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Resource efficient plasmon-based 2D-photovoltaics with reflective support

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Abstract

For ultrathin (~10 nm) nanocomposite films of plasmonic materials and semiconductors, the absorptance of normal incident light is typically limited to about 50%. However, through addition of a non-absorbing spacer with a highly reflective backside to such films, close to 100% absorptance can be achieved at a targeted wavelength. Here, a simple analytic model useful in the long wavelength limit is presented. It shows that the spectral response can largely be characterized in terms of two wavelengths, associated with the absorber layer itself and the reflective support, respectively. These parameters influence both absorptance peak position and shape. The model is employed to optimize the system towards broadband solar energy conversion, with the spectrally integrated plasmon induced semiconductor absorptance as a figure of merit. Geometries optimized in this regard are then evaluated in full finite element calculations which demonstrate conversion efficiencies of up to 64% of the Shockley-Queisser limit. This is achieved using only the equivalence of about 10 nanometer composite material, comprising Ag and a thin film solar cell layer of a-Si, CuInSe2 or the organic semiconductor MDMO-PPV. A potential for very resource efficient solar energy conversion based on plasmonics is thus demonstrated.

©2010 Optical Society of America

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Figures (6)

Fig. 1
Fig. 1 Basic light absorbing structures under consideration. Light is assumed incident from the left in a dielectric medium of refractive index ni . In (a), a light absorbing, planar thin film (complex refractive index m, thickness d) is supported by a dielectric spacer (refractive index ns , thickness h) and an optically thick reflective substrate (to the right). In (b), the absorbing film is replaced by an array of identical, ellipsoidal shaped core/shell nanoparticles. The cores have a circular cross section of radius a in the array plane, and a semi-axis length c in the normal direction. The shells extend the core semi-axes by a fixed thickness. The array has an effective thickness de . Incident wave vectors and their normal components are represented by black arrows in (a), but it should be noted that their amplitudes are complex inside the film. In (b), the black arrows illustrate incident and specularly reflected fields for normal incidence of light. Scattered fields mediating lateral interactions between the particles in the array are shown as green, dashed arrows, while fields mediating interactions via the reflector are indicated by red, dashed arrows.
Fig. 2
Fig. 2 Angular responses for practically 2D thin films (δ ~10−4), maximizing the absorptance at normal incidence of TE- (solid lines) and TM-polarized light (dashed lines). The incident wavelength was λ = 840 nm and ni = 1.5. The center wavelength was either λc = λ = 840 nm (red, thick lines) or λc = 550 nm (black, thin lines). The refractive index of the spacer layer was in (a) ns = 1; in (b) ns = 1.5 and in (c), ns = 2. The dip in the TM-polarized case is at the critical angle between the external media, here occurring at 42, 90 and 90-46i° (complex angle), respectively. The influence of λc (and thus spacer thickness) is less dramatic.
Fig. 3
Fig. 3 (a) Model absorptance in a square Ag-core/CuInSe2-shell nanoparticle array, as a function of the normalized lattice constant Λ and the aspect ratio a/c of the cores. The target wavelength was λ 0 = 800 nm and the external medium refractive index ne = 2. The volume equivalent radii of the particle cores were 20 nm, the shell thicknesses 10 nm and the spacer thickness such that the center wavelength was λc = 800 nm. For very small aspect ratios, the requirement that the particles do not touch the back reflector limits the parameter space. The further condition that they should not touch each other bounds the parameter space from below. These limits are indicated by solid white lines to the far left and below the maxima. The vertical, dashed white line distinguish prolate (left) and oblate (right) particle shapes. Maximum absorptance of 100% is predicted at the white cross. The cross size represents ± 10% changes of the underlying variables, and ends above the 90% absorptance contour. This indicates a relatively high robustness of the optimum in this parameter space. In (b), the absorptance for the geometrical conditions at the cross in (a) are shown as a function of incident light wavelength. The model calculation is compared to calculations by FEM for the same set of parameters, including an ideal backside reflector. The black arrow indicates λc and the vertical line λ 0. In (c) and (d), the same conditions applies, except that the center wavelength λc of the support is offset to 550 nm. In (e) and (f), λc is offset to 1050 nm instead. The main effect of these offsets is a skewing of the absorptance peak shape about the maximum.
Fig. 4
Fig. 4 Optical constants of thin film solar cell materials considered. The approximate positions of the bandgap thresholds are indicated by the arrows.
Fig. 5
Fig. 5 Spectrally weighted plasmon induced absorptance [Φ, see Eq. (7)] as a function of the equivalent sphere radius of the core and the peak wavelength λ 0. In this map, the particle aspect ratios and the lattice constants were optimized to maximize the total absorptance for each value of ro and λ 0. The particle cores are assumed to be Ag, and the shells are CuInSe2 with a fixed thickness of 5 nm. The external medium refractive index is ne = 2. Particles are prolate to the left of the white dashed curve, and oblate to the right. Unphysical overlap of the particles occurs below the solid white line, which leads to an approximate position of the valid local maximum at the cross mark. At this point, the core aspect ratio is a/c ≈2.7 and the lattice constant Λ ≈38 nm. The cross arms have lengths corresponding to 10% of the underlying parameters, and show that the optimum is relatively robust to deviations also for these parameters.
Fig. 6
Fig. 6 Analytic model and FEM calculated absorptance for core/shell systems selected on merits of their high spectrally weighted plasmon induced absorptance. The spectral photon flux distribution of AM1.5G sunlight (light grey, in arbitrary units) is included for comparison. The particle cores consist of Ag and the shells of different solar cell materials. Identical systems are considered in the different types of calculations, except that a more realistic Al backside reflector is simulated in the FEM calculations instead of the perfect reflector assumed in the model. In (a) and (b), the PV shells consist of CuInSe2, with the difference that the RS center wavelength is chosen equal to the peak wavelength at 840 nm in (a), and to 550 nm in (b), respectively. In (c), the shell material is a-Si, and in (d), it is the organic semiconductor MDMO-PPV. The circular symbols show estimates for the shell absorption at maximum, based on the analytic model.

Tables (1)

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Table 1 Conditions and results for optimized Ag-core/semiconductor-shell nanoparticle arrays

Equations (9)

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r ˜ = r i r d γ 2 1 r i r d γ 2   ,
m 2 i n i n ˜ s δ = λ 2 π d [ i n i + n s cot ( π λ c 2 λ ) ]   .
r i = q i q m q i + q m   and   r d = i q s cot ( q s h ) q m i q s cot ( q s h ) + q m   ,
r i = n i 2 q m m 2 q i n i 2 q m + m 2 q i   and   r d = i n s 2 q m cot ( q s h ) m 2 q s i n s 2 q m cot ( q s h ) + m 2 q s   .
m e 2 = 2 n e F α ¯ δ e ( 1 f α ¯ )  ,
[ f 2 i n e n e n ˜ s F ] α ¯ = 1   .
Φ = 0 λ G w ( λ ) Δ A ( λ ) d λ   .
A s c ( λ 0 ) = Γ 0 A ( λ 0 )  ,
A s c = 0 λ G w ( λ ) A s c ( λ ) d λ  ,
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