Wafer production process optimization method and device for improving epitaxial rate consistency

Abstract

The application discloses a wafer production process optimization method and device for improving epitaxial rate consistency, and particularly relates to the technical field of production process optimization; by collecting wafer surface stress change data and wafer geometric appearance data in the epitaxial process, a wafer local area heat conduction and mass transfer evaluation model and an epitaxial reaction cavity three-dimensional simulation geometric model are constructed, wafer local heat mass transport dynamic characteristic parameters and wafer boundary layer heat mass transport dynamic characteristic parameters are output; according to the wafer local heat mass transport dynamic characteristic parameters, a wafer local area epitaxial rate change trend is predicted, according to the wafer boundary layer heat mass transport dynamic characteristic parameters, the influence of wafer local boundary layer change on precursor concentration distribution and local area epitaxial rate is analyzed, epitaxial rate trend prediction data and epitaxial rate disturbance prediction data are generated, and the temperature setting and precursor flow control strategy of wafer epitaxial process are optimized, so that the manufacturing quality and yield of the wafer are improved.

Description

Technical Field

[0001] This invention relates to the field of manufacturing process optimization technology, and more specifically, to a method and apparatus for optimizing wafer manufacturing processes to improve epitaxial ratio consistency. Background Technology

[0002] In the epitaxial growth process of semiconductor wafers, the uniformity of the epitaxial rate on the wafer surface is directly related to the uniformity of wafer material properties and the yield of electronic devices. Existing wafer epitaxial manufacturing processes typically use fixed temperature and precursor flow parameters. They lack precise monitoring and analysis of the stress distribution and dynamic changes in wafer geometry during the epitaxial process, and do not consider the complex influence of these factors on local heat conduction, mass transfer, and reaction boundary layer conditions. This leads to deviations between the actual epitaxial rate and the design target in local wafer regions.

[0003] Existing wafer epitaxial manufacturing processes lack sophisticated analysis and dynamic control methods to address the impact of wafer surface stress distribution and dynamic changes in wafer geometry on the epitaxial rate in local wafer regions. This results in poor consistency of the epitaxial rate on the wafer surface, making it difficult to meet the process requirements for high-precision, high-consistency wafer manufacturing. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, the embodiments of the present invention provide a wafer manufacturing process optimization method and apparatus for improving epitaxial ratio consistency to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A wafer fabrication process optimization method for improving epitaxial ratio consistency includes the following steps: S1: Collect stress change data and wafer geometry data on the wafer surface during wafer epitaxy, perform preprocessing, and output characteristic parameters of wafer surface stress distribution and wafer geometry change. S2: Based on the characteristic parameters of stress distribution on the wafer surface, evaluate the changes in heat conduction and mass transfer conditions in the local area of ​​the wafer caused by stress distribution, and output the dynamic characteristic parameters of local heat and mass transfer on the wafer. S3: Based on the characteristic parameters of wafer geometry variation, simulate the changes in local airflow and heat transfer boundary layer under different wafer local morphology conditions, and output the dynamic characteristic parameters of wafer boundary layer heat and mass transport. S4: Based on the dynamic characteristic parameters of local heat and mass transfer in the wafer, predict the epitaxial rate change trend in the local region of the wafer and output the epitaxial rate trend prediction data. S5: Based on the dynamic characteristic parameters of thermal and mass transport in the wafer boundary layer, analyze the influence of local boundary layer changes on precursor concentration distribution and local epitaxial rate, and output epitaxial rate perturbation prediction data. S6: Based on the epitaxial rate trend prediction data and epitaxial rate disturbance prediction data, dynamically optimize the temperature setting and precursor flow control strategy of the wafer epitaxial process.

[0006] In a preferred embodiment, S1 specifically refers to: Data on wafer surface stress variation and wafer geometry were collected during the wafer epitaxy process. Denoising and data smoothing are performed on wafer surface stress variation data and wafer geometric morphology data; Extract characteristic parameters of wafer surface stress distribution from wafer surface stress variation data that has undergone noise reduction and data smoothing; Extract wafer geometry variation feature parameters from wafer geometry variation data that has undergone denoising and data smoothing.

[0007] In a preferred embodiment, S2 specifically refers to: Based on the characteristic parameters of stress distribution on the wafer surface, a finite element analysis model of a local region of the wafer is established; Using a finite element analysis model of a local region of a wafer, the changes in heat conduction characteristics caused by stress distribution in that local region are calculated; Using a finite element analysis model of a local region of the wafer, the changes in mass transfer characteristics caused by stress distribution in the local region of the wafer are calculated; Based on the changes in heat conduction and mass transfer characteristics, the dynamic variation law of heat conduction and mass transfer conditions in local areas of the wafer with stress is determined, and the dynamic characteristic parameters of local heat and mass transfer in the wafer are output.

[0008] In a preferred embodiment, S3 specifically refers to: Based on the characteristic parameters of wafer geometry variation, a three-dimensional simulation geometric model is established that includes wafer surface morphology information and the airflow channel structure in the epitaxial reaction cavity. In the three-dimensional simulation geometric model, the wafer local region is divided, and the airflow calculation region and heat transfer boundary layer calculation region corresponding to each wafer local region are defined; The gas velocity distribution and gas pressure distribution within each airflow calculation region are solved to obtain local airflow distribution data; In each heat transfer boundary layer computational region, the temperature distribution and heat flux distribution are calculated to obtain heat transfer boundary layer variation data; Based on local airflow distribution data and heat transfer boundary layer variation data, dynamic characteristic parameters of heat and mass transport in the wafer boundary layer are extracted.

[0009] In a preferred embodiment, S4 specifically refers to: Based on the dynamic characteristic parameters of local heat and mass transfer in wafers, time series data of heat conduction characteristic parameters and mass transfer characteristic parameters corresponding to local regions of each wafer are determined; Based on time-series data of thermal conduction and mass transfer characteristic parameters, a functional relationship model is established between the dynamic characteristic parameters of local thermal and mass transfer on the wafer and the epitaxial rate of the local region of the wafer. The epitaxial rate of a local region of the wafer was calculated using a functional relationship model at different time points, and the trend data of the epitaxial rate of a local region of the wafer was obtained. The epitaxial rate trend data of local areas of the wafer are combined according to the spatial distribution of the local areas on the wafer to form epitaxial rate trend prediction data.

[0010] In a preferred embodiment, S5 specifically refers to: Based on the dynamic characteristic parameters of thermal mass transport in the wafer boundary layer, the airflow velocity distribution, airflow pressure distribution, temperature distribution, and heat flux distribution data corresponding to the local region of the wafer are determined. Based on airflow velocity distribution data and airflow pressure distribution data, calculate the gas residence time distribution and gas precursor concentration distribution; Based on temperature distribution data and heat flux distribution data, the local reaction temperature gradient and thermal boundary layer thickness are calculated. Based on the gas residence time distribution, gas precursor concentration distribution, local reaction temperature gradient, and thermal boundary layer thickness, the dynamic relationship between precursor concentration distribution and local epitaxial rate under the condition of local boundary layer variation is determined, and epitaxial rate perturbation prediction data is output.

[0011] In a preferred embodiment, S6 specifically refers to: Based on epitaxial rate trend prediction data and epitaxial rate disturbance prediction data, an evaluation standard for the prediction deviation of epitaxial rate in local areas of wafers is established. Based on the evaluation criteria for the prediction deviation of the epitaxial rate in a local area of ​​the wafer, it is determined whether the epitaxial rate in a local area of ​​the wafer deviates from the target range of the epitaxial rate. When the epitaxial rate in a local area of ​​the wafer deviates from the target range of the epitaxial rate, the temperature control curve in the epitaxial reaction chamber and the precursor flow rate setting parameters entering the epitaxial reaction chamber are dynamically adjusted. Based on the adjusted temperature control curve and precursor flow setting parameters, a dynamically optimized temperature setting and precursor flow control strategy is obtained.

[0012] On the other hand, the present invention provides a wafer manufacturing process optimization apparatus for improving epitaxial ratio consistency, comprising: a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, a wafer manufacturing process optimization method for improving epitaxial ratio consistency is implemented.

[0013] The technical effects and advantages of the wafer fabrication process optimization method and apparatus for improving epitaxial ratio uniformity of the present invention are as follows: By simultaneously acquiring and preprocessing stress variation data and wafer geometry data on the wafer surface during epitaxy, characteristic parameters of wafer surface stress distribution and wafer geometry variation are used to characterize the actual stress state and morphological evolution during epitaxial growth. Based on the characteristic parameters of wafer surface stress distribution, the changes in heat conduction and mass transfer conditions in local wafer regions caused by stress distribution are evaluated. Combined with characteristic parameters of wafer geometry variation, the changes in local airflow and heat transfer boundary layer under different wafer local morphological conditions are simulated, resulting in a wafer boundary layer thermal mass transfer model that comprehensively reflects the thermal and mass transport behavior of local wafer regions and the wafer boundary layer. Dynamic characteristics of heat and mass transport in wafer locality are used to predict the epitaxial rate change trend in local wafer regions. Based on the dynamic characteristics of heat and mass transport in wafer boundary layer, the influence of local boundary layer changes on precursor concentration distribution and local epitaxial rate is analyzed, forming epitaxial rate trend prediction data and epitaxial rate disturbance prediction data. During epitaxial growth, temperature setting and precursor flow control strategies are dynamically optimized based on the epitaxial rate trend prediction data and epitaxial rate disturbance prediction data. This can reduce thickness inhomogeneity and inter-wafer differences caused by process fluctuations, and improve epitaxial production stability and wafer yield. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of a wafer fabrication process optimization method to improve epitaxial ratio consistency according to the present invention. Detailed Implementation

[0015] 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. Example 1

[0016] Figure 1 This invention provides a wafer fabrication process optimization method to improve epitaxial ratio consistency, which includes the following steps: S1: Collect stress change data and wafer geometry data on the wafer surface during wafer epitaxy, perform preprocessing, and output characteristic parameters of wafer surface stress distribution and wafer geometry change. S2: Based on the characteristic parameters of stress distribution on the wafer surface, evaluate the changes in heat conduction and mass transfer conditions in the local area of ​​the wafer caused by stress distribution, and output the dynamic characteristic parameters of local heat and mass transfer on the wafer. S3: Based on the characteristic parameters of wafer geometry variation, simulate the changes in local airflow and heat transfer boundary layer under different wafer local morphology conditions, and output the dynamic characteristic parameters of wafer boundary layer heat and mass transport. S4: Based on the dynamic characteristic parameters of local heat and mass transfer in the wafer, predict the epitaxial rate change trend in the local region of the wafer and output the epitaxial rate trend prediction data. S5: Based on the dynamic characteristic parameters of thermal and mass transport in the wafer boundary layer, analyze the influence of local boundary layer changes on precursor concentration distribution and local epitaxial rate, and output epitaxial rate perturbation prediction data. S6: Based on the epitaxial rate trend prediction data and epitaxial rate disturbance prediction data, dynamically optimize the temperature setting and precursor flow control strategy of the wafer epitaxial process.

[0017] Specifically, S1: Collects stress change data and wafer geometry data on the wafer surface during wafer epitaxy, performs preprocessing, and outputs characteristic parameters of wafer surface stress distribution and wafer geometry change, including: Data on wafer surface stress variation and wafer geometry were collected during the wafer epitaxy process. A stress measurement sensor array is configured on the top and back of the wafer. The sensor array includes an optical interferometric displacement sensor for measuring wafer warpage and a Raman spectroscopy acquisition device for measuring the stress-related spectral response within the material. The optical interferometric displacement sensor is arranged with multiple measurement points at preset spatial sampling intervals along the wafer radius and circumference. At each measurement point, the sensor acquires the wafer surface height change signal during epitaxial growth at fixed time intervals and converts the height change signal into local wafer curvature change data. The Raman spectroscopy acquisition device acquires Raman peak displacement data at different times on the wafer surface using a measurement point layout matched to the optical interferometric displacement sensor and converts the Raman peak displacement data into equivalent stress change data for local wafer regions. The local wafer curvature change data obtained from the optical interferometric displacement sensor and the local equivalent stress change data obtained from the Raman spectroscopy acquisition device are interpolated and registered on a unified time axis and a unified spatial grid to form a wafer surface stress change data matrix covering the entire wafer surface over the entire epitaxial growth time interval. Each matrix element corresponds to a stress change value at a time sampling point and a spatial sampling location.

[0018] A full-field 3D topography measurement device is configured above the wafer. For example, this device can employ a white-light interferometry system to periodically scan the wafer surface, obtaining 3D height distribution data at multiple growth time points. The 3D height distribution data is recorded as multiple time frames at fixed time intervals. Each time frame corresponds to a two-dimensional matrix composed of height values, and the row and column indices of each two-dimensional matrix correspond one-to-one with the discrete grid coordinates of the wafer surface, thus forming a sequence of wafer geometric topography data covering the entire epitaxial growth process. To ensure a one-to-one spatial correspondence between the wafer surface stress variation data and the wafer geometric topography data, the spatial grid division of the wafer geometric topography data uses the same polar or Cartesian coordinate division method as the wafer surface stress variation data. The spatial sampling interval and temporal sampling interval are set according to a unified configuration. The wafer geometric topography data is mapped to the same spatial and temporal sampling points as the wafer surface stress variation data through interpolation.

[0019] Denoising and data smoothing are performed on wafer surface stress variation data and wafer geometric morphology data; In the time dimension, wafer surface stress variation data are processed using a finite impulse response (FIR) digital low-pass filter. The order and normalized cutoff frequency of the FIR filter are determined based on the typical timescale of stress evolution during epitaxial growth and the spectral distribution of measurement noise. Frequency domain analysis of historical epitaxial growth data from multiple batches of wafers is used to obtain the main frequency bands where signal energy is concentrated. The filter cutoff frequency is then set in the transition region between the main signal and noise frequency bands, thus preserving the effective components of stress variation and suppressing high-frequency noise components. In the spatial dimension, wafer surface stress variation data are smoothed using a weighted moving average method between adjacent spatial sampling points. The weighting coefficients are set based on the spatial distance from the center sampling point; spatial sampling points closer to the center sampling point have larger weighting coefficients, while those farther away have smaller weighting coefficients. The size of the weighted moving average window is determined based on the spatial correlation length of the wafer surface stress variation.

[0020] In the time dimension, wafer geometry data is processed using a combination of median filtering and low-pass filtering. Median filtering removes abrupt height outliers, while low-pass filtering suppresses high-frequency jitter noise. The median filtering window length in the time dimension is set based on the epitaxial growth thickness change rate and sampling time interval, while the cutoff frequency of the low-pass filter is set based on the typical spectrum of height changes. In the spatial dimension, the wafer geometry data is processed using a bidirectional weighted smoothing method. One-dimensional weighted smoothing operations are performed in both the radial and circumferential directions, and the two smoothing results are then combined to preserve the overall wafer curvature trend and local morphological features.

[0021] Extract characteristic parameters of wafer surface stress distribution from wafer surface stress variation data that has undergone noise reduction and data smoothing; The characteristic parameters of wafer surface stress distribution quantify the spatial and temporal distribution characteristics of wafer surface stress. These parameters include the overall average stress value, the radial average stress distribution at different radii, the angular average stress distribution at different circumferential angles, the stress gradient in the radial direction, the stress asymmetry index in the circumferential direction, and the stress change rate over the epitaxial growth time dimension. The overall average stress value is obtained by summing the stress values ​​at all spatial sampling points on the entire wafer surface and dividing by the number of sampling points. The radial average stress distribution is obtained by averaging the stress at all circumferential sampling points within each radius ring. The angular average stress distribution is obtained by averaging the stress at different radii within each fixed angular sector. The stress gradient is obtained by calculating the stress difference between adjacent radii and adjacent angular positions and dividing by the spatial distance. The stress asymmetry index is obtained by normalizing and comparing the average stresses at different angular directions. The stress change rate is obtained by dividing the stress difference between sampling points at different times by the time interval.

[0022] Extract wafer geometry variation characteristic parameters from wafer geometry variation data that has undergone noise reduction and data smoothing; The wafer geometric morphology variation characteristic parameters quantify the degree of macroscopic bending, local warping, and morphology evolution trajectory of the wafer before, during, and after epitaxial growth. These parameters include the overall wafer bending, the average height difference between the central and edge regions, the morphology curvature distribution at different radii, the morphology evolution trajectory at different time points, and a morphology non-uniformity index describing the inhomogeneity of morphology changes. The overall wafer bending is obtained by fitting the three-dimensional height distribution data of the entire wafer to a plane and calculating the maximum and root mean square values ​​of the height deviation from the plane. The average height difference between the central and edge regions is obtained by calculating the average height in the predefined central circular region and outer ring region and then subtracting the values. The morphology curvature distribution is obtained by approximating the three-dimensional height distribution data using second-order difference in the radial and circumferential directions. The morphology evolution trajectory is obtained by comparing the height distribution difference sequences corresponding to different sampling points at different times. The morphology non-uniformity index is obtained by statistically analyzing the standard deviation or coefficient of variation of the height deviation in different regions.

[0023] S2: Based on the characteristic parameters of wafer surface stress distribution, evaluate the changes in heat conduction and mass transfer conditions in local areas of the wafer caused by stress distribution, and output the dynamic characteristic parameters of local heat and mass transfer on the wafer, including: Based on the characteristic parameters of stress distribution on the wafer surface, a finite element analysis model of a local region of the wafer is established; The finite element analysis model for local wafer regions adopts a spatial partitioning method consistent with the wafer surface stress variation data matrix, dividing the entire wafer surface into multiple local wafer regions with defined spatial coordinates. Each local wafer region corresponds to one or more finite element elements. The geometry of the local wafer regions can be defined using polar coordinate annular partitioning, based on the circular shape of the actual wafer. For example, the wafer radius can be divided into several concentric annular zones, and each concentric annular zone can be further divided into several sector-shaped regions, thus forming a finite element mesh structure composed of multiple sector-shaped elements. The spatial position of each element node in the finite element mesh corresponds one-to-one with the spatial sampling point position in the wafer surface stress distribution characteristic parameters, facilitating the mapping of the wafer surface stress distribution characteristic parameters into the finite element analysis model as stress boundary conditions or body force loading conditions.

[0024] When establishing a finite element analysis model for a local region of a wafer, it is necessary to assign corresponding material parameters to each finite element element, including elastic modulus, Poisson's ratio, density, thermal conductivity, specific heat capacity, and mass diffusion coefficient. Elastic modulus and Poisson's ratio describe the elastic response characteristics of the wafer material under stress, density describes the material mass distribution, thermal conductivity and specific heat capacity describe the heat conduction process, and the mass diffusion coefficient describes the diffusion process of the precursor in a fluid environment. Material parameters can be obtained from experimental measurement data based on the type of wafer material, or they can be calibrated through pre-experiments within multiple candidate value ranges. By binding the material parameters with the characteristic parameters of wafer surface stress distribution in each local region of the wafer, a finite element analysis model for a local wafer region is formed that includes both stress loading information and material property information.

[0025] Using a finite element analysis model of a local region of a wafer, the changes in heat conduction characteristics caused by stress distribution in that local region are calculated; The calculation of thermal conductivity characteristics uses the radial average stress distribution, angular average stress distribution, stress gradient in the radial direction, and stress asymmetry index in the circumferential direction, all included in the stress distribution characteristic parameters of the wafer surface, as inputs. These stress distribution characteristics are converted into parameters affecting thermal conductivity and local heat sources in the finite element unit. Under high stress, wafer materials exhibit local lattice distortion, leading to changes in microscopic lattice vibration behavior, which in turn manifests as changes in macroscopic equivalent thermal conductivity. In the finite element analysis model of a local wafer region, a thermal conductivity adjustment coefficient is used to correlate the equivalent thermal conductivity of the local wafer region with the stress level of that region. This adjustment coefficient can be determined based on experimental data through a fitting method; for example, it can be set as a linear or piecewise linear function, ensuring that the equivalent thermal conductivity of the local wafer region monotonically decreases with increasing average stress value.

[0026] To calculate the changes in heat conduction characteristics, transient heat conduction equilibrium equations are established for each local region of the wafer. The heat flux density provided by the external heating source during wafer epitaxy, the convective heat transfer coefficient between the gas environment within the epitaxial reaction chamber and the wafer surface, and the local heat source terms caused by stress concentration within the local region of the wafer are all incorporated into the finite element equations. In the time dimension, the entire epitaxial growth time interval is discretized into several time steps. The length of each time step is set according to the sampling period and temperature change rate of the epitaxial process control system, for example, a time step set between 0.1 seconds and 5 seconds. In the spatial dimension, for each time step, finite element analysis solves for the temperature distribution at each finite element node within the local region of the wafer. By comparing the temperature distribution results under a baseline stress-free condition with the temperature distribution results under the influence of stress distribution characteristic parameters on the wafer surface, the amount of temperature change, temperature gradient change, and heat flux density change caused by stress distribution in each local region of the wafer are obtained, constituting the data on the changes in heat conduction characteristics of the local region of the wafer.

[0027] Using a finite element analysis model of a local region of the wafer, the changes in mass transfer characteristics caused by stress distribution in the local region of the wafer are calculated; The changes in mass transfer characteristics mainly reflect the changes in the transport behavior of precursor gas near the wafer surface within the epitaxial reaction chamber after being affected by local deformation and temperature distribution variations in the wafer. Deformation in local wafer regions under stress alters the local boundary layer thickness and the micro-geometry along the local surface normal direction, thus affecting the velocity distribution and diffusion path of the precursor gas near the wall. Combining the finite element analysis model of the local wafer region, the gas flow and mass transfer processes are introduced into the finite element equations. The evolution of the precursor concentration distribution near the wafer surface is described by introducing the mass conservation equation and the convection-diffusion equation. The convection term in the convection-diffusion equation is determined by the gas velocity field within the epitaxial reaction chamber, while the diffusion term is determined by the diffusion coefficient of the precursor in the reaction atmosphere. The diffusion coefficient can be obtained experimentally based on different precursor types and process temperature ranges. For example, for a certain type of precursor molecule, the diffusion coefficient can be set within the range of 1 × 10⁻⁵ m² / s to 5 × 10⁻⁵ m² / s.

[0028] The characteristic parameters of wafer surface stress distribution are incorporated into the mass transfer equation to describe the impact of stress-induced local geometric changes on the convection-diffusion process. The stress level in a local wafer region, correlated with the characteristic parameters of wafer geometry changes, affects the local surface normal displacement, thereby altering the local boundary layer thickness and local gas velocity distribution. Changes in the temperature distribution in a local wafer region alter the diffusion coefficient and reaction rate constant of the precursor at different locations. In the finite element analysis model, by updating the local boundary conditions and local diffusion coefficient, these influencing factors are integrated into the mass transfer calculation, solving for the precursor concentration distribution at different time steps and spatial locations. By comparing the precursor concentration distribution under the influence of wafer surface stress distribution characteristics with that under reference conditions, the changes in precursor concentration, precursor concentration gradient, and effective supply rate of the precursor on the wafer surface within a given time step can be obtained for each local wafer region, constituting the mass transfer characteristic change data for the local wafer region.

[0029] Based on the changes in heat conduction characteristics and mass transfer characteristics, the dynamic variation law of heat conduction and mass transfer conditions in local areas of the wafer with stress is determined, and the dynamic characteristic parameters of local heat and mass transfer in the wafer are output. The dynamic characteristic parameters of local heat and mass transport on a wafer are used to reflect the combined effect of wafer surface stress distribution on the temperature field and precursor concentration field of the local wafer region. These include the temperature-time evolution curve of the local wafer region, the precursor concentration-time evolution curve, the temperature gradient-time variation trend, the precursor concentration gradient-time variation trend, and the functional relationship between different stress levels and heat and mass transport parameters within the epitaxial growth time interval. The temperature-time evolution curve of the local wafer region is obtained by recording the temperature calculation results at each time step at a fixed spatial location. The precursor concentration-time evolution curve of the local wafer region is obtained by recording the precursor concentration calculation results at each time step at the corresponding spatial location. The temperature gradient-time variation trend and the precursor concentration gradient-time variation trend are obtained by statistically analyzing the changes in temperature and concentration differences between adjacent spatial locations over time. The functional relationship between stress level and heat and mass transport parameters is obtained by repeatedly performing finite element calculations under different stress levels and solving the problem using a fitting method.

[0030] S3: Based on the characteristic parameters of wafer geometry variation, simulate the changes in local airflow and heat transfer boundary layer under different wafer local morphology conditions, and output the dynamic characteristic parameters of wafer boundary layer heat and mass transport, including: Based on the characteristic parameters of wafer geometry variation, a three-dimensional simulation geometric model is established that includes wafer surface morphology information and the airflow channel structure in the epitaxial reaction cavity. Using wafer geometry variation characteristic parameters and 3D height distribution data as input data, a 3D simulation geometric model is established in a 3D coordinate system that matches the actual structure of the epitaxial reaction chamber. This model includes wafer surface morphology information and the airflow channel structure within the epitaxial reaction chamber. During geometric construction, the wafer is treated as a solid disk with actual diameter and thickness, the supporting structure is used as a supporting entity, and the airflow channels, gas inlet region, gas outlet region, space above the reaction zone, and adjacent chamber walls within the epitaxial reaction chamber are all modeled as fluid computational spaces. The spatial position of the wafer surface within the 3D simulation geometric model is determined by mapping the 3D height distribution data from the wafer geometry variation characteristic parameters to the ideal plane position of the wafer. Specifically, at each discrete grid coordinate on the wafer surface, the height value of the 3D height distribution data is superimposed onto the ideal plane height, resulting in the wafer surface shape with actual warping and bending morphology. This allows the morphology variation state described by the wafer geometry variation characteristic parameters to be reflected in the 3D simulation geometric model.

[0031] In the three-dimensional simulation geometric model, the wafer local region is divided, and the airflow calculation region and heat transfer boundary layer calculation region corresponding to each wafer local region are defined; The wafer local region is divided as follows: the wafer surface is divided into several concentric rings in the radial direction, and each concentric ring is further divided into several fan-shaped regions with equal angles in the circumferential direction. Each fan-shaped region is considered a wafer local region. For each wafer local region, a gas flow calculation region is defined by extending upwards a certain distance in a direction perpendicular to the wafer surface. The upper boundary of the gas flow calculation region can extend to a position in the main gas flow channel within the epitaxial reaction chamber where the gas flow velocity is close to the mainstream velocity. This position can be estimated using pre-calculation results of velocity distribution under typical process conditions. The heat transfer boundary layer calculation region is defined near each wafer local region as a thin layer region that is close to the wafer surface and has a thickness less than that of the gas flow calculation region. The thickness of the heat transfer boundary layer calculation region is estimated based on the predicted Reynolds number, Prandtl number, and boundary layer theory within the typical flow velocity range in the epitaxial process. For example, it can be calculated by taking the thickness of the local boundary layer when the gas flows above the wafer surface and using the thickness value that includes all temperature gradient changes and concentration gradient changes within the local boundary layer thickness range as the thickness of the heat transfer boundary layer calculation region.

[0032] The gas velocity distribution and gas pressure distribution within each airflow calculation region are solved to obtain local airflow distribution data; Computational fluid dynamics (CFD) methods are used to solve for the gas velocity and pressure distributions in each gas flow calculation region to obtain local gas flow distribution data. The gas is treated as a continuous medium, and three-dimensional incompressible fluid control equations are established within the calculation region, including mass and momentum conservation equations. The inclusion of a turbulence model is selected based on the process conditions of the epitaxial reaction chamber. Volumetric flow rate or velocity boundary conditions are applied to the gas inlet boundary. For example, based on the carrier gas and precursor flow rates set by the epitaxial process, the average velocity at the gas inlet cross-section is set to the value obtained by dividing the flow rate by the cross-sectional area. Velocity distribution patterns can be superimposed to simulate the actual inlet flow field characteristics. A fixed pressure boundary condition is used at the gas outlet boundary, setting the absolute pressure at the gas outlet location to a value close to that of an external vacuum or exhaust system. No-slip velocity boundary conditions are applied to the wafer surface and chamber walls, setting the gas velocity near the solid surface to zero to reflect the viscous constraint between the fluid and solid. During numerical discretization, a 3D mesh consistent with the 3D simulation geometry is generated within the airflow computation region. The mesh density is increased in regions with rapid changes in airflow velocity and significant abrupt changes in geometry, while a coarser mesh is used in regions with relatively uniform airflow. By iteratively solving the governing equations, the velocity components and pressure of the gas in the three coordinate directions are obtained at each mesh node. The velocity and pressure field data obtained in each airflow computation region are then recombined according to the local wafer region location to form local airflow distribution data corresponding to each wafer region. The local airflow distribution data includes at least the gas velocity vector distribution and gas pressure distribution near the surface of each wafer region.

[0033] In each heat transfer boundary layer computational region, the temperature distribution and heat flux distribution are calculated to obtain heat transfer boundary layer variation data; Temperature and heat flux distributions are calculated based on local airflow distribution data and temperature boundary conditions in local wafer regions to obtain heat transfer boundary layer variation data. The heat transfer boundary layer calculation region uses an energy conservation equation to describe the heat exchange process between the gas and the wafer surface. This equation includes convection and conduction terms. The velocity distribution in the convection term is provided by the local airflow distribution data obtained from the airflow calculation region, while the thermal conductivity in the conduction term is provided by the thermophysical parameters of the epitaxial process atmosphere. Wafer surface temperature boundary conditions can be obtained by using the temperature at the corresponding time step from the transient heat conduction balance equation to solve the temperature evolution curve of the local wafer region, or by using the epitaxial heating set temperature as the wafer surface temperature boundary condition. The energy conservation equation is spatially and temporally discretized within the heat transfer boundary layer calculation region. The spatial discretization is aligned with the grid of the airflow calculation region near the wafer surface to ensure accurate information transfer between the velocity and temperature fields at the interface. Through numerical solution, the gas temperature distribution at multiple height positions within the heat transfer boundary layer calculation region is obtained at each time step, and the temperature gradient change along the normal direction perpendicular to the wafer surface is calculated. At the interface between the gas and the wafer surface, the heat flux per unit area is calculated based on the product of the temperature gradient in the normal direction and the thermal conductivity of the gas. This is used as the heat flux distribution value of the local region of the wafer over the time step, thereby obtaining the temperature distribution data and heat flux distribution data in the heat transfer boundary layer change data.

[0034] Based on local airflow distribution data and heat transfer boundary layer variation data, dynamic characteristic parameters of heat and mass transport in the wafer boundary layer are extracted. The dynamic characteristics of thermo-mass transport in the wafer boundary layer are used to quantitatively describe the comprehensive characteristics of gas flow, heat transfer, and precursor transport in a thin region near the wafer surface. These parameters include at least the local boundary layer thickness, gas residence time within the boundary layer, average tangential velocity, local convective heat transfer coefficient, and local mass transfer coefficient. The boundary layer thickness can be determined by finding the transition point where the gas velocity gradually changes from zero at the wafer surface to the mainstream velocity in a direction perpendicular to the wafer surface. The location where the gas velocity reaches 95% or 99% of the mainstream velocity is defined as the outer edge of the boundary layer, and the boundary layer thickness is defined as the distance from the outer edge to the wafer surface. The gas residence time within the boundary layer can be obtained by integrating the reciprocal of the velocity along the streamlines within the boundary layer; that is, integrating the ratio of the path length to the local velocity in a given streamline direction to obtain the average residence time of gas particles from the inlet to the outlet within the boundary layer.

[0035] The average tangential velocity within the boundary layer of a local wafer region can be obtained by selecting tangential velocity components at multiple height locations within the boundary layer thickness and performing a weighted average. The weights can be set according to the distance from the wafer surface at different height locations, ensuring that the velocity closer to the wafer surface contributes more to the average value than the velocity farther from the wafer surface. The local convective heat transfer coefficient within the boundary layer of a local wafer region can be calculated using the ratio of heat flux distribution to temperature difference. Specifically, at each location within the local wafer region, the heat flux distribution at the interface corresponding to the wafer surface in the heat transfer boundary layer variation data is divided by the temperature difference between the gas volume average temperature and the wafer surface temperature to obtain the local convective heat transfer coefficient. The local mass transfer coefficient within the boundary layer of a local wafer region can be calculated using the ratio of precursor flux to concentration difference. The precursor flux is obtained by synthesizing the precursor diffusion flux and convection flux perpendicular to the wafer surface from the mass transfer characteristic variation data. The concentration difference is calculated by the difference between the precursor concentration at the outer edge of the boundary layer and the precursor concentration near the wafer surface.

[0036] S4: Based on the dynamic characteristic parameters of local heat and mass transfer on the wafer, predict the epitaxial rate variation trend in local areas of the wafer, and output the epitaxial rate trend prediction data, including: Based on the dynamic characteristic parameters of local heat and mass transfer in wafers, time series data of heat conduction characteristic parameters and mass transfer characteristic parameters corresponding to local regions of each wafer are determined; Using the dynamic characteristic parameters of local heat and mass transfer on the wafer as input data, and combining a unified time axis and a unified spatial grid, time series data of heat conduction characteristic parameters and mass transfer characteristic parameters corresponding to each local region of the wafer are determined. In the dynamic characteristic parameters of local heat and mass transfer on the wafer, for each local region and each epitaxial growth time step, the instantaneous temperature in the temperature-time evolution curve of the local region, the instantaneous temperature gradient in the temperature gradient-time change trend of the local region, the instantaneous precursor concentration in the precursor concentration-time evolution curve of the local region, and the instantaneous concentration gradient in the precursor concentration-time change trend of the local region are read. The instantaneous temperature, instantaneous temperature gradient, and instantaneous heat flux density change are combined to form the local heat conduction characteristic parameters of the wafer. The instantaneous precursor concentration, instantaneous precursor concentration gradient, and the change in the effective supply rate of precursor on the wafer surface at the corresponding time step are combined to form the local mass transfer characteristic parameters of the wafer. By repeatedly extracting data over all epitaxial growth time steps, time-series data of thermal conductivity characteristic parameters and mass transfer characteristic parameters for each local region of the wafer can be obtained.

[0037] Based on time-series data of thermal conduction and mass transfer characteristic parameters, a functional relationship model is established between the dynamic characteristic parameters of local thermal and mass transfer on the wafer and the epitaxial rate of the local region of the wafer. A functional relationship model is established between the dynamic characteristic parameters of local heat and mass transfer on the wafer and the epitaxial rate of the local wafer region for each local wafer area. The establishment of the functional relationship model includes training data construction, function form selection, and parameter calibration. Specifically, training data construction involves obtaining a large number of samples using historical process operation data or pre-designed epitaxial process experimental data. Each sample corresponds to a local wafer region, an epitaxial growth time interval, and the actual epitaxial thickness increment corresponding to the epitaxial growth time interval. The average epitaxial rate of the local wafer region within the epitaxial growth time interval is calculated by dividing the actual epitaxial thickness increment by the length of the epitaxial growth time interval. The time series data of heat conduction characteristic parameters and mass transfer characteristic parameters corresponding to the local wafer region and the epitaxial growth time interval are aggregated into a time window and compressed into a heat and mass transfer characteristic vector through time averaging, time integration, or time-weighted statistical methods. The heat and mass transfer characteristic vector includes representative temperature levels, temperature gradient levels, heat flux density levels, precursor concentration levels, precursor concentration gradient levels, and effective supply rate levels within the time window. Each time window of a local region of each wafer corresponds to a thermal mass transfer feature vector and an average epitaxial rate, thus forming a training sample set for the functional relationship model.

[0038] Specifically, the function form is selected based on the characteristics of epitaxial reaction kinetics. For example, a reaction rate expression based on the Arrhenius equation can be used, representing the local epitaxial rate of the wafer as a combination of a precursor concentration term, a precursor concentration gradient term, and a temperature-related exponential term. The local epitaxial rate of the wafer is set to be equal to the product of undetermined coefficients and the power function terms of the precursor concentration, precursor concentration gradient, and exponential function. The exponent in the exponential function term is expressed as the ratio of activation energy to gas constant multiplied by the negative of the reciprocal of temperature, thus reflecting the characteristic that increasing temperature promotes an increase in reaction rate. The exponent, activation energy, and undetermined coefficients in the power function term can be solved using the least squares method on the training sample set.

[0039] The epitaxial rate of a local region of the wafer was calculated using a functional relationship model at different time points, and the trend data of the epitaxial rate of a local region of the wafer was obtained. In the target epitaxial growth batch, instantaneous heat conduction and mass transfer characteristic parameters corresponding to each time step and each local region of the wafer are extracted according to the dynamic characteristic parameters of local thermal and mass transfer on the wafer. The instantaneous characteristic parameters are then aggregated using the same time window strategy as in the training phase, generating a thermal and mass transfer feature vector consistent with the training data structure. Each thermal and mass transfer feature vector is input into the corresponding functional relationship model. The functional relationship model calculates and outputs the predicted epitaxial rate of the local region of the wafer within the time window based on the temperature, temperature gradient, heat flux density, precursor concentration, precursor concentration gradient, and effective supply rate in the thermal and mass transfer feature vector. By repeating the above calculation for each local region of the wafer throughout the entire epitaxial growth time interval, a discrete time series of the epitaxial rate change of each local region of the wafer can be obtained. Each time point in the discrete time series corresponds to a predicted epitaxial rate, constituting the trend data of the epitaxial rate change of the local region of the wafer.

[0040] The epitaxial rate trend data of local areas of the wafer are combined according to the spatial distribution of the local areas on the wafer to form epitaxial rate trend prediction data. The epitaxial growth rate trend data of local wafer regions are combined according to the spatial distribution of these regions on the wafer to form the full-wafer epitaxial growth rate trend prediction data. The combination process is based on discrete grid coordinates on the wafer surface, mapping the spatial location of each local wafer region to its epitaxial growth rate trend data. At each time step, the predicted epitaxial growth rates of all local wafer regions covering the entire wafer surface are filled into a two-dimensional grid. Each grid cell in the two-dimensional grid corresponds to a local wafer region, and the value of the grid cell is equal to the predicted epitaxial growth rate of that local wafer region at the current time step. By repeating this filling process at all time steps, a three-dimensional data set consisting of both temporal and spatial dimensions is obtained. The temporal dimension reflects the evolution of the epitaxial growth rate, while the spatial dimension reflects the spatial distribution of the epitaxial growth rate at various locations on the wafer surface at any given time.

[0041] S5: Based on the dynamic characteristic parameters of the wafer boundary layer thermal and mass transport, analyze the impact of local boundary layer changes on precursor concentration distribution and local epitaxial rate, and output epitaxial rate perturbation prediction data, including: Based on the dynamic characteristic parameters of thermal mass transport in the wafer boundary layer, the airflow velocity distribution, airflow pressure distribution, temperature distribution, and heat flux distribution data corresponding to the local region of the wafer are determined. For each local region of the wafer, the corresponding airflow velocity distribution, airflow pressure distribution, temperature distribution, and heat flux distribution data are determined under a unified time axis and a unified spatial grid. In the wafer boundary layer thermo-mass transport dynamic characteristic parameters, for each local region, the local gas velocity vector field, local gas pressure field, local gas temperature field, and wafer surface normal heat flux field corresponding to the location of the local region at different time steps are read. The three directional velocity components of each grid node in the local gas velocity vector field are reconstructed according to the discrete grid coordinates of the wafer surface to form the airflow velocity distribution data of the local region; the pressure of each grid node in the local gas pressure field is reconstructed to form the airflow pressure distribution data of the local region; the temperature of several grid nodes near the wafer surface in the local gas temperature field is reconstructed to form the temperature distribution data of the local region; and the heat flux of the wafer surface normal heat flux field at the corresponding location in the local region is reconstructed to form the heat flux distribution data of the local region.

[0042] Based on airflow velocity distribution data and airflow pressure distribution data, calculate the gas residence time distribution and gas precursor concentration distribution; The calculation of gas residence time distribution is based on the velocity field within the boundary layer of a local region on the wafer. Multiple representative streamlines are selected within the thickness of the boundary layer in this local region. Each streamline is obtained by tracing the trajectory of gas particles along the tangential velocity direction within the gas flow calculation region. The streamlines are discretized into several adjacent path segments, the length of which is equal to the geometric distance between adjacent grid nodes. For any streamline, the local gas velocity at the corresponding grid node is read at each path segment location. The path segment length is divided by the local gas velocity to obtain the time required for a gas particle to traverse the path segment. The traversal times of all path segments are summed to obtain the residence time of the gas particle along the streamline from the boundary layer inlet section to the boundary layer outlet section. By statistically analyzing the residence times of multiple streamlines, a spatial interpolation method is used to map the streamline residence times onto the grid nodes within the boundary layer of the local region on the wafer, thus forming the gas residence time distribution data for the local region on the wafer.

[0043] The calculation of the gas precursor concentration distribution is based on the mass conservation equation and the convection-diffusion equation. Local gas velocity and pressure distribution data within the wafer are used as inputs for the convection and pressure terms, respectively. The diffusion coefficient of the precursor in the reaction atmosphere and the inlet precursor concentration are used as physical property parameters and boundary conditions. The steady-state precursor concentration field is solved iteratively on the boundary layer grid of the local wafer region. The diffusion coefficient can be obtained through previous experimental measurements within a given temperature range, for example, it can be calibrated within the range of 1 × 10⁻⁵ m² / s to 5 × 10⁻⁵ m² / s. The inlet precursor concentration can be calculated based on the ratio of precursor flow rate to carrier gas flow rate in the epitaxial process. Through this solution process, the precursor concentration is obtained at each time step and each spatial grid node, forming the gas precursor concentration distribution data for the local wafer region.

[0044] Based on temperature distribution data and heat flux distribution data, the local reaction temperature gradient and thermal boundary layer thickness are calculated. The calculation of the local reaction temperature gradient involves sequentially reading temperature values ​​at multiple height locations along the normal direction perpendicular to the wafer surface, starting from the first grid layer adjacent to the wafer surface. The local temperature gradient is approximated by dividing the temperature difference between adjacent height locations by the geometric distance. These local temperature gradients at multiple height locations are then interpolated and smoothed to form a continuously varying local reaction temperature gradient distribution along the height. The thermal boundary layer thickness can be determined based on either the local reaction temperature gradient distribution or the velocity distribution along the normal direction. For example, a transition region where the gas velocity gradually transitions from zero velocity at the wafer surface to the mainstream velocity can be identified along the normal direction. The location where the gas velocity reaches 95% or 99% of the mainstream velocity can be taken as the outer edge of the boundary layer, and the thermal boundary layer thickness is defined as the normal distance from the outer edge of the boundary layer to the wafer surface. Alternatively, for a temperature gradient-based determination, a location where the temperature gradient decreases significantly along the normal direction and the temperature is close to the mainstream gas temperature can be identified as the outer edge of the boundary layer. The thermal boundary layer thickness is then calculated by determining the distance from this location to the wafer surface. By repeating the above calculations at different spatial locations in a local area of ​​the wafer, the spatial distribution of the local reaction temperature gradient and the thermal boundary layer thickness in the local area of ​​the wafer can be obtained at each time step.

[0045] Based on the gas residence time distribution, gas precursor concentration distribution, local reaction temperature gradient and thermal boundary layer thickness, the dynamic relationship between precursor concentration distribution and local epitaxial rate under the condition of local boundary layer variation is determined, and epitaxial rate perturbation prediction data is output. At each wafer local region and at each time step, the effective reaction utilization rate of the precursor near the wafer surface is calculated based on the gas residence time distribution and the gas precursor concentration distribution. The effective reaction utilization rate is defined as the ratio of the mass of precursor consumed per unit time within the boundary layer of the wafer local region to the mass of precursor entering the boundary layer section of the wafer local region; the total mass of precursor entering the boundary layer is obtained by integrating the precursor flux at the boundary layer inlet section, and the total mass of precursor consumed is obtained by integrating the precursor reaction flux at the location adjacent to the wafer surface.

[0046] Quantitative relationships are established between the local epitaxial rate and precursor concentration distribution, local reaction temperature gradient, and thermal boundary layer thickness within each wafer local region. Based on the epitaxial reaction kinetics mechanism, the local epitaxial rate is expressed as the smaller of the surface reaction control term and the mass transfer control term. The surface reaction control term can be expressed as the product of the surface reaction rate constant and the precursor concentration near the wafer surface. The surface reaction rate constant can be expressed exponentially as the reference rate constant multiplied by an exponential function, where the exponent is the ratio of the negative activation energy to the gas constant multiplied by the reciprocal of the absolute temperature. The absolute temperature is the temperature closest to the wafer surface in the local reaction temperature gradient distribution of the wafer local region. The mass transfer control term can be expressed as the product of the local mass transfer coefficient and the concentration difference between the precursor concentration at the outer edge of the boundary layer and the precursor concentration near the wafer surface. The local mass transfer coefficient can be estimated using a dimensionless correlation based on the thermal boundary layer thickness, local gas flow velocity distribution, and precursor diffusion coefficient. Dimensionless correlations can be expressed using empirical relationships between the Nusselt number, Sherwood number, Reynolds number, and Schmidt number. For example, the Sherwood number can be set to equal the constant coefficient multiplied by a power of the Reynolds number multiplied by a power of the Schmidt number, with the constant coefficient and power exponent obtained through fitting experimental data. The local region epitaxial rate is taken as the smaller value between the surface reaction control term and the mass transfer control term.

[0047] The local epitaxial rate is differentiated from the reference local epitaxial rate under a baseline condition to obtain the perturbation of the local epitaxial rate relative to the baseline condition. The baseline condition can be defined as the local epitaxial rate calculated using the same temperature and precursor flow rate settings, under conditions of zero surface stress and ideal wafer geometry. The perturbation of the local epitaxial rate equals the local epitaxial rate under the current condition minus the local epitaxial rate under the baseline condition. It can be positive or negative; a positive value indicates the local epitaxial rate is higher than the baseline condition, and a negative value indicates the local epitaxial rate is lower than the baseline condition. By repeating the above calculations for each local region of the wafer and each time step throughout the entire epitaxial growth time interval and across the entire wafer surface, predicted epitaxial rate perturbation data covering all spatial locations and all time steps can be obtained.

[0048] S6: Based on epitaxial rate trend prediction data and epitaxial rate disturbance prediction data, dynamically optimize the temperature setting and precursor flow control strategy for the wafer epitaxial process, including: Based on epitaxial rate trend prediction data and epitaxial rate disturbance prediction data, an evaluation standard for the prediction deviation of epitaxial rate in local areas of wafers is established. During the formulation setting stage, the target value and target range of epitaxial rate for local areas of the wafer are determined based on the uniformity requirements of the epitaxial thickness of the target product and historical process statistics. The target value of the epitaxial rate for local areas of the wafer can be obtained by statistically analyzing the measured epitaxial thickness of local areas of the wafer during multi-wafer stable batch epitaxial production, dividing the average epitaxial thickness by the total epitaxial growth time to obtain the target epitaxial rate, and determining the allowable relative deviation range. For example, the target range of the epitaxial rate can be set to the interval from the target epitaxial rate multiplied by (1 minus a preset relative deviation coefficient) to the target epitaxial rate multiplied by (1 plus a preset relative deviation coefficient). The preset relative deviation coefficient is determined by analyzing the impact of different deviation levels on device performance and yield. Through the above analysis, the target value and target range of the epitaxial rate are obtained for each local area of ​​the wafer, providing a benchmark for evaluating the prediction deviation of the epitaxial rate in local areas of the wafer.

[0049] A wafer local region epitaxial rate prediction deviation evaluation standard is constructed based on epitaxial rate trend prediction data and epitaxial rate perturbation prediction data. The epitaxial rate trend prediction data provides the predicted epitaxial rate time series for each wafer local region at each time step, under the current temperature and precursor flow rate settings. The epitaxial rate perturbation prediction data provides the increase or decrease in epitaxial rate relative to the baseline condition for each time step and each wafer local region. The wafer local region epitaxial rate prediction deviation can be defined as the predicted epitaxial rate value of the wafer local region at the current time step in the epitaxial rate trend prediction data minus the target epitaxial rate value of the wafer local region. The wafer local region epitaxial rate prediction deviation evaluation standard characterizes the severity of the deviation by setting multiple graded deviation intervals. For example, a first deviation threshold can be set as the target epitaxial rate multiplied by a first deviation coefficient, and a second deviation threshold can be set as the target epitaxial rate multiplied by a second deviation coefficient. The first deviation coefficient is less than the second deviation coefficient. The values ​​of the first and second deviation coefficients are determined through simulation analysis and experimental calibration, thereby dividing the predicted deviation of the epitaxial rate in a local area of ​​the wafer into deviation intervals within the target range, slight deviation intervals, and severe deviation intervals. When the absolute value of the predicted deviation is less than or equal to the first deviation threshold, it is defined as a deviation within the target range; when the absolute value of the predicted deviation is between the first and second deviation thresholds, it is defined as a slight deviation; and when the absolute value of the predicted deviation is greater than the second deviation threshold, it is defined as a severe deviation. This hierarchical threshold system constitutes the evaluation standard for the predicted deviation of the epitaxial rate in a local area of ​​the wafer.

[0050] Based on the evaluation criteria for the prediction deviation of the epitaxial rate in a local area of ​​the wafer, it is determined whether the epitaxial rate in a local area of ​​the wafer deviates from the target range of the epitaxial rate. At each epitaxial growth time step, the wafer local region epitaxial rate prediction deviation evaluation standard is used to determine whether the wafer local region epitaxial rate deviates from the target epitaxial rate range. At the current time step, the predicted wafer local region epitaxial rate value in the epitaxial rate trend prediction data is read, and the difference between the predicted value and the target value is calculated to obtain the wafer local region epitaxial rate prediction deviation. The absolute value of the wafer local region epitaxial rate prediction deviation is compared with the upper limit of the allowable deviation corresponding to the target epitaxial rate range. If the absolute value of the wafer local region epitaxial rate prediction deviation is less than or equal to the first deviation threshold, the wafer local region epitaxial rate is determined not to have deviated from the target epitaxial rate range, and no adjustment to the wafer local region epitaxial growth conditions is required. If the absolute value of the wafer local region epitaxial rate prediction deviation is between the first and second deviation thresholds, the wafer local region epitaxial rate is determined to be in a slightly deviated state, requiring a small correction to the temperature control curve and precursor flow rate setting parameters. If the absolute value of the predicted epitaxial rate in a local area of ​​the wafer is greater than the second deviation threshold, it is determined that the epitaxial rate in the local area of ​​the wafer is in a state of severe deviation, and the temperature control curve and the precursor flow rate setting parameters need to be significantly corrected.

[0051] When the epitaxial rate in a local area of ​​the wafer deviates from the target range of the epitaxial rate, the temperature control curve in the epitaxial reaction chamber and the precursor flow rate setting parameters entering the epitaxial reaction chamber are dynamically adjusted. After completing the deviation state judgment, when the epitaxial rate in a local area of ​​the wafer deviates from the target range, the temperature control curve and the precursor flow rate setting parameters entering the epitaxial reaction chamber are dynamically adjusted based on the epitaxial rate trend prediction data and the epitaxial rate disturbance prediction data. The temperature control curve is defined as the target trajectory of the temperature setpoint changing over time in each heating region of the epitaxial reaction chamber in the epitaxial growth time dimension, and the precursor flow rate setting parameters are defined as the volumetric flow rate or mass flow rate setting values ​​of each precursor supply channel in the epitaxial growth time dimension. The dynamic adjustment is based on the analysis of epitaxial rate perturbation prediction data to determine the sign and spatial distribution of the epitaxial rate in the local area of ​​the wafer under the current operating conditions. If the predicted data for the epitaxial rate perturbation in the local area of ​​the wafer is positive and exceeds the target range of the epitaxial rate, it indicates that the epitaxial rate in the local area of ​​the wafer is higher than the baseline operating conditions under the current temperature control curve and precursor flow rate settings. The temperature settings and precursor flow rate settings need to be adjusted to suppress the epitaxial rate. If the predicted data for the epitaxial rate perturbation in the local area of ​​the wafer is negative and the absolute value exceeds the target range of the epitaxial rate, it indicates that the epitaxial rate in the local area of ​​the wafer is lower than the baseline operating conditions. The temperature settings and precursor flow rate settings need to be adjusted to increase the epitaxial rate.

[0052] In the dynamic adjustment stage of the temperature control curve, a mapping relationship is established between the temperature setpoint correction and the predicted deviation of the epitaxial rate in the local wafer region for each heating area of ​​the epitaxial reaction chamber. This mapping relationship can be expressed as a piecewise linear function: within the slightly deviated range, the temperature setpoint correction equals the temperature correction coefficient multiplied by the predicted deviation of the epitaxial rate in the local wafer region; within the heavily deviated range, the temperature setpoint correction equals a larger temperature correction coefficient multiplied by the predicted deviation of the epitaxial rate in the local wafer region. The temperature correction coefficient is obtained by fitting the response curves of different temperature correction magnitudes to changes in the epitaxial rate during the experimental phase. For example, the sensitivity coefficient of the epitaxial rate to a unit temperature change can be measured through a single-variable temperature step experiment. A temperature correction coefficient smaller than the reciprocal of the epitaxial rate sensitivity coefficient is set for online control to ensure that each temperature adjustment does not cause overshoot in the epitaxial rate. For a heating region spatially covered by multiple wafer local areas, a weighted average of the epitaxial rate prediction deviations of all wafer local areas within the heating region's coverage area can be calculated. The weights can be set based on the importance of each wafer local area in the device layout or based on the weighting coefficient of the wafer local area in the overall uniformity evaluation. This yields the comprehensive epitaxial rate prediction deviation corresponding to the heating region, and a uniform temperature setpoint correction is calculated for the heating region. This temperature setpoint correction is then superimposed on the temperature setpoint value of the temperature control curve at the current time step to obtain the updated temperature control curve segment.

[0053] In the dynamic adjustment stage of precursor flow rate setting parameters, a mapping relationship is established between the precursor flow rate setting correction and the epitaxial rate disturbance prediction data for each precursor supply channel. This mapping relationship can be determined by referring to the sensitivity of the epitaxial rate to precursor supply under mass transfer control epitaxial conditions. During the offline testing phase, the change in epitaxial rate is measured by altering the precursor flow rate to obtain an empirical linear or nonlinear relationship between the precursor flow rate change and the epitaxial rate change, and the precursor flow rate correction coefficient is determined. In the online control phase, the precursor flow rate setting correction is calculated as the product of the precursor flow rate correction coefficient and the wafer's overall or local average disturbance in the epitaxial rate disturbance prediction data. For spatial regions requiring increased epitaxial rate, the precursor flow rate setting can be increased to tilt the precursor concentration distribution towards that region; for spatial regions requiring decreased epitaxial rate, the precursor flow rate setting can be decreased or the distribution ratio between different supply channels can be adjusted to moderately reduce the local precursor concentration.

[0054] Based on the adjusted temperature control curve and precursor flow setting parameters, a dynamically optimized temperature setting and precursor flow control strategy is obtained. After obtaining the temperature setting correction and precursor flow setting correction at each time step, a dynamically optimized temperature setting and precursor flow control strategy is formed based on the adjusted temperature control curve and precursor flow setting parameters. On the time axis, this dynamically optimized strategy is represented by adding a series of correction values ​​to the initial formula temperature control curve and initial precursor flow setting trajectory, which change in real time with the epitaxial rate trend prediction data and epitaxial rate perturbation prediction data. Spatially, it is represented by setting correction rules coupled with the local epitaxial rate deviation of the wafer for different heating regions and different precursor supply channels. The dynamically optimized temperature setting and precursor flow control strategy can be represented as a time scheduling table. Each row in the time scheduling table corresponds to a time step, and each column corresponds to a heating region or a precursor supply channel. Each table cell records the temperature setting value and precursor flow setting value that need to be executed for that heating region or precursor supply channel at that time step. By updating the temperature setpoints of each heating zone and the flow setpoints of each precursor supply channel in real time according to the time schedule during the epitaxial production process, the process conditions are corrected in a closed loop using epitaxial rate trend prediction data and epitaxial rate disturbance prediction data at each epitaxial growth time step, ensuring that the epitaxial rate of the local area of ​​the wafer gradually approaches the preset epitaxial rate target range throughout the entire epitaxial growth process. Example 2

[0055] The difference between Embodiment 2 and Embodiment 1 is that this embodiment introduces a wafer fabrication process optimization device to improve epitaxial ratio consistency.

[0056] A wafer fabrication process optimization apparatus for improving epitaxial ratio consistency includes: a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, a wafer fabrication process optimization method for improving epitaxial ratio consistency is implemented.

[0057] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0058] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0059] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and modules described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0060] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0061] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0062] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0063] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0064] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0065] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing wafer fabrication processes to improve epitaxial growth uniformity, characterized in that, Includes the following steps: S1: Collect stress change data and wafer geometry data on the wafer surface during wafer epitaxy, perform preprocessing, and output characteristic parameters of wafer surface stress distribution and wafer geometry change. S2: Based on the characteristic parameters of stress distribution on the wafer surface, evaluate the changes in heat conduction and mass transfer conditions in the local area of ​​the wafer caused by stress distribution, and output the dynamic characteristic parameters of local heat and mass transfer on the wafer. S3: Based on the characteristic parameters of wafer geometry variation, simulate the changes in local airflow and heat transfer boundary layer under different wafer local morphology conditions, and output the dynamic characteristic parameters of wafer boundary layer heat and mass transport. S4: Based on the dynamic characteristic parameters of local heat and mass transfer in the wafer, predict the epitaxial rate change trend in the local region of the wafer and output the epitaxial rate trend prediction data. S5: Based on the dynamic characteristic parameters of thermal and mass transport in the wafer boundary layer, analyze the influence of local boundary layer changes on precursor concentration distribution and local epitaxial rate, and output epitaxial rate perturbation prediction data. S6: Based on the epitaxial rate trend prediction data and epitaxial rate disturbance prediction data, dynamically optimize the temperature setting and precursor flow control strategy of the wafer epitaxial process.

2. The wafer fabrication process optimization method for improving epitaxial ratio consistency according to claim 1, characterized in that, S1, specifically: Data on wafer surface stress variation and wafer geometry were collected during the wafer epitaxy process. Denoising and data smoothing are performed on wafer surface stress variation data and wafer geometric morphology data; Extract characteristic parameters of wafer surface stress distribution from wafer surface stress variation data that has undergone noise reduction and data smoothing; Extract wafer geometry variation feature parameters from wafer geometry variation data that has undergone denoising and data smoothing.

3. The wafer fabrication process optimization method for improving epitaxial ratio consistency according to claim 2, characterized in that, S2, specifically: Based on the characteristic parameters of stress distribution on the wafer surface, a finite element analysis model of a local region of the wafer is established; Using a finite element analysis model of a local region of a wafer, the changes in heat conduction characteristics caused by stress distribution in that local region are calculated; Using a finite element analysis model of a local region of the wafer, the changes in mass transfer characteristics caused by stress distribution in the local region of the wafer are calculated; Based on the changes in heat conduction and mass transfer characteristics, the dynamic variation law of heat conduction and mass transfer conditions in local areas of the wafer with stress is determined, and the dynamic characteristic parameters of local heat and mass transfer in the wafer are output.

4. The wafer fabrication process optimization method for improving epitaxial ratio consistency according to claim 3, characterized in that, S3, specifically: Based on the characteristic parameters of wafer geometry variation, a three-dimensional simulation geometric model is established that includes wafer surface morphology information and the airflow channel structure in the epitaxial reaction cavity. In the three-dimensional simulation geometric model, the wafer local region is divided, and the airflow calculation region and heat transfer boundary layer calculation region corresponding to each wafer local region are defined; The gas velocity distribution and gas pressure distribution within each airflow calculation region are solved to obtain local airflow distribution data; In each heat transfer boundary layer computational region, the temperature distribution and heat flux distribution are calculated to obtain heat transfer boundary layer variation data; Based on local airflow distribution data and heat transfer boundary layer variation data, dynamic characteristic parameters of heat and mass transport in the wafer boundary layer are extracted.

5. The wafer fabrication process optimization method for improving epitaxial ratio consistency according to claim 4, characterized in that, S4, specifically: Based on the dynamic characteristic parameters of local heat and mass transfer in wafers, time series data of heat conduction characteristic parameters and mass transfer characteristic parameters corresponding to local regions of each wafer are determined; Based on time-series data of thermal conduction and mass transfer characteristic parameters, a functional relationship model is established between the dynamic characteristic parameters of local thermal and mass transfer on the wafer and the epitaxial rate of the local region of the wafer. The epitaxial rate of a local region of the wafer was calculated using a functional relationship model at different time points, and the trend data of the epitaxial rate of a local region of the wafer was obtained. The epitaxial rate trend data of local areas of the wafer are combined according to the spatial distribution of the local areas on the wafer to form epitaxial rate trend prediction data.

6. The wafer fabrication process optimization method for improving epitaxial ratio consistency according to claim 5, characterized in that, S5, specifically: Based on the dynamic characteristic parameters of thermal mass transport in the wafer boundary layer, the airflow velocity distribution, airflow pressure distribution, temperature distribution, and heat flux distribution data corresponding to the local region of the wafer are determined. Based on airflow velocity distribution data and airflow pressure distribution data, calculate the gas residence time distribution and gas precursor concentration distribution; Based on temperature distribution data and heat flux distribution data, the local reaction temperature gradient and thermal boundary layer thickness are calculated. Based on the gas residence time distribution, gas precursor concentration distribution, local reaction temperature gradient, and thermal boundary layer thickness, the dynamic relationship between precursor concentration distribution and local epitaxial rate under the condition of local boundary layer variation is determined, and epitaxial rate perturbation prediction data is output.

7. The wafer fabrication process optimization method for improving epitaxial ratio consistency according to claim 6, characterized in that, S6, specifically: Based on epitaxial rate trend prediction data and epitaxial rate disturbance prediction data, an evaluation standard for the prediction deviation of epitaxial rate in local areas of wafers is established. Based on the evaluation criteria for the prediction deviation of the epitaxial rate in a local area of ​​the wafer, it is determined whether the epitaxial rate in a local area of ​​the wafer deviates from the target range of the epitaxial rate. When the epitaxial rate in a local area of ​​the wafer deviates from the target range of the epitaxial rate, the temperature control curve in the epitaxial reaction chamber and the precursor flow rate setting parameters entering the epitaxial reaction chamber are dynamically adjusted. Based on the adjusted temperature control curve and precursor flow setting parameters, a dynamically optimized temperature setting and precursor flow control strategy is obtained.

8. A wafer fabrication process optimization apparatus for improving epitaxial ratio consistency, characterized in that, include: A processor, a memory, and a program or instructions stored in the memory and executable on the processor, wherein when the program or instructions are executed by the processor, they implement a wafer fabrication process optimization method for improving epitaxial ratio consistency as described in any one of claims 1-7.

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