Design of μc-Si:H/a-Si:H coaxial tandem singlenanowire solar cells considering photocurrent matching Guoyang Cao,1,2 Xiaofeng Li,,1,2,* Yaohui Zhan,1,2 Shaolong Wu,1,2 Aixue Shang,1,2 Cheng Zhang,1,2 Zhenhai Yang,1,2 and Xiongfei Zhai1,2 1

College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China. 2 Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China. * [email protected]

Abstract: The single nanowire solar cells (SNSCs) with radial junctions are expected to show the superiority in efficient carrier collection benefited from the largely shortened junction length. Considering that the conversion efficiency of the existing SNSCs is still limited due to the low operation voltage, we design μc-Si:H(core)/a-Si:H(shell) radial tandem SNSCs, giving much attention to the intrinsic optical and electrical properties. The core and shell cells are carefully engineered in order to realize the photocurrent matching. It is found that under matching condition the radius of the entire cell (R) shows linear dependence on the radius of the core cell (r), i.e., R ~1.2r. Under an optimal design of the tandem cell, the opencircuit voltage (photoconversion efficiency) is increased by 160% (34% relative) compared to the equivalent-size μc-Si:H SNSCs. © 2014 Optical Society of America OCIS codes: (040.5350) Photovoltaic; (350.4238) Nanophotonics and photonic crystals.

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#222706 - $15.00 USD Received 10 Sep 2014; revised 17 Oct 2014; accepted 22 Oct 2014; published 31 Oct 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. S7 | DOI:10.1364/OE.22.0A1761 | OPTICS EXPRESS A1761

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1. Introduction Nanowire solar cells (SCs) have recently gained much attention due to their unique photonic and electronic benefits [1–6]. Unlike the nanowire arrays synthesized in large scale for conventional photovoltaic applications [5–13], compact single-nanowire solar cells (SNSCs) begin to come into focus by their promising potential in serving as the locally integrated power sources for nanophotonic or nanoelectronic circuits [3, 4, 14–16]. SNSCs are usually doped along the radial direction, since the radial junction in nanoscale permits a larger illumination area and a smaller diffusion length, which dramatically relaxes the stringent requirement of the high-quality materials. Therefore, materials with low diffusion length, such as amorphous silicon, can be wisely used to fabricate radial-junction SNSCs. However, as a prototype of radial p-i-n nanowire solar cell, the first SNSC fabricated by B. Tian et al was made of polycrystalline silicon and grown by the nanocluster-catalysed vapour-liquid-solid method [13]. The conversion efficiency of such a SNSC is 3.4%, limited by the low open-circuit voltage (Voc). To raise the Voc, tandem or multiple junctions are normally used in bulk photovoltaic cells [17]. Recently, the tandem Si SNSCs with axially doped semiconductor junctions were proposed and fabricated by Kempa et al and a Voc increment of 57% was realized [14]. However, the study on tandem SNSCs is still rare. The special photonic response and system configuration of SNSCs lead to quite uncommon optical and photoconversion performance when configured into tandem cells. In this paper, we focus on the μc-Si:H(core)/a-Si:H(shell) tandem SNSCs with radially doped semiconductor junctions, where the band gap wavelengths of μc-Si:H and a-Si:H materials are ~800 and 1100 nm, respectively. Through comprehensive optoelectronic simulations, the light-harvesting behavior based on leaky-mode resonance, the detailed intrinsic photoconversion process, and the photocurrent matching between junctions have been analyzed. It is found that the optimized and matched photocurrent can be realized by tuning the sizes of the core and shell cells, which are observed to exhibit an interesting linear relation. The electrical evaluation further indicates that a tandem design of SNSCs can dramatically improve the Voc, which leads to much enhanced photoconversion efficiency. Our #222706 - $15.00 USD Received 10 Sep 2014; revised 17 Oct 2014; accepted 22 Oct 2014; published 31 Oct 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. S7 | DOI:10.1364/OE.22.0A1761 | OPTICS EXPRESS A1762

complete optoelectronic design of tandem SNSCs permits an accurate and convincing prediction of the electrical performance of the nanowire photovoltaic devices. 2. Device and method The sketch of the tandem μc-Si:H/a-Si:H SNSCs is shown in Fig. 1(a), where the crosssectional architecture is inserted. The radial layers (outward direction) are doped selectively into p, i, n+, p+, i, and n regions, respectively, where n+ and p+ represent the heavily doped layers in order to form the tunnel junction [14]. The electrodes/contacts are highlighted in yellow. The radius of the core (i.e., μc-Si:H cell) is r and the thickness of the shell (a-Si:H cell) is R−r. The absorption coefficient spectra of α-Si:H (yellow) and μc-Si:H (pink) are plotted in Fig. 2(b) [18]. The optical absorption efficiency (i.e., Qabs) under transverse electric (TE) or transverse magnetic (TM) illumination can be obtained by solving the Maxwell's equations using finiteelement method (FEM) [19] with the optical constants taken from Palik [20]. The definitions of TE and TM waves can be found in Fig. 1(a). Qabs is defined as the calculated absorption cross-section Cabs divided by the geometric cross-section Cgeom, i.e., Qabs = Cabs/Cgeom, where Cgeom is the product of the diameter and the length of the nanowire and can be reduced to the diameter in a two-dimensional model as what is performed in our calculation. This is a rational simplification for a typical lying nanowire with an ultrahigh length-diameter ratio + QTM ) / 2. Therefore, the [21]. The unpolarized situation can be simulated by Qabs = (QTE abs abs ultimate photocurrent density Jph assuming a perfect internal quantum process [9] can be expressed by J ph =  λ2 λ1 qFS (λ)Qabs (λ)dλ , where q is the electron charge, λ is the wavelength, and FS is the spectral photon flux density of AM1.5G [22]. It should be noted that the above calculation of Jph has to be conducted for each cell which absorbs solar incidence within a specific spectral range. The output photocurrent of a tandem SC where the cells are connected in series is normally regulated by the lowest one. Therefore, the overall photocurrent (summation of all junctions) only reflects the total optical absorption, without containing sufficient information to show the actual electrical outcomes. Photocurrent matching is thus a crucial factor for the design of tandem or multi-junction SCs.

Fig. 1. (a) Sketch of the tandem SNSCs, where the doping categories, physical sizes and definitions of TE/TM incidences are all shown. (b) The absorption coefficient spectra of αSi:H (yellow) and μc-Si:H (pink).

3. Results and discussions For SNSCs, the device dimension plays a key role in determining the optical absorption efficiency [23–25], as the optical resonating characteristics of the subwavelength cavity are extremely sensitive to the system configuration. To maximize the photoconversion efficiency of the tandem SNSCs, the dimensions of the core and shell cells have to be carefully designed so that the highest matched photocurrent can be achieved. Figure 2 plots Qabs vs λ and R, where r is fixed to be 200 nm for initial evaluation. In this study, both TE and TM incidences are considered and the absorptions by the core and shell cells are distinguished. We can see clearly that μc-Si:H core (a-Si:H shell) absorbs mainly long-wavelength (short-wavelength) solar incidence. In the short-wavelength region, the absorption pattern is relatively flat, #222706 - $15.00 USD Received 10 Sep 2014; revised 17 Oct 2014; accepted 22 Oct 2014; published 31 Oct 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. S7 | DOI:10.1364/OE.22.0A1761 | OPTICS EXPRESS A1763

showing that no strong cavity modes have been excited from the shell where the extinction coefficient of a-Si material is very high; nevertheless, multiple cavity resonances can be formed in the μc-Si:H core [see the absorption bands shown in Figs. 2(a) and 2(c)]. Increasing R without changing r (i.e., enlarging the shell cavity), the absorption of μc-Si:H core is weakened gradually and the corresponding resonances are red-shifted continuously, leaving more solar energy to be absorbed by the shell. The absorption redistribution greatly modifies the device output and can be effectively tuned to obtain a good match between the junction photocurrents. To validate the high tunability of the tandem SNSC, we calculate the Jph for the core and shell cells as a function of R [see Fig. 2(e)]. It shows that (under unpolarized incidence) Jph for the shell (core) is increased (decreased) rapidly with increasing R. A matched Jph = 6.76 mA/cm2 is realized when R ~245 nm. Moreover, according to Fig. 2(e), the virtual total Jph (i.e., core + shell) is increased gradually under an increasing device volume.

Fig. 2. (a)–(d): Qabs vs R and λ with r = 200 nm, where TE and TM incidences are considered and the absorptions of the core and shell cells are distinguished. (e): Jph (under unpolarized incidence) of the core and shell cells vs R with r = 200 nm, after spectral integration of the results shown in Figs. 2(a)–2(d) and taking the average of TE and TM incidences.

We next concentrate on the photocurrent output of the tandem SNSCs under a varying core radius r. As suggested by Fig. 2(e), to match the photocurrents for each r, a proper R has to be used, which can be realized through screening R. We have carried on such calculations and the results are plotted in Fig. 3, where the Qabs spectra (for the core and shell cells) under photocurrent-matching condition versus r under TE and TM incidences are displayed, respectively. Compared to Fig. 2, the resonance-shift in the spectrum is more distinct here as the device size is varied in a larger range. Moreover, the resonant wavelength shows a linear dependence on r. This can be explained by the coupled leaky-mode theory (CLMT) [24, 25], which indicates that the optical properties of semiconductor nanostructures are dictated by the complex eigenvalues (N) of the supported leaky modes. The real part of N (i.e., NRe) can be expressed as neffkr, where neff is the real effective refractive index of the system, k is the wavenumber, and r is the radius of the nanowire. NRe dictates the resonant condition and the  2πn eff  imaginary part of N (NIm) reflects the radiative decay. We then get λ s =   r. , which  N Re  clearly shows the linear dependence between λS and r. This theory applies as well to the considered tandem SNSCs since the real refractive indices of μc-Si:H and a-Si:H are very close. We now study on how to design the size of the entire cell (R) for a specific core radius (r) in order to maximize the matched photocurrent from the tandem SNSCs. For a design convenience, it would be very useful if an analytical relation between R and r could be derived. Using the method of Fig. 2(e), we calculated and recorded the appropriate R for r and plot the R−r curve in Fig. 4(a), where the matched Jph values are also shown for the readers’ information. An interesting finding is that R displays a linear dependence upon r, i.e., R ~1.2r. This allows to directly obtain the best design of the tandem SNSCs under a giving r without conducting the full-wave electromagnetic calculations. We have verified that this relationship

#222706 - $15.00 USD Received 10 Sep 2014; revised 17 Oct 2014; accepted 22 Oct 2014; published 31 Oct 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. S7 | DOI:10.1364/OE.22.0A1761 | OPTICS EXPRESS A1764

holds excellently for TE and TM incidences [see Fig. 4(b)], which is good to design tandem SNSCs. Above equation reveals that the photocurrents can be matched as long as the ratio between shell thickness (i.e., R − r) and the core radius (r), i.e., (R − r)/r, is ~0.2, e.g., r = 200 nm requires the shell thickness to be 40 nm (i.e., R ~240 nm). Concentrating on the device Jph after photocurrent matching [see Fig. 4(a)], we can easily find that Jph increases rapidly first, followed by the slow increment and slight fluctuation due to the varied resonant condition of the leaky modes inside the nanowire cavity. We get nearly saturated Jsc to 7.13 mA/cm2 when r = 300 nm and R = 360 nm.

Fig. 3. Qabs of the core and shell cells vs λ and r, where an optimal R has been selected for each r. Both TE and TM incidences have been considered in this study.

Fig. 4. (a): optimal R under photocurrent matching vs r, where the matched Jph is also shown and unpolarized incidence is considered. (b): optimal R under photocurrent matching vs r for TE and TM incidences.

For a further insight into the absorption property of the tandem SNSC, the absorption spectra of the core, shell, and entire cells are plotted in Fig. 5(a), where r = 300 nm, R = 360 nm, and TE incidence is exemplified. It clearly displays that the outer a-Si:H layer absorbs solar incidence in the band between 300 and 800 nm; however, the absorption to the longwavelength light is very low. On the contrary, although the absorption of μc-Si:H layer is relatively weak (i.e., peak Qabs < 50%), it happens in a very broad spectral range, yielding a photocurrent density which is well balanced with that from the a-Si:H layer. In the shortwavelength region, the absorption curve is quite flat; nevertheless, in the long-wavelength region, multiple absorption peaks can be observed. To further indicate this difference, it is necessary to examine the absorption patterns inside the nanowire cavity. Insets (a−h) shown in Fig. 5(b) are the absorption patterns under eight wavelengths, which have been marked directly in Fig. 5(a). It is obvious that under a short-wavelength incidence no cavity mode is formed due to the strong absorption of a-Si:H material. However, as increasing the wavelength, solar incidence penetrates into the μc-Si:H core layer and forms strong cavity resonances. For example, insets f and g exhibit the Fabry-Perot resonances, inset h denotes the whispering-gallery mode, and insets c − e are the hybrid modes. The cavity effects strongly improve the Qabs.

#222706 - $15.00 USD Received 10 Sep 2014; revised 17 Oct 2014; accepted 22 Oct 2014; published 31 Oct 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. S7 | DOI:10.1364/OE.22.0A1761 | OPTICS EXPRESS A1765

Fig. 5. (a) Qabs spectra of the core, shell and entire tandem cells with r = 300 nm and R = 360 nm; (b): insets a−h are the absorption patterns under the marked wavelengths.

Based on the above analysis, a device simulation coupling both optical absorption and carrier transport is performed by FEM [26–28]. This is necessary for an accurate prediction of the cell performance as the intrinsic electronic process is never perfect as assumed by the purely optical treatment; instead, rich semiconductor processes and mechanisms have to be comprehensively addressed [26]. In this study, the core and shell junctions are assumed to be connected in series, which means the lowest photocurrent is extracted from the tandem cell, while the operating voltage is significantly improved. The nondegenerated doping concentration for both a-Si:H (n-type) and μc-Si:H (p-type) is 5 × 1016 cm−3, and the degenerated doping concentration (i.e., p+ for a-Si:H and n+ for μc-Si:H) is 4 × 1017 cm−3. Here, n+ and p+ represent the heavily doped layers in order to form the tunnel junction. The other key electrical parameters used and more details on the implementation of optoelectronic simulations can be obtained by referring to our previous work [26, 27]. The diffusion lengths for electrons and holes in a-Si:H are from [27], while those for μc-Si:H are 10 times over aSi:H. Actually, due to the ultra-compact size of SNSCs, the diffusion lengths have no qualitative effect on the electrical outcomes of the device. Figure 6(a) plots the J-V curve of the entire tandem SNSC with r = 300 nm and R = 360 nm. Moreover, a μc-Si:H SNSC with R = 360 nm is also plotted in Fig. 6(b) for reference. The typical electrical parameters have been directly inserted into the figures. It is obvious that the short-circuit photocurrent density (Jsc) for tandem cell is around half of that from the single-junction cell, showing that the lighttrapping capability has not been qualitatively improved (compared to the single-junction μcSi:H cell) after the tandem design; however, the new Voc is almost 2.6 times of that based on μc-Si:H cell, leading to a much higher photoconversion efficiency η, i.e., enhancement factor of ~34%.

Fig. 6. J-V characteristics and power densities of (a) a tandem μc-Si:H/a-Si:H SNSC with r = 300 nm and R = 360 nm and (b) a μc-Si:H SNSC with R = 360 nm.

4. Conclusion We proposed the μc-Si:H (core)/a-Si:H (shell) radial tandem SNSCs in order to enhance the photoconversion efficiency of the compact photovoltaic devices. The absorption tunability of the core and shell cells was investigated, which showed that the junction photocurrents could be effectively controlled by adjusting the core and shell radii. Further study indicated that the

#222706 - $15.00 USD Received 10 Sep 2014; revised 17 Oct 2014; accepted 22 Oct 2014; published 31 Oct 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. S7 | DOI:10.1364/OE.22.0A1761 | OPTICS EXPRESS A1766

core and shell radii under photocurrent matching condition exhibits a linear relation, enabling a convenient design of tandem SNSCs with a maximized and matched photocurrent without requiring the large number of electromagnetic calculations. We further performed the device simulations to evaluate the electrical performance of the proposed tandem SNSCs by considering the carrier transport, recombination and collection processes. It is found that the tandem design for SNSCs actually does not yield an obviously improved Jsc, but a much higher Voc, which is responsible for the much improved photoconversion efficiency. Acknowledgments This work is supported by National Natural Science Foundation of China (No. 61204066, No. 91233119), Ph.D. Programs Foundation of Ministry of Education of China (No. 20133201110021), China Postdoctoral Science Foundation (No. 2014M550301), Jiangsu Planned Projects for Postdoctoral Research Funds (No. 1302100B), Natural Science Foundation of Jiangsu Province (Nos. BK20141200, BK20140349), “Thousand Young Talents Program” of China, and Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.

#222706 - $15.00 USD Received 10 Sep 2014; revised 17 Oct 2014; accepted 22 Oct 2014; published 31 Oct 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. S7 | DOI:10.1364/OE.22.0A1761 | OPTICS EXPRESS A1767

a-Si:H coaxial tandem single-nanowire solar cells considering photocurrent matching.

The single nanowire solar cells (SNSCs) with radial junctions are expected to show the superiority in efficient carrier collection benefited from the ...
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