Simulation method, device and equipment for plasma etching process

Abstract

The invention discloses a simulation method, device and equipment for a plasma etching process, relates to the technical field of plasma etching, and aims to solve the problem that in the prior art, when the plasma etching process is simulated, etching contour prediction is not accurate. The method comprises the following steps: acquiring model input parameters of a plasma etching process simulation model; obtaining a corresponding etching area based on a cellular method; based on the energy distribution and the angle distribution, an initial velocity vector and an initial incidence position of each particle are determined by adopting a Monte Carlo method; determining a particle motion track according to the initial velocity vector and the initial incidence position; performing electric field distribution calculation and surface etching reaction based on the relationship between the particle motion trail and the etching region; when the etching time is over, model output of the plasma etching process simulation model is output, and the model output at least comprises electric field distribution and a simulation etching contour after the surface etching reaction is over. The simulated etching contour output by the method is more accurate.

Description

Technical Field

[0001] The present invention relates to the field of plasma etching technology, and in particular to a simulation method, device and equipment for a plasma etching process. Background Art

[0002] Plasma etching is an important dry etching process in microelectronics manufacturing. It selectively removes materials by using active ions and neutral substances in plasma. In this process, the components in the plasma act on the wafer surface through physical bombardment and chemical reactions, forming a highly anisotropic etching morphology. The basic process of plasma etching is as follows:

[0003] First, the etching chamber is evacuated to a vacuum state, and then the reaction gas is introduced. By applying a radio frequency (RF) electric field, the reaction gas is ionized and excited into a plasma. The plasma contains high-energy ions, electrons, and neutral free radicals. Secondly, under the combined action of the electric field and the vacuum flow field, the various components in the plasma move to the surface of the wafer respectively. Finally, the charged particles (such as ions) and neutral active species (such as free radicals) in the plasma interact with the surface of the material to be etched, achieving precise removal of the material to be etched.

[0004] The charging effect is a key mechanism that affects the etching profile. It is caused by the difference in the angular distribution of ions and electrons in the plasma. Under the action of the bias voltage, positive ions are accelerated by the electric field when passing through the sheath, and their speed in the direction perpendicular to the wafer is significantly enhanced, resulting in a strong anisotropy in the angular distribution of the incident ions. In contrast, electrons are lighter in mass and faster in speed. Although they are also affected by the electric field, their angular distribution is relatively weak and has a smaller anisotropy. This difference in the distribution of ions and electrons causes negative charges to accumulate more on the side walls of the mask, while positive ions tend to concentrate at the bottom of the etched trench.

[0005] As the etching time increases, charges gradually accumulate on the sidewalls and the bottom of the trench, forming a micro-local electric field. This local electric field has a significant effect on the direction of the incident charged particles. On the one hand, positively charged ions are deflected by the local electric field, causing the ions to bombard the etched sidewalls, weakening the anisotropy in the etching process; on the other hand, the local electric field further exacerbates the trench effect by changing the incident angle of the charged particles, which speeds up the etching rate at the bottom of the trench during the etching process, resulting in uneven etching depth.

[0006] Plasma etching processes are widely used in large-scale integrated circuit manufacturing at advanced technology nodes due to their excellent conformality and anisotropy. However, in the actual plasma etching process, due to complex physical and chemical mechanisms, the final profile often has undesirable morphological defects. The charging effect is an important mechanism that affects the etching profile, but it is difficult to directly observe in experiments because the local charge differences are often small and quickly neutralized. As advanced etching process technology nodes have entered the nanoscale, this will further lead to more serious distortion of ion trajectories caused by the charging effect. If a model can be established to accurately simulate the potential distribution and electric field distribution as well as the motion trajectory of charged particles in the electric field, the etching profile can be predicted more accurately. Summary of the invention

[0007] The object of the present invention is to provide a method, device and equipment for simulating a plasma etching process, so as to improve the accuracy of etching profile prediction during the simulation of the plasma etching process.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] In a first aspect, the present invention provides a simulation method for a plasma etching process, comprising:

[0010] Obtaining model input parameters of a plasma etching process simulation model; the model input parameters at least include an initial surface profile, energy distribution and angle distribution of each particle in the plasma; the initial surface profile is a graphic profile including a substrate and a hard mask;

[0011] Based on the cellular method, the simulation area in the plasma etching process simulation model is discretized into a plurality of cells, and the corresponding cells are marked based on the initial surface contour to obtain the corresponding etching area;

[0012] Based on the energy distribution and the angle distribution, using a Monte Carlo method to determine an initial velocity vector and an initial incident position of each particle;

[0013] Determining a particle motion trajectory according to the initial velocity vector and the initial incident position;

[0014] Based on the relationship between the particle motion trajectory and the etching area, electric field distribution calculation is performed and surface etching reaction is performed;

[0015] When the etching time is over, the model output of the plasma etching process simulation model is output, and the model output at least includes the electric field distribution and the simulated etching profile after the surface etching reaction is completed.

[0016] Optionally, the calculation of electric field distribution and surface etching reaction based on the relationship between the particle motion trajectory and the etching area includes:

[0017] Judging whether the particle reaches the surface cell of the etching area according to the particle movement trajectory, if the particle reaches the surface cell, calculating the potential distribution of the particle after charge transfer, and, if the particle reaches the surface cell, continuing to judge whether the particle is reflected, and performing a surface etching reaction when the particle does not reflect;

[0018] Based on the potential distribution, the electric field distribution is determined.

[0019] Optionally, determining the particle motion trajectory according to the initial velocity vector and the initial incident position includes:

[0020] Based on Newton's second law, the ordinary differential equation of particle motion is constructed:

[0021]

[0022] Among them, v(x, y) is the particle velocity vector, q p is the charge of the particle, m p is the mass of the particle, t is the time, and E(x, y) is the electric field distribution;

[0023] The initial velocity vector and the initial incident position are used as initial conditions to solve the ordinary differential equation to obtain the particle motion trajectory.

[0024] Optionally, the calculation of the potential distribution of the particle after charge transfer comprises:

[0025] Record the charge distribution of particles after charge transfer;

[0026] Based on the charge distribution, the potential distribution is calculated using Poisson's equation.

[0027] Optionally, the calculating the potential distribution based on the charge distribution using the Poisson equation includes:

[0028] The second-order derivative is approximated using the central difference method and substituted into the Poisson equation:

[0029]

[0030] The transformation equation is derived: Wherein, ∈ is the dielectric constant of vacuum, φ is the electric potential, and ρ is the charge distribution; (i, j) is the grid point corresponding to a charge; Δx is the spacing of the grid points in the x-axis direction, and Δy is the spacing of the grid points in the y-axis direction;

[0031] Based on the number of cells and the transformation equation, a linear system of equations is constructed:

[0032] Aφ=b

[0033] The linear equations are solved to obtain the potential distribution; wherein A is a coefficient matrix, φ is a vector of potentials, and b is a vector containing charge density and dielectric constant.

[0034] Optionally, when solving the linear equations, the upper and lower boundary potentials of the simulation area satisfy the Dirichle boundary condition: φ=0;

[0035] The left and right boundaries of the simulation area are periodic boundaries, satisfying the Neumann boundary condition: dφ / dx=0.

[0036] Optionally, the surface etching reaction comprises:

[0037] Substituting the energy of the particle and the angle of incidence of the particle into the formula:

[0038]

[0039] The probability of occurrence of reaction events during the surface etching reaction is calculated, where p(ε p ,θ) is the occurrence probability, ε p is the energy of the particle, θ is the incident angle; ε th is the threshold energy of the reaction, ε ref is the reference energy, p0 is the reaction probability at the reference energy, n is an empirical parameter, and f(θ) is the angular dependence;

[0040] The angular dependence is approximated by Yamamura's semi-empirical formula; wherein Yamamura's semi-empirical formula is:

[0041] Among them, C1, C2 and C3 are fitting parameters.

[0042] Optionally, the reaction mechanism corresponding to the reaction event includes: adsorption, removal, desorption and sputtering of the hard mask.

[0043] Compared with the prior art, the simulation method of a plasma etching process provided by the present invention is essentially based on the Monte Carlo method and the cellular method to establish a plasma etching process model that takes into account the charging effect, which can calculate the electric field distribution and changes during the etching simulation process, simulate the movement trajectory of charged particles in the local electric field, and ultimately accurately predict the etching morphology. The simulation method of a plasma etching process provided by the present invention innovatively adds the influence of the charge carried by the particles on their etching morphology in the etching simulation, takes into account the charge transfer and accumulation of charged particles in the plasma during the etching process, and their trajectory deviation affected by the local electric field. Ultimately, the prediction accuracy of the etching morphology is improved.

[0044] In a second aspect, the present invention further provides a simulation device for a plasma etching process, comprising:

[0045] An acquisition module, used for acquiring model input parameters of a plasma etching process simulation model; the model input parameters at least include an initial surface profile, energy distribution and angle distribution of each particle in the plasma; the initial surface profile is a graphic profile including a substrate and a hard mask;

[0046] A discretization module, used for discretizing the simulation area in the plasma etching process simulation model into a plurality of cells based on a cellular method, and marking corresponding cells based on the initial surface contour to obtain corresponding etching areas;

[0047] A first determination module, configured to determine an initial velocity vector and an initial incident position of each particle by using a Monte Carlo method based on the energy distribution and the angle distribution;

[0048] A second determination module, used to determine the particle motion trajectory according to the initial velocity vector and the initial incident position;

[0049] A calculation module, used to calculate the electric field distribution and perform surface etching reaction based on the relationship between the particle motion trajectory and the etching area;

[0050] The output module is used to output the model output of the plasma etching process simulation model when the etching time ends, and the model output at least includes the electric field distribution and the simulated etching profile after the surface etching reaction ends.

[0051] In a third aspect, the present invention also provides a simulation device for a plasma etching process, comprising: a processor, a communication interface, a memory and a communication bus; wherein the processor, the communication interface and the memory communicate via the communication bus; the memory stores a computer program that can be run by the processor; when the processor runs the computer program, it executes any one of the above-mentioned methods for simulating a plasma etching process. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The drawings described herein are used to provide further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention. In the drawings:

[0053] Figure 1 A schematic flow chart of a simulation method for a plasma etching process provided by an embodiment of the present invention;

[0054] Figure 2 A schematic diagram of the working state of a plasma etching process simulation model provided by one embodiment of the present invention;

[0055] Figure 3 A schematic diagram of an algorithm for calculating particle reflection based on least squares fitting provided by another embodiment of the present invention;

[0056] Figure 4 A schematic flow chart of a simulation method for a plasma etching process provided by another embodiment of the present invention;

[0057] Figure 5 A schematic diagram of the structure of a simulation device for a plasma etching process provided by an embodiment of the present invention;

[0058] Figure 6 A schematic diagram of the structure of a simulation device for a plasma etching process provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0059] In order to clearly describe the technical solutions of the embodiments of the present invention, in the embodiments of the present invention, words such as "first" and "second" are used to distinguish the same items or similar items with basically the same functions and effects. For example, the first threshold and the second threshold are only used to distinguish different thresholds, and their order is not limited. Those skilled in the art can understand that words such as "first" and "second" do not limit the quantity and execution order, and words such as "first" and "second" do not necessarily limit them to be different.

[0060] It should be noted that, in the present invention, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the present invention should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0061] In the present invention, "at least one" means one or more, "more than one" means two or more. "And / or" describes the association relationship of the associated objects, indicating that three types of relationships may exist.

[0062] like Figure 1 As shown, an embodiment of the present invention provides a simulation method for a plasma etching process, which may include:

[0063] Step 110: obtaining model input parameters of a plasma etching process simulation model; the model input parameters at least include an initial surface profile, energy distribution and angle distribution of each particle in the plasma; the initial surface profile is a graphic profile including a substrate and a hard mask;

[0064] It is understandable that the simulation method of the plasma etching process provided by the embodiment of the present invention is applied to the plasma etching process simulation model.

[0065] Step 120: based on the cell method, discretize the simulation area in the plasma etching process simulation model into a plurality of cells, and mark the corresponding cells based on the initial surface contour to obtain the corresponding etching area;

[0066] Simulation area such as Figure 2 As shown. First, the simulation area is discretized into multiple cells using the cell method, each of which is a square. The side length of each square cell can be, for example, 1 nm.

[0067] Then, based on the initial surface profile, digital labels are used to indicate the presence of different materials or states in each cell, e.g. Figure 2 As shown in the figure, there are four different states of cells: 0-vacuum, 1-substrate (Si), 2-hard mask (SiO2) and 3-plasma source. When a hard mask cell or substrate cell is etched away by particles, the state of the cell changes to vacuum. The particles in the plasma include at least electrons, positive ions and central particles.

[0068] Step 130: Based on the energy distribution and the angle distribution, the Monte Carlo method is used to determine the initial velocity vector and the initial incident position of each particle;

[0069] It should be noted that the Monte Carlo method is a computational method based on random numbers and probability statistics, which can be applied to simulate physical processes with randomness.

[0070] First, we need to determine the energy distribution of the particles. This is usually a probability distribution function, such as normal distribution, uniform distribution, or other forms of distribution. Based on this distribution, we can randomly assign an energy value to each particle. The specific implementation steps are: determine the type and parameters of the energy distribution (such as mean, variance, etc.); use a random number generator to generate a random energy value based on the distribution type.

[0071] Next, we need to determine the incident angle distribution of the particles. This is also a probability distribution, which may involve the angle between the incident direction of the particle and a reference direction (such as the normal direction). The specific implementation steps are to determine the type and parameters of the angle distribution (such as angle range, distribution form, etc.); use a random number generator to generate a random angle value according to the distribution type. This embodiment assumes that the angular distribution of neutral particles obeys a cosine distribution, the positive ion angular distribution (IEDF) obeys a Gaussian distribution, and the electron angular distribution (EEDF) is uniformly distributed. The particles enter downward from the plasma source region at the top of the simulation area, and their incident positions are uniformly distributed in the plasma source region.

[0072] With the energy value and the angle of incidence, we can then calculate the initial velocity vector of the particle. The specific calculation steps include: using the relationship between energy and velocity (such as the kinetic energy formula) to calculate the magnitude of the velocity. Based on the randomly generated angle, the velocity is decomposed into two components in the direction (x and y).

[0073] Finally, the initial impact position of the particle needs to be determined. This is usually also a random process, which may involve randomly selecting a point on a surface or volume. The specific implementation steps are: determine the two-dimensional plane area (also known as the simulation area) where the particle may be incident; use a random number generator to select a random point in the simulation area as the initial impact position of the particle.

[0074] Step 140: Determine the particle motion trajectory according to the initial velocity vector and the initial incident position;

[0075] Following step 130 , the particle movement trajectory needs to be determined after the particle enters the simulation area.

[0076] It is understandable that at the beginning of etching, no local electric field is generated. After the particles enter the simulation area, they reach the substrate or hard mask along the initial velocity vector. At this time, the charge carried by the particles will accumulate on the hard mask. As the charge accumulates, a local electric field sufficient to affect the movement of the particles will be generated in the simulation area (that is, the electric field distribution obtained in the subsequent steps), which is the charging effect mentioned in the background technology. After the local electric field is formed, the subsequently incident particles continue to move under the action of the local electric field.

[0077] In the prior art, when simulating the plasma etching process, or in other words, when constructing the plasma etching process simulation model, the prior art often only considers the movement of particles along the initial velocity vector without the action of an electric field, and the factors considered are relatively simple. In addition, the charges carried by the particles in the plasma will accumulate on the hard mask, and the difference in the distribution of ions and electrons causes more negative charges to accumulate on the side walls of the hard mask, forming a local electric field. This local electric field causes the displacement of the particles. If the influence of the local electric field on the movement of the particles is not considered, the final predicted etching profile is often not accurate enough.

[0078] In order to improve the prediction accuracy of the final etching profile, the embodiment of the present invention also takes into account the local electric field generated in the simulation area during the charging effect when designing the simulation model of the plasma etching process. This makes the description of the particle motion trajectory more consistent with the actual situation, thereby improving the accuracy of the description of the particle motion trajectory and further improving the prediction accuracy of the final etching profile.

[0079] Step 140 may specifically include:

[0080] Step 1: Based on Newton's second law, construct the ordinary differential equation of particle motion:

[0081]

[0082] Among them, v(x, y) is the particle velocity vector, q p is the charge of the particle, m p is the mass of the particle, t is the time, and E(x, y) is the electric field distribution;

[0083] After the particle is incident, the movement of the particle under the action of the electric field conforms to Newton's second law. Therefore, the trajectory of the particle can be determined by solving a set of ordinary differential equations derived from Newton's second law.

[0084] The first step may specifically include: determining the electric field distribution. First, we need to know the distribution of the electric field strength in space, that is, E(x, y). The initial electric field distribution can be obtained through a theoretical model. This can be referred to in related technologies and will not be described here. Next, based on the electric field distribution and Newton's second law, an ordinary differential equation for particle motion is established. This is usually a second-order differential equation about time, involving the position of the particle.

[0085] Step 2: Using the initial velocity vector and the initial incident position as initial conditions, solve the ordinary differential equation to obtain the particle motion trajectory.

[0086] Step 150: Based on the relationship between the particle motion trajectory and the etching area, calculate the electric field distribution and perform a surface etching reaction;

[0087] The electric field distribution calculation step in step 150 may specifically include:

[0088] Step 1: Determine whether the particle reaches the surface cell of the etching area according to the particle motion trajectory. If the particle reaches the surface cell, calculate the potential distribution of the particle after charge transfer. If the particle reaches the surface cell, continue to determine whether the particle is reflected. If the particle does not reflect, perform surface etching reaction.

[0089] Combination Figure 2It is understood that the surface cells may be cells on the surface of the substrate or cells on the surface of the hard mask.

[0090] When the particle reaches the surface cell, it is assumed that all charged particles transfer charge at their impact point, and the charge (positive charge and electron) carried by the particle will be completely transferred to the surface cell, and the transferred charge will be accumulated or neutralized with the charge in the original cell, and the charge in each cell constitutes the charge distribution in the simulation area. It should be noted that if a cell with charge is removed due to physical or chemical reaction, its charge is redistributed to the adjacent surface cells in a certain proportion to be retained. For example, in an embodiment of the present invention, the conductor (Si) as a substrate will not accumulate charge, and charge accumulation only occurs in the dielectric (SiO2), that is, the hard mask.

[0091] The plasma etching process simulation model can record the charge distribution in the simulation area, that is, record the charge distribution of particles after charge transfer, and then calculate the potential distribution based on the charge distribution using the Poisson equation.

[0092] The specific calculation process of the electric potential distribution is explained as follows:

[0093] 1) Construct Poisson's equation:

[0094] Among them, ∈ is the dielectric constant of vacuum, φ is the electric potential, and ρ is the charge distribution;

[0095] 2) Use the central difference method to approximate the second-order derivative, substitute it into Poisson equation (2), and derive the transformation equation:

[0096] Regarding step 2), for a grid point (i, j) corresponding to a charge, its second-order derivative can be approximated as:

[0097]

[0098]

[0099] Where Δx is the spacing between grid points in the x-axis direction, and Δy is the spacing between grid points in the y-axis direction. Substituting (4) and (5) into Poisson's equation (2), we can obtain formula (3).

[0100] Since the grid is uniform (the cells are square), that is, Δx = Δy, rearranging formula (3) yields:

[0101]

[0102] Equation (6) is the discretized form of Poisson's equation (2) at the grid point (i, j), which can be solved by an appropriate numerical method (eg, an iterative method).

[0103] 3) Based on the number of cells (the number of all cells) and the transformation equation, a linear equation system is constructed: Aφ=b(7); where A is the coefficient matrix, φ is the vector of electric potential, and b is the vector containing charge density and dielectric constant;

[0104] Following step 2), in the actual calculation, it is necessary to establish similar equations for each grid point in the entire simulation area (that is, the two-dimensional coordinates of each cell) in order to obtain the linear equation group (7).

[0105] 4) Solve the linear equations to obtain the potential distribution.

[0106] Specifically, an appropriate numerical solution method (such as the conjugate gradient method) can be used to solve equation (7) to obtain the potential value at each grid point.

[0107] During the solution process, the upper and lower boundary potentials of the simulation area satisfy the Dirichle boundary condition: φ=0; the left and right boundaries of the simulation area are periodic boundaries and satisfy the Neumann boundary condition: dφ / dx=0.

[0108] Step 2: Based on the potential distribution, determine the electric field distribution.

[0109] Electric potential is a physical quantity that describes the electric potential energy at a point in an electric field. It is a scalar quantity and is relative. In an electric field, different points have different electric potentials. The electric potential distribution describes the change of electric potential in an electric field with spatial position. In an electrostatic field, the electric potential distribution is usually determined by the charge distribution.

[0110] The electric field strength is the negative of the potential gradient, i.e. the electric field strength vector is equal to the opposite of the gradient vector of the potential function at that point. This is the basic relationship between the electric field and the electric potential, which states that the direction of the electric field is the direction in which the electric potential decreases most rapidly. Therefore, by solving for the electric potential distribution, we can use the above relationship to obtain the electric field distribution. In practical calculations, this usually involves taking the derivative of the potential function to obtain the individual components of the electric field strength.

[0111] In the step of performing the surface etching reaction, it is understandable that the present embodiment adopts the Monte Carlo algorithm to simulate the occurrence of etching reaction events, and for this purpose, it is necessary to define the probability of occurrence of each event in the etching reaction process. For example, many kinds of reactions will occur in the actual process of chloride ion plasma etching Si. In order to simplify the model, the following four main reaction mechanisms are selected: adsorption, removal, desorption, and sputtering hard mask. The probability of some of these reactions is affected by the particle incident energy. The higher the particle energy, the greater the possibility of the reaction. For those reactions that are energy-dependent, the probability of the reaction when the particle is incident on the surface at a certain energy and angle is: Therefore, in the specific simulation, the particle energy and the particle incident angle are substituted into formula (8) to calculate the probability of the reaction event in the surface etching reaction process, where p(ε p ,θ) is the probability of occurrence, ε p is the energy of the particle, θ is the incident angle; ε th is the threshold energy of the reaction, ε ref is the reference energy, p0 is the reaction probability at the reference energy, n is an empirical parameter, and f(θ) is the angular dependence; for example, n is 0.5.

[0112] The angular dependence is approximated by Yamamura's semi-empirical formula; wherein Yamamura's semi-empirical formula is: Among them, C1, C2 and C3 are fitting parameters. It should be noted that the specific reaction equation and various parameters of reaction probability set in this model are shown in Table 1 below.

[0113] Table 1: Relevant parameters of reaction events

[0114]

[0115]

[0116] In Table 1, if ε th and ε ref If ε is blank, the reaction has no energy dependency and the probability of the reaction is a constant p0. th and ε ref has a non-zero value, then the reaction has an energy-dependent probability.

[0117] Regarding particle reflection, it should be noted that there is a certain probability of reflection after the particle reaches the surface, and the reflection probability is related to the impact angle. When the particle hits the surface cell close to the normal direction, the particle should transfer most of its energy to the surface, causing surface etching reaction or sputtering; but when it passes over the surface at a smaller impact angle, almost no energy is transferred to the surface, and it is more likely to be reflected in a manner close to a mirror surface. Therefore, when the incident angle is small, the reflection probability is expected to be close to 1, and decrease when the impact angle increases. When the maximum reflection angle threshold is exceeded, no reflection occurs. The relationship between the reflection probability and the angle is set as follows:

[0118]

[0119] Where f(θ) is the reflection probability, θ is the incident angle; θ min is the complete reflection angle threshold; θ max is the angle threshold for completely non-reflective reflections. If a particle reflects, its reflection direction will be randomly sampled according to the cosine distribution of the specular reflection.

[0120] Combination Figure 3 To understand, when square cells are used to discretize the simulation area, the etched surface will be over-shadowed, which will cause the plasma flow entering the surface protrusion cells to increase compared to the actual situation, and the plasma flow that the lower cells should have received may be blocked, thus affecting the etching accuracy, so the impact point needs to be smoothed. We first select the surface cells within the area of ​​±5 cells from the impact point, for example, and use its center coordinates as the reference point to perform least squares fitting to obtain the local surface fitting line. After reaching the etched surface cell, the particle will continue to move until it crosses the local surface fitting line to obtain the real impact point. Take the direction of the velocity vector of the last Δt as the impact direction, and the angle θ between it and the local surface fitting line is the impact angle (that is, the above-mentioned incident angle). It should be noted that Figure 3 Where a is the initial incident angle, that is, the angle of entering the simulation area in step 130 .

[0121] Step 160: When the etching time ends, output the model output of the plasma etching process simulation model, and the model output at least includes potential distribution, electric field distribution, and a simulated etching profile after the surface etching reaction ends.

[0122] The present invention establishes a plasma etching process simulation model that takes into account the charging effect based on the Monte Carlo method and the cellular method. It can calculate the potential distribution, electric field distribution, potential change and electric field change during the etching process, and can also simulate the motion trajectory of charged particles in the electric field, and finally predict the etching morphology. This model incorporates the charging effect, takes into account the charge transfer and accumulation of charged particles in the plasma during the etching process, as well as the trajectory deviation affected by the local electric field, and provides a quantitative approach for the charging effect that is difficult to characterize experimentally in actual manufacturing. It can better help understand the physical mechanism of plasma etching, and also has great guiding significance for process manufacturing production, and can save a lot of time and material costs for experimental testing.

[0123] The following combination Figure 4 , the simulation process in the simulation model of plasma etching process is explained in detail:

[0124] Step 401: Obtaining the etching surface profile, energy distribution and angle distribution of particles;

[0125] Step 402: performing particle injection;

[0126] Step 403: Determine the trajectory of the particle under the action of the electric field.

[0127] Step 404: judging whether the particles have reached the etching surface according to the particle motion trajectory;

[0128] If yes, proceed to step 405 and step 406, if no, proceed to step 403;

[0129] Step 405: Determine whether the reflection condition is met;

[0130] If yes, proceed to step 403; if no, proceed to step 409;

[0131] Step 406: performing charge transfer;

[0132] Step 407: Recording charge distribution;

[0133] Step 408: Calculate the electric potential and electric field based on the charge distribution; the calculated electric field updates the electric field in step 403;

[0134] Step 409: performing a surface etching reaction;

[0135] Step 410: Determine whether all particles have been injected;

[0136] If no, proceed to step 402; if yes, proceed to step 411;

[0137] Step 411: End the simulation and draw the etching morphology.

[0138] The simulation device for the plasma etching process provided by the present invention is described below. The simulation device for the plasma etching process described below and the simulation method for the plasma etching process described above can be referred to each other.

[0139] like Figure 5 As shown, an embodiment of the present invention further provides a simulation device for a plasma etching process, which is used to implement the simulation method for a plasma etching process in any of the above embodiments. The simulation device for a plasma etching process may include:

[0140] The acquisition module 510 is used to acquire the model input parameters of the plasma etching process simulation model; the model input parameters at least include the initial surface profile, the energy distribution and the angle distribution of each particle in the plasma; the initial surface profile is the graphic profile including the substrate and the hard mask;

[0141] A discretization module 520 is used to discretize the simulation area in the plasma etching process simulation model into a plurality of cells based on a cell method, and mark the corresponding cells based on the initial surface profile to obtain the corresponding etching area;

[0142] A first determination module 530 is used to determine the initial velocity vector and initial incident position of each particle using a Monte Carlo method based on the energy distribution and the angle distribution;

[0143] A second determination module 540 is used to determine the particle motion trajectory according to the initial velocity vector and the initial incident position;

[0144] A calculation module 550, for calculating the electric field distribution and performing surface etching reaction based on the relationship between the particle motion trajectory and the etching area;

[0145] The output module 560 is used to output the model output of the plasma etching process simulation model when the etching time ends. The model output at least includes the electric field distribution and the simulated etching profile after the surface etching reaction ends.

[0146] The second determining module 540 is specifically used for:

[0147] Based on Newton's second law, the ordinary differential equation of particle motion is constructed:

[0148]

[0149] Among them, v(x, y) is the particle velocity vector, q p is the charge of the particle, m p is the mass of the particle, t is the time, and E(x, y) is the electric field distribution;

[0150] Taking the initial velocity vector and the initial incident position as initial conditions, the ordinary differential equation is solved to obtain the particle motion trajectory.

[0151] The calculation module 550 is specifically used for:

[0152] According to the particle motion trajectory, it is determined whether the particle reaches the surface cell of the etching area. If the particle reaches the surface cell, the potential distribution of the particle after charge transfer is calculated. If the particle reaches the surface cell, it is further determined whether the particle is reflected. If the particle does not reflect, a surface etching reaction is performed.

[0153] Based on the potential distribution, the electric field distribution is determined.

[0154] The calculation module 550 is specifically used for:

[0155] Record the charge distribution of particles after charge transfer;

[0156] Based on the charge distribution, the Poisson equation is used to calculate the potential distribution.

[0157] The calculation module 550 is specifically used for:

[0158] Use the central difference method to approximate the second-order derivative and substitute it into the Poisson equation:

[0159]

[0160] The transformation equation is derived: Where, ∈ is the dielectric constant of vacuum, φ is the electric potential, and ρ is the charge distribution; (i, j) is the grid point corresponding to a charge; Δx is the spacing of the grid points in the x-axis direction, and Δy is the spacing of the grid points in the y-axis direction;

[0161] Based on the number of cells and the transformation equation, a linear system of equations is constructed:

[0162] Aφ=b

[0163] Solving the linear equations gives the potential distribution, where A is the coefficient matrix, φ is the vector of potentials, and b is the vector containing the charge density and dielectric constant.

[0164] When solving the linear equations, the upper and lower boundary potentials of the simulation area satisfy the Dirichle boundary condition: φ = 0;

[0165] The left and right boundaries of the simulation area are periodic boundaries and satisfy the Neumann boundary condition: dφ / dx=0.

[0166] The calculation module 550 is specifically used for:

[0167] Substituting the energy of the particle and the angle of incidence of the particle into the formula:

[0168]

[0169] The probability of occurrence of reaction events during the surface etching reaction is calculated, where p(ε p ,θ) is the probability of occurrence, ε p is the energy of the particle, θ is the incident angle; ε th is the threshold energy of the reaction, ε ref is the reference energy, p0 is the reaction probability at the reference energy, n is an empirical parameter, and f(θ) is the angular dependence;

[0170] The angular dependence is approximated by Yamamura's semi-empirical formula; wherein Yamamura's semi-empirical formula is:

[0171] Among them, C1, C2 and C3 are fitting parameters.

[0172] When a particle is reflected, the particle continues to move along the particle motion trajectory under the action of the electric field distribution until it reaches the surface cell and no longer reflects.

[0173] like Figure 6As shown, an embodiment of the present invention further provides a plasma etching process simulation device, which may include: a processor (processor) 610, a communication interface (CommunicationsInterface) 620, a memory (memory) 630 and a communication bus, wherein the processor 610, the communication interface 620 and the memory 630 communicate with each other through the communication bus. The memory 630 stores a computer program that can be run by the processor 610; when the processor 610 runs the computer program, it can execute the simulation method of the plasma etching process in any of the above embodiments.

[0174] In addition, the logic instructions in the above-mentioned memory 630 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods of each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0175] On the other hand, the present invention further provides a non-transitory computer-readable storage medium, in which instructions are stored. When the instructions are executed, the simulation method of the plasma etching process in any of the above embodiments is implemented.

[0176] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art may understand and implement other variations of the disclosed embodiments by viewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "one" or "an" does not exclude multiple situations. A single processor or other unit may implement several functions listed in the claims. Certain measures are recorded in different dependent claims, but this does not mean that these measures cannot be combined to produce good results.

[0177] Although the present invention has been described in conjunction with specific features and embodiments thereof, it is apparent that various modifications and combinations may be made thereto without departing from the spirit and scope of the present invention. Accordingly, this specification and the accompanying drawings are merely exemplary illustrations of the present invention as defined by the appended claims and are deemed to cover any and all modifications, variations, combinations or equivalents within the scope of the present invention. Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, the present invention is intended to include such modifications and variations if they fall within the scope of the claims of the present invention and their equivalents.

Claims

1. A method for simulating a plasma etching process, characterized in that: include: Obtaining model input parameters of a plasma etching process simulation model; the model input parameters at least include an initial surface profile, an energy distribution and an angular distribution of each particle in the plasma; The initial surface profile is a pattern profile including a substrate and a hard mask; Based on the cellular method, the simulation area in the plasma etching process simulation model is discretized into a plurality of cells, and the corresponding cells are marked based on the initial surface contour to obtain the corresponding etching area; Based on the energy distribution and the angle distribution, using a Monte Carlo method to determine an initial velocity vector and an initial incident position of each particle; Determining a particle motion trajectory according to the initial velocity vector and the initial incident position; Based on the relationship between the particle motion trajectory and the etching area, electric field distribution calculation is performed and surface etching reaction is performed; When the etching time is over, the model output of the plasma etching process simulation model is output, and the model output at least includes the electric field distribution and the simulated etching profile after the surface etching reaction is completed.

2. The method for simulating a plasma etching process according to claim 1, characterized in that: The electric field distribution calculation and surface etching reaction are performed based on the relationship between the particle motion trajectory and the etching area, including: Judging whether the particle reaches the surface cell of the etching area according to the particle movement trajectory, if the particle reaches the surface cell, calculating the potential distribution of the particle after charge transfer, and, if the particle reaches the surface cell, continuing to judge whether the particle is reflected, and performing a surface etching reaction when the particle does not reflect; Based on the potential distribution, the electric field distribution is determined.

3. The method for simulating a plasma etching process according to claim 1, characterized in that: Determining the particle motion trajectory according to the initial velocity vector and the initial incident position includes: Based on Newton's second law, the ordinary differential equation of particle motion is constructed: Among them, v(x, y) is the particle velocity vector, q p is the charge of the particle, m p is the mass of the particle, t is the time, and E(x, y) is the electric field distribution; The initial velocity vector and the initial incident position are used as initial conditions to solve the ordinary differential equation to obtain the particle motion trajectory.

4. The method for simulating a plasma etching process according to claim 2, characterized in that: The calculation of the potential distribution of the particle after charge transfer comprises: Record the charge distribution of particles after charge transfer; Based on the charge distribution, the potential distribution is calculated using Poisson's equation.

5. The method for simulating a plasma etching process according to claim 4, characterized in that: The step of calculating the potential distribution based on the charge distribution using the Poisson equation comprises: The second-order derivative is approximated using the central difference method and substituted into the Poisson equation: The transformation equation is derived: Wherein, ∈ is the dielectric constant of vacuum, φ is the electric potential, and ρ is the charge distribution; (i, j) is the grid point corresponding to a charge; Δx is the spacing of the grid points in the x-axis direction, and Δy is the spacing of the grid points in the y-axis direction; Based on the number of cells and the transformation equation, a linear system of equations is constructed: Aφ=b The linear equations are solved to obtain the potential distribution; wherein A is a coefficient matrix, φ is a vector of potentials, and b is a vector containing charge density and dielectric constant.

6. The method for simulating a plasma etching process according to claim 5, characterized in that: When solving the linear equations, the upper and lower boundary potentials of the simulation area satisfy the Dirichle boundary condition: φ=0; The left and right boundaries of the simulation area are periodic boundaries, satisfying the Neumann boundary condition: dφ / dx=0.

7. The method for simulating a plasma etching process according to claim 1, characterized in that: The surface etching reaction comprises: Substituting the energy of the particle and the angle of incidence of the particle into the formula: The probability of occurrence of reaction events during the surface etching reaction is calculated, where p(ε p ,θ) is the occurrence probability, ε p is the energy of the particle, θ is the incident angle; ε th is the threshold energy of the reaction, ε ref is the reference energy, p0 is the reaction probability at the reference energy, n is an empirical parameter, and f(θ) is the angular dependence; The angular dependence is approximated by Yamamura's semi-empirical formula; wherein Yamamura's semi-empirical formula is: Among them, C1, C2 and C3 are fitting parameters.

8. The method for simulating a plasma etching process according to claim 5, characterized in that: The reaction mechanisms corresponding to the reaction events include: adsorption, removal, desorption and sputtering of hard mask.

9. A simulation device for a plasma etching process, characterized in that: include: An acquisition module, used for acquiring model input parameters of a plasma etching process simulation model; the model input parameters at least include an initial surface profile, energy distribution and angle distribution of each particle in the plasma; the initial surface profile is a graphic profile including a substrate and a hard mask; A discretization module, used for discretizing the simulation area in the plasma etching process simulation model into a plurality of cells based on a cellular method, and marking corresponding cells based on the initial surface contour to obtain corresponding etching areas; A first determination module, configured to determine an initial velocity vector and an initial incident position of each particle by using a Monte Carlo method based on the energy distribution and the angle distribution; A second determination module, used to determine the particle motion trajectory according to the initial velocity vector and the initial incident position; A calculation module, used to calculate the electric field distribution and perform surface etching reaction based on the relationship between the particle motion trajectory and the etching area; The output module is used to output the model output of the plasma etching process simulation model when the etching time ends, and the model output at least includes the electric field distribution and the simulated etching profile after the surface etching reaction ends.

10. A simulation device for a plasma etching process, characterized in that: include: A processor, a communication interface, a memory and a communication bus; wherein the processor, the communication interface and the memory communicate via the communication bus; The memory stores a computer program that can be executed by the processor; when the processor executes the computer program, the simulation method of the plasma etching process according to any one of claims 1 to 8 is executed.

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