Design of High-Efficiency Silicon Nitride Grating Coupler with Self-Compensation for Temperature Drift

Abstract

In order to solve the problem of the efficiency reduction and complex manufacturing of traditional grating couplers under environmental temperature fluctuations, a Si₃N₄ high-efficiency grating coupler integrating a distributed Bragg reflector (DBR) and thermo-optical tuning layer is proposed. In this paper, the double-layer DBR is used to make the down-scattered light interfere with other light and reflect it back into the waveguide. The finite difference time domain (FDTD) method is used to simulate and optimize the key parameters such as grating period, duty cycle, incident angle and cladding thickness, achieving a coupling efficiency of −1.59 dB and a 3 dB bandwidth of 106 nm. In order to further enhance the temperature stability, the amorphous silicon (a-Si) thermo-optical material layer and titanium metal serpentine heater are embedded in the DBR. The reduction in coupling efficiency caused by fluctuations in environmental temperature is compensated via local temperature control. The simulation results show that within the wide temperature range from −55 °C to 150 °C, the compensated coupling efficiency fluctuation is less than 0.02 dB, and the center wavelength undergoes a blue shift. This design is compatible with complementary metal-oxide-semiconductor (CMOS) processes, which not only simplifies the fabrication process but also significantly improves device stability over a wide temperature range. This provides a feasible and efficient coupling solution for photonic integrated chips in non-temperature-controlled environments, such as optical communications, data centers, and automotive systems.

1. Introduction

In recent years, Si₃N₄ platforms have attracted extensive attention, owing to their lower propagation loss and higher manufacturing tolerance than insulator-on-silicon platforms [1,2], and they have broad application prospects in optical fiber communication, microwave photonics, quantum information processing, sensing, and ranging [3,4,5,6,7]. Efficient fiber–chip coupling is one of the key technologies for photonic integrated circuits (PICs). At present, the mainstream fiber–chip coupling solutions can be divided into two types: edge coupling and grating coupling. Edge coupling enables optical transmission through the precise alignment of the optical fiber to the waveguide end face, which has the advantages of low insertion loss and wide bandwidth [8]. However, this method has high requirements for end face polishing quality and optical alignment accuracy, and the edge coupling scheme is difficult to meet the industrial needs of wafer-level testing. The grating coupler is a module component for coupling optical fiber to PIC. It uses periodic micro-nano-structures for light field mode conversion and provides an effective way to overcome the problem of mode field mismatch. This structure can realize the efficient energy coupling of optical fibers and photonic integrated components without the assistance of lens. It can eliminate complex processes such as slicing, polishing and lens optical fiber coupling and become an important input/output (I/O) device for optical coupling between submicron waveguides and optical fibers. Compared with edge coupling solutions, grating couplers enable fast alignment between fiber cores and gratings and facilitate wafer-level testing [9]. Moreover, the device layout has spatial flexibility, facilitating the I/O design of multi-channel optical fields.

Many grating coupling schemes based on Si₃N₄ platforms have been widely reported [10,11,12,13]. Jeroen Goyvaerts et al. designed a Si₃N₄ fully etched grating with a center wavelength of 850 nm through micro-transfer printing technology. This grating is integrated on a Si₃N₄ PIC with a bottom-emitting VCSEL, achieving an output power exceeding 100 μW and a coupling efficiency of −7.78 dB [14]. Eli Ohaha et al. proposed an O-band shallowly etched uniform grating coupler based on a Si₃N₄ structure. The grating tooth grooves were filled with SiO₂, and its coupling efficiency was increased to −5.52 dB. This device has a broadband characteristic of 90 nm, so that even under wavelength drift, the coupling efficiency can be maintained above −6.19 dB, ensuring the stability of the test signal, and it also mitigates the laser drift effect [12]. In 2024, Liu et al. proposed an efficient fully etched grating coupler for integrating area-emitting blue lasers with Si₃N₄ waveguides. They added DBR to the top and sides of the grating to improve the coupling efficiency, and the average coupling efficiency of the optimized grating structure for the TE mode reached −1.4 dB [15]. In addition, many solutions utilize non-uniform gratings [10,11,16,17] or edge couplers. Although these approaches improve coupling efficiency, they often involve cumbersome fabrication processes and high costs. For example, the fabrication of inhomogeneous gratings requires precise control of the grating structure and size, and even a very small fabrication error can significantly affect the performance of the device. In addition, existing Si₃N₄ platform grating couplers are prone to wavelength drift and efficiency degradation under environmental temperature fluctuations, which limits their application and deployment in non-temperature control scenarios (such as data centers and in-vehicle systems). Traditional solutions mainly rely on global temperature control [18,19] or complex packaging [20,21,22,23], resulting in increased power consumption and costs. Kim et al. integrated an N-type doped silicon heater into a silicon-based micro-ring resonator. By adjusting the refractive index of silicon through Joule heat, they solved the resonant detuning problem of silicon-based ring resonant filters when there were temperature fluctuations or input wavelength drifts. They achieved the function of wavelength adaptive locking, and the total power consumption for temperature control was less than 32.7 mW. However, this type of silicon heater will produce considerable optical loss. Global temperature control technology is mainly regulated by maintaining the overall temperature of the device, such as a thermos-electric cooler (TEC) [24] or an incubator, which requires continuous high energy consumption and make dynamic control at the wafer stage difficult.

In order to solve the above problems, a CMOS-compatible wide-bandwidth Si₃N₄ grating coupler based on DBR and thermo-optical tuning is proposed. It integrates a double-layer DBR and a serpentine Ti heater to achieve high coupling efficiency and wide bandwidth; meanwhile, local temperature control through the heater is realized to compensate for the decrease in coupling efficiency caused by ambient temperature fluctuations. This design achieves temperature compensation by local heating, which provides a feasible solution for the design and application of high-performance photonic integrated devices.

2. Structural Design of Grating Coupler

The cross-section of the Si₃N₄ grating coupler is shown in Figure 1. The grating is composed of periodically distributed toothed structures. Assuming the grating period is $\mathrm{\Lambda }$ and the width of the toothed structure is $\omega$, then the duty cycle $ff$ is $\omega /\lambda$. The incidence angle of the optical fiber is $\theta$ and the thickness of the upper cladding is $d_{Cladding}$. According to the Bragg condition, the center wavelength of the grating coupler is

$$\lambda =\mathrm{\Lambda }\left(n_{eff}-n_c\sin {\theta }_c\right)$$

(1)

where $n_{eff}$ is the effective refractive index of the grating, $n_c$ is the refractive index of the cladding, ${\theta }_c$ is the diffraction angle, and $\lambda$ is the wavelength of the incident light. Suppose the effective refractive index of the grating teeth is $n_{eff1}$ and the effective refractive index of the grating groove is $n_{eff2}$, then the effective refractive index of the grating region can be expressed as

$$n_{eff}=ff·n_{eff1}+\left(1-ff\right)·n_{eff2}$$

(2)

To achieve the adaptive temperature compensation for the device, a thermo-optical material layer (amorphous silicon, a-Si) is incorporated into the double-layer DBR, and the local temperature control is implemented using a Ti serpentine heater. Its structure is shown in Figure 2. The original DBR is composed of alternating stacks of Si and SiO₂. For the selection of thermo-optical materials, the thermo-optical coefficient of titanium dioxide (TiO₂) (~−1 × 10⁻⁴ K⁻¹) [25] is significantly lower than that of a-Si (~−2.5 × 10⁻⁴ K⁻¹). This implies that a-Si requires lower power consumption than TiO₂ for equivalent temperature compensation. Moreover, TiO₂ exhibits intrinsic absorption peaks within its transmission window (400–2000 nm), introducing additional optical losses [26]. In addition, a-Si can be deposited via plasma-enhanced chemical vapor deposition (PECVD) process, a process fully compatible with CMOS fabrication. Therefore, to implement the thermo-optical effect, we replace the first layer of Si with the thermo-optical material a-Si. At the same time, a Ti serpentine resistor is integrated above the a-Si layer of DBR to cover the non-light field area at the edge of the grating, and the SiO₂ layer is used to isolate and insulate the Si₃N₄ layer. Power is applied across the terminals of the metal wire, and the a-Si layer below is heated by Joule heating to adjust its refractive index, thereby compensating for the temperature-induced drift. The serpentine heater is designed to avoid the light field area in the center of the grating, which prevents the absorption or scattering of the light field by the heater.

2.1. Optimized Design of Grating Parameters

The optimization of the Si₃N₄ grating couplers was performed using Lumerical 2020 R2.4 software via a two-dimensional FDTD method. In our simulation, “Perfect Matched Layer (PML)” boundary conditions were applied. A “Frequency-domain field and power” monitor was positioned at the straight waveguide to capture optical parameters. The light source was configured to emit the “fundamental TM mode”. And the mesh accuracy was set to 3, which achieved a good balance between accuracy, memory requirements, and simulations time. Based on parameters commonly used in foundries, we set the Si₃N₄ waveguide thickness to 400 nm. Using Equation (1), we calculated a grating period of 1.16 μm for an incident wavelength of 1550 nm. We performed a parameter sweep of the grating period around 1.16 μm while fixing other parameters. Figure 3a shows the resulting relationship between period and coupling efficiency. Figure 3b presents the corresponding spectral response for different periods. As shown in Figure 3a, the coupling efficiency first increases and then decreases with grating period, peaking at 1.13 μm. The parametric sweep in Figure 3b shows that as the period increases from 1.1 μm to 1.2 μm, the center wavelength shifts from 1515 nm to 1590 nm. This yields a grating period tuning coefficient $\delta \lambda /\delta \mathrm{\Lambda }$ of 0.75 nm/nm. This small tuning factor is beneficial for improving the stability of the grating coupler and reduces wavelength shifts due to manufacturing errors.

The grating duty cycle critically affects the coupling efficiency. Equation (2) shows that the duty cycle affects the grating’s average effective refractive index. Combined with Equation (1), a larger grating duty cycle results in a higher effective refractive index and a larger center wavelength. When the grating period is determined to be 1.13 μm and other parameters remain unchanged, the duty cycle $ff$ of the grating is scanned for parameters. The relationship between the duty cycle and the coupling efficiency is shown in Figure 4a. As the duty cycle increases, the coupling efficiency first rises and then falls, peaking at 0.44. A parameter sweep of the duty cycle was then performed over the range of 0.4 to 0.5, and the results are shown in Figure 4b. When the duty cycle changes from 0.4 to 0.5, the center wavelength changes from 1539 nm to 1560 nm, and the tuning coefficient of the duty cycle is 0.18 nm/nm. Comparison shows that the grating period has a stronger influence on the central wavelength than the duty cycle.

The incident angle is another critical parameter affecting the coupling efficiency. The incident angle determines the direction of light propagation and influences the phase matching condition within the grating coupler. Equation (1) indicates that the incident angle also affects the center wavelength. With the period fixed at 1.13 μm and duty cycle at 0.44, we swept the incident angle. Figure 5 shows the resulting coupling efficiency versus incident angle. It can be seen that with the increase in the incident angle, the coupling efficiency decreases gradually and reaches the peak at 6°. When the incident angle changes from 6° to 24°, the central wavelength of the grating decreases from 1548 nm to 1545 nm. This corresponds to an incident angle tuning coefficient of 0.17 nm/(°).

The thickness of the upper cladding and buried oxide layer of the grating coupler are two important factors affecting the coupling efficiency. As shown in Figure 1, during the process of light coupling into the waveguide through a grating, reflections ($P_{r1}$, $P_{r2}$, $P_{r3}$ and $P_{r4}$) occur at different interfaces. The interference between these reflections significantly impacts the insertion loss of the grating coupler. When $P_{r1}$ and $P_{r2}$ are destructive interference, and $P_{r3}$ and $P_{r4}$ are constructive interference, the insertion loss of the grating coupler can be minimized, thereby enhancing the coupling efficiency of the grating. Therefore, while ensuring that other parameters remain unchanged, we perform parameter sweeps on the thickness of the buried oxide layer and the upper cladding layer of the grating coupler, respectively. As shown in Figure 6, the simulation results of the thickness of the buried oxide layer and the upper cladding layer changing from 0.4 μm to 2.4 μm are presented, respectively. It can be seen that the coupling efficiency of the grating coupler oscillates in a sinusoidal form with the increase in the thickness of the buried oxide layer and the upper cladding layer. And with peaks occurring at 2.1 μm and 2 μm, respectively. This indicates that at these thicknesses, the interference between $P_{r1}$ and $P_{r2}$ is destructive, and the interference between $P_{r3}$ and $P_{r4}$ is constructive, achieving the minimum insertion loss. Moreover, Figure 6a,b show that variations in buried oxide thickness have a larger impact on coupling efficiency than variations in upper cladding thickness.

Based on these optimization results, the grating structure was further refined. The finalized key parameters are listed in

Table 1. The main parameters of the grating coupler.

Parameters	Value	Tuning Coefficient
Period	1.13 μm	0.75 nm/nm
Duty cycle	0.44	0.18 nm/nm
Incident angle	6°	0.17 nm/(°)
The thickness of buried oxide layer	2.1 μm	-
The thickness of upper cladding	2 μm	-

. The FDTD method was used to simulate the optimized grating. The relationship between the grating coupling efficiency and wavelength is shown in Figure 7. The simulation results show a coupling efficiency of approximately −3.08 dB at 1550 nm, and the 3 dB bandwidth is approximately 100 nm.

As noted, upon light incidence, a portion scatters downward into the substrate, reducing coupling efficiency. Therefore, adding a DBR between the BOX and substrate layers reflects downward-diffracted light back upwards, reducing substrate absorption loss.

When light propagates in the DBR, reflection and refraction occur at interfaces with different refractive indices. Careful design of the thickness and refractive index of each layer ensures constructive interference of the reflected waves and destructive interference of the transmitted waves, thereby achieving a high reflectivity. Calculations determine that one period of the DBR consist of a 110 nm thick Si layer and a 270 nm thick SiO₂ layer. Based on the grating parameters in Table 1, the relationship between the grating coupling efficiency and wavelength is obtained after DBR is added and the overall grating is optimized, as shown in Figure 8. Adding DBR increases the coupling efficiency by approximately 20% compared to the case without DBR. Moreover, the improvement of coupling efficiency after adding DBR with different layers is slightly different. Adding three periods of the DBR provides negligible improvement compared to the two-period structure. Therefore, two periods of DBR can be added, and the corresponding coupling efficiency is −1.59 dB and a 3 dB bandwidth is 106 nm.

2.2. Integrated Serpentine Heater

For the heater material, the resistivity of tungsten (W) (8 μΩ∙cm) [27] is lower than that of Ti (170 μΩ∙cm), which indicates that under the same applied voltage, Ti can produce higher-energy Joule heating than W. Moreover, Ti can be deposited using physical vapor deposition (PVD), which is compatible with the CMOS back-end process. Furthermore, the native titanium oxide (TiO₂) layer provides protection at high temperatures, enabling long-term stable operation. Therefore, we choose Ti as the material of the heater.

For the thermal simulation, we employed COMSOL Multiphysics 6.3 software using the physical fields of “Thermal Stress in Layered Shells” and “Electric Currents in Layered Shells (ecis)” to model heat conduction in this three-dimensional structure. The model dimensions (18 × 11 μm²) correspond to the overall grating design area. The thickness of the Si₃N₄ and buried oxide layers match the actual design parameters. Meanwhile, the material properties—including refractive indices and thermo-optical coefficients—remain consistent with those used in prior optical simulations. The heater covers the non-light field area at the edge of the grating in the form of a serpentine metal wire, as shown in the right figure in Figure 2. This design avoids the absorption or scattering of the central light field by the heater and ensures that the light coupling efficiency is not affected. The serpentine heater features a line width and height of 200 nm, with a spacing of 400 nm between lines. By optimizing the distribution of resistance, the uniformity of heat distribution is improved and the generation of local high-temperature spots is avoided. Figure 9a displays the temperature distribution of the buried oxide and the Si₃N₄ layer when the heating temperature reaches 450 °C. Figure 9b shows the temperature variation curve of the model in the Z-axis direction. When the heater reaches 450 °C, the temperature change in the Si₃N₄ layer is less than 5 °C due to the thermal isolation provided by the buried oxide layer. Due to the thermo-optical coefficient of Si₃N₄ is relatively small, the influence of the temperature change on the Si₃N₄ is negligible and the optical properties of Si₃N₄ are relatively stable within this temperature range. Figure 9c shows the temperature distribution of the a-Si layer during heating. It can be seen that although the color gradient appears pronounced in Figure 9c, the associated color bar indicates a uniform temperature of 51.45 °C across the plane. At a drive power of only 10 mW, the maximum temperature difference within the heater-enclosed central region is <0.01 °C. Therefore, it can be considered that the heat distribution within this range is uniform. Furthermore, only 35 mW of driving power is required to heat the a-Si layer to 450 °C.

For a-Si, its refractive index decreases with the increase in temperature. To compensate for the grating coupler’s resonance wavelength drift induced by ambient temperature changes, the refractive index of the a-Si layer can be heated to decrease, causing a blue shift in the reflection spectrum of the DBR, thereby compensating for the wavelength drift caused by the ambient temperature. As shown in Figure 10, when the whole photonic device is exposed to the high-temperature environment of 150 °C, the thermal expansion effect and thermo-optical effect will cause the coupling efficiency of the device to decrease. However, by adjusting the a-Si layer temperature via the heater, it significantly suppresses the reduction in device coupling efficiency, effectively compensating for the temperature drift. A coupling efficiency of −1.37 dB and a 3 dB bandwidth of 95 nm are achieved under these conditions. In addition, the coupling situation of the device in the low-temperature (−55 °C) environment is also verified. Due to material contraction and reduced thermo-optical effect strength, the refractive index of a-Si will slightly increase. It can be known from the simulation results that the reflection spectrum of DBR is redshifted at this time. Effective compensation is still achieved through heater adjustment. Furthermore, the heater can also be used at room temperature to improve coupling efficiency. This demonstrates that the device can also dynamically compensate for fabrication process errors via thermo-optical tuning, improving the stability of the device in a wide temperature range and converting the process errors into a correctable parameter.

3. Discussion

From the above, the results demonstrate that under three ambient temperature conditions (low, room, and high temperature), the reflection spectrum of DBR exhibits significant blue-shifting after heater activation, with an average shift of 9 nm (from 1572 nm to 1563 nm at −55 °C, from 1563 nm to 1554 nm at 25 °C, and from 1566 nm to 1557 nm at 150 °C). Concurrently, coupling efficiency enhancements of 0.22 dB, 0.17 dB, and 0.30 dB are achieved at these respective temperature points.

Furthermore, Figure 11 compares the optical field distributions in the Si₃N₄ grating under different conditions. Figure 12 compares the one-dimensional field distribution curves within the waveguide under different temperature conditions. To quantify the thermal disturbance caused by the integrated heater to the optical mode, we used FDTD to analyze the changes in light intensity at the center point of the waveguide after the light was coupled into the waveguide and transmitted to 5 μm (points A to F in Figure 11) under different temperature conditions. The relative intensity change ($∆I/I$) is defined as ${\displaystyle \frac{\left(I_{heat}-I_{pre}\right)}{I_{pre}}}\ast 100\%$, where $I_{pre}$ and $I_{heat}$ are the light intensity of the waveguide center point before and after heating, respectively. The calculated $∆I/I$ values are: 39% at 25 °C, 35% at −55 °C, and 39.7% at 150 °C. The results show that the thermal disturbance introduced by local heating is small compared with the unheated state, and the effect on the optical mode propagating within the waveguide is negligible. This minor disturbance is attributed to the spatial separation of the heater from the reflective region and the effective thermal isolation provided by the BOX layer. Moreover, under the heating state, the light intensity within the waveguide is enhanced, but the trend of its light field distribution is similar.

Table 2. Performance Comparison of Si₃N₄ Grating Couplers. (The results of the references cited in the table are all simulation results).

Ref.	Max CE (dB)	Bandwidth (nm)	Center Wavelength (nm)	Si3N4 Thickness (nm)	Cladding Type	Complexity	Bottom Reflector (Y/N)	Integrated Heater (Y/N)
[28]	−1.2	30@1 dB	1310	400	SiO2	Y	N	N
[29]	−3.6	37@1 dB	1550	400	air	N	N	N
[30]	−2.95	69@3 dB	1317	400	SiO2	Y	N	N
[31]	−0.52	24@1 dB	1310	600	SiO2	Y	N	N
[32]	−1.7	42@3 dB	450	-	SiO2	Y	Y	N
[15]	−1.4	-	445	150	SiO2	Y	Y	N
[12]	−5.52	-	1310	760	SiO2	N	N	N
This work	−1.37	95@3 dB	1550	400	SiO2	N	Y	Y

compares the performance of our grating coupler with reported Si₃N₄ designs in the literature, including the coupling efficiency, bandwidth, central wavelength, manufacturing complexity, etc. Grating couplers with coupling efficiencies above −2 dB typically involve relatively complex fabrication processes. However, our proposed device achieves high coupling efficiency with a relatively simple structure, low cost, and ease of manufacturing. In addition, the synergy between the a-Si thermo-optical layer and the serpentine heater can dynamically compensate for manufacturing errors, giving the device a high tolerance for manufacturing errors. This design significantly improves the device’s stability over a wide temperature range (−55 °C to 150 °C). This operating temperature range is suitable for most applications.

4. Conclusions

This paper proposes a CMOS-compatible Si₃N₄ grating coupler based on DBR and thermo-optical tuning, which achieves high coupling efficiency and features self-compensation for temperature drift through structural optimization and functional integration. Simulation results show that the optimized grating with a double-layer DBR achieves a coupling efficiency of −1.59 dB at 1550 nm with a 3 dB bandwidth of 106 nm. Furthermore, the integrated a-Si thermo-optical layer and Ti serpentine heater effectively suppress efficiency reduction induced by environmental temperature fluctuations via local temperature control. After compensation, the coupling efficiency fluctuation is less than 0.02 dB, and the center wavelength undergoes a blue shift. The key innovation of this work lies in the synergistic combination of DBR-enhanced reflection and a thermo-optical dynamic compensation mechanism, effectively addressing the issues of high temperature sensitivity and complex fabrication processes associated with traditional grating couplers. Compared to existing solutions relying on global temperature control, this design requires only 35 mW of power to achieve local temperature control and dynamic compensation for fabrication process errors, providing a viable approach for deploying photonic chips in non-temperature-controlled environments.