Nanocavity absorption enhancement for two-dimensional material monolayer systems

Haomin Song; Suhua Jiang; Dengxin Ji; Xie Zeng; Nan Zhang; Kai Liu; Chu Wang; Yun Xu; Qiaoqiang Gan

doi:10.1364/OE.23.007120

1. Introduction

Two-dimensional (2D) material monolayers are promising candidates to function as active layers for atomically thin energy harvesting devices [1]. For instance, the optical absorption of a monolayer graphene (GR) can compare to that of a 20-nm-thick silicon film [2]. In recent years, 2D-material photodetectors, phototransistors and solar cells have been reported based on monolayers of GR [3,4], molybdenum disulfide (MoS₂) [5,6], and Van der Waals heterostructures [7], respectively. However, considering their atomically-thin thicknesses, the absolute value of absorption in 2D material monolayers is relatively weak. It was reported that a suspended monolayer of GR can absorb approximately 2.3% of the incident light over a relatively broadband spectral regime [8]. Therefore, it is essential to enhance the optical absorption to improve the performance of these atomically-thin energy harvesting devices. Earlier attempts to increase the absorption in GR monolayers aimed to make it more visible by placing them on top of SiO₂/Si substrates [9–11]. However, the obtained peak optical absorption is still relatively low, which is 8%~9%. In recent years, different methods were proposed to enhance the optical absorption with impressively high optical absorption records reported theoretically [12–14] and experimentally [15,16]. However, for many enhancement mechanisms, 2D material monolayers were usually embedded inside microcavities, resulting in that the enhanced optical absorption cannot be conveniently used in applications like biosensing [17,18] and surface-enhanced photocatalysis [19] where the interaction between the 2D materials and the surrounding environment is needed. Although some designs employed 2D matierial monolayers or patterns (e.g. nanodisk [12] or nanoribbons [20]) on top of 1D or 2D patterned substrates (e.g. one-dimensional photonic crystals [21] or gratings [22], hole-array based photonic crystals [14], etc.), costly and complicated fabrication techneques imposed significant barriers to develop practical applications based on these platforms. In this article, we will propose an alternative simpler planar nanocavity strategy with an air spacer to enhance the exclusive optical absorption in 2D material monolayers on top of this structure, which is particularly useful for the development of atomically-thin energy harvesting/conversion devices.

2. Numerical simulation of total absorption

In a recent report, ultra-thin Germanium (Ge) films were coated on flat Au surfaces to realize strong interference effects and achieve high total absorption at resonant wavelengths in visible to near infrared (IR) spectral region [23]. According to the mechanism of the resonant absorption in this two-layered system, the key issue is that the light can penetrate into the metal reflector and obtain a larger phase change, which, on the other hand, will inevitably introduce optical loss in the metal film. Due to the intrinsic optical property of Au, a significant part of the incident light attenuates in the bottom metal film, which is undesired for ultra-thin film energy harvesting applications. To manipulate the optical absorption distribution and maximize the absorption in the semiconductor material, we proposed a planar nanocavity structure by introducing a phase compensation layer between the top semiconductor film and the bottom highly reflective metal mirror [24]. According to our previously reported theoretical modeling and experimental validation, over 75% of the incident resonant wavelength can be absorbed by a 1.5-nm-thick Ge film on a Al₂O₃/Al cavity. In this article, we will apply this cavity structure to enhance the optical absorption in 2D material monolayers. Here we take GR monolayers as an example by placing it on top of a Al₂O₃/Al cavity structure (other 2D material monolayers are also applicable), as illustrated by the inset of Fig. 1(a). For comparison, the absorption spectrum of a free-standing GR monolayer is shown by the black curve in Fig. 1(a). In this modeling, the thickness of the GR monolayer is set to 0.4 nm for simplicity in modeling. The dispersive optical constants of GR and Al₂O₃ are adopted from [25] and [26], respectively. The absorption of this free-standing GR monolayer is almost a constant of 3~4% in the simulation range (if the thickness is set to 0.33 nm [2], the absorption is ~2.3%, which agrees with the experimental report [8]). By introducing a 40-nm-thick Al₂O₃ spacer layer between the GR monolayer and the Al mirror, the total optical absorption of the three-layered system at the wavelength of 400 nm is enhanced to 32.9% as shown by the red curve in Fig. 1(a). To reveal the resonant cavity behavior, the absorption spectrum of the 0.4-nm-thick GR film is modeled as the function of the Al₂O₃ spacer layer thickness, as shown in Fig. 1(b). One can see that the Fabry-Perot (FP)-like absorption resonance branches can be obtained as the thickness of the spacer layer increases. The total absorption can be effectively enhanced when the nanocavity is finely tuned. To further demonstrate the enhancement potential of this planar cavity structure, in Fig. 1(c), the thickness and optical constants of the lossless spacer layer were tuned from 1 nm to 500 nm and 0.01 to 2.5, respectively. In this modeling, the incident wavelength is set to 400 nm. One can see that the resonant absorption is highly dependent on these two parameters. The total absorption can be enhanced by tuning the thickness and the optical constant of the spacer layer. For instance, when the refractive index is tuned to 2.4, the peak total absorption reaches 42.4% with a 29-nm-thick spacer layer. In contrast, when the refractive index is 1, the peak total absorption is only 22.5% with an 85-nm-thick one.

Fig. 1 (a) Modeled absorption spectra of a free-standing GR (black) and a three-layered system with a GR monolayer on a 40-nm-thick-Al₂O₃/Al film (red). Inset: Schematic of a GR monolayer on top of a lossless spacer layer and a Al film. (b) Modeled total absorption spectra of the three-layered system as the function of the thickness of the Al₂O₃ spacer layer. (c) Simulated total absorption of the three-layered system as the function of the spacer layer thickness and its refractive index under normal incident light at the wavelength of 400 nm.

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To reveal the physical mechanism of this total absorption enhancement, one can plot the phasor diagram to analyze reflection components and determine the reflectivity of the nanocavity system [23,24], as shown by Fig. 2(a). The ultimate reflection and absorption can be determined by the termination of the phasor trajectory, i.e., $R = {R e [r]}^{2} + {I m [r]}^{2}$ and $A = 1 - R$ , respectively. By manipulating the phase of the reflected light to approach the destructive interference condition, one can enhance the total absorption, A, of the three-layered planar cavity system. For instance, the phasor diagrams of GR monolayers on an 85-nm-thick-air ( $n = 1$ )/Al, a 40-nm-thick-Al₂O₃ ( $n = 1.79$ )/Al and a 29-nm-thick-spacer ( $n = 2.4$ )/Al with normal incidence are plotted in Fig. 2(a) (see black, red and blue solid curves, respectively). The dotted circles, centered at the origin, represent the total reflection of $R = 1 %$ , $R = 25 %$ and $R = 81 %$ , respectively (i.e., $A = 1 - R = 99 %$ , $75 %$ and $19 %$ , respectively). The phasor trajectory starting from the origin indicates the successive reflection components occurred in the cavity. Each phasor change was calculated using analytical Fresnel equations [27]. One can see that the black, red and blue phasor trajectory curves end up at points of $R = 77.5 %$ (i.e., $A = 22.5 %$ ), $R = 67.1 %$ (i.e., $A = 32.9 %$ ) and $R = 57.6 %$ (i.e., $A = 42.4 %$ ) for $n = 1$ (i.e., air), $n = 1.79$ (i.e., Al₂O₃) and $n = 2.4$ spacer layer structures, respectively. Therefore, when the thickness of the spacer layer is optimized, the larger refractive index can better match the destructive interference condition, and hence enhance the total optical absorption. As shown in Fig. 2(b), the absorption spectra of the three-layered structures with three different spacer layers are plotted. Compared with the total absorption of the nanocavity with the Al₂O₃ spacer layer (i.e., the red curve), the absorption can be enhanced or depressed throughout the entire modeled spectral region from 400 nm to 1000 nm with a larger (blue curve) or smaller refractive index spacer layer (black curve), respectively.

Fig. 2 (a) The phasor diagram and (b) modeled total absorption spectra of the GR monolayer on an 85-nm-thick-air/Al film (black), a 40-nm-thick-Al₂O₃/Al (red) and a 29-nm-thick-spacer (n = 2.4)/Al film (blue) under normal incidence. (c) and (d) are simulated angle and polarization dependent total absorption spectra of a GR monolayer on an air/Al cavity under (c) s-polarized and (d) p-polarized light, respectively.

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Since the phasor trajectories are dependent on both polarization states and incident angles [27], we then analyze the dependence on these two parameters. Here we choose $n = 1$ as an example (i.e., an air spacer layer). As shown in Figs. 2(c) and 2(d), the absorption spectra of the GR monolayer are plotted as the function of the incident angle and the thickness of the spacer layer under the illumination of s-polarized [see Fig. 2(c)] and p-polarized states [see Fig. 2(d)], respectively. One can see that as the incident angle increases, absorption peak values under two polarization states are both enhanced, but their angle dependent behaviors are quite different. For the s-polarization case as shown in Fig. 2(c), when the thickness of the air spacer and the incident angle are 270 nm and 70°, respectively, the peak total absorption of the three-layered structure can be enhanced to 42.0% at the wavelength of 400 nm. For the p-polarization incidence as shown in Fig. 2(d), the peak total absorption value grows to 34.6% at 825 nm with a 300-nm-thick air spacer and an incident angle of 70°. This angle and polarization dependent absorption characteristic is due to the light path change introduced by the large spacer layer thickness and/or the large refractive angle at the spacer/GR interface, which shares the similar principle to the recently reported GR absorption enhancement using prism coupling system [28]. However, the prism makes the structure too bulky to be implemented in potential GR-based miniaturized and portable devices. The sandwich-like structure also limited its applications for biosensors [17,18] and photocatalysis [19], which require sufficient interactions between the GR films and the surrounding environment. Moreover, to achieve the total internal reflection, the incident angle should be finely tuned to meet the critical-angle requirement, narrowing the incident angle window for the absorption enhancement to only approximately 0.5°. In contrast, our nanocavity structure with the GR films on top has a much larger contact surface area for the interaction with external ambience and can realize the enhanced absorption in a broader incident angle window (e.g. 0 to at least 70° in Fig. 2), making it a strong contender for omnidirectional light harvesting devices. Further numerical modeling indicate that larger incident angles may result in higher absorption enhancement. However, due to the projection of the oblique incident beams, this situation will require very large area graphene monolayers which will impose a barrier in practical fabrication, and thicker spacer layers beyond “nanocavity” scope of this work.

3. Numerical simulation of exclusive absorption

However, in the design and optimization process discussed above, we only focused on enhancing the total absorption of the three-layered system. To develop atomically thin energy harvesting devices, it is important to explore how much light is actually absorbed in the GR monolayer exclusively. Here we further analyze the absorption distribution in the GR monolayer and the Al film at the wavelength of 400 nm as shown in Fig. 3(a), where red and black parts represent the exclusive absorption in GR monolayer and in the Al film, respectively. In this modeling, the optical constant of the spacer layer is tuned from 0.2 to 2.4. The spacer layer thicknesses labeled on top of those bars are optimized values for the exclusive absorption in GR monolayers [see empty dots in Fig. 4(b)]. One can see that although the spacer layer with larger optical constants renders a higher total absorption enhancement, more absorption occurs in the Al layer rather than in the top GR monolayer. For example, when the refractive index is 2.4, the optical absorption in the Al layer and the GR monolayer are around 28.8% and 13.6%, respectively. When the refractive index is tuned to 1, the absorption in the Al layer is depressed to ~6.9% while the absorption in the GR monolayer is enhanced to 15.6%. Intringuingly, when $n = 0.2$ , the absorption in the GR monolayer is 16.1% while almost 0 in the Al film. Therefore, the enhancement in the total optical absorption is unnecessarily corresponding to the absorption enhancement in the GR monolayer in the three-layered system. The surpression of the absorption in Al layer should also be considered and the exclusive absorption in the GR monolayer should be revisited. Figure 3(a) indicates that low refractive index materials (e.g. epsilon-near-zero materials [29]) with proper thicknesses are ideal candidates for the spacer layer to enhance the exclusive absorption in GR monolayers. In this article, however, we only consider a natural material with a refractive index ≥1. Therefore, the air spacer is the best one in the simulation range. With this air spacer layer as shown in Fig. 3(b), the absorption in GR monolayer is enhanced over the entire modeled spectrum, although its total absorption is lower than other two structures with Al₂O₃ and $n = 2.4$ spacer layers. To better compare with the total absorption in the three-layered system [i.e., Figs. 2(c) and 2(d)], we then model the exclusive absorption spectra of the GR monolayer as the function of the incident angle and the thickness of the air spacer layer under the illumination of s- and p-polarized states, respectively. One can see that at larger incident angles, s-polarized light can enhance the exclusive absorption in the GR monolayer [see Fig. 3(c)]) while the absorption for p-polarized light is weak [see Fig. 3(d)]. In contrast, we plot the exclusive absorption in the Al layer under s- and p-polarized light by subtracting the exclusive absorption in the GR monolayer [i.e., Figs. 3(c) and 3(d)] from the total absorption [i.e., Figs. 2(b) and 2(c)]. As shown in Figs. 3(e) and 3(f), the absorption in the Al layer shows an opposite absorption characteristic, i.e., the absorption under p- and s-polarized light increases and decreases, respectively, at larger angles, which will be discussed further in the next section. In summary, as the incident angle increases, the absorption in GR and Al layers are quite different for the two polarization states, which can enable atomically thin photo-detectors/transistors/conductors with unique polarization/angle sensing and detection functionalities.

Fig. 3 (a) Modeled peak absorption of a GR monolayer on a spacer/Al film as the function of the optical constant of the lossless spacer layer. The red and black parts represent the absorption in the GR monolayer and Al layer, respectively. (b) Modeled exclusive absorption spectra of a GR monolayer on 85-nm-thick-air/Al (black), 40-nm-thick-Al₂O₃/Al (red) and 29-nm-thick-spacer (n = 2.4)/Al (blue) under normal incidence. (c) and (d) are simulated angle and polarization dependent exclusive absorption spectra of a GR monolayer on an air/Al cavity under s-polarized and p-polarized incidence, respectively. (e) and (f) are simulated angle and polarization dependent exclusive absorption spectra of the bottom Al film under s-polarized and p-polarized light, respectively.

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Fig. 4 (a) Total absorption as the function of the spacer layer thickness and its refractive index under normal incident light at the wavelength of 400 nm modeled by Eq. (1). (b) Exclusive absorption in a GR monolayer as the function of the spacer layer thickness and its refractive index under normal incident light at the wavelength of 400 nm modeled by Eq. (3).

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4. Analytical analysis using Fresnel equations

To further interpret the results obtained in previous sections using numerical modeling, now we employ analytical equations to analyze underlying physical mechanisms. The total absorption ( $A$ ) under normal incidence is calculated by Fresnel equations [27]:

A = 1 - {| \frac{{\tilde{r}}_{01} + {\tilde{r}}_{12} \exp (i 2 {\tilde{β}}_{1}) + [{\tilde{r}}_{01} {\tilde{r}}_{12} + \exp (i 2 {\tilde{β}}_{1})] {\tilde{r}}_{23} \exp (i 2 {\tilde{β}}_{2})}{1 + {\tilde{r}}_{01} {\tilde{r}}_{12} \exp (i 2 {\tilde{β}}_{1}) + [{\tilde{r}}_{12} + {\tilde{r}}_{01} \exp (i 2 {\tilde{β}}_{1})] {\tilde{r}}_{23} \exp (i 2 {\tilde{β}}_{2})} |}^{2} .

Here, the reflection coefficients for s- and p-polarized light are

{\tilde{r}}_{x y, s} = \frac{{\tilde{n}}_{x} \cos {\tilde{θ}}_{x} - {\tilde{n}}_{y} \cos {\tilde{θ}}_{y}}{{\tilde{n}}_{x} \cos {\tilde{θ}}_{x} + {\tilde{n}}_{y} \cos {\tilde{θ}}_{y}} and {\tilde{r}}_{x y, p} = \frac{{\tilde{n}}_{x} \cos {\tilde{θ}}_{y} - {\tilde{n}}_{y} \cos {\tilde{θ}}_{x}}{{\tilde{n}}_{x} \cos {\tilde{θ}}_{y} + {\tilde{n}}_{y} \cos {\tilde{θ}}_{x}}, respectively,

where

{\tilde{n}}_{x} = n_{x} + i k_{x}

and

{\tilde{n}}_{y} = n_{y} + i k_{y}

are the complex refractive indices of layer

x

and layer

y

, respectively;

{\tilde{θ}}_{x}

and

{\tilde{θ}}_{y}

are the incident and refraction angles at the

x

/

y

interface, respectively, governed by

{\tilde{n}}_{x} \sin {\tilde{θ}}_{x} = {\tilde{n}}_{y} \sin {\tilde{θ}}_{y}

. 0, 1, 2 and 3 indicate the air environment, the GR monolayer, the spacer layer and the Al reflector, respectively.

{\tilde{β}}_{x} = \frac{2 π}{λ} {\tilde{n}}_{x} \cos {\tilde{θ}}_{x} h_{x}

, where

h_{1}

and

h_{2}

are the thicknesses of GR monolayer and the spacer layer, respectively.

In addition, the spacer layer also affects the absorption distribution significantly. The exclusive absorption in the GR monolayer ( $A_{G R}$ ) can be calculated by:

A_{G R} = A - A_{A l},

A_{A l} = \frac{n_{3}}{n_{0}} | \frac{\cos {\tilde{θ}}_{3}}{\cos {\tilde{θ}}_{0}} | {| \frac{{\tilde{t}}_{01} {\tilde{t}}_{12} {\tilde{t}}_{23} e x p [i ({\tilde{β}}_{1} + {\tilde{β}}_{2})]}{1 + {\tilde{r}}_{01} {\tilde{r}}_{12} e x p (i 2 {\tilde{β}}_{1}) + [{\tilde{r}}_{12} + {\tilde{r}}_{01} e x p (i 2 {\tilde{β}}_{1})] {\tilde{r}}_{23} e x p (i 2 {\tilde{β}}_{2})} |}^{2} .

Here,

A_{A l}

is the exclusive absorption in the Al layer. The transmission coefficients for s- and p-polarized light can be described by

{\tilde{t}}_{x y, s} = \frac{2 {\tilde{n}}_{x} \cos {\tilde{θ}}_{y}}{{\tilde{n}}_{x} \cos {\tilde{θ}}_{x} + {\tilde{n}}_{y} \cos {\tilde{θ}}_{y}} and {\tilde{t}}_{x y, p} = \frac{2 {\tilde{n}}_{x} \cos {\tilde{θ}}_{x}}{{\tilde{n}}_{x} \cos {\tilde{θ}}_{y} + {\tilde{n}}_{y} \cos {\tilde{θ}}_{x}}, respectively .

These analytical equations can be used to reveal the effects of the refractive indices and thicknesses of the spacer layers on the total absorption of the three-layered structure in Fig. 1(c). Therefore, one can obtain the same results of Figs. 1-3 using these analytical Fresnel equations.

4.1 Refractive index dependence of the spacer layer

For instance, we plot the total absorption as the function of the spacer layer thickness and its refractive index under normal incident light at the wavelength of 400 nm, as shown in Fig. 4(a), which is identical to the numerical simulation shown in Fig. 1(c). In Fig. 4(b), we further plot the exclusive absorption in GR monolayers under normal incidence at this wavelength (the white empty circles represent the parameters plotted in Fig. 3(a)). Compared with Fig. 4(a), one can see that the refractive index of the spacer layer plays a different role in the total and exclusive absorption, i.e., a larger n leads to a larger total absorption while a smaller n results in a larger exclusive absorption in GR monolayers (i.e., up to ~16% when n~0).

4.2 Angle and polarization dependence

To interpret the polarization dependence of the Al-absorption, we simplified the corresponding Eq. (4) based on the particular structure of the nanocavity in the air ambient with an air spacer layer. The reflection coefficients ${\tilde{r}}_{01, s} = - {\tilde{r}}_{12, s}$ and ${\tilde{r}}_{01, p} = - {\tilde{r}}_{12, p}$ because of the two GR/air interfaces. Also, $| e x p (i 2 {\tilde{β}}_{2}) | = 1$ and $| e x p (i {\tilde{β}}_{2}) | = 1$ since the air spacer is lossless, i.e., $k_{2} = 0$ , and therefore, $I m [{\tilde{β}}_{2}] = 0$ . Consequently, Eq. (4) can be simplified as:

A_{A l} = \frac{n_{3}}{n_{0}} | \frac{\cos {\tilde{θ}}_{3}}{\cos {\tilde{θ}}_{0}} | {| \frac{{\tilde{t}}_{01} {\tilde{t}}_{12} {\tilde{t}}_{23} e x p (i {\tilde{β}}_{1})}{1 - {\tilde{r}}_{01}^{2} e x p (i 2 {\tilde{β}}_{1}) - {\tilde{r}}_{01} [1 - e x p (i 2 {\tilde{β}}_{1})] {\tilde{r}}_{23} e x p (i 2 {\tilde{β}}_{2})} |}^{2} .

As shown in Figs. 3(e) and 3(f), the Al layers largely absorb near-infrared light with the peak wavelength centered at around 830 nm, which is mainly because that the peak of its real part of refractive index (i.e., $n_{3}$ ) is close to 830 nm. Besides, $h_{2}$ is only in one term, $e x p (i 2 {\tilde{β}}_{2})$ in Eq. (6). Due to the atomically-thin thickness of the GR monolayer, i.e., $\frac{h_{1}}{λ} \approx 0$ , $A_{A l}$ is insensitive to $h_{2}$ since $e x p (i 2 {\tilde{β}}_{1}) \approx 1$ [see Figs. 3(e) and 3(f)].

In addition, by comparing Figs. 2(c) and 2(d) with Fig. 3(c)-3(f), one can see that at large incident angles, the major part of the total absorption of the three-layered system under s-polarized incidence [Fig. 2(c)] occurred in the GR monolayer [Fig. 3(c)]. In contrast, the total absorption under p-polarized incidence [Fig. 2(d)] mainly occurred in the Al film [Fig. 3(f)]. This difference can be attributed to the angle and polarization dependent reflection and transmission described by Eqs. (2) and (5). Using these two equations, one can calculate polarization dependent transmission coefficients from the spacer layer to the Al film, indicating how much light can penetrate into the bottom Al film under various incident angles. As shown in Fig. 5, we plot the ratio between absolute values of these two transmission coefficients (i.e., $| t_{23, s} |$ for s-polarized incidence and $| t_{23, p} |$ for p-polarized incidence). One can see that $| t_{23, s} | / | t_{23, p} |$ decreases with larger incident angles, indicating that more p-polarized light will penetrate into the Al layer at larger incident angles and therefore have longer light-matter interaction time to be absorbed. Consequently, the polarization-dependent total absorption shown in Figs. 2(c) and 2(d) will re-distribute into the GR and Al layers quite differently at large incident angles, i.e., more in GR monolayers under s-polarized incidence and more in Al layers under p-polarized incidence.

Fig. 5 The ratio between the absolute values of the transmission coefficients between s- and p-polarized light, $| t_{23, s} | / | t_{23, p} |$ , as the function of the wavelength and the incident angle.

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5. An application in a real device structure

Finally, we discuss the feasibility to implement the proposed cavity structure to enhance the performance of 2D material photodetectors or photovoltaic devices [7]. In recent years, GR [3,4,30], MoS₂ [5,6,31], tungsten diselenide (WSe₂) [7] and tungsten disulfide [32] monolayers have been employed as the light absorbing layers for 2D phototransistors. Impressively high photoresponsivity have been reported, based on interlayer tunneling current [30], ultrafast conversion from photons to electrons due to high carrier mobility [3,4] and ultrahigh charge transfer resulted from semiconductor heterojunctions [32]. Most of these GR or GR-like 2D materials were placed on top of SiO₂/Si substrates. However, Si is highly absorptive in visible range, resulting in a large total absorption of the visible light with a significant dissipation in the Si layer rather than in 2D materials. The interaction between light and 2D materials is thus relatively weak. Based on our discussion above, the replacement of SiO₂/Si with air/Al cavity [see Fig. 6(a) for example] can suppress the undesired absorption in substrates and enhance the beneficial light-matter interactions in the atomically thin 2D materials. For instance, in [7], a WSe₂/MoS₂ hybrid was placed on a SiO₂/Si substrate. The combined optical absorption spectrum of the MoS₂ and WSe₂ hybrid-monolayer is shown by the black solid curve in Fig. 6(b), agreeing well with [7] (see Fig. S9 in the supporting material of [7]). In this modeling, the thicknesses of MoS₂ and WSe₂ monolayers are set to 0.67 nm and 0.7 nm, respectively. The optical constants of MoS₂ and WSe₂ are taken from [33] and [34], respectively. When the SiO₂/Si substrate is replaced by the proposed air/Al substrate, as illustrated in Fig. 6(a), significant absorption enhancement can be achieved under the normal incidence, especially in the 450~530 nm wavelength region, as shown by the red solid curve in Fig. 6(b). The angle and polarization dependence can also be employed to further enhance the absorption. For instance, when the thickness of the air spacer and the incident angle are further tuned to 175 nm and 61°, respectively, the absorption in the 2D material layer can be enhanced up to 100% under s-polarized light, as shown by the black dashed curve in Fig. 6(b). Although the absorption under p-polarized light is smaller (see the red dashed curve), the averaged absorption (see the blue dashed curve) under two polarizations is close to the absorption under normal incidence (see the red solid curve). Based on this strong absorption enhancement in properly designed nanocavity structures, 2D material p-n junctions are promising for the development of atomically thin photovoltaic devices with enhanced power conversion efficiencies [7,35].

Fig. 6 (a) Schematic illustration of an atomic-layer photodetector structure with a suspended atomic layer on top of an air spacer/metal cavity. (b) Modeled absorption spectra of MoS₂/WSe₂ hybrid-monolayers on a 280-nm-thick-SiO₂/Si cavity (black solid) under normal incidence, a 90-nm-thick-air/Al film (red solid) under normal incidence, a 175-nm-thick-air/Al under s-polarized (black dashed), p-polarized (red dashed) and unpolarized incidence (blue dashed) with an incident angle of 61°.

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6. Conclusion

In summary, we implemented a nanocavity structure to enhance the optical absorption of the three-layered system based on interference mechanism. Numerical and analytical analysis revealed that an air spacer layer is desirable to enhance the exclusive optical absorption of a suspended GR monolayer. With s-polarized incident light at an angle of 70°, a GR monolayer can absorb ~40% at the resonant wavelength of 400 nm on top of an air/Al-cavity, which is ten times that of a free-standing GR monolayer. Due to the polarization and angle dependence of the proposed GR/air/Al nanocavity, one can control the exclusive absorption in GR and Al films accordingly. According to a recent report [36], a tunable air gap under the GR monolayer is achievable by controlling the pressure difference between the air gap and the external environment, which is particularly useful to control the optical absorption in the proposed suspended 2D material monolayers. Therefore, the proposed low refractive index spacer layer is realizable based on these reported technologies. As the optical properties of air is more stable than other dielectrics [26] and the Al film maintains its highly reflectivity over a broad spectral range, the proposed idea can be extended from visible to mid-IR where the intrinsic optical property of GR monolayer remains almost constant [37,38]. Importantly, this strategy can also be employed for other 2D materials and hybrid-layer systems, which is quite general and will pave the way towards intriguing applications requiring stronger light-matter interactions, especially for the enhancement of the responsivity of suspended-GR detectors [1,39] and enhanced photoluminescence signals from 2D materials [40].

Acknowledgments

S. Jiang is supported by NSFC (Award #51001029). Y. Xu is supported by NSFC (Award #61177070). Q. Gan acknowledges funding support from National Science Foundation (grant no. ECCS1128086 and ECCS1425648).

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Nanocavity absorption enhancement for two-dimensional material monolayer systems

Abstract

1. Introduction

2. Numerical simulation of total absorption

3. Numerical simulation of exclusive absorption

4. Analytical analysis using Fresnel equations

4.1 Refractive index dependence of the spacer layer

4.2 Angle and polarization dependence

5. An application in a real device structure

6. Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Equations (6)

Optics Express