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Sub-bandgap light absorption enhancement in germanium films through Berreman mode weak coupling to a microcavity mode

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Abstract

light absorption is a substantial problem that profoundly influences a wide range of disciplines. Whereas it is fundamentally restricted by the bandgap energy of the involved materials. Herein, we study the sub-bandgap light absorption in germanium films via Berreman mode (BE) and its enhancement through weak coupling to Fabry-Perot cavity mode. This enhancement is performed by integrating the semiconductor film into a microcavity structure and tune its resonance frequency to match the epsilon-near-zero (ENZ) wavelength of the film material in a planar multilayer structure. We ascertained that our approach of electric field confinement in the semiconductor layer could perform significant light absorption at large incidence angles. That provides a novel, general, and simple method to enhance the optical and optoelectronic responses of any ENZ material, especially semiconductors below their bandgap energies.

© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Light absorption in semiconductors is a fundamental property that plays a vital role in modern photonics and optoelectronics. For example, imaging sensors, lasers, modulators, solar cells, and photodetectors are all based on light absorption by means of converting photons energy to another form of energy such as electrical or thermal. Therefore, absorption spectrum tailoring concerning spectral selectivity, absorption strength, and bandwidth is highly beneficial for these devices and expanding their application range. [15] _ENREF_1Nevertheless, it is well known that semiconductors’ light absorption is intrinsically limited by their bandgap energy; light can not be absorbed efficiently below the bandgap energy because of absorption coefficients’ rapid drop near the bandgap edge [1,6,7].

Over the past decades, some approaches have been reported to conquer this problem, such as creating mid-gap energy levels [810] -via heavy doping- or growing surface microstructures [11,12]. Profound insight into silicon as an example of semiconductors, its sub-bandgap light absorption could be increased up to a few percentage points by integrating dopants at a concentration of the order of ${10^{20}}c{m^{ - 3}}$, which also extended the optoelectronic response of the hyperdoped silicon to IR wavelengths as long as 2.2 $\mu m$ [13]. Furthermore, to fulfill near-perfect absorption below silicon's bandgap energy, laser-induced surface features patterning has been utilized [11,14]. However, both approaches have very poor overall quantum efficiency.

In general, many designs have been reported to engineer materials’ absorption, including nanostructured films, [15] epsilon-near-zero (ENZ) materials, [16,17] ultrathin semiconductor gratings, [18] plasmonic-based antennas, [19] and metamaterials [20,21]. In recent years, ENZ materials have been given much attention because of their unique features and applications [2225]. The material could be considered an Epsilon-near-zero material if its electric permittivity real part crosses zero at one or various wavelengths. Doped semiconductors and transparent conductive oxides are the most popular artificial engineered ENZ materials [22]. Their ENZ wavelength can be tuned within a particular spectral range over the mid-and near-infrared regions by changing the growth conditions or/and the doping concentration [25,26]. Sb-doped Ge is one of such ENZ materials with an interestingly wide range tunability of the ENZ wavelength throughout 4-21 $\mu m$ [27].

Only thin films composed of an ENZ material can support Berreman mode (BE) or epsilon-near-zero mode (ENZ). [28,29] The BE and ENZ modes are two confined polaritons near ENZ wavelength; their dispersions are separated by the light line $\omega = c{K_\parallel }$ where ${K_\parallel }$ is the in-plane wave vector, c is the speed of light, and $\omega $ is the angular frequency [29]. BE mode is for wave vectors lying in the light cone, so it is a radiative mode [30] excitable from the free space by a P-polarized light that provides a ${E_ \bot }$ in thin films of thickness $\le 200\; nm$. [31] But ENZ mode wavevectors are located out of the light cone; that is why it is a non-radiative mode [28] that needs to be locally excited by coupling to localized plasmon resonances (LSPR) near field ${E_ \bot }$ [32,33] in ultrathin films of thickness $\le$ 20nm [29]. Both BE and ENZ modes grant strong manipulation of IR light-matter interaction at the nanoscale by the spectral and spatial distribution of confined and enhanced electric fields near the ENZ wavelength. Thence, Thin films’ IR absorption spectrum can be beneficially tailored.

In this work, we show that integrating a nanofilm of Sb-doped Ge into a Fabry-Perot microcavity can significantly strengthen the absorption peak when the microcavity and Berreman modes are weakly coupled at the ENZ wavelength. By modifying the incidence angle and the multilayer film geometry, a significant increase in light absorption up to several tenths of percentage points (49%) has been achieved below the germanium bandgap energy (approximately 0.8 eV). Our approach does not require complicated surface patterning; instead, we provide a powerful, simple but general method that can also be applied to other potential applications in photon detection and light harvesting. To the best of our knowledge, this approach has not been previously reported. Besides that, our first proposed device could be used in polarization switching applications as long as it shows selective polarization absorption.

2. Experimental section

2.1 Experimental part

Three samples of different structures, all containing Sb-doped Ge layers, were grown with a constant germanium deposition rate of 0.511 Å/s and a constant Sb flux of $1.4 \times {10^{12}}\; c{m^{ - 2}}{S^{ - 1}}$ at a constant growth temperature of 150 °C by molecular beam epitaxy (MBE) system. The MBE system was implemented with an electron beam evaporator for Si growth (EVBB-63-5, MBE-Komponenten, Germany) and two knudsen cell sources (WEZ-63-35, MBE-Komponenten, Germany) for Ge and Sb evaporation. Besides, a reflection high-energy electron diffraction (RHEED) system (RH 20 SS, Stable Instrumente, Germany) for in-situ crystalline quality and surface morphology monitoring. The antimony flux monitoring is performed using the quadrupole mass spectrometer. The base pressure of the MBE chamber is kept under $2 \times {10^{ - 10}}\; Torr.$

The zeroth sample (sample-0) was carried out to extract Sb-doped Ge film's complex permittivity under those constant growth conditions. To fabricate this sample, a 2-inch Si wafer was RCA cleaned then loaded into the MBE chamber. A 50 nm homo-epitaxial silicon layer was deposited at 500 °C on the Si substrate to smooth the terraces after degassing and removing the residual oxides. 1 $\mu m$ Sb-doped Ge film was grown on silicon substrates with constant Ge deposition rate, Sb flux, and substrate temperature, as mentioned above. Sample-1 was fabricated following the same procedures as sample-0 except that a 160 nm pure Ge layer was deposited before the 80 nm Sb-doped Ge film. This Ge layer is composed of a low temperature (LT, 380°C) seed layer (30 nm) and a high temperature (HT, 600°C) epilayer (130 nm) in order to achieve high crystallinity. After that, a thick gold layer was deposited on top of the 80 nm Sb-doped Ge film (see Fig. 3(a)) by magnetron sputtering equipment. The sputtering system mainly consists of a Thin Film Deposition Monitor (SQM-160, Inficon), RF power supply (CESAR Power Generator, Advanced Energy), and Magnetron Sputtering Sources (Kurt J. Lesker). In sample-2, the TiN layer was deposited first on the Si substrate using magnetron sputtering. Then, both (80 nm Sb-doped Ge) and (160 nm Ge) layers were deposited respectively on top of the TiN layer at 150 °C (see the schematic of Fig. 5(a)) by the MBE equipment. Cross section transmission electron microscopy (XTEM) (200 KV, Tecnai G2) was utilized to examine the crystal quality of the Sb-doped germanium films.

 figure: Fig. 1.

Fig. 1. Optical response of Sb-doped Ge film. Real and imaginary parts of the permittivity of the Sb-doped Ge film as a function of wavelength obtained by fitting the reflectivity data with the Drude-Lorentz formula for 1 $\mu m$ thick Sb-doped Ge film deposited on Si substrate with constant Sb flux of $1.4 \times {10^{12}}\; c{m^{ - 2}}{S^{ - 1}}$ at a constant growth temperature of 150 °C. The ENZ wavelength is marked with the red dashed line.

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 figure: Fig. 2.

Fig. 2. Simulations to optimize sample-1 structure a) Schematic of a structure composed of Si substrate, Sb-doped Ge film, and 300 nm gold layer inverted upside-down to simulate the reflectivity inside Si substrate for different Sb-doped Ge thicknesses varying from zero to 320 nm by step of 20 nm, whilst fixed incidence angle at ${16^\circ }$. b) Simulated reflectivity spectra for different Sb-doped Ge thicknesses for each S-polarization and P-polarization, severally. c) The calculated absorption spectra of P-polarized light. d) The maximum absorption (black triangles) and the peak height (blue circles) as a function of Sb-doped Ge thickness depending on the calculated absorption. The red dashed line in d denotes the optimized Sb-doped Ge film thickness. e) Map of simulated reflectivity as a function of wavelength and the second incidence angle inside the Si substrate. f) Schematic of a sample structure-1 composed of Si substrate, Ge layer, 80 nm Sb-doped Ge film, and 300 nm gold layer inverted upside-down to simulate the reflectivity inside Si substrate for different Ge thicknesses varying from zero to 220 nm by step of 20 nm, whilst fixed incidence angle at ${16^\circ }$. g) Simulated reflectivity spectra for different Ge thicknesses for each S-polarization and P-polarization, severally. h) The calculated absorption spectra of P-polarized light. i) The maximum absorption (black circles) and the peak height (blue squares) as a function of Ge thickness depending on the calculated absorption. The red dashed line in i denotes the optimized Ge layer thickness.

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 figure: Fig. 3.

Fig. 3. Experimental measurements of the fabricated sample-1. a) Schematic of sample-1 with a numerical example of the first and second incidence angles. b) The absolute reflectance of P-Polarized (solid lines) and S-polarized (dotted lines) light at different incidence angles. c) Reflection high-energy electron diffraction (RHEED) pattern of Ge layer grown directly on Si substrate. d) RHEED pattern after depositing Sb-doped Ge film on the previous Ge layer with constant Sb flux of $1.4 \times {10^{12}}\; c{m^{ - 2}}{S^{ - 1}}$ at a constant growth temperature of 150 °C. e) High resolution cross section transmission electron microscope (HR-XTEM) bright-field (BF) images of sample-1 show that the planar layers of the device are uniform, and the entire Sb-doped Ge and Ge layers are single crystalline (Taking into account that HR-XTEM could not distinguish between them). Scale bar, 500 nm (left) and 10 nm (top right). The corresponding selective area electron diffraction (SAED) pattern (bottom right) of the Sb-doped Ge layer emphasizes its single crystalline quality [44,45].

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 figure: Fig. 4.

Fig. 4. Simulations to optimize sample-2 structure. a,b) The profile of the |Ez|2 normalized to the maximum value vs. the spatial variable z at ENZ wavelength for the long-range SPP supported by an 80 nm thick Sb-doped Ge film without an additional Ge layer (a) and with it (b), the color bar refers to the medium refractive index. c) Schematic of a sample structure-2 composed of Si substrate, 300 nm TiN layer, 80 nm Sb-doped Ge film, and Ge layer to simulate the reflectivity in the air for different Ge thicknesses varying from zero to 220 nm by step of 20 nm, whilst fixed incidence angle at ${50^\circ }$. d) Simulated reflectivity spectra for different Ge thicknesses for each S-polarization and P-polarization, severally. e) The calculated absorption spectra of P-polarized light. f) The P-polarization maximum absorption (black squares) and both S-polarization (blue squares), P-polarization (blue triangles) resonance peak positions as a function of Ge thickness. The red dashed line denotes the optimized Ge layer thickness.

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 figure: Fig. 5.

Fig. 5. Simulation results of structure-2 at the optimized conditions (incidence angle, layers thicknesses). a,b) Simulated reflectivity and transmissivity spectra with the calculated absorption for structure-2 as shown in the sub-schematic at a fixed incidence angle of ${50^\circ }$ for both S-polarized light (a) and P-polarized light (b).

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It is worth mentioning at this point that it was appropriate to use gold as a metallic ground plane in sample-1 because, in addition to its optical properties, it could be deposited at substrate temperatures less than 150 °C [34]. This represents a vital necessity when depositing it on top of the Sb-doped Ge layer, which is epitaxially grown at a substrate temperature of 150 °C. However, in the case of depositing Germanium films on top of a metallic ground plane such as the before mentioned structure, gold is not a good choice because of its low melting point (∼1,064°C) [35] compared to the germanium vapour temperature (1,280°C). In such a situation, gold can cause harmful consequences on the MBE system besides a bad quality planar multilayer film structure due to its diffusion into germanium. That is why in this case, titanium nitride (TiN) – which could not be deposited with a metallic character at substrate temperatures less than 600°C – [36] provides an excellent alternative for gold as a metallic ground plane due to its high melting point (∼3,000°C) [37] and suitable optical properties to support Berreman mode confinement in the Sb-doped Ge layer.

The reflectance spectra are measured with a Fourier transform infrared (FTIR) spectroscopy (Bruker, VERTEX 70) for wavelengths greater than 2.5 $\mu m$. While (Agilent Cary 7000) is used for smaller wavelengths. Complex permittivity is extracted from the normal-incidence reflectance spectrum by fitting the data with the Drude-Lorentz dispersion model [27,38,39].

$$\varepsilon = \varepsilon ^{\prime} + \varepsilon ^{\prime\prime} = {\varepsilon _\infty }\left( {1 - \frac{{\omega_P^2}}{{{\omega^2} + i\omega \mathrm{\Gamma }}}} \right) + \mathop \sum \limits_{j = 1}^n \frac{{S_j^2}}{{({\omega_j^2 - {\omega^2}} )- i\omega {\mathrm{\Gamma }_j}}}$$
where ${\varepsilon _\infty }$ (${\varepsilon _\infty } \approx 16$ for Ge) is the high-frequency dielectric constant; ${\omega _P}$ is the plasma frequency $\left(\omega_{P}=\left(n e^{2} / \varepsilon_{0} \varepsilon_{m} m_{c}\right)^{1 / 2}\right.$ is the momentum scattering rate $\left(\Gamma=e / \mu m_{c}\right)$; [40] and ${\mathrm{\Gamma }_j}$, ${\omega _j}$, and ${S_j} $ are the damping, resonance frequency, and the strength of the Lorentz oscillators, respectively. While (${m_c} = 0.12{m_e} $ for Ge) which is the conductivity effective mass, $\mu $ is the carrier mobility, ${\varepsilon _0}$ is the permittivity of free space, and $n$ is the carrier concentration.

2.2 Simulation part

Finite-difference time-domain (FDTD) simulations were carried out to optimize and study each structure (FDTD Solutions, Lumerical Solutions, Inc., Canada). The simulation region boundary conditions are set as Perfect match layer (PML), which are overridden by Broadband Fixed Angle Source Technique (BFAST) for the non-parallel boundaries to the film's plane. The reflectance monitor was located behind the source, whereas the transmission one was situated after the 300 nm metallic layer. A frequency-domain power monitor was located perpendicular to the film plane to figure out the electric near-field distribution. We used the dielectric constants of Au, TiN, Ge, and Si provided by the software, whereas that of Sb-doped Ge film was newly imported according to the FTIR reflectance data fitting results. The electric field magnitude was set to be 1 V/m.

3. Results and discussion

3.1 Results

Figure 1 shows the extracted real and imaginary parts of the electric permittivity of a 1 $\mu m$ thick Sb-doped Ge film, where the ENZ wavelength was found to be at 4.17 $\mu m$. When the real part of permittivity vanishes, the permittivity has an imaginary part of 2.4, which is low enough to support some kind of field confinement modes if its conditions are satisfied. The low imaginary part is attained in Sb-doped Ge film by its high electron mobility and crystal quality, which is crucial for large field enhancement [23]. Furthermore, the ENZ wavelength can be tuned by adjusting the doping level and growth conditions of Sb-doped Ge film [27].

In this paper, two devices of different structures are fabricated; the first absorbs light only due to Berreman mode confinement, and the second has absorption enhancement due to weak coupling. They will be mentioned as sample-1 and sample-2, respectively, while structure-1 and structure-2 stand for the planar nanoscaled multilayer structures in these devices.

To calculate the absorption in sample-1 as a whole device composed of the Si-substrate and the structure-1 of (Ge, Sb-doped Ge, Au) layers (see Fig. 3(a)), we firstly should calculate it for the Sb-doped Ge layer, which represents the active layer of absorption. In the samples considered here, an optically thick metallic ground plane is used, then the transmission (T) could be regarded as zero in $A = 1 - R - T;$ therefore, the absorption (A) and reflectivity (R) are simply related by $A = 1 - R$ [24]. Thus, the very first step to obtaining the absorption is to get the reflectivity.

Figure 2(b) represents the simulated reflectivity spectra under S- and P-polarized incidence for different Sb-doped Ge thicknesses at a constant incidence angle of ${16^\circ }$ inside the Si-substrate. Because it was found to be the optimized incidence angle to achieve the highest absorption, as shown in Fig. 2(e). The reflection dips under p-polarized incidence in Fig. 2(b) can be attributed to the Berreman Effect, with thickness independent resonance frequency that coincides with the Sb-doped Ge ENZ wavelength (4.17 $\mu m$). The calculated absorption spectra are plotted in Fig. 2(c); the observed absorption behavior features a clear thickness dependence of the absorption strength. Relying on the absorption peak maximum and the thickness of each Sb-doped Ge film as shown in Fig. 2(d), we concluded that the 80 nm Sb-doped Ge is the optimized film thickness to support Berreman mode between Si substrate and the thick gold ground plane. Furthermore, inserting a pure 160 nm Ge layer between the Si substrate and the Sb-doped Ge film could enhance the absorption at the ENZ wavelength by a percent of 7%, as shown in (Fig. 2 f, g, h, and i). Besides, this pure Ge layer acts as a virtual substrate from the experimental fabrication perspective, which improves the Sb-doped Ge film's crystal quality during its epitaxial growth [27].

The undoped Si substrate has no absorption band in the mid-IR range; [41] in addition to that, it has a negligible refractive index dispersion all over the simulations and measurements bandwidth (2-8 $\mu m$). Therefore, the Si substrate refractive index could be taken as 2.43 [42]. As well, Snell's law could be easily used to relate the first incidence angle (on the air-Si substrate interface) to the second incidence angle (on the Si substrate-structure interface), as shown in Fig. 3(a). The greater the second incidence angle, the deeper the reflection dip of P-polarized incidence due to Berreman resonance, as illustrated in Fig. 2(e). That is why we measured the reflectivity spectra of sample-1 at high incidence angles for both S- and P-polarized light, as Fig. 3(b) displays. Sample-1 shows selective absorption of only P-polarized light with an excellent agreement with the simulation results, as clarified in the discussion sub-section. Reflection high-energy electron diffraction (RHEED) patterns in Fig. 3 c and d indicate a high crystal quality and smooth surface morphology for both Ge and Sb-doped Ge layers, successively [27].

Since a Berreman mode is a radiative mode that can be excited from the free space, we considered another device structure that can support Berreman mode and Fabry-Perot cavity mode to enhance the absorption at the ENZ wavelength by coupling them. This way, the device can absorb both S- and P-polarized light, not only P-polarized as in sample-1. In addition to saving P-polarized light for more round trips of multiple reflections to strengthen the Berreman mode itself. Our simulation results reveal that the simple structure of Sb-doped Ge film on top of the 300 nm titanium nitride (TiN) layer could support Berreman mode up to Sb-doped Ge thickness of 440 nm (see Fig. S1, Supplement 1). However, the Fabry-Perot bare cavity mode resonance frequency could not be tuned at the ENZ wavelength, regardless of the Sb-doped Ge layer thickness. Thus, they could not be coupled.

It is clear from the foregoing that the additional Ge layer, as in Fig. 4(c), plays two critical roles. First of all, to support the long-range surface plasmon polariton on the opposite side of the TiN-(Sb-doped Ge) interface that helps to confine the electric field inside the Sb-doped Ge film supporting Berreman mode and lowering the leaky field (see Fig. 4 a and b). The second is to engineer its thickness to tune the Fabry-Perot bare cavity mode resonance frequency to cross the Berreman mode resonance frequency. Those two combined factors achieved the best p-polarized light absorption at the ENZ wavelength when the Ge layer's thickness was 160 nm, as shown in (Fig. 4 c, d, e, and f). All mentioned above simulations pursuing optimize sample-2 geometry are carried out at a fixed incidence angle of 50° to neutralize the effect of incidence angle and maximize the absorption (see Fig. S2, Supplement 1). This is according to our simulations of sample-2 reflectivity spectra for different incidence angles in the air.

Figure 5 insets show the proposed device structure “structure-2” of the optimized conditions to couple Fabry-Perot cavity mode to the Berreman mode. Besides that, Fig. 5 presents the comparison between the bare cavity mode (s-polarization) and the coupling result (p-polarization), which implies that the cavity can provide only 40.5% maximum absorption without Berreman mode. It also confines p-polarized light to give more chance of Berreman mode absorption to occur, enhancing the P-polarized incidence absorption by 49%, as Fig. 4(f) clarifies by comparing the absorption spectrum maximum of the 0 nm Ge layer structure with the other one of 160 nm Ge. Moreover, in the case of unpolarized light incidence, the tuned S-polarized light absorption of percent 40.5% -which would not exist before, as in Fig. 3(b) - should be added to the 68% of P-polarization absorption at the ENZ wavelength (see Fig. 5(b)) to get a total absorption of 54.25% (see Table 1).

Tables Icon

Table 1. Summary of maximum absorption values and enhancement percentages due to coupling to cavity mode for both p-polarized and unpolarized light.

We fabricated sample-2 as we designed it in the inset of Fig. 5, except that the Ge and Sb-doped Ge layers were not single crystalline films; instead, there were polycrystalline films as the rings of the RHEED [43] and XTEM selective area electron diffraction (SAED) [44,45] patterns indicate in Fig. 6 a and e, respectively. This was because there is no practical way to grow Ge single-crystalline film on top of a TiN film. Nevertheless, the experimental measured S- and P-reflectivity spectra of sample-2 in Fig. 6(b) show a remarkable agreement with our simulated ones as for spectral selectivity (resonance wavelength), absorption strength, except in the absorption bandwidth (see Fig. 6 c and d). This could be attributed to the crystal structure difference, as evident when comparing Fig. 3(e) and 7(e).

 figure: Fig. 6.

Fig. 6. Experimental measurements of the fabricated sample-2 and comparing its results with the simulated results of structure-2. a) Reflection high-energy electron diffraction (RHEED) pattern of 80 nm Sb-doped Ge film deposited on a thick ground TiN layer with constant Sb flux of $1.4 \times {10^{12}}\; c{m^{ - 2}}{S^{ - 1}}$ at a constant growth temperature of 150 °C. b) The absolute reflectance of P-Polarized (blue line) and S-polarized (magenta line) with light at a fixed incidence angle of ${50^\circ }$ for both. c,d) Calculated absorption based on reflectivity data (measured for sample-2 and simulated for structure-2) for both S-polarized light (c) and P-polarized light (d). e) HR-XTEM bright-field images of sample-2 show that the planar layers of the device are uniform, and the entire Sb-doped Ge and Ge layers are polycrystalline (Taking into account that HR-XTEM could not distinguish between them). Scale bar, 500 nm (left) and 10 nm (top right). The corresponding SAED pattern (bottom right) of the Sb-doped Ge layer emphasizes its polycrystalline quality. [44,45]

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 figure: Fig. 7.

Fig. 7. Correlate sample-1 experimental reflectivity results to the simulated ones. a) Schematic for rays intensity of one complete trip. b) Representation of many multiple reflections showing the partial waves’ intensities in terms of the simulated reflectivity and transmittivity spectra at each interface. c-e) Experimentally measured reflection spectrum (black curve) compared with simulated reflection spectrums either considers up to higher-order partial waves, starting from the first partial wave to the fourth (green, blue, red, violet). Each graph at a different incidence angle on the Si substrate.

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3.2 Discussion

To get a more profound insight into the experimental reflectivity results of sample-1 and their relation to the simulated ones, we analyzed the simulated results to test its validity of reproducing the experimental results.

$${{\boldsymbol{R}}_{{\boldsymbol {total}}}} = \frac{{{{\boldsymbol{I}}_4} + {{\boldsymbol{I}}_1}}}{{{{\boldsymbol{I}}_0}}} = \frac{{{{\boldsymbol{I}}_1} + {{{\boldsymbol{\dot{T}}}_1}}{\boldsymbol R}_2{{\boldsymbol T}_1}{{\boldsymbol I}_0}}}{{{{\boldsymbol I}_0}}} = \frac{{{{\boldsymbol R}_1}{{\boldsymbol I}_0} + {{\boldsymbol R}_2}{{\boldsymbol T}_1}^2{{\boldsymbol I}_0}}}{{{{\boldsymbol I}_0}}} = {{\boldsymbol R}_1} + {{\boldsymbol R}_1}^0{{\boldsymbol R}_2}^1{{\boldsymbol T}_1}^2$$
$${\boldsymbol {since}\; },{\boldsymbol \; }{{\boldsymbol T}_1} = {\boldsymbol \; }{{{\boldsymbol{\dot{T}}}_1}} {\boldsymbol \; \; },{\boldsymbol \; \; }{{\boldsymbol I}_1} = {{\boldsymbol R}_1}{{\boldsymbol I}_0}.$$
where ${R_{total}}$ is the resultant reflectivity after one complete trip of light rays through sample-1; ${R_1} $ and ${T_1}$ are the reflectivity and transmissivity from air to Si substrate at the air-Si interface, respectively; ${R_2}$ is the reflectivity at the Si-(structure-1) interface; ${{T_1}}$ is the and transmissivity from Si substrate to air at the air-Si interface; and ${I_0},{\; }{I_1},{\; }{I_2},{\; }{I_3},\; and\; {\; }{I_4}$ are the intensities of the incident, first reflected, first transmitted, second reflected, second transmitted rays, respectively, as shown in Fig. 7(a). Taking into consideration that ${R_1}\; $, ${T_1}$, $\; {R_2}$, and ${{T_1}}$ are simulated spectra, each simulated individually. Conceding the probable multiple reflections in the Si substrate, as in Fig. 7(b), we can get:
$${{\boldsymbol R}_{{\boldsymbol {total}}}} = {\boldsymbol \; }{{\boldsymbol R}_1} + {{\boldsymbol R}_1}^0{{\boldsymbol R}_2}^1{{\boldsymbol T}_1}^2 + {{\boldsymbol R}_1}^1{{\boldsymbol R}_2}^2{{\boldsymbol T}_1}^2 + {{\boldsymbol R}_1}^2{{\boldsymbol R}_2}^3{{\boldsymbol T}_1}^2 + {{\boldsymbol R}_1}^3{{\boldsymbol R}_2}^4{{\boldsymbol T}_1}^2 + \ldots \; $$

However, according to Fig. 7 c, d, and e, our approach succeeded to a large extent in reproducing the experimental reflectivity spectra considering only the first partial reflected wave at all studied incidence angles.

$$\therefore {{\boldsymbol R}_{{\boldsymbol {total}}}} \approx ({{\boldsymbol R}_1} + {{\boldsymbol R}_1}^0{{\boldsymbol R}_2}^1{{\boldsymbol T}_1}^2)$$

This gives a shred of solid evidence that the only reason for the obtained absorption that causes this dip in reflectivity spectrum herein is attributed to the Berreman mode, as manifested by the absence of multiple reflections or any other reason of absorption, the constancy of reflection dip position at the ENZ wavelength of Sb-doped Ge active film, and the selective absorption of only P-polarized light of nonzero incidence angle. Moreover, it provides high credibility for all simulation results that we build our argument on.

In structure-2, films act as an optical microcavity confines photons to increase their lifetime inside the material and favor their interaction with Berreman mode of the active Sb-doped Ge film [46]. The weak coupling between the engineered Fabry-Perot cavity mode and the Berreman mode is apparent, as presented in Fig. 8. Taking into account that, Fig. 8(b) represents the Berreman mode branch because only the P-polarized incidence can excite Berreman mode; however, Fig. 8(a) emphasizes that there is no cavity mode by its almost zero absorption of S-polarization. But Fig. 8(c) represents just the bare cavity mode branch because the S-polarized incidence can not excite Berreman mode, while Fig. 8(d) depicts the coupling between the two modes because the P-polarized light can excite both modes. In these coupling regimes, the dispersion curves do not avoid crossing each other; instead, they maximize the crossing region's resonance achieving a greater absorption, [4749] as in Fig. 8(e).

 figure: Fig. 8.

Fig. 8. Cavity mode-Berreman mode weak coupling. a,b) Structure-1 simulated reflectivity as a function of wavelength and Ge layer thickness for S-polarized light (a) and P-Polarized light (b). c,d) Structure-2 simulated reflectivity as a function of wavelength and Ge layer thickness for S-polarized light (c) and P-Polarized light (d). e) Description of (d) as the resultant of both pure cavity mode in (c) and pure Berreman mode in (b), whose are coupled together by weak coupling.

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4. Conclusion

We presented an easy and efficient method for sub-bandgap light absorption by coupling a Berreman mode and Fabry-Perot cavity mode at the ENZ wavelength. This approach enhanced the semiconductor light absorption by an additional 49% at energies below its bandgap. It involves integrating the Sb-doped Ge as an active layer into a planar multilayers structure, which is designed to form a microcavity that resonates at a wavelength corresponding to the active layer’s ENZ wavelength. Planar multilayers structures are optimized and fabricated to absorb light at large incidence angles through Berremam mode confinement with and without coupling. As a result, we observed a significant enhancement in light absorption strength with coupling. Also, a bandwidth broadening is noticed, which could be attributed to the crystal structure difference of the absorption active layer as demonstrated in TEM images.

We believe that our approach and results sufficiently indicate that it is now possible to engineer a sub-bandgap near-perfect absorber utilizing ENZ materials, which could lead to new and interesting applications in near- and mid-IR ranges. Furthermore, such a device can be easily fabricated without surface patterning difficulties and limitations. That is paving the road for further enhancement in optical and optoelectronic responses below materials bandgap energies, which were representing stumbling blocks for many applications of light-matter interaction in diverse disciplines.

Funding

State Key Laboratory of Modern Optical Instrumentation; Zhejiang University; National Natural Science Foundation of China (91950205); National Key Scientific and Technological Infrastructure for Translational Medicine, Shanghai (TMSK-2020 125).

Disclosures

The authors declare no conflicts of interest.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Supplementary Material (1)

NameDescription
Supplement 1       (1) Testing the validity of Sb-doped Ge film on top of 300 nm TiN layer to support both Berreman and cavity modes at the ENZ wavelength; (2) Influence of the incidence angle on the P-polarization absorption in structure-2.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Figures (8)

Fig. 1.
Fig. 1. Optical response of Sb-doped Ge film. Real and imaginary parts of the permittivity of the Sb-doped Ge film as a function of wavelength obtained by fitting the reflectivity data with the Drude-Lorentz formula for 1 $\mu m$ thick Sb-doped Ge film deposited on Si substrate with constant Sb flux of $1.4 \times {10^{12}}\; c{m^{ - 2}}{S^{ - 1}}$ at a constant growth temperature of 150 °C. The ENZ wavelength is marked with the red dashed line.
Fig. 2.
Fig. 2. Simulations to optimize sample-1 structure a) Schematic of a structure composed of Si substrate, Sb-doped Ge film, and 300 nm gold layer inverted upside-down to simulate the reflectivity inside Si substrate for different Sb-doped Ge thicknesses varying from zero to 320 nm by step of 20 nm, whilst fixed incidence angle at ${16^\circ }$. b) Simulated reflectivity spectra for different Sb-doped Ge thicknesses for each S-polarization and P-polarization, severally. c) The calculated absorption spectra of P-polarized light. d) The maximum absorption (black triangles) and the peak height (blue circles) as a function of Sb-doped Ge thickness depending on the calculated absorption. The red dashed line in d denotes the optimized Sb-doped Ge film thickness. e) Map of simulated reflectivity as a function of wavelength and the second incidence angle inside the Si substrate. f) Schematic of a sample structure-1 composed of Si substrate, Ge layer, 80 nm Sb-doped Ge film, and 300 nm gold layer inverted upside-down to simulate the reflectivity inside Si substrate for different Ge thicknesses varying from zero to 220 nm by step of 20 nm, whilst fixed incidence angle at ${16^\circ }$. g) Simulated reflectivity spectra for different Ge thicknesses for each S-polarization and P-polarization, severally. h) The calculated absorption spectra of P-polarized light. i) The maximum absorption (black circles) and the peak height (blue squares) as a function of Ge thickness depending on the calculated absorption. The red dashed line in i denotes the optimized Ge layer thickness.
Fig. 3.
Fig. 3. Experimental measurements of the fabricated sample-1. a) Schematic of sample-1 with a numerical example of the first and second incidence angles. b) The absolute reflectance of P-Polarized (solid lines) and S-polarized (dotted lines) light at different incidence angles. c) Reflection high-energy electron diffraction (RHEED) pattern of Ge layer grown directly on Si substrate. d) RHEED pattern after depositing Sb-doped Ge film on the previous Ge layer with constant Sb flux of $1.4 \times {10^{12}}\; c{m^{ - 2}}{S^{ - 1}}$ at a constant growth temperature of 150 °C. e) High resolution cross section transmission electron microscope (HR-XTEM) bright-field (BF) images of sample-1 show that the planar layers of the device are uniform, and the entire Sb-doped Ge and Ge layers are single crystalline (Taking into account that HR-XTEM could not distinguish between them). Scale bar, 500 nm (left) and 10 nm (top right). The corresponding selective area electron diffraction (SAED) pattern (bottom right) of the Sb-doped Ge layer emphasizes its single crystalline quality [44,45].
Fig. 4.
Fig. 4. Simulations to optimize sample-2 structure. a,b) The profile of the |Ez|2 normalized to the maximum value vs. the spatial variable z at ENZ wavelength for the long-range SPP supported by an 80 nm thick Sb-doped Ge film without an additional Ge layer (a) and with it (b), the color bar refers to the medium refractive index. c) Schematic of a sample structure-2 composed of Si substrate, 300 nm TiN layer, 80 nm Sb-doped Ge film, and Ge layer to simulate the reflectivity in the air for different Ge thicknesses varying from zero to 220 nm by step of 20 nm, whilst fixed incidence angle at ${50^\circ }$. d) Simulated reflectivity spectra for different Ge thicknesses for each S-polarization and P-polarization, severally. e) The calculated absorption spectra of P-polarized light. f) The P-polarization maximum absorption (black squares) and both S-polarization (blue squares), P-polarization (blue triangles) resonance peak positions as a function of Ge thickness. The red dashed line denotes the optimized Ge layer thickness.
Fig. 5.
Fig. 5. Simulation results of structure-2 at the optimized conditions (incidence angle, layers thicknesses). a,b) Simulated reflectivity and transmissivity spectra with the calculated absorption for structure-2 as shown in the sub-schematic at a fixed incidence angle of ${50^\circ }$ for both S-polarized light (a) and P-polarized light (b).
Fig. 6.
Fig. 6. Experimental measurements of the fabricated sample-2 and comparing its results with the simulated results of structure-2. a) Reflection high-energy electron diffraction (RHEED) pattern of 80 nm Sb-doped Ge film deposited on a thick ground TiN layer with constant Sb flux of $1.4 \times {10^{12}}\; c{m^{ - 2}}{S^{ - 1}}$ at a constant growth temperature of 150 °C. b) The absolute reflectance of P-Polarized (blue line) and S-polarized (magenta line) with light at a fixed incidence angle of ${50^\circ }$ for both. c,d) Calculated absorption based on reflectivity data (measured for sample-2 and simulated for structure-2) for both S-polarized light (c) and P-polarized light (d). e) HR-XTEM bright-field images of sample-2 show that the planar layers of the device are uniform, and the entire Sb-doped Ge and Ge layers are polycrystalline (Taking into account that HR-XTEM could not distinguish between them). Scale bar, 500 nm (left) and 10 nm (top right). The corresponding SAED pattern (bottom right) of the Sb-doped Ge layer emphasizes its polycrystalline quality. [44,45]
Fig. 7.
Fig. 7. Correlate sample-1 experimental reflectivity results to the simulated ones. a) Schematic for rays intensity of one complete trip. b) Representation of many multiple reflections showing the partial waves’ intensities in terms of the simulated reflectivity and transmittivity spectra at each interface. c-e) Experimentally measured reflection spectrum (black curve) compared with simulated reflection spectrums either considers up to higher-order partial waves, starting from the first partial wave to the fourth (green, blue, red, violet). Each graph at a different incidence angle on the Si substrate.
Fig. 8.
Fig. 8. Cavity mode-Berreman mode weak coupling. a,b) Structure-1 simulated reflectivity as a function of wavelength and Ge layer thickness for S-polarized light (a) and P-Polarized light (b). c,d) Structure-2 simulated reflectivity as a function of wavelength and Ge layer thickness for S-polarized light (c) and P-Polarized light (d). e) Description of (d) as the resultant of both pure cavity mode in (c) and pure Berreman mode in (b), whose are coupled together by weak coupling.

Tables (1)

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Table 1. Summary of maximum absorption values and enhancement percentages due to coupling to cavity mode for both p-polarized and unpolarized light.

Equations (5)

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ε = ε + ε = ε ( 1 ω P 2 ω 2 + i ω Γ ) + j = 1 n S j 2 ( ω j 2 ω 2 ) i ω Γ j
R t o t a l = I 4 + I 1 I 0 = I 1 + T ˙ 1 R 2 T 1 I 0 I 0 = R 1 I 0 + R 2 T 1 2 I 0 I 0 = R 1 + R 1 0 R 2 1 T 1 2
s i n c e , T 1 = T ˙ 1 , I 1 = R 1 I 0 .
R t o t a l = R 1 + R 1 0 R 2 1 T 1 2 + R 1 1 R 2 2 T 1 2 + R 1 2 R 2 3 T 1 2 + R 1 3 R 2 4 T 1 2 +
R t o t a l ( R 1 + R 1 0 R 2 1 T 1 2 )
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