Optical waveguide based on AlScN piezoelectric driving and bayesian optimization design method thereof

Abstract

This invention discloses an optical waveguide based on AlScN piezoelectric drive and its Bayesian optimization design method. The optical waveguide has a silicon dioxide lower cladding, a silicon nitride waveguide core, and a silicon dioxide upper cladding sequentially disposed on a silicon substrate. The upper cladding has a stepped profile with a higher center and lower sides. A lower metal electrode, an AlScN piezoelectric layer, and an upper metal electrode are sequentially covered on the stepped surface, with the cross-section symmetrical along the centerline. This structure concentrates piezoelectric stress in the optical mode field region of the waveguide, improving stress-mode field overlap and modulation efficiency per unit voltage. It enhances modulation capability without increasing the driving voltage, and the scandium-doped aluminum nitride piezoelectric layer combines high piezoelectric coefficient with CMOS process compatibility. This invention also provides a Bayesian optimization design method, using the combination of waveguide geometric parameters as input and the effective refractive index change per unit voltage as the objective function. It combines multiphysics simulation, a Gaussian process proxy model, and an expected improvement function for iterative optimization.

Description

Technical Field

[0001] This invention belongs to the field of piezoelectric elastic optical waveguides, specifically relating to an optical waveguide based on AlScN piezoelectric drive and its Bayesian optimization design method. Background Technology

[0002] With the continuous growth in data center traffic and on-chip interconnect bandwidth demands, photonic integrated circuits are increasingly used in optical interconnects, optical switching, and programmable optical signal processing. Among various integrated photonic platforms, schemes using dielectric materials (such as silicon nitride and alumina) as waveguide core layers have attracted attention due to their lower propagation loss, wider transparency windows, and higher power handling capabilities. Silicon nitride is currently a relatively mature technology. Currently, the most commonly used active modulation method in such dielectric waveguide photonic circuits is thermo-optical modulation. This method achieves phase modulation by heating the waveguide to change its refractive index, but its response speed is typically only in the kilohertz to megahertz range, and it suffers from non-negligible static power consumption. In dense optical switch arrays and reconfigurable photonic circuits, the power accumulation and thermal crosstalk issues of numerous thermo-optic modulators limit the system's scalability, which is particularly prominent in large-scale data center optical switching scenarios.

[0003] As an alternative to thermo-optical tuning, piezoelectric-driven stress-optical modulation has been explored in recent years for active phase control of dielectric waveguide platforms. This method generates a stress field in the piezoelectric layer by applying an external voltage, and then uses the piezoelectric-optical effect to convert mechanical stress into a change in the waveguide's refractive index, thereby achieving phase modulation. In the steady state of maintaining the bias voltage, only a very small current flows through the piezoelectric layer, eliminating the need for continuous power consumption to maintain the temperature field as in thermo-optical tuning. Therefore, it can reduce static power consumption while maintaining the phase state.

[0004] In the selection of piezoelectric materials, lead zirconate titanate (PZT) films have a high piezoelectric coefficient, which can generate large deformation and stress at relatively low voltages. However, the integration of PZT on the silicon nitride platform has several process limitations: its lead content does not meet the cleanliness requirements of some CMOS production lines; its ferroelectric hysteresis characteristics can introduce nonlinearity and zero-point drift in the modulation response; and its typical crystallization temperature is above 500–600°C, exceeding the thermal budget of some advanced CMOS back-end processes.

[0005] Aluminum nitride (AlN) is another piezoelectric material with advantages such as being lead-free, having no ferroelectric hysteresis, and being compatible with CMOS processes. Its sputtering deposition temperature is typically below 400°C. However, its piezoelectric coefficient is relatively small, resulting in limited refractive index changes under the same driving voltage, which needs to be compensated for by increasing the voltage or increasing the device size.

[0006] In the existing technical literature "Stress-optic modulator in TriPleX platform using apiezoelectric lead zirconate titanate (PZT) thin film" (Hosseini et al., OpticsExpress, Vol. 23, Issue 11, pp. 14018-14026, 2015), researchers demonstrated a piezoelectric-optical phase modulator using a lead zirconate titanate (PZT) thin film on the silicon nitride-based TriPleX platform. This approach relies on a lead zirconate titanate material that requires a high-temperature crystallization step. Its lead content makes it incompatible with standard CMOS back-end processes, and its ferroelectric hysteresis introduces nonlinear response, limiting long-term stability in high-precision modulation applications. This work employs a planar cladding structure and does not specifically optimize the structure for the spatial overlap between the stress field and the optical field.

[0007] Furthermore, traditional planar cladding waveguide geometries have certain limitations in piezoelectric stress optical modulation. The stress induced by the piezoelectric layer diffuses disorderly laterally within the uniform oxide cladding, resulting in insufficient stress concentration in the waveguide core region. The low spatial overlap between the stress distribution and the guided wave optical field also limits the refractive index modulation efficiency per unit voltage. Moreover, waveguide structure optimization is a high-dimensional, computationally expensive multiphysics coupling problem. Traditional parameter scanning methods exhibit exponentially increasing computational complexity when dealing with the optimization of combinations of six or more geometric parameters, leading to inefficiency and difficulty in fully covering the parameter space.

[0008] In summary, the shortcomings of existing technologies can be summarized as follows: 1) Dielectric waveguide photonic platform solutions suffer from high static power consumption, and are constrained by thermal crosstalk and power accumulation in dense optical switch arrays, resulting in poor scalability. While lead zirconate titanate has a high piezoelectric coefficient, its lead content, high ferroelectric hysteresis, and high crystallization temperature make it incompatible with standard CMOS back-end processes, and its nonlinear response leads to insufficient modulation accuracy. Aluminum nitride has a piezoelectric coefficient of only about 3.9–5.1 pm / V, requiring higher drive voltages or larger device sizes, which is unfavorable for low-power and high-integration applications.

[0009] 2) In traditional planar cladding waveguides, piezoelectrically induced stress diffuses laterally, resulting in insufficient spatial overlap between the stress field and the optical mode field, which limits the efficiency of elasto-optic modulation. Waveguide structures involve the coupled optimization of multiple geometric parameters, and traditional exhaustive scanning methods are computationally expensive and difficult to fully explore the parameter space.

[0010] In summary, current technologies lack a high-efficiency piezoelectric material with high CMOS compatibility, and also suffer from varying degrees of shortcomings in waveguide cladding stress focusing structures and high-dimensional parameter global optimization. Combining CMOS-compatible piezoelectric materials, waveguide cross-sectional structures that facilitate stress focusing, and appropriate global optimization methods will improve the efficiency of piezo-elastic-optical phase modulation on dielectric waveguide platforms. Summary of the Invention

[0011] The purpose of this invention is to solve the problems existing in the prior art and to provide an optical waveguide based on AlScN piezoelectric drive and its Bayesian optimization design method. Specifically, the technical problems solved by this invention and the corresponding solutions can be divided into the following three aspects: To address the problem in existing piezoelectric-optical modulation schemes where piezoelectric layer-induced stress diffuses laterally within conventional planar clad waveguides, resulting in insufficient spatial overlap between the stress field and the optical mode field and consequently low refractive index modulation efficiency per unit voltage, this invention designs a stepped cladding stress-focusing structure (SCSS) to achieve low-voltage, low-power phase modulation. By reshaping the boundary conditions above the waveguide, the piezoelectric stress is effectively concentrated in the optical mode field region of the waveguide core, improving stress-mode field overlap and modulation efficiency.

[0012] Among existing piezoelectric materials, PZT has a high piezoelectric coefficient but contains lead and is incompatible with CMOS back-end processes, while AlN is compatible with CMOS but has a relatively low piezoelectric coefficient. A material solution that combines a high piezoelectric coefficient with CMOS process compatibility is needed. This invention uses scandium-doped aluminum nitride (AlScN) as the piezoelectric actuation layer. AlScN has a deposition temperature below 400°C, is lead-free, has no ferroelectric hysteresis, is thermally compatible with CMOS back-end processes, and has a piezoelectric coefficient several times higher than AlN, which is beneficial for obtaining a larger refractive index change at lower driving voltages.

[0013] For waveguide structures involving the coupled optimization of multiple geometric parameters, traditional exhaustive scanning methods are computationally expensive and struggle to fully explore the parameter space within a reasonable timeframe. This invention addresses the problem of low efficiency in traditional parameter scanning by establishing a multiphysics coupled design method based on Bayesian optimization algorithms. This method rapidly locates the globally optimal structural parameters in a high-dimensional geometric parameter space with a limited number of simulation iterations.

[0014] To achieve the above-mentioned objectives, the specific technical solution adopted by this invention is as follows: In a first aspect, the present invention provides an optical waveguide based on AlScN piezoelectric drive. The optical waveguide uses a silicon wafer as a substrate, and a silica lower cladding capable of isolating optical leakage of the substrate is deposited with equal thickness on the top surface of the substrate. A silicon nitride waveguide core layer is deposited in a central local area on the top surface of the silica lower cladding. A silica upper cladding with equal thickness is deposited on the top surface of the silicon nitride waveguide core layer and the top surface of the silica lower cladding where the silicon nitride waveguide core layer is not deposited. After etching, the cross-sectional outer contour of the silica upper cladding is a stepped surface that is high in the middle and low on both sides along the width direction of the optical waveguide; a lower metal electrode, an AlScN piezoelectric layer, and an upper metal electrode are sequentially covered on the stepped surface; the cross-section of the entire optical waveguide is mirror-symmetrical along the center line.

[0015] As a preference of the above first aspect, the stepped surface is a single-step or multi-step surface.

[0016] As a preference of the above first aspect, the angle of each step in the stepped surface is 90° or close to 90°; preferably, the angle of each step in the stepped surface is 90° ± 5°.

[0017] As a preference of the above first aspect, the thickness of the silica lower cladding is 2 - 5 μm; the thickness of the silicon nitride waveguide core layer is 300 - 800 nm.

[0018] As a preference of the above first aspect, the materials of the lower metal electrode and the upper metal electrode are gold (Au), copper (Cu), platinum (Pt), or aluminum (Al).

[0019] As a preference of the above first aspect, the material of the AlScN piezoelectric layer is aluminum scandium nitride Al 1-x Sc x N, where 0 < x < 1; preferably, x = 0.4.

[0020] In a second aspect, the present invention provides a Bayesian optimization design method for an optical waveguide based on AlScN piezoelectric drive as described in the above first aspect, which includes: S1. Construct all structural geometric parameters to be optimized in the optical waveguide into a geometric parameter combination X, randomly sample in the parameter design space Ω to obtain sampling values of multiple groups of geometric parameter combinations X; use the change amount of the effective refractive index under a unit voltage as the objective function, and perform the multi-physics field coupling simulation for each sampling value of the geometric parameter combination X respectively, calculate the objective function value based on the simulation results, so as to construct an initial training data set; S2. Based on the training data set, use the geometric parameter combination X as the input and the change amount of the effective refractive index under a unit voltage as the output to train a Gaussian process surrogate model, which is used to provide a predicted mean μ(X) and a predicted standard deviation σ(X) for the objective function value of any group of geometric parameter combinations X in the parameter design space Ω; S3. Select the maximum value of the objective function from the samples in the current training dataset as the current optimal objective function value, and use it to construct the expected improvement (EI) acquisition function. Then, based on the Gaussian process surrogate model, find the geometric parameter combination X with the largest expected improvement value in the parameter design space Ω as the next evaluation point. S4. Re-execute the multiphysics coupling simulation on the geometric parameter combination X, which is the next evaluation point, calculate the objective function value based on the simulation results, and then construct it as a new sample increment to update the training dataset, thereby retraining and updating the Gaussian process surrogate model. S5. Repeat steps S3 and S4 until the preset convergence condition is met, and output the geometric parameter combination X that maximizes the objective function value.

[0021] As a preferred embodiment of the second aspect above, the stepped surface is a single-level step, and the step profile is formed by connecting the middle high step plane to the two low step planes on both sides through vertical step planes on both sides; the geometric parameter combination X consists of six structural geometric parameters of the optical waveguide cross-section, namely: the step width a1 of the low step plane, the full width a2 of the optical waveguide, the step height b1 of the high step plane relative to the low step plane, the height b2 of the low step plane relative to the top surface of the substrate, and the electrode thickness h of the lower metal electrode and the upper metal electrode. e The thickness h of the AlScN piezoelectric layer p .

[0022] As a preferred embodiment of the second aspect above, when performing the multiphysics coupling simulation for any set of geometric parameter combinations X, it is necessary to construct a finite element model of the optical waveguide based on the geometric parameter combination X, and then for two different bias voltages V bias The simulation analysis will be performed sequentially in the following two phases: The first phase involves performing a static electromechanical analysis: In an electrostatic field, the current bias voltage V is applied to the upper metal electrode. bias The lower metal electrode is grounded, the remaining outer surface of the optical waveguide is set as an electrically insulating boundary, and the bottom surface of the substrate is set as a fixed constraint. The electromechanical response of the AlScN piezoelectric layer is described by the linear piezoelectric constitutive equation. The stress field distribution σ(x, y) in the waveguide structure is obtained by solving the linear piezoelectric constitutive equation by finite element numerical method. The second stage involves optical mode analysis: the stress field distribution obtained in the first stage is mapped to the refractive index distribution of the optical waveguide through the elastic-optical relationship. The updated refractive index distribution is then substituted into the electromagnetic wave frequency domain module for eigenmode analysis to extract the current bias voltage V. bias Effective refractive index of the lower TE0 mode.

[0023] As a preferred embodiment of the second aspect above, in the first stage, the linear piezoelectric constitutive equation takes the form of: Where T is the stress tensor; S is the strain tensor; D is the electric displacement vector; and E is the electric field vector. Let e ​​be the constant electric field stiffness matrix, and e be the piezoelectric coupling matrix. For the constant strain dielectric constant matrix, generate e The required elastic stiffness, piezoelectric coupling coefficient, and dielectric constant of the AlScN piezoelectric layer are respectively arranged in the material coordinate system with the c-axis perpendicular to the substrate; at the same time, the density of the AlScN piezoelectric layer is also arranged in the material coordinate system with the c-axis perpendicular to the substrate.

[0024] As a preferred embodiment of the second aspect above, in the second stage, the formula for the elastic-optical relationship mapping between the stress field and the refractive index distribution is expressed as: in Let be the three principal diagonal components of the stress tensor at each location in the stress field. The three principal diagonal components of the refractive index tensor at the same location. The intrinsic refractive index under stress-free conditions. and This is the stress optical coefficient.

[0025] As a preferred embodiment of the second aspect above, the objective function is calculated by: taking two different bias voltages V... bias The difference in effective refractive index of the TE0 mode is divided by the difference in the two different bias voltages to obtain the change in effective refractive index per unit voltage, which is used as the objective function value.

[0026] Compared with the prior art, the present invention has the following advantages: 1) Compared with the flat-top cladding reference structure, the stepped cladding stress focusing structure of the present invention increases the peak stress in the waveguide core region from 14.36 MPa to 23.22 MPa (under 10 V bias) through geometric stress focusing, and the modulation efficiency Δn eff / V from 1.26×10 -6 V -1 Increased to 2.26×10 -6 V -1 This achieves a 1.8x enhancement, effectively improving modulation capability without increasing the driving voltage.

[0027] 2) The AlScN material used in this invention is lead-free and free of ferroelectric hysteresis. Its deposition temperature is within the thermal budget range of most CMOS back-end processes, which is beneficial for integration with existing silicon photonics foundry processes. It solves the problem of potential contamination risks and high-temperature crystallization steps of other piezoelectric materials that make them incompatible with standard silicon photonics production lines.

[0028] 3) Compared with the solution based on aluminum nitride piezoelectric layer, the present invention uses AlScN to achieve about 4 times the modulation efficiency under the same optimized structure, can obtain the same phase modulation amount at a lower driving voltage, reduces device power consumption, and is beneficial to the scalability of dense optical switch array.

[0029] 4) Compared to the traditional exhaustive parameter scanning method, the Bayesian optimization method used in this invention, after 170 numerical simulations, shows that the objective function tends to converge in the six-dimensional parameter space, reducing the number of simulations required compared to equivalent precision mesh scanning. This optimization process can also be applied to other similar multiphysics coupled device parameter design problems. Attached Figure Description

[0030] Figure 1 This is a schematic diagram showing the structure and parameter definitions of an optical waveguide based on AlScN piezoelectric drive.

[0031] Figure 2 This is a schematic diagram of the Bayesian global optimization algorithm based on the Gaussian process regression surrogate model.

[0032] Figure 3 The image shows a comparison of the stress field distribution and TE0 mode field contour lines of the waveguide structure under a 10 V bias voltage between the optimized SCSS structure and the flat-top cladding reference structure; where (a) is the optimized stepped cladding stress focusing structure and (b) is the flat-top cladding reference structure.

[0033] Figure 4 A comparison of modulation performance under different structural types and piezoelectric layer materials; where (a) is the same Al 0.6 Sc 0.4 A bar chart comparing the effective refractive index changes of different top cladding structures in N-piezoelectric materials. The horizontal axis, from left to right, represents: flat-top cladding structure, stepped cladding stress-focused structure, and SCSS structure with a 5° sidewall tilt angle. The vertical axis represents the absolute value of the effective refractive index change |Δn| under a 10 V bias voltage. eff | (×10) -5 (b) shows the curves of effective refractive index variation with bias voltage for AlScN piezoelectric materials with different scandium doping ratios under stepped cladding stress focusing structure. The horizontal axis represents the bias voltage, and the vertical axis represents the effective refractive index variation Δn. eff (×10) -5 The five curves in the figure correspond to AlN and Al respectively. 0.9Sc 0.1 N, Al 0.75 Sc 0.25 N, Al 0.65 Sc 0.35 N and Al 0.6 Sc 0.4 N.

[0034] The figures are labeled as follows: 1. Substrate, 2. Silicon dioxide lower cladding, 3. Silicon nitride waveguide core, 4. Silicon dioxide upper cladding, 5. Lower metal electrode, 6. AlScN piezoelectric layer, 7. Upper metal electrode. Detailed Implementation

[0035] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in various embodiments of the present invention can be combined accordingly without mutual conflict.

[0036] This invention proposes a piezoelectric elastic-optical waveguide based on a scandium-doped aluminum nitride stepped cladding stress-focusing structure and its structural design method based on Bayesian optimization. The overall technical solution can be divided into three levels: device material and waveguide basic platform design, stepped cladding stress-focusing structure design, and multiphysics coupling modeling and Bayesian global optimization method.

[0037] The waveguide platform of this invention uses a silicon wafer as a substrate. Silicon dioxide is deposited on the silicon substrate as a lower cladding layer, and the thickness of the lower cladding layer is selected within a range that can effectively isolate optical leakage from the substrate (preferably 2–5 μm). Subsequently, a dielectric waveguide core layer film is deposited above the lower cladding layer, and the waveguide core layer material is preferably silicon nitride. The thickness of the waveguide core layer is selected while taking into account bending loss, coupling efficiency, and process feasibility (the thickness of the silicon nitride waveguide core layer is preferably 300–800 nm).

[0038] The width of the optical waveguide can be determined using the finite element method. A model is constructed with silicon dioxide as the top and bottom cladding and silicon nitride as the core layer. The waveguide width is then scanned to calculate the relationship between the effective refractive index and the width for different modes at the operating wavelength. The waveguide width should be selected to ensure stable propagation of the fundamental mode (TE0), suppress higher-order modes, and provide sufficient near-field lateral extension for stress coupling.

[0039] The upper and lower metal electrode materials can be selected from conductive metals such as gold (Au), copper (Cu), platinum (Pt), aluminum (Al), etc. The specific selection needs to consider the resistivity, adhesion to the piezoelectric layer, and process temperature compatibility.

[0040] The piezoelectric layer is scandium-doped aluminum nitride (Al 1-x Sc x N), where 0 < x < 1; preferably, scandium-doped aluminum nitride (Al 0.6 Sc 0.4 N) with a molar fraction of 0.4. While maintaining the advantages of low dielectric constant, lead-free, and CMOS process compatibility, the effective piezoelectric coefficient d 33 can be increased to 15 - 20 pm / V, which is several times that of aluminum nitride. Its physical parameters such as density, elastic stiffness matrix, dielectric constant, and piezoelectric coupling tensor can be calculated and determined by the scandium doping ratio and are uniformly used in multi-physics field simulations. The scandium-doped aluminum nitride piezoelectric material of the present invention is used for the modulation of a piezoelectrically driven optical waveguide. This piezoelectric material has the advantages of high piezoelectric coefficient, low dielectric constant, and CMOS compatibility.

[0041] The stepped cladding stress focusing structure proposed in the present invention is to form a central region higher than the two sides in the silica upper cladding directly above the waveguide. A stepped transition is formed between the central region and the lower regions on both sides, thereby reshaping the mechanical boundary conditions under the piezoelectric layer, suppressing the lateral diffusion of piezoelectric stress, and making the stress preferentially converge to the waveguide core region.

[0042] Based on the design of the above device materials, waveguide basic platform, and stepped cladding stress focusing structure, as Figure 1 shown, a specific structural form of an optical waveguide based on AlScN piezoelectric drive provided in an embodiment of the present invention is demonstrated. This optical waveguide uses a silicon wafer as the substrate 1, and a silica lower cladding 2 with a sufficient thickness to isolate the optical leakage of the substrate is deposited on the top surface of the substrate 1. A silicon nitride waveguide core layer 3 is deposited in a central local region on the top surface of the silica lower cladding 2. A silica upper cladding 4 with an equal thickness is deposited on the top surface of the silicon nitride waveguide core layer 3 and the top surface of the silica lower cladding 2 where the silicon nitride waveguide core layer 3 is not deposited. After etching, the cross-sectional outer contour of the silica upper cladding 4 is a stepped surface that is high in the middle and low on both sides along the width direction of the optical waveguide; a lower metal electrode 5, an AlScN piezoelectric layer 6, and an upper metal electrode 7 are sequentially covered on the stepped surface. The cross-section of the entire optical waveguide is symmetric about the vertical center line in Figure 1 the middle.

[0043] Continue to refer to Figure 1As shown, the specific configuration of the stepped cladding profile in this device is as follows: With the centerline of the silicon nitride waveguide core layer 3 as the axis of symmetry, the silicon dioxide upper cladding layer 4 forms a central region higher than both sides directly above the waveguide. A stepped transition is formed between the central region and the lower regions on both sides, with the top surface of the silicon nitride waveguide core layer 3 and the top surface of the undeposited silicon dioxide lower cladding layer 2 continuously forming stepped surfaces. It should be noted that... Figure 1 The diagram illustrates a single-step implementation, where the step surface contains only one higher step plane. The outer contour of the step is formed by connecting the central higher step plane to the lower step planes on either side via vertical step planes. However, the number of steps in this invention is not limited to one. Figure 1 The single-level step can also be expanded into multiple levels to further refine the control of stress distribution.

[0044] by Figure 1 Taking the optical waveguide structure with a single-stage step as an example, it has several key parameters, where a1 is the step width of the lower step plane; a2 is the full width of the optical waveguide, which is the width covered by the upper and lower metal electrodes and the AlScN piezoelectric layer; b1 is the step height of the higher step plane relative to the lower step plane, i.e., the vertical height difference between the top surface of the central region and the top surfaces of the lower regions on both sides; b2 is the height of the lower step plane relative to the top surface of substrate 1; h e h represents the electrode thickness of the lower metal electrode 5 and the upper metal electrode 7. p The thickness of the AlScN piezoelectric layer 6 is given. This invention involves sequentially depositing a thickness of h on the entire outer surface of the aforementioned stepped profile. e The lower metal electrode layer 5 has a thickness of h. p AlScN piezoelectric layer 6 with a thickness of h e The upper metal electrode layer 7, therefore, these three layers of structure also undulate synchronously with the step contour. The above 6 key geometric parameters can be constructed as a geometric parameter combination in the form of a parameter vector X = [a1, a2, b1, b2, h e , h p ] T In addition to the six key geometric parameters mentioned above, the value ranges of the remaining parameters are determined based on the silicon dioxide etching depth and the void-free oxide backfill process window. Of course, in other embodiments of the present invention, other geometric features of the step-covered contour (including but not limited to the horizontal extension width of each step, the vertical segment height, the electrode thickness, and the piezoelectric layer thickness, etc.) can also be used as parameters to be optimized, and there are no restrictions on this.

[0045] Furthermore, in the stepped surface described above in this invention, the step angle is not strictly required to be 90 degrees, and can be selected according to process tolerances and design requirements. That is, the angle of each step in the stepped surface is 90° or close to 90°. In the embodiments of this invention, a good overall effect can be obtained when the angle of each step in the stepped surface is 90°±5°.

[0046] Furthermore, in the optical waveguide structure described above in this invention, the dimensional parameters of each structure can be optimized and adjusted according to actual conditions. Preferably, the thickness of the silicon dioxide lower cladding layer 2 is preferably 2~5 μm; the thickness of the silicon nitride waveguide core layer 3 is preferably 300~800 nm; and the thickness of the lower metal electrode 5 and the upper metal electrode 7 is preferably h. e Preferably not less than 50 nm; the thickness h of the AlScN piezoelectric layer 6 p Preferably not less than 200 nm. Set h e h p The thickness constraint ensures the electrical continuity of the metal electrode and guarantees the breakdown voltage margin of the piezoelectric film.

[0047] This invention reshapes the mechanical boundary conditions by making the upper cladding layer above the waveguide higher than the two side regions, forming a stepped transition. This concentrates the piezoelectric-induced stress in the optical mode field distribution area of ​​the waveguide core region, improving the stress-mode field spatial overlap and thus enhancing the elasto-optic modulation efficiency. Specifically, the working principle of the stepped cladding stress focusing structure of this invention is as follows: when a bias voltage is applied to the upper metal electrode 7 and the lower metal electrode 5 is grounded, the electric field excites the inverse piezoelectric effect in the AlScN piezoelectric layer 6, generating strain. Because the stepped structure forms a local mechanical constraint region above the waveguide, the stress generated by the piezoelectric strain is guided by the step profile and concentrated in the silicon nitride waveguide core region, rather than diffusing laterally along the uniform oxide layer as in traditional planar cladding structures. The concentrated stress changes the refractive index distribution of the waveguide core and cladding materials through the elasto-optic effect. Since the high-stress region highly overlaps with the spatial distribution of the TEO optical field, a higher Δn is obtained. eff / V.

[0048] Furthermore, due to the geometric parameter combination X = [a1, a2, b1, b2, h] formed by the above 6 key geometric parameters, e ,h p ] T The structure parameters have a significant impact on the final performance of the optical waveguide. Therefore, this invention establishes a simulation framework with sequential coupling of electrostatics, piezoelectricity, mechanics and optics, and combines it with Bayesian optimization algorithm to search for a better combination of structural parameters in a multidimensional geometric parameter space with fewer simulations.

[0049] First, it describes the need to perform multiphysics coupled simulations on any set of geometric parameter combinations X, and to calculate the objective function value based on the simulation results. The simulation process jointly solves for four physical fields: electrostatics, piezoelectric structure, solid mechanics, and electromagnetic wave frequency domain, executed sequentially in two stages. The simulation can be implemented using finite element simulation software. Before performing multiphysics coupled simulations on any set of geometric parameter combinations X, it is necessary to construct a [structure / mechanism] based on that geometric parameter combination X. Figure 1 The finite element model of the optical waveguide is shown, and then for two different bias voltages V bias The simulation analysis will be performed sequentially in the following two phases: The first phase involves performing a static electromechanical analysis: In an electrostatic field, the current bias voltage V is applied to the upper metal electrode 7. bias The lower metal electrode 5 is grounded, the remaining outer surfaces of the optical waveguide are set as electrically insulating boundaries, and the bottom surface of the substrate 1 is set as a fixed constraint. The electromechanical response of the AlScN piezoelectric layer 6 is described by the linear piezoelectric constitutive equation. The stress field distribution σ(x, y) in the waveguide structure is obtained by solving the linear piezoelectric constitutive equation by finite element numerical method.

[0050] The linear piezoelectric constitutive equation describing the electromechanical response of scandium-doped aluminum nitride piezoelectric layers can be expressed in formulaic form as follows: Where T is the stress tensor; S is the strain tensor; D is the electric displacement vector; and E is the electric field vector. Let e ​​be the constant electric field stiffness matrix, and e be the piezoelectric coupling matrix. The constant strain dielectric constant matrix, e It can be generated by configuring the elastic stiffness, piezoelectric coupling coefficient, and dielectric constant. In this embodiment, the generation... e The required elastic stiffness, piezoelectric coupling coefficient, and dielectric constant of the AlScN piezoelectric layer are respectively arranged in the material coordinate system with the c-axis perpendicular to the substrate; at the same time, the density of the AlScN piezoelectric layer is also arranged in the material coordinate system with the c-axis perpendicular to the substrate.

[0051] When solving the aforementioned linear piezoelectric constitutive equation using the finite element method, the stress tensor T is the ultimate objective. The stress tensor T is a tensor field that varies with spatial coordinates (x, y), and can be represented as the aforementioned stress field distribution σ(x, y). The stress tensor at each spatial coordinate (x, y) in the stress field distribution σ(x, y) actually has a series of component vectors, which can be considered as a second-order stress tensor (i.e., a 3×3 matrix), where the three main diagonal components are denoted as... These three main diagonal components will be used for the mapping in the second stage.

[0052] The second stage involves optical mode analysis: the stress field distribution obtained in the first stage is mapped to the refractive index distribution of the optical waveguide through the elastic-optical relationship. The updated anisotropic refractive index distribution is then substituted into the electromagnetic wave frequency domain module for eigenmode analysis, and the current bias voltage V is extracted. bias The effective refractive index n of the lower TE0 mode eff (V bias ).

[0053] In embodiments of the present invention, the elastic-optical relationship between the stress field and the refractive index distribution can be expressed by the following formula: in Let be the three principal diagonal components of the stress tensor at each spatial coordinate position in the stress field. The three principal diagonal components of the refractive index tensor at the same spatial coordinate position. The intrinsic refractive index under stress-free conditions. and It is the stress optical coefficient (i.e., the elastic-optical coefficient of the material).

[0054] It should also be noted that the above-mentioned method of substituting the updated refractive index distribution into the electromagnetic wave frequency domain module for eigenmode analysis is existing technology in this field and can be implemented using existing simulation software. Taking COMSOL Multiphysics as an example, the Electromagnetic Waves, Frequency Domain (ewfd, electromagnetic wave, frequency domain) interface of the Wave Optics Module can be used to perform frequency domain electromagnetic simulation and achieve eigenmode analysis.

[0055] Furthermore, the objective function to be calculated in this invention is the effective refractive index change per unit voltage, which is defined as: To calculate this objective function, it is necessary to consider a set of geometric parameter combinations X, under a bias voltage... and The effective refractive index n of the TE0 mode is obtained through the two-stage method described above. eff (V bias Bias voltage and The effective refractive index is denoted as follows: and Then two different bias voltages V biasThe difference in effective refractive index of the lower TE0 mode is divided by the difference in the two different bias voltages to obtain the change in effective refractive index per unit voltage, which is used as the objective function value. In the embodiments of the present invention, the two bias voltages are preferably... , .

[0056] Based on the above two-stage multiphysics coupling simulation method, the present invention can further provide a method for... Figure 1 The Bayesian optimization design method specifically employed in the AlScN piezoelectric driven optical waveguide shown includes the following steps: S1. Construct a geometric parameter combination X for all structural geometric parameters to be optimized in the optical waveguide. Randomly sample within the parameter design space Ω to obtain multiple sets of sampled values ​​for the geometric parameter combination X. Using the effective refractive index change under unit voltage as the objective function, perform the multiphysics coupling simulation for each set of sampled values ​​for the geometric parameter combination X, and calculate the objective function value based on the simulation results. This allows us to construct the initial training dataset.

[0057] It should be noted that the parameter design space Ω mentioned above should include the value range of each parameter in the geometric parameter combination X. The specific range can be determined based on prior knowledge or other constraint information. The six-dimensional parameter vector X = [a1, a2, b1, b2, h] corresponding to the first step is... e , h p ] T For example, the feasible region constraints for the six parameters in the parametric design space Ω are: h e ≥ 50 nm, h p ≥ 200 nm, the ranges of a1, a2, b1, b2 are set according to the process window.

[0058] It should be noted that each sample in the training dataset is composed of a combination of geometric parameters X and the objective function value. The data pairs constitute The Gaussian process surrogate model is obtained by training a Gaussian process regression model using these samples, and employs a squared exponential kernel function to describe the smooth correlation between input variables. This model provides posterior distributions of the predicted mean μ(X) and predicted standard deviation σ(X) for the entire parameter space.

[0059] S2. Based on the training dataset, with the geometric parameter combination X as input and the effective refractive index change under unit voltage as output, train a Gaussian process surrogate model to provide the predicted mean μ(X) and predicted standard deviation σ(X) for the objective function value of any set of geometric parameter combinations X in the parameter design space Ω.

[0060] S3. Select the maximum value of the objective function from the samples in the current training dataset as the current optimal objective function value, and use it to construct the expected improvement (EI) acquisition function. Then, based on the Gaussian process surrogate model, find the geometric parameter combination X with the largest expected improvement value in the parameter design space Ω as the next evaluation point.

[0061] It should be noted that the Expected Improvement (EI) acquisition function is a commonly used acquisition function in Gaussian process regression models, and its formula can be expressed as: in Let ξ be the current optimal objective function value, i.e., the maximum value of the objective function for all samples in the current training dataset; ξ is the exploration factor, and Φ(Z) and φ(Z) are the cumulative distribution function and probability density function of the standard normal distribution, respectively. Within the allowable design space Ω that satisfies the geometric feasibility constraint, the option with the maximum expected improvement value is selected, which yields the desired result. The largest parameter combination X is used as the evaluation point for the next simulation.

[0062] S4. Re-execute the multiphysics coupling simulation on the geometric parameter combination X, which is the next evaluation point, calculate the objective function value based on the simulation results, and then construct it as a new sample increment to update the training dataset, thereby retraining and updating the Gaussian process surrogate model.

[0063] S5. Repeat steps S3 and S4 until the preset convergence condition is met, and output the geometric parameter combination X that maximizes the objective function value.

[0064] It should be noted that the convergence condition in step S5 above can be either the objective function value stabilizing or reaching the preset upper limit of the number of iterations. Reaching either condition is considered the termination of the iteration, and after optimization, the optimal combination of geometric parameters and the corresponding modulation efficiency are output.

[0065] The optimization methods described in S1-S4 above use the geometric feature dimensions of the stepped contour to construct a multi-dimensional parameter vector, which is then used to parameterize the waveguide structure. A simulation framework sequentially coupled with electrostatics, piezoelectricity, mechanics, and optics is established. Combined with a Bayesian optimization algorithm using a Gaussian process as a surrogate model and the desired improvement as the acquisition function, the optimal structural parameters are searched in the multi-dimensional parameter space with a limited number of simulation evaluations, significantly reducing the computational overhead of traditional exhaustive scanning methods.

[0066] It should be noted that in the above optimization process, all candidate designs can meet the following feasibility constraints: maintain the symmetry of the step cladding profile with respect to the waveguide centerline; retain sufficient tolerance for oxide etching and piezoelectric film deposition, and the electrode thickness should not be too low to avoid excessive trace resistance; the piezoelectric layer thickness needs to ensure a breakdown voltage margin.

[0067] It should be noted that the above technical solution can be modified in various ways: regarding the piezoelectric actuation layer material, the scandium doping ratio x can be adjusted within the range of 0 to 0.5 to adapt to different process conditions and performance requirements; regarding the waveguide core layer, the silicon nitride thickness can be adjusted within the range of 300–800 nm to match different grating coupler designs or bending radius requirements; regarding the Bayesian optimized acquisition function, in addition to the desired improvement, other acquisition strategies such as the upper confidence bound (UCB) can also be adopted; other probabilistic regression models can also be used to replace the Gaussian process in the surrogate model; the dimension of the parameterized vector can be increased or decreased according to the actual structural complexity.

[0068] The following section applies the AlScN piezoelectric driven optical waveguide and the Bayesian optimization design method described in S1~S5 to a specific embodiment, thereby demonstrating its specific implementation process and technical effects.

[0069] Example 1: Design Method for Stepped-Clad Piezoelectric Elastic Waveguide Structure Based on Bayesian Optimization In this embodiment, for Figure 1 The optical waveguide based on AlScN piezoelectric drive shown utilizes a Bayesian optimization method to search for optimal geometric parameters of the stepped cladding stress-focusing structure, realizing a Bayesian optimization-based design method for stepped cladding piezoelectric elastic optical waveguide structures. For example... Figure 2 As shown, the flow of this design method is as follows: Step 1: Determine the basic waveguide parameters and material properties. The silicon nitride waveguide core layer 3 is made of silicon nitride, with a thickness of 400 nm, a width of 1.2 μm, and an operating wavelength of 1550 nm. The silicon dioxide lower cladding layer 2 is 3 μm thick silicon dioxide. The lower metal electrode 5 and the upper metal electrode 7 are made of Au. The AlScN piezoelectric layer 6 is made of Al. 0.6 Sc 0.4 N. In the above materials, the stress optical coefficient of silicon nitride is taken as C1 = 3.44 × 10⁻⁶. -12 Pa -1 C2 = -0.3×10 -12 Pa -1 The stress optical coefficient of silicon dioxide is taken as C1 = 0.65 × 10⁻⁶. -12 Pa -1 C2 = 4.2 × 10 -12 Pa -1 .

[0070] Step two, establish a parametric simulation model. Using the geometric parameter combination X = [a1, a2, b1, b2, h] from the aforementioned model of the first step... e , h p ] T Parametric modeling of the stepped cladding waveguide structure is performed, where the finite element model structure is as follows: Figure 1 As shown, the structure from bottom to top consists of: substrate 1, silicon dioxide lower cladding 2, silicon nitride waveguide core layer 3, and silicon dioxide upper cladding 4 with a stepped profile. A lower metal electrode 5, an AlScN piezoelectric layer 6, and an upper metal electrode 7 are sequentially deposited on the outer surface of the stepped profile. The overall structure of the optical waveguide is strictly symmetrical about the centerline of the silicon nitride waveguide. The finite element model jointly solves for four physical fields: electrostatics, piezoelectric structure, solid mechanics, and electromagnetic wave frequency domain. The boundary conditions are set as follows: a bias voltage of 10 V is applied to the upper electrode, the lower electrode is grounded, the remaining outer surfaces are electrically insulated, and the bottom surface of the silicon substrate is set as a fixed constraint. Therefore, according to the aforementioned two-stage multiphysics coupling simulation, each set of geometric parameter combinations X can be solved separately. =10 V and The effective refractive index of the TE0 mode under two bias voltage conditions of =0 V is denoted as follows: and Furthermore, based on the simulation results, the objective function can be defined as follows: Step 3, Initialize Sampling. Generate 50 sets of geometric parameter combinations within the feasible region of the six-dimensional parameter design space Ω using either Latin hypercube or random sampling methods. The specific feasible region constraints of the parameter design space Ω are: h e ≥ 50 nm, h p ≥ 200 nm, the ranges of a1, a2, b1, and b2 are set according to the process window. Perform multiphysics simulation in step two for each set of parameters to obtain 50 [parameters / values]. The data pairs are added as samples to the initial training dataset.

[0071] Step four: Train the Gaussian process surrogate model. Using 50 initial sample data sets from the training dataset, with the geometric parameter combination X as input, and the objective function value... For output, a Gaussian process regression model is trained, using a squared exponential kernel. The resulting Gaussian process surrogate model outputs the objective function value of any combination of geometric parameters X in the parameter space. The predicted mean μ(X) and predicted standard deviation σ(X).

[0072] Step 5, Bayesian optimization iteration. The following iterative process is executed repeatedly. In each iteration: (a) a set of candidate geometric parameters are densely sampled in the feasible region of the six-dimensional parameter design space Ω; (b) the expected improvement acquisition function EI(X) is calculated for each set of candidate geometric parameters. The function definition of EI(X) is as described above and will not be repeated here; (c) the candidate geometric parameter with the largest EI value is selected as the parameter combination for the next simulation evaluation, i.e., the next evaluation point; (d) the multiphysics coupling simulation is re-executed for the geometric parameter combination X used as the next evaluation point, and the objective function value is calculated based on the simulation results. Then, construct the new sample increment and update it to the training dataset; (e) retrain the updated Gaussian process surrogate model using the updated training dataset. Repeat the above iterative process for a total of 120 Bayesian optimization iterations.

[0073] Step 6: Convergence Determination and Result Output. Observe the objective function value. The evolution trend with the number of iterations. In this embodiment, the objective function tends to saturate after approximately 110 total evaluations (50 initial samplings plus approximately 60 optimization iterations), and the final convergence value is Δn. eff / V ≈ 2.26×10 -6 V -1 The optimal output geometric parameters are: a1 = 2.18 μm, a2 = 8.60 μm, b1 = 2.10 μm, b2 = 1.59 μm, h e = 50 nm, h p = 200 nm.

[0074] Based on this set of optimal geometric parameters, the performance of the optical waveguide is as follows: Simulations show that under a 10 V bias voltage applied to the upper metal electrode 7, the transverse principal stress at the waveguide center is... The peak pressure reached 23.22 MPa, a 62% improvement compared to the 14.36 MPa of the flat-top cladding reference structure. This corresponds to a modulation efficiency Δn. eff / V ≈2.26×10 -6 V -1 Half-wave voltage-length product V πL ≈ 0.342 V·m. Compared with the flat-top cladding reference structure, it achieves a 1.8-fold enhancement, effectively improving the modulation capability of the optical waveguide without increasing the driving voltage.

[0075] Example 2: Fabrication of an optimized stepped piezoelectric waveguide and simulation comparison of different structural material parameters This embodiment provides the device fabrication process based on the optimal geometric parameters obtained in Embodiment 1.

[0076] Step 1: Waveguide Platform Fabrication. Using a silicon wafer as substrate 1, a 3 μm thick silicon dioxide lower cladding layer 2 is deposited on the silicon substrate by thermal oxidation or plasma-enhanced chemical vapor deposition. A 400 nm thick silicon nitride film is grown on top of the silicon dioxide lower cladding layer 2 by low-pressure chemical vapor deposition. Then, the silicon nitride films on both sides are removed by photolithography and dry etching processes, leaving only the silicon nitride film in the central region. The silicon nitride is patterned into a 1.2 μm wide strip waveguide, i.e., the silicon nitride waveguide core layer 3.

[0077] Step 2: Silicon Dioxide Upper Cladding Deposition and Step Structure Etching. The silicon dioxide upper cladding 4 is deposited on the surface above the silicon dioxide lower cladding 2 and the silicon nitride waveguide core layer 3 using plasma-enhanced chemical vapor deposition. A symmetrical step profile is formed in the silicon dioxide upper cladding 4 directly above the waveguide using photolithography and dry etching processes. The entire step structure is symmetrical with respect to the waveguide centerline. In this embodiment, the geometric parameters of each structure are the optimized values ​​output in Example 1. The aforementioned step profile can also be achieved through alternative methods such as photolithography, multiple oxide deposition-planarization-etching processes, or single etching combined with tilted sidewall control.

[0078] Step 3: Lower Electrode Deposition. A 50 nm thick metal electrode layer is deposited on the outer surface of the silicon dioxide cladding 4 using electron beam evaporation, serving as the lower metal electrode 5. The lower metal electrode 5 must cover the entire outer surface of the step profile to maintain electrical continuity.

[0079] Step 4: AlScN piezoelectric layer deposition. A 200 nm thick Al layer is deposited above the lower electrode using reactive magnetron sputtering. 0.6 Sc 0.4 N piezoelectric thin film, as AlScN piezoelectric layer 6. Controlling the uniformity of sputtering target composition, nitrogen / argon atmosphere ratio and substrate temperature to maintain the c-axis orientation of wurtzite structure in the thin film, ensuring that the piezoelectric polarization direction is perpendicular to the substrate plane.

[0080] Step 5: Upper Electrode Deposition and Patterning. A 50 nm thick upper metal electrode 7 is deposited above the AlScN piezoelectric layer 6. The upper and lower electrodes are patterned by photolithography and etching to define the electrode regions and bring out the electrical connection pads.

[0081] In this embodiment, to compare the performance of different structural types and different scandium doping ratios, a coupled simulation comparison was performed on three structures: flat-top cladding structure, stepped cladding stress focusing structure (SCSS, i.e., the stepped profile in this embodiment), and SCSS structure with a 5° sidewall tilt angle. Simulation results are as follows Figure 3 as well as Figure 4 As shown in (a). Under a bias voltage of 10 V, the |Δn| of the flat-top cladding structure eff | is 1.26 × 10-5 |Δn of the stepped cladding stress-focusing structure eff | is 2.26 × 10 -5 The latter is 1.8 times that of the former. After introducing a 5° sidewall inclination angle, |Δn eff | is 2.3 × 10 -5 The change is no more than 5% compared to the right-angled step structure, indicating that the structure has a certain tolerance for the sidewall angle deviation common in micro-nano fabrication.

[0082] While keeping all the optimized step-covering geometric parameters unchanged in Example 2, the piezoelectric layer materials were respectively aluminum nitride and Al. 0.9 Sc 0.1 N (x=0.1), Al 0.75 Sc 0.25 N (x=0.25), Al 0.65 Sc 0.35 N (x=0.35), Al 0.6 Sc 0.4 N(x=0.4) and solve for it.

[0083] Simulation results are as follows Figure 4 As shown in (b), the modulation efficiency Δn eff / V increases monotonically with scandium concentration, and the Al used in this invention patent 0.6 Sc 0.4 The modulation efficiency of the N scheme is much greater than that of the aluminum nitride scheme (Δn). eff / V is 2.26×10 -6 V -1 and 5.37×10 -7 V -1 ), Δn eff The modulation efficiency maintains a good linear relationship with the bias voltage across all scandium contents. These results indicate that, under the same structural conditions, the modulation efficiency increases with increasing scandium doping ratio. The increase in modulation efficiency is more significant when the stepped coating structure is used in conjunction with a piezoelectric layer with a higher scandium content.

[0084] The embodiments described above are merely some preferred implementations of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. An optical waveguide based on AlScN piezoelectric driving, characterized in that, The optical waveguide uses a silicon wafer as a substrate (1). A silicon dioxide lower cladding layer (2) of equal thickness is deposited on the top surface of the substrate (1) to isolate optical leakage from the substrate. A silicon nitride waveguide core layer (3) is deposited in the central local area of ​​the top surface of the silicon dioxide lower cladding layer (2). A silicon dioxide upper cladding layer (4) of equal thickness is deposited on the top surface of the silicon nitride waveguide core layer (3) and the top surface of the silicon dioxide lower cladding layer (2) without silicon nitride waveguide core layer (3). After etching, the cross-sectional outer contour of the silicon dioxide upper cladding layer (4) is a stepped surface with a high middle and low sides along the width direction of the optical waveguide. A lower metal electrode (5), an AlScN piezoelectric layer (6), and an upper metal electrode (7) are sequentially covered on the stepped surface. The cross-section of the entire optical waveguide is mirror symmetrical along the center line.

2. The AlScN piezoelectric driven optical waveguide of claim 1, wherein, The step surface is a single step or multiple steps.

3. The AlScN piezoelectric driven optical waveguide of claim 2, wherein, The angle of each step in the stepped surface is 90° or close to 90°; preferably, the angle of each step in the stepped surface is 90°±5°.

4. The AlScN piezoelectric driven optical waveguide of claim 1, wherein, The thickness of the silicon dioxide lower cladding (2) is 2~5 μm; the thickness of the silicon nitride waveguide core layer (3) is 300~800 nm.

5. The AlScN piezoelectric driven optical waveguide of claim 1, wherein, The materials of the lower metal electrode (5) and the upper metal electrode (7) are gold (Au), copper (Cu), platinum (Pt) or aluminum (Al).

6. The AlScN piezoelectric driven optical waveguide of claim 1, wherein, The material of the AlScN piezoelectric layer (6) is scandium-doped aluminum nitride Al 1-x Sc x N, wherein 0 < x < 1; preferably, x = 0.

4.

7. The Bayesian optimization design method of an optical waveguide based on AlScN piezoelectric driving according to claim 1, characterized in that, include: S1. Construct all the structural geometric parameters to be optimized in the optical waveguide into a geometric parameter combination X, and randomly sample within the parameter design space Ω to obtain multiple sets of sampled values ​​of geometric parameter combination X; Using the effective refractive index change per unit voltage as the objective function, multiphysics coupling simulations are performed on the sampled values ​​of each set of geometric parameter combinations X. The objective function value is calculated based on the simulation results, thereby constructing the initial training dataset. S2. Based on the training dataset, with the geometric parameter combination X as input and the effective refractive index change under unit voltage as output, train a Gaussian process surrogate model to provide the predicted mean μ(X) and predicted standard deviation σ(X) for the objective function value of any set of geometric parameter combinations X in the parameter design space Ω. S3. Select the maximum value of the objective function from the samples in the current training dataset as the current optimal objective function value, and use it to construct the expected improvement (EI) acquisition function. Then, based on the Gaussian process surrogate model, find the geometric parameter combination X with the largest expected improvement value in the parameter design space Ω as the next evaluation point. S4. Re-execute the multiphysics coupling simulation on the geometric parameter combination X, which is the next evaluation point, calculate the objective function value based on the simulation results, and then construct it as a new sample increment to update the training dataset, thereby retraining and updating the Gaussian process surrogate model. S5. Repeat steps S3 and S4 until the preset convergence condition is met, and output the geometric parameter combination X that maximizes the objective function value.

8. The Bayesian optimization design method of claim 7, wherein, The step surface is a first-level step, and the step outline is formed by connecting the middle high step plane through the vertical step planes on both sides to the low step planes on both sides respectively; the geometric parameter combination X is composed of 6 structural geometric parameters of the optical waveguide cross section, namely: the step width of the low step plane, the full width of the optical waveguide, the step height of the high step plane relative to the low step plane, the height of the low step plane relative to the top surface of the substrate (1), the electrode thickness of the lower metal electrode (5) and the upper metal electrode (7), and the thickness of the AlScN piezoelectric layer (6).

9. The Bayesian optimization design method of claim 7 wherein, When performing the multiphysics coupling simulation on any set of geometric parameter combinations X, it is necessary to construct the finite element model of the optical waveguide based on the geometric parameter combination X, and then perform the simulation analysis in the following two-stage manner for two different bias voltages: The first stage performs static electromechanical analysis: In the electrostatic field, the current bias voltage is applied to the upper metal electrode (7), the lower metal electrode (5) is grounded, the remaining outer surface of the optical waveguide is set as an electrically insulating boundary, and the bottom surface of the substrate (1) is set as a fixed constraint; the electromechanical response of the AlScN piezoelectric layer (6) is described by the linear piezoelectric constitutive equation, and the stress field distribution in the waveguide structure is obtained by solving the linear piezoelectric constitutive equation by finite element numerical method. The second stage performs optical mode analysis: the stress field distribution obtained in the first stage is mapped to the refractive index distribution of the optical waveguide through the elastic-optical relationship, and the updated refractive index distribution is substituted into the electromagnetic wave frequency domain module to perform eigenmode analysis and extract the effective refractive index of the TE0 mode under the current bias voltage.

10. The Bayesian optimization design method of claim 7 wherein, The objective function is calculated by dividing the difference in effective refractive index of the TE0 mode under two different bias voltages by the difference between the two different bias voltages, and obtaining the change in effective refractive index per unit voltage as the objective function value.

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