Device for optical coupling and method for manufacturing an optical device

By building a multi-layer grating structure on a semiconductor chip and independently adjusting the grating parameters of each layer, the problems of low coupling efficiency and limited bandwidth of traditional grating couplers are solved, and efficient and stable optical signal transmission is achieved.

CN120276093APending Publication Date: 2025-07-08TAIWAN SEMICONDUCTOR MANUFACTURING CO LTD
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Patent Information

Application Number
CN202510305873.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Priority Date
2024-07-12
Filing Date
2025-03-14
Publication Date
2025-07-08

AI Technical Summary

Technical Problem

Traditional single-layer grating couplers have problems such as low coupling efficiency, limited bandwidth, and susceptibility to interference and attenuation in semiconductor integrated circuits, making it difficult to meet the needs of miniaturization and complex chips.

Method used

Using a multi-layer grating structure, by forming a reflective layer, a lower grating layer and an upper grating layer on the substrate, each layer grating coupler has independent grating topology and parameters, adjusting the spacing and angle to improve coupling efficiency and bandwidth, and reducing interference and attenuation.

Benefits of technology

Improves the coupling efficiency and bandwidth of optical signals, enhances the stability and reliability of the system, is suitable for silicon photonic input/output applications, and is convenient for wafer-level testing and low-cost packaging.

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Abstract

An apparatus for optical coupling according to the present disclosure includes a substrate, a reflective layer disposed on the substrate, a lower grating layer over the reflective layer, and an upper grating layer over the lower grating layer. The lower grating layer includes a base layer and a lower grating coupler over the base layer. The upper grating layer includes an upper grating coupler and a coating over the upper grating coupler. In a top view of the device, a centerline of the lower grating coupler is aligned with a centerline of the upper grating coupler. The embodiment of the invention also relates to a method for manufacturing the optical device.
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Description

Technical Field

[0001] Embodiments of the present disclosure relate to devices for optical coupling and methods for manufacturing optical devices. Background Art

[0002] The semiconductor integrated circuit (IC) industry has experienced exponential growth. Technological advances in IC materials and design have produced multiple generations of ICs, with each generation having smaller and more complex circuits than the previous one. During the evolution of ICs, the functional density (i.e., the number of interconnected devices per chip area) generally increases, while the geometric size (i.e., the smallest component (or line) that can be created using a manufacturing process) decreases. This scaling process typically provides benefits by increasing production efficiency and reducing related costs. This scaling also increases the complexity of processing and manufacturing ICs.

[0003] For example, gratings have been used to enable communication between a light source and other components (e.g., photodetectors). A grating can be used to redirect light from an optical fiber into an optical detector. By traversing the grating laterally by reflecting from the inner surface at a shallow angle, the light coupled to one end of the grating can be redirected such that it impinges on the inner surface at a steeper angle greater than the critical incident angle, causing the redirected light to escape from the other end of the grating. After escaping, the light may impinge on an optical detector. Then, the detected light can be used for various purposes, such as receiving an encoded communication signal transmitted through the grating. Unfortunately, in the context of a conventional single-layer grating coupler, this process and the reverse process of using a grating to redirect light from an on-chip light source to an optical fiber may exhibit poor coupling efficiency and limited bandwidth, where most of the redirected light fails to reach the optical detector. A single-layer grating coupler is also vulnerable to interference and attenuation. Therefore, there is a need to develop devices and systems for efficient optical coupling using gratings other than single-layer grating couplers. Summary of the Invention

[0004] Embodiments of the present disclosure provide a device for optical coupling, comprising: a substrate; a reflective layer disposed on the substrate; a lower grating layer located above the reflective layer, the lower grating layer comprising a base layer and a lower grating coupler located above the base layer; and an upper grating layer located above the lower grating layer, the upper grating layer comprising an upper grating coupler and a coating located above the upper grating coupler, wherein, in a top view of the device, a center line of the lower grating coupler is aligned with a center line of the upper grating coupler.

[0005] Another embodiment of the present disclosure provides an apparatus for optical coupling, comprising: a substrate; a reflective layer disposed on the substrate; a lower grating layer located above the reflective layer, the lower grating layer including a lower grating coupler formed therein; and an upper grating layer located above the lower grating layer, the upper grating layer including an upper grating coupler formed therein, wherein the lower grating coupler includes a lower waveguide, the upper grating coupler includes an upper waveguide, and the lower waveguide and the upper waveguide are configured to combine photons propagating therein into one of the lower waveguide and the upper waveguide.

[0006] Another embodiment of the present disclosure provides a method for manufacturing an optical device, comprising: forming a reflective layer on a substrate; depositing a base layer on the reflective layer; patterning a top portion of the base layer to form a plurality of first trenches; depositing a first optically transparent material on the base layer, wherein the first optically transparent material fills the first trenches when forming a plurality of first grating teeth of a first grating coupler; depositing a second optically transparent material on the first optically transparent material; patterning a top portion of the second optically transparent material to form a plurality of second grating teeth of a second grating coupler; and depositing a coating on the second optically transparent material, wherein the coating fills a plurality of second trenches defined between adjacent second grating teeth. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Aspects of the present disclosure are best understood from the following detailed description when read in conjunction with the accompanying drawings. It should be emphasized that, in accordance with standard practice in the industry, the various components are not drawn to scale. In fact, the dimensions of the various components may be arbitrarily increased or decreased for clarity of discussion.

[0008] Figure 1A A cross-sectional view of a fiber-to-chip system in accordance with some aspects of the present disclosure is shown.

[0009] Figure 1B A top view of a grating coupler implemented in a fiber-to-chip system in accordance with some aspects of the present disclosure is shown in Figure 1A is shown.

[0010] Figure 2A , Figure 2B , Figure 2C and Figure 2D are cross-sectional views of grating portions in a grating coupler in accordance with various aspects of the present disclosure.

[0011] Figure 3A , Figure 3B and Figure 3C A top view and a cross-sectional view of a multi-layer grating coupler in an embodiment in accordance with some aspects of the present disclosure are shown.

[0012] Figure 4A and Figure 4B show a top view and a cross-sectional view of a multi-layer grating coupler in another embodiment according to some aspects of the present disclosure.

[0013] Figure 5A 、 Figure 5B and Figure 5C show a top view and a cross-sectional view of a multi-layer grating coupler in yet another embodiment according to some aspects of the present disclosure.

[0014] Figure 6A 、 Figure 6B 、 Figure 6C 、 Figure 6D and Figure 6E show an embodiment of a waveguide portion of a multi-layer grating coupler according to some aspects of the present disclosure.

[0015] Figure 7A 、 Figure 7B 、 Figure 7C 、 Figure 7D and Figure 7E show alternative embodiments of a waveguide portion of a multi-layer grating coupler according to some aspects of the present disclosure.

[0016] Figure 8 show a flowchart of a method for manufacturing a multi-layer grating coupler according to some aspects of the present disclosure.

[0017] Figure 9A 、 Figure 9B 、 Figure 9C 、 Figure 9D 、 Figure 9E 、 Figure 9F and Figure 9G show a partial cross-sectional view of a workpiece during a manufacturing process of a method according to Figure 8 .

[0018] Figure 10 show a cross-sectional view of a multi-layer grating coupler in an alternative embodiment according to some aspects of the present disclosure.

[0019] Figure 11A and Figure 11B show a perspective view of an optical fiber to chip coupling system according to some aspects of the present disclosure. Detailed Description

[0020] Numerous different embodiments or examples are provided below for implementing the different features of the provided subject matter. Specific examples of components and arrangements are described below to simplify the present disclosure. Of course, these are merely examples and are not intended to be limiting. For example, in the following description, forming a first component above or on a second component may include embodiments in which the first and second components are formed in direct contact, and may also include embodiments in which additional components may be formed between the first and second components such that the first and second components may not be in direct contact. Additionally, the present disclosure may repeat reference numerals and / or letters in the various examples. This repetition is for simplicity and clarity purposes and does not in itself indicate a relationship between the embodiments and / or configurations being discussed.

[0021] Additionally, for ease of description, spatially relative terms such as “below,” “beneath,” “lower,” “above,” “upper,” etc. may be used herein to describe the relationship of one element or component to another as shown in the figures. In addition to the orientation shown in the figures, the spatially relative terms are intended to encompass different orientations of the device in use or operation. The device may be positioned otherwise (rotated 90 degrees or in other orientations), and the spatially relative descriptors used herein may be interpreted accordingly.

[0022] Moreover, when describing a numerical value or range of numerical values with terms such as “about,” “approximate,” etc., the term is intended to cover a reasonable range of values, taking into account the inherent variations during manufacturing understood by those of ordinary skill in the art. For example, based on known manufacturing tolerances associated with fabricating a component having a characteristic associated with that numerical value, the numerical value or range of numerical values covers a reasonable range including the described numerical value, such as within + / - 10% of the described numerical value. For example, a material layer having a thickness of “about 5 nm” may cover a dimension range from 4.25 nm to 5.75 nm, where the manufacturing tolerance associated with depositing the material layer is known to be + / - 15% to those of ordinary skill in the art. Depending on the context, when describing aspects of a transistor, the source / drain regions may refer to the source or the drain individually or collectively.

[0023] Optical communication between chips has been used to allow information to be rapidly transferred from one device to another. Grating couplers (or simply referred to as grating couplers) are used to couple optical signals from inside a semiconductor chip to an optical fiber extending between different devices and vice versa. However, as the size of semiconductor chips continues to decrease, the density of components increases. Conventional grating couplers based on a single-layer structure must be scaled down, which may result in poor coupling efficiency and limited bandwidth. The distance between adjacent grating couplers must be reduced to accommodate the limited chip area, which may result in increased interference and attenuation.

[0024] The present disclosure provides a grating coupler based on a multi-layer structure to improve the coupling efficiency, bandwidth, and stability of the device. In the multi-layer structure, each grating layer has its own grating topology, which can adjust the spacing and angle to guide the optical wave to the optimal position and reduce energy loss. In addition, the multi-layer structure can increase the distance between the input port and the output port to reduce interference and attenuation, and thus improve stability. An exemplary grating coupler may include a plurality of vertically stacked grating layers. Each grating layer may have optical waveguides formed therein with different refractive indices, which can guide optical signals in different directions. The grating layers are used to couple optical signals to the optical waveguides and may independently have different grating parameters (e.g., grating period, grating duty cycle, grating aspect ratio, etc.) and directions to achieve different coupling efficiencies. An exemplary multi-layer grating coupler can utilize two different characteristics to superimpose two types of light energy to achieve broadbandwidth and low loss. The disclosed multi-layer grating coupler has high coupling efficiency, bandwidth, and stability of optical signals, as well as the reliability and scalability of the device. In addition, the disclosed multi-layer structure for gratings is easy to implement in any suitable silicon photonics input / output (I / O) and high-speed applications, and is convenient for wafer-level testing and low-cost packaging.

[0025] Now refer jointly to Figure 1A and Figure 1B . Figure 1A is a cross-sectional view of an optical fiber to chip coupling system 100 according to some embodiments. Figure 1B is a top view of a grating coupler 124 implemented in the system 100. The system 100 includes an optical fiber 110 configured to emit an optical signal 115. The system 100 also includes a chip 120. The chip 120 includes a substrate 122. The grating coupler 124 is positioned above the substrate 122. A coating 126 covers the grating coupler 124. An etch stop layer 128 is disposed above the coating 126. An interconnect structure 130 is located above the etch stop layer 128. The interconnect structure 130 includes an inter-metal dielectric (IMD) layer 132 and a conductive layer 134. Figure 1A includes a single IMD layer 132 and a conductive layer 134. However, those of ordinary skill in the art will recognize that the interconnect structure 130 may include multiple IMD layers and conductive layers to electrically connect different components of the chip 120. An opening 136 extends through a portion of the interconnect structure 130.

[0026] The grating coupler 124 includes a grating portion 140 and a waveguide portion 142. The grating portion 140 includes grating members (also referred to as grating teeth) 144 that project upward from the grating coupler 124 and a tapered waveguide transition member 146. In the depicted embodiment, each grating member 144 has an arcuate shape. The grating portion 140 is configured to receive the optical signal 115 through the tapered waveguide transition member 146 and direct the optical signal 115 into the waveguide portion 142. The waveguide portion 142 includes a waveguide 148 that receives the optical signal 115 transmitted from the tapered waveguide transition member 146 and relays the optical signal 115 to the optoelectronic components of the chip 120. Those of ordinary skill in the art will recognize that additional layers, such as cladding layers and reflective layers, may be included in the system 100.

[0027] The optical fiber 110 can be a single-mode or multimode optical fiber. The optical fiber 110 is configured to transmit the optical signal 115 from an external device to the chip 120. The optical fiber 110 can be vertically positioned relative to the top surface of the chip 120 (or the top surface of the grating coupler 124). Optionally, the optical fiber 110 can be angled away from the normal position by an angle α. Depending on the system requirements, the range of the angle α can be up to 2 degrees, 5 degrees, or 10 degrees.

[0028] The optical signal 115 has a wavelength. In some embodiments where the optical fiber 110 is a single-mode optical fiber, the wavelength range of the optical signal 115 can be from about 1260 nanometers (nm) to about 1360 nm. In some embodiments where the optical fiber 110 is a multimode optical fiber, the wavelength range of the optical signal 115 can be from about 770 nm to about 910 nm. The wavelength of the optical signal 115 is based on the light source used to generate the optical signal. In some embodiments where the optical fiber 110 is a single-mode optical fiber, the light source can be a laser or a laser diode. In some embodiments where the optical fiber 110 is a multimode optical fiber, the light source of the optical fiber can be a light-emitting diode (LED). The optical signal 115 may diverge when it exits the optical fiber 110.

[0029] The chip 120 includes at least one optoelectronic component, such as a laser driver, a digital control circuit, a photodetector, a waveguide, a small form-factor pluggable (SFP) transceiver, a high-speed phase modulator (HSPM), a calibration circuit, a distributed Mach-Zehnder interferometer (MZI), a grating coupler, a light source (i.e., a laser), etc. The optoelectronic components are configured to receive the optical signal 115 from the grating coupler 124 and convert the optical signal 115 into an electrical signal. Although Figure 1A the chip 120 is depicted as receiving the optical signal 115 from the optical fiber 110, those of ordinary skill in the art will understand that the system 100 can also be used to transmit the optical signal from the chip 120 to the optical fiber 110. That is, in some embodiments, the optoelectronic components generate an optical signal and then transmit the optical signal to the optical fiber 110 through the grating coupler 124.

[0030] In some embodiments, the substrate 122 includes elemental semiconductors, including silicon or germanium in crystalline, polycrystalline, or amorphous structures; compound semiconductors, including silicon carbide, gallium arsenide, gallium phosphide, indium phosphide, indium arsenide, and indium antimonide; alloy semiconductors, including SiGe, GaAsP, AlInAs, AlGaAs, GaInAs, GaInP, and GaInAsP; any other suitable materials; or combinations thereof. In some embodiments, the alloy semiconductor substrate has a graded SiGe component, where the Si and Ge components vary from one ratio at one location of the graded SiGe component to another ratio at another location. In some embodiments, alloy SiGe is formed over a silicon substrate. In some embodiments, the substrate 122 is a strained SiGe substrate. In some embodiments, the semiconductor substrate has a semiconductor-on-insulator structure, such as a silicon-on-insulator (SOI) structure. In some embodiments, the semiconductor substrate includes a doped epitaxial layer or a buried layer. In some embodiments, the compound semiconductor substrate has a multi-layer structure, or the substrate includes a multi-layer compound semiconductor structure.

[0031] The grating coupler 124 is configured to direct the optical signal 115 from the grating section 140 and the waveguide section 142 to the optoelectronic components of the chip 120. The grating coupler 124 includes an optically transparent material. In some embodiments, the grating coupler 124 includes silicon, silicon nitride, or other suitable optically transparent materials. In some embodiments, the waveguide 148 includes a material different from the grating component 144. In some embodiments, the waveguide 148 is a slab waveguide, a planar waveguide, or an optical tube. In order for the grating component 144 to effectively couple the optical signal 115 into the waveguide 148, the grating component 144 redirects the incident optical signal 115 to the acceptance angle of the waveguide 148. The acceptance angle of the waveguide 148 is based on the wavelength of the optical signal, the frequency of the optical signal, and the dimensions of the waveguide 148.

[0032] The coating 126 includes a dielectric material, such as silicon oxide (e.g., quartz and / or glass). The etch stop layer 128 is located above the coating 126 and has an etch chemistry different from that of the coating 126 and the IMD layer 132. In some embodiments, chemical vapor deposition or another suitable deposition process is used to deposit the etch stop layer 128. In some embodiments, the etch stop layer 128 includes silicon carbide, silicon nitride, aluminum oxide, or another suitable material.

[0033] The interconnect structure 130 is configured to electrically connect the optoelectronic component to other components within the chip 120 or external devices, e.g., via chip bonding. The IMD layer 132 includes a dielectric material. The IMD layer 132 provides electrical insulation between the conductive layer 134 and other conductive elements within the chip 120. The IMD layer 132 is deposited on the etch stop layer 128 using chemical vapor deposition, physical vapor deposition, or another suitable deposition process. In some embodiments, the IMD layer 132 includes a low-k dielectric material. In some embodiments, the IMD layer 132 includes the same material as the coating 126. In some embodiments, the IMD layer 132 includes a different material from the coating 126. The conductive layer 134 is configured to transmit electrical signals to various components in the chip 120, such as optoelectronic components. In some embodiments, the conductive layer 134 includes copper, aluminum, tungsten, their alloys, or another suitable conductive material.

[0034] The cavity 136 reduces the amount of material that the optical signal 115 passes through before being guided to the grating coupler 124. The cavity 136 extends through the conductive layer 134 and partially through the IMD layer 132. In some embodiments, the cavity 136 extends through the entire interconnect structure 130 to expose the etch stop layer 128. The sidewalls of the cavity 136 are substantially vertical. In some embodiments, the sidewalls of the cavity 136 are tapered. In some embodiments, the width of the cavity is in the range of about 10% to about 20% larger than the width of the optical fiber 110. The additional width helps to address misalignment between the optical fiber 110 and the cavity 136. The additional width also helps to allow the entire optical signal 115 to pass through the cavity 136, even if the optical signal 115 may diverge when leaving the optical fiber.

[0035] Now refer to Figures 2A to 2D 。 Figures 2A to 2D A cross-sectional view of the grating portion 140 in the grating coupler 124 according to various embodiments of the present disclosure is shown. In the various illustrated embodiments, the grating coupler 124 differs in the geometric dimensions of the grating component 144 and in optimizing different design parameters, such as the incident angle, coupling efficiency, bandwidth, or a combination thereof. In Figure 2A , the grating portion 140 includes a grating component 144 having consistent geometric dimensions, such as a width (also referred to as the duty cycle in the context of the grating coupler) W0, a pitch P0, and a depth D0. Thus, the trenches between adjacent grating components 144 also have consistent geometric dimensions, where the width is defined by the difference between the pitch P0 and the width W0 (i.e., P0 - W0), and the depth is equal to D0.

[0036] In some embodiments, in addition to the uniform grating portion, the grating portion 140 includes a variable grating portion that includes grating components having different geometric dimensions. The variable grating portion may include grating components 144 having variations in width, pitch, depth, or combinations thereof. For example, in Figure 2B , the grating portion 140 includes a uniform grating portion having consistent geometric dimensions and a variable grating portion having variable depths Dx (such as D1, D2, D3, etc.). The uniform grating portion and the variable grating portion still have the same pitch P0 and width W0. In Figure 2C , the grating portion 140 includes a uniform grating portion having consistent geometric dimensions and a variable grating portion having variable widths Wx (such as W1, W2, W3, etc.) and corresponding variable pitches Px (such as P1, P2, P3, etc.). The variable grating portion that is closer to the optoelectronic component than the uniform grating portion helps the grating portion 140 redirect the optical signal 115 at a smaller angle. For example, the grating portion 140 can redirect the incident light at a smaller angle (such as 85 degrees instead of 88 degrees) and still couple the optical signal 115 into the waveguide.

[0037] In Figure 2B and Figure 2C , within the variable grating portion, the geometric dimensions of the grating components 144 vary in a monotonic gradient (e.g., from a larger depth to a smaller depth and / or from a smaller pitch to a larger pitch along the longitudinal direction). However, one of ordinary skill in the art will recognize that the geometric dimensions of the grating components 144 can be more randomly distributed without following a monotonic gradient, as shown in Figure 2D where the widths Wx, pitches Px, and depths Dx are more randomly distributed individually or in combination. Additionally, the grating portion 140 may include a variable grating portion without having a uniform grating portion. The various configurations of the geometric dimensions of the grating components 144 help achieve different design optimizations, such as a smaller angle, higher coupling efficiency, larger bandwidth, or combinations thereof.

[0038] Now refer to Figures 3A to 3C . Figure 3A A top view of an exemplary multi-layer grating coupler 200 including a lower grating layer 202 and an upper grating layer 204 is shown. The lower grating layer 202 includes a lower grating coupler 206, and the upper grating layer 204 includes an upper grating coupler 208. The lower grating coupler 206 and the upper grating coupler 208 are arranged back-to-back. That is, the grating components of the lower grating coupler 206 face downward (towards the underlying substrate 122), and the grating components of the upper grating coupler 208 face upward (away from the substrate 122).

[0039] As described above with respect to Figures 2A to 2DAs discussed, each of the lower grating coupler 206 and the upper grating coupler 208 can be independently implemented with the geometric dimensions of the grating component. Figure 3B Fig. shows a cross-sectional view of a multi-layer grating coupler 200 cut along the Figure 3A line A-A in according to one embodiment, where the geometric dimensions of the grating components in the lower grating coupler 206 and the upper grating coupler 208 are the same. In Figure 3B , the trenches between the grating components in the lower grating coupler 206 and the upper grating coupler 208 are aligned with the adjacent grating components. Figure 3C Fig. shows a cross-sectional view of a multi-layer grating coupler 200 cut along the Figure 3A line A-A in according to an alternative embodiment, where the geometric dimensions of the grating components in the lower grating coupler 206 and the upper grating coupler 208 are different. In Figure 3C , due to the different geometric dimensions, the trenches between some or all of the grating components in the lower grating coupler 206 and the upper grating coupler 208 and the adjacent grating components are misaligned.

[0040] The multi-layer grating coupler 200 is disposed above a reflective layer 210, and the reflective layer 210 is deposited on a substrate 122. As discussed above, the substrate 122 can include elemental semiconductors, including silicon or germanium having a crystalline, polycrystalline, or amorphous structure; compound semiconductors, including silicon carbide, gallium arsenide, gallium phosphide, indium phosphide, indium arsenide, and indium antimonide; alloy semiconductors, including SiGe, GaAsP, AlInAs, AlGaAs, GaInAs, GaInP, and GaInAsP; any other suitable materials; or combinations thereof. The reflective layer 210 can be a metal layer, such as a copper layer or an aluminum layer. In one example, the substrate 122 is crystalline silicon, and the reflective layer 210 is an aluminum-coated layer.

[0041] The lower grating layer 202 includes a base layer 205, and a lower grating coupler 206 is formed on the base layer 205. In some embodiments, the base layer 205 includes a dielectric material, such as silicon oxide or other suitable dielectric materials. The lower grating coupler 206 includes an optically transparent material. In some embodiments, the lower grating coupler 206 includes silicon, silicon nitride or other suitable optically transparent materials. The upper grating layer 204 includes a coating 209 located above the upper grating coupler 208. In some embodiments, the coating 209 includes a dielectric material, such as silicon oxide or other suitable dielectric materials. In one example, the base layer 205 and the coating 209 include the same dielectric material, such as silicon oxide. In another example, the base layer 205 and the coating 209 include different dielectric materials. The upper grating coupler 208 includes an optically transparent material. In some embodiments, the upper grating coupler 208 includes silicon, silicon nitride or other suitable optically transparent materials. In one example, the lower grating coupler 206 and the upper grating coupler 208 include the same optically transparent material, such as silicon nitride, and there is no obvious boundary between the lower grating layer 202 and the upper grating layer 204. In another example, the lower grating coupler 206 and the upper grating coupler 208 include different optically transparent materials, such as one made of silicon and the other made of silicon nitride, and there is a visible boundary between the lower grating layer 202 and the upper grating layer 204.

[0042] During operation, a portion of the incident light (e.g., Figure 1A the optical signal 115 in ) is redirected by the upper grating coupler 208 into the corresponding upper waveguide in the upper grating layer 204, and the remaining portion of the incident light passes through the upper grating layer 104. The reflective layer 210 reflects the remaining portion of the incident light into the lower grating layer 202, and is redirected by the lower grating coupler 206 into the corresponding lower waveguide in the lower grating layer 202. The light guided into the upper waveguide and the lower waveguide can be combined into one of the waveguides, which will be discussed in more detail later. By recollecting the remaining portion of the incident light, a higher percentage of the incident light will be collected. Therefore, the coupling efficiency of the multi-layer grating coupler is higher than that of the conventional grating coupler implemented in a single layer. Additionally, since the coupling efficiency in the multi-layer configuration is naturally higher, the design of the grating coupler can be relaxed to be more conducive to bandwidth, which allows the multi-layer grating coupler to have a wider bandwidth than the conventional grating coupler implemented in a single layer.

[0043] Since the geometric dimensions of the grating components in the lower grating coupler 206 and the upper grating coupler 208 are implemented independently, the pitch of the grating components in the lower grating coupler 206 can be greater than the pitch in the upper grating coupler 206, and vice versa; the width of the grating components in the lower grating coupler 206 can be greater than the pitch in the upper grating coupler 208, and vice versa; and the depth of the grating components in the lower grating coupler 206 can be greater than the pitch in the upper grating coupler 208, and vice versa. The geometric dimensions of the grating components independently define the performance of the lower grating coupler 206 and the upper grating coupler 208. In some embodiments, both the lower grating coupler 206 and the upper grating coupler 208 are based on a low-loss configuration. In some embodiments, both the lower grating coupler 206 and the upper grating coupler 208 are based on a broadband configuration. In some embodiments, the lower grating coupler 206 is based on a broadband configuration and the upper grating coupler 208 is based on a low-loss configuration, and vice versa. That is, the lower grating coupler 206 can have a greater bandwidth than the upper grating coupler 208, and the upper grating coupler 208 can have a higher coupling efficiency than the lower grating coupler 206, and vice versa.

[0044] Figure 4A and Figure 4B shows an alternative embodiment of the multi-layer grating coupler 200, in which the grating portions of the lower grating coupler 206 and the upper grating coupler 208 do not overlap, but are offset along the center line of the grating coupler. Figure 4A shows a top view of the multi-layer grating coupler 200, and Figure 4B shows a cross-sectional view taken along the Figure 4A line A-A in. In the illustrated embodiment, the grating portion of the lower grating coupler 206 has a length designated as L 下部 , which measures the distance from the tip (center point) of the first arcuate grating component to the end point of the tapered waveguide transition component. Similarly, the grating portion of the upper grating coupler 208 has a length designated as L 上部 . The lengths L 下部 and L 上部 can be the same (i.e., L 下部 = L 上部 ) or different (i.e., L 下部 < L 上部 or L 下部 > L 上部 ). In the illustrated embodiment, the two grating portions do not have an overlapping region, but are offset by a distance designated as D. In some embodiments. The spacing D is not less than the length L 上部about 10% (e.g., 10%, 20%, 30%, 40%, 50% or even greater). A range of not less than 10% is not trivial or arbitrary. If the range is less than about 10%, the interference may become non-negligible and deteriorate the device performance. It is noted that the lower waveguide of the lower grating coupler 206 still propagates below the grating portion of the upper grating coupler 208 and overlaps with the upper waveguide of the upper grating coupler 208 (not shown in Figure 4A for clarity, but shown in Figure 4B ).

[0045] Since the geometric dimensions of the grating components in the lower grating coupler 206 and the upper grating coupler 208 are independently implemented, the pitch of the grating components in the lower grating coupler 206 can be greater than the pitch in the upper grating coupler 206, and vice versa; the width of the grating components in the lower grating coupler 206 can be greater than the pitch in the upper grating coupler 208, and vice versa; and the depth of the grating components in the lower grating coupler 206 can be greater than the pitch in the upper grating coupler 208, and vice versa. The geometric dimensions of the grating components independently define the performance of the lower grating coupler 206 and the upper grating coupler 208. In some embodiments, both the lower grating coupler 206 and the upper grating coupler 208 are based on a low-loss configuration. In some embodiments, both the lower grating coupler 206 and the upper grating coupler 208 are based on a broadband configuration. In some embodiments, the lower grating coupler 206 is based on a broadband configuration and the upper grating coupler 208 is based on a low-loss configuration, and vice versa. That is, the lower grating coupler 206 can have a greater bandwidth than the upper grating coupler 208, and the upper grating coupler 208 can have a higher coupling efficiency than the lower grating coupler 206, and vice versa.

[0046] Figures 5A to 5C An alternative embodiment of the multi-layer grating coupler 200 is shown, in which the grating portions of the lower grating coupler 206 and the upper grating coupler 208 do not overlap, but are offset in a direction perpendicular to the center line of the grating coupler. Figure 5A A top view of the multi-layer grating coupler 200 is shown, Figure 5B showing a cross-sectional view cut along the A-A line in Figure 5A , and Figure 5C showing a cross-sectional view cut along the B-B line in Figure 5A . In the illustrated embodiment, the grating portion of the lower grating coupler 206 has a length denoted as L 下部 , which measures the distance from the tip (center point) of the first arc-shaped grating component to the end point of the tapered waveguide transition component. Similarly, the grating portion of the upper grating coupler 208 has a length denoted as L 上部The length. The length L 下部 and L 上部 can be the same (i.e., L 下部 = L 上部 ) or different (i.e., L 下部 < L 上部 or L 下部 > L 上部 ). In the illustrated embodiment, the two grating portions do not have an overlapping region but are offset by a distance represented as D. In some embodiments. The spacing D is not less than about 10% of the length L 上部 (e.g., 10%, 20%, 30%, 40%, 50% or even greater). A range of not less than 10% is not trivial or arbitrary. If the range is less than about 10%, the interference may become non - negligible and deteriorate the device performance. Nevertheless, such a D is much smaller than the typical distance between two conventional grating couplers formed in a single layer without affecting the interference level. This is because in the depicted embodiment, having the upper grating coupler and the lower grating coupler in two different layers effectively reduces the interference.

[0047] Since the geometric dimensions of the grating components in the lower grating coupler 206 and the upper grating coupler 208 are independently implemented, the pitch of the grating components in the lower grating coupler 206 can be greater than the pitch in the upper grating coupler 206, and vice versa; the width of the grating components in the lower grating coupler 206 can be greater than the pitch in the upper grating coupler 208, and vice versa; and the depth of the grating components in the lower grating coupler 206 can be greater than the pitch in the upper grating coupler 208, and vice versa. The geometric dimensions of the grating components independently define the performance of the lower grating coupler 206 and the upper grating coupler 208. In some embodiments, both the lower grating coupler 206 and the upper grating coupler 208 are based on a low - loss configuration. In some embodiments, both the lower grating coupler 206 and the upper grating coupler 208 are based on a broadband configuration. In some embodiments, the lower grating coupler 206 is based on a broadband configuration and the upper grating coupler 208 is based on a low - loss configuration, and vice versa. That is, the lower grating coupler 206 can have a greater bandwidth than the upper grating coupler 208, and the upper grating coupler 208 can have a higher coupling efficiency than the lower grating coupler 206, and vice versa.

[0048] Now refer to Figures 6A to 6E , Figures 6A to 6E which shows various embodiments of the waveguide portion of the multi - layer grating coupler 200, particularly the portion that combines the optical signals propagating in the upper waveguide and the lower waveguide into the upper waveguide. Figure 6A is a top view, and Figures 6B to 6E is along according to various embodiments of the present disclosure Figure 6ACross-sectional view of the A-A line cut in

[0049] Since the optical signal is combined into the upper waveguide in the illustrated embodiment, the upper waveguide extends longer than the lower waveguide. The upper waveguide has a constant width W 上部 . The lower waveguide starts from a first part with a constant width W 下部 , has a length of L1, and gradually tapers in its second part with a length of L2. The length L1 can be equal to or less than the length L2. As the second part tapers, the photons in the lower waveguide can be gradually guided to the upper waveguide. The waveguide with a lower refractive index can be thicker and wider in width, while the waveguide with a higher refractive index can be thinner and narrower in width. In the depicted embodiment, the upper waveguide has a lower refractive index, and thus the width W of the upper waveguide 上部 is greater than the width W of the first part of the lower waveguide 下部 , and is also thicker. Although not shown, if the upper waveguide has a higher refractive index, the width W of the upper waveguide 上部 is less than the width W of the first part of the lower waveguide 下部 , and is also thinner.

[0050] In Figure 6B , the end of the lower waveguide has vertical sidewalls. By comparison, in Figure 6C , the end of the lower waveguide has inclined sidewalls and vertical sidewalls intersecting with the upper waveguide, which reduces the reflection at the terminal. Similarly, in Figure 6D , the end of the lower waveguide has inclined sidewalls intersecting with the upper waveguide, which also reduces the reflection at the terminal. In addition, as shown in Figure 6E , the optical absorption material 220 can optionally be placed near the end of the lower waveguide as a terminator to further reduce reflection. In Figure 6A , the terminator 220 is represented by a dashed rectangular box. Those of ordinary skill in the art will recognize that the terminator 220 can have other shapes, such as circular, oval, square, or other suitable shapes. The terminator 220 absorbs the photons escaping from the end of the lower waveguide to suppress the interference caused by the escaping photons. The terminator 220 can also be added to the embodiments shown in Figure 6C and Figure 6D .

[0051] Now referring to Figures 7A to 7E , Figures 7A to 7E shows various embodiments of the waveguide portion of the multilayer grating coupler 200, particularly the portion that combines the optical signals propagating in the upper waveguide and the lower waveguide into the lower waveguide. Figure 7A is a top view, and Figures 7B to 7E is a cross-sectional view taken along the A-A line cut in Figure 7A according to various embodiments of the present disclosure.

[0052] Since the optical signal is combined into the lower waveguide in the illustrated embodiment, the lower waveguide extends longer than the upper waveguide. The lower waveguide has a constant width W 下部 . The upper waveguide starts from a first part with a constant width W 上部 , has a length L1, and tapers gradually in its second part with a length L2. The length L1 can be equal to or less than the length L2. As the second part tapers, the photons in the upper waveguide can be gradually guided into the lower waveguide. The waveguide with a lower refractive index can be thicker and wider in width, while the waveguide with a higher refractive index can be thinner and narrower in width. In the depicted embodiment, the upper waveguide has a lower refractive index, and thus the width W 上部 of the first part of the upper waveguide is greater than the width W 下部 of the lower waveguide, and is also thicker. Although not shown, if the upper waveguide has a higher refractive index, the width W 上部 of the first part of the upper waveguide is less than the width W 下部 of the lower waveguide, and is also thinner.

[0053] In Figure 7B , the end of the upper waveguide has vertical sidewalls. By comparison, in Figure 7C , the end of the upper waveguide has inclined sidewalls and vertical sidewalls intersecting with the lower waveguide, which reduces the reflection at the terminal. Similarly, in Figure 7D , the end of the upper waveguide has inclined sidewalls intersecting with the lower waveguide, which also reduces the reflection at the terminal. Additionally, as shown in Figure 7E , the optical absorption material 220 can optionally be placed near the end of the upper waveguide as a terminator to further reduce reflection. In Figure 7A , the terminator 220 is represented by a dashed rectangular box. Those of ordinary skill in the art will recognize that the terminator 220 can have other shapes, such as circular, oval, square, or other suitable shapes. The terminator 220 absorbs the photons escaping from the end of the upper waveguide to suppress the interference caused by the escaping photons. The terminator 220 can also be added to the embodiments shown in Figure 7C and Figure 7D .

[0054] Figure 8 is a flowchart showing a method 300 for forming a multilayer grating coupler according to an embodiment of the present disclosure. The method 300 is merely an example and is not intended to limit the present disclosure to what is explicitly shown in the method 300. Additional steps can be provided before, during, and after the method 300, and for additional embodiments of the method, some of the described steps can be replaced, eliminated, or rearranged. For simplicity, not all steps are described in detail here. The method 300 is described below in conjunction with Figures 9A to 9G ,Figures 9A to 9G is a partial cross-sectional view of a workpiece at different manufacturing stages according to an embodiment of method 300.

[0055] At step 302, as Figure 9A shown, a reflective layer 210 is deposited on a substrate 122. The substrate 122 may include an elemental semiconductor, including silicon or germanium having a crystalline, polycrystalline, or amorphous structure; a compound semiconductor, including silicon carbide, gallium arsenide, gallium phosphide, indium phosphide, indium arsenide, and indium antimonide; an alloy semiconductor, including SiGe, GaAsP, AlInAs, AlGaAs, GaInAs, GaInP, and GaInAsP; any other suitable material; or a combination thereof. The reflective layer 210 may be a metal layer, such as a copper layer or an aluminum layer. The metal layer may be deposited by a chemical vapor deposition (CVD) process, a physical vapor deposition (PVD) process, an atomic layer deposition (ALD) process, a plating process, or other suitable processes. Then, the deposited metal layer is thinned and planarized, for example, by a chemical mechanical polishing (CMP) process to improve surface reflectivity.

[0056] At step 304, as Figure 9B shown, a base layer 205 is deposited on the reflective layer 210. The base layer 205 may include a dielectric material, such as silicon oxide or other suitable dielectric materials. The base layer 205 may be deposited using a CVD process, an ALD process, an oxygen plasma oxidation process, a spin coating process, or other suitable processes.

[0057] At step 306, as Figure 9C shown, the top portion of the base layer 205 is patterned in a lithography process to form trenches that will define a grating component to be formed later. The lithography process may include photoresist coating (e.g., spin coating), soft baking, mask alignment, exposure, post-exposure baking, photoresist development, rinsing, drying (e.g., spin drying and / or hard baking), other suitable lithography techniques, and / or combinations thereof. In some embodiments, the etching process may include dry etching (e.g., RIE etching), wet etching, and / or other etching methods.

[0058] At step 308, as Figure 9DAs shown, a first optically transparent material is deposited on the base layer 205 to form a lower grating coupler 206. The optically transparent material may include silicon, silicon nitride, or other suitable optically transparent materials. The optically transparent material may be deposited using a CVD process, a PVD process, an ALD process, or other suitable processes. The portion of the optically transparent material deposited in the trenches (previously defined in the top portion of the base layer 205) forms the grating component of the lower grating coupler 206. Then, the deposited optically transparent material is thinned and planarized to a suitable thickness, for example, by a CMP process, to form a lower waveguide above the base layer 205. The base layer 205 and the lower grating coupler 206 together define a lower grating layer 202.

[0059] At step 310, as Figure 9E shown, a second optically transparent material is deposited on the lower grating coupler 206, denoted as layer 207. The optically transparent material may include silicon, silicon nitride, or other suitable optically transparent materials. The optically transparent material may be deposited using a CVD process, a PVD process, an ALD process, or other suitable processes. In one example, the first optically transparent material and the second optically transparent material include the same optically transparent material, such as silicon nitride, and there is no distinct boundary between the two optically transparent materials. In another example, the first optically transparent material and the second optically transparent material include different optically transparent materials, such as one made of silicon and the other made of silicon nitride, and there is a visible boundary between the first optically transparent material and the second optically transparent material. The deposited second optically transparent material may be thinned and planarized to a suitable thickness, for example, by a CMP process, to form an upper waveguide above the lower grating coupler 206.

[0060] At step 312, as Figure 9F shown, the second optically transparent material is patterned in a lithography process to form an upper grating coupler 208 having a grating component. The lithography process may include photoresist coating (e.g., spin coating), soft baking, mask alignment, exposure, post-exposure baking, photoresist development, rinsing, drying (e.g., spin drying and / or hard baking), other suitable lithography techniques, and / or combinations thereof. In some embodiments, the etching process may include dry etching (e.g., RIE etching), wet etching, and / or other etching methods.

[0061] At step 314, as Figure 9G shown, a coating 209 is deposited on the upper grating coupler 208. The coating 209 may include a dielectric material, such as silicon oxide or other suitable dielectric materials. The coating 209 may be deposited using a CVD process, an ALD process, an oxygen plasma oxidation process, a spin coating process, or other suitable processes. The upper grating coupler 208 and the coating 209 together define an upper grating layer 204.

[0062] In some alternative embodiments, the lithography process performed at step 312 may include multiple etching processes performed at multiple regions of the second optically transparent material to form a stack of two or more grating couplers from a single second optically transparent material. Figure 10 An exemplary resulting structure is shown, which includes an upper grating coupler 208-I formed in region I of the second optically transparent material and an intermediate grating coupler 208-II formed in region II of the second optically transparent material. A lower grating coupler 206 is stacked below the intermediate grating coupler 208-II and the upper grating coupler 208-I. In one exemplary lithography process performed at step 312, a first etching process is performed to recess the second optically transparent material in region II while region I is protected under a mask layer; subsequently, a second etching process is performed to form a grating component in region I to form the upper grating coupler 208-I while region II is protected under the mask layer; then, a third etching process is performed to form a grating component in region II to form the intermediate grating coupler 208-II while region I is protected under the mask layer; at the end of step 312, the mask layer is removed to expose the entire patterned second optically transparent material, and a coating 209 is deposited thereon in a subsequent step 314. Similar to the discussion above, the geometric dimensions of the grating components in each of the three grating couplers 208-I, 208-II, and 206 can be defined independently to meet various application requirements.

[0063] For semiconductor chips with a large number of optical I / O ports, the proposed multi-layer grating coupler architecture can be used to integrate the I / O ports into one or more edges of the semiconductor chip, reducing the area and complexity of the I / O ports while improving system reliability and performance. In addition, for measurement or packaging, a large number of optical fibers can be integrated into an optical fiber bus or an optical fiber array, which can be configured for simultaneous transmission, improving stability and locality. Figure 11A and Figure 11B A perspective view of an optical fiber to chip coupling system 400 according to some embodiments is shown. The optical fiber to chip coupling system 400 includes a chip 120 and a multi-layer grating coupler 200. In Figure 11A this, the multi-layer grating coupler 200 includes a row of lower grating couplers 206 and a row of upper grating couplers 208. For example, based on Figures 5A to 5C the topology in, each of the lower grating couplers 206 and the upper grating couplers 208 can operate independently. A first optical fiber bus 402-1 including an array of optical fibers arranged in a row is coupled to the upper grating coupler 208, and a second optical fiber bus 402-2 including an array of optical fibers arranged in a row is coupled to the lower grating coupler 206. In Figure 11BIn [the figure], the multi-layer grating coupler 200 includes a row of lower grating couplers 206 and a row of upper grating couplers 208. Each lower grating coupler 206 and a corresponding upper grating coupler 208 form a pair. For example, based on Figures 3A to 3C the topology in Figures 4A to 4B or the topology in

[0064] The optical fiber bus 402 including an optical fiber cluster arranged in a row is commonly coupled to the upper grating coupler 208 and the lower grating coupler 206. That is, each optical fiber in the optical fiber bus 402 feeds the lower grating coupler 206 and the corresponding upper grating coupler 208 in the same pair simultaneously.

[0065] In an example aspect, the present disclosure provides an apparatus for optical coupling. The apparatus includes: a substrate; a reflective layer disposed on the substrate; a lower grating layer located above the reflective layer, the lower grating layer including a base layer and a lower grating coupler located above the base layer; and an upper grating layer located above the lower grating layer, the upper grating layer including an upper grating coupler and a coating located above the upper grating coupler. In a top view of the apparatus, a centerline of the lower grating coupler is aligned with a centerline of the upper grating coupler. In some embodiments, the lower grating coupler includes a lower grating portion and a lower waveguide portion, the upper grating coupler includes an upper grating portion and an upper waveguide portion, and the lower grating portion overlaps the upper grating portion in the top view. In some embodiments, the lower grating portion and the upper grating portion are substantially the same. In some embodiments, the lower grating portion and the upper grating portion have different geometric dimensions. In some embodiments, the lower grating coupler includes a lower grating portion and a lower waveguide portion, the upper grating coupler includes an upper grating portion and an upper waveguide portion, and the lower grating portion does not overlap the upper grating portion in the top view. In some embodiments, the lower waveguide portion overlaps the upper grating portion in the top view. In some embodiments, the lower grating portion and the upper grating portion are substantially the same. In some embodiments, the lower grating portion and the upper grating portion have different geometric dimensions. In some embodiments, the lower grating coupler is in physical contact with the upper grating coupler. In some embodiments, the lower grating coupler and the upper grating coupler include different optically transparent materials.

[0066] Another aspect of the present disclosure provides an apparatus for optical coupling. The apparatus includes: a substrate; a reflective layer disposed on the substrate; a lower grating layer located above the reflective layer, the lower grating layer including a lower grating coupler formed therein; and an upper grating layer located above the lower grating layer, the upper grating layer including an upper grating coupler formed therein. The lower grating coupler includes a lower waveguide, the upper grating coupler includes an upper waveguide, and the lower waveguide and the upper waveguide are configured to combine photons propagating therein into one of the lower waveguide and the upper waveguide. In some embodiments, in a top view of the apparatus, the lower waveguide and the upper waveguide overlap. In some embodiments, one of the lower waveguide and the upper waveguide has a constant-width portion and a tapered-width portion. In some embodiments, the constant-width portion is shorter than the tapered-width portion. In some embodiments, one of the lower waveguide and the upper waveguide is shorter than the other and includes an inclined terminal sidewall. In some embodiments, the apparatus further includes an optical absorption material that overlaps a terminal of one of the lower waveguide and the upper waveguide in a top view of the apparatus.

[0067] Yet another aspect of the present disclosure provides a method for manufacturing an optical device. The method includes forming a reflective layer on a substrate, depositing a base layer on the reflective layer, patterning a top portion of the base layer to form a plurality of first trenches, depositing a first optically transparent material on the base layer, filling the first trenches with the first optically transparent material when forming a plurality of first grating teeth of a first grating coupler, depositing a second optically transparent material on the first optically transparent material, patterning a top portion of the second optically transparent material to form a plurality of second grating teeth of a second grating coupler, and depositing a coating on the second optically transparent material. The coating fills a plurality of second trenches defined between adjacent second grating teeth. In some embodiments, the method further includes thinning the first optically transparent material to form a first waveguide. In some embodiments, the method further includes thinning the second optically transparent material to form a second waveguide before patterning the top portion of the second optically transparent material. In some embodiments, the first optically transparent material is different from the second optically transparent material.

[0068] The features of several embodiments are outlined above so that those skilled in the art may better understand aspects of the present disclosure. Those skilled in the art should understand that they can readily use the present disclosure as a basis to design or modify other processes and structures for implementing the same purposes and / or achieving the same advantages as the embodiments described herein. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the present disclosure, and that various changes, substitutions, and alterations can be made therein without departing from the spirit and scope of the present disclosure.

Claims

1. An apparatus for optical coupling, comprising: A substrate; A reflective layer disposed on the substrate; A lower grating layer above the reflective layer, the lower grating layer including a base layer and a lower grating coupler above the base layer; And An upper grating layer above the lower grating layer, the upper grating layer including an upper grating coupler and a coating above the upper grating coupler, Wherein, in a top view of the apparatus, a center line of the lower grating coupler is aligned with a center line of the upper grating coupler.

2. The device according to claim 1, wherein The lower grating coupler includes a lower grating portion and a lower waveguide portion, the upper grating coupler includes an upper grating portion and an upper waveguide portion, and the lower grating portion overlaps the upper grating portion in the top view.

3. The apparatus according to claim 2, wherein, The lower grating portion and the upper grating portion are substantially the same.

4. The apparatus according to claim 2, wherein, The lower grating portion and the upper grating portion have different geometric dimensions.

5. The device according to claim 1, wherein, The lower grating coupler includes a lower grating portion and a lower waveguide portion, the upper grating coupler includes an upper grating portion and an upper waveguide portion, and the lower grating portion does not overlap the upper grating portion in the top view.

6. The device according to claim 5, wherein, The lower waveguide portion overlaps the upper grating portion in the top view.

7. The apparatus according to claim 5, wherein, The lower grating portion and the upper grating portion are substantially the same.

8. The device according to claim 5, wherein The lower grating portion and the upper grating portion have different geometric dimensions.

9. An apparatus for optical coupling, comprising: A substrate; A reflective layer disposed on the substrate; A lower grating layer above the reflective layer, the lower grating layer including a lower grating coupler formed therein; and An upper grating layer above the lower grating layer, the upper grating layer including an upper grating coupler formed therein, Wherein, the lower grating coupler includes a lower waveguide, the upper grating coupler includes an upper waveguide, and the lower waveguide and the upper waveguide are configured to combine photons propagating therein into one of the lower waveguide and the upper waveguide.

10. A method for manufacturing an optical device, comprising: Forming a reflective layer on a substrate; Depositing a base layer on the reflective layer; Patterning a top portion of the base layer to form a plurality of first trenches; Depositing a first optically transparent material on the base layer, wherein when forming a plurality of first grating teeth of a first grating coupler, the first optically transparent material fills the first trenches; Depositing a second optically transparent material on the first optically transparent material; Patterning a top portion of the second optically transparent material to form a plurality of second grating teeth of a second grating coupler; and Depositing a coating on the second optically transparent material, wherein the coating fills a plurality of second trenches defined between adjacent second grating teeth.