ABSTRACT The radial junction (RJ) architecture has proven beneficial for the design of a new generation of high performance thin film photovoltaics. We herein carry out a comprehensive

modeling of the light in-coupling, propagation and absorption profile within RJ thin film cells based on an accurate set of material properties extracted from spectroscopic ellipsometry

measurements. This has enabled us to understand and evaluate the impact of varying several key parameters on the light harvesting in radially formed thin film solar cells. We found that the

resonance mode absorption and antenna-like light in-coupling behavior in the RJ cell cavity can lead to a unique absorption distribution in the absorber that is very different from the

light trapping due to the presence of the RJ cell array. SIMILAR CONTENT BEING VIEWED BY OTHERS ELECTRICAL PERFORMANCE OF EFFICIENT QUAD-CRESCENT-SHAPED SI NANOWIRE SOLAR CELL Article Open

access 07 January 2022 EFFECTIVE INDEX MODEL AS A RELIABLE TOOL FOR THE DESIGN OF NANOSTRUCTURED THIN-FILM SOLAR CELLS Article Open access 17 April 2023 PROGRESS AND PROSPECTS FOR ULTRATHIN

SOLAR CELLS Article 02 November 2020 INTRODUCTION Radial junction (RJ) solar cells1,2 have been fabricated by deposition on top of a matrix of Si nanowires (SiNWs), prepared either by

template-assisted etching into Si wafers3,4,5 or by self-assembled growth on low-cost substrates6,7,8,9. Prototype devices of this kind indeed demonstrate superior light harvesting

performance, achieved due to _a__long__optical absorption length_ while using only _a__thin absorber/or junction layer_4,5,10,11. Though several recent works have addressed the full-field

simulation of an array of Si nanowire/rods or radial _p-n_ junctions12,13,14, the light in-coupling and absorption profile in a more sophisticated and complex multilayer _p-i-n_ thin film

solar cell structure, as well their implications for device performance, remain largely unexplored. Within a coaxial RJ thin film solar cell, a sequence of layers of materials with

distinctive optical properties are deposited around individual SiNW cores7,9,15,16. In such a 1D cavity-like composite, photonic and resonant mode-matching effects in the RJ units via

optical antenna coupling or leaky-mode-resonance13,17,18,19 can play an important role in determining light absorption and scattering. These phenomena have been observed experimentally in RJ

solar cells fabricated over individual upright20 or surface-lying15 nanowires. How this resonant absorption or scattering will affect the light harvesting behavior in a coaxial _p-i-n_

junction thin film solar cell remains an interesting aspect to address. Furthermore, in pursuit of an optimal light harvesting configuration but that can be easily electrically contacted, a

“forest” of nanowires standing upright on a substrate surface could provide an ideal and realistic architecture for making and contacting large areas of RJ solar cells. Therefore, a

comprehensive and accurate description of the light in-coupling, propagation and absorption profile within the coaxial multilayer structure will be very helpful to shed more light upon the

critical issues and to design a new generation of high performance RJ thin film solar cells. In this study, we focus on a coaxial RJ solar cell, as illustrated in Fig. 1(a), fabricated

around SiNWs grown via a vapor-liquid-solid (VLS) mechanism catalyzed by a low-melting-point metal such as tin (Sn)21,22,23,24. Low-melting-point metal catalysts, including Sn, In, Ga and

Bi, allow one to achieve the low-temperature growth (down to 240°C) of a well-defined matrix of SiNWs22,25. This low-temperature process is compatible with becoming a mature thin film

technology, as well as having the benefit that the metal remnants can be cleaned off easily by a simple H2 plasma etching without the need to break vacuum for _ex-situ_ chemical

etching/cleaning7,9,24. Figure 1(b) presents a scanning electron microscopy (SEM) view of such a structure. Our recent progress using this structure has led to the demonstration of high

performance radial p-i-n junction amorphous silicon (a-Si:H) thin film solar cells with a power conversion efficiency of 8.14%7, all fabricated in a conventional plasma enhanced chemical

vapor deposition (PECVD) system. Our goal in this work is therefore to establish a comprehensive optical model for a coaxially-deployed multilayer RJ thin film solar cell, in order to

develop critical clues and a new strategy for optimizing such devices. EXPERIMENTAL DESCRIPTION The RJ solar cells were deposited on a matrix of SiNWs grown on top of ZnO:Al coated Corning

glass (Cg) substrates. The Sn catalyst droplets were formed _in situ_ by a H2 plasma treatment of a 2 nm thick (nominal) Sn layer evaporated on the ZnO:Al substrate. SiNWs were grown and

doped p-type by flowing a mixture of silane (SiH4) and H2-diluted TMB [(CH3)3B] during the plasma-enhanced VLS growth. The detailed fabrication procedure and deposition parameters are

available in our previous work7. As one can see in Fig. 1(b), the typical SiNW features a gradually tapering shape with a length of _L__w_ ~ 1.7 μm, a diameter of ~40 nm in the middle and a

sharp tip of <20 nm. As the next step, an intrinsic a-Si:H layer (typically ~100 nm thick) and an n-type doped a-Si:H emitter layer (of ~10 nm) were coated consecutively over the SiNWs,

followed by a sputtered indium-tin-oxide (ITO) top contact (Tito ~ 50 nm) over the RJ cell. The RJ cells without and with the TCO coating layers are shown in Fig. 1(c) and 1(d),

respectively, while an internal multilayer structure consisting of p-type SiNW-core (_p_)/intrinsic a-Si:H (_i_)/n-type a-Si:H (_n_)/ITO contact is depicted in Fig. 1(a). FORMULATION AND

SIMULATIONS To carry out an accurate simulation, the optical dispersion n-k curves of each material have been extracted from the modeling of spectroscopic ellipsometry measurements on

co-deposited planar thin films (as shown in S.1 in Supplemental Materials). In this RJ simulation, we assume the SiNW core is represented by a cylinder of radius _R__w_ = 20 nm and with

lengths (_L__w_) from 0.6 μm to 2.4 μm. The intrinsic a-Si:H layer thickness (_T__i_) has been varied from 20 nm to 140 nm, while the thickness of the n-type a-Si:H layer and ITO layers are

fixed to be typical values of _T__n_ = 10 nm and _T__ito_ = 50 nm, respectively, consistent with what is seen in Fig. 1(b) to 1(d). In our simulation, a single radial cell is placed at the

center of a square simulation box (1.5 μm × 1.5 μm) on top of a glass substrate. Polarized light propagating along the y-axis originates from the top plane. Dissipative scattering conditions

are applied to the entirety of the wall and bottom boundaries. The finite element solver module in COMSOL MULTIPHYSICS was used to carry out the structural modeling and optical simulation.

In contrast to the situation of radial p-n junction solar cells fabricated on Si wafers3,26, the incident light has to go through first the top TCO and then the n-type emitter layers before

arriving at the inner intrinsic a-Si:H absorber in the radial p-i-n junction thin film solar cell. As a consequence, assessing the optical propagation and losses within the coaxial radial

configuration is a critical issue. In the upper panel in Fig. 2(a), we show the _E__y_-field distribution in a SiNW RJ solar cell unit under different incident wavelengths of λ = 350 nm, 550

 nm and 750 nm, with a SiNW length of _L__w_ = 1.7 μm and i-layer thickness of _T__i_ = 100 nm. At λ = 350 nm (with high energy photons), the incident light is screened by the outer ITO and

n-type emitter layers, with only a small fraction reaching the buried absorber i-layer. At long wavelengths (λ = 550 nm to 750 nm), the incident light propagates deeper into the RJ and can

be better coupled into the cavity-like RJ cell, which starts to behave particularly like a waveguide or antenna at λ = 750 nm. Based on these field distribution results, the local power

dissipation - that is the local absorption occurring within the RJ multilayer - is calculated according to where _I__light_ is the local electromagnetic energy intensity, _c_ is the speed of

light in vacuum, α(λ) and _k_(λ) are the absorption coefficient and the imaginary part of the complex refractive index . The corresponding power absorption mappings in the RJ cell structure

are calculated and presented in the lower panel of Fig. 2(b). The absorption of high energy photons (λ = 350 nm) mostly takes place within the outer ITO and n-type emitter layers, with

little absorption occuring in the PV active inner intrinsic a-Si:H layer. At λ = 550 nm, the inner i-layer becomes the dominant zone for light harvesting, while the absorption in the c-SiNW

core remains still very weak, in spite of a strong field within the core region as seen in the corresponding _E__y_ field distribution in Fig. 2(a). This is because at λ = 550 nm, the

absorption coefficient of a-Si:H is almost two orders of magnitude higher than that of c-Si (typically α_a-Si:H_/α_c-Si_ ~ 102). At the even longer wavelength of λ = 750 nm, when the

incident photon energy approaches the optical bandgap of the a-Si:H absorber matrix, the incident light has been strongly confined within the RJ cell. However, the effective absorption

realized within the intrinsic a-Si:H layer drops dramatically, see Fig. 2(b), while most incident photons get absorbed in the center SiNW, which is considered as a dead zone because the high

doping level in the SiNW core electrode. Close examination of the absorption mapping at λ = 550 nm shown in Fig. 2(b) reveals yet more intriguing features of the absorption profile within a

single RJ cell. For example, the highest absorption regions in the i-layer are actually located very close to the inner i-layer/SiNW interface, as witnessed in the enlarged inset in Fig.

2(b) for λ = 550 nm, instead of at the outer emitter/i-layer interface, as one would expect in a planar p-i-n thin film solar cell. In Supplemental Material S2, absorption profiles within

the RJ solar cell unit at varying incident wavelengths running from 300 nm to 800 nm are compiled and displayed in an animation clip. We found that this feature is a rather common

characteristic for wavelengths longer than roughly λ > 475 nm. Furthermore, to give a quantitative estimation of PV performance, we also calculate a solar-spectrum-weighted absorption

profile _P__av_ within a RJ solar cell unit, as shown in Fig. 3, defined as where _W__AM_1.5(λ) is the weighting factor derived from the standard AM1.5 solar mass spectrum with when

integrating over λ = 300 nm to 800 nm (the most relevant spectrum range for a-Si:H absorption). Note that, the _x_-axis to _y_-axis aspect ratio in Fig. 3 has been intentionally enlarged to

3:1 to deliver a better view of the low absorption density variation in the lateral direction. It is clear that the absorption intensity profile shows its highest absorption zones in the

vicinity of the inner i-layer/SiNW core interface, instead of the outer emitter/i-layer interface. This phenomenon indicates that the incident light has been coupled effectively into the RJ

structure, following the field distributions of the resonant propagating modes within the 1D RJ cell cavity. We note that this scenario is strikingly different to the situation in planar

p-i-n junction a-Si:H cells, where the highest absorption zones are always located at the outer emitter/i-layer interface and therefore a p-type emitter layer is always preferable to shorten

the collection distance of photo-generated holes (considering its lower mobility in the a-Si:H matrix). Our finding here reveals however a quite different situation, in that a higher

concentration of photo-carriers are generated in close proximity to the inner interface and thus a p-type SiNW core should become more favorable. This is indeed an important design

constraint for optimizing RJ a-Si:H thin film solar cells. Furthermore, by integrating the absorption in each material layer of the RJ solar cell, we are able to calculate the effective

absorption power _P__eff_(λ) within the absorber i-layer as a function of photon wavelength ranging from 300 nm to 800 nm. As we can see in Fig. 2(a), the RJ cell can harness the incident

light over a cross sectional area much larger than its physical diameter, that is, the light can be effectively collected into the 1D RJ cell (like a waveguide or an antenna)20,27. This

becomes more prominent for the incidence at long wavelengths. So, when we hope to address the absorption potential of an individual RJ, the finite lateral dimension of the square simulation

box _W__sub_ should be large enough to exclude (or at least minimize) the boundary effects. To be sure of this point, we first calculate the _P__eff_(λ) curves with different box dimensions,

extending from _W__sub_ = 0.8 μm to 2.2 μm. Their corresponding _P__eff_(λ) curves and overall absorption integral (_P__oa_) from λ = 300 nm to 800 nm are presented in Fig. 4(a) and 4(b),

respectively. We found that the overall integral increases gradually with _W__sub_ before saturating at _W__sub_ = 1.5 μm and above, indicating that from this point on the RJ cell becomes

basically optically isolated within the wavelength range investigated here. Based on this observation, we define an effective overall absorption cross-section area of for such a single RJ

a-Si:H cell and extract an enlargement factor (_F_) of _S__oc_ over its physical cross section area (_S__RJ_) of the RJ cell as From this point on, we choose to fix the simulation box

dimension to _W__sub_ = 1.5 μm in the following simulations unless otherwise specified. To understand the optical losses and effective absorption within the RJ cell, let us look at the

absorption broken down by layer in Fig. 5(a), for a typical RJ a-Si:H solar cell unit, as seen in Fig. 1(b)–1(d) with _L__w_ = 1.7 μm, _T__i_ = 100 nm and _W__sub_ = 1.5 μm. The absorbed

power is plotted the on y-axis in log-scale. It is clear that a majority of the absorption losses at short photon wavelengths (below 400 nm) are caused by the outer ITO and n-type a-Si:H

emitter layers. In particular, the n-type a-Si:H accounts for quite a large portion of the overall losses, emphasizing the need to adopt a wider band-gap emitter, for instance doped a-SiC28

or μc-SiOx29,30 layers. In the long wavelength region, the absorption losses in ITO contact become dominant, while the absorption in both i-layer and n-type emitter drop rapidly when

approaching the bandgap of a-Si:H. Figure 4(b) shows the absorption occurring in the i-layer as a percentage of the total absorption in the RJ cell, shown for i-layer thicknesses (_T__i_)

ranging from 20 nm to 140 nm. As expected, a thicker i-layer can boost absorption for longer wavelengths λ > 450 nm, but this tends saturate for _T__i_ > 100 nm. Further increasing the

thickness up to 140 nm leads to only marginal gain and only for wavelengths >700 nm when the absorption in a-Si:H becomes very weak. It is noteworthy that the i-layer thickness of 100 ~

140 nm used here is only 1/3 ~ 1/2 of the typical a-Si:H i-layer thicknesses used in optimized planar p-i-n junction a-Si:H solar cell (280 or 300 nm to balance absorption and collection). A

thinner i-layer establishes a stronger electric field in the i-layer, facilitating photo-carrier separation and collection and thus helps to improve solar cell efficiency and

stability28,31,32. Another important parameter of the RJ thin film solar cell is the length _L__w_ of SiNW, which represents a new dimension to adjust in the 3D RJ architecture, in contrast

to their planar counterparts. In Fig. 5(c), we plot _P__eff_ as a function of the length of SiNWs, ranging from 0.6 μm to 2.4 μm. With increasing _L__w_, there is an overall enhancement of

the i-layer absorption for wavelengths λ < 650 nm, while for the longer wavelengths the absorption enhancement is rather marginal. The integral of _P__eff_ from 300 nm to 800 nm has been

calculated and shown in Fig. 5(d), where we see first a fast increase of _P__eff_ absorption with the SiNW length, then followed by a clear saturation trend. At λ > 650 nm, the absorption

coefficient of a-Si:H matrix drops quickly and the absorption of incident light is dominated by the ITO layer and c-SiNW core as shown in Fig. 5(a), as well as by the dissipation on the

damping boundary walls. To quantify the overall light harvesting behavior as a function of the length of RJ cell, we fit the data in Fig. 5(d) following the formulation of _Lambert-Beer_

law, which can be written as and extract a saturation absorption of _P__eff_0 = 2.67 × 10−12 _W_ for _L__w_ → ∞, as shown in Fig. 5(d) by a dashed horizontal line and an overall

_pseudo-absorption coefficient_ for such a single RJ cell to be α_RJ_ = 1.16/_μm_ (or 1.16 × 104/cm). According to this prediction, a RJ cell with a 1.7 μm long SiNW core already absorbs

~86% of the light absorbed by an infinitely long RJ cell. This provides a very useful and practical guide to evaluate the benefit of growing long SiNWs, against the need to keep the SiNW

short to facilitate the conformal coating of closely spaced SiNWs. Furthermore, the impact of the i-layer thickness (_T__i_) on the total light harvesting behavior has been studied. In this

simulation, we fix the length of the SiNW at _L__w_ = 1.7 um. The calculated absorption curves for different _T__i_ ranging from 20 nm to 140 nm are shown in Fig. 6(a). With the increase of

i-layer thickness from 20 nm to 80 nm, the effective light absorption _P__eff_ enhances greatly over the full spectrum, particularly in the range from 450 nm to 650 nm. Interestingly, upon

all the _P__eff_ curves, we observe superimposed absorption peaks that seem to shift systematically with i-layer thickness. To clarify this trend, we have normalized all these curves to

their maxima in Fig. 6(b) to reveal a clear blue-shifting of the absorption peaks with decreasing i-layer thickness. To understand this point, we have carried out a 2D mode analysis on the

cross section of a coaxial RJ cell with an i-layer thickness of _T__i_ = 140 nm. At the wavelength of the absorption peak at λ = 614 nm, we search for the first 6 propagation modes in the RJ

cavity and then integrate their individual contributions to the power absorbed within the i-layer region. We found that the highest contribution comes from a pair of propagation modes with

mutually orthogonal field distribution patterns, one of which is shown in Fig. 6(c). As we can see, for this cavity mode, the field distribution is concentrated in the annular i-layer,

resulting in a maximal useful absorption in the RJ cell. On the contrary, other propagation modes found in the RJ cavity (not shown here) display effective wave-guiding around the RJ cavity,

but have their field intensity maxima falling out of the intrinsic absorber layer (either in the outer ITO/n-type layer or concentrated into the highly doped p-type SiNW core). Such

distributions lead to a much lower useful absorption for the radial p-i-n junction thin film solar cell. This resonant-mode-selection feature/or criterion is indeed a unique aspect in the

coaxial radial p-i-n cell, as compared to the situation in a simple radial p-n junction solar cells. Finally, assuming that the absorption of one incident photon (with energy higher than the

bandgap of a-Si:H) generates only one electron-hole pair and a rapid thermalization of the hot photo-carriers occurs, the absorption _P__eff_ curve should correspond/or be proportional to

the external quantum efficiency of a single RJ cell (excluding recombination issues). We therefore compare, in Fig. 7(a), the normalized _P__eff_ curves with i-layer thickness of 80 nm

(red), 100 nm (green) and 120 nm (blue) to the normalized experimental EQE spectrum (black), measured on a real RJ cell array shown in the top-view SEM image of Fig. 7(b). The i-layer

thickness of the RJ cell array is around 100 nm with a statistical spread as shown in the inset of Fig. 7(c). As a consequence, though there is a specific resonant peak position for each

i-layer thickness, the weighted-average response curve becomes rather smooth and featureless. As we can see in Fig. 7(c), the agreement between the simulated overall absorption curve and the

actual normalized EQE curve over the short-wavelengths (from λ = 300 nm to 550 nm) is indeed excellent, indicating that the light harvesting of short-wavelength photons can be mostly

assigned to the separately contribution from individual RJ cells. In other words, the short-wavelength photons have been effectively harvested during their first pass through the radial

_p-i-n_ junction, with basically no contribution from the light trapping among neighboring RJ cells. At longer wavelengths, we notice a higher EQE response was measured for the actual

“forest” of RJ solar cells, compared to the simulated response for a single RJ solar cell. This can be seen more clearly in Fig. 7(d), where the enhancement ratio of the normalized

experimental EQE over the absorption response of a single RJ cell is plotted as a function of incident wavelength. We note that the enhancement factor is close to unity for wavelengths below

<550 nm, but scales up monotonically with the increase of the wavelength. This observation implies that the contribution of light trapping arising from multiple scattering events among

individual RJ units is indeed wavelength-dependent. This is reasonable if we recall the fact that at long wavelengths, the absorption coefficient of a-Si:H absorber drops rapidly and

therefore allows multiple passes of the incident photons through the RJ cell units before being absorbed. Therefore, the benefit of strong light trapping gradually manifests itself at longer

incident wavelengths. Alternatively, the greater experimental long-wavelength EQE can also be explained by the overlapping of the absorption cross-sections of neighboring RJ cells within a

dense RJ forest as seen in Fig. 7(b). Though other factors or geometrical considerations (for example the somewhat random orientation of the VLS-grown Si nanowires on glass) could also be

responsible for this behavior and need to be better understood in future studies, we emphasize that this comparison provides a unique perspective, emphasizing the relative importance of the

light trapping effect in a matrix of RJ cells compared with the impact of the geometry of individual RJ cells. CONCLUSION In summary, we have presented a comprehensive optical model of a

single radial junction a-Si:H thin film solar cell, which incorporates a complete set of accurate optical material properties in each layer. Our simulations have been able to reveal the

detailed light in-coupling, propagation and absorption profile in the complex coaxial multilayer solar cell structure, as well as the impact of varying a set of critical geometrical

parameters. We also investigate the impact of photonic effect/resonant-mode enhanced absorption within the quasi-1D cavity radial junction cells and NW design criteria for achieving maximal

light absorption. These simulation results are further compared to experimental results on radial junction a-Si:H thin film solar cells fabricated on VLS-grown SiNWs. We note that the

findings developed herein for RJ a-Si:H thin film solar cells are, in principle, applicable to radial junction solar cells fabricated by other techniques in different material systems and

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CAS  Google Scholar  Download references ACKNOWLEDGEMENTS The authors L. YU, J. Wang, S. Qian, J. Xu and Y. Shi thank the following for financial support: Jiangsu Province Natural Science

Foundation (Young Talent Program No. BK20130573) and National Basic Research 973 Program under Grant Nos 2014CB921101, 2013CB932900 and NSFC under Nos 61036001 and 61204050. AUTHOR

INFORMATION AUTHORS AND AFFILIATIONS * School of Electronics Science and Engineering/National Laboratory of Solid State Microstructures, Nanjing University, 210093, Nanjing, China Linwei Yu,

 Junzhuan Wang, Shengyi Qian, Jun Xu & Yi Shi * Laboratoire de Physique des Interfaces et Couches Minces (LPICM), Ecole Polytechnique/CNRS, 91128, Palaiseau, France Linwei Yu, Soumyadeep

Misra, Martin Foldyna, Erik Johnson & Pere Roca i Cabarrocas Authors * Linwei Yu View author publications You can also search for this author inPubMed Google Scholar * Soumyadeep Misra

View author publications You can also search for this author inPubMed Google Scholar * Junzhuan Wang View author publications You can also search for this author inPubMed Google Scholar *

Shengyi Qian View author publications You can also search for this author inPubMed Google Scholar * Martin Foldyna View author publications You can also search for this author inPubMed 

Google Scholar * Jun Xu View author publications You can also search for this author inPubMed Google Scholar * Yi Shi View author publications You can also search for this author inPubMed 

Google Scholar * Erik Johnson View author publications You can also search for this author inPubMed Google Scholar * Pere Roca i Cabarrocas View author publications You can also search for

this author inPubMed Google Scholar CONTRIBUTIONS L.Y., S.M., J.W. and P.R. designed/conducted the experiments and simulations, wrote the main manuscript text and prepared the figures. S.Q.,

M.F., J.X., Y.S. and E.J. have participated in analyzing the data and reviewing this manuscript. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial

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ARTICLE CITE THIS ARTICLE Yu, L., Misra, S., Wang, J. _et al._ Understanding Light Harvesting in Radial Junction Amorphous Silicon Thin Film Solar Cells. _Sci Rep_ 4, 4357 (2014).

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