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Abstract
Hybrid 3D Finite difference time domain-Monte Carlo ray tracing (FDTD-MCRT) algorithm has been developed to model and optimise small and large scale plasmonically-enhanced luminescent solar concentrator (pLSC) devices for photovoltaic (PV) applications. The configuration parameters (for example, dimensions, shape, and optical properties of metal nanoparticles, luminescent species, and host material) were used to characterise the probability of optical energy transfer and loss processes, as well as reflection, refraction, absorption, emission enhancement, and total internal reflection (TIR) in the pLSC. The algorithm was validated through modelling of various doping concentrations of CdSe/ZnS quantum dots (QD) and gold nano spheres (Au NS) where ∼50% enhancement in optical conversion efficiency (OCE) was observed for a plasmonic composite of 2 ppm Au NS and 0.008 wt. % QD.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Advanced pLSC [1–3] was introduced to improve the energy conversion efficiency (ECE) and enlarge the size of conventional LSCs to make it a promising semi- transparent component in building integrated photovoltaic (BIPV) systems. In pLSC, metal nanoparticles (MNP) such as gold nano particles (Au NP) and silver nano particles (Ag NP) are plasmonically coupled to luminescent molecules in a polymeric waveguide. The waveguide traps incident solar energy and concentrates the energy to the lateral edge (where a PV solar cell is located) through TIR. During the TIR process, the incident solar spectrum is also modified by the coupled nanoparticles and luminescent molecules to ensure optical matching with the PV solar cell, improving the power conversion efficiency (PCE). Chandra et al., investigated the performance of CdSe/ZnS core-shell QD coupled with 10 nm gold nano spheres (Au NS) [3,4]. ∼53% enhancement in OCE (depending on doping concentration of QD and Au NS) was observed in small samples (20 × 12 × 12 mm cuvette). Later, El-Bashir et al., measured a ∼2.4 and 4.75 fold fluorescence enhancement when the luminescent material was coupled to 60 nm and 100 nm Ag NP respectively [5]. They also manufactured various double-layer pLSCs (20 × 8 × 0.3 cm) based on Au NPs and Ag NPs doped with coumarin dye attached to mc-Si, c-Si and a-Si PV solar cells [1]. ∼53% enhancement in PCE was observed in the pLSC with a-Si PV solar cell and 20 ppm MNP doping concentration. MNP doping concentration has an impact on pLSC performance e.g. PCE enhancement rate of the pLSC with c-Si PV solar cell varied from ∼15% to 25% for a MNP doping concentration of 5 ppm to 10 ppm respectively while further increases in doping concentration mitigated the device PCE due quenching [6].
Due to the complex optical and plasmonic interaction procedures, optimising pLSCs in terms of their size, doping concentration (distance between MNP and luminescent molecule) and their spectral overlap is more challenging compared to conventional LSCs, both in modelling and experiment [1–3,5]. Although various studies have been undertaken to model conventional LSC [7–18] and to fabricate large scale LSC [19–21], there is no algorithm established for modelling, optimising and sensitivity analysis of small and large scale pLSC.
This research presents a new hybrid 3D finite difference time domain-Monte Carlo ray tracing (FDTD-MCRT) model to optimise and analyse both small and large pLSCs with the aim to reduce the complexity of the optimisation and manufacturing process of pLSCs. It comprises a pLSC mathematical model developed based on the probability of the optical and energy transfer processes occurring in a pLSC (such as absorption, enhancement, quenching and emission in the MNP-Luminescent molecule coupling as well as reflection, refraction, TIR and loss mechanisms). The designed mathematical pLSC model is deployed through a MCRT algorithm [15,22–24]. The FDTD algorithm [25–27] is combined and developed in the MCRT pre-processing stage to achieve the plasmonic optical properties of doped MNP required in pLSC modelling. Prior to combining and developing the hybrid model, both MCRT and FDTD were individually validated [15,27]. The complete model has been then developed as an .exe file which can be installed and used as a tool on computers.
1.2. Energy conversion efficiency (ECE) parameters in pLSC
After running the model, the pLSC performance was evaluated in the post-processing stage from two perspectives: (i) analysis of energy loss mechanisms such as reflection as well as thermal losses including re-absorption, non-unity quantum yield (QY), energy quenching, host material attenuation losses; (ii) evaluation of device ECE parameters including OCE, solar concentration ratio (C) and PCE. OCE is the ratio of photons reaching the pLSC edge (${N_{edg}}$) to photons incident on top of the pLSC (${N_{inc}}$) [28]:
The product of OCE and the device geometric gain (${G_g}$) results in calculating C [28]:
By coupling PV solar cell (with efficiency of ${\eta _0}$) to the edge of pLSC, PCE is calculated [28]:
1.3 Plasmonic coupling of MNP and luminescent material
Understanding of plasmonic interaction induced energy transfer in coupled MNP and luminescent materials is required to develop a pLSC mathematical model. The absorption, excitation and emission rate of luminescent materials can be improved due to localized surface plasmon resonance (SPR) enhancing plasmonic properties of the coupled MNP [29,30] and pLSC concentrated photon flux [5]. This means the coupled MNP and luminescent molecule in pLSC are able to absorb more photons and consequently emit a higher portion of the incident energy compared to luminescent molecules in a traditional LSC.
In conventional LSC, the luminescent molecules absorb the incoming photons, whose energy is equal to or greater than the energy difference between energy levels of molecule. When a molecule is excited to a higher energy level beyond the ground state, electrons are excited to higher energy electronic states, this process is known as excitation. These electronically excited states are short lived and move to a lower energy level by either spontaneously emitting a photon equal to the energy difference of energy level or with no photon emission. The former is called radiative decay and latter as a non-radiative decay relaxation returning the molecule to the ground state. Their decay rates are ${{\rm{\varGamma }}_{r\;\;}}$ and ${{\rm{\varGamma }}_{nr}}$, respectively. The radiative decay rate results in luminescent emission while the non-radiative decay rate causes thermal loss. QY (i.e. emission efficiency of luminescent molecule) and life time (${\tau _0}$) is correlated to the radiative and non-radiative decay rates calculated by [6]:
On the other hand, in pLSC, when a MNP (such as Au NP) is coupled and interacts with a luminescent molecule, the device performance can be improved due to the photon density enhancement factor (PDEF) [31–33] which is a product of excitation and emission efficiencies:
${\lambda _{ex}}$ and ${\lambda _{em}}$ are the excitation and emission wavelengths respectively, ${x_d}$ is the location of the particle with a unit dipole moment of ${e_p}$. $\varPsi ({{e_p},\;{x_d},\;{\lambda_{ex}}} )$ is excitation efficiency defined as [6]:This information is used in developing the mathematical model and configuration of pLSC in Section 2. In Section 3, the modelling results are studied and validated. The validated model is then used to optimise and study both small and large scale pLSCs in Section 4. The developed model is also used to analyse the sensitivity of pLSC to several parameters such as background absorption, QD Stokes’ shift, as well as QY variations.
2. Hybrid FDTD-MCRT 3D model for pLSC
Based on the plasmonic interactions between MNP and luminescent material, the configurations and schematic diagram of pLSC is proposed in Fig. 1.
Fig. 1. (a) Configuration of pLSC which shows: 1- incident photon strikes the pLSC, 2- it is absorbed by the coupled luminescent-MNP, then 3- re-emitted at longer wavelength and 4- waveguided by TIR and 5- reaches the PV solar cell. Energy losses include: 6- the fraction of photons exited from the device, 7- front surface reflection and 9- the emitted photon which is reabsorbed by other particles and losses some part of its energy. (b) Energy transfer procedures taking place in luminescent-MNP coupling: Based on the spectral overlap and optical properties of coupled luminescent-MNP, some photons are absorbed by 9- luminescent molecule or 10- MNP resulting in SPR energy generation and contributing in characterisation of excitation/emission efficiencies (11 and 12) and emitted based on PDEF and energy quenching of the coupling. Note that, other energy loss mechanisms are not shown here including photons scattered or attenuated by the host material, those lost due to multi-scattering of light with multi-MNPs and self-quenching of MNPs and those lost due to chemical interface damping.
2.1 pLSC mathematical model
Based on configuration introduced in Fig. 1, a mathematical model for pLSC was developed. All physical and optical energy transfer phenomena were deployed in the model using separate mathematical functions based on their occurrences’ weighted probability (PR). PR for various optical interaction phenomena are calculated from the pLSC specifications such as host material type, optical properties and doping concentration of the MNP and luminescent material, as well as inner and outer refraction indices and dimension of pLSC.
A portion of the incident solar radiation (${P_{in}}(\lambda )$) is reflected from the top surface of pLSC due to mismatched refraction indices of media (${P_{reflect}}({\lambda ,{\theta_i},{\eta_{out}},{\eta_{host}}} )$) while the rest is refracted:
Where $P{R_r}({{\theta_i},{\eta_{out}},{\eta_{host}}} )$ is the reflection probability of pLSC as a function of incident angle (${\theta _i}$), refraction indices of the host material (${\eta _{host}}$) and ambient air (${\eta _{out}}$) and calculated by Fresnel equation [57,58]. For simplicity, ${P_{refract}}({\lambda ,{\theta_i},{\eta_{out}},{\eta_{host}}} )$ is denoted as ${P_{refract}}(\lambda )$.
A portion of ${P_{refract}}(\lambda )$ directly reaches the PV (${P_{direct}}(\lambda )$) mounted on pLSC. The rest of the rays are trapped (${P_{trap}}(\lambda )$) and waveguided by TIR based on critical angle (${\theta _c}$) and Snell’s law [59]. The non-trapped and non-absorbed energy exit the pLSC as escape cone (${P_{cone}}(\lambda )$) and transmission losses.
A fraction of the trapped energy is directly absorbed by luminescent material based on $PR_{abs}^L(\lambda )$ and a portion of the trapped energy is absorbed by MNP based on $PR_{abs}^{MNP}(\lambda )$ generating SPR energy (${P_{SPR\;}}(\lambda )$). Note that $PR_{abs}^L(\lambda )$ and $PR_{abs}^{MNP}(\lambda )$ are calculated from absorbance spectrum of luminescent material and extinction spectrum of the MNP respectively by using Beer Lambert law [9,58,60,61]. The SPR energy is then radiated to the coupled luminescent species based on $P{R_{PDEF}}({di} )$ and $P{R_{QF}}({di} )$ which are achieved from PDEF and quenching respectively as a function of distance (di) between the MNP and luminescent material. Therefore, the absorbed energy of luminescent material can be given as:
The summation is applied in the wavelength range of interest; i.e. ${\lambda _{min}}$ to ${\lambda _{max}}$. The absorbed energy is then emitted with the probability of $P{R_{QY}}$ (calculated from $QY$) and with a wavelength based on $P{R_{emit}}(\lambda )$ calculated from the normalised emission spectrum of luminescent material:
The rest of the absorbed power is lost thermally due to non-unity QY:
The total energy emitted by the luminescent material in pLSC is:
The non-absorbed and emitted radiation are transmitted through TIR inside the device which is:
Host material attenuation and scattering are obtained by:
As can be seen in Eqs. (15) and (16), the probabilities of energy loss mechanisms are also a function of Dim (i.e. “pLSC dimension” including its size and shape). Moreover, $\;P{R_{re - abs}}({\lambda ,Dim} )$ depends on the Stokes’ shift of the luminescent material. $P{R_{atte}}({\lambda ,Dim} )$ and $P{R_{scat}}({\lambda ,Dim} )$ are respectively the attenuation and scattering coefficients of the blank host material (waveguide) calculated using Beer Lambert law and measured using a spectrometer. By denoting these losses as total loss (${P_{lost}}({\lambda ,di,Dim} )$), the pLSC total output energy reaching the edge-mounted PV is given by:
2.2 FDTD-MCRT development
The introduced mathematical pLSC model was then used to develop a 3D hybrid FDTD-MCRT algorithm, illustrated in Fig. 2 and includes four main stages (i) Graphical User Interface (GUI); (ii) Pre-Process; (iii) Main Loop and (iv) Post-Process:
- (i) In the first step, pLSC configuration parameters (such as dimensions, medium refractive indices, incident solar radiation spectrum, MNP specifications, optical properties of luminescent and host materials) are imported through the GUI (See Fig A1 in Appendix).
- (ii) In the Pre-Process stage, our developed 3D FDTD model [27] is used to simulate and obtain MNP optical properties including extinction, scattering, absorption and PDEF. Our FDTD algorithm uses the Lorentz-Drude [62] model to simulate MNP frequency-dependent permittivity and achieves its electromagnetic characteristics by solving Maxwell’s equations in a 3D FDTD Yee grid. The FDTD model has been already validated through modelling of MNPs with various shape, size and doping concentration [27]. Using the FDTD modelling results and pLSC configuration input parameters, a 3D pLSC structure along with its boundary-planes are created in a 3D tracing-space.
- (iii) The developed pLSC mathematical model is applied to the structure in the Main Loop which includes an additional iterative loop for the “Internal Cycles” (shown in the green box in Fig. 2) which determines the status of each incident ray (by determining the probability of reflection, absorption, scattering, attenuation and transmission) in the 3D tracing-space according to their allocated PR. The Main Loop is iterated for each incident rays until the final fate is known (shown in the yellow boxes in Fig. 2).
- (iv) After finishing the main iterative loop, the modelling results are produced from the Post-Process stage. The detailed final results include the enhancement, output emission spectra, ECE parameters (OCE, C and PCE), total energy losses such as reflection as well as total thermal losses including re-absorption, non-unity QY, energy quenching and host material attenuation losses.
3. Model validation
3.1 Model inputs
The experimental results obtained from 12 small samples (20 × 12 × 12 mm cuvettes) [3,4] were used to validate the proposed algorithm and model. The samples (denoted as D1 to D12) were doped with various concentration of QD (QD-c) and Au NS (Au NS-c) classified in Group 1 to 3 as can be seen in Table 1. The host material was epoxy resin doped with ∼10 nm Au NS and core-shell CdSe/ZnS QDs (QD 575) with ∼50% QY manufactured by Plasmachem Germany.
Table 1. QD and Au NS doping concentration of experimental samples used for model validation
The QD emission and absorption spectra is shown in Fig. 3 exhibited a single emission peak of ∼575 nm and a wide absorption band with a peak at ∼555 nm, resulting in ∼20 nm Stokes’ shift.
Among the available methods to model MNP optical properties [6,63]; we have used a 3D FDTD algorithm which is accurately able to model Au NS optical properties including its scattering, absorption, extinction and PDEF. FDTD model requires the Au NS input specifications including its size, shape and doping concentration as well as defining unit dipole moment (${e_p}$) and its location (${x_d}$) in the FDTD Yee grid. Au NS particles were considered to be homogeneously dispersed with the same shape and size (10 nm diameter). For a homogenous device, FDTD modelling of a single particle can result in achieving the required outputs if well-designed boundary conditions are applied in all directions of the Yee grid [25]. Giving this condition, a single Au NS was modelled in a 3D FDTD Yee grid with discretization of 5.8 nm (Fig. 4(a)). Periodic boundary conditions (PBC) were defined in x and y axes of the grid and that is why the electric field seems to discontinue in these axes. Absorbing boundary condition (ABC) were defined at z axis by placing a perfectly matched layer (PML) at both boundaries of the grid in the z-axis to absorb and gradually diminish the energy exiting from the scattering boundaries. The modelled particle was radiated by a Gaussian source electric field (representing the solar radiation spectrum) which was injected as a plane wave and propagated in the z-direction while it was polarized along x-y plane. Figure 4(a) shows the electric field distribution (3D and top-view) at the moment the Gaussian source strikes the Au NS during FDTD simulation. As can be seen, the electric field was enhanced at the boundary of Au NS due to SPR. Once the field was terminated in the grid, fast Fourier transform (FFT) was used to achieve the extinction spectra and electric field enhancement from the time-domain-response of the Yee grid. Figure 4(b) shows the electric field enhancement of the modelled Au NS over time and its location (x-view) in the grid which was used to generate PDEF. As can be seen, the field plasmonic enhancement maximum value was ∼4.7 fold on the particle’s boundary which exponentially decreased to 1 (background electric field) as a function of distance from the particle’s surface. The extinction spectra of Au NS can be seen in Fig. 5(a) where the SPR peak was at ∼550 nm in close agreement with reference experimental results. By changing the spacing between the particle and PBC, different doping concentrations of Au NS could be modelled whose results were used to obtain Fig. 5(b) showing the linear variation of the extinction peak over various Au NS-c.
Fig. 4. Single 10 nm Au NS under simulation in 3D FDTD Yee grid: (a) screenshot of the electric field distribution when Gaussian field source strikes the Au NS (3D and top-view) and (b) electric field enhancement over time and location (x-view) used to generate PDEF.
Fig. 5. FDTD simulated modelling results for Au NS: (a) extinction spectra (validated by experimental data) whose (b) SPR peak is in close match with experiment and increasing linearly by increasing Au NS doping concentration.
By using the FDTD simulated results and specifications of Group 1 to 3 (Table 1), all samples were simulated by MCRT algorithm under standard direct solar radiation spectrum (AM1.5) [64]. Figure 6(a) shows a visual configuration of a sample (20 × 12 × 12 mm cuvette) under radiation of ∼350 direct incident rays (only for visualization purposes and validation).
Fig. 6. Visualization of pLSC simulation where samples were illuminated by irradiation of ∼350 direct incident rays: (a) small sample (in 20 × 12 × 12 mm cuvette), and (b) Large scale pLSC (900 × 900 × 3 mm). Black dots show the incident ray source, the green dots show the first intersection point of the incident rays with the top surface. Red dots represent the rays lost due to thermal losses. Cyan dots for the rays exited from the device and yellow dots illustrate the TIR wave-guided rays to the black edge-mounted plane (PV solar cell).
3.2 Model validation without considering Au NS plasmonic coupling
The developed model was then run for 1,000,000 direct solar incident rays. This was undertaken to guarantee modelling accuracy (as the algorithm is implemented based on probabilities) and to mitigate the noise in the edge-emission spectrum which was found in close agreement with experimental reference results (Fig. 7(a)). By increasing QD-c from 0.005 wt. % to 0.1 wt. % in 0-ppm sample (sample with no Au NS), the maximum emission intensity was achieved for QD-c of ∼0.05 wt. % (Fig. 7(b)). A further increase in QD-c reduced the emission intensity due to an increase in re-absorption losses.
Fig. 7. Results of samples with no Au NS: (a) Edge-emission spectrum and (b) edge-emission intensity over QD doping concentration (curves are normalised to experimental peak).
3.3 Model validation considering Au NS plasmonic coupling
In the following of coupling Au NS to QD, Au NS-c was increased from 0 to 6.5 ppm in the model for each group of samples. The maximum enhancement in performance of each group was compared to experimental reference results and found in close agreement with average modelling accuracy of ∼96%. As is reported in Table 2, maximum enhancement of ∼53%, 17% and 12% in ECE parameters were achieved for Group 1 to 3 when QD were coupled to ∼2.3 ppm, 2.2 ppm and 1 ppm Au NS respectively.
Table 2. Comparison of the Best Modelling and Experimental Results for Each Group of Samples
Figure 8 shows the edge-emission spectra for Group 1 to 3 comparing the emission intensity of 0 ppm samples (no Au NS) with samples in which the maximum enhancement in emission intensity was achieved after coupling Au NS to QD. The modelled edge-emission peak (at ∼575 nm) was found to be a close match with experimental results. As can be seen, by increasing Au NS-c, the emission peak was enhanced and maximum enhancement was observed at Au NS-c of 2.3 ppm, 2.2 ppm and 1.1 ppm for Group 1 to 3 respectively. A further increase in Au NS-c, reduced the emission intensity due to an increase in the rate of energy quenching in QD-Au NS coupling. More details can be found in Fig. 9 where the enhancement in integrated emission and ECE parameters are also compared to experimental results. A curve fitting technique was also applied to get the consistent trend of the results and minimize both modelling and experimental errors. The modelling enhancement peaks in Group 1 (∼53% at 2.3 ppm), Group 2 (∼17.27% at 2.2 ppm) and Group 3 (∼12.1% at 1.1 ppm) were in close agreement with the experimental results obtained for D3 (53% at 2 ppm), D9 (16.8% at 2 ppm) and D11 (12.5% at 1 ppm) respectively. It can also be observed that by reducing QD-c from 0.02 wt. % to 0.008 wt. %, the Au NS-c range which was required to keep the sample in the enhancement region (positive side of the enhancement graph) was extended from [0, 2.4] ppm to [0, 5.7] ppm.
Fig. 8. Enhancement in edge-emission intensity (normalized to 0-ppm experimental results) for: (a) Group 1, (b) Group 2 and (c) Group 3 after coupling QD to Au NS (Zoom-in view: 520–630 nm).
Fig. 9. Enhancement in ECE parameters for: (a) Group 1 (D1 to D5), (b) Group 2 (D6 to D9) and (c) Group 3 (D10 to D12) after coupling QD to Au NS.
The observed discrepancy between the modelling and experimental results, are possibly contributed to experimental measurement factors such as doping concentration of MNPs and QDs. Also, experimental Au NS and QD samples may not have been homogeneously dispersed in the samples. Modelling errors occur as particles are considered monodispersed in size and shape; however, the synthesised Au NS always have size and shape dispersion. Non-linear parameters such as chemical interference, the effect of temperature changes and material degradation are not considered in the model. QY of luminescent species are changed as a function of host material and wavelength [65]; however, QY is considered as a constant number in the model.
4. Modelling, optimisation and sensitivity analysis of small and large scale pLSC
4.1 Statistical modelling results of the optimised sample
The optimised sample from Group 1 (0.008 wt. % QD+2.3 ppm Au NS) which resulted in the highest enhancement peak were used for small and large scale pLSC optimisation and analysis. Table 3 presents the detailed statistical modelling results obtained for the best and worst samples of Group 1 compared to the 0 ppm sample. As can be seen, ∼4% of direct solar radiation was reflected from the top surface of all samples due to mismatching of air and epoxy refractive indices. The rest of the incident rays (∼96%) were refracted inside the devices. When Au NS-c was 2.3 ppm (Best Case), the total thermal losses increased from ∼9% to ∼22% due to an increase in the quenched energy (∼13%). However, the plasmonic enhancement was dominant in comparison with quenching resulting in an increased trapping efficiency which reduced the rate of photons exited from the device from ∼84% to ∼80%. The rate of photons reaching the edge-mounted PV cell (OCE) increased from 2.45% (in 0 ppm sample) to 3.75% (in QD-Au NS sample). The same results were obtained for C due to unity ${{\rm{G}}_{\rm{g}}}$ of the sample. By considering a mc-Si PV cell with an average bare cell efficiency of ${{\rm{\eta }}_0} \approx 22{\rm{\%\;}}$ [66] and using Eq. (2), PCE was also enhanced by ∼53% from ∼0.6% to ∼0.9%. When the sample was doped with 6.5 ppm Au NS (Worst Case), the amount of quenched energy increased (∼26%) due to the high Au NS-c inside the sample, reducing the spacing between MNP and QDs and increasing the total rate of thermal losses to ∼36%. In this case, quenching was dominant which significantly decreased OCE and PCE to ∼1.9% and ∼0.42% respectively which were ∼23% less than 0 ppm sample.
Table 3. Detailed Statistical Modelling Results of the Optimized Sample
Figure 10 evaluates the performance of Group 1 over Au NS-c variations focusing on thermal loss and the rate of photons exited from the device as well as OCE. As is observed in Fig. 10(a), when Au NS-c increased from 0 to 6.5 ppm, the rising slope in thermal losses was steeper than the declining slope in the rate of photons exited from the device. This also justifies the dominance of quenched energy and low OCE value (1.9%) at Au NS-c = 6.5 ppm. Figure 10(b) illustrates OCE variations indicating the enhancement and quenching regions of the group. As can be seen, for Au NS-c > ∼5.7 ppm, samples were operating in the quenching region where the amount of quenched energy in QD-Au NS coupling was more dominant than enhancement.
Fig. 10. Performance evaluation in Group 1 over variations of Au NS-c: (a) Thermal losses comparing with the rate of photons exited from the device. (b) OCE indicating enhancement and quenching regions.
4.2 Small and large scale pLSC optimisation
This validated hybrid algorithm was then extended to optimise large scale pLSC by the following methodology. The optimised configuration (0.008 wt. % QD+2.3 ppm Au NS) was first used to develop a model for small scale 20 × 20 × 3 mm pLSC (Fig. 6(b)) simulated under direct solar radiation. The detector was placed at the lateral edge of pLSC. Then, ${{\rm{G}}_{\rm{g}}}$ was increased from ∼6 to 500 by increasing the aperture dimensions (L = W) of pLSC from 20 mm to 1500 mm (Fig. 11(a)). This characterised all ECE parameters including OCE, PCE and C of pLSC. OCE exponentially dropped from ∼1.8% to 0.01% by increasing ${{\rm{G}}_{\rm{g}}}$ (Fig. 11(b)) due to increase in reabsorption and ultimately total thermal losses from ∼18% to 21%. However, as can be seen in Fig. 11(c) solar concentration ratio increased from ∼12% (at ${{\rm{G}}_{\rm{g}}}$ of ∼6) to 39% (at ${{\rm{G}}_{\rm{g}}}$ of ∼300) representing the optimised large scale 900 × 900 × 3 mm pLSC (The device under only ∼350 incident rays can be found in Fig. 6(c)). Further increase in ${{\rm{G}}_{\rm{g}}}$ significantly reduced C due to the domination of thermal losses as well as near-zero OCE at ${{\rm{G}}_{\rm{g}}}$=500.
Fig. 11. (a) Geometric gain variations over pLSC dimension (L = W). ECE parameters of pLSC under direct, diffuse and global solar radiation in various geometric gains: (b) OCE, PCE and (c) C.
4.3 Impact of local diffuse/direct solar radiation on pLSC performance
Performance of small and large scale pLSCs were investigated and compared under standard AM 1.5 global, diffuse and direct solar radiation where the best results were obtained under diffuse solar radiation (Figs. 11(b) and 11(c)). Figure 12 was achieved by modelling results and can be used to estimate the performance of large scale pLSC based on the local rate of diffuse and direct solar radiation [67]. Transmission losses decreased from ∼62% (under direct solar radiation) to ∼51% (under diffuse solar radiation). The total amount of transmitted photons and emission photons exited from the device (i.e., transmission and escape cone losses) decreased from ∼85% (under direct solar radiation) to ∼69% (under diffuse solar radiation). Further to these, ∼3% increase in thermal losses was observed under diffuse solar radiation. Surface reflection of 4% and 16% was recorded for direct and diffuse radiation, respectively. The overall decrease (from ∼85% to ∼69%) in the light exited from the device was contributed to higher fraction of light and emission photons trapped by TIR in the pLSC. Moreover, the trapping efficiency was improved by light and emission photons scattered by Au NS in conjunction with luminescent enhancement. Therefore, under 100% diffuse solar radiation, pLSC could reach the highest C of ∼52% which implied ∼33% enhancement in C, OCE and PCE in comparison with the results under pure direct solar radiation.
Fig. 12. C variations in large scale pLSC (900 × 900 × 3 mm) based on local rate of diffuse and direct solar radiation.
4.4 Impact of background absorption (attenuation loss), QD stokes’ shift and QY variations on pLSC performance
By considering ideal transparent polymeric host material (zero background absorption) in large scale pLSC, thermal losses reduced from ∼22% to ∼19% as no incident energy was attenuated by the ideal host material. However, this had an impact on increasing the rate of photons exited from the device from ∼85% to ∼87% (due to the open bottom layer of pLSC) which resulted in only a slight enhancement in device performance (∼0.5% enhancement).
Re-absorption losses are governed by Stokes’ shift of the utilised QD. Using current luminescent materials with near-zero spectral overlap of absorption and emission spectra can reduce reabsorption losses in LSCs. However, more attention must be paid in the pLSC optimisation process to its performance is a function of both MNP and the luminescent material’s optical properties and spectral overlap. For example, increasing Stokes’ shift of QD in the presented pLSC (i.e. red-shifting of the QD emission spectrum seen in Fig. 13(a), resulted in two procedures: it reduced (i), re-absorption losses and (ii) spectral overlap of QD emission and Au NS extinction peak at ∼550 nm (Fig. 13(a)) mitigating the emission efficiency of the plasmonic coupling. As can be observed in Fig. 13(b), when the Stokes’ shift of the original QD575 was increased from 20 nm to 50 nm, the former procedure was dominant and resulted in a ECE enhancement of ∼35% (in OCE, PCE and C). For QD Stokes’ shift > 50 nm, the impact of the latter procedure was dominant which reduced the plasmonic enhancement (e.g. to ∼27% for Stokes’ shift of 70 nm).
Fig. 13. (a) Spectral overlap between Au NS extinction, QD absorption and emission spectra, (b) Enhancement in ECE parameters of large scale pLSC (900 × 900 × 3 mm) over increasing the QD Stokes’ shift (red-shifting QD emission spectrum), and (c) Enhancement in ECE of large scale pLSC (900 × 900 × 3 mm) over increasing QY of QD.
Increasing QY of the QD can reduce waveguiding thermal losses (mainly non-unity QY loss) and also increase the rate of isotropic emission of QD in pLSC. This can enhance the energy trapping rate and OCE of the pLSC. For example, Fig. 14© illustrates that by increasing QY from 50% to 70% in large scale pLSC ∼38% enhancement was observed in ECE parameters.
5. Conclusion
Optimising the spectral overlap, doping concentration of luminescent material and MNP as well as size of pLSC have been found to be a complex and critical task for pLSC development. In this paper, a novel hybrid FDTD-MCRT algorithm and mathematical model were developed and used as a promising 3D tool to optimise the configuration of small and large scale pLSCs and ease their manufacturing process. The model was validated for several samples doped with coupled QD-Au NS and results were found to be in close agreement with experimental outputs with an average modelling accuracy of ∼96%. The plasmonic composite of ∼2 ppm Au NS-c and 0.008 wt. % QD-c resulted in ∼50% ECE enhancement in a small sample (20 × 12 × 12 mm cuvettes). Close distance between QD and Au NS (characterising by their doping concentration) increases the non-radiative decay rate and energy quenching, which could reduce the total emission enhancement of coupling. Only ∼2-3 ppm variation in Au NS-c could alter the coupling operational statues from “enhancement region” to “quenching region” and vice versa. The validated algorithm was used to model small scale pLSC (20 × 20 × 3 mm) followed by optimising ${{\rm{G}}_{\rm{g}}}$ to obtain the highest C in large scale pLSC. ${\rm{C}} \approx {\rm{\;}}$ 39% was achieved for 900 × 900 × 3 mm pLSC under direct solar radiation. ECE was enhanced by ∼33%, when pLSC was irradiated by only diffuse solar irradiation which was due to enhanced energy trapping efficiency and TIR in pLSC owing to plasmonic interaction improving the optical properties of QDs. Ideal zero background absorption in large scale pLSC is not very effective in improving the device ECE due to the increase in the rate of photons exited from the device. Enlarging the Stokes’ shift of the QD from 20 nm to 50 nm resulted in ∼35% enhancement in pLSC ECE. Although further increase in QD Stokes’ shift decreased re-absorption losses, it dominantly reduced the device performance due to reducing the spectral overlap between QD emission and SPR of Au NS mitigating total emission efficiency of the coupling. Increasing QY from 50% to 70% reduced thermal losses as well as the rate of photons exited from the device and enhanced pLSC ECE by ∼38%. These promising modelling results implies the capability of the proposed algorithm for modelling both conventional and plasmonically enhanced luminescent solar devices.
Funding
IDEAS project (815271); PEDAL project (639760).
Acknowledgments
This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme through the PEDAL project (Grant Agreement 639760) and IDEAS project (Grant agreement 815271). The authors would also like to acknowledge the support from Science Foundation Ireland (SFI) for their support under the SFI ERC support fund and the PEARL PV Cost action network for their insights.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analysed in the presented research.
Supplemental document
See Supplement 1 for supporting content.
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