Modelling and optimization of UV absorbing photovoltaic windows using a thin film AlN:Eu3+ luminescence library

Abstract Building-integrated photovoltaics are drawing much attention to make the built environment self-sufficient in terms of electricity. Luminescent solar concentrators (LSCs) can provide this electricity generation when used as photovoltaic windows. Paramount to an efficient LSC are non-overlapping absorption and emission spectra, to avoid self-absorption. This non-overlap can be achieved by absorbing incoming UV light and emitting in the red to infrared. In this article, we present a technique for optimizing LSCs without self-absorption, using Eu 3+ -doped AlN as a model system. The parameters affecting light absorption, emission and transport are extracted from a combinatorially sputtered gradient material library. This library results from a single deposition, with a gradient in thickness and Eu concentration. AlN:Eu 3+ absorbs strongly until 450 nm, with a peak solar absorption of 499 cm −1  at% −1 at 350 nm due to a charge transfer band. The strongest emission is at 622 nm, thereby exhibiting no self-absorption. The presented optimization model strikes a balance between concentration quenching and absorptivity of Eu dopants by using the parameters extracted from the material library. For thicker films, concentration quenching can be avoided by using a lower dopant concentration, while still outperforming thinner films due to fast increasing absorption. The results demonstrate that, while AlN:Eu 3+ itself should only be viewed as a model system, thin films doped with rare earths can yield industry-compatible, high efficiency LSCs because of their high absorption coefficients and lack of self-absorption.


Introduction
Building-integrated photovoltaics (BIPVs) can turn the passive building envelope into a source of electricity. For example, when utilizing the principle of a luminescent solar concentrator (LSC), luminescent thin films on window glass can transform these windows into electricity generating surfaces. Fig. 1a shows the working principle of a thin film LSC. Sunlight incident on the window is captured by luminescent centers in the coating on the window, which convert the captured light to a different wavelength. The converted light is emitted isotropically. Light emitted at an angle larger than the critical angle of the LSC is then waveguided through the LSC towards the windowpane by total internal reflection. In the windowpane PV cells are placed, which face the edges of the LSC. These cells convert the waveguided light into electricity. The light absorbed by the LSC is effectively concentrated on the PV cells. The area covered by the PV cells is therefore very small compared to the large LSC surface. In addition, the cells only need to be optimized for the LSC emission, a much narrower range of wavelengths than the solar spectrum. Therefore, the PV cells can have unity external quantum efficiency (EQE) at the LSC emission wavelengths. LSCs could replace ordinary windows as transparent energy generating BIPV at no high additional investment and no wiring blocking the view.
The concept of LSCs has existed since the 1970s [1], but wide adaptation was mainly impeded by these LSCs displaying bright coloration, making them unsuitable for use as windows in the building envelope. A recent development in LSCs is to use materials that absorb in the ultraviolet (UV) and have a large Stokes' shift [2][3][4]. This combination leads to high transmission in the visible spectrum, and emission in the red to near infrared (NIR), yielding the appearance of an ordinary window without coloring. Another advantage of this nonoverlapping absorption and emission is that no parasitic absorption of the luminescence center itself (self-absorption) occurs. The absence of self-absorption means that when a photon is emitted under total internal reflection (in a perfect waveguide), it will reach the perimeter of the LSC, regardless of the LSC's size. The absence of self-absorption is therefore of great importance to the overall efficiency of the LSC.
Optimization of the composition of the luminescent coating is often a laborious process. The light-conversion efficiency of the LSC material has to be measured for many individual  compositions. To overcome this laborious optimization, another approach is to fabricate thin film libraries of LSC materials using combinatorial gradient magnetron sputtering [5]. With combinatorial gradient magnetron sputtering, a single substrate from a single deposition provides many compositions (a composition library) that can all be characterized automatically. Additionally, magnetron sputtering is already commonly used for window coatings [6]. The optimal composition found by this gradient method can therefore be implemented in glass coating on an industrial scale with relative ease.
In this work, we want to optimize the optical efficiency of an LSC without self-absorption based on experimental data from a composition library. As a model system for materials absorbing in the UV and having emission in the red to NIR, a good choice for a thin film LSC coating is Eu 3+ -doped AlN. AlN:Eu 3+ can be excited by light below 400 nm, shows strong emission at 600 nm-625 nm at room temperature [7][8][9], can be coated on glass through sputter deposition [10], and is chemically inert [11].
The optical efficiency of an LSC can be described with [12] = R (1 ) .
Here, each factor describes one step in the light conversion-concentration process. R 1 describes the amount of light transmitted into the film. abs is the fraction of transmitted light absorbed by the luminescent particles. QY is the internal photoluminescent quantum efficiency of Eu 3+ , i.e. the ratio of photons emitted to photons absorbed by Eu 3+ . trap is the fraction of emitted photons that remain trapped within the LSC through total internal reflection. WG describes the efficiency of the waveguiding of light to the perimeter of the LSC.
WG can be affected by scattering losses and absorption by the waveguide. SA is a factor to take self-absorption into account.
Assuming an optical density of 0.8 and an index of refraction of = n 2, a UV-absorbing LSC without self-absorption could have an optical efficiency of 2.3 to 5.8% when = 1 QY . This value is highly dependent on where the absorption maximum of the LSC lies. When this maximum lies to the visible spectrum, the amount of photons in the solar spectrum increases tremendously. In practice, these optical efficiencies are not attained with UV-absorbing LSCs due to low QY of typically 10% for quantum dots, to 80% for dye molecules.
The product × abs QY , shown in Fig. 1b, is crucial to the overall performance of an LSC. When the concentration of luminescent centers is low, QY tends to be high, but at the same time, abs is low due to the low amount of absorbing centers. Conversely, at higher concentrations, abs is high due to many absorbing centers, but QY drops as a consequence of concentration quenching [13]. Apart from the dopant concentration within the film, the film thickness (at equal dopant concentration) will increase abs (to a first order, when disregarding interference effects). The optimum for × abs QY is therefore also specific to the thickness of the luminescent layer. As industrial throughput decreases (and cost increases) with increasing film thickness, it is of great importance to establish methods that can find the optimal dopant concentration for the desired thickness.
In this work, we present a general approach that only requires the deposition of a single thin film to optimize × abs QY . We do this optimization in three steps. Firstly, we deposit a film with a thickness-and a Eu concentration gradient, employing off-axis combinatorial sputtering of Al and Eu sources in a reactive O 2 +N 2 +Ar atmosphere. Here O 2 is added as dopant, which reduces the need for heat treatments to improve the intensity of the luminescence. Secondly, we determine the composition-dependent thickness, index of refraction, absorption, and quantum efficiency through a combination of energy-dispersive X-ray spectroscopy (EDX) and automated mapping of the transmission and laser-excited luminescence properties of the thin film. Thirdly, using the parameters extracted from the gradient thin film, we maximize the optical efficiency of AlN:Eu 3+ thin film LSCs as a function of both thickness and Eu concentration, through optics simulations employing the transfer-matrix method.

Experimental
Library creation. The AlN:Eu thin film library was deposited on a square 44 × 44 mm 2 UV fused silica substrate (PGO) within an AJA ATC Orion 5 magnetron sputtering system (Fig. 2) with a base pressure of 1 × 10 9 bar. Prior to the deposition, the substrate had been cleaned by rinsing three times with DI water and ethanol, followed by a 15 min bath in an ultrasonic cleaner with DI water. The deposition was carried out with 5.08 cm diameter metal Al (99.9995%, Lesker) and Eu (99.99%, Demaco) targets, which were reactively co-sputtered with  respectively 150 W and 32 W RF power for 12.5 h. The deposition rate of Eu was reduced by a stainless steel mask with a pattern of concentric holes, blocking 88% of the surface of the Eu target. The process gas flow consisted of 18 sccm 6 N purity Ar, 0.25 sccm 5 N purity O 2 and 13.75 sccm 5 N purity N 2 into the sputtering chamber at a working pressure of 4 × 10 3 mbar. Oxygen was included in small amounts to the sputtering gas, and therefore to AlN, as alternative to thermal treatments at high temperatures [14]. O 2 and N 2 were introduced next to the substrate, while Ar was introduced at the Al source. Just before deposition, the substrate was heated to 400 ∘ C. During the deposition, the sample was not actively heated. The cooling of the sample during deposition can be seen in Fig. S1 in the Supplementary Materials. To realize a thin film with both a gradient in Eu and in film thickness, the substrate was sputtered without rotation. Following the deposition, the luminescence of the library was improved by subsequently heating to 300 ∘ C and 500 ∘ C, both for 20 min, in a Solaris 150 rapid thermal processing (RTP) system. The RTP system was flushed with 9 standard liters per minute (SLM) N 2 (5 N purity) during the entire annealing procedure. Fig. S2 shows that this annealing treatment yields a 12-fold improvement in luminescence.
An undoped AlN reference sample was made with identical treatment, but with the Eu source switched off.
Composition analysis. A JEOL IT-100, operated at 15 keV with probing current at 70%, was used for SEM/EDX analysis. Quantitative elemental analysis without a conductive coating was achieved by employing the device in low vacuum mode (35 Pa pressure). Elemental compositions were quantified at × 3000 magnification (31 × 23 µm 2 measurement area). XRD measurements were performed using a PANalytical X'pert Pro MPD diffractometer in Bragg-Brentano geometry, with a Cu Kα anode ( = 0.1540598 nm) operating at 45 kV and 40 mA. The area illuminated by the X-ray beam was around 1 × 5 mm 2 in size.
Optical characterization. The total transmission was measured by placing the samples between a collimated (2.7 mm diameter) xenon light source and the entrance port of a 5.08 cm diameter integrating sphere (IS200-4, Thorlabs), with an Ocean Optics QEPro spectrometer (200 μm slit width) connected to the off-axis detector port. The samples were moved through the collimated beam with a sample holder placed on top of two stacked Thorlabs DDSM100 linear translation stages. Transmission spectra were recorded across the samples at × 16 16 positions with a step size of 2.6 mm. Each position is recorded with an integration time of 250 ms and averaged × 32 . Dark spectra were recorded by blocking the entrance of the integrating sphere with highly absorbing and reflecting Al tape. Lamp spectra were recorded by directly exposing the integrating sphere to the collimated light. The presented transmission spectra were corrected using these two reference measurements, measured with identical settings.
Photoluminescent excitation, emission, and decay measurements were carried out with a home-built xy-scanner setup, as described in Ref. [5]. An Ekspla NT230 OPO Laser was used as excitation source, operated at excitation wavelengths ranging from 210 nm to 420 nm in steps of 0.25 nm. Combined emission/excitation spectra were integrated for 300 ms and averaged × 4 per excitation wavelength. These spectra were recorded with an Ocean Optics QE65000 spectrometer with a 100 μm entrance slit. A 430 nm longpass filter (Semrock) was used to remove reflected laser light. The emission was corrected for the quantum efficiency and non-linearity of the detector. For decay studies, the emission, filtered with a 355 nm longpass filter, was passed directly to a Hamamatsu R7600U-03 PMT operating at −600 V linked to a CAEN DT5730 Digitizer with 64 ns per channel. The sample was excited at 350 nm, with the laser pulsing at 50 Hz. Decay traces were collected over 200 laser pulses at × 20 20 locations across the film, with 2 mm between steps. Fig. 3b show the final product: a thin film, transparent in the visible spectrum, but with red emission when excited by UV light. The interference fringes are a consequence of the thickness gradient of the film, which ranges from 0.8 μm to 2.1 μm, as reported in Fig. 3c. The thickness is retrieved from fitting × 16 16 local transmission measurements (see Fig. S4) to an extended Sellmeier model, as presented in Ref. [15]. A low Eu concentration is already indicated by the thickness measurement. If the Eu concentration was high, the shape of the thickness gradient would more follow the cosine distribution caused by the Eu source. In this case, the thickness directly follows the cosine sputtering distribution dictated by the Al source.

Fig. 3a and
EDX measurements provide the local chemical composition of the gradient thin film at 24 positions, shown by the white dots in Fig. 3d. These measurements can be accurately fit ( < RMSE 0.2 at.%) and interpolated with the surface-source evaporation equation [5,16]. Fig. 3d shows the result of this fitting, with the Eu concentration varying from 0.6 at.% to 8.6 at.%. X-ray diffraction measurements (Fig. S3) show that the AlN film has a hexagonal wurtzite structure, with a preferential growth direction. Fig. 4a provides the excitation-emission map taken at an arbitrary location [(x,y)=(30 mm, 40 mm)] on the film. Fig. 4a shows that AlN:Eu 3+ produces red emission when excited from 210 nm to 420 nm. The multiple emission lines are all resultant from 4f-4f emission of Eu 3+ . The relative intensities of the emission lines are the same for all excitation wavelengths, and all emission lines have the same excitation spectrum, which is a strong indication that Eu 3+ occupies a single site within the AlN lattice. A closer look at the strongest emission at 622 nm (indicated by the blue line in Fig. 4a), displayed in Fig. 4b, shows that the excitation can be clearly resolved in 3 Gaussian bands. The 0.53 eV wide (FWHM) band, centered at 3.54 eV ( 350 nm) can be attributed to the charge transfer (CT) band from the valence band of AlN to Eu 3+ [17,18]. The CT band is the energy required to displace an electron from a neighboring nitride (valence) anion onto Eu 3+ , therefore providing the energy difference between the valence band and the Eu 2+ ground state [19], shown by the arrow marked Fig. 4c. The 0.52 eV wide band at = E 5.60 eV exc ( 221 nm) can be attributed to the creation of an exciton. The optical bandgap for the thin film AlN:Eu is 6.05 eV wide, 8% above the exciton energy [20], in agreement with Ref. [21].
With these properties, a vacuum referred binding energy (VRBE) diagram can be constructed [22]. Such a diagram is helpful in elucidating how the energy levels of defects compare to the same defects in other hosts. Based on what is reported for other nitride-type materials [23], the energy difference U (Eu) between Eu 3+ and Eu 2+ is taken at 6.4 eV. Using the relation [ CT band is usually positioned around 4.7 eV in aluminates [19]. Therefore, since the thin film is produced in an environment containing O 2 , the band at 4.61 eV can most likely be attributed to the + O Eu 2 2 CT band. When comparing Fig. 3b with Fig. 3c and d, we see that the AlN:Eu 3+ library presents local maxima in emission intensity (indicated by the white dashed line) at different thicknesses and Eu concentrations. When following the white dashed line shown in Fig. 3b, we can observe that the thicker the film, the lower the optimum Eu concentration. These optima imply that for each thickness within the film there is a balance between quantum yield and absorption strength, as shown schematically in Fig. 1b. To evaluate if these optima translate to an optimum for LSC functionality, the absorption of light and quantum yield are resolved as a function of film thickness and Eu concentration in the next section.
To retrieve the concentration-dependent index of refraction n and molar absorption coefficient ε, the measured transmittance is fit to the thin film transmittance equation [25] for every measured wavelength. From this equation, ε can be derived from the extinction coefficient k with

Eu Eu AlN Eu
This type of fitting yields n and ε, as presented in Fig. 5a for both undoped and Eu doped AlN. In the Supplementary Materials (Section S1, Figs. S4 and S5) a more in-depth explanation is given on how the fittings are done.
For undoped AlN, an index of refraction of = n 1.90 is found at = 622 nm. An increase in Eu concentration goes paired with an increase in refractive index, from = n 1.92 at 0.9 at.% to = n 1.96 at 6.7 at. % (Fig. 5b). The molar absorption coefficient of Eu 3+ in AlN (Fig. 5a) shows the same bands as observed in the excitation spectrum (Fig. 4b).
The N 3− Eu 2+ CT band at 350 nm has a molar absorption coefficient of 499 cm −1 at.% −1 . In absorption, the bands have a different relative intensity than in excitation. This difference in intensity can come from different relaxation pathways for the different CT transitions. A different relaxation pathway goes associated with a different quantum yield, which alters the intensity of the band in excitation, where only radiative relaxation can be measured. Fig. 5a reveals that doping Eu in AlN slightly alters the absorption of AlN itself. AlN is mostly reported to have no absorption for wavelengths larger than 400 nm [26], while in our films the absorption extends to longer wavelengths. It might therefore be that our film contains defects that may be removed when e.g. growing the film at elevated temperatures or annealing in a N 2 +H 2 atmosphere. Given the emissions as reported in Fig. 4a, Eu exhibits no self-absorption and the emission is not absorbed by the AlN host either.
The quantum yield QY can be estimated from the decay spectra, shown in Fig. 6a. In the first hundred nanoseconds a very quick decay can be observed. After this initial quick drop, the decay for any concentration in the library shows strong non-exponential behavior. As seen in Fig. 6a for selected concentrations, and in Fig. 6b for the entire library, the decay time decreases at higher Eu concentrations. Given the faster decays at higher concentrations, this effect can be explained by concentration quenching.
The data presented in Fig. 6b is collected at × 20 20 locations across the film, which gives multiple data points for a specific concentration. These data come from areas with markedly different thicknesses. No relation between decay time and thickness is found, confirming that the decay time solely depends on the dopant concentration. The good correspondence between measured decay time and the interpolated Eu concentration (Fig. 3d) also confirms the correctness of the EDX measurements and the usage of the source-surface evaporation equation.
To obtain QY per concentration, the decay can be compared to decays reported at much lower concentrations, where concentration quenching can be excluded [27]. report a decay of = 428 µs for an AlN:Eu 3+ thin film doped with 5 ppm Eu. This low-concentration Eu film does not show thermal quenching of the intensity of cathodoluminescence. This implies that in the film of Jadwisienczak et al.  is largely uninfluenced by the fast decay in the first hundred nanoseconds, as the surface underneath the curve is negligible compared to the surface from the remaining hundreds of microseconds. Fig. 6b shows both mean and the estimated QY . Even for a Eu doping as low as 1 at.%, AlN:Eu 3+ does not exceed a quantum efficiency of 50%. From Fig. 6b, QY can be extrapolated to its value at 0 at.% Eu. Extrapolating the dashed curve would lead to (0 at. % ) 1 QY . In materials with a CT band at low energy, the CT state can overlap with the Eu 3+ ground state [28]. This overlap with the Eu 3+ ground state opens a temperature-independent non-radiative pathway for relaxation of the excited Eu to the ground state. In practice this means that even at 0 K, the quantum yield does not equal unity. , the method presented in this article is still valid. The results found here will then have to be multiplied by this non-unity quantum yield to obtain the correct efficiencies.
An optimum in optical efficiency for an AlN:Eu 3+ LSC can now be retrieved, because the parameters required by Eq. (1) have been determined as a function of Eu concentration and film thickness, as will be detailed in the following.
As this study concerns a thin film, the amount of absorbed incident light cannot be calculated using geometrical optics. The transfer-matrix method [29] that takes multiple reflections at the interfaces of the thin film into account is used to calculate how much sunlight (AM1.5g) is absorbed. The absorbance and index of refraction reported by Fig. 5a are used to calculate the number of reflected, transmitted and absorbed solar photons. The amount of emission is calculated by multiplying the number of photons absorbed by Eu 3+ by the estimated QY from Fig. 6b. Eu 3+ is assumed to be distributed randomly in the AlN host. Therefore, we can safely assume light emitted by Eu 3+ to be transported incoherently through the thin film and the substrate [30]. Thanks to this incoherent transport, geometrical optics can be used to calculate the light transport after emission. The amount of trapped light can be calculated by multiplying the number of emitted photons by = = ( 622 nm) 85.5% trap . This takes both transport through the film and through the glass substrate into account. A perfect (scatter-free) waveguide is assumed: Since no reabsorption of Eu 3+ is present, = 1 SA and the efficiency optimization is irrespective of the overall LSC geometry [12]. Fig. 7a shows the result of this optimization. The percentages shown in Fig. 7a are the optical efficiencies of the LSC for AM1.5g solar photons until 450 nm. These photons constitute 7.7% of the total amount of photons in the solar spectrum. To retrieve the optical efficiency when considering the entire solar spectrum, the percentages reported in Fig. 7a should be multiplied with a factor 0.077. Fig. 7a reflects what was already observed in Fig. 3b: a higher concentration of Eu 3+ , at equal film thickness, does not have to imply a higher optical efficiency. The white curve, drawn perpendicular to the contour lines, indicates the optimum concentration per thickness. This curve follows the behavior schematically sketched in Fig. 1b: at higher thickness, a lower Eu concentration is required to achieve optimal optical efficiency. Fig. 7b details the distribution of the incident AM1.5g UV photons (integrated until 450 nm) for the optimized Eu concentrations at every thickness. At film thicknesses below 2 μm, the effect of thin film interference is evident in the transmission and reflection, with transmission being the most prevalent fate for an incident photon. With increasing film thicknesses, the reflection starts converging to what would be expected from geometrical optics, while the transmission drops drastically as a result of increased absorption. At the same time, the fraction of absorbed photons yielding luminescence increases for thicker films. This increase is a consequence of the lower Eu concentration an optimized LSC with a thicker film requires, hence resulting in less concentration quenching. However, even with this lowered quenching, only 7% of incoming UV photons will be converted and concentrated at the LSC's edges for a 5 μm thick film. Fig. 7c provides a breakdown of the eventual fate of all incident solar photons for an optimized 5 μm thick LSC. The interference effect caused by a thin film can still be clearly observed from the oscillations between transmission and reflection. The effect of the N 3− Eu 2+ CT absorption (Fig. 5a) can also be observed, with most absorption and conversion resulting from this band. The high absorption from this CT band (1697 cm −1 at 350 nm) does not counteract the high non-radiative loss due to the low quantum yield of 27% at 3.4 at.% Eu doping.
In an idealized case, where the dashed curve displayed in Fig. 6b is scaled such that = 1 QY at 0 at.% Eu, illustrated in the Supplementary Materials (Section S2, Fig. S6), 3.4 at.% Eu doping has = 47% QY . In this idealized case, 13% of the incident UV photons will be concentrated at the LSC's edges for a 5 μm thick film. The goal of this study is however to present a method where experimental data from a luminescence library is used to model, understand, and optimize a thin film LSC, not to produce an LSC of high efficiency. Even so, to put the efficiency of this simulated AlN:Eu 3+ thin film LSC into perspective, a comparison can be drawn to other emerging UV-absorbing LSCs without self-absorption. A recent example of such a UV-absorbing LSC are perovskite nanocrystals doped with Mn 2+ dissolved in a polymer matrix, laminated on glass. The absorptance of these laminated nanocrystals lies between 1 and 2 cm −1 [4]. These perovskites have nonoverlapping absorption (until 400 nm) and emissions (maximal at 600 nm), comparable to AlN:Eu 3+ . Given the low absorptance, these perovskites require much thicker ( 1 mm thick) films to achieve absorption equivalent to a 1 μm thick AlN:Eu 3+ film. Even with such thick films, the nanocrystals' low quantum yields culminates into an LSC of low efficiency. Compared to these nanocrystals, rare earth doped thin films show their potential as LSC due to their high absorptivity. Rare earth doped thin films are compatible with industrial fabrication processes, and, with materials that exhibit a lower degree of concentration quenching, can yield an LSC with a high optical efficiency.

Conclusion
We have shown that using the deposition of a single thin film, it is possible to calculate the thickness-dependent optimum dopant concentration of a thin film LSC, yielding a maximized optical efficiency. As a model system, we have fabricated an AlN:Eu 3+ library co-doped with O 2− . The library shows red 4f-4f emission after UV excitation and features a large thickness-and Eu 3+ concentration gradient.
Optimization shows that a 5 μm thick film performs best with 3.4 at.% Eu doping. This combination would yield an optimal optical efficiency for incoming UV light of 7%. The fabrication and optimization method presented in this paper can assist in quickly finding the maximally achievable performance for a self-absorption free thin film LSC.