A Process Optimization Method for the Thickness Uniformity of Silicon Epitaxial Growth Films
By combining the process optimization method of DOE experimental design ideas, the uniformity of silicon epitaxial growth film thickness is optimized, and the problems of many experiments and resource consumption in the existing technology are solved, and rapid debugging and optimal uniformity prediction are achieved.
Patent Information
- Application Number
- CN202510066544.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-16
- Publication Date
- 2025-05-30
- Estimated Expiration
- 2045-01-16
AI Technical Summary
When optimizing the uniformity of silicon epitaxial growth film thickness, the prior art requires a large number of experiments and resources, making it difficult to quickly debug to achieve optimal uniformity.
Using a process optimization method combined with the DOE experimental design idea, we use a process optimization method to determine process variables and design different experimental process parameters, optimize the number of experimental test groups, reduce the number of experiments, and achieve the best uniformity prediction through nonlinear planning solutions.
It effectively reduces the wafer and machine consumption of the experiment, reduces the number of experiments, and achieves optimal uniformity prediction and rapid debugging.
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Figure CN119530963B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of silicon epitaxial growth, and particularly relates to a process optimization method for the film thickness uniformity of silicon epitaxial growth. Background Art
[0002] Silicon epitaxial growth is usually carried out using a silicon epitaxial furnace, and the reaction precursors are usually SiH 4 or dichlorosilane (DCS), etc., which are transported into the reaction chamber through H 2 The wafers and gases are heated by heating devices such as infrared lamps or incandescent lamps. The gas decomposes and adsorbs on the wafer surface to form an epitaxial layer. For silicon epitaxy, its thickness uniformity is an important index for measuring the quality of epitaxial growth. In the daily process debugging, one of the main tasks of process engineers is to achieve uniform growth of epitaxy by adjusting various parameters.
[0003] The growth rate of epitaxial silicon is closely related to parameters such as temperature, pressure, process gas flow rate, and process time. Taking temperature as an example, both the growth rate and temperature follow the Arrhenius curve. Under the condition of a given flow rate, the growth rate of epitaxial silicon on the wafer surface is mainly related to the temperature at the corresponding position. To optimize the film thickness of the epitaxial silicon layer on the wafer surface, it is mainly achieved by adjusting the power of the heating element. For an epitaxial reaction chamber, there are often many types of heating elements, such as strip lamps or circular incandescent lamps. It is difficult to explore and optimize the optimal lamp power ratio by adjusting the power of a single lamp, and a large number of experiments are required. Moreover, often only adjusting a single lamp cannot obtain the optimal uniformity, and a combination adjustment of multiple lamps is required to obtain better uniformity.
[0004] In the actual operation process, the DOE method is usually used for experimental design, and then the linear response degree of each group of parameters is calculated. A good uniformity is obtained through the linear combination of the response degrees of these parameter groups. This method can simplify the number of experimental groups required for single variable adjustment to a certain extent during experimental design. However, for the solution of the optimal lamp ratio, many linear combination experiments are still required.
[0005] Therefore, it is necessary to develop a process optimization method for the film thickness uniformity of silicon epitaxial growth, in order to reduce the actual experimental requirements and achieve the purpose of rapid debugging. Summary of the Invention
[0006] In view of the problems existing in the prior art, the present invention provides a process optimization method for the film thickness uniformity of silicon epitaxial growth. Combining the experimental design idea of DOE, by determining process variables and respectively designing i groups (i≥3) of different experimental process parameters, the number of experimental tests can be optimized, effectively reducing the consumption of wafers and machines in the experiment, effectively reducing the number of experiments, and realizing the prediction of the best uniformity.
[0007] To achieve this purpose, the present invention adopts the following technical solutions:
[0008] The object of the present invention is to provide a process optimization method for the thickness uniformity of silicon epitaxial growth films. The process optimization method includes the following steps:
[0009] (1) Determine the basic conditions: Prepare i identical substrates, and based on the chemical vapor deposition method, use the same basic process parameters to grow Si layers on the substrates respectively;
[0010] (2) Design the experimental scheme: Determine the process variables, design i groups of different experimental process parameters, where i≥3, perform silicon epitaxial growth on the i groups of Si layers obtained in step (1) respectively, and measure the silicon epitaxial growth film thickness curves Ai respectively;
[0011] (3) Calculate the sensitivity: Normalize the silicon epitaxial growth film thickness curves Ai obtained in step (2), calculate the sensitivity of the silicon epitaxial growth film thickness to the i groups of different experimental process parameters respectively, and obtain i sensitivity curves;
[0012] (4) Nonlinear programming solution: Based on the i sensitivity curves obtained in step (3), set a group of parameter sets (α1, α2, to αi) as the prediction parameter sets, linearly combine the two, obtain the ideal film thickness curve and solve its ideal uniformity characterization value R 理想 ;
[0013] (5) Experimental verification: Integrate the prediction parameter sets described in step (4) with the basic process parameters described in step (1), perform experimental verification on the obtained verification process parameters, obtain the verification group film thickness curve and solve its verification uniformity characterization value R 验证 ; Calculate the comparison difference Q = │100% - R 验证 / R 理想 │; If the comparison difference Q meets the requirements and conforms to the prediction, the verification process parameters are used as the process optimization group; otherwise, if it does not conform to the prediction, return to re - establish the optimization model.
[0014] The process optimization method described in the present invention combines the experimental design idea of DOE. By determining process variables and designing i groups (i≥3) of different experimental process parameters respectively, it effectively reduces the consumption of wafers and machines in experiments. After the first round of experiments, the best parameter group is obtained by calculating non-linear programming using a Python script, effectively reducing the number of experiments and realizing the prediction of the best uniformity. Through this prediction script, it is possible to quickly know the best uniformity of the Si epitaxial layer under corresponding parameter changes and make effective adjustments according to the parameter group. If the Si uniformity obtained from the current process variables cannot meet the target process requirements, the process variables can also be changed or added according to this result and prediction, and non-linear programming can be carried out again for prediction. This prediction model establishes virtual measurement for the epitaxial machine, effectively reducing the need for actual experiments and providing a solution for rapid debugging.
[0015] Regarding step (5), the comparison difference Q = │100% - R 验证 / R 理想 │ is the absolute value. If the comparison difference Q meets the requirements and conforms to the prediction, it proves that the feasibility of this optimization model is high, and the best uniformity under the corresponding variable conditions can be obtained according to the prediction parameters given by this optimization model; otherwise, it does not conform to the prediction. If the deviation is large, it proves that the sensitivity feasibility of the parameter variables in this optimization model is not high, and it is necessary to return to step (2) to re-collect sensitivity data under the predicted best uniformity conditions and re-establish the optimization model; if the deviation is small, it is possible to return to step (4) to adjust the value of the prediction parameter group.
[0016] As a preferred technical solution of the present invention, the process variables in step (2) include any one or at least two combinations of temperature, pressure, process gas flow rate, and process time.
[0017] As a preferred technical solution of the present invention, the process variable in step (2) is temperature. By grouping the heating elements and adjusting the power ratio of the heating elements relative to the rated power, i groups of different experimental process parameters are designed; regarding the grouping of heating elements, it is often divided according to the positional relationship of the heating elements, especially the symmetry relationship.
[0018] As a preferred technical solution of the present invention, the normalization process in step (3) includes: dividing the silicon epitaxial growth film thickness curves Ai obtained in step (2) by their respective film thickness average values.
[0019] As a preferred technical solution of the present invention, the non-linear programming solution in step (4) includes: using the non-linear programming solver in the sicpy package, defining the variable upper and lower bounds and initializing, calling the minimize function, performing optimization, solving for the minimum value and outputting the optimization result, and giving the parameter conditions.
[0020] As a preferred technical solution of the present invention, the ideal uniformity characterization value R 理想 and the verification uniformity characterization value R 验证 are both the maximum differences obtained by subtracting the minimum value from the maximum value of the corresponding film thickness curve.
[0021] As a preferred technical solution of the present invention, in step (5), if the comparison difference Q ≤ 10%, it conforms to the prediction, and a process optimization group is obtained.
[0022] As a preferred technical solution of the present invention, in step (5), if 10% < comparison difference Q < 20% is satisfied, it does not conform to the prediction, and the specific values of the prediction parameter group are returned to step (4) for adjustment.
[0023] As a preferred technical solution of the present invention, in step (5), if the comparison difference Q ≥ 20%, it does not conform to the prediction, and step (2) is returned to re-determine the process variables or add process variables, and i different sets of experimental process parameters are re-designed.
[0024] As a preferred technical solution of the present invention, in step (5), when the process variables are re-determined and i different sets of experimental process parameters are re-designed, and the obtained comparison difference satisfies 10% < comparison difference Q < 20%, the specific values of the prediction parameter group are returned to step (4) for adjustment.
[0025] Compared with the prior art solutions, the present invention has at least the following beneficial effects:
[0026] The present invention provides a process optimization method for the film thickness uniformity of silicon epitaxial growth, including successively determining the basic conditions, designing the experimental scheme, calculating the sensitivity, solving by nonlinear programming, and experimental verification. Finally, a process optimization group can be obtained to optimize the actual process. The process optimization method of the present invention combines the experimental design idea of DOE. By determining the process variables and respectively designing i sets (i ≥ 3) of different experimental process parameters, the number of experimental test groups can be optimized, effectively reducing the consumption of wafers and machines in the experiment, effectively reducing the number of experiments, and realizing the prediction of the best uniformity. BRIEF DESCRIPTION OF THE DRAWINGS
[0027] Figure 1 is a schematic diagram of an epitaxial reaction chamber according to a specific embodiment of the present invention.
[0028] Figure 2 is Figure 1 a schematic diagram of the lamp tube arrangement in
[0029] Figure 3 is a schematic diagram of successive depositions on a substrate according to a specific embodiment of the present invention.
[0030] Figure 4It is a map of the film thickness distribution of the Si layer in the basic group of a specific embodiment of the present invention.
[0031] Figure 5 It is a curve graph of the film thickness distribution of the Si layer on the X-axis in the basic group of a specific embodiment of the present invention.
[0032] Figure 6 It is the sensitivity curve corresponding to Adjustment Group 1 in a specific embodiment of the present invention.
[0033] Figure 7 It is the sensitivity curve corresponding to Adjustment Group 2 in a specific embodiment of the present invention.
[0034] Figure 8 It is the sensitivity curve corresponding to Adjustment Group 3 in a specific embodiment of the present invention.
[0035] Figure 9 It is the sensitivity curve corresponding to Adjustment Group 4 in a specific embodiment of the present invention.
[0036] Figure 10 It is a triple-line comparison graph after normalization of the basic group, prediction parameter group, and verification group in a specific embodiment of the present invention.
[0037] Figure 11 It is a logical execution block diagram of the process optimization method for the film thickness uniformity of silicon epitaxial growth according to the present invention. Specific Embodiment
[0038] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings and through specific embodiments.
[0039] To better illustrate the present invention and facilitate understanding of its technical solution, typical but non-limiting embodiments of the present invention are as follows:
[0040] The present invention provides a process optimization method for the film thickness uniformity of silicon epitaxial growth, as Figure 11 shown, the process optimization method includes the following steps:
[0041] (1) Determine the basic conditions: Prepare i identical substrates, and based on the chemical vapor deposition method, use the same basic process parameters to grow Si layers on the substrates respectively;
[0042] (2) Design an experimental plan: Determine the process variables, design i groups of different experimental process parameters, i≥3, and perform silicon epitaxial growth on the i groups of Si layers obtained in step (1) respectively, and measure the silicon epitaxial growth film thickness curve Ai;
[0043] (3) Calculate the sensitivity: Normalize the silicon epitaxial growth film thickness curve Ai obtained in step (2), and calculate the sensitivity of the silicon epitaxial growth film thickness to i groups of different experimental process parameters respectively to obtain i sensitivity curves;
[0044] (4) Nonlinear programming solution: Based on the i sensitivity curves obtained in step (3), set a group of parameter sets (α1, α2, to αi) as the prediction parameter sets, linearly combine the two, obtain the ideal film thickness curve and solve its ideal uniformity characterization value R 理想 ;
[0045] (5) Experimental verification: Integrate the prediction parameter sets described in step (4) with the basic process parameters described in step (1), conduct experimental verification on the obtained verification process parameters, obtain the verification group film thickness curve and solve its verification uniformity characterization value R 验证 ; Calculate the comparison difference Q = │100% - R 验证 / R 理想 │; If the comparison difference Q meets the requirements and conforms to the prediction, the verification process parameters are used as the process optimization group; otherwise, if it does not conform to the prediction, return to re - establish the optimization model; specifically, if the comparison difference Q ≤ 10%, it conforms to the prediction and the process optimization group is obtained; if 10% < comparison difference Q < 20%, it does not conform to the prediction, return to step (4) to adjust the specific values of the prediction parameter sets; if the comparison difference Q ≥ 20%, it does not conform to the prediction, return to step (2) to re - determine the process variables and re - design i groups of different experimental process parameters. Specifically, returning to step (2) includes but is not limited to re - determining the process variables, or re - determining the process variable range (upper and lower limits), adding process variables, etc.
[0046] The process variable selection of the present invention includes any one or a combination of at least two of temperature, pressure, process gas flow rate, and process time.
[0047] A specific embodiment of the present invention provides a process optimization method for the uniformity of the silicon epitaxial growth film thickness. The process variable is determined to be temperature, and the process optimization method includes the following content:
[0048] Use a silicon epitaxial furnace for growth. As Figure 1 shown, the heating of the epitaxial reaction chamber is usually carried out by heating elements (infrared lamps) outside the quartz chamber. The energy is radiated into the gas and wafers in the quartz chamber through the reflection gold plate above the infrared lamps, and the outside of the chamber is cooled by water cooling and air cooling to ensure that the components will not be damaged due to high temperature. During the heating process, the actual temperature in the chamber is measured by a thermometer and compared with the set value. The PID temperature control is carried out through a program. The program outputs a PID calculated value, which is multiplied by the power ratio of the infrared lamps to obtain the actual output power of each infrared lamp.
[0049] Due to the relatively complex infrared lamp tubes and heat dissipation structure, in order to achieve a uniform temperature field on the surface of the quartz cavity wafer, it is necessary to adjust the power ratio of each infrared lamp tube to obtain a relatively uniform temperature field. As Figure 2 shown, there are a total of 22 linear infrared lamp tubes in the actual silicon epitaxial furnace and 4 lighting lamps ( Figure 2 not shown in the figure) located at the middle position directly below the quartz cavity wafer. It is relatively complex to individually adjust the power ratio of the infrared lamp tubes to obtain a uniform temperature field. A change in the power ratio of each infrared lamp tube will cause a change in the power of other infrared lamp tubes and a change in the temperature at each point on the wafer surface.
[0050] During the process of silicon epitaxial growth, since the growth rate of SiH 4 in the low-temperature section is mainly determined by temperature, adjusting the film thickness uniformity of epitaxial silicon is mainly achieved by optimizing the temperature field uniformity. During the actual process debugging, in order to effectively measure the thickness of the epitaxial Si layer, a SiGe layer is first grown on the substrate, and then a Si layer is grown. Since the n and k coefficients of SiGe and Si are different, both the SiGe and Si layers can be measured and fitted through an ellipsometer.
[0051] Determine the basic conditions: During the process of determining the basic conditions, prepare 4 identical substrates, and set the power of the 22 linear infrared lamp tubes and the 4 lighting lamps at the bottom according to the power ratio of the basic group compared to the rated power in Table 1; it should be noted that the power ratio of the 4 lighting lamps changes uniformly. Taking the basic group as an example, if the power ratio of the lighting lamp numbered 23 is 50%, it means that the power of all 4 lighting lamps is set to 50% of the rated power; as Figure 3 shown, using chemical vapor deposition, deposit a SiGe layer and a Si layer on the Si substrate in sequence. Measure the basic Si layer film thickness curve through an ellipsometer, and then perform silicon epitaxial growth on the Si layer. Measure 4 Si layer film thickness curves through an ellipsometer respectively, and subtract the 4 Si layer film thickness curves from the corresponding Si layer film thickness curve of the basic group to obtain 4 silicon epitaxial growth film thickness curves Ai; although the basic group is carried out 4 times and 4 deposited Si layers can be obtained, under completely the same process conditions, one of the deposited Si layers can be selected to test the deposited film thickness distribution. Figure 4 The map of the Si layer film thickness distribution of the basic group is shown, Figure 5 The curve graph of the Si layer film thickness distribution on the X-axis of the basic group is shown, Figure 5 where the abscissa is the distance from the coordinate origin (unit: mm), the ordinate is the Si layer film thickness on the X-axis (unit: angstrom), and a total of 49 test points are selected;
[0052] Design the experimental plan: Design the experiment through DOE, divide it according to the positions of each heating element, mainly according to the symmetry relationship. Select 4 groups of infrared lamps or lighting lamps, and adjust the power ratio of each group respectively. The specific adjustment situations are shown in Table 1. Compared with the basic group, in adjustment group 1, the central infrared lamps are adjusted. Specifically, the power ratios of the three infrared lamps at the upper center (numbered 3, 4, 5) and the three infrared lamps at the lower center (numbered 10, 11, 12) are increased respectively. Compared with the basic group, in adjustment group 2, the inner ring infrared lamps are adjusted. Specifically, the power ratios of the two infrared lamps at the upper layer (numbered 1, 2, 6, 7) and the two infrared lamps at the lower layer (numbered 8, 9, 13, 14) are increased respectively. Compared with the basic group, in adjustment group 3, the outer ring infrared lamps are adjusted. Specifically, the power ratios of the two infrared lamps at the upper layer (numbered 17, 18, 21, 22) and the two infrared lamps at the lower layer (numbered 15, 16, 19, 20) are increased respectively. Compared with the basic group, in adjustment group 4, the lighting lamps are adjusted. Specifically, the power ratios of the 4 lighting lamps numbered 23 are increased.
[0053] Table 1
[0054]
[0055] Note: The percentages in the table all refer to the ratio of the actual power of the infrared lamp or lighting lamp to the rated power.
[0056] It should be noted that during the execution of the formula, the power ratio distribution of the lamps in the SiGe layer still follows the basic power ratio. After the SiGe is deposited, the power ratio of the lamps is switched to a new power ratio of the lamps. After waiting for the temperature to stabilize, Si epitaxial deposition is carried out. The grown wafer is measured by an ellipsometer again to obtain the film thickness distribution of the Si layer after changing the power ratio of the lamps.
[0057] Calculate the sensitivity: Subtract the Si layer film thickness curves of 4 groups from the Si layer film thickness curve corresponding to the basic group respectively, and then obtain 4 silicon epitaxial growth film thickness curves Ai. Normalize each silicon epitaxial growth film thickness curve Ai, that is, divide each silicon epitaxial growth film thickness curve Ai by its respective film thickness average value, and then calculate the sensitivity of the silicon epitaxial growth film thickness to the power change of the aforementioned 4 groups of infrared lamps or lighting lamps respectively, and obtain 4 sensitivity curves, as shown respectively Figures 6 - 9 shown;
[0058] Nonlinear programming solution: Based on the aforementioned 4 sensitivity curves, the parameter sets (α1, α2, α3, α4) corresponding to adjustment group 1, adjustment group 2, adjustment group 3, and adjustment group 4 are set to (2, 1, 0.5, -2) as the prediction parameter set. According to the process conditions, its upper and lower bounds are specified, and the linear combination of this prediction parameter set and the corresponding sensitivity curves is calculated to obtain an ideal film thickness curve under the adjustment of the prediction parameter set. The maximum difference corresponding to this film thickness curve is solved to be 18.97 Å, which is used as the ideal uniformity characterization value R 理想 ;
[0059] Experimental verification: According to the integration of the prediction parameter set and the power ratio of the basic group in Table 1, the power ratio corresponding to the verification group in Table 1 is obtained, and experimental verification is carried out to obtain the film thickness curve of the verification group. The maximum difference corresponding to this film thickness curve is solved to be 20.23 Å, which is used as the verification uniformity characterization value R 验证 ; Calculate the comparison difference Q = │100% - R 验证 / R 理想 │ = 6.64%. Since the comparison difference Q ≤ 10%, which is in line with the prediction, the power ratio corresponding to the verification group is used as the process optimization group.
[0060] For intuitive comparison, after normalizing the X-axis Si layer film thickness distribution curve diagram, that is, each silicon epitaxial growth film thickness curve is divided by its respective film thickness average value, the normalized curves of the basic group, prediction parameter group, and verification group are integrated in Figure 10 the three-line comparison diagram in. It can be seen that the prediction parameter group and the verification group basically coincide, indicating that the process optimization method of the present invention has a high feasibility.
[0061] It should be noted that all parameters during the DOE design experiment are subjected to the above-mentioned experimental measurements and calculations to obtain the sensitivity data corresponding to each parameter. After obtaining these data, program writing is carried out. A numerical variable is set for each parameter, a reasonable upper and lower limit is determined according to the actual on-site requirements, and then a target thickness is calculated. The specific calculation method is the normalized thickness of the base film plus the linear combination of these parameters and sensitivity data. Then, the minimum value of the range of the target thickness is solved using the nonlinear programming in the sicpy package of python. The specific logical steps include: defining the variable upper and lower bounds and initializing them, calling the minimize function in the SciPy library, performing optimization, outputting the optimization results, and giving the parameter conditions. Through script calculation, the target film thickness with the best uniformity and the corresponding parameter values under the current parameter group can be obtained. According to the calculated parameter values, the corresponding parameters can be directly modified and the experiment is verified again to see whether the actual film thickness and the calculated film thickness meet under this condition. If it meets the prediction, it proves that the optimization model has a high feasibility. According to the best parameters given by the model, the best uniformity can be obtained under the corresponding variable conditions. If it does not meet the expectation, it means that the sensitivity of these parameter variables has a low feasibility, and it is necessary to re-collect the sensitivity data based on the predicted parameter group and re-establish the optimization model. In addition, the best uniformity under the current parameter group conditions can be judged according to this calculated film thickness. If the current uniformity still cannot meet the requirements, other parameter groups need to be additionally introduced for sensitivity testing. Nonlinear programming is performed again to obtain the film thickness topography with the best uniformity. Through continuous iteration and optimization, better uniformity can be obtained. This method can effectively and quickly give the corresponding experimental conditions and predict the best experimental results. As an important auxiliary means of virtual metrology, it greatly improves the actual debugging efficiency.
[0062] The present invention provides a process optimization method for the film thickness uniformity of silicon epitaxial growth, including determining the basic conditions, designing an experimental scheme, calculating sensitivity, solving by nonlinear programming, and experimental verification carried out in sequence. Finally, a process optimization group can be obtained to optimize the actual process. The process optimization method of the present invention combines the experimental design idea of DOE. By determining the process variables and respectively designing i groups (i≥3) of different experimental process parameters, the number of experimental test groups can be optimized, effectively reducing the consumption of wafers and machines in the experiment, effectively reducing the number of experiments, and realizing the prediction of the best uniformity.
[0063] The present invention illustrates the detailed structural features of the present invention through the above embodiments, but the present invention is not limited to the above detailed structural features, that is, it does not mean that the present invention must rely on the above detailed structural features to be implemented. Those skilled in the art should understand that any improvement to the present invention, the equivalent replacement of the components selected for the present invention, the addition of auxiliary components, the selection of specific methods, etc. all fall within the protection scope and the disclosure scope of the present invention.
[0064] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.
[0065] In addition, it should be noted that, among the various specific technical features described in the above specific embodiments, they can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not separately describe various possible combination methods.
[0066] In addition, any combination can be made between various different embodiments of the present invention, as long as it does not violate the idea of the present invention, it should also be regarded as the content disclosed by the present invention.
Claims
1. A process optimization method for uniformity of silicon epitaxial growth film thickness, characterized in that: The process optimization method comprises the following steps: (1) Determine the basic conditions: prepare i identical substrates, and grow Si layers on the substrates respectively using the same basic process parameters based on the chemical vapor deposition method; (2) Designing an experimental plan: Determine the process variable as temperature, design i groups of different experimental process parameters by grouping the heating elements and adjusting the power ratio of the heating elements relative to the rated power, i ≥ 3, perform silicon epitaxial growth on the i groups of Si layers obtained in step (1), and measure the silicon epitaxial growth film thickness curves Ai respectively; (3) Calculating sensitivity: dividing the silicon epitaxial growth film thickness curves Ai obtained in step (2) by their respective average film thickness values for normalization, and calculating the sensitivity of the silicon epitaxial growth film thickness to i groups of different experimental process parameters, respectively, to obtain i sensitivity curves; (4) Nonlinear programming solution: Based on the i sensitivity curves obtained in step (3), a set of parameters (α1, α2, to αi) is set as the prediction parameter set, and the two are linearly combined to obtain the ideal film thickness curve and solve its ideal uniformity characterization value R 理想 ; Wherein, the nonlinear programming solution includes: defining upper and lower bounds of variables and initializing them, calling minimize function, performing optimization, solving the minimum value and outputting the optimization result, and giving parameter conditions; (5) Experimental verification: Integrate the predicted parameter group described in step (4) with the basic process parameters described in step (1), conduct experimental verification on the obtained verification process parameters, obtain the film thickness curve of the verification group and solve its verification uniformity characterization value R 验证 ; Calculate the contrast difference Q =│100%-R 验证 / R 理想 │; If the comparison difference Q meets the requirements and conforms to the prediction, the process parameters are verified as the process optimization group; otherwise, it does not conform to the prediction and returns to re-establish the optimization model; Among them, if the comparison difference Q≤10%, it is consistent with the prediction and the process optimization group is obtained; If 10% < contrast difference Q < 20% is satisfied, the prediction is not met, and the process returns to step (4) to adjust the specific values of the prediction parameter group; If the comparison difference Q ≥ 20%, which does not meet the prediction, return to step (2), redefine the process variables or increase the process variables, and redesign i groups of different experimental process parameters; if the process variables are redetermined and i groups of different experimental process parameters are redesigned, the obtained comparison difference satisfies 10% < comparison difference Q < 20%, return to step (4) to adjust the specific values of the prediction parameter group or increase the process variables.
2. The process optimization method according to claim 1, characterized in that: Ideal uniformity characterization value R 理想 , Verify the uniformity characterization value R 验证 They are the maximum differences obtained by subtracting the maximum and minimum values of the corresponding film thickness curves.
Citation Information
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