Method for optimizing epitaxial growth of semiconductor film

Abstract

The invention belongs to the technical field of semiconductor preparation, and particularly relates to an optimization method for epitaxial growth of a semiconductor film. The method comprises the following steps: simulating a thin film chemical vapor deposition process by using a finite element method to obtain an epitaxial layer distribution result; comparing a simulation result with an experimental result, and verifying the accuracy of the simulation result; using a support vector machine to establish a relationship between the process parameters and the target function; optimizing the epitaxial growth process by using a multi-objective optimization algorithm; wherein the process parameters are growth temperature, chamber pressure and total flow of reaction gas; the objective function is the epitaxial layer growth rate and the variation coefficient of the epitaxial layer; the variable coefficient is equal to the ratio of the standard deviation of the epitaxial layer thickness to the average value of the thickness; the multi-objective optimization algorithm comprises a multi-objective particle swarm algorithm and a non-dominated sorting genetic algorithm. The method can reduce the number of experiments, improve the growth efficiency and reduce the production cost.

Description

Technical Field

[0001] The invention belongs to the technical field of semiconductor preparation, and in particular relates to an optimization method for epitaxial growth of a semiconductor film. Background Art

[0002] In the semiconductor production process, epitaxial thin film growth is one of the important processes in semiconductor device and chip manufacturing. The uniformity of epitaxial thin film growth is an important indicator to measure the quality of the film. Epitaxial films with more uniform thickness can produce semiconductor devices with better performance.

[0003] The growth rate of the epitaxial layer affects the growth efficiency of the epitaxial wafer, and its coefficient of variation is an important indicator for measuring the quality of the epitaxial layer, so these two parameters need to be optimized. Traditional epitaxial growth process optimization mostly uses trial and error, which is heavily dependent on the experience of the staff, and has high time and economic costs. At the same time, it will produce some unusable waste wafers, causing serious waste. With the development of numerical simulation technology, more and more researchers are applying simulation technology to process optimization to reduce the number of experiments. However, although simple numerical simulation can reduce the number of experiments to a certain extent and optimize the process parameters to a certain extent, it is also more dependent on the experience of the researchers and cannot obtain the optimal process parameters. Combining numerical simulation with optimization algorithms can not only reduce the number of experiments, but also obtain the optimal process parameters.

[0004] However, in current research, there are few studies on the simulation and optimization of thin film epitaxial growth, and most of them still adopt experimental optimization methods. Therefore, it is urgent to design a method for simulating and optimizing epitaxial thin films to achieve the purpose of improving the growth rate and uniformity of epitaxial thin films. Summary of the invention

[0005] In view of the complexity and high cost of the existing thin film epitaxial growth optimization method, the purpose of the present invention is to provide a method for optimizing the epitaxial growth of semiconductor thin films.

[0006] The optimization method for epitaxial growth of semiconductor thin films provided by the present invention comprises the following specific steps:

[0007] (1) The finite element method was used to simulate the thin film chemical vapor deposition process. Specifically, the finite element simulation software COMSOL was used to establish a three-dimensional model of the epitaxial furnace, and laminar flow, fluid heat transfer, dilute material transfer, chemistry, and surface reaction were added to the physical field. The reaction source gas used in the simulation was: SiHCl 3 and C 2 H 4 ; The specific chemical reaction is:

[0008] SiHCl3 →SiCl 2 +HCl,#(1)

[0009] 2C 2 H 4 →C 2 H 3 +C 2 H 5 ,#(2)

[0010] SiCl 2 →SiCl s +Cl,#(3)

[0011] C 2 H 3 →C s +CH s +H 2 ,#(4)

[0012] C 2 H 5 →C s +CH s +2H 2 ,#(5)

[0013] SiCl s +C s →SiC b +Cl,#(6)

[0014] SiCl s +CH s →SiC b +HCl,#(7)

[0015] The subscript s represents the surface material, and the subscript b represents the bulk material. The chemical vapor deposition process is divided into three parts: first, SiHCl 3 and C 2 H 4 Entering the reaction chamber, it decomposes at high temperature to generate intermediate substances; the intermediate substances that move to the substrate surface are adsorbed by the substrate and react on the surface to generate surface substances; the surface substances on the substrate surface continue to react to generate SiC. In the calculation results, the distribution of SiC thickness is analyzed, and the average thickness and coefficient of variation of SiC are calculated.

[0016] (2) Compare the simulation results with the experimental data to verify the accuracy of the simulation results; if the simulation results are significantly different from the experimental results, adjust the simulation model until the error between the simulation results and the experimental results is within an acceptable range, that is, less than 5%.

[0017] (3) Use support vector machine to establish the relationship between process parameters and objective function;

[0018] (4) Optimizing the chemical vapor deposition process using a multi-objective optimization algorithm;

[0019] in:

[0020] The process parameters are the growth temperature, reaction chamber pressure and total flow rate of reaction gas for epitaxial growth of semiconductor thin film;

[0021] The objective function is the epitaxial layer growth rate and the coefficient of variation of the epitaxial layer; the film growth time of all experiments and simulations is the same, so the average thickness and growth rate mentioned have the same meaning; the coefficient of variation is equal to the ratio of the standard deviation of the epitaxial layer thickness to the average value of the thickness;

[0022] The multi-objective optimization algorithms include a multi-objective particle swarm optimization algorithm [1] and a non-dominated sorting genetic algorithm [2].

[0023] Further:

[0024] The finite element simulation is a simulation of SiC chemical vapor deposition, in which the physical fields include laminar flow, fluid heat transfer, dilute material transfer, chemistry and surface reaction, and the input reaction gas is SiHCl 3 and C 2 H 4 .

[0025] The reaction chamber structure is a three-dimensional structure.

[0026] The reaction chamber is constructed based on an industrial hot-wall horizontal epitaxial furnace.

[0027] The verification of the accuracy of the simulation results includes the verification of the epitaxial layer growth rate and the coefficient of variation.

[0028] The multi-objective optimization is to import the function model between the objective function and the process parameters obtained by support vector regression, that is, a black box model with a Gaussian function as the kernel function, into the multi-objective optimization algorithm for optimization, that is, to find the optimal solution of the objective function according to the function model, and output the process parameters corresponding to the optimal solution.

[0029] The multi-objective optimization output result is the Pareto front of the objective function, wherein each point on the Pareto front is a non-dominated solution, that is, an optimal solution.

[0030] The Pareto front needs to be verified again using finite element simulation, that is, the process parameters corresponding to the optimal solution on the Pareto front are input into the established finite element simulation model for calculation, and then the simulation data is compared with the Pareto front again to verify the accuracy of the multi-objective optimization.

[0031] The beneficial effects of the present invention are mainly:

[0032] (1) The chemical vapor deposition process was simulated using the finite element method and compared with experimental results to ensure the accuracy of the simulation results, while reducing the number of experiments and saving costs.

[0033] (2) A support vector machine is used to establish the relationship between process parameters and the objective function. The regression result is highly accurate, and an accurate functional relationship is obtained with less time cost, avoiding a large number of mathematical operations.

[0034] (3) Use numerical simulation to obtain data, then use support vector machines to establish functional relationships, and then use a multi-objective optimization algorithm to output the Pareto frontier of the objective function. This method experiments with the optimization adjustment of thin film epitaxial growth, while avoiding the huge consumption caused by multiple experiments, improving growth efficiency, and reducing production costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The present invention is a flowchart of the optimization method for epitaxial growth of semiconductor thin films.

[0036] Figure 2 It is a structural diagram of the epitaxial reaction chamber of the present invention.

[0037] Figure 3 This is the epitaxial layer thickness distribution diagram and the comparison diagram between simulation and experiment.

[0038] Figure 4 Support vector regression results for epitaxial layer thickness and coefficient of variation.

[0039] Figure 5 (a) Pareto of multi-objective particle swarm optimization algorithm; (b) Pareto of non-dominated sorting genetic algorithm; (c) finite element simulation results of Pareto endpoints and turning points; (d) comparison chart of finite element simulation results and Pareto front. DETAILED DESCRIPTION

[0040] The present invention is further described below by means of specific examples in conjunction with the accompanying drawings.

[0041] A simulation and optimization method for epitaxial growth of semiconductor thin films, such as Figure 1 The specific steps are:

[0042] First, the epitaxial furnace is modeled using the finite element simulation software COMSOL, and then physical fields are added: laminar flow, fluid heat transfer, dilute material transfer, chemistry, and surface reaction. After the simulation model obtains the calculation results, the average film thickness and coefficient of variation of the simulation results are compared with the experimental results. If the error is less than 5%, the simulation result is considered accurate; if the error is greater than 5%, the model is adjusted until the error is less than 5%. Then, a process parameter is changed each time the simulation is performed to observe the effect of the process parameter on the average film thickness and coefficient of variation, and to determine the process parameter with the greater influence.

[0043] For the process parameters with greater influence, the corresponding boundary conditions are determined, and a set of random numbers are generated within the boundary conditions. Then, the set of random numbers is used for simulation to obtain the corresponding results.

[0044] Use support vector machine to regress the above simulation results. Support vector machine is a binary classification algorithm model. Its core idea is to find an optimal hyperplane to separate samples of different categories. Use support vector machine to regress data. The implementation method is as follows for a given data set:

[0045] D={(x 1 ,y 1 ),(x 2 ,y 2 ),…,(x m ,y m )},y i ∈R, (1)

[0046] Among them, m is the number of data groups in the data set, and R is a real number set.

[0047] Find a hyperplane: f(x) = w T x+b, so that the model is i The predicted value f(x i ) and the true value y i The error between them is as small as possible, where w is the normal vector, which determines the direction of the hyperplane, and T represents the transposition. The function form of the final hyperplane is:

[0048]

[0049] in, The sample is the support vector of support vector regression, κ(x i T x) is the kernel function, which is in the form of inner product:

[0050] κ(x i T x) =φ(x i ) T φ(xj ), (3)

[0051] The φ function is used to map x from the original feature space X to another feature space Z. Here, Gaussian kernel feature mapping is used. The Gaussian kernel can be understood as an "infinite-dimensional" polynomial expansion. The specific dimension can be determined according to the specific problem, which has great flexibility. After the support vector machine regresses the data, it outputs a function model;

[0052] Then the function model is imported into the multi-objective optimization algorithm to find the optimal solution. The two multi-objective optimization algorithms used in this optimization problem are the multi-objective particle swarm algorithm ( Figure 1 The right box in the middle) and the non-dominated sorting genetic algorithm ( Figure 1 The two boxes give the specific processes of the two optimization algorithms. Both optimization algorithms eventually output the Pareto frontiers of the two objective functions. For two solutions A and B, if at least one objective function of A is better than B, and all objective functions of B are not better than A, then A is said to dominate B, that is, A is not dominated by B. If a solution is not dominated by all other solutions, then this solution is called a non-dominated solution, and the set of all non-dominated solutions of the optimization problem is called the non-dominated solution set, that is, the Pareto frontier.

[0053] In the present invention, the structure of the epitaxial reaction chamber is as follows Figure 2 As shown, there are three groups of gas inlets on the left, with the numbers being 5:16:5 respectively, and the gas flow ratio of the three groups of gas inlets is 1:2:1. There is a rotatable tray in the middle of the reaction chamber, on which the substrate is placed, and it rotates with the tray. The unreacted gas and the gas produced by the reaction are discharged from the gas outlet on the right.

[0054] The chemical vapor deposition process in the simulation is as follows: the reaction gas enters from the left inlet, undergoes a gas phase reaction in the high temperature environment of the reaction chamber, and generates an intermediate substance; the intermediate substance is adsorbed on the substrate to generate a surface substance; the surface substance continues to react to grow a thin film; the unreacted gas and the gas generated by the reaction are discharged from the outlet. In the simulation results, the distribution of the epitaxial layer shows the characteristics of being thin in the middle and thick at the edges. By comparing it with the experimental results, it can be found that the error between the simulation results and the experimental results is small, and the chemical vapor deposition model is accurate. Figure 3 shown.

[0055] In the simulation model, a single factor analysis was performed on a series of process parameters, and it was found that the chamber pressure, growth temperature and total gas flow rate had a great influence on the average thickness and coefficient of variation of the film, so these three factors were analyzed. While analyzing these three factors, other settings remained unchanged. The chamber pressure can affect the flow field in the reaction chamber and the adsorption of intermediate substances on the substrate surface, thereby affecting the growth of epitaxial films. The chamber pressure is an important factor in the epitaxial growth process of thin films. The simulation of chemical reactions generally uses the Arrhenius formula to describe the chemical reaction rate, where the expression of the Arrhenius formula is:

[0056]

[0057] Where k is the reaction rate, A is the pre-exponential factor, T is the temperature, n is the exponent, E is the activation energy, and R g is the ideal gas constant. The relationship between temperature and reaction rate can be intuitively seen from the Arrhenius formula. Therefore, growth temperature is an important influencing factor in the epitaxial growth process of thin films. In general, the reaction rate of a chemical reaction has a great relationship with the concentration of the reaction. When the total flow rate of the reaction gas is changed, the growth of the film will be affected to a certain extent. This optimization problem contains three variables: chamber pressure, growth temperature and total gas flow rate. The objective function of this optimization problem is the growth rate and the coefficient of variation.

[0058] The support vector machine has excellent classification and regression capabilities, good generalization ability when processing small sample data, and high accuracy and stability. The regression results of growth rate and coefficient of variation are as follows Figure 4 As shown, Figure 4 (a) and Figure 4 (b) are the comparison diagrams of the actual and predicted values ​​of the training and test sets for the average thickness, Figure 4 (c) and Figure 4 (d) is a comparison chart of the true and predicted values ​​of the training set and the test set of the coefficient of variation. The errors between the true and predicted values ​​of the two objective functions are relatively small, and the regression model is accurate.

[0059] Multi-objective particle swarm optimization and non-dominated sorting genetic algorithm are two commonly used multi-objective optimization algorithms. The processes of the two algorithms are as follows: Figure 1 As shown in Figure 2, both algorithms use the Pareto frontier to analyze the optimization results when dealing with multi-objective optimization problems. The function model of support vector machine regression is introduced into the two multi-objective optimization algorithms, and the Pareto frontier is obtained as shown in Figure 2. Figure 5As shown in (a) and (b), the two Pareto fronts have the same shape, with an inflection point in the middle, and the two almost overlap. Each point in the Pareto front is the optimal solution, but the average thickness and coefficient of variation of different optimal solutions are different. It is necessary to choose between the two objective functions according to the actual situation.

[0060] Select three representative points in the Pareto frontier, two endpoints and the inflection point in the middle, and import the process parameters of these three points into the simulation model. The simulation results are as follows: Figure 5 (c) shows that the two endpoints are the two extreme cases of maximum growth rate and minimum coefficient of variation. According to the experimental data, the Pareto front is divided into three regions, such as Figure 5 As shown in (d), the growth rate and coefficient of variation in the Pareto front in region 2 are optimized compared with the experimental data. Figure 5 (d) also shows that the results of finite element simulation cannot be better than the Pareto front.

[0061] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

[0062] References

[0063] [1]Q.Huang et al., "MOPSO process parameter optimization in ultrasonicvibration-assistedgrinding of hardened steel," The International Journal ofAdvanced Manufacturing Technology,

[0064] vol.128, no.1-2, pp.903-914, 2023, doi:10.1007 / s00170-023-11949-2.

[0065] [2]M.Darvish Damavandi,M.Forouzanmehr,and H.Safikhani,"Modeling andPareto basedmulti-objective optimization of wavy fin-and-elliptical tube heatexchangers using CFD andNSGA-II algorithm,"Applied Thermal Engineering,vol.111,pp.325-339,2017 / 01 / 25 / 2017,doi: https: / / doi.org / 10.1016 / j.applthermaleng.2016.09.120 。

Claims

1. A method for optimizing epitaxial growth of semiconductor thin films, characterized in that: The specific steps are: (1) The finite element method is used to simulate the thin film chemical vapor deposition process; specifically, the finite element simulation software COMSOL is used to establish a three-dimensional model of the epitaxial furnace, and laminar flow, fluid heat transfer, dilute material transfer, chemistry and surface reaction are added to the physical field. The reaction source gases used in the simulation are: SiHCl3 and C2H4; the specific chemical reaction is: SiHCl3→SiCl2+HCl,#(1) 2C2H4→C2H3+C2H5,#(2) SiCl2→SiCl s +Cl,#(3) C2H3→C s +CH s +H2,#(4) C2H5→C s +CH s +2H2,#(5) SiCl s +C s → SiC b +Cl,#(6) SiCl s + CH s → SiC b +HCl,#(7) Among them, the subscript s represents the surface material, and the subscript b represents the bulk material; the chemical vapor deposition process is divided into three parts. First, SiHCl3 and C2H4 enter the reaction chamber and decompose at high temperature to generate intermediate materials; the intermediate materials moving to the substrate surface are adsorbed by the substrate and react on the surface to generate surface materials; the surface materials on the substrate surface continue to react to generate SiC; in the calculation results, the distribution of SiC thickness is analyzed, and the average thickness and coefficient of variation of SiC are calculated; (2) Compare the simulation results with the experimental data to verify the accuracy of the simulation results; if the simulation results are significantly different from the experimental results, adjust the simulation model until the error between the simulation results and the experimental results is within an acceptable range, that is, less than 5%; (3) Use support vector machine to establish the relationship between process parameters and objective function; (4) Optimizing the chemical vapor deposition process using a multi-objective optimization algorithm; in: The process parameters are the growth temperature, reaction chamber pressure and total flow rate of reaction gas for epitaxial growth of semiconductor thin film; The objective function is the epitaxial layer growth rate and the coefficient of variation of the epitaxial layer; the thin film growth time of all experiments and simulations is the same, and the average thickness and growth rate have the same meaning; the coefficient of variation is equal to the ratio of the standard deviation of the epitaxial layer thickness to the average value of the thickness; The multi-objective optimization algorithm includes a multi-objective particle swarm algorithm and a non-dominated sorting genetic algorithm.

2. The method for optimizing epitaxial growth of semiconductor thin films according to claim 1, characterized in that: The reaction chamber structure is a three-dimensional structure, and the reaction chamber is constructed based on an industrial hot-wall horizontal epitaxial furnace.

3. The method for optimizing epitaxial growth of semiconductor thin films according to claim 1, characterized in that: The verification of the accuracy of the simulation results includes the verification of the epitaxial layer growth rate and the verification of the coefficient of variation.

4. The method for optimizing epitaxial growth of semiconductor thin films according to claim 3, characterized in that: The multi-objective optimization is to import the function model between the objective function and the process parameters obtained by support vector regression into the multi-objective optimization algorithm for optimization, that is, to find the optimal solution of the objective function according to the function model, and output the process parameters corresponding to the optimal solution; the function model here is a black box model with a Gaussian function as the kernel function; The multi-objective optimization output result is the Pareto front of the objective function, wherein each point on the Pareto front is a non-dominated solution, that is, an optimal solution.

5. The method for optimizing epitaxial growth of semiconductor thin films according to claim 4, characterized in that: The Pareto front is verified again using finite element simulation, that is, the process parameters corresponding to the optimal solution on the Pareto front are input into the established finite element simulation model for calculation, and then the simulation data is compared with the Pareto front again to verify the accuracy of the multi-objective optimization.

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