1. Introduction

Mid-infrared (MIR) integrated optical sensors have received widespread attentions because many gas molecules exhibit characteristic rotational or vibrational transition bands in the MIR spectrum (3 ∼ 14 µm) [1]. Waveguide photodetector is a key component for an integrated MIR gas sensor. The MIR photodetector can be classified into two categories: photon detectors and thermal detectors based on the working principle [2]. Compared with photon detectors, thermal detectors can operate at room temperature, thus they do not require the expensive and bulky cryogenic equipment. One of the most widely used thermal detectors is bolometer, which generally comprises an absorber and a thermistor. The light sensing capability of the bolometer is achieved by detecting the resistance variation due to opto-thermal conversion [3–5]. Remarkable progress has been made in the development of waveguide bolometers on silicon-on-insulator (SOI) over the last decade [6–13]. Nonetheless, the transparent window of SOI platform limits the detection of carbon dioxide (CO₂) and other mid-infrared gases at the wavelengths beyond 4 µm. The germanium-on-silicon (GOS) platform has a transparent window from 3 to 14 µm [14–17]. Therefore, bolometers based on GOS waveguide platform is a potential solution of MIR integrated gas sensors.

One of the figures of merit for a bolometer is responsivity, which defined as the change in the resistance value per unit incident light power. There are two feasible methods to improve a bolometer’s responsivity. The first approach is to utilize thermal sensitive materials with high temperature coefficient of resistance (TCR). Amorphous silicon (a-Si) and vanadium oxide (VO_x) are commonly used as the thermal sensitive materials of thermistors. Though the intrinsic a-Si has a high TCR of −10%/K, the high electrical resistivity (∼10⁹ Ω·cm) has set a barrier to measure the resistance changes by read-out integrated circuits. The resistivity of a-Si can be suppressed by doping. However, its TCR is reduced accordingly to a much lower value of −2.8%/K [18]. The other material VO_x has relatively low compatibility with the complementary metal-oxide-semiconductor (CMOS) process. Amorphous germanium tin (a-Ge_1-ySn_y) is a promising candidate material for bolometers, as it has a high TCR, low resistivity and is CMOS-compatible. When the Sn concentration is at 17%, the a-Ge_0.83Sn_0.17 has a high TCR of −3.96%/K and relatively low resistivity of 164 Ω·cm [19,20]. The second approach is to implement the resonance structures on the waveguide to enhance light absorption efficiency. When light frequency is matched with the resonance frequency of the metasurface, the local surface plasmon resonance (LSPR) effect greatly enhances the electric field. This increases light absorption which finally enhances the photo-thermal conversion efficiency.

In this work, a room-temperature a-Ge_0.83Sn_0.17 waveguide bolometer on the GOS platform with high photodetection responsivity working at mid-infrared wavelength is proposed. This device features with a 1D tungsten (W) metasurface on top of the a-Ge_0.83Sn_0.17 waveguide. The metasurface induced LSPR effect results in strong light absorption, based on which the responsivity of the bolometer has been significantly increased. An absorption efficiency of nearly 93% at λ = 4.2 µm is achieved, and the responsivity is improved to −3.17%/µW. In addition, a 3-dB roll-off frequency of beyond 10 kHz is obtained.

2. Device design

Figure 1(a) is a three-dimensional (3D) schematic diagram of an a-Ge_0.83Sn_0.17 waveguide bolometer on the GOS platform. The bolometer consists of a 1D metasurface light absorber, a suspended a-Ge_0.83Sn_0.17 waveguide and an a-Ge_0.83Sn_0.17 thermistor. Within the 1D metasurface, the meta-atoms have a radius r = 180 nm, thickness t = 20 nm and pitch p = 400 nm, as shown in the inset of Fig. 1(a). The meta-atom length (l_m) varies from 300 to 400 nm to investigate the l_m impact on the bolometer’s performance. Tungsten is adopted as the metasurface material due to its corrosion resistance, high melting point and CMOS compatibility. All the meta-atoms are arranged uniformly on the suspended a-Ge_0.83Sn_0.17 waveguide with width w_GeSn = 2.5 µm, thickness t_GeSn = 0.5 µm and length l_w = 15 µm. At the end of the waveguide, there is a thermistor with length l_th = 5 µm. There is a gap l_g = 1 µm between the metasurface and the thermistor. The bolometer is built on the GOS waveguide, which enables the photodetection beyond λ = 4 µm as compared to those on the SOI platform. The Ge waveguide has 2 µm width (w_Ge) and 1.35 µm thickness (t_Ge). A bilevel taper coupler with a tip width w_tip = 800 nm and coupling length l_c = 40 µm is utilized between the Ge and the a-Ge_0.83Sn_0.17 waveguides. The tapered structure is designed on both a-Ge_0.93Sn_0.17 and Ge waveguides. Similar structures have been reported in Ref. [21]. Such bilevel taper coupler can be used to improve the light coupling efficiency between the Ge and a-Ge_0.93Sn_0.17 waveguides [22]. In addition, it can reduce the multimode effects to an almost negligible level [23]. We have designed two types of waveguide bolometers: Device A_i (the subscript i represents the number of meta-atoms) and Device B_i. The a-Ge_0.83Sn_0.17 thermistor of Device A_i is suspended, whereas the one of Device B_i is on top of SiO₂, as shown in Fig. 1(b). The responsivity as well as response speed of the two types of bolometers are investigated by numerical simulation.

 

Fig. 1. (a) 3D schematic of the 1D metasurface assisted a-Ge_0.83Sn_0.17 waveguide bolometer (Device A_i). (b) The top view and the right-side view for Device A_i and Device B_i.

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The electromagnetic (EM) field distribution of the GOS waveguide at λ = 4.2 µm is obtained by numerical simulation using the commercial software Ansys Lumerical. The mode profile of the fundamental transverse electric mode (TE₀) of the GOS waveguide is depicted in Fig. 2(a), which demonstrates a decent light confinement within the waveguide. To couple the light from the Ge waveguide into the a-Ge_0.83Sn_0.17 waveguide, a bilayer taper coupler is designed by finite-difference time domain (FDTD) method. The refractive index n of a-Ge_0.83Sn_0.17 is obtained by a linear interpolation method based on the refractive indices of c-Ge_1-ySn_y [24]. In Figs. 2(b) and 2(c), the n value of a-Ge_0.83Sn_0.17 is 4.28 and k value is assumed to be 0. The cross-sectional electric field (E) profile of the coupler at λ = 4.2 µm is shown in Fig. 2(b), and a power coupling efficiency of 80% is achieved. With a proper design of the W meta-atoms, the LSPR could be excited by the EM field traveling in the a-Ge_0.83Sn_0.17 waveguide, as depicted in Fig. 2(c). Owing to the ohmic losses in the metal metasurface, the incident EM energy is effectively converted into heat [25]. After that, the heat is conducted to the a-Ge_0.83Sn_0.17 waveguide, which results in a temperature change of the a-Ge_0.83Sn_0.17 thermistor. This leads to the change of the electrical resistance of the thermistor, which is connected in a bridge configuration between two contact pads. Thus, the measurement of resistance change could be conducted by applying voltage to the pads and measuring the current change.

 

Fig. 2. (a) TE₀ mode distribution of the Ge waveguide at 4.2 µm wavelength. (b) X-Z cross-sectional view of the E-field at the bilevel coupler region. (c) Near-field E-field profile of 10 meta-atoms with r = 180 nm, t = 20 nm, p = 400 nm at λ = 4.2 µm.

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3. Results and discussion

3.1 Design of the meta-atoms

To analyze light absorption (A) of the bolometer, 3D simulation is carried out by FDTD method. The n of W at mid-infrared wavelengths are obtained from Ref. [26]. It should be noted that the n values of a-Ge_1-ySn_y at mid-infrared are seldomly reported. According to experimental data from Ref. [27], the n values of a-Ge_1-ySn_y are close to those of crystalline c-Ge_1-ySn_y. In this work, therefore, the refractive indices of a-Ge_0.83Sn_0.17 is approximated using a linear interpolation method based on the refractive indices of c-Ge_1-ySn_y at mid-infrared [24]. The absorption coefficient (α) of a-Ge_0.83Sn_0.17 near λ = 4.2 µm is another important parameter in device simulation. Although it has been shown experimentally that the absorption cut-off of c-Ge_0.83Sn_0.17 is about 4.13 µm [28], unfortunately, the experimental α of a-Ge_0.83Sn_0.17 near 4.2 µm wavelength has not been reported yet. One should be noted that the absorption cutoff of a-Ge might be shorter [29] or longer [30] than that of c-Ge. Analogous to a-Ge_0.83Sn_0.17, it might be ambiguous if the α of a-Ge_0.83Sn_0.17 near λ = 4.2 µm is negligible or not. In this work, therefore, we have simulated and compared the waveguide bolometer performances with various α of a-Ge_0.83Sn_0.17, i.e. 0, 10, 100, and 1000 cm⁻¹.

To achieve high absorption, the dipole oscillation frequency in the metasurface should be designed to match the input light frequency ω_l. The dipole oscillation frequency is determined by the geometry of the metasurface. Here, the α of a-Ge_0.83Sn_0.17 is set as 0 cm⁻¹. The l_w and l_g are fixed at 15 and 1 µm, respectively. Figure 3(a) shows the energy fraction results at λ = 4.2 µm as the number of meta-atoms increases from 1 to 20. The absorption A increases as more meta-atoms are added, exceeding 90% when the number of meta-atoms is larger than 10. Meanwhile, the scattering (S), reflection (R) and transmission (T) are decreased. The enhancement of A origins from the excited collective oscillation mode of the W metasurface [31], which results in a strong confinement of light in meta-atoms. Due to the high absorption of metal W, the confinement of light leads to the strong absorption. The absorption rates A as a function of l_m at 4.2 µm wavelength are extracted and presented in Fig. 3(b). The A increases at first, continuously comes to a “peak value” and then decreases with the increase of l_m. In general, the strength of the E-field in metasurface affects the absorption rate. Thus, the variation trend of the field enhancement factor |E/E₀| (E₀ is the source E-field amplitude in numerical simulations [32,33]) with meta-atom length is consistent with the absorption, as shown in the inset of Fig. 3(b). The field enhancement factor reaches 7.5 at l_m = 350 nm, while an absorption rate of 93% is achieved.

 

Fig. 3. (a) Energy fraction of A, T, R, S as a function of the number of meta-atoms at 4.2 µm wavelength. The l_w is 15 µm and the l_g is 1 µm. (b) Absorption of meta-atoms with different lengths l_m at 4.2 µm wavelength. The inset shows the field enhancement factor with different lengths l_m. (c) The absorption spectra by 3D FDTD simulation (solid lines) and by TCMT curve fitting (dashed lines) in frequency domains. A decent matching between the TCMT results and the FDTD curves can be observed. (d) Extracted values of η and −γ/(γ²+ β²) for different devices.

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Figure 3(c) shows the absorption spectra for lengths l_m ranging from 300 nm to 400 nm, while keeping the r, t and p fixed at 180, 20 and 400 nm, respectively. Since the dipole moments in the two ends of the meta-atoms are in opposite direction, increasing the l_m weakens the restoring force between them, resulting in a red-shift of the resonance peak [34]. It is noteworthy that the resonant peak of l_m = 360 nm is at the wavelength around 4.2 ∼ 4.3 µm, which is corresponded to the absorption peak of CO₂.

To gain the underlying mechanism of the absorption, a fast and less compute-intensive temporal coupled-mode theory (TCMT) model is adopted, the absorption can be obtained by [32,33]:

Next, the effects of various a-Ge_0.83Sn_0.17 absorption coefficients α_GeSn on the bolometer absorption are studied, as shown in Table 1. The entire FDTD absorption simulation region includes the a-Ge_0.17Sn_0.83 waveguide and the metasurface. The wavelength is set as 4.2 µm. The 1D metasurface consists of 10 meta-atoms. The l_m of meta-atoms is 360 nm. The A_GeSn is the absorption rate of a-Ge_0.83Sn_0.17. The total absorption A_total represents the sum of the absorption of the waveguide and the metasurface. The parameter A_m, which equals to (A_total -A_GeSn)/A_total, is the ratio of the absorption rate of the metasurface to the total absorption. In Table 1, the A_GeSn reaches 86.2% when α_GeSn is 1000 cm⁻¹, which corresponds to an A_m of 3.1%. It should be noted that a high α_GeSn may lead to large optical loss within the bilayer taper as well as the a-Ge_0.17Sn_0.83 waveguide. This inevitably degrades the opto-thermal energy conversion efficiency. Therefore, the bolometer designed in this work is more suitable at the wavelengths where the a-Ge_1−ySn_y has low absorption coefficient.

Table 1. Absorption of the bolometers in the FDTD simulation

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3.2 Thermal simulation of bolometers

Simulations based on the Ansys Lumerical Heat Transport (HEAT) solver are carried out to investigate the thermal and electrical properties of the bolometer. In the thermal simulation, the setting of the heat source is based on the FDTD absorption simulation results. The l_m of meta-atoms is 360 nm. The input light power is set as 5 µW. The boundary temperature is fixed at room temperature of 293.15 K. A constant convection boundary condition is added between the surface of the bolometer and air. The convective heat flux coefficient of air is 5 W/(m²·K). In addition, the voltage boundary conditions are applied to the contact pads. The thermal properties of different materials are summarized in Table 2. In this table, the specific heat and density of a-Ge_0.83Sn_0.17 is obtained by linearly interpolation method based on the value of Ge [35] and Sn [36]. Besides, the thermal conductivity of a-Ge_0.83Sn_0.17 is obtained through an empirical formula in Ref. [37].

Table 2. Thermal properties of the materials in device simulation

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Temperature distributions of the bolometers with different number of meta-atoms (Device A₅, A₁₀, A₁₅), and device structures (Device A₁₀, B₁₀) are compared in Fig. 4. The cross-sectional temperature distributions of the thermistor along the orange dashed lines in Figs. 4(a)-(d) are described in Figs. 4(e)-(h), respectively. From Fig. 4(c), the heat is mainly concentrated in the a-Ge_0.83Sn_0.17 waveguide due to its low G_th. This leads to a maximum temperature T_max above 305.75 K within this region. The heat is then conducted to both sides along the a-Ge_0.83Sn_0.17 waveguide. The a-Ge_0.83Sn_0.17 thermistor experiences a maximum temperature of 301.97 K, as shown in Fig. 4(g). However, the T_max in the metasurface region of Device A₁₀ is reduced to 304.27 K due to the relatively low absorption rate A of the W metasurface. Correspondingly, the T'_max of its thermistor is reduced to 301.14 K, as shown in Fig. 4(f). Similarly, the T_max and the T'_max in Device A₅ are 298.71 and 297.25 K, respectively. Furthermore, the high thermal conductivity of the SiO₂ beneath the a-Ge_0.83Sn_0.17 thermistor results in a smaller temperature change. As can be seen from Fig. 4(d) that the T_max of Device B₁₀ is only 300.29 K, which is lower than that of Device A₁₀.

 

Fig. 4. Top view (a), (b), (c), (d) and cross-sectional view (e), (f), (g), (h) of the temperature distribution for Device A₅/A₁₀/A₁₅/B₁₀. The P_in is 5 µW and the λ is 4.2 µm.

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The current-voltage (I - V) characteristics of Device A₁₀ are simulated using finite element method with various input power P_in ranging from 0 to 10 µW, as shown in Fig. 5(a). It can be seen that a higher input light power leads to a larger slope of the I - V curve. Moreover, the resistance response (ΔR/R₀, where R₀ is the resistance without light illumination) for the four types of bolometers are shown in Fig. 5(b). It should be noted that the nonlinear change process of G_th and C_th with temperature can be approximated by a linear model, when the temperature range is small [10]. Based on this concept, Device A₁₀ and Device A₁₅ shows a similar responsivity of around −3.17%/µW, which is higher than those of the other bolometers. The metasurfaces of Device A₁₀ and A₁₅ can absorb almost all of the incident light power, resulting in the generation of more heat, which leads to a significant resistance change of the thermistor. Due to the presence of SiO₂ under the thermistor which increases the thermal conductance, the responsivity of Device B₁₀ is degraded to −0.645%/µW. In addition, the responsivity of Device A₁₀ is analyzed at the wavelength range from 4.1 to 4.3 µm with P_in = 5 µW, as plotted in Fig. 5(c). The nearly flat responsivity spectrum indicates a relatively broadband property of the metasurface-enhanced bolometer, which is beneficial for the detection of CO₂ gas molecules with the fingerprint absorption peak at around λ = 4.2 µm.

 

Fig. 5. (a) I - V curves of the Device A₁₀ with various P_in from 0 to 10 µW. The ΔT represents the average temperature change in the thermistor. (b) The resistance response as a function of P_in for each bolometer. (c) Wavelength-dependence of the responsivity for waveguide bolometer A₁₀.

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The impacts of α_GeSn on the bolometer responsivity are investigated, as summarized in Table 3. The responsivity of the bolometer with metasurface (Device A₁₀) decreases as the α_GeSn increases, due to the fact that a-Ge_1-ySn_y waveguide with high α_GeSn absorbs more EM energy, resulting in a lower opto-thermal conversion efficiency. In addition, the responsivity of the bolometer without metasurface is −0.042%/µW when the α_GeSn = 1000 cm⁻¹. It can be seen from Table 3 that a maximum responsivity of −3.13%/µW can be achieved when α_GeSn = 0 cm⁻¹. Thus, reducing the α_GeSn is one of the feasible ways to achieve a high responsivity waveguide bolometer.

Table 3. Responsivities of the Device A₁₀ with different α_GeSn

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Furthermore, the G_th of each device is calculated according to Eq. (2). The absorption rates A are 36.7%, 71.6%, 82.0%, and 71.6% for Devices A₅, A₁₀, A₁₅, B₁₀, respectively. The temperature responsivities (ΔT/ΔP_in) are 1.186, 1.974, 2.249 and 0.455 K/µW for the above-mentioned devices. In a steady state, the frequency-dependent term (${f^2}C_{th}^2$) can be ignored. Therefore, G_th is calculated to be 3.094 × 10⁻⁷, 3.627 × 10⁻⁷, 3.646 × 10⁻⁷ and 1.560 × 10⁻⁶ W/K for Device A₅, A₁₀, A₁₅, B₁₀, respectively.

Another critical metric of a bolometer is the light response speed. The temporal response of waveguide bolometers at λ = 4.2 µm, P_in = 5 µW and modulation frequency f = 1 kHz is studied, as shown in Fig. 6(a). The rise response time t_rise is defined as the time needed to increase the temperature from 10% to 90% of its maximum, and vice versa for the fall response time t_fall. It is observed that t_rise (t_fall) becomes larger when the number of meta-atoms i is increased from 5 to 15. This could be explained by the increasing of C_th resulting from the larger number of meta-atoms. The normalized temperature change as a function of f is shown in Fig. 6(b). The 3 dB roll-off frequency (f_3 dB) of Device A₅, A₁₀, A₁₅ and B₁₀ are 16, 14, 12 and 25 kHz, respectively. It is noted that f_3 dB of Device B₁₀ is higher than those of Device A_i in this work. The fast response speed of Device B₁₀ could be attributed to its higher thermal conductance as the thermal conductivity of SiO₂ is much larger than that of air. With further optimizing the device design, e.g., by decreasing the thermal capacity, the f_3 dB of the bolometer could be significantly improved, which is the subject of our future works.

 

Fig. 6. (a) Temporal responses of ΔT as a function of time t. The optical power and bias voltage are 5 µW and 1 V, respectively. (b) Normalized temperature change with respect to the modulating frequency f of the heat power in the simulation.

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In addition, a possible fabrication process for the proposed waveguide bolometer is discussed. The starting substrate for the a-Ge_0.93Sn_0.17 waveguide bolometer could be a commercially-available GOS wafer. The Ge waveguide could be formed by electron beam lithography (EBL) and inductively coupled plasma (ICP) etching. After that, the SiO₂ film could be deposited by plasma enhanced chemical vapor deposition (PECVD). To expose the surface of Ge waveguide, the chemical-mechanical polishing (CMP) could be used to polish the SiO₂ film. Then, the a-Ge_0.93Sn_0.17 waveguide could be formed by magnetron sputtering, EBL and ICP etching. After that, the metal contact pads and 1D metasurface could be formed by lift-off process. Finally, the suspended a-Ge_0.93Sn_0.17 structure could be formed by selective removal of SiO₂, possibly using the diluted hydrofluoric (DHF) chemical or vapor hydrofluoric (VHF) etching process.

There are a few literatures regarding the design of Si-based waveguide bolometer in infrared region. The comparison between our device and the reported waveguide bolometers are summarized in Table 4. As a proof of concept, our designed waveguide bolometer exhibits an improved responsivity in comparison to the previously reported devices. This could be attributed to the large TCR and low thermal conductance of the suspended a-Ge_0.83Sn_0.17 waveguide, as well as the enhanced absorption from the 1D metasurface. In addition, a decent 3 dB bandwidth of beyond 10 kHz can be achieved, which should be enough for a variety of sensor applications.

Table 4. Benchmark between the reported Si-based waveguide bolometers

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4. Conclusion

In summary, we have proposed a mid-infrared metasurface assisted a-Ge_0.83Sn_0.17 waveguide bolometer with high responsivity. The designed bolometer takes advantage of the LSPR effect from the 1D metasurface, exhibiting a high responsivity of around −3.17%/µW within the 4.1 ∼ 4.3 µm wavelength range. In addition, a f_3 dB beyond 10 kHz is realized. The proposed bolometer in this work paves the way for high responsivity and high-speed MIR integrated photonic sensors on Si substrates.