incident angle dependence of absorption enhancement in plasmonic solar cells

Incident angle dependence of absorption enhancement in plasmonic solar cells

Meng Yang,1,2

Zhengping Fu,1 Feng Lin,

1 and Xing Zhu

1,3,*

1School of Physics, State Key Laboratory for Mesoscopic Physics, Peking University, Beijing 100871, China 2Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China

3National Center for Nanoscience and Technology, Beijing 100190, China *[email protected]

Abstract: The enhancement of solar light absorption in a solar cell is a challenging issue. In this article we show that in a thin-film silicon solar cell covered with silver nanoparticles on the surface, the absorption of the incident light can be particularly enhanced at certain angular range and wavelength. Such absorption enhancements are associated with the resonant localized surface plasmon (LSP) modes of the nanoparticle and nanoparticle-induced local Fabry-Perot (FP) modes. Our simulations suggest that the spectral shift of the LSP modes due to changing the incident angle leads to an incident-angle-sensitive absorption enhancement of the solar cell. Selecting the incident angle in a well-defined range of 0° to 35° is essential for optimizing the performance of a thin-film solar cell.

©2011 Optical Society of America

OCIS codes: (240.6680) Surface plasmons; (350.6050) Solar energy; (310.6860) Thin films, optical properties; (350.4990) Particles.

References and links:

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#145889 - $15.00 USD Received 14 Apr 2011; revised 26 May 2011; accepted 27 May 2011; published 3 Jun 2011(C) 2011 OSA 4 July 2011 / Vol. 19, No. S4 / OPTICS EXPRESS A763

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1. Introduction

Conventional silicon wafer based solar cells are not a cost-effective way of energy generation because the large amount of silicon materials requires high production costs. On the other hand, the thin-film silicon cells of a few micrometers need much less silicon materials, and therefore offer a possible solution for low-cost solar energy conversion. However, thin-film silicon solar cells suffer from a low light absorption because of the weak-absorbing nature of silicon. The traditional methods for increased light absorption, such as surface texturing methods can‟t be applied to a thin silicon film of a few micrometers, so other light harvesting and trapping mechanisms are required. Metallic nanoparticles that support localized surface plasmon (LSP) modes are excellent candidates for such a task because they can effectively interact with light and confine light [1,2]. Recent experiments on various solar cells [3,4], LED devices [5] and silicon waveguides [6] have proven that performance of photovoltaic can be greatly improved using metallic nanoparticles. The metallic nanoparticle has a scattering cross-section much larger than its geometrical cross-section near the LSP resonant wavelengths. For large nanoparticles forward scattering can dominate over backward scattering [7], which could enhance light scattering into the substrate and the optical path lengths [8]. Also the high dielectric constant of the silicon substrate allows the evanescent wave scattered by the metallic nanoparticle to propagate in it [6]. More than 90% of the incident light can be scattered into the silicon substrate due to the abundance of optical modes available [9].

To achieve the better performance of surface plasmon enhanced solar cells, it‟s necessary to tune the spectral position of the LSP resonant modes, which corresponds to highest scattering or in-coupling into the solar cell [9]. The tuning of LSP modes have been previously achieved via altering the size or the shape of the particle [10], or the refractive index (or the dielectric constant) of the medium surrounding the metallic particle [11,12]. In an asymmetric environment in which the particle is placed on a substrate, the LSP modes are also affected by the particle-substrate interaction, which enables us to tune the LSP modes with the polarization of the incident light. In this article, we perform numeral simulations to study the optimization of the enhancing effects of silver nanoparticles with the incident light. We discuss the main mechanisms of how the silver nanoparticle significantly enhances the absorption in thin-film silicon solar cells. We also reveal a possibility to control the enhanced performance of the solar cell using the light itself.

2. Light scattering by metallic nanoparticles

A metallic nanoparticle supports LSP modes distinguished by a series of discrete resonant eigen frequencies [2]. According to Mie Theory [13], light interacts with all normal modes of the nanoparticle. The cross sections of scattering and absorption of the particle are the sum of contributions from every normal mode. For a metallic sphere with a diameter much smaller than the wavelength λ of the LSP mode, the resonant LSP modes can be easily obtained using the electrostatic approximation:

( ) 1l

l

(1)

where ε(ω) is a frequency-dependent dielectric function of metal and ε is the dielectric constant of the surrounding medium, and l is an integer, l = 1,2,3…. . The l = 1 mode is called the dipole mode and the l = 2 is called the quadrupole mode. Other high-order modes of larger


values are likely to correspond to invisible UV frequencies. Hence for plasmonic solar cells, only the first few modes are important. The normalized Mie cross sections of such a small nanosphere considering only the dipole mode (or both the dipole mode and the quadrupole mode)are [1]:

8 ( ) 1

Im( )( ) 2

abs

aQ

(2)

24 4

4

128 ( ) 1

( ) 23sca

aQ

(3)

2 2 2 2

2 2

8 ( ) 1 ( ) 1 2Im[ ( ( ) 1)]

( ) 2 ( ) 1.53 15abs

a a aQ

(4)

2 24 4 4 4 4 42

4 4 4

128 ( ) 1 ( ) 1 4[ ( ) 1 ]

( ) 2 ( ) 1.53 15 225sca

a a aQ

(5)

where a is the radius of the sphere and λ is the wavelength. We can see from Eq. (2)–(5) that scattering and absorption cross sections have peak values when the metal dielectric function

equals 2 or 1.5, respectively, which are the first two LSP modes given in Eq. (1). It should be noticed that the finite size of the particle induces a size effect on its resonant condition [13]. As the particle size increases, more terms should be added to Eq. (1), shifting the resonant frequency to lower values. It‟s also obvious that as the particle radius becomes larger, the scattering cross section will dominate over the absorption cross section. For the SPP enhanced solar cells, ohmic loss in the nanoparticles leads to a negative contribution to the enhancing effects. So a larger nanoparticle with a greater scattering efficiency clearly has an advantage. Also, the forward scattering cross section gets much larger than the backward one near the plasmonic mode frequencies for large silver and gold nanoparticles [7,8,14].

Fig. 1. (a) Dipole and quadrupole mode resonant wavelengths as a function of the silver nanosphere size. (b) (c) Electric field profile of the dipole mode (b) or Quadrupole mode (c) of a 200nm-diamater spherical silver nanoparticle obtained through FEM simulation.


We‟ve also used a modified Debye model to calculate the LSP modes of silver nanoparticles with a commercial finite element method (FEM) software package (COMSOL) using the parameters taken from [15]. The resonant wavelengths and field distributions of the dipole and quadrupole modes of the nanoparticle in vacuum are calculated with the RF

eigenfrequency solver. The dipole mode of ε(ω) = 2 given in Eqs. (2) and (3) yields a resonant wavelength at 343 nm while the dipole mode of a 50 nm silver nanosphere in our calculations is found at 342 nm. This suggests our calculations are in good agreement with analytical results when the particle is small compared to wavelength. The dipole modes are shifted to 390 nm, 433 nm and 578 nm for particle diameter of 100 nm, 150 nm and 200 nm, respectively, due to size effect. We fail to find a quadrupole mode for the 50 nm particle. It is suggested that the dipolar behavior is dominant for the 50 nm small particle. The quadrupole modes of the 100 nm, 150 nm and 200 nm particle are found at 335 nm, 380 nm and 404 nm. The result shows that the resonant wavelengths red shift as the size of the particle gets larger as shown in Fig. 1.

3. Absorption enhancements under normal incidence

We used the two-dimensional FEM software package (COMSOL) in our following calculations. We designed a simple model of one single spherical silver nanoparticle placed on top of a thin-film amorphous silicon (a-Si) solar cell to study the absorption enhancing mechanisms of the single nanoparticle (Fig. 2). We used perfectly matched layers (PML) as boundary conditions for the system, so that inter-particle coupling didn‟t exist. A monochromatic plane wave was used as the incident light. The optical constants for silicon are referred from Palik [16]. The silver nanoparticle was calculated with the modified Debye model as previously mentioned. We defined the absorption in silicon as an integration of the Poynting vectors over all surfaces of the silicon substrate. The absorption enhancement was then calculated by dividing the absorption with the on-top silver nanoparticle by the absorption of the bare silicon substrate.

Fig. 2. Sketch of the simulation configuration of a single silver nanoparticle on top of an a-Si solar cell.

We first look at the absorption of bare a-Si substrates and a-Si substrates coated with a continuous silver film to study the Fabry-Perot (FP) cavity modes which play a very important role in the absorption of thin-film solar cells. The FP resonant condition under normal incidence is given by:

2

k

nd

k (6)

where n is the refractive index of the cavity, d is the thickness of the cavity and k is an integer. In Fig. 3(a) and 3(b) we show the absorption in bare a-Si substrates 100 nm and 150 nm thick and the absorption enhancements when the FP cavity resonance is disrupted by adding a


continuous silver film 80 nm thick. The 100 nm thick bare a-Si substrate features one absorption maximum due to FP mode at 805 nm and the 150 nm thick bare a-Si substrate has two absorption maximums due to FP modes at 651 nm and 1073 nm. By adding the silver film, the FP resonant condition is disrupted. New FP modes are generated at 602 nm for the 100 nm a-Si substrate and 802 nm for the 150 nm a-Si substrate associated with absorption enhancements, and great absorption reductions are generated at the FP wavelengths of the bare substrate [17].

When the silver nanoparticle is placed on the a-Si substrate, the absorption in silicon is enhanced due to scattering by the particle and near-field light concentration [8,9,14]. Figure 3(c) and 3(d) shows the absorption enhancement in the a-Si substrate with a single nanoparticle on the top. The absorption enhancement peaking around 800 nm in the 150 nm substrate matches with the FP mode shown in Fig. 3(b). This enhancement is not seen in the 100 nm substrate. So we believe this enhancement is a local FP mode induced by the nanoparticle. In the 100 nm substrate a major absorption enhancement peak is seen around 900-950 nm which shifts to the red as the particle diameter increases while the absorption is greatly reduced in this wavelength range when a silver film is added as shown in Fig. 3(a). This enhancement is greater for a larger particle despite a larger blocking area. We also observed absorption reduction in the entire wavelength range under TE incidence, which can‟t excite any LSP mode because there isn‟t an in-plane electric field component. These results indicate that this enhancement peak is due to the LSP mode of the nanoparticle as predicted in Eq. (2)–(5). We infer from the LSP mode wavelengths shown in Fig. 1 that it corresponds to the l = 1 dipole LSP mode shifted to the red due to the a-Si substrate. If the substrate is 150 nm thick the dipole mode enhancement overlaps with the strong FP mode at 1073 nm, so no major absorption enhancement peak is seen. However, the dipole mode compensates the reduced absorption near 1000 nm as seen in Fig. 3(d). There is also a minor enhancement peak in the short wavelength range for both substrate thicknesses. Since no FP mode is seen in this wavelength range in the 150 nm substrate by adding the silver film, we believe this enhancement peak results from the l = 2 quadrupole mode. However, in the 100 nm substrate it may contain contributions from a local FP mode corresponding to the FP mode at 602 nm in the silver film case. The quadrupole mode is much more confined to the surface of the nanoparticle than the dipole mode, and it interacts less strongly with the substrate, which is why the enhancement given by the quadrupole mode is less significant than the dipole mode. The quadrupole mode absorption enhancement doesn‟t increase linearly as the particle diameter increases unlike the dipole mode or local FP mode enhancement.


Fig. 3. (a) (b) Absorption (W/m) in a 100 nm (a) or 150 nm (b) thick bare a-Si substrate or a-Si substrate coated with an 80 nm silver film under a normally incident TM plane wave and the corresponding absorption enhancement. Black curve: absorption in the bare a-Si substrate. Red curve: absorption in the a-Si substrate coated with an 80 nm silver film. Blue curve: absorption enhancement by adding the silver film. (c) (d) Absorption enhancement in a 100 nm (c) or 150 nm (d) thick a-Si substrate with a single on-top spherical silver particle of diameters D (nm) under a normally incident TM plane wave.

The surface coverage η of nanoparticles greatly influences the enhancing effects. At a low surface coverage rate where the nanoparticle coupling is weak, a denser distribution of silver nanoparticles yields a greater broadband absorption enhancement at the nanoparticle-induced LSP or local FP mode wavelengths. In Fig. 4 a 20% surface coverage of the 200 nm diameter nanoparticles enhances absorption by up to 30% near the resonant wavelengths. Due to the relatively low surface coverage the LSP mode enhancement peaks are not shifted due to inter-particle coupling.

Fig. 4. Absorption enhancement for 100 nm thick and 150 nm thick a-Si substrates as the surface coverage of the 200 nm diameter nanoparticles increases from 6.67% to 20%.


It‟s well known that the LSP modes can be tuned by changing the shape of the particle or the dielectric environment. The former method has limited effects considering that a larger nanoparticle is further away from the high-dielectric-constant substrate. The larger particle interacts less strongly with the substrate than a smaller particle [9], so the red shift caused by the substrate is greater for smaller particles. For example, the dipole mode of the silver nanoparticle in the air shifts about 230 nm in wavelength as the particle diameter is increased from 50 nm to 200 nm. When the particle is placed on a 100-nm-thick silicon substrate, the enhancement peaks corresponding to the dipole mode is shifted by only 50 nm with the same change in particle diameter. The later method also has limited choices because the layer added to the solar cell surfaces must be transparent or conductive, and the thickness of the layer might need to be precisely controlled. Next we‟ll discuss a more flexible tuning of the LSP modes by setting the incident angle of light.

4. Absorption enhancements under varying incident angles

We swept the incident angle (α) from 0° to 45° to investigate how the enhanced absorption responses using the same model parameters as in the normal incident case. The results are plotted in Fig. 5. The particle-induced local FP mode enhancement shown in Fig. 5(c) and 5(d) around 800 nm is affected very little by sweeping α. But the LSP mode enhancements shown in Fig. 5(a) and 5(b) are sensitive to α. Increasing α will shift the spectral position of the LSP modes. And the magnitude of the dipole mode enhancement varies with α, reaching its maximum of nearly 120% at around α = 35°.

Fig. 5. Absorption enhancement mappings for a-Si solar cells of thickness d (nm) covered by a single silver nanoparticle of diameter D (nm) under TM incidence with α ranging from 0° to 45°. (a) d = 100 nm, D = 150 nm. (b) d = 100 nm, D = 200 nm. (c) d = 150 nm, D = 150 nm. ((d) d = 150 nm, D = 200 nm.

We noted that the field distribution of the dipole mode of the nanoparticle is [1]:

2

2

3 5

( ) [ 3 ( )](1 )iie e i

E krkr r r p r p r r p

k krr r

(7)

P is the dipole moment. The field generated by the dipole mode includes terms proportional to

r1

, r2

and r3

. The r1

term gives a far-field radiation. The near-field r2

and r3

terms decay greatly at long distances, but they give an intense field close to the surface around the nanoparticle. The near-field terms reach the maximum intensity when r is parallel with P,


which we can see in Fig. 1(b) as near-field “hotspots” bounded to the particle surface along the polarization of the incident light where giant local field enhancements are present. When the light scattered with large in-plane wave vectors evanescent in air interacts with the silicon substrate, it can be coupled into silicon as propagating light because of the high dielectric constant of silicon, resulting in an enhanced light scattering into the silicon substrate and more importantly a spectral shift of the dipole mode. As P is always parallel to the polarization of the incident light, the coupling between the particle and the substrate is dependent on α. As a result of the coupling the dipole mode is shifted in the spectrum. The absorption enhancement peaking at the dipole mode is also shifted correspondently, revealing a possibility to tune the enhanced absorption of the solar cell as shown in Fig. 5(a) and 5(b). We can infer from Fig. 5(a) and 5(b) that the strongest red shift occurs at around α = 15°. However, it should be noted that the LSP wavelength can‟t be shifted beyond a certain upper limit which is shorter than the LSP wavelength of the particle embedded in silicon. The quadrupole mode contains

components proportional to r5

, and it decays much faster from the particle surface than the dipole mode. The shifting of the quadrupole modes is much less obvious compared to the dipole mode because of its weak coupling with the substrate. Figure 6 shows the dipole LSP mode is sensitive to the incident angle. The dipole mode can be tuned by more than 200 nm with the incident angles from 0° to 45°. In summary, the near-field particle-substrate coupling combined with the enhanced light scattering give the main mechanisms of the enhancements from LSP modes, whose spectral positions could be tuned as our results showed.

Fig. 6. The spectral positions of the dipole mode enhancement peak of the silver nanoparticle on a 100 nm thick a-Si solar cell as a function of the incident angle.

We defined the normalized absorption enhancement as the integration of the absorption enhancements over the AM 1.5G solar spectrum multiplied by a normalized factor to study the average enhancing effect in the entire spectral range. As seen in Fig. 7(a), the normalized enhancement reaches a dip at around α = 15°, where the dipole peak meets its largest red shift. This is because solar power is relatively much weaker in the infrared range. The average enhancement falls as the dipole mode enhancement is shifted further into the infrared, and then recovers as the dipole mode is shifted to the blue when increasing α beyond 15°. However, when applied to a thick monocrystalline or polycrystalline silicon wafer solar cell of several hundred micrometers which suffers from insufficient absorption only near the bandgap of silicon, the silver nanoparticles may provide the optimized enhanced absorption if we shift their dipole modes to the silicon bandgap with the incident angle, which could work together with surface texturing and anti-reflection coatings to push further towards the upper limit of the conversion efficiency. We note that recent experimental works have observed absorption enhancements in silicon wafer solar cells 300 μm thick [18].

The incident angle has a lesser influence in the average enhancement of the 150nm thick solar cell, because the major contribution to its enhanced absorption is from the local FP mode


around 800nm whose spectral position is nearly not affected by α as shown in Fig. 5(c) and 5(d). The particle-induced local FP modes we found are insensitive to the incident angle because the refractive index of silicon is very large. In our case the incident angle didn‟t increase over 45 degrees, so the refracted light in the silicon cavity stayed approximately normal for all of our calculations, leaving the FP resonant condition relatively unaffected.

Fig. 7. (a) Normalized absorption enhancement in a 100nm thick a-Si solar cell with on-top silver nanoparticles of diameters D = 200nm or 150nm at a surface coverage of 6.67%, calculated by integrating the absorption enhancements over the AM 1.5G solar spectrum. (b) Normalized absorption enhancement in a 150nm thick a-Si solar cell.

Finally, it‟s worth noticing that the absorption of bare thin-film a-Si solar cells depends heavily on a few FP cavity modes. When increasing α, the light absorption at the FP modes is reduced. To achieve a balance between the enhancement and the absolute amount of light absorbed, it‟s suggested to keep the incident angle close to normal for thin-film solar cells. The incident angles over 35° should be avoided because they result in both a reduced amount of light absorbed and a much lower absorption enhancement. For a thick commercial silicon solar cell of about 100 μm thick, which suffers only from insufficient absorption near the silicon bandgap, we can still tune the incident angle to shift the LSP modes towards the bandgap to have enhancements. It should also be pointed out that under unpolarized sunlight illumination, the incoming light will excite separated TE and TM LSP modes in a three-dimensional particle. The TE dipole mode stays parallel to the substrate while the TM dipole mode will be shifted as discussed above.

5. Conclusion

We have performed a theoretical study of the enhanced absorption in a thin-film silicon solar cell covered with silver nanoparticles. We discussed two mechanisms of absorption enhancement of a single silver nanoparticle: the resonant localized surface plasmon (LSP) modes of the nanoparticle and nanoparticle-induced local Fabry-Perot (FP) modes, and found the incident angular dependence of the absorption enhancement. Tuning the incident angle will shift the spectral positions of the LSP modes while local FP modes are affected very little. The LSP mode shifting mechanism influences greatly the average absorption enhancement, hence the incident angles must be taken into consideration when we pursue the optimized performance of a thin-film solar cell using nanoparticles. Our results suggest the incident angle should be kept normal to the surface of thin-film a-Si solar cells. Incident angles over 35° should be avoided. The average enhancement can reach up to 6% for a single nanoparticle which corresponds to a 7% surface coverage. This mechanism can also be applied to other cases where plasmonic nanoparticles are placed on a dielectric substrate.

Acknowledgments

This work was supported by National Basic Research Program of China (973 Program), Grant No. 2007CB936800, and National Natural Science Foundation of China (Grant No. 60977015 and 10574002).


incident angle dependence of absorption enhancement in plasmonic solar cells

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