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Abstract
Single nanowire solar cells show great promise for next-generation photovoltaics and for powering nanoscale devices. Here, we present a detailed study of light absorption in a single standing semiconductor-dielectric core-shell nanowire (CSNW). We find that the CSNW structure can not only concentrate the incident light into the structure, but also confine most of the concentrated light to the semiconductor core region, which boosts remarkably the light absorption cross-section of the semiconductor core. The CSNW can support multiple higher-order HE modes, as well as Fabry-Pérot (F-P) resonance, compared to the bare nanowire (BNW). Overlapping of the adjacent higher-order HE modes results in broadband light absorption enhancement in the solar radiation spectrum. Results based on detailed balance analysis demonstrate that the super light concentration of the single CSNW gives rise to higher short-circuit current and open-circuit voltage, and thus higher apparent power conversion efficiency (3644.2%), which goes far beyond that of the BNW and the Shockley-Queisser limit that restricts the performance of a planar counterparts. Our study shows that the single CSNW can be a promising platform for construction of high performance nanoscale photodetectors, nanoelectronic power sources, super miniature cells, and diverse integrated nanosystems.
© 2017 Optical Society of America
1. Introduction
Single nanowire solar cells (SNSCs) are receiving more and more attentions in the scientific community due to their unique features of enhanced light trapping, efficient carrier collection, ultra-compact volume, and convenience of incorporating into integrated chips, and are believed to be the promising candidates for powering ultralow-power electronics and diverse nanosystems [1, 2]. The strong interaction between the incident light and nanowires has been utilized to greatly increase light concentration as well as the equivalent light absorption cross-section of a nanowire solar cell [3]. Recently, a breakthrough has been made by using single vertical bare nanowire (BNW) which concentrates light remarkably by virtue of the antenna effect, leading to an apparent efficiency beyond the Shockley-Queisser limit–a fundamental efficiency limit imposed by the detailed balance condition on the planar solar cells [4]. Furthermore, a theoretical guideline for maximizing the conversion efficiency of a single standing nanowire solar cell based on the detailed analysis of the nanowire optical absorption mechanism has been presented [5]. Despite the antenna-effect-mediated strong absorption at short wavelengths, the overall performance of the single standing nanowire solar cells is still far below expectation due to narrow resonant bands and relatively low absorption at long wavelengths. In addition, previous researches pertinent to SNSCs are limited to the bare type, and the purpose of these researches is to maximize their performance based on the low order HE modes [6–8]. It is well known that a nanowire of small diameter has less supporting modes, and most of the incident light cannot be guided into the nanowire [9, 10]. Comparing with the bare nanowire, semiconductor core-dielectric shell nanowire not only possesses the high light concentration effect, but also provides the possibility to tune the resonant mode position by changing the thickness of the shell. However, the existing research focuses on the horizontal lying core-shell nanowire or the vertically arranged nanowire array, as well as the low order resonance mode corresponding to the thin shell layer [11–13].
In this article, we present a detailed study of light absorption in a single standing semiconductor-dielectric core-shell nanowire (CSNW) structure. We show that the structure can concentrate more incident light into the semiconductor core and yield much higher short-circuit current density and open-circuit voltage than the BNW and planar counterpart do. Furthermore, we show that the apparent power conversion efficiency of the CSNWs notably exceeds that of the BNWs and the Shockley-Queisser limit due to the substantially enlarged optical absorption cross-section of the standing CSNWs.
2. Proposed structure, performance parameters and design method
Figure 1 illustrates schematically a single standing BNW and CSNW, and the cross-section of the CSNW, along with the equivalent light concentration effect. The material of the core and shell is assumed to be active semiconductor and dielectric, respectively. The incident plane wave propagates along the z-direction and polarizes with the electric field parallel to the x direction, i.e., Ei = (Ex,0,0). The incident electric field intensity is assumed to be Ex = [1V/m]exp(-jkz). The absorption cross-section is defined as [14]
where S is the cross-section area of the active semiconductor nanowire, m the azimuthal mode number, I0 the incident intensity, J* and E the conjugate current and electric field vector in cylindrical coordinate, respectively. In a lossy medium, the light absorption efficiency is defined as Qabs = Cabs/Cgeom, where Cgeom = πr12 is the area of the geometrical cross-section of the active semiconductor nanowire. In the numerical simulation, the finite element method was adopted [15].
Fig. 1 Perspective view of (a) a single standing BNW and (b) CSNW, and equivalent built-in concentration effect. (c) Top view of the CSNW, where r1 and r2 are radii of the semiconductor core and dielectric shell, and ε1, ε2, ε3 are relative permittivity of the core, shell, and surrounding medium, respectively. θ is the angle between the propagation vector of the incident light and the nanowire axis, while ϕ is the azimuthal angle of the propagation vector in cylindrical coordinates. They are drawn here for the following detailed balance analysis.
We adopt detailed balance analysis to reveal the electric current density-voltage (J-V) characteristics in the nanowire solar cells. The J-V equation associated with the radiative generation rate and radiative recombination rate and non-radiative recombination rate is [3, 16–19]:
whereis the radiative generation rate per unit area of hole-electron pairs by the incident sunlight,is the radiative recombination rate when the cell is in thermal equilibrium with a surrounding blackbody at ambient temperature Tc, and R(0) and R(V) are the total rates of nonradiative hole-electron pair generation and recombination, respectively. I(E) is the incident rate of solar photons per unit area per unit bandwidth at the photon energy E, and Eg is the band gap of the active semiconductor material.is Planck’s law for the incident spectral irradiance at a temperature Tc. Qabs(E,θ,ϕ) is the cell’s absorption efficiency spectrum averaged over the transverse electric (TE) and transverse magnetic (TM) incident polarizations.Knowledge of propagation modes is expected to provide better understanding, prediction, and guidance for optimizing the solar radiation absorption. We notice that the theory of dielectric resonator antenna (DRA) [20, 21] is only applicable to a dielectric cylinder supporting HE11 resonant mode, but not to our CSNW structure as the resonant modes discussed here also include higher order propagation modes. Therefore, to design and tune the resonant modes supported by the CSNW, we derived the dispersion eigen-equation of a core-shell coaxial cylinder based upon the Maxwell’s equations and the boundary conditions at the core/shell and shell/surrounding medium interfaces as follows:
whereHere Jn, Yn, and Kn are the first kind Bessel function, the second kind Bessel function, and the second kind modified Bessel function, respectively. The primes denote the derivative of the corresponding variables in the function. ε1, ε2, ε3 are relative permittivity of the core, shell, and surrounding medium, and μ0 and ε0 are the permeability and permittivity of free space, respectively. ω is the angular frequency, k is wavevector in the vacuum, and β is the propagation constant along the nanowire axis.3. Results and discussion
To depict how the core-shell structure supports higher-order modes and concentrates incident light into the semiconductor core region, a detailed analysis was provided on a specific example of a GaAs-ZnO CSNW. The dielectric coefficients for GaAs are taken from Ref [22], and those for ZnO and the surrounding medium are set to a constant of 4.0 and 1.0 respectively, unless mentioned otherwise. The radius of the core to be 50 nm, as it has shown to be optimum for current-voltage performance [5].
We simulated numerically the light absorption efficiency as a function of wavelengths and shell thicknesses of the CSNW structure, and the results are shown as the color pattern in Fig. 2(a). The absorption peaks systematically red-shift and increase in the number as a function of increasing shell thickness. This aspect was described previously by Kim et al [23] and Bezares et al [24]. However, it is worth mentioning that the former arises from the increase in the dielectric shell thickness, while the latter from the increase in the active wire diameter.
Fig. 2 (a) The dispersions of the HE11 mode (black line) of BNW (r = 50nm) and the HE13 mode (blue line) of CSNW(r = 50 nm and t = 160nm). The dashed line is the dispersion of light in vacuum. (b) Light absorption efficiency as a function of the incident light wavelength and shell thickness for a CSNW with GaAs core of 50 nm radius and ZnO shell. The color curves are the dispersion relation obtained using Eq. (6).
In order to identify the resonance modes corresponding to the absorption peaks, the relation between the light wavelength and the shell thickness of the CSNW for HE1m modes was calculated analytically employing Eq. (6) and propagation constant β, shown as the color solid curves in Fig. 2(a). It is clear that the position of the main resonant absorption peaks is well consistent with that achieved by the analytical calculation, allowing us to assign the resonant modes excited within the CSNW. Moreover, the higher-order modes present higher absorption efficiency than the lower-order modes do, and the absorption efficiency at the wavelengths between the adjacent resonance modes increases as well.
Considering that the propagation constant β is the component of the wave vector along the axis of the nanowire, it should be proportional to the wave vector k = 2π/λ, where λ is the light wavelength in vacuum, and be affected by the nanowire length. Then the β can be approximately expressed as β = ak + b, where the coefficients a and b can be determined from the dispersion curves of core-shell structures. Figure 2(b) illustrates the dispersion curves of the HE11 mode (black line) of the BNW (r = 50 nm) and the HE13 mode (blue line) of the CSNW (r = 50 nm and t = 160 nm). For the absorption peak of the HE11 mode at 605 nm and that of the HE13 mode at 440 nm shown in Fig. 2(a), the a and b are calculated to be 0.87 and 2.28, respectively. It should be noticed that β is homogeneous in the radial direction, that is, homogeneous in the core and shell, which has been pointed out by Wang and Magnusson [25].
The assignment of the resonant modes can be further confirmed by the cross sectional electric field patterns. Figures 3(a)-3(d) show the normalized electric field intensity corresponding to the positions denoted by A3~A6 in Fig. 2(a), respectively, where the insets in the figures are the enlarged views of the core region. The electric field intensity is normalized to that of the incident light. In order to clearly show the pattern of the electric field, the bars in Figs. 3(a)-3(d) are of different scale. It can be recognized that the number of the nodes increases successively from Figs. 3(a)-3(d), corresponding to HE13 to HE16 modes. Figures 3(e)-3(h) show the normalized electric field intensity corresponding to the positions denoted by B1~B4 in Fig. 2(a). It reveals that, in the core region, the higher-order HE mode possesses higher electric field intensity compared with the lower-order HE mode. It is worth noting that the electric field intensities corresponding to HE1m (m = 3~6) resonant modes in the semiconductor core region of the CSNW are all substantially greater than that corresponding to the HE11 mode in the BNW.
Fig. 3 Electric field intensity corresponding to the positions denoted by (a) ~(d) A3 ~A6 and (e) ~(h) B1 ~B4 in Fig. 2(a). The insets in (a) ~(d) are the enlarged core region view of the corresponding patterns.
Figure 4 displays visually the light concentration in the BNW and CSNW, and the energy flux density at the bottom of the two nanowires. Figures 4(a)-4(d) show the electric field intensity and Poynting power flow distribution of the BNW of 50 nm radius and the CSNW of 50 nm radius and 500 nm thick shell in the x-z plane. The wavelength is 605 nm, corresponding to the HE11 mode in the 50 nm BNW and HE14 mode in the 50/500 nm core/shell nanowire. The red arrows in Figs. 4(c) and 4(d) represent the direction and density of the power flows.
Fig. 4 Electric field intensity and power flow distribution. Electric field distribution in (a) 50 nm radius BNW and (b) 50/500 nm radius CSNW, and energy flux density distribution in (c) 50 nm radius BNW, and (d) 50/500 nm radius CSNW. (e) The energy flux density along x and y axis at the bottom of the BNW and CSNW. The vertical dashed lines denote the interface of the core and shell. The incident wavelength is 605 nm and the arrows in (d) are drawn to half scale of those in (c).
It is evident from Figs. 4(a) and 4(b) that the CSNW displays a stronger electric field and electric field confinement than the BNW does. In addition, the strong electric field is confined mostly to the core region in the CSNW, while it falls upon mostly at the outer surface of the nanowire in the BNW, which accords with the characteristics of HE11 mode [26]. Furthermore, in the CSNW, the electric field is significant in the region deeper from the light incident surface, which can decrease the surface recombination loss of carriers for the axial p-n junction configuration solar cell. The same argument also applies to the radial direction. As it can be seen from Fig. 4(d), in the case of the CSNW, not only the incident electromagnetic wave that enters the CSNW, but also that propagates around the shell is concentrated to the center axis of the core nanowire, resulting in a substantial increase of power flow density in the semiconductor core region, and a relative decrease of the power flow density that passes through the transparent dielectric shell region. Clearly, this effect not only promotes the cell efficiency, but also loosens the constraints on the critical parameters such as doping concentrations and emitter thicknesses in cell designs. Whereas for the BNW shown in Fig. 4(c), the incident electromagnetic wave passes the nanowire without being concentrated into the nanowire noticeably, resulting in a weak coupling of the incident electromagnetic wave with the semiconductor core and absorption in it.
In the central region of the bottom of the BNW and CSNW, as shown in Figs. 4(c) and 4(d), both the arrows directing into and out of the core nanowires are observed. We calculated the net power flow Pz along the x and y axis shown in Figs. 4(c) and 4(d) and displayed the results in Fig. 4(e). We find that the net power flow is less than zero in the 50 nm radius region for the BNW, i.e., the energy flows out of the nanowire. However, it is greater than zero in the 50 nm radius region for the CSNW, which means that the energy flows into the semiconductor core region. The average net power flow over the semiconductor core cross-section is −3.1 × 10−2 and 4.26 × 10−2 W/m2 for the BNW and the CSNW, respectively, while that over the region between 50 and 500 nm radius is −1.56 × 10−3 and −3.97 × 10−4 W/m2, respectively. Here we come across an interesting phenomenon, i.e., at the bottom, the energy flows into the semiconductor nanowire for the CSNW, while it flows out of the semiconductor nanowire for the BNW. In the 550 nm radius region, the electromagnetic wave energy that flows out of the structure is greatly reduced in the case of the CSNW compared with that in the case of the BNW, though the net power flow remains less than zero in both structures. In addition, the dynamic propagation of electromagnetic wave in the BNWs (r = 50 nm and r = 280 nm) and CSNW at 605 nm wavelength is presented in the Visualization 1, Visualization 2, and Visualization 3, respectively, where we can see visually stronger mode resonances and longer path of the electromagnetic wave in the CSNW than those in the BNW. These results suggest that the shell greatly reduces the transparent power flow, and the reduced power flow returns back partly to the core nanowire and enhances the absorption in the CSNW.
Figure 5(a) shows the line-cuts from Fig. 2(a) for the four selected shell thicknesses of 0, 160, 330, and 500 nm. It is clear from Fig. 5(a) that, in addition to the resonant absorption peaks corresponding to the HE modes, several narrow and sharp resonant absorption peaks emerge and are superimposed on the absorption curve profile of the HE modes, and the background absorption also increases. This enhances the solar light absorption efficiency of the CSNW structure. To explore the origin of the narrow and sharp resonant absorption peaks, the absorption spectra of the BNW and CSNWs in the length region between the horizontal dashed lines (as shown in the insets of Fig. 5(b)) are calculated and shown in Fig. 5(b). The model for the calculation of the infinite nanowire is shown in Fig. 5(c), where both ends of the nanowire are extended into the perfectly matching layer (PML). The incident light source (scattered-field) is arranged in the nanowire so as to avoid the scattering interference from the top end and to make the light that passing through the bottom be absorbed entirely by the PML layer. In the calculation, the radii of the BNW and core nanowire of the CSNWs are chosen to be 50 nm, the shell thickness of the CSNWs to be 500 nm. The height of the nanowires is assumed to be 2.5 μm, semi-infinite, and infinite.
Fig. 5 (a) Line-cuts from Fig. 2(a) for four selected shell thicknesses of 0, 160, 330, and 500 nm, (b) absorption spectra of the BNW and CSNW in the length region of 2.5 μm, and (c) the model for the calculation of the infinite nanowire. The height of the nanowires is 2.5 μm, semi-infinite, and infinite. The radius of the BNW and core nanowire of the CSNW is 50 nm, and the shell thickness of the CSNW is 500 nm. (d) the dispersion of the HE1m (m = 1-7) mode of the CSNW(r = 50 nm and t = 500 nm). The dashed line is the dispersion of light in vacuum. (e), (f) and (g) the electric distribution of x component at the x-z cross section corresponding to 735 nm, 786 nm, and 830 nm, respectively.
We find that several narrow absorption peaks (e.g., 735 nm, 786 nm and 830 nm) denoted in Fig. 5(b) in the 2.5 μm height CSNW do not exist in the semi-infinite structure, indicating that these absorption peaks are relevant to the bottom interface of the 2.5 μm structure, which implies the existence of Fabry-Pérot (F-P) resonant absorption induced by the resonant cavity between the front and back interfaces. The condition for F-P resonance can be approximately described by [27]
where h is the height of the CSNW, βm is the guided mode wave-vector along the CSNW axis and obeys the dispersion Eq. (6). Calculations showed that the wave-vectors satisfying Eq. (7) should correspond to the HE11 mode, as shown in Fig. 5(d), and the wave node number corresponding to 735 nm, 786 nm, and 830 nm resonant wavelength is 14, 13, and 12, respectively, which is consistent with the electric field patterns shown in Figs. 5(e)-5(g). From Fig. 5(d), it can also be found that the CSNW (r = 50 nm and t = 500 nm) can support HE13, HE12, and HE11 modes at the wavelengths around 786 nm, which explains why the electric field distribution shows more complex patterns than conventional F-P resonances. The superposition of the HE13 pattern on the HE11 associated F-P resonant pattern makes the electric field patterns complex, though the electric field of the former might be less than that of the latter. The HE12 mode does not contribute to the electric field patterns since it is difficult to be excited due to its great transverse wave-vector. The reduction of the absorption coefficient in GaAs material, especially in the band edge region, brings about the reduction of absorption contributed by HE modes. However this reduction promotes the F-P resonance, and efficiently enhances the absorption of the CSNW, which can also be found in the work for single nanowire [4, 27] and those for nanowire arrays [28, 29].Comparing the absorption efficiency spectrum of the semi-infinite CSNW structure with that of the infinite one, we find that the former undulates distinctly, and more quickly especially in the short wavelengths. This can be attributed to the diffractional effect of incident light at the front surface of the semi-infinite structure, as the size of the front surface of the CSNW is comparable to the wavelength of incident light. The same argument also applies to the observation of the narrow and sharp resonant absorption peaks superimposed on the absorption curve of the HE modes in the 2.5 μm height CSNW. However, this effect is not obvious in the case of the BNW due to the fact that the size of its front surface is far less than the wavelength of the incident light. The phenomenon that the spectral absorption efficiency of the semi-infinite CSNW is lower than that of the infinite one can be attributed to the back scattering loss on the front interface of the semi-infinite structure.
Basically, with a large shell layer, more light will be confined to interact with the central photoactive layer. However, the large shell layer will generally have many defects, which will reducing the light concentration performance of the structure. We assume that the extinction coefficients of the dielectric material can be used to characterize the optical losses induced by these defects, and the complex refractive indices of the shell can be expressed as N = n + ik’. Then, we calculated the relationship between the short-circuit current and the shell thickness at different k’, as shown in Fig. 6(a). The results show that the short-circuit current increases with the increase of the shell thickness when the absorption is zero, i.e., no saturation occurs. With the increase of extinction coefficient, the short-circuit current exhibits a maximum at a certain shell thickness, and then decreases with the increase of the shell thickness. The larger the extinction coefficient is, the smaller the maximum short-circuit current and the shell thickness corresponding to the maximum short-circuit current are. However, even if the extinction coefficient is typically 0.03 [30], the short-circuit current is still increasing when the shell thickness is 500nm, which provides the possibility for the practical application of the core-shell structure.
Fig. 6 (a) The change of short-circuit current as a function of the shell thickness for the dielectric shell with different extinction coefficients. (b) The absorption efficiency of the CSNW and the pure nanowires with the same diameter as the CSNW.
We calculated the absorption efficiency of the CSNW and the pure nanowires with the same diameter as the CSNW, as shown in Fig. 6(b). The short-circuit currents are 2.68*10−7mA and 5.20*10−7mA, respectively, i.e., the total short-circuit current of the core shell structure is about half of the pure nanowire. But the light absorption efficiency of the core-shell structure is about 50 times that of the pure nanowires if the short-circuit current per unit volume were compared. In other words, the semiconductor material required in the core-shell structure is only two percent that in the bare nanowire if the short-circuit current per unit volume were compared. This design obviously reduces the consumption of semiconductor materials and can effectively reduce the cost of solar cell devices, especially for precious GaAs materials.
We also analyzed how the shape of the shell influences the absorption of CSNW. Figure 7 shows the light absorption efficiency spectra of the CSNWs with the core being circular, and the shell being either circular, hexagonal, or square. The absorption efficiency spectrum of the 50 nm radius BNW is also displayed in the Fig. 7 for comparison. In the calculation, the cross-sectional area of the shell is chosen to be the same as that of the 50/500 nm (core/shell) coaxial nanowire structure. It is found that the light absorption efficiency spectra of the CSNWs with different shell shape are quite different, indicating that the shape of the shell dominates the light absorption of the CSNW. The spectrum of the structure with the circular shell exhibits distinct HE resonant absorption peaks, and the corresponding absorption efficiency is the highest. In the spectrum of the structure with the hexagonal shell, the HE resonant absorption peaks can still be identified, and some narrow absorption peaks emerge on the background, but the absorption efficiency in the whole spectrum is somewhat reduced. As for the spectrum of the structure with square shell, two high and broad absorption peaks can be observed, more narrow absorption peaks emerge and the absorption efficiency is reduced further. We conjecture that when the shape of the shell deviates from circles, the conditions that support HE modes are disrupted, resulting in the decrease of the energy that can be concentrated into the core region and thus the absorption efficiency. In contrary, the light absorption efficiency spectra of the CSNW with different core but the same shell shape are basically identical (not shown), indicating that the shape of the core does not affect the light absorption efficiency of the solar cell structure. This can be attributed to the fact that the dimension of the core nanowire is far less than the wavelength of incident light.
Fig. 7 Light absorption efficiency as a function of the incident light wavelength. The shape of the core is circular, and that of the shell is circular, hexagonal, and square. C-C: Circular-Circular, H-C: Hexagonal-Circular, S-C: Square-Circular. The core-shell structure shown in the figure is schematic and not drawn to scale.
To show the electric performance of the CSNW structure, we calculated the current density−voltage (J−V) transport characteristics utilizing Eq. (2), as shown in Fig. 8. The height of the nanowire is 2.5 μm, the core and shell radius are 50 and 550 nm respectively. The J−V characteristics of the BNW of the same height and core radius, and that of the bulk GaAs cell are also shown in Fig. 8 for comparison.
In the calculation, we assume, in the same way as Sandhu et al [3] and Miller et al [31] have done, that the CSNW structure is a defect-free GaAs cell with perfect surface passivation. Based on this assumption, the non-radiative recombination of Shockley-Read-Hall and surface recombination is ignored. Then by assuming that the cell is approximately intrinsic under illumination, we obtain the non-radiative Auger recombination rate that is given by [31],
where the Cn and Cp is the conduction-band and valence-band Auger coefficient, respectively, and the sum of Cn and Cp equals 7 × 10−30 cm6/s, ni is the intrisic carrier concentration (2 × 106 cm−3), and L is the height of the nanowire for an axial p-n junction solar cell or the diameter of the nanowire for an radial p-n junction solar cell. We notice that the non-radiative Auger recombination rate (~10−15) is much less than the radiative recombination (~103), therefore it is ignored in the calculation of axial or radial voltage. When the voltage is zero, the short-circuit current of the CSNW, the BNW, and the bulk structure is 3411.9, 921.4, and 32.5 mA/cm2, and the maximal power density value is 3644.2, 974.9, and 32.8 mW/cm2 respectively. The short-circuit current of the CSNW structure is 3.7 times more than that of the BNW, and 105.1 times that of the bulk cell. The scale of the vertical axis in Fig. 8 is logarithmic for proper displaying. It is important to point out that the electrical evaluation is based on the Shockley–Queisser analysis and gives the theoretical efficiency limit, though it cannot predict the exact situation of the solar cells. The more accurate electric performance of the solar cell response could be predicted using optoelectronic simulation [32] or even with consideration of the thermal effect [33].We found that the open-circuit voltage of the CSNW (1.19V) shows slight increase in comparison with that of the BNW (1.18V) and noticeable increase in comparison with that of the bulk cell (1.13V). The radiation of the incident sunlight increases Voc, while the emission of the photons due to radiative recombination decreases Voc as can be derived from Eqs. (2)-(5). Analysis shows that, although both the radiative generation rate Fs and the thermal equilibrium recombination rate Fc0 in the CSNW are higher than that in the BNW, the former displays a higher degree of increasement. Therefore, the contrast between Fs and Fc0 is higher in the CSNW, resulting in a higher Voc.
It is important to note that, unlike single-junction nanowire arrays synthesized in large scale for conventional solar cells which have the Shockley-Queisser limit of ~31% under AM1.5 solar illumination [16, 18], the apparent efficiency, defined as the ratio between the output power and light power incident on the core area, of a single nanowire has opportunities to exceed 100% [5, 34] due to its large light concentration mechanism which is differentiated from the light trapping mechanism of a nanowire array [3–5, 19, 35–38]. Here in this study, the apparent power conversion efficiency of the single standing CSNW goes up to 3644.2%.
Comparing with horizontally lying core-shell configurations [3, 35, 38], the standing core-shell configuration displays distinct advantages. Firstly, absorption enhancement increases nearly monotonically, rather than achieves a moderate enhancement and then undulates around this value with increasing dielectric shell thickness. Secondly, the standing configuration not only enhances the interaction between the incident light and the leaky wave guided modes, including higher-order HE1m modes, in the core-shell structure, but also strongly confines the electric field to the core nanowire. Thirdly, the standing configuration retains the advantage of the radial p-n junction as light absorption and carrier separation can be orthogonal. Finally, the major factors that restrict the absorption enhancement are the surface roughness and the profile of the shell, which can be overcome with the state of the art of microstructure fabrication. Experimentally, the single standing CSNWs structure can be enabled by techniques such as solid-source chemical vapor deposition and selective area growth in metal-organic chemical vapor deposition, which are capable of fabricating GaAs NWs with diameters as small as 100 nm [39, 40]. Anttu et al have shown, theoretically and experimentally, that the core-shell structure with thin core and thick shell in the supplementary material [41]. The nanowire core they used is InAs with its diameter of 62 nm, while the shell is Al2O3 with its thickness of 357 nm. The ratio of the shell thickness to core diameter is even greater than that of our design. From their work we can deduce that our designed core-shell structure can be achieved experimentally and has advantages in optical properties, since the materials we adopted are similar to those of their materials. We believe that a core-shell structure of approximate one micrometer in diameter is achievable utilizing the state of the art of microstructure fabrication, and we anticipate to verify our proposal experimentally in our next research work.
4. Conclusions
In summary, single standing semiconductor-dielectric CSNW structure cannot only concentrate incident light into the structure, but also confine most of the concentrated light to the semiconductor core region, which remarkably boost the light absorption cross-section of the semiconductor core. The CSNW utilizes higher-order HE1m modes, and the F-P resonance modes as well. Overlapping of the adjacent higher-order HE modes results in broadband light absorption enhancement in solar radiation spectrum. The super light concentration of the CSNW gives rise higher short-circuit current and open-circuit voltage, and thus higher apparent power conversion efficiency, which makes the single standing CSNWs a promising candidate for nanoscale photodetectors, nanoelectronic power sources, super miniature cells, and diverse integrated nanosystem.
Funding
National Natural Science Foundation of China (NSFC) (No. 60977028); Key Project Foundation of Shanghai (No. 09JC1413800).
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