Deep silicon etching detection method based on terahertz metasurface and deep learning

Abstract

The invention provides a deep silicon etching detection method based on a terahertz metasurface and deep learning, and the method comprises the steps: employing the terahertz metasurface which comprises a silicon substrate and a resonant structure; the silicon substrate is located at the bottom of the resonant structure and provides support; and the area around the resonant structure is etched to form a deep silicon etching area surrounding the resonant structure. The detection method comprises the following steps: acquiring metasurface reflection spectrums under different etching structure parameters through simulation software, and constructing a training data set; training a neural network to establish a mapping model of a reflection spectrum and an etching structure parameter; measuring the actual reflection spectrum of the metasurface to be measured; and inputting the actual reflection spectrum into the trained mapping model, and inverting the depth of the etching area and the transverse etching line width. Terahertz measurement can be carried out in the etching process, a real-time depth change curve in the etching process is obtained, the change of the etching rate is found in time, and a basis is provided for dynamic adjustment of process parameters.

Description

Technical Field

[0001] This invention relates to the field of semiconductor manufacturing process inspection technology, specifically to a deep silicon etching inspection method based on terahertz metasurfaces and deep learning. Background Technology

[0002] Deep reactive ion etching (DRIE) is a key process for fabricating high aspect ratio micro / nano structures, widely used in MEMS, TSV, and terahertz devices. However, precise monitoring of this process remains a significant challenge. Traditional process inspection methods, such as scanning electron microscopy (SEM) and white light interferometry, have obvious limitations: first, they are mostly offline inspections, unable to achieve real-time monitoring during the process; second, the inspection process often requires destructive treatment of the sample; and third, these methods have low inspection efficiency, failing to meet the high precision and high efficiency requirements of modern semiconductor manufacturing.

[0003] In recent years, terahertz waves have been explored for non-destructive testing due to their excellent penetration through dielectric materials and sensitivity to the dimensions of micro and nanostructures. Some studies have proposed using terahertz metasurfaces for non-invasive monitoring of the etching process. These methods typically use a specially designed metasurface as an independent monitoring sensor, fabricated on a wafer along with the device to be etched or the test structure. This type of method indirectly inverts the etching depth by correlating the electromagnetic response of the metasurface with the geometric parameters of the surrounding etched region. However, most of these methods rely on traditional numerical fitting algorithms, i.e., solving for the target parameters through extensive parameter scanning and simulation database matching. This method is not only computationally intensive and inefficient, but also has limited prediction accuracy when dealing with complex nonlinear relationships, making it difficult to meet the real-time requirements of high-precision etching control. Therefore, providing a fast and high-precision parameter inversion scheme for this metasurface monitor integrated into the process has become crucial for driving the technology towards practical application. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention proposes a deep silicon etching detection method based on terahertz metasurfaces and deep learning. Addressing the problems of non-in-situ, sample-damaging, and low-efficiency traditional deep silicon etching detection techniques, as well as the reliance on numerical fitting, high resource consumption, and insufficient accuracy of existing terahertz spectroscopy detection techniques, this invention proposes a deep silicon etching detection method based on terahertz metasurfaces and deep learning, aiming to achieve in-situ, non-destructive, high-precision, and high-efficiency process inspection.

[0005] To achieve the above objectives, this invention proposes a terahertz metasurface unit for deep silicon etching process inspection, comprising:

[0006] An integrally formed silicon body, the silicon body comprising a silicon substrate (3) and a resonant structure located on the silicon substrate (3);

[0007] The resonant structure includes four semi-cylinders (1) made of silicon material and a cross-shaped beam (2) made of silicon material. The cross-shaped beam (2) is located on top of the four semi-cylinders (1) and connects them into an integrated resonant structure.

[0008] The silicon substrate (3) is located at the bottom of the resonant structure, providing support for the resonant structure;

[0009] The area surrounding the resonant structure is etched to form a deep silicon etched region around the resonant structure.

[0010] The electromagnetic resonance characteristics of the resonant structure are sensitive to changes in the depth of the deep silicon etched region surrounding the resonant structure.

[0011] Furthermore, the height of the semi-cylinder (1) is 75 micrometers, the bottom diameter of the semi-cylinder (1) is 60 micrometers, the beam width of the cross-shaped beam (2) is 5 micrometers, and the thickness of the silicon substrate (3) is 225 micrometers.

[0012] Furthermore, the period of the metasurface unit is 135 micrometers.

[0013] A terahertz metasurface for deep silicon etching process detection is formed by periodically arranging the aforementioned terahertz metasurface units.

[0014] A detection method for deep silicon etching processes, applicable to the aforementioned terahertz metasurface used for deep silicon etching process detection, includes the following steps:

[0015] Step S1: Design and fabricate the terahertz metasurface as described in claim 4;

[0016] Step S2: Construct a simulation dataset. In the electromagnetic simulation software, parametrically adjust the depth and lateral etching linewidth of the etched region below the metasurface, perform full-wave simulation, collect the reflection spectrum and its corresponding structural parameters, and form a training dataset.

[0017] Step S3: Train the deep neural network. Using the simulation dataset obtained in step S2, perform supervised training on the Transformer-based neural network, with the reflection spectrum as input and the etching depth and lateral etching linewidth as output targets, and train until the model converges.

[0018] Step S4: Actual measurement and parameter inversion. During or after the actual etching process, the reflection spectrum of the integrated metasurface is measured using a terahertz time-domain spectrometer.

[0019] Step S5: Input the reflection spectrum data measured in step S4 into the neural network model trained in step S3, and directly output the predicted values ​​of etching depth and lateral etching linewidth to achieve quantitative and non-destructive inversion of process parameters.

[0020] Furthermore, the deep neural network adopts a neural network model based on the Transformer architecture.

[0021] Furthermore, the Transformer architecture includes a linear layer and two Transformer encoder layers, with reflection spectrum data as input and predicted etching depth and lateral etching linewidth as output.

[0022] Further, in step S2, the transverse etching linewidth is defined as the average of the bottom diameter of the semi-cylinder and the beam width of the cross-shaped beam in the metasurface unit.

[0023] Furthermore, the prediction accuracy of the etching depth is less than 1 micrometer, and the prediction accuracy of the lateral etching linewidth is less than 0.5 micrometers.

[0024] Furthermore, the detection method enables in-situ, non-destructive, and high-precision process inspection.

[0025] Compared with the prior art, the beneficial effects of the present invention are:

[0026] 1. This invention provides a deep silicon etching detection method based on terahertz metasurfaces and deep learning, enabling real-time monitoring during deep reactive ion etching (DRIE) processes without removing the sample from the etching equipment. By periodically performing terahertz measurements during etching, real-time depth change curves can be obtained, allowing for timely detection of changes in the etching rate and providing a basis for dynamic adjustment of process parameters. This in-situ monitoring capability is not available in traditional offline detection methods, significantly improving the real-time performance and response speed of process control.

[0027] 2. This invention provides a deep silicon etching detection method based on terahertz metasurfaces and deep learning. It employs terahertz waves for non-contact measurement, eliminating the need for sample cutting or damage. Terahertz waves exhibit excellent penetration into dielectric materials and are sensitive to changes in micro / nano structure dimensions, enabling detection without compromising sample integrity. This means that the same sample can be repeatedly measured, or subsequent processing can continue after etching, avoiding sample loss and cost waste caused by traditional destructive detection methods and improving the economics of the detection process.

[0028] 3. This invention provides a deep silicon etching detection method based on terahertz metasurfaces and deep learning. By establishing a nonlinear mapping relationship between the reflection spectrum and etching parameters through deep learning, it achieves extremely high prediction accuracy. Compared to traditional numerical fitting methods, this invention significantly improves prediction accuracy, accurately identifying minute changes in etching depth and lateral etching linewidth, meeting the stringent requirements of high-precision process control in modern semiconductor manufacturing. This high-precision detection capability helps reduce process deviations and improve product yield and consistency.

[0029] 4. This invention provides a deep silicon etching detection method based on terahertz metasurfaces and deep learning. It employs a trained neural network for inference, resulting in extremely fast prediction speed. This high efficiency enables the invention to meet the requirements of real-time monitoring and rapid feedback control, significantly improving detection efficiency and production cycle time, and reducing time costs in process development and production.

[0030] 5. This invention provides a deep silicon etching detection method based on terahertz metasurfaces and deep learning. It can monitor not only the vertical etching depth but also simultaneously predict the lateral etching linewidth, thereby comprehensively evaluating the quality of deep reactive ion etching (DRIE) processes. The lateral etching linewidth reflects the impact of the etching process on the overall size of the resonant structure and is an important indicator for evaluating sidewall quality and etching uniformity. By simultaneously monitoring these two key parameters, it is possible to more accurately determine whether the etching process has achieved the expected results, providing comprehensive data support for process optimization.

[0031] 6. This invention provides a deep silicon etching detection method based on terahertz metasurfaces and deep learning. The terahertz metasurface unit designed in this invention exhibits extremely high sensitivity to changes in etching depth. Simulation and experimental results show that even minute changes in etching depth can cause a significant shift in the resonant frequency. This high sensitivity is the physical basis for achieving high-precision detection, ensuring that even minute changes in etching depth can be accurately captured, providing a reliable sensing foundation for precision process control. Attached Figure Description

[0032] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0033] Figure 1 A terahertz metasurface whose resonant characteristic parameters are sensitive to structural geometry parameters;

[0034] Figures 2(a), 2(b), and 2(c) are schematic diagrams, top views, and front views of a terahertz metasurface unit, respectively.

[0035] Figure 3(a) and Figure 3(b) are simulation results of the reflection spectrum of the terahertz metasurface as a function of etching depth error ΔH and the curve of the normalized frequency point of the main mode of the terahertz metasurface as a function of etching depth error ΔH, respectively. ΔH is defined as the simulation setting deviation between the actual etching depth and the target etching depth (75 micrometers).

[0036] Figure 4 This is a diagram of the neural network architecture based on the Transformer architecture used in this invention to achieve high-precision parameter inversion;

[0037] Figure 5 The results show a comparison between the measured and simulated reflection spectra of the terahertz time-domain spectrometer.

[0038] Figure 6 This is a comparison of the accuracy of structural parameter prediction between Transformer-based neural networks and numerical fitting methods. Detailed Implementation

[0039] The technical solution of the present invention will be more clearly and completely explained below with reference to the accompanying drawings and through the description of preferred embodiments of the present invention.

[0040] like Figure 1 The image shows a terahertz metasurface whose resonant characteristic parameters are sensitive to the structural geometry.

[0041] Implementation Case 1 is described in conjunction with Figures 2(a), 2(b), and 2(c).

[0042] This embodiment details the specific structure of the terahertz metasurface unit sensitive to etching parameters used in this invention. The metasurface unit has a period of 135 micrometers, and each unit comprises a silicon substrate 3, four silicon semi-cylinders 1, and a silicon cross-shaped beam 2. The silicon substrate 3 has a thickness of 225 micrometers. The silicon semi-cylinders 1 are located on the substrate, with a height of 75 micrometers and a base diameter of 60 micrometers. The cross-shaped beam is located on top of the four semi-cylinders and connects them into an integrated resonant structure with a beam width of 5 micrometers.

[0043] Implementation Case 2 is described in conjunction with Figures 3(a) and 3(b).

[0044] This case study demonstrates the simulation verification of metasurface sensitivity. Figures 3(a) and 3(b) show the simulation results of the terahertz metasurface reflection spectrum as a function of etching depth error ΔH, and the curve of the normalized frequency point of the terahertz metasurface master mode as a function of etching depth error ΔH, respectively. Here, ΔH is defined as the simulation setting deviation between the actual etching depth and the target etching depth (75 micrometers). Figure 3(a) shows the overall shift trend of the reflection spectrum with the etching depth error, while Figure 3(b) quantitatively demonstrates the high linearity and high sensitivity between the master resonant frequency and the etching depth error. When the etching depth changes by 20 micrometers, its resonant frequency shifts by more than 100 GHz, verifying its effectiveness as a process monitoring sensor.

[0045] Combination Figure 4 and Figure 5 Description of Implementation Case 3

[0046] This case study demonstrates the training and experimental validation of a neural network model. We use simulation data generated by parametric scanning to train the network, establishing a precise mapping between the spectrum and structural parameters. During the simulation data construction process, to simplify the model and establish a quantitative relationship between the reflection spectrum and the degree of lateral etching, the lateral etching linewidth is defined as an equivalent parameter, set to the average of the base diameter of the semi-cylinder and the beam width of the crossbeam in the metasurface unit. By varying the etching depth and the value of this lateral etching linewidth within the process variation range, a training dataset containing various parameter combinations and their corresponding reflection spectra is generated. Using this dataset, a neural network based on the Transformer architecture is trained, and the model is as follows: Figure 4 As shown, it contains one linear layer and two Transformer encoder layers. The input is reflection spectrum data, and the output is the predicted etching depth and lateral etching linewidth.

[0047] To verify its actual performance, the metasurface from Case 1 was prepared and tested, and multiple sets of measured reflection spectra were obtained. Figure 5 The black solid line in the figure represents one set of measured reflection spectra that fit the simulation results very well. The measured spectra are input into the trained neural network model and prediction is performed using traditional numerical fitting methods. Figure 6 This figure compares the prediction accuracy of two methods for predicting etching parameters: a Transformer-based neural network architecture and numerical fitting. The area enclosed by the black dashed box represents the high-precision region, specifically the range where the prediction accuracy for lateral etching linewidth is less than 0.5 micrometers and the prediction accuracy for longitudinal etching linewidth is less than 1 micrometer. The vast majority of the data points corresponding to the prediction errors of the Transformer for etching depth and lateral etching linewidth fall within this high-precision region, and their distribution is more concentrated. This indicates that its accuracy is significantly better than that of the numerical fitting method.

[0048] As a specific embodiment, this invention uses standard semiconductor processes to fabricate terahertz metasurface units. A high-resistivity silicon wafer with a resistivity >5000 Ω·cm and a thickness of 225 μm is selected as the substrate. First, the silicon wafer is sequentially immersed in acetone, isopropanol, and deionized water for ultrasonic cleaning, 5 minutes each time. Then, it is dried with nitrogen and baked at 120°C for 10 minutes to remove moisture. Positive photoresist is then spin-coated onto the cleaned silicon wafer surface. The spin-coating speed is initially 500 rpm for 5 seconds for spreading, followed by 4000 rpm for 30 seconds to form a uniform film with a photoresist thickness of approximately 1.4 μm. After soft baking on a hot plate at 110°C for 90 seconds, ultraviolet exposure is performed using a mask aligned with an exposure machine at an exposure dose of 12 mJ / cm². 2 The exposure pattern consists of a periodically arranged array of circular openings, each with a diameter of 135 μm and a period of 135 μm, covering the entire wafer except for the 5 mm edge. After exposure, the wafer is developed in a developer solution for 60 seconds, rinsed with deionized water, and dried with nitrogen gas.

[0049] The first deep reactive ion etching (DRIE) step employed the Bosch process. SF6 and O2 were used as etching gases at flow rates of 130 sccm and 13 sccm, respectively, with an RF power of 600 W, a bias power of 15 W, and a chamber pressure of 25 mTorr. Each etching cycle lasted 7 seconds. The passivation step used C4F8 as the passivation gas at a flow rate of 85 sccm, an RF power of 600 W, a bias power of 0 W, and a chamber pressure of 25 mTorr. Each passivation cycle lasted 5 seconds. After approximately 60 minutes of etching, a deep trench of approximately 150 μm was formed on the silicon substrate. The remaining silicon pillars formed the desired semi-cylindrical structure with a height of 75 μm. Following etching, residual photoresist was removed using oxygen plasma at an oxygen flow rate of 200 sccm, an RF power of 300 W, and a processing time of 10 minutes.

[0050] To form the cross-shaped beam, a second photolithography process is performed. Photoresist is recoated onto the silicon wafer surface, and a second mask is used for alignment and exposure. The second mask pattern is a cross shape, with the center of each cross aligned with the center of the semi-cylinder. The cross beam width is 5 μm, and the alignment accuracy is ±2 μm. After development, shallow reactive ion etching is performed using a low RF power of 200 W and a high chamber pressure of 50 mTorr, an SF6 flow rate of 50 sccm, an O2 flow rate of 5 sccm, an etching depth of 5 μm, an etching rate of approximately 0.5 μm / min, and a total time of approximately 10 min. After etching, the photoresist is removed again, followed by RCA cleaning.

[0051] The fabricated metasurface units were examined using a scanning electron microscope. The semi-cylindrical height was 75±2 μm, the cross-shaped beam width was 5±0.5 μm, the surface roughness was <100 nm, and the sidewall tilt angle was 88-90°. Approximately 200,000 metasurface units were successfully fabricated on a 4-inch wafer, arranged in a periodic array, with a yield >95%. As shown in Figures 2(a), 2(b), and 2(c), the fabricated metasurface units exhibit a clear semi-cylindrical and cross-shaped beam structure.

[0052] The definition of "lateral etching linewidth" requires special explanation. In deep reactive ion etching (DRIE), due to the lateral etching effect and sidewall tilt, the actual etched structural dimensions deviate from the design values. The "lateral etching linewidth" defined in this invention is an equivalent parameter used to characterize the comprehensive influence of the etching process on the lateral dimensions of the metasurface unit. Specifically, it is calculated by averaging the bottom diameter of the etched semi-cylinder and the beam width of the etched crossbeam. For example, if the ideal design is a semi-cylinder diameter of 135 μm and a crossbeam width of 5 μm, then the ideal lateral etching linewidth is (135 + 5) / 2 = 70 μm. If the actual measured etched dimensions are a semi-cylinder diameter of 133 μm and a crossbeam width of 4 μm, then the actual lateral etching linewidth is (133 + 4) / 2 = 68.5 μm. This parameter reflects the influence of the etching process on the overall dimensions of the resonant structure, and consequently, the electromagnetic resonant frequency of the metasurface.

[0053] The sensitivity of the metasurface was verified using full-wave simulation software. In the simulation model, periodic boundary conditions were set for the metasurface elements in the x and y directions, and open boundary conditions were set in the z direction. The excitation source was a plane wave, incident perpendicularly from the positive z direction, linearly polarized, with a frequency range of 0.2-1.8 THz. The relative permittivity of silicon was set to 11.68, and the loss tangent was 0.001. The mesh was adaptively refined with a minimum mesh size of 0.5 μm. Parametric scanning etching depth ranged from 30 μm to 100 μm, with a step size of 10 μm. As shown in Figure 3, when the etching depth increased from 50 μm to 60 μm, the main resonant peak frequency shifted from approximately 0.72 THz to approximately 0.67 THz, a frequency shift >50 GHz, corresponding to a sensitivity >5 GHz / μm.

[0054] A complete deep silicon etching detection system includes a terahertz metasurface, a terahertz time-domain spectrometer, and a data processing unit. This embodiment uses a commercially available terahertz time-domain spectrometer with a frequency range of 0.1-3.0 THz, an effective measurement range of 0.2-1.8 THz, a frequency resolution of 7.5 GHz, and a dynamic range >60 dB. The scanning time window is 120 ps, ​​the time step is 0.1 ps, 1200 data points are collected per scan, and the average is performed 32 times, with a single measurement time of approximately 2 seconds. The measurement uses a reflection mode, with the terahertz wave incident perpendicularly onto the metasurface at an incident angle of 0°±1°. The polarization mode is linear polarization, with the electric field direction parallel to one arm of the crossbeam. The focused spot diameter is approximately 3 mm, covering approximately 20 × 20 metasurface units. The distance between the sample and both the terahertz transmitter and receiver is 20 cm. To reduce moisture absorption, the entire optical system is protected by nitrogen gas at a flow rate of 5 L / min, with a relative humidity <5%. The ambient temperature is maintained at 23±1℃. Before each sample measurement, a reference signal is measured. The reference sample is an unetched high-resistivity silicon wafer of the same thickness. The frequency domain signal is obtained through Fast Fourier Transform, and the reflectivity of the sample is equal to the amplitude of the sample's frequency domain signal divided by the amplitude of the reference frequency domain signal. Reflectance spectrum data in the range of 0.2-1.8 THz are extracted and input into the neural network model.

[0055] To train the deep neural network, a training dataset was constructed using parametric simulations. The longitudinal etching depth was scanned from 10 μm to 120 μm with a step size of 2 μm. The lateral etching linewidth was scanned from 62 μm to 72 μm with a step size of 0.5 μm. In the simulation, the lateral etching linewidth was modeled by simultaneously adjusting the semi-cylinder diameter and the crossbeam width. A lateral etching linewidth of 70 μm corresponds to the ideal case without lateral etching, where the semi-cylinder diameter is 135 μm and the crossbeam width is 5 μm. Training samples were generated through parametric scanning, with small-amplitude random perturbations added near each parameter point to generate multiple variants, simulating noise in actual measurements. The final training dataset contained thousands of samples, covering the complete parameter space of the etching process. Min-max normalization was applied to the reflectance spectrum data, mapping the value of each spectrum to the range of 0-1. The corresponding label data was also normalized, with the longitudinal etching depth and lateral etching linewidth normalized to the 0-1 range respectively. The dataset was randomly divided into a training set (70%), a validation set (15%), and a test set (15%).

[0056] This invention employs a neural network model based on the Transformer architecture. For example... Figure 4As shown, the network architecture includes an input layer, a Transformer encoder layer, and an output layer. The input layer receives normalized reflectance spectrum data, maps the spectrum data to a high-dimensional feature space through a linear embedding layer, and then adds positional encoding. The Transformer encoder layer is the core of the network; this invention uses two cascaded Transformer encoder layers. Each encoder layer contains a multi-head self-attention mechanism and a feedforward neural network. The number of attention heads is set to 8, the hidden layer dimension is 512, the feedforward network dimension is 2048, and the activation function is GELU. The dropout ratio is 0.1. The output layer maps the output of the Transformer encoder to the target parameter space, first performing global average pooling, and then obtaining the final prediction through two fully connected layers. The output 2D vector corresponds to the normalized vertical etching depth and horizontal etching linewidth, respectively. The training process uses mean squared error as the loss function, the optimizer is Adam, the initial learning rate is 0.0001, and the batch size is 32. During training, the validation set loss is monitored, and training is stopped early when the validation loss no longer decreases. Training is performed on a high-performance computer configured with a GPU. After training, the model performance was evaluated on the test set. The prediction errors for both vertical etching depth and horizontal etching linewidth were within the high accuracy range. Figure 5 As shown, compared with traditional numerical fitting methods, the Transformer-based neural network method significantly improves both prediction accuracy and computational efficiency. The advantage of the Transformer architecture lies in its self-attention mechanism, which can adaptively learn the complex correlations between different frequency points in the spectral data.

[0057] As a specific embodiment, to verify the practical application effect of the method of the present invention, a series of test samples with different etching depths were prepared. Terahertz metasurfaces were prepared using the method described above, and then deep reactive ion etching (DRIE) was performed for different durations to obtain samples with different etching depths. Terahertz reflection spectrum measurements were performed on each sample using the detection system described above. The measured reflection spectrum was input into a trained neural network model, which outputs the predicted etching depth and lateral etching linewidth. To verify the accuracy of the prediction, some samples were cut and the actual etching depth and structural dimensions were directly measured using a scanning electron microscope (SEM) as reference values. For the sample with an etching time of 0 min, the method of the present invention predicted an etching depth of 0.5 μm, and the SEM measurement was 0 μm. For the sample with an etching time of 10 min, the predicted value was 24.3 μm, the SEM measurement was 24.8 μm, and the error was 0.5 μm. For the sample with an etching time of 20 min, the predicted value was 48.6 μm, the SEM measurement was 49.2 μm, and the error was 0.6 μm. For a sample etched for 30 minutes, the predicted value was 72.8 μm, the SEM measured value was 73.5 μm, and the error was 0.7 μm. For a sample etched for 40 minutes, the predicted value was 96.4 μm, the SEM measured value was 97.3 μm, and the error was 0.9 μm. For a sample etched for 50 minutes, the predicted value was 119.5 μm, the SEM measured value was 120.8 μm, and the error was 1.3 μm. The prediction error for all tested samples was <1.5 μm, demonstrating that the method of this invention can achieve high-precision deep silicon etching detection. The standard deviation of the prediction results for the same sample measured at different locations was <0.5 μm, indicating that the method has good repeatability. The total time for each measurement and prediction was <3 seconds, meeting the requirements for real-time monitoring. Compared with traditional detection methods such as scanning electron microscopy and white light interferometry, the method of this invention is non-destructive, does not require cutting or damaging the sample, and can perform multiple measurements on the same sample or in-situ monitoring during the etching process.

[0058] The in-situ detection capability of the method of this invention was further tested. A silicon wafer integrated with a terahertz metasurface was placed in a DRIE device. During the etching process, etching was paused every 5 minutes, the sample was removed for terahertz measurement, and then placed back to continue etching. Real-time depth change curves of the etching process were obtained. The results showed that the etching depth increased approximately linearly with time, with an etching rate of approximately 2.4 μm / min. The etching rate was slightly lower (approximately 2.0 μm / min) in the first 10 minutes of etching, and also decreased in the later stages. This information is very valuable for optimizing etching process parameters.

[0059] The prediction of the lateral etching linewidth was also verified. Three typical samples were selected, and the diameter of the semi-cylinder base and the width of the crossbeam were measured from the side using SEM. The true value of the lateral etching linewidth was calculated. For sample 1, the semi-cylinder diameter was 135.2 μm, the crossbeam width was 5.1 μm, the true value of the lateral etching linewidth was 70.15 μm, and the predicted value by the method of this invention was 70.3 μm, with an error of 0.15 μm. For sample 2, the semi-cylinder diameter was 133.8 μm, the crossbeam width was 4.3 μm, the true value of the lateral etching linewidth was 69.05 μm, the predicted value was 68.8 μm, with an error of 0.25 μm. For sample 3, the semi-cylinder diameter was 131.5 μm, the crossbeam width was 3.2 μm, the true value of the lateral etching linewidth was 67.35 μm, the predicted value was 67.7 μm, with an error of 0.35 μm. The prediction errors are all <0.5μm, proving that the present invention can accurately predict both the longitudinal etching depth and the lateral etching linewidth at the same time.

[0060] To investigate the influence of metasurface unit structure parameters on detection performance, several variant structures were designed and simulated. First, the effect of the semi-cylinder height was studied. Keeping other parameters constant, three structures with semi-cylinder heights of 60 μm, 75 μm, and 90 μm were designed. Simulation results show that a higher semi-cylinder height increases sensitivity to changes in etching depth, but also increases fabrication difficulty. A semi-cylinder height of 75 μm achieves a good balance between sensitivity and fabrication feasibility. Three structures with cross-shaped beam widths of 3 μm, 5 μm, and 7 μm were also designed. Simulation results show that a smaller beam width increases sensitivity, but excessively small beam widths lead to insufficient mechanical strength and fabrication difficulties. A beam width of 5 μm achieves a good balance between sensitivity, mechanical strength, and fabrication process. The effect of the unit cell period was also investigated. Three structures with periods of 120 μm, 135 μm, and 150 μm were designed. A smaller period increases sensitivity, but excessively small periods can lead to enhanced coupling between adjacent units, potentially affecting the stability of the resonance characteristics. A period of 135 μm is a preferred choice, ensuring sufficient sensitivity while avoiding strong coupling between adjacent units. These findings provide guidance for the structural design of metasurface units. In practical applications, structural parameters can be flexibly adjusted according to the specific etching depth detection range, accuracy requirements, and fabrication conditions. The technical solution of this invention is not limited to specific parameter values; other parameter combinations within a reasonable range that can achieve a high-sensitivity response to changes in etching depth are also within the scope of protection of this invention.

[0061] It should be further explained that the terahertz metasurface unit described in this invention is a monolithically formed silicon structure, with the four semi-cylinders and the cross-shaped beam formed simultaneously through a single deep reactive ion etching (DRIE) process. In actual fabrication, different mask designs and etching strategies can be employed depending on the specific process conditions and equipment capabilities. For example, in a preferred embodiment, a composite pattern mask containing the positions of the four semi-cylinders and the cross-shaped beam can be designed, allowing the entire resonant structure to be fabricated in a single photolithography and deep reactive ion etching process, avoiding the precision loss and process complexity caused by secondary alignment. This integrated fabrication method ensures precise connection between the four semi-cylinders and the cross-shaped beam, forming a unified resonant structure, thereby guaranteeing the metasurface's electromagnetic resonance characteristics and high sensitivity to changes in etching depth.

[0062] When constructing the neural network training dataset, special attention needs to be paid to the definition and parameterization method of the lateral etching linewidth. As mentioned earlier, the lateral etching linewidth is defined as the average of the diameter of the semi-cylinder's base and the width of the crossbeam. In electromagnetic simulation, different lateral etching scenarios can be simulated by simultaneously adjusting these two geometric parameters. Specifically, when the design values ​​are a semi-cylinder diameter of 60 μm and a crossbeam width of 5 μm, the ideal lateral etching linewidth is 32.5 μm. If lateral etching causes the semi-cylinder diameter to decrease to 58 μm and the crossbeam width to decrease to 4 μm, the lateral etching linewidth becomes 31 μm. When constructing the simulation dataset, the lateral etching linewidth can be scanned within the range of 28 μm to 38 μm. Each adjustment simultaneously modifies both the semi-cylinder diameter and the crossbeam width, ensuring that their average value equals the target lateral etching linewidth value. This parameterization method can realistically reflect the impact of lateral etching on the overall structure in deep reactive ion etching processes.

[0063] Regarding the specific implementation of the neural network model, the Transformer-based architecture adopted in this invention has several advantages. First, the Transformer's self-attention mechanism can capture the long-range dependencies between different frequency points in the reflection spectrum, which is crucial for understanding the shape, position, and intensity variations of resonance peaks. Second, the introduction of positional encoding enables the model to perceive the sequential information of the spectral data, thereby better identifying resonance modes. Third, the multi-head attention mechanism allows the model to learn spectral features from multiple perspectives, improving the model's expressive power and generalization performance. In the specific implementation, the linear embedding of the input layer maps the spectral data from the original dimension to a 512-dimensional hidden space. The two Transformer encoder layers each contain eight attention heads, and each encoder layer is followed by a 2048-dimensional feedforward network. The output layer aggregates sequential features through global average pooling, and then maps the features to a 2-dimensional output space through two fully connected layers, corresponding to the etching depth and lateral etching linewidth, respectively. During training, the Adam optimizer is used with a learning rate of 0.0001, a batch size of 32, and an early stopping strategy is employed to prevent overfitting.

[0064] In practical applications, the detection method of this invention can be integrated with deep reactive ion etching (DRIE) equipment to achieve true in-situ real-time monitoring. The specific integration scheme includes: installing a terahertz measurement window outside the etching chamber, using a terahertz-transparent material (such as high-density polyethylene) as the observation window to ensure vacuum sealing while allowing terahertz waves to pass through; periodically pausing the plasma during etching to perform terahertz scanning of the wafer through the measurement window; inputting the obtained reflection spectrum into a pre-trained neural network model in real time to obtain the current etching depth and lateral etching linewidth within seconds; and dynamically adjusting etching process parameters, such as RF power, gas flow rate, and pressure, based on the monitoring results to achieve precise control of the etching process. This combination of in-situ monitoring and feedback control significantly improves the repeatability and yield of the DRI process, making it particularly suitable for manufacturing high aspect ratio structures and high-precision devices. The advantages of this invention also lie in its adaptability to different etching conditions. Changes in DRI process parameters, such as temperature, pressure, and power, can lead to changes in the etching rate and lateral etching extent. Traditional monitoring methods often require recalibration for each process condition, while the deep learning method of this invention, by including simulation samples under various process conditions in the training dataset, can learn the intrinsic relationship between changes in process parameters and spectral variations. Even when actual process conditions shift, the trained model can still accurately predict etching parameters, demonstrating good robustness. Furthermore, if it is necessary to extend to new process conditions or parameter ranges, only the corresponding simulation data needs to be supplemented and incremental training performed, without modifying the entire algorithm framework, greatly improving the scalability of the method.

[0065] This invention can also employ advanced techniques to further enhance performance. For example, data augmentation techniques can be used to simulate various interference factors in actual measurements by superimposing different types of noise (such as Gaussian noise, Poisson noise, etc.) onto the simulated spectrum, making the trained model more robust to noise. Ensemble learning methods can be used to train multiple models with different initializations or architectures, and then their prediction results can be weighted and averaged to obtain more stable and accurate predictions. Uncertainty quantification techniques can also be introduced, enabling the model to output not only the predicted value but also the confidence interval of the prediction, providing more comprehensive information for process control. The application of these techniques can further enhance the reliability and practicality of the method of this invention in actual production environments.

[0066] The technical solution of this invention also has good scalability. Although the specific embodiments describe applications in the terahertz band, the same principle can be extended to other electromagnetic bands. By scaling the size of the metasurface units proportionally, the operating frequency can be adjusted to the microwave, millimeter-wave, infrared, or visible light bands. For example, reducing all dimensions by a factor of 10 can raise the resonant frequency to the infrared band for monitoring finer micro / nano fabrication processes. Similarly, scaling up the dimensions allows the method to be applied to macroscopic structural inspection. Furthermore, the framework of this invention is not only applicable to deep silicon etching but also to other micro / nano fabrication processes requiring precise monitoring, such as plasma-enhanced chemical vapor deposition, atomic layer deposition, and electron beam lithography. By designing corresponding sensitive metasurface structures according to specific processes and constructing corresponding training datasets, high-precision monitoring of the process can be achieved.

[0067] The above-described specific embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Various modifications, substitutions, and improvements made by those skilled in the art to the technical solutions of the present invention based on the provided textual description and drawings, without departing from the design concept and spirit of the present invention, should all fall within the scope of protection of the present invention. The scope of protection of the present invention is determined by the claims.

Claims

1. A terahertz metasurface unit for deep silicon etching process detection, characterized in that, The application relates to a terahertz metasurface unit, comprising: a one-piece silicon body, which comprises a silicon substrate (3) and a resonant structure located on the silicon substrate (3); wherein the resonant structure comprises four semicylinders (1) made of silicon material and a cross-shaped beam (2) made of silicon material, the cross-shaped beam (2) is located on the top of the four semicylinders (1) and connects the four semicylinders (1) into an integrated resonant structure; the silicon substrate (3) is located at the bottom of the resonant structure and provides support for the resonant structure; a region around the resonant structure is etched to form a deep silicon etching region surrounding the resonant structure; the electromagnetic resonance characteristics of the resonant structure are sensitive to the depth variation of the deep silicon etching region surrounding the resonant structure.

2. The THz metasurface unit for deep silicon etching process detection according to claim 1, characterized in that, The height of the semicylinders (1) is 75 microns, the diameter of the bottom surface of the semicylinders (1) is 60 microns, the beam width of the cross-shaped beam (2) is 5 microns, and the thickness of the silicon substrate (3) is 225 microns.

3. The THz metasurface unit for deep silicon etching process detection according to claim 1, characterized in that, The period of the metasurface unit is 135 microns.

4. A terahertz metasurface for deep silicon etching process detection, characterized in that, The terahertz metasurface unit according to any one of claims 1-3 is arranged in a periodic array.

5. A detection method for deep silicon etching process, suitable for the terahertz metasurface for deep silicon etching process detection according to claim 4, characterized in that, The application further relates to a detection method, comprising the following steps: Step S1: designing and preparing the terahertz metasurface according to claim 4; Step S2: constructing a simulation data set, in an electromagnetic simulation software, parameterizing the depth of the etching region below the metasurface and the lateral etching line width, performing full-wave simulation, collecting the reflection spectrum and the corresponding structure parameters to form a training data set; Step S3: training a deep neural network, using the simulation data set obtained in step S2, supervising the training of the neural network based on the Transformer, taking the reflection spectrum as the input and taking the etching depth and the lateral etching line width as the output target, and training until the model converges; Step S4: actual measurement and parameter inversion, using a terahertz time-domain spectrometer to measure the reflection spectrum of the integrated metasurface during the actual etching process or after the process; Step S5: inputting the reflection spectrum data measured in step S4 into the neural network model trained in step S3 to directly output the predicted values of the etching depth and the lateral etching line width, thereby realizing quantitative and non-destructive inversion of the process parameters.

6. The method of claim 5, wherein the method is used for a deep silicon etching process. The deep neural network adopts a neural network model based on the Transformer architecture.

7. The method of claim 6, wherein the method is used for a deep silicon etching process. The Transformer architecture comprises a linear layer and two Transformer encoder layers, the input is the reflection spectrum data, and the output is the predicted etching depth and lateral etching line width.

8. The method of claim 5, wherein the method is used for a deep silicon etching process. In step S2, the lateral etching line width is defined as the average value of the diameter of the bottom surface of the semicylinder and the beam width of the cross-shaped beam in the metasurface unit.

9. The method of claim 5, wherein the method is used for a deep silicon etching process. The prediction accuracy of the etching depth is less than 1 micron, and the prediction accuracy of the lateral etching line width is less than 0.5 micron.

10. The method of claim 5, wherein the method is used for a deep silicon etching process. The detection method realizes in-situ, non-destructive and high-precision process detection.

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