Light absorption in semiconductors is a fundamental problem that has broad impact on a wide range of fields. However, it is intrinsically limited by the bandgap energy of the semiconductor. Herein, we study the enhancement of sub-bandgap light absorption in inorganic-organic hybrid perovskite semiconductor films via critical coupling. This is achieved at large incidence angles by balancing radiative and nonradiative decay rates in a planar multilayer structure. We found that a very small loss in the semiconductor layer can result in substantial light absorption. This simple but general method can be used to enhance the optical and optoelectronic responses of semiconductors below the bandgap energy.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Light absorption in semiconductors is a fundamental problem that has broad impacts on diverse disciplines, including energy harvesting, photodetectors, sensors, imaging, communication, and photocatalysis [1,2]. However, light absorption is intrinsically limited by the semiconductor bandgap energy; absorption coefficients drop rapidly near the band edge, and incident light cannot be efficiently absorbed below the bandgap energy. To overcome this problem, for example, heavy doping of impurities has been used to generate mid-gap energy levels and induce sub-bandgap light absorption [3–5]. This approach has been employed for intermediate bandgap solar cells, infrared photodetectors, and imaging sensors. More specifically, it was found that the incorporation of dopants at a concentration of the order of 1020 cm−3 in silicon increased light absorption by up to a few percentage points in the sub-bandgap region, and the optoelectronic response of hyperdoped silicon was extended to infrared wavelengths, at room temperature, to wavelengths as long as 2200 nm . Moreover, laser-induced patterning of micrometer-scale surface features has been employed to achieve near-perfect absorption below the bandgap energy of silicon [7,8]. However, both high impurity densities and the presence of surface microstructures can create large numbers of nonradiative recombination centers, and consequently the electrical performance can be severely degraded, with very poor overall quantum efficiency as a result.
Here, we demonstrate light absorption enhancement in the sub-bandgap spectral region using a nano-optical approach. Specifically, we observed the enhancement of light absorption in the sub-bandgap region using solution-processed perovskite semiconductor films, specifically, inorganic–organic hybrid perovskite (methylammonium lead iodide, MAPbI3) films [9,10]. By adjusting the multilayer film geometry and incidence angle, we were able to substantially increase light absorption via critical coupling below the bandgap energy (approximately 1.6 eV). Absorption enhancement was achieved in planar films without surface patterning. In our experiments, we observed that in a perovskite layer a very small loss (k = Im[n] ≈ 0.001) can result in substantial light absorption, approximately 4.8%, in the sub-bandgap region around 1000 nm. We also measured several reference samples and compared experimental data to theoretical calculations. In our analysis, we considered both diffuse reflection (due to surface roughness) and side absorption in other layers (including a bottom metal layer). Our approach does not require heavy doping and thus will not degrade electrical performance. This simple but general method can be also applied to other semiconductors for potential applications in light harvesting and photon detection below the semiconductor bandgap energy.
Figure 1 explains a general idea on our approach. Light absorption in bulk semiconductors is determined by the absorption coefficient α, and the intensity of the incident light I(x) gradually attenuates as it propagates: I(x) = I0e-αx. Therefore, high optical losses or very thick materials are required to absorb a significant amount of incident power. However, when an absorbing material is integrated within an optical resonator, incident light can be strongly absorbed even in a low-loss film via critical coupling (Fig. 1). From the temporal coupled-mode theory [11,12], we find that light absorption in a resonant optical structure can be described by two parameters (the radiative and nonradiative damping rates γrad and γnonrad)
Therefore, when γrad = γnonrad, we can achieve total absorption of incident light, Am = 1. This corresponds to the critical coupling condition in an optical resonator [13,14]. When the two damping rates are not equal, incident light is partially reflected (corresponding to over-damping or under-damping cases). The radiative damping rate γrad is related to the rate of photon leakage from a resonant optical structure, while the nonradiative (or internal) damping rate γnonrad results from material losses. These two parameters can be also related to cavity quality (Q) factors; γrad and γnonrad are inversely proportional to a radiative Q factor, Qrad, and an absorption Q factor, Qabs, respectively.
In this work, we consider an approach based on planar perfect absorber structures that do not require sophisticated structural patterning. Planar perfect absorbers have been actively studied in recent years because they provide a means of enhancing light absorption over large areas, without the use of complicated lithographic patterning [15–26]. In the structure we investigate here, a perovskite semiconductor layer is spincoated on a reflecting metal substrate, together with a non-absorbing phase controller, to allow the critical coupling condition to be generally satisfied at large incidence angles. The resulting sub-bandgap absorption is tunable over a broad spectral region via adjustment of the structure of the film. Such a multilayer film forms a planar Fabry–Perot–type resonator, and critical coupling is achieved by balancing the radiative and nonradiative decay rates. In this way, large-area enhancement of sub-bandgap absorption can be achieved without heavy impurity doping. Such critical coupling has been considered in graphene and other two-dimensional materials for enhancement of light absorption [27–29], but it has not yet been investigated in the case of semiconductors in the sub-bandgap region, where the absorption coefficients are generally very small.
2. Sample preparation and characterization
To prepare MAPbI3 precursor solutions, a 0.77 : 1 molar ratio of methylammonium iodide (MAI) and PbI2 were dissolved in a mixture of dimethylformamide (DMF) and dimethyl sulfoxide (DMSO) solvents (7 : 3 [v/v]). The concentration of the precursor solutions was carefully controlled to acquire a film of the desired thickness. The perovskite (MAPbI3) precursor solutions were spin-cast on precleaned substrates at 3500 rpm and 6500 rpm for 30 and 5 seconds, respectively. At the start of second step, the films were treated with a drop of chlorobenzene solvent to prevent fast crystallization. After spincoating, the films were annealed at 90 °C for 10 min. Poly(methyl methacrylate) (PMMA) solution was prepared with a concentration of 1 wt% in chlorobenzene. The solution was spin-cast onto the perovskite samples at 3000 rpm for 30 seconds to prevent the samples from degradation. The thicknesses of the perovskite films were measured using a surface profile (P6, KLA Tencor) and atomic force microscopy (AFM; DI-3100, Veeco). After making scratches on the film, we performed scanning over scratches on the surface and averaged the measured values to determine the final film thickness. The surface roughness of the perovskite films was also measured using AFM. The perovskite film on the quartz substrate had a root-mean-square (RMS) roughness of 11.9 nm, but after PMMA top-layer coating, the roughness was reduced to a value in the range of 4–5 nm.
The quality of the spincoated perovskite films was confirmed by x-ray diffraction (XRD) measurements (Fig. 2). Two strong X-ray diffraction peaks at 2θ = 14.2 and 28.5° correspond to the (110) and (220) planes of MAPbI3 tetragonal phase. Less dominant peaks at 2θ = 20.0, 23.6, 24.6, 32.0, 35.0, 40.5, 43.2, and 50.3° correspond to the (112), (211), (202), (222), (312), (224), (314), and (404) planes, respectively. As the proportion of MAI in the precursor solution—which is controlled to ensure the surface is smooth—is reduced, a sharp peak at 12.7° appears and begins to grow. This peak corresponds to the (001) plane of PbI2, and its presence in the XRD spectra implies that a PbI2 phase coexists with the MAPbI3 phase in the sample. Its relative intensity increases continuously as the volume of MAI in the precursor solutions decreases. Although two distinct phases are observed in the sample, the intense MAPbI3 peaks in the XRD spectra indicate that the quality of perovskite crystal is not significantly affected by the neighboring PbI2.
For our multilayer film ([PMMA/MAPbI3/SiO2/silver/quartz]), a thick silver film (≈ 200 nm) was first deposited on a quartz substrate (area: 1 inch × 1 inch) by electron-beam evaporation. Then, a silicon dioxide (SiO2) layer was deposited on top of the silver by plasma-enhanced chemical vapor deposition (PECVD). This oxide spacer layer works as a phase controller in our sample. The thickness of the oxide layer was varied in the range from 50 to 100 nm, and the thickness was measured using ellipsometry, after film deposition. We also prepared a reference sample without a perovskite layer ([PMMA/SiO2/silver/quartz]) to measure side absorptions in other layers. For near-normal incidence measurements (at an incident angle of 3.3° with respect to the surface normal), we used a spectrophotometer (Cary 5000, Varian) with an integrating sphere. In this way, we were able to measure both specular and diffuse components. For oblique incidence, we were able to measure only the specular reflection.
3. Results and discussion
Our key experimental results are presented in Fig. 3. We first measured a perovskite film (thickness ≈ 270 nm) on a quartz substrate at normal incidence [Fig. 3(a)]. Absorption A is obtained by taking A = 1 – R – T, where R and T are the measured reflection and transmission, respectively. For all the near-normal incidence measurements, we obtained net absorption Anet in the sample, considering both the specular and diffuse components of light: Anet = 1 – Rspecular – Rdiffuse. Light absorption in the perovskite film decreases rapidly at wavelengths longer than 750 nm because absorption coefficients drop rapidly near the band edge. However, our perovskite film still has small but non-zero absorption in the sub-bandgap region (850–1400 nm). For comparison, we also measured bare quartz [Appendix Fig. 8] and, in this case, absorption was nearly zero across the entire visible and near-IR region. The small sub-bandgap absorption in the perovskite film could originate from defect states in the mid-gap region that naturally arose during the solution-processing and crystallization of the perovskite layer [30,31]. This small but non-zero optical absorption can be further enhanced by critical coupling, as detailed below.
We now consider a perovskite sample with a metal back layer. Because the metal layer is sufficiently thick, there is essentially no transmission (T ≈ 0). Therefore, strong absorption can be obtained by suppressing reflection via destructive interference. Our multilayer film includes an oxide spacer layer (50-nm thick) and a PMMA top layer (30-nm thick) together with a perovskite layer ([PMMA/MAPbI3/SiO2/silver/quartz]). The metal substrate with oxide spacer effectively works as a dispersive reflecting medium. The phase change from this reflecting medium combined with that from the absorbing semiconductor film can generate destructive interference of incident light . We measured sub-bandgap absorption at both normal and oblique incidences. At normal incidence [Fig. 3(b)], resonance absorption is clearly visible (approx. 4% at 1100 nm).
At oblique incidence, we observe more drastic changes with incidence angle. Sub-bandgap absorption increases rapidly as the angle increases. Incidence angles were varied between 20° and 70°, and the measured s-polarized absorption spectra are shown in Fig. 3(c). A prominent sub-bandgap absorption peak occurs for large incidence angles, reaching about 20% absorption at 70°. This absorption peak gradually blueshifts with incidence angle, as expected for a Fabry–Perot resonance . The measured p-polarized absorption spectra are given in Appendix Fig. 9. These also show angle-dependent behavior, but the absorption is generally smaller than the s-polarized light absorption.
For comparison, we also measured absorption spectra from a reference sample without a perovskite layer [Figs. 3(d) and 3(e)]. The sample structure is the same as the previously mentioned samples, except that it does not include a semiconductor layer ([PMMA/ SiO2/silver/quartz]). In this case, the thickness of the PMMA layer was further increased to approximately 590 nm, to ensure that the optical resonance remains in the same spectral region. Using this sample, we can observe the effects of side absorption in the metal and other layers. For both the normal and oblique incidences, we obtain some absorption features, but they are much smaller than those observed for the previous sample with the perovskite layer. This indicates that the drastic change in Fig. 3(c) is indeed related to absorption in the perovskite layer.
The surface roughness of the perovskite layer can cause diffuse reflection and affect our measurements. In the case of the normal incidence measurements, we were able to directly measure diffuse-reflection spectra using an integrating sphere. Figure 4 shows the measured diffuse-reflection spectra. The perovskite layer on quartz has an RMS roughness of approximately 11.9 nm, but we found that this bare perovskite layer has very weak diffuse reflection [Fig. 4(a)]. In case of the multilayer sample with a metal back layer (RMS surface roughness, approx. 6.08 nm), we measured a diffuse reflection level of 4.3% at 1040 nm [Fig. 4(b)]. Note that the RMS value in Fig. 4(b) was reduced by the PMMA top layer coating. The multilayer film in Fig. 4(b) supports a Fabry–Perot–type resonance centered at 1040 nm and scatters more light during multiple reflections in the film compared to the single layer film in Fig. 4(a). In Fig. 3(b) (normal incidence), we included both diffuse- and specular-reflection components, presenting the net absorption in our sample. However, in the case of oblique incidence, we were only able to measure specular reflection, and thus the spectrum in Fig. 3(c) is overestimated as it also includes diffuse reflection. Therefore, we denote the quantity in Fig. 3(c) as the nominal absorption: Anominal = 1 – Rspecular = Anet + Rdiffuse.
In Fig. 5, measured (red lines) and simulated (dotted lines) spectra are compared, and the net absorption for oblique incidence is estimated. The optical constants for silver that we used for simulations are given in Appendix Fig. 10(a). Using data from the reference sample without the perovskite layer [Figs. 3(d) and 3(e)], we confirmed that our simulation agrees well the experimental spectra for both normal and oblique incidences [see Appendix Figs. 10(b) and 10(c)]. The refractive indices of the oxide and PMMA layers were determined from ellipsometry measurements. However, for the perovskite layer, it was not easy to accurately measure the extinction coefficient k (i.e., the imaginary part of the complex refractive index, Im[n] = k) in the sub-bandgap region, because ellipsometry fitting often tends to simply set the very small extinction coefficient below the bandgap energy to zero. Instead, we compared our experimental data with simulations and estimated the extinction coefficient k of the perovskite layer. For normal incidence, the net absorption measured in the sample was compared to the multilayer calculation and we found that using k ≈ 0.001 gave good agreement with the measured spectrum [Fig. 5(a)]. For oblique incidence, we calculated net absorption with k ≈ 0.001, and this was compared to the measured spectrum (Anominal = 1 – Rspecular) in Fig. 5(b). From our calculations, we obtained a net absorption value of about 11.5% at 1000 nm for an incidence angle of 70°. We suggest that the difference between the measured (red line) and calculated (black dotted line) spectra in Fig. 5(b) was caused by diffuse reflection from our sample. In fact, the perovskite extinction coefficient is very small in the sub-bandgap region and identifying its exact value is not straightforward. For example, when we compared the experimental data in Fig. 3(a) (bare perovskite on quartz) to calculation, we obtained a larger extinction coefficient, about k ≈ 0.0045, in the perovskite layer. Figure 11 in the Appendix includes more results related to this aspect.
The sub-bandgap absorption peak can be tuned over a broad spectral region by adjusting the thickness of the oxide spacer layer. Appendix Fig. 12 displays the measured spectra for the 75- and 100-nm oxide layers, where it can be seen that the resonance peaks shift to longer wavelengths (1100 and 1200 nm, respectively).
Figure 6(a) shows the absorption colormap as a function of wavelength and incidence angle for s-polarized incident light, obtained from transfer matrix method (TMM) calculations. In our measurements, the range of incidence angles was limited to a maximum of 70°. However, in the TMM calculations, we considered the full range of incidence angles (0–90°). Enhanced absorption band in the sub-bandgap region is apparent in Fig. 6(a); the peak blueshifts with increasing angle, in agreement with our measured spectra [Fig. 3(c)]. Moreover, we obtain very strong absorption at a large incidence angles (>85°). We also investigated the fraction of incident light energy that is actually absorbed within the perovskite layer. To this end, we calculated the absorbed power profile of our multilayer film ([PMMA/MAPbI3/SiO2/silver/quartz]) using finite-difference time domain (FDTD) simulations. The absorbed power per unit volume (Pabs) can be determined from the divergence of the Poynting vector, and we obtained the following relation :
To explicitly assess the critical coupling condition in our multilayer film, we directly compared the radiative and nonradiative damping rates. Figure 7(a) shows the simulated absorption spectra for different incidence angles, assuming a perovskite extinction coefficient of k ≈ 0.001. We used these spectra to extract radiative and nonradiative damping rates. Absorption spectra were fitted to a Lorentzian function to determine the resonance linewidth, 2γtotal. Using Eq. (1) and the total damping rate (γtotal = γrad + γnonrad), we obtained the two damping rates γrad and γnonrad. Figure 7(b) displays the extracted damping rates; it can be seen that the radiative damping rate gradually decreases with incident angle, while the nonradiative one remains almost constant. At large angles of incidence (>85°), the two rates approach the same value, and thus we can obtain strong absorption even in a low-loss film. For a film with higher optical losses, the nonradiative damping rate is greater, and an exact crossing of two damping rates would occur at a smaller incidence angle. This critical coupling is a very general phenomenon, and therefore we expect this approach could be applied to other semiconductors. Although a large incidence angle is required in the low-loss sub-bandgap region, it could be achieved with appropriate mirror configurations .
In conclusion, we described a simple but general approach to obtain light absorption enhancement via critical coupling at wavelengths that correspond to energies below the semiconductor bandgap. Such critical coupling can be achieved at a large incidence angle by balancing the radiative and nonradiative decay rates in planar semiconductor films. Planar multilayer structures are easily fabricated, and straightforwardly integrated with other device components. Specifically, we demonstrated sub-bandgap absorption enhancement in inorganic–organic hybrid perovskite semiconductor films. In our analysis, we considered the effect of surface roughness and side absorptions and identified the net sub-bandgap absorption in the semiconductor layer. Our approach does not require heavy impurity doping and thus will not degrade electrical performance. Furthermore, it can also be applied to other semiconductors, to enhance optical and optoelectronic responses below the semiconductor bandgap energy.
National Research Foundation of Korea (NRF-2017R1A2B3010049, NRF-2018R1E1A2A02086050, NRF-2019R1A2C1008330); Ulsan National Institute of Science and Technology (1.190109.01).
We thank Prof. Kyoung Jin Choi and Chan Ul Kim for the help of film deposition.
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