CN115293013A - Plasma etching model simulation method based on cellular automaton - Google Patents
Plasma etching model simulation method based on cellular automaton Download PDFInfo
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Abstract
The method comprises the steps of firstly improving a current etching surface evolution model, researching the influence of different mask shapes on the etching surface evolution model, redefining an optimization target of the plasma etching model, optimizing the ion etching model by utilizing actual etching processing data, accelerating the optimization process by adopting a parallel method in order to shorten the time for optimizing the model, and finally applying the obtained etching model parameters to the plasma etching model simulation.
Description
Technical Field
The application relates to the technical field of microelectronic processing, and discloses a plasma etching model simulation method based on a cellular automaton.
Background
Plasma surface etching is a commonly used process in the production of electronic products such as semiconductors and integrated circuits. The method utilizes the typical gas ionization to form gas-phase plasma with strong etching property to react with a substrate on the surface of an object to generate gases such as CO, CO2, H2O and the like, thereby achieving the purpose of etching. Carbon tetrafluoride (CF 4) is a colorless and odorless gas for realizing the etching function, and is non-toxic and non-combustible. Carbon tetrafluoride (CF 4) generates an etching gas-phase plasma containing hydrofluoric acid after ionization, can etch various organic surfaces to remove damaged layers, and is widely applied to the industries of wafer manufacturing, circuit board manufacturing, solar cell panel manufacturing and the like. The reaction process of etching the silicon wafer Si by the plasma after the CF4 and the O2 are introduced into the working cavity is as follows:
O 2 +CF 4 +Si＝SiF 4 ↑+CO 2 ↑
SiF4 generated after reaction can be pumped away along with the work cavity of the plasma etcher in a vacuumizing way.
The etching method comprises chemical wet etching, plasma dry etching and other physical and chemical etching technologies, and the performance of any etching method can be inspected by using two basic parameters: the first is the etching resistance ratio of the mask, and the second is the etching directionality or anisotropy. The etching resistance ratio of the mask shows the consumption degree of the mask material in the process of etching the substrate material, and the high etching resistance ratio shows that the loss of the mask is less, so that the mask can bear long-time etching and is more favorable for deep etching. The etching anisotropy represents the ratio of etching rates in different directions of the substrate, and if the etching rates in all the directions are the same, the etching is isotropic; if the etch is greatest in one direction and least in the other, the etch is anisotropic, with a portion of the anisotropic etch in between.
Plasma etching is the most widely used and the strongest processing capability of dry processing techniques. The plasma etching is carried out in plasma, a large number of charged particles are accelerated by an electric field vertical to the surface of a silicon wafer and vertically incident on the surface of the silicon wafer to carry out physical etching with larger momentum, and meanwhile, the charged particles and the surface of a film have strong chemical reaction to generate volatilizable products which are pumped away by a vacuum system, and the material is etched layer by layer to a specified depth along with the periodic cycle of 'reaction-stripping-discharging' on the surface layer of the material. The plasma etching is not only widely applied to the field of microelectronics, but also one of the important means for integrating optics and micro-opto-electro-mechanical integrated processing, the plasma etching is a process of complex physical and chemical reaction processes, and the etching characteristics are closely related to etching conditions such as radio frequency power, gas flow, working pressure and the like, and are related to etching equipment and environment.
The plasma etching process is subjected to expansion of conditions such as ion energy, angle distribution, ion particle ratio, etching patterns and the like, so that an etching model needs to reflect the relation between the etching patterns and the conditions, and the etching model needs to simulate etching profiles under various conditions, so that the design of a plasma etching model considering various conditions to simulate plasma etching under various conditions is important.
Content of application
The present application is directed to solve at least one of the technical problems in the prior art, and therefore, a plasma etching model simulation method based on a cellular automaton is provided.
A plasma etching model simulation method based on a cellular automaton comprises the following steps: initializing optimization algorithm parameters and etching parameters;
calculating the actual etching rate according to experimental data;
calculating a simulated etching rate by using an ion etching model;
and comparing the error between the simulated etching rate and the actual etching rate, judging whether the error meets the precision requirement, outputting etching parameters if the error meets the precision requirement, continuously adjusting the etching parameters by an optimization algorithm if the error does not meet the precision requirement, and solving the simulated etching rate by using the ion etching model again.
Compared with the prior art, the embodiment of the application has the following beneficial effects:
firstly, initializing etching parameters, solving a simulated etching rate by using an ion etching model, then taking the error of the simulated etching rate relative to the actual etching rate as an optimization target, adjusting the parameters of the etching model by using a multi-objective evolutionary algorithm, and continuously reducing the error to finally obtain the etching parameters meeting the requirements. The method comprises the steps of firstly improving a current etching surface evolution model, researching the influence of different mask shapes on the etching surface evolution model, redefining an optimization target of the plasma etching model, optimizing the ion etching model by using actual etching processing data, accelerating the optimization process by adopting a parallel method in order to shorten the time for optimizing the model, and finally applying the obtained etching model parameters to the plasma etching model for simulation.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required to be used in the embodiments will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a plasma etch optimization model in the present application;
FIG. 2 is an etching line extracted from an etched surface at different time points in the present application;
FIG. 3 is a cellular etching model of the present application;
FIG. 4 is a flowchart of a multi-objective evolutionary algorithm based on decomposition according to the present application.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Because plasma etching has an extremely complex mechanism, in order to carry out deep research on plasma etching, an etching model is indispensable, and the etching model can greatly promote the understanding of the whole etching process, thereby guiding the application to carry out the improvement of equipment and a technological process. The plasma etching model mainly has two modeling ideas, one is a model based on a particle method, and the model mainly comprises a Monte Carlo model, a particle grid method and a mixed model combining the Monte Carlo model and the particle grid method; the other is a dynamic method model which mainly comprises a reaction site model, a molecular dynamic model and a mixed layer dynamic model.
The traditional plasma modeling is based on a particle method, and there are two different modeling methods, one is a monte carlo model: in the Monte Carlo model, a finite collection of particles is used to represent the entire population of particles. The statistical nature of the particles is simulated by letting a series of processes occur randomly, i.e. the particles are generated or disappear via elastic or inelastic collisions, while the average probability is to follow the true frequency of occurrence. This method relies on the corresponding basic concept that particle motion follows newton's law and the aggregation of individual particles, and nowadays there are hundreds of millions of particle models. It is clear that combining such a large number of particles into a list is not suitable for human use.
The other is a particle grid method: particle grids are a finite particle method for modeling multicomponent plasmas and particle beams, which are powerful tools for numerical simulation of continuous medium, air, plasma dynamics. The basic idea of plasma particle simulation is as follows: a large number of charged particles have initial positions and velocities, the initial positions and the velocities are counted to obtain the charge and current density distribution of a plasma space, and then electric fields and magnetic fields at each position are obtained through Maxwell equations to obtain the Lorentz force applied to each particle. And the position and velocity of each particle at the next time can be found by the equation of motion. And circulating in this way, tracking and calculating the motion of a large number of charged particles, and counting certain physical quantities of the large number of charged particles according to the interested problems to obtain the material characteristics and the motion process of the macroscopic plasma.
Mixing the models: the result of the monte carlo model is the position and velocity of the particle, so that a series of desired parameters, such as density, velocity, average energy, etc., can be obtained directly. These parameters can be used in the continuous model. This model combining the different methods is a hybrid model.
The above method requires a long calculation time.
Referring to fig. 1, the present application provides a plasma etching model simulation method based on a cellular automata, which includes obtaining an actual etching rate according to experimental data; utilizing an ion etching model to obtain a simulated etching rate; and comparing the error between the simulated etching rate and the actual etching rate, judging whether the error meets the precision requirement, outputting the etching parameters if the error meets the precision requirement, continuously adjusting the etching parameters by the optimization algorithm if the error does not meet the precision requirement, and solving the simulated etching rate by using the ion etching model again.
In the process of calculating the actual etching rate according to the etching experimental data, the correct calculation of the actual etching rate of the selected point on the etching surface is the key of the ion etching yield optimization model. The original method for solving the etching rate is to solve the etching rate of a selected point on an etching surface by using a level set method according to initial conditions of an experiment, however, due to the limitation of the level set method, the solved etching rate is different from the actual etching rate by an order of magnitude when the error is the largest, and the subsequent optimization process is seriously influenced.
The application firstly designs an accurate and efficient etching processing experiment.
Compared with the original work of solving the etching rate, the method and the device utilize actual etching processing data to solve the etching rate of the selected point on the etching surface. Because the etching experiment is long in time consumption and high in cost, the reasonable and efficient etching experiment is designed in the application due to the accuracy of the required etching rate and the consideration of the whole experiment cost.
In order to obtain the etching rate of the etched surface point, firstly, the etching profiles at different moments in the etching process need to be obtained. However, in the actual plasma etching process, for the same etched silicon wafer, the scanning electron microscope cannot be used to scan at intervals to obtain the etched section pictures at different times. Before scanning by using a scanning electron microscope, the silicon wafer needs to be correspondingly processed each time, so that the next etching environment is different from the previous etching environment. In order to overcome the problem, a plurality of silicon wafers with the same material and size are selected, the silicon wafers are subjected to the same pretreatment before etching, and then the silicon wafers with different numbers are etched for different times under the same etching environment. Because the environment is consistent, the method can approximately reproduce the etching morphology of a silicon wafer at different moments, so that the etching profile result of the silicon wafers can be taken as the etching result of the same silicon wafer at different moments by integrating the etching profile results of the silicon wafers.
For the etching sections with the same etching width at different moments, corresponding etching lines are extracted on the same picture by an image processing method and are represented as a cellular model, as shown in fig. 2.
Setting the attribute of a cell occupied by an etched line in the cell model to be 1; the cell not occupied by the etched line has its property set to 0. The present application uses this model to find the etching rate of a selected point on an etched line.
In FIG. 3, the black block is a cell occupied by etched lines and has the attribute set to 1; the property of the white block is set to 0 for the cells not occupied by the etched lines.
To obtain the etching rate of the selected point on the surface, for the cellular etching model shown in fig. 3, two pieces of information are required to be known for obtaining the actual etching rate of the selected point on the etching surface: the normal vector of the dot and the intersection of the dot with the etched line at the next time along the normal vector direction. The calculation of the normal vector can be obtained by fitting occupied cells within a certain distance range of the point and then according to the obtained expression. For the intersection point, the distribution of points on the etching line has no specific rule, so the position of the intersection point is directly obtained.
A dichotomy is described below for fast point location finding.
First, a point Y is found at a position long enough along the normal vector direction to be located below the etching line, and the point X is set as a point. Then, the middle point Z of X and Y is taken to judge whether the Z point is positioned on the etching line. If yes, the Z point is the point to be solved; if the Z point is positioned below the etching line, Y is taken as the Z point, otherwise, X is taken as the Z point. The conditional judgment process is repeated until a point is found.
Since the etching rate itself is small, the etching rate of the spot can be approximated by the equation (1):
wherein, V 0 Is the dot etch rate, OO 'is the distance from point O to point O', and Δ t is the time interval between two etched lines.
The above-mentioned embodiments are only used to illustrate the technical solutions of the present application, and not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the embodiments of the present application, and they should be construed as being included in the present application.
In the process of solving the simulated etching rate by using the etching model, the etching rate of the selected point on the etching surface is closely related to the etching yield of the incident ions. For the same ions with fixed energy and fixed incidence angle, the etching rate of the same ions to the selected point of the etching surface satisfies the formula (2):
wherein E is Y (P) is the etch yield of incident ions at point P, J (P) is the ion flux incident at point P, N t Is the atomic density of the material being etched, and ER (P) is the etching rate of the same ion pair P point at a fixed energy and a fixed incident angle at a certain flow rate.
In the evolution process of the etching surface, for a given etching yield model parameter, the simulation etching rate of a selected point of the etching surface can be obtained by using the formula (3). But the incident ions at that point may not be only one but should be the result of the interaction of all the ions incident at that point. Assuming that a total of n types of ions are incident at this point, the actual etch rate at that point can be expressed as the sum of the etch rates of these ions at selected points on the etch surface, i.e.
Wherein ER (P) is the sum of etching rates of N types of ions to a P point at a certain flow rate and a fixed incident angle, N t Is the atomic density of the material being etched,
is the etch yield of the i-th incident ion at point P, J i (P) is the ion flux of the i-th ion incident on the point P.
In the process of comparing the error between the simulated etching rate and the actual etching rate, the optimal ion etching yield model parameter can be obtained through the error between the actual etching rate and the simulated etching rate in the plasma etching processing process.
In the actual etching process, if only one etching evolution section with one width is selected, the error between the actual etching rate and the true value is easily caused by the error of the experiment, so that the difference between the simulated etching rate and the actual etching rate has an error. In order to reduce errors, the method selects the evolution results of the etching profile under various widths, and defines (4) formula as an error function for the evolution results of the profile with the first width:
wherein x is an etching yield model parameter, n represents the number of sections used for optimization in the evolution process of the etching section under the k-th width, m represents the number of points selected for optimization on each etching evolution surface, and v represents the number of points selected for optimization rij Is the actual etching rate of the jth selected position point of the ith profile under the kth width, v sij Is and v rij Corresponding to the simulated etch rate, w (i, j) is a weighting factor, representing v sij With respect to v rij The degree of influence of the deviation of (a) on the overall error.
The corresponding objective function at this time is:
f(x)＝(e 1 (x)，e 2 (x)，…，e p (x)) (5)
where P is the number of trenches of different widths of the etch evolution profile, e i (x) Means the error between the actual etching rate and the simulated etching rate on different etching lines under the ith width.
The ion etching optimization objective function comprehensively considers different e i (x) This is important to find the optimum parameters throughout the etch process.
The objective of the present application is to minimize the function f (x) and find the corresponding x, so that the simulated etch rate is as close as possible to the actual etch rate. Since f (x) is a function vector, only one component of f (x) cannot be optimized, and different components in f (x) need to be balanced, the problem of etching yield model parameter optimization is converted into a multi-objective optimization problem.
In the process of the multi-objective optimization algorithm, the current optimization algorithm is mostly applied to the optimization of a physical model. The multi-objective evolutionary algorithm provides a new approach for solving the multi-objective optimization problem, and the optimization direction is only adjusted correspondingly according to the result of the objective function without clearly knowing the internal structure of the objective function. In the multi-objective evolutionary algorithm, the multi-objective evolutionary algorithm based on decomposition has low computation complexity when solving the multi-objective optimization problem, and the result obtained under a specific condition is better than that obtained by other multi-objective evolutionary algorithms, so that the multi-objective evolutionary algorithm based on decomposition is selected as the optimization algorithm.
Regarding the problem of converting into a single target, a multi-target evolutionary algorithm based on decomposition can be used for converting a multi-target optimization problem into a single-target optimization problem by selecting uniformly distributed weight vectors and utilizing a method based on decomposition, wherein a Chebyshev method is selected as a method based on decomposition, and the method comprises the following steps:
where P is the number of targets, λ i Is a weight vector and satisfies
And satisfy z * ＝max{f i And | x ∈ Ω } stores the minimum value of each target in the optimization process.
Regarding the selection of the evolution operator, the evolution operator is a core part in the evolution algorithm, and relates to selection, intersection and mutation operations.
Cross-over operation-for individuals
Randomly selecting two individuals from the corresponding set
And
generation of new individuals using differential evolution operators
Namely:
wherein R is 1 Is [0,1 ]]F is a scaling factor and CR is the crossover probability.
Mutation operation for individuals
Individuals after mutation can be obtained by polynomial mutation, y = (y) 1 ，y 2 ，...y n ) Namely:
wherein, a k And b k Lower and upper bounds, R, respectively, of the kth parameter to be optimized 2 Is [0,1 ]]A random number in between, and a k And satisfies the following conditions:
where γ is a control parameter, R 3 Is [0,1 ]]A random number in between.
Selection operation for an individual
Obtaining a new individual y = (y) after cross operation and mutation operation 1 ，y 2 ，...y n ) If there is an individual x i Neighbor x of j Satisfies the following conditions:
g te (x|λ j ，z * )≤g te (x j |λ j ，z * ) (10)
then replace individual x with individual y j 。
Regarding the elite reservation strategy, the present application employs the elite reservation strategy to avoid losing good individuals during the optimization process. In the optimization process, the external population is always used for storing the current optimal solution obtained in the optimization process. Thus, for a newly generated individual y, if there is an individual with a fitness value inferior to y in the outer population, then the individual is removed from the outer population; and if the solution of y is not inferior to the individuals in the external population, adding y to the external population.
Claims (1)
1. A plasma etching model simulation method based on a cellular automaton is characterized by comprising the following steps:
initializing optimization algorithm parameters and etching parameters;
calculating the actual etching rate according to experimental data;
calculating a simulated etching rate by using an ion etching model;
and comparing the error between the simulated etching rate and the actual etching rate, judging whether the error meets the precision requirement, outputting the etching parameters if the error meets the precision requirement, continuously adjusting the etching parameters by the optimization algorithm if the error does not meet the precision requirement, and solving the simulated etching rate by using the ion etching model again.
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