wavelengths of 550 nm, 650 nm and 725 nm for the up-right standing RJ units, as marked by three arrows in Fig. 4(d), while these signals quickly disappear or displace under tilting angles. Therefore, as long as the RJ matrix is dense enough, probably within the range of effective absorption cross-section of individual RJ units, a tilting angle by itself is not a critical parameter. This finding paves the way for adopting a properly controlled random matrix of VLS-grown SiNWs as the framework in pursuit of high performance RJ thin film solar cells.

Compared to the planar thin film solar cells, resonant mode incoupling and absorption enhancement represents another unique aspect for the RJ solar cell units. Within a matrix of random RJ solar cells, as schematically illustrated in Fig. 5(d) , there could be two conceptually distinct ways that the incident light could interact with the RJ units, that is, 1) the incident light is captured and in-coupled into the resonant mode in a cavity-like RJ unit, following the concept of light injection into a fiber (that is possible only at the open end, not from the sidewall); or 2) the incident light scatters among RJ units and gets absorbed, but does not involve any mode resonance mechanism. In order to assess and distinguish the contribution arising solely from the fancy “resonant-mode-enhanced” absorption, we developed a simple but instructive simulation strategy, where the top end of the RJ units is set to be open or blocked (by boundary setting in simulation) to allow or forbid a resonant mode incoupling into the RJ units. Then, the difference in light absorption between these two situations is assign to the contribution only due to the resonant mode incoupling and absorption. As seen in Figs. 5(a) and 5(b), with tilting angle of $\theta =0 or 30$ Degree, the resonant mode contribution accounts for a small portion less than 20%. The highest contribution is recorded for up-right standing configuration, and then continuously decreases down to 12% with larger and larger tilting angles. This observation indicates that most of the light harvesting has been accomplished in a “scattering-absorption” scenario, while the resonant-mode-absorption accounts for only a relatively small portion.

 

Fig. 5 (a) presents the total absorption response (red), the absorption realized in a scattering scenario (black) and the absorption realized in a resonant mode incoupling into the RJ units (green), as schematically illustrated in (d), in an up-right standing RJ array; (b) shows the absorption breakdown for the situation with 30 Degree tilted RJ array; The influence of the tilting angle on the percentage of the absorption contributions from different light incoupling scenarios are summarized in (c).

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4. Summary

In summary, we have carried out a comprehensive investigation of the impacts of geometric tilting and arrangement of radial junction thin film solar cells, by examining the detailed absorption profile and different light incoupling mechanisms, and comparing the simulation results to the experimental quantum efficiency responses. We found that the light harvesting realized by a 3D radial junction structure is quite robust against a tilting arrangement, or in other words the effect of mutual and self-shadowing, given a relatively close packing with respect the length of RJ unit. More interestingly, our simulation has been able to single out the contribution arising from the resonant-mode-enhanced absorption into the cavity-like RJ unit. These results have provided a unique perspective and practical guide in seeking an optimal structural design dedicated to RJ thin film solar cells.