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Abstract
In order to remarkably enhance the absorption capability of (CH3NH3)PbI3, a tunable narrow-band (CH3NH3)PbI3-based perfect absorber based on the critical coupling with guided resonance is proposed. By using the finite-difference time-domain (FDTD) simulations, a complete absorption peak is achieved at the wavelength of 1310 nm. Moreover, we have compared the simulation results with theoretical calculations, which agree well with each other. By changing related structural parameters, the wavelength of absorption peak can be tuned effectively. Furthermore, the proposed absorber can tolerate a relatively wide range of incident angles and demonstrate polarization-independence. In addition to (CH3NH3)PbI3, the complete optical absorption in the other halide perovskites can be realized by the same mechanism.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As a research focus in the optoelectronics and nanophotonics, effective light matter interaction has attracted a lot of attention in recent years [1–2]. Many reports have demonstrated based on the various materials, such as graphene [3–7], black phosphorus [8–10], transition-metal dichalcogenides [11–14], hexagonal boron nitride [15–16], and so on. Recently, as a new class of materials, halide perovskites have extensively attracted a lot of attention not only for photonic sources [17–19], but also for photovoltaic devices [20–21]. The main reason is that halide perovskites have remarkable photonic and electronic properties, such as excellent optical absorption coefficient in the visible band, intense photoluminescence, extremely broadband spectral tunability, long carrier diffusion length, and high quantum efficiency [22–24]. Actually, halide perovskites described by the general formula ABX3 (A = organic ammonium cation, Cs+; B = Pb2+, Sn2+; X = Cl, Br, I) have been discovered for more than thirty years. Since A. Kojima et al., reported their initial application to achieve a power conversion efficiency (PCE) of 3.8% on a CH3NH3PbI3-based solar cell in 2009 [25], halide perovskites have been extensively explored as new semiconductor materials in photovoltaic devices.
In the solar field, great efforts have been made in recent years. In 2012, H. S. Kim et al., [26] increased the PCE to 9.7% by using the solid-state mesoscopic heterojunction solar cells employing nanoparticles of (CH3NH3)PbI3 as light harvesters. In 2013, by decreasing the processing temperature in CH3NH3PbI3-xClx perovskite solar cells from 500 to <150°C, J. M. Ball et al., [27] achieved the PCE up to 12.3%. By manipulating the formation of the perovskite layer and carefully choosing the other materials, H. Zhou et al., [28] produced the PCE of 19.3% in a planar geometry without antireflective coating in 2014. To date, the validated PCE of perovskite solar cell has exceeded 23% with potential for more than 30% [29–30]. Moreover, it is worth noting that the efficiency has already been better than that of solar cells based on the multi-crystalline silicon (22.3%), which demonstrates the huge potential for photovoltaic applications. All of above halide perovskite solar cells are based on the high optical absorption coefficient of halide perovskite in the visible band. However, due to the weak optical absorption coefficient, halide perovskite devices are rarely concerned in the near-infrared regime, especially near the communication band. In fact, halide perovskites are of great value in the study of photodetectors and other optoelectronic devices in the communication band.
In this paper, to realize the tunable complete optical absorption of halide perovskites in the communication band, we make use of the critical coupling [31] with guided resonance based on the structure consisting of a (CH3NH3)PbI3 layer sandwiched between a silicon-based photonic crystal and silver (Ag) substrate. By using the finite-difference time-domain (FDTD) methods, the complete optical absorption can be realized at the optimal ratio of the hole radius to the period of the photonic crystal, where the leakage rate of the guided resonance equals to the absorption rate of the (CH3NH3)PbI3 layer. Moreover, we have compared the simulation results with theoretical calculations, which agree well with each other. By changing the thickness and period of photonic crystal, the wavelength of absorption peak can be tuned effectively. Furthermore, the proposed absorber can tolerate a relatively wide range of incident angles and demonstrate polarization-independence. In addition to (CH3NH3)PbI3, the complete absorption peaks in the other halide perovskites are realized by the same mechanism. Thus, our results have a promising potential for developing advanced nanoscale photonic devices working in the communication band.
2. Models and methods
As seen from Fig. 1, the proposed structure is composed of a silicon-based photonic crystal on the Ag substrate, which sandwiches a (CH3NH3)PbI3 layer. The thickness (z direction) of photonic crystal is h1=127 nm, and the thickness of (CH3NH3)PbI3 layer is h2=100 nm. The periods of the photonic crystal in the x and y directions are both p=600 nm. Meanwhile, the radius of air hole in an unit is $r = {D \mathord{\left/ {\vphantom {D 2}} \right.} 2} = \textrm{65}$nm. The refractive indexes of silicon based photonic crystal and air hole are set as 3.45 and 1, respectively. Simultaneously, the permittivity of Ag substrate is described by the Drude formula [32]. Moreover, due to its center symmetric feature, the proposed structure also exhibits polarization-insensitive. When an incident plane wave is perpendicular to the proposed structure, a perfect absorption peak is realized in the communication band by using the FDTD simulation. In our calculation, the perfectly matched layer absorbing boundary condition is applied along the z direction. The periodic boundary conditions are employed in the x and y directions, respectively. The non-uniform mesh is adopted, and the minimum mesh size inside the (CH3NH3)PbI3 layer equals 0.2 nm and gradually increases outside the (CH3NH3)PbI3 layer, for saving storage space and computational time. Moreover, the wavelength of absorption peak can be effectively tuned in a wide wavelength range by manipulating related structural parameters. Furthermore, the proposed absorber tolerates a relatively wide range of incident angles. Although this work focuses on numerical investigation, the proposed CH3NH3PbI3-based absorber can be relatively easier to realize experimentally compared with the other CH3NH3PbI3-based absorbers. Subwavelength metamaterials based on silica nanostructures are easy for integration to the current CMOS technology, and CH3NH3PbI3 layer grown by chemical vapor deposition (CVD) can be transferred over the Ag substrate using standard transfer techniques [33].
Fig. 1. Schematic diagram of the dual band (CH3NH3)PbI3-based perfect absorber with dimensions specified.
It should be pointed out that the dielectric function ($\varepsilon \textrm{ = }{\varepsilon _1}\textrm{ - }i{\varepsilon _2}$) of (CH3NH3)PbI3 is calculated by the first-principles calculation software VASP code [34–35]. The electron exchange-correlation energy is adopted by the generalized gradient approximation (GGA) method with Perdew Burke-Ernzerhof (PBE) [36]. The kinetic cutoff energy for the plane-wave basis is 500 eV, and the first Brillouin zone is sampled with a $15 \times 15 \times 15$ Monkhorst-Pack k-points grid. The convergence criterion is set as $1 \times {10^{\textrm{ - }8}}$eV in energy and $1 \times {10^{\textrm{ - }8}}$eV/Å in force. Then, the real part ${\varepsilon _1}$ can be obtained based on the usual Kramers-Kronig transformation, while the imaginary part ${\varepsilon _2}$ of the dielectric function is derived by summation over empty states. As shown in Fig. 2, the dielectric function of (CH3NH3)PbI3 in our simulation is almost consistent with the experimental result reported in Ref. [37], and matched well with the dielectric constant parameter model reported in Ref. [38]. Due to the high value of ${\varepsilon _2}$ in the visible band, the (CH3NH3)PbI3 is widely used in photovoltaic field. However, it is worth noting that the value of ${\varepsilon _2}$ is very low in the communication band, which limits the further application of (CH3NH3)PbI3 in the optical communication. Thus, it is very meaningful to study on improving the optical absorption of (CH3NH3)PbI3 in the communication band.
Fig. 2. (a) Real part ${\varepsilon _1}$ and (b) imaginary part ${\varepsilon _2}$ of dielectric function of (CH3NH3)PbI3 based on the first-principles calculation.
3. Results and discussion
Firstly, it is worth noting that due to its center symmetric feature, the proposed absorber demonstrates polarization-insensitive. Thus, we will not discuss the influence of the polarization direction of the incident light on the performances of the proposed absorber on the next content. Normally, when the incident light is coupled into the silicon-based photonic crystal, both the guide mode and guided resonance can be excited. Similar to the guided mode, the guided resonance can strongly confine its electromagnetic power within the photonic crystal. Moreover, the guided resonance can also couple to external radiations, which is different from the guide mode. Then, when the silicon-based photonic crystal is placed on a thin (CH3NH3)PbI3 layer, the condition of guided resonance is hardly influenced. Due to the tightly confined electromagnetic power, the light fields are enhanced surrounding the (CH3NH3)PbI3 layer, which significantly improves its light-matter interaction. Incidentally, if the thickness and period of photonic crystal are much small than the wavelength of incident light, the higher-order guided resonance will be inhibited, then there is only a zero-order guided resonance. Thus, we take advantage of the characteristics of photonic crystal to improve light absorption of (CH3NH3)PbI3 in the communication band.
The proposed structure is shown in the Fig. 1(a). As the penetration depth of optical wave is much less than the thickness (D=800 nm) of the Ag substrate, the transmission from this structure is nearly approached to zero (T=0). Thus, the absorption of the proposed (CH3NH3)PbI3-based absorber can be expressed by A=1-R, where R is reflection from the structure. Then, the coupled-mode theory (CMT) [39–40] can be used to analyze this structure. As shown in Fig. 1(b), the amplitudes of normalized input and output light waves are assumed as ${S_ + }$ and ${S_ - }$, respectively. The external leakage rate is expressed as $\mu$, which means the time rate of the amplitude is altered in the guided resonance of the photonic crystal without input waves. The normalized amplitude of the guided resonance with the resonant frequency ${\omega _0}$ is assumed as A. When the photonic crystal layer is placed on the lossy (CH3NH3)PbI3 layer, the dissipative loss will be introduced in the guided resonance, which is depicted as a small intrinsic loss rate $\tau$. Normally, when the incident light with the frequency $\omega$ is coupled into this port, according to the time reversal symmetry and energy conservation [39], the whole system can be described as:
where $i$ stands for the imaginary unit. The reflection coefficient of this system can be calculated by using the frequency domain ${e^{i\omega t}}$ to isolate the ${{{S_ - }} \mathord{\left/ {\vphantom {{{S_ - }} {{S_ + }}}} \right.} {{S_ + }}}$, which is expressed as:Thus, we clearly see from Eq. (4) that the key to realize complete optical absorption is to get the same intrinsic loss rate $\tau$ and external leakage rate $\mu$, when the system is undergone the guided resonance with $\omega = {\omega _0}$. That is to say, when the leakage rate $\mu$ of the guided resonance out of the structure equals to the absorption rate of (CH3NH3)PbI3 layer, the system is said to be critically coupling and all the incident light is absorbed.
To demonstrate the above analysis, FDTD simulation is utilized to verify the complete absorption in the proposed absorber. As shown in Fig. 3, a complete absorption peak is achieved at the wavelength of 1310 nm. Meanwhile, the magnetic field distributions of the top and cross section of proposed structure at the wavelength of absorption peak have been described in the Figs. 4(a) and 4(b), respectively. We can clearly see that the guided resonance with extensive field confinement happens in the photonic crystal layer, and the magnetic fields surrounding the (CH3NH3)PbI3 layer are remarkably accumulated and strengthened. Moreover, due to the the critical coupling and metal substrate, the transmission and reflection of proposed structure are inhibited. Thus, all incident light energy is absorbed by this structure. On the other hand, as shown in Fig. 3, when $\mu \textrm{ = }\tau \textrm{ = }3.24\textrm{THz}$ is fitted, the CMT results are in good agreement with that of FDTD simulation. The values of $\mu$ and $\tau$ can be obtained by a simple method that was proposed in Refs. [31,41]. First, the external leakage rate $\mu$ can be obtained when the (CH3NH3)PbI3 layer is assumed to be lossless. Then, when the calculation is repeated with the loss, we can get the value of $\mu \textrm{ + }\tau$. Finally, the intrinsic loss $\tau$ can be obtained by $\tau \textrm{ = }( \mu \textrm{ + }\tau ) \textrm{ - }\mu$. Then, ${Q_\mu } = {{{\omega _0}} \mathord{\left/ {\vphantom {{{\omega_0}} 2}} \right.} 2}\mu$ and ${Q_\tau } = {{{\omega _0}} \mathord{\left/ {\vphantom {{{\omega_0}} 2}} \right.} 2}\tau$ are the quality factors related to the external leakage and intrinsic loss of the guided resonance, respectively. Then, the total quality factor of the guided resonance can be estimated according with the $Q = {{{Q_\mu }{Q_\tau }} \mathord{\left/ {\vphantom {{{Q_\mu }{Q_\tau }} {({Q_\mu } + }}} \right.} {({Q_\mu } + }}{Q_\tau }) = 111$. Meanwhile, the total quality factor can be calculated by the $Q = {{{\lambda _\textrm{0}}} \mathord{\left/ {\vphantom {{{\lambda_\textrm{0}}} \varDelta }} \right.} \varDelta }\lambda$, where $\varDelta \lambda$ is the full width at half maximum (FWHM) of the absorption peak. According to the results of FDTD simulation, $\varDelta \lambda = \textrm{11}$ nm and $Q = \textrm{119}$ are obtained. Due to the critical coupling, which effectuates the excellent complete absorption, there is a slight difference of Q between the theoretical and simulation results. Moreover, as shown in Fig. 3, it is worth noting that there is a slight deviation between the CMT and FDTD absorption spectra at a position away from the wavelength of the resonance, because the CMT assumes that there is no loss away from the resonance [10,31]. Simultaneously, according to the macroscopic electromagnetic theory, when the complete absorption is arose from critical coupling, the impedance of the free space (${Z_0} = 1$) should equal to that of proposed structure at the wavelength of absorption peak. Then, the effective impedance of this structure can be calculated as [42–43]:
Fig. 3. Absorption of proposed (CH3NH3)PbI3-based absorber by using CMT method and FDTD simulation under illumination of normal incident light, respectively.
Fig. 4. Contour profiles of normalized magnetic field of (a) top and (b) cross section of the proposed absorber at the wavelength of absorption peak.
As mentioned above, to realize the critical coupling, the external leakage rate $\mu$ should match to the intrinsic loss rate $\tau$ of the guided resonance. However, the intrinsic loss $\tau$ mainly caused by the lossy (CH3NH3)PbI3 layer is considered to be almost frequency-independent. Thus, manipulating external leakage rate $\mu$ plays an important role in realizing the critical coupling. For the photonic crystal layer, the external leakage rate $\mu$ of the guided resonance is mostly decided by r/p, that is, the ratio of radius of air hole to the period. When p=600 nm is fixed, the external leakage rate $\mu$ is increased with radius of air hole. As shown in Fig. 6(a), when the radius of air hole is increased from 50 to 75 nm, the whole system experiences from undercoupling, then critical coupling, to overcoupling procedure. Thus, the condition of critical coupling can be flexibly controlled by changing the radius of air hole. In addition, it is worth noting that when the radius of air hole is increased, the wavelength of absorption peak will be blue-shifted due to the decrease of effective refractive index of the guided resonance. On the other hand, when r=65 nm is fixed, the wavelength of absorption peak will be red-shifted with the increase of p, and the value of absorption peak almost keeps unchange, as shown in Fig. 6(b). Meanwhile, as shown in Fig. 6(c), the wavelength of the absorption peak tends to exhibit red shift with the increase of the thickness of photonic crystal, because the effective refractive index of the guided resonance will also be increased. Moreover, as shown in Fig. 6(d), when the thickness of (CH3NH3)PbI3 layer is increased from 80 nm to 120 nm, the wavelength of the absorption peak also exhibits red shift, and the value of absorption peak reaches maximum and then decreases. This is because that the intrinsic loss will increase with the thickness of (CH3NH3)PbI3 layer, and then the whole structure undergoes from undercoupling, then critical coupling, to overcoupling procedure. Thus, such a perfect absorption system is proposed with good adjustability, which can find important applications in nano-scale metamaterial absorbers.
Fig. 6. Absorption spectra for different (a) radii of air hole, (b) periods of the photonic crystal, (c) thicknesses of photonic crystal, and (d) thicknesses of (CH3NH3)PbI3 layer. The other structural parameters are the same as Fig. 1.
On the other hand, it should be emphasized that the physical mechanism of our proposed structure can also be applied to enhance absorption of other halide perovskites, such as (CH3NH3)PbBr3, and (CH3NH3)PbCl3, not just the (CH3NH3)PbI3. In the simulation, we use the first-principles calculation software VASP code to calculate the dielectric functions of (CH3NH3)PbBr3, and (CH3NH3)PbCl3, and they are also matched well with the dielectric constant parameter model of (CH3NH3)PbBr3 and (CH3NH3)PbCl3 reported in Ref. [38]. As shown in Fig. 7(a), when the (CH3NH3)PbI3 layer of proposed structure is replaced by (CH3NH3)PbBr3 and (CH3NH3)PbCl3 respectively, and the other parameters keep the same, the absorption peaks are still realized in the near-infrared regime. Thus, it is demonstrated that this method is a general approach to design halide perovskite-based absorbers in the near-infrared regime. Furthermore, it is worth noting that all of the above results are based on normal incident light, however, the proposed absorber need to maintain excellent absorption efficiency on the relatively wide incident angles in the application. Then, we investigate the optical absorption of (CH3NH3)PbI3 as a function of angle of incidence and incident light wavelength, as seen from Fig. 7(b). When the incident angle increases to 60°, the absorption peak of proposed absorber is still higher than 85%. Thus, the proposed absorber can tolerate a relatively wide incident angles in practical application.
Fig. 7. Light absorption of (CH3NH3)PbI3 as a function of the wavelength and angle of incidence. The other parameters are the same as Fig. 2.
4. Conclusion
To conclude, a narrowband (CH3NH3)PbI3-based perfect absorber is proposed in the communication band, and the corresponding absorption characteristics are investigated by using the FDTD method. Simulated results exhibit that a complete absorption peak is achieved at the wavelength of 1310 nm by making use of the critical coupling with guided resonance. Moreover, we have compared the simulation results with theoretical calculations, which agree well with each other. By changing the thickness and period of photonic crystal, the wavelength of absorption peak can be tuned effectively. Furthermore, the proposed absorber can tolerate a relatively wide range of incident angles and demonstrate polarization-independence. In addition to (CH3NH3)PbI3, the complete absorption peaks in the other halide perovskites are realized by the same mechanism. Thus, we believe our designed absorber can find some potential applications in the frequency-selective photodetectors working in the communication band.
Funding
National Natural Science Foundation of China (11764018, 61505052); Natural Science Foundation of Jiangxi Province (20192BAB212003, 20192BAB212004); Education Department of Jiangxi Province (GJJ190360).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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