Etching uniformity optimization method based on plasma density adjustment

Abstract

The invention relates to the technical field of semiconductor processing control, and provides an etching uniformity optimization method based on plasma density adjustment, which comprises the following steps of: 1, acquiring plasma density and etching rate, generating a coordinate system by taking the center of a wafer as an original point and partitioning along the radial direction, mapping the plasma density and the etching rate to the coordinate system, obtaining a continuous space distribution function; 2, constructing a correlation model, and fitting the correlation model by adopting a nonlinear least square method to obtain a relationship between the plasma density and the etching uniformity; and step 3, constructing a multivariable prediction model, monitoring the plasma density in etching, and when the plasma density distribution exceeds a preset threshold value, feeding back and adjusting plasma density control parameters in real time by the multivariable prediction model. According to the method, the relation between the plasma density and the etching uniformity is quantified, then the plasma density space distribution is monitored to predict the etching uniformity, and the plasma distribution deviation is dynamically adjusted to improve the etching uniformity.

Description

Technical Field

[0001] This invention relates to the field of semiconductor processing control technology, specifically to an etching uniformity optimization method based on plasma density adjustment. Background Technology

[0002] Semiconductor manufacturing processes are extremely complex, involving the precise control of numerous key parameters, such as temperature, pressure, gas flow rate, radio frequency power, and plasma density. Even subtle changes in these parameters directly impact the quality, yield, and production cost of the final product. To achieve high-quality, high-efficiency, and low-cost semiconductor manufacturing, precise control and optimization of equipment chamber operating parameters are crucial. For example, patent CN116844955A discloses an etching method for semiconductor devices. This method uses a gas containing a high proportion of etching elements and a low proportion of protective elements in the first etching stage to rapidly form open trenches, balancing etching rate with initial sidewall protection. In the second etching stage, the proportion of etching elements is reduced, the proportion of protective elements is increased, and the reaction chamber pressure is adjusted to enhance sidewall verticality and reduce damage to the underlying film. However, the physical field state within the chamber is dynamically changing during actual etching. This etching method only optimizes the etching effect through static gas composition ratios and fixed process parameters, lacking real-time monitoring and dynamic adjustment capabilities, resulting in extremely limited effectiveness.

[0003] Based on this, the technical problem to be solved by this application is: how to solve the problem of difficulty in dynamically controlling plasma density to improve etching uniformity. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides an etching uniformity optimization method based on plasma density adjustment. This method constructs a corresponding correlation model by quantifying the relationship between plasma density and etching uniformity. Then, it predicts etching uniformity by real-time monitoring of the spatial distribution of plasma density in the etching process. When deviations occur, feedback is provided to adjust and correct the plasma distribution deviations in real time, thereby addressing the dynamic fluctuations in plasma density during the etching process and improving etching uniformity.

[0005] The technical solution of this invention is:

[0006] A method for optimizing etching uniformity based on plasma density adjustment, characterized by comprising the following steps:

[0007] Step 1: Collect historical plasma density and etching rate data, generate a coordinate system with the wafer center as the origin and radial partitions, and map the collected plasma density and etching rate data to the coordinate system to obtain a continuous spatial distribution function.

[0008] Step 2: Construct a correlation model using a continuous spatial distribution function, fit the correlation model using the nonlinear least squares method, calculate the coefficient of determination and wafer internal uniformity, and statistically verify the correlation model to obtain the relationship between plasma density and etching uniformity.

[0009] Step 3: Construct a multivariate prediction model to monitor the spatial distribution of plasma density in the etching process in real time. When the plasma density distribution exceeds the preset threshold, the multivariate prediction model provides feedback and adjusts the plasma density control parameters in real time.

[0010] Preferably, step 1 includes the following steps:

[0011] Step 1A: Measure the plasma density using a Langmuir probe array;

[0012] The etching depth at various points on the wafer surface is measured using an atomic force microscope, and the etching rate is calculated and expressed as: ;

[0013] in, Etching depth; t represents the etching rate; t represents the etching time.

[0014] Step 1B: Based on the plasma density and etching rate, a coordinate system is generated with the wafer center as the origin and radially partitioned. The collected plasma density and etching rate are mapped to the coordinate system. A continuous spatial distribution function is generated by data alignment using a bicubic spline interpolation algorithm. The continuous spatial distribution function is expressed as:

[0015] .

[0016] in, The plasma density; Etching rate; , All are basis functions; , All are fitting coefficients.

[0017] Preferably, step 2 includes the following steps:

[0018] Step 2A: Construct a correlation model based on the continuous spatial distribution function. The key model is represented as follows:

[0019] .

[0020] in, The rate constant is related to the chemical properties of the gas. Density sensitivity index The activation energy (eV) for the etching reaction. The Boltzmann constant is approximately 8.617 × 10⁻⁵ eV / K. To determine the electron temperature based on the probe IV characteristic curve, Non-plasma contribution items;

[0021] Step 2B: Fit the correlation model using the nonlinear least squares method. The fitted model is expressed as:

[0022] .

[0023] in, This represents the measured value of the etching rate; This is a predicted value for the etching rate;

[0024] Step 2C: Calculate the coefficient of determination and inhomogeneity within the wafer to statistically validate the correlation model, and calculate the effect of plasma density gradient on etching uniformity. Perform sensitivity analysis and output the key sensitive regions, represented as follows:

[0025] , .

[0026] in, This is the sensitivity coefficient of plasma density to etching uniformity; It represents a density range; Number of partitions; The RF amplitude in the k-th region; Let be the RF phase angle of the k-th region; The plasma wavelength and , The speed of light; For RF frequency; It is the characteristic angular frequency of plasma.

[0027] Preferably, step 3 includes the following steps:

[0028] Step 3A: Set the target value for plasma density distribution, monitor the plasma density distribution during the etching process, and calculate the deviation between the real-time plasma density distribution and the target value;

[0029] Step 3B: Construct a multivariate prediction model based on the plasma drift-diffusion equation, optimize the multivariate prediction model using a rolling optimization method and define constraints. When deviations occur, obtain the optimized plasma density control parameters through the multivariate prediction model and feed them back to the etching process.

[0030] Preferably, in step 3B, a multi-physics field is used to coordinate the spatial distribution of plasma density, and the control parameters include electromagnetic field regulation, airflow regulation, and pressure regulation.

[0031] Preferably, electromagnetic field modulation controls the sheath electric field distribution based on the phase difference of RF sources in different regions and the spatial distribution of ion flux; gas flow modulation optimizes multi-region gas intake based on local reactive gas concentration; and pressure modulation drives the plasma based on the radial pressure difference in multiple regions.

[0032] Preferably, the process further includes step 4: using uniformity, rate, and selectivity as optimization objectives to constrain the process parameters of the etching process and define the feasible domain boundary of the mass production process.

[0033] Preferably, step 4 involves analyzing the constraints of uniformity, rate, and selectivity through DOE experiments, defining the feasible domain boundary of the mass production process, and solving for the process parameter window based on the constraints.

[0034] It needs to be further explained that:

[0035] Bicubic spline interpolation algorithm: uses local cubic polynomials for interpolation, and generates new data points by ensuring the continuity and smoothness of the interpolation.

[0036] Design of Experiments (DOE): An experimental design methodology used to explore and validate the effects of factors on outcomes. In DOEs, experiments are typically divided into multiple combinations, each controlling for one factor and measuring its impact on the results. This approach allows for a more comprehensive understanding of the factors' influence on outcomes and helps determine the optimal combination of factors.

[0037] Compared with existing technologies, this solution has the following advantages:

[0038] This application constructs a correlation model by quantifying the relationship between plasma density and etching uniformity. Plasma density distribution is used as the core control target. By controlling plasma density through multi-variable collaborative control, the spatial uniformity of plasma is effectively optimized. By constructing a real-time monitoring and feedback mechanism, deviations in plasma distribution can be quickly captured and correction commands can be issued in a timely manner. This ensures that the plasma maintains good spatial uniformity during the etching process, effectively copes with dynamic fluctuations caused by various factors, and thus improves the uniformity, quality and stability of etching.

[0039] Meanwhile, this application uses a bicubic spline interpolation algorithm to describe the relationship, which has no discontinuities across the entire wafer and allows for a smooth transition of density values ​​between any adjacent coordinates. It can accurately describe the density differences between the center and the edge, and between different radial partitions. It can not only calculate the plasma density at a single point, but also completely describe the continuous variation of plasma density throughout the entire wafer space. Attached Figure Description

[0040] Figure 1 This is a flowchart of Embodiment 1 of the present invention;

[0041] Figure 2 This is a flowchart of Embodiment 2 of the present invention. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0043] Example 1

[0044] refer to Figure 1 A method for optimizing etching uniformity based on plasma density adjustment includes the following steps:

[0045] Step 1: Collect plasma density and etching rate, generate a coordinate system with the wafer center as the origin and radially partitioned, and map the collected plasma density and etching rate to the coordinate system to obtain a continuous spatial distribution function;

[0046] Preferably, step 1 includes the following steps:

[0047] Step 1A: Measure plasma density using a Langmuir probe array. ;

[0048] The etching depth at various points on the wafer surface was measured using an atomic force microscope. Calculate the etching rate , represented as Where t is the etching time; thus, the historical plasma density is obtained. and etching rate ;

[0049] Step 1B: Based on historical plasma density and etching rate Using the wafer center as the origin, the system is divided radially, and the collected plasma density and etching rate are mapped to the coordinate system. A bicubic spline interpolation algorithm is used to align the data and generate a continuous spatial distribution function, which is expressed as:

[0050] .

[0051] in, , All are basis functions. , All are fitting coefficients.

[0052] It should be noted that:

[0053] : Refers to the planar coordinates of any position on the wafer, for example ;

[0054] basis functions , All belong to bicubic B-spline basis functions. Corresponding plasma density, basis function The corresponding etching rate is determined by both the "interpolation algorithm characteristics" and the "wafer radial partitioning method";

[0055] Fit coefficients k j All results are fitting results based on measured data, and require substituting discrete data and minimizing the error to solve the problem; specifically, The method for determining the value is as follows: The values ​​measured by the Langmuir probe array and the emission spectrometer are... Discrete data, substituted into the continuous spatial distribution function The least squares method is used to find the value that minimizes the sum of squared errors between the fitted value and the measured value; specifically, The method for calculating the value is as follows: Calculate the discrete data of the etching rate from the etching depth measured by the atomic force microscope, and substitute it into... The value obtained by solving the least squares method is the value that minimizes the sum of squared errors between the fitted value and the measured value.

[0056] Step 2: Construct a correlation model using a continuous spatial distribution function, fit the correlation model using the nonlinear least squares method, calculate the coefficient of determination and wafer internal uniformity, and statistically verify the correlation model to obtain the relationship between plasma density and etching uniformity.

[0057] Preferably, step 2 includes the following steps:

[0058] Step 2A: Construct a correlation model based on the continuous spatial distribution function of etching rate and plasma density after data alignment. The key model is represented as follows:

[0059] .

[0060] in, , , All parameters were obtained by fitting using the nonlinear least squares method. The rate constant is related to the chemical properties of the gas. Density sensitivity index The activation energy for the etching reaction is (eV). Boltzmann's constant; The electron temperature is obtained by inverting the characteristic curve of probe IV; Non-plasma contribution items;

[0061] Step 2B: Fit the correlation model using the nonlinear least squares method. The fitted model is expressed as:

[0062] .

[0063] Step 2C: Calculate the coefficient of determination It reflects the goodness of fit of the correlation model and calculates the inhomogeneity within the wafer. Statistical validation of the association model was performed.

[0064] in, This represents the measured value of the etching rate; The predicted etching rate is obtained by substituting the measured plasma density into the key model mentioned above.

[0065] To achieve the average etching rate, all measured points across the entire wafer were collected. Substitute the data into the arithmetic mean formula to calculate: , where N is the total number of measured points;

[0066] The standard deviation of the etching rate. Where N is the total number of measured points, and takes a single non-negative value (e.g., 2.5 nm / s). The standard deviation of the etching rate reflects the dispersion of the etching rate across the entire wafer. The smaller the value, the more uniform the rate.

[0067] Then, by calculating the effect of the plasma density gradient on etching uniformity, a sensitivity analysis is performed to evaluate the impact of input parameter variations on the correlation model output, and the key sensitive regions are output, represented as follows:

[0068] , .

[0069] in, The above formula is the sensitivity coefficient of plasma density to etching uniformity. It is the partial derivative of the inhomogeneity within the wafer with respect to the relative change in plasma density. It refers to the change in wafer etching uniformity (WIWNU) when the relative change in plasma density is 1%, and is used to locate the key sensitive areas of etching uniformity.

[0070] Density range is the difference between the maximum and minimum plasma density within a wafer plane, and is a core parameter reflecting the degree of non-uniformity in the spatial distribution of plasma density. Number of partitions; The RF amplitude in the k-th region; Let be the RF phase angle of the k-th region; The plasma wavelength and ,in, The speed of light; For RF frequency; It is the characteristic angular frequency of plasma, also known as the "plasma oscillation angular frequency", which is an inherent parameter describing the collective oscillation characteristics of electrons in plasma.

[0071] In summary, step 2 yields a correlation model that accurately maps the relationship between etching rate and plasma density.

[0072] Step 3: Construct a multivariate prediction model to monitor the spatial distribution of plasma density in the etching process in real time. When there is a deviation in the plasma density distribution, feedback is provided and the plasma density control parameters are adjusted in real time.

[0073] Preferably, step 3 includes the following steps:

[0074] Step 3A: Define the target plasma density distribution. Use the same method as in Step 1 to monitor the plasma density distribution during etching in real time, and then calculate the real-time deviation of the plasma density distribution. The real-time deviation is expressed as:

[0075] .

[0076] in, Real-time plasma density refers to the real-time plasma density at the wafer radial coordinate r and time t, which is a core physical quantity monitored in real time during the etching process; Target plasma density;

[0077] e(r,t) is the real-time deviation of plasma density, which refers to the difference between the real-time plasma density at the wafer radial coordinate r and time t and the target plasma density. It is the core indicator for judging whether the plasma distribution deviates from the expectation.

[0078] Based on the real-time deviation, radial gradient deviation and non-uniformity are extracted as key control indicators, expressed as follows:

[0079] Radial gradient deviation: Non-uniformity: ;

[0080] Where e(R,t) is the real-time deviation of the wafer edge, which is the difference between the real-time plasma density and the target density in the wafer edge region at time t, reflecting the degree of density deviation in the edge region.

[0081] e(0,t) represents the real-time deviation of the wafer center. At time t, it is the difference between the real-time plasma density in the wafer center region and the target value, reflecting the degree of density deviation in the center region.

[0082] Step 3B: Construct a multivariate prediction model based on the plasma drift-diffusion equation. The equation expression is as follows:

[0083] .

[0084] Among them, control vector (j=1,2,3) contains three core control parameters as follows: (Partition RF power) (District air valve opening) (Coil current), i.e. =[u1, u2, u3] T (Column vector form);

[0085] This is the actuator gain matrix, used to... The change in the control quantity is converted into the change rate of plasma density. The contribution value is used to ensure the accuracy of the model;

[0086] τ is the plasma electron characteristic lifetime, a key parameter describing the existence time of electrons in plasma. It refers to the average time for electrons to disappear from plasma (such as recombination and collision loss).

[0087] Then, a rolling optimization method is used to optimize the multivariate prediction model, and the optimization objective function is set as follows:

[0088] .

[0089] in, ; Let be the integrand, and let represent the weighted objective term; For prediction in the time domain; To control the weights;

[0090] Then, define the constraints as follows:

[0091] .

[0092] in, Let be the maximum allowable value of the j-th control parameter, where j=1,2,3, corresponding to u1 (zone RF power), u2 (zone air valve opening), and u3 (coil current), respectively. Let j be the rate of change of the j-th control parameter. This represents the maximum permissible rate of change.

[0093] This step yields a multivariate prediction model capable of predicting plasma density and etching result deviations based on actual etching control parameters. During the etching process, when the aforementioned key control indicators exceed the set limits, the optimized plasma density control parameter u is obtained through the multivariate prediction model. j (RF power, magnetic field, airflow) and timely dynamic feedback to the etching process actuator to ensure that the plasma maintains good spatial uniformity during the etching process, effectively cope with dynamic fluctuations caused by various factors, and thus improve the quality and stability of etching.

[0094] Preferably, in step 3B, a multi-physics field is used to coordinate the spatial distribution of plasma density, and the control parameters include electromagnetic field regulation, airflow regulation, and pressure regulation.

[0095] Specifically:

[0096] Methods of electromagnetic field manipulation include:

[0097] 1. Adjusting the radio frequency matching network according to the phase difference of the RF source in different regions controls the sheath electric field distribution to change the plasma coupling efficiency. The corresponding phase optimization model is expressed as follows:

[0098] .

[0099] in, For the number of partitions, Let be the RF amplitude of the k-th region. Let be the RF phase angle of the k-th region. The plasma wavelength and , At the speed of light, For RF frequency;

[0100] 2. Based on controlling the spatial distribution of ion flux, the electric field modulation of the sheath is achieved by enhancing the edge electric field compensation with a radial electric field. The corresponding ion flux optimization model is expressed as follows:

[0101] .

[0102] in The electric field strength at the center is (V / m). The edge enhancement coefficient, The radius of the wafer;

[0103] The airflow control method is as follows: based on adjusting the concentration of locally reacting gases, a gas diffusion-dissociation equilibrium equation is constructed to achieve multi-zone air intake optimization. The equation expression is as follows:

[0104] .

[0105] in For gas density, The diffusion coefficient is... For the Laplace operator, The dissociation rate constant is If the intake flow rate is zoned, then the total intake flow rate is: ;

[0106] The spatial uniformity of the reaction gas distribution can be quantified and described using the gas diffusion-dissociation equilibrium equations described above.

[0107] The pressure control method is as follows: a radial pressure difference is established to drive the plasma to achieve dynamic pressure gradient control, and the pressure distribution formula is:

[0108] .

[0109] in As the central pressure, The pressure difference from the edge point to the center. This is the pressure distribution index.

[0110] Example 2

[0111] refer to Figure 2 Based on the above embodiment 1, preferably, it also includes step 4: using uniformity, rate, and selectivity as optimization objectives to constrain the process parameters of the etching process and define the feasible domain boundary of the mass production process. This method coordinates uniformity, rate, and selectivity to achieve the best balance between quality, efficiency, and cost: while ensuring high product uniformity and high selectivity, it maximizes production rate, thereby maximizing economic benefits.

[0112] Preferably, the constraints include:

[0113] Condition 1: Etching rate boundary, defining the allowable fluctuation range of the etching rate as follows: ;

[0114] Condition 2: Uniformity, set uniformity constraint as follows This refers to the non-uniformity of the etching rate within the wafer; The standard deviation of the etching rate; This represents the maximum allowable threshold for etching rate uniformity.

[0115] Condition 3: Selection ratio, setting the mask and material selection ratio constraint as follows: ,in, To select the ratio, The etching rate of the material to be etched. The etching rate of the mask material, The minimum allowable selection ratio;

[0116] Condition 4: Profile control, set profile angle constraints as follows .

[0117] Preferably, step 4 involves analyzing multiple constraints through DOE experiments, including the following steps:

[0118] Step 4A: Select the control variable as An experimental matrix is ​​constructed using the center point, axis points, and factor points as experimental points; among them, For RF power, For pressure difference, This represents the edge-to-center gas flow ratio; all variables in this step serve the plasma density. The degree of plasma ionization is affected; the more fully the plasma is ionized, the higher the plasma density. The more stable ΔP is, the more uniform the plasma density distribution will be. The plasma density distribution at the wafer edge and center is affected; when the ratio is appropriate, the plasma density at the wafer edge and center tends to be consistent.

[0119] Step 4B: Construct a response surface model using a second-order polynomial fitting method based on the response quantities at different experimental points. The response surface model is represented as follows:

[0120] .

[0121] in, This is the process response quantity; This is a constant term, representing the model's fundamental offset, determined by the average response value across all experimental points. Let x be the coefficient of the linear term, and x be the coefficient of the i-th control variable. i The linear influence coefficient on the response y; The coefficient of the quadratic term is x, the i-th control variable. i The coefficient of the quadratic term reflects the nonlinear effect of the variable on the response; For the interaction term coefficient, the interaction coefficient between the i-th and j-th regulatory variables; To regulate variables, For random error terms, the residual errors of model fitting (such as measurement errors and environmental disturbances) are usually assumed to follow a normal distribution.

[0122] Set the feasible region boundary for mass production process, and set the objective function and constraints as follows:

[0123] .

[0124] It should be noted that the core of the non-uniformity in the etching rate within the wafer in condition 2 is... ,and The size of the etching rate is essentially determined by the uniformity of the plasma density distribution. In other words, plasma density and etching rate are positively correlated. If the plasma density within the wafer is not uniform, A large standard deviation in plasma density leads to significant differences in the concentration of active particles in different regions of the wafer, directly resulting in higher etching rates in some areas and lower etching rates in others. An increase in the standard deviation of the etching rate may eventually exceed the threshold. Conversely, if the plasma density within the wafer is uniform, the active particles are evenly distributed throughout the entire wafer, resulting in minimal regional differences in etching rate. It will decrease naturally and automatically meet the requirements. <η R The constraints.

[0125] In addition, plasma density and control variables , , For directly related metrics, setting the objective function based on plasma density, compared to etching rate, allows for more precise optimization.

[0126] Then, the boundary of the feasible region for mass production process is solved, including the following steps:

[0127] 1) Construct the Lagrange function and solve iteratively, expressed as: ;in, For the vector of control variables; The Lagrange multiplier vector; The Lagrange multiplier vector; The standard deviation of plasma density; The constraint function vector;

[0128] 2) Solve the QP subproblem, the formula of which is: ;in, This is the search direction vector; Let Hessian matrix be the result of the k-th iteration; The gradient of the standard deviation of plasma density; This is the transpose of the constraint gradient in the k-th iteration; This represents the constraint function value in the k-th iteration. It is a quadratic term;

[0129] It should be noted that the core of the QP problem is determined by the Hessian matrix, ensuring that the optimization direction is a local optimum. It is a linear term, determined by the gradient, guiding the search direction towards... Shift in the direction of decrease;

[0130] 3) Update , This is the vector of control variables for the (k+1)th iteration; Let be the vector of control variables in the k-th iteration; Step size; Let be the search direction vector for the k-th iteration;

[0131] The NSGA-II algorithm is used to solve the Pareto optimal front, obtaining the process parameter window, and the optimization objective is set as follows: , For multi-objective optimization vectors, The standard deviation of plasma density, The average etching rate is negative. Negative selection ratio This is the transpose symbol.

[0132] Table 1: Comparison of Etching Indicators between Conventional Process and Example Process

[0133]

[0134] Results analysis:

[0135] Compared to conventional processes (where plasma density is not dynamically adjusted based on plasma density deviation during etching), this embodiment ensures that the plasma maintains good spatial uniformity throughout the etching process. Therefore, the uniformity, etching rate, selectivity, and etching morphology of the finished wafer are significantly improved.

[0136] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for optimizing etching uniformity based on plasma density adjustment, characterized in that, Includes the following steps: Step 1: Collect historical plasma density and etching rate data, generate a coordinate system with the wafer center as the origin and radial partitions, and map the collected plasma density and etching rate data to the coordinate system to obtain a continuous spatial distribution function. Step 2: Construct a correlation model using a continuous spatial distribution function, fit the correlation model using the nonlinear least squares method, calculate the coefficient of determination and wafer internal uniformity, and statistically verify the correlation model to obtain the relationship between plasma density and etching uniformity. Step 3: Construct a multivariate prediction model to monitor the spatial distribution of plasma density in the etching process in real time. When the plasma density distribution exceeds the preset threshold, the multivariate prediction model provides feedback and adjusts the plasma density control parameters in real time.

2. The etching uniformity optimization method based on plasma density adjustment according to claim 1, characterized in that, Step 1 includes the following steps: Step 1A: Measure the plasma density using a Langmuir probe array; The etching depth at various points on the wafer surface is measured using an atomic force microscope, and the etching rate is calculated. Step 1B: Based on the plasma density and etching rate, a coordinate system is generated with the wafer center as the origin and radially partitioned. The collected plasma density and etching rate data are mapped to the coordinate system. A continuous spatial distribution function is generated by aligning the data using a bicubic spline interpolation algorithm. The continuous spatial distribution function is expressed as: ； in, The plasma density; Etching rate; , All are basis functions; , All are fitting coefficients.

3. The etching uniformity optimization method based on plasma density adjustment according to claim 2, characterized in that, Step 2 includes the following steps: Step 2A: Construct a correlation model based on the continuous spatial distribution function. The key model is represented as follows: ； in, The rate constant is related to the chemical properties of the gas. Density sensitivity index The activation energy (eV) for the etching reaction. The Boltzmann constant is approximately 8.617 × 10⁻⁵ eV / K. To determine the electron temperature based on the probe IV characteristic curve, Non-plasma contribution items; Step 2B: Fit the correlation model using the nonlinear least squares method. The fitted model is expressed as: ； in, This represents the measured value of the etching rate; This is a predicted value for the etching rate; Step 2C: Calculate the coefficient of determination and inhomogeneity within the wafer to statistically validate the correlation model, and calculate the effect of plasma density gradient on etching uniformity. Perform sensitivity analysis and output the key sensitive regions, represented as follows: ， ； in, This is the sensitivity coefficient of plasma density to etching uniformity; It represents a density range; Number of partitions; The RF amplitude in the k-th region; Let be the RF phase angle of the k-th region; The plasma wavelength and , The speed of light; For RF frequency; It is the characteristic angular frequency of plasma.

4. The etching uniformity optimization method based on plasma density adjustment according to claim 1, characterized in that, Step 3 includes the following steps: Step 3A: Set the target value for plasma density distribution, monitor the plasma density distribution during the etching process, and calculate the deviation between the real-time plasma density distribution and the target value; Step 3B: Construct a multivariate prediction model based on the plasma drift-diffusion equation, optimize the multivariate prediction model using a rolling optimization method and define constraints. When the deviation exceeds the preset threshold, obtain the optimized plasma density control parameters through the multivariate prediction model and feed them back to the etching process.

5. The etching uniformity optimization method based on plasma density adjustment according to claim 4, characterized in that, In step 3B, a multi-physics field is used to coordinate the spatial distribution of plasma density. The plasma density control parameters include electromagnetic field regulation, airflow regulation, and pressure regulation.

6. The etching uniformity optimization method based on plasma density adjustment according to claim 5, characterized in that, Electromagnetic field modulation controls the sheath electric field distribution based on the phase difference of RF sources in different regions and the spatial distribution of ion flux; gas flow modulation optimizes multi-region gas intake based on local reactive gas concentration; and pressure modulation drives the plasma based on the radial pressure difference in multiple regions.

7. The etching uniformity optimization method based on plasma density adjustment according to claim 1, characterized in that, It also includes step 4: using uniformity, rate, and selectivity as optimization objectives, constraining the process parameters of the etching process, and defining the boundary of the feasible domain for mass production.

8. The etching uniformity optimization method based on plasma density adjustment according to claim 7, characterized in that, Step 4 involves analyzing the constraints of uniformity, rate, and selectivity through DOE experiments, defining the feasible domain boundary for mass production, and solving for the process parameter window based on these constraints.

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