Simulation method and system for double-sided polishing removal amount, terminal and medium

Abstract

The invention provides a simulation method and system for double-sided polishing removal amount, a terminal and a medium, and the method comprises the steps: carrying out the stress analysis of each point on a silicon wafer, and obtaining the contact pressure of each point of the silicon wafer; meanwhile, motion trail analysis is conducted on all points of the silicon wafer, and the motion distances of the points in the inner area, the middle area and the outer area of the polishing pad large disc are determined; and the removal amount of each point of the silicon wafer is calculated based on the obtained movement distance of each point of the silicon wafer in the inner area, the middle area and the outer area of the polishing pad large disc and the contact pressure of each point of the silicon wafer. According to the method, the influence of various factors such as a machine table, pressure and rotating speed is considered, accurate calculation of the double-sided polishing removal rate is achieved, the calculation mode is simple, convenient and efficient, and important guidance and basis can be provided for follow-up DSP process optimization and high-planarization large silicon wafer production.

Description

Technical Field

[0001] This invention relates to the field of silicon wafer polishing technology, and in particular to a simulation method, system, terminal, and medium for double-sided polishing removal. Background Technology

[0002] Chemical mechanical polishing (CMP) is an indispensable process in semiconductor manufacturing, using synergistic chemical and mechanical actions to remove impurities from the surface of a workpiece. Double-sided CMP, due to its ability to achieve better global planarization of silicon wafers, has become a crucial step in the fabrication of large silicon wafers for semiconductor substrates. Its ability to achieve global planarization lies in the fact that during polishing, the silicon wafer is placed within a planetary gear, between upper and lower polishing pads, and rotated by internal and external gears. The polishing pads, carrying abrasive particles, simultaneously remove features from both sides of the wafer, improving overall uniformity in the thickness direction. This technology, by simultaneously treating two surfaces of the material, not only significantly improves processing efficiency but also ensures consistent surface quality on both sides, avoiding surface differences that may occur with single-sided polishing. Therefore, research on material removal rates during double-sided polishing is of great significance.

[0003] Although some methods and studies exist for calculating material removal rates in single-sided polishing, such as CN111079287A which discloses a CMP abrasion rate calculation method and simulation system, providing a method for calculating material removal rates in single-sided polishing, there is almost no corresponding method for calculating material removal rates for the more complex process of double-sided polishing. Therefore, providing a method for calculating material removal rates suitable for double-sided polishing has become an urgent problem to be solved. Summary of the Invention

[0004] In view of the shortcomings of the prior art described above, the purpose of this invention is to provide a simulation method, system, terminal and medium for double-sided polishing removal amount, in order to solve the technical problem that the prior art lacks an accurate and simple method for calculating the material removal rate of double-sided polishing.

[0005] To achieve the above and other related objectives, this invention provides a simulation method for double-sided polishing removal amount. The method includes: performing force analysis on each point on the silicon wafer to obtain the contact pressure at each point; performing motion trajectory analysis on each point on the silicon wafer and calculating the movement distance of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad; and calculating the removal amount at each point on the silicon wafer based on the movement distance of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad and the contact pressure at each point on the silicon wafer.

[0006] In one embodiment of the present invention, the step of performing force analysis on each point on the silicon wafer to obtain the contact pressure at each point on the silicon wafer includes: obtaining the contact pressure at each point on the silicon wafer based on the position of the planetary wheel, the upper polishing pad, the lower polishing pad, the polishing head and the wafer and the mechanical parameters, based on solid mechanics finite element simulation; wherein the mechanical parameters include: Young's modulus, Poisson's ratio and density.

[0007] In one embodiment of the present invention, the step of analyzing the motion trajectory of each point on the silicon wafer and calculating the motion path of each point on the silicon wafer in the inner, middle and outer areas of the polishing pad includes: calculating the motion trajectory of each point on the silicon wafer on the polishing pad based on the operating parameters of the double-sided polishing equipment; and calculating the motion path of each point on the silicon wafer in the inner, middle and outer areas of the polishing pad based on the motion trajectory of each point on the silicon wafer.

[0008] In one embodiment of the present invention, the step of calculating the movement path of each point on the silicon wafer in the inner, middle and outer areas of the polishing pad based on the movement trajectory of each point on the silicon wafer includes: extracting the movement trajectory of each point on the silicon wafer in the inner, middle and outer areas of the polishing pad from the movement trajectory of each point on the silicon wafer, and calculating the movement path of each point on the silicon wafer in the inner, middle and outer areas of the polishing pad respectively.

[0009] In one embodiment of the present invention, the step of calculating the removal amount of each point on the silicon wafer based on the movement path of each point on the inner, middle, and outer regions of the polishing pad and the contact pressure of each point on the silicon wafer includes: obtaining the contact pressure of the silicon wafer in the inner, middle, and outer regions of the polishing pad based on the contact pressure of each point on the silicon wafer; calculating the removal amount of each point on the silicon wafer in the inner, middle, and outer regions of the polishing pad based on the movement path of each point on the silicon wafer in the inner, middle, and outer regions of the polishing pad and the contact pressure of the silicon wafer in the inner, middle, and outer regions of the polishing pad; and calculating the removal amount of each point on the silicon wafer based on the removal amount of each point on the silicon wafer in the inner, middle, and outer regions of the polishing pad.

[0010] In one embodiment of the present invention, obtaining the contact pressure of the silicon wafer in the inner, middle and outer regions of the polishing pad based on the contact pressure at each point on the silicon wafer includes: statistically analyzing the contact pressure at points on the silicon wafer located in the inner, middle and outer regions of the polishing pad, respectively, and calculating the contact pressure of the silicon wafer in the three regions.

[0011] In one embodiment of the present invention, calculating the removal amount of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad, based on the movement path of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad and the contact pressure of the silicon wafer in the inner, middle, and outer areas of the polishing pad, includes: calculating the removal amount of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad based on the Preston formula, based on the movement path of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad and the contact pressure of the silicon wafer in the inner, middle, and outer areas of the polishing pad; wherein, the Preston formula is: MRA = K × P × L; where MRA is the removal amount of a point on the silicon wafer in a region on the polishing pad, P is the contact pressure of the silicon wafer in the corresponding region, L is the movement path of the point in the corresponding region, and K is an empirical parameter.

[0012] To achieve the above and other related objectives, this invention provides a simulation system for double-sided polishing removal amount. The system includes: a force analysis module for performing force analysis on various points on a silicon wafer to obtain the contact pressure at each point; a trajectory analysis and motion path statistics module for performing motion trajectory analysis on various points on the silicon wafer and calculating the motion path of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad; and a removal amount calculation module connected to the force analysis module and the trajectory analysis and motion path statistics module for calculating the removal amount at each point on the silicon wafer based on the motion path of each point on the inner, middle, and outer areas of the polishing pad and the contact pressure at each point on the silicon wafer.

[0013] To achieve the above and other related objectives, the present invention provides an electronic terminal, comprising: one or more memories and one or more processors; the one or more memories are used to store a computer program; the one or more processors are connected to the memories and are used to run the computer program to perform the simulation method for double-sided polishing removal amount.

[0014] To achieve the above and other related objectives, the present invention provides a computer-readable storage medium storing a computer program that is executed by one or more processors to perform the method.

[0015] As described above, this invention provides a simulation method, system, terminal, and medium for double-sided polishing removal, offering the following advantages: This invention analyzes the forces acting on various points on a silicon wafer to obtain the contact pressure at each point; simultaneously, it analyzes the motion trajectory of each point on the silicon wafer to determine its travel distance within the inner, middle, and outer areas of the polishing pad; and then calculates the removal amount at each point on the silicon wafer based on the obtained travel distances within the inner, middle, and outer areas of the polishing pad and the contact pressure at each point. This invention not only considers the influence of various factors such as the machine tool, pressure, and rotation speed, achieving accurate calculation of the double-sided polishing removal rate, but also employs a simple and efficient calculation method. Furthermore, it provides important guidance and basis for subsequent optimization of DSP processes and the production of highly flattened large silicon wafers. Attached Figure Description

[0016] Figure 1 The diagram shown is a flowchart illustrating a simulation method for double-sided polishing removal in one embodiment of the present invention.

[0017] Figure 2 The diagram shows a geometric structure of a finite element model of solid mechanics according to an embodiment of the present invention.

[0018] Figure 3 The diagram shows a mechanical simulation of a silicon wafer at three different locations—inner, middle, and outer—in one embodiment of the present invention.

[0019] Figure 4 a shows a schematic diagram of the contact stress of a silicon wafer located inside the large disk under different gap conditions in an embodiment of the present invention.

[0020] Figure 4 b shows a schematic diagram of the contact stress of a silicon wafer located on the middle side of the large disk under different gap conditions in one embodiment of the present invention.

[0021] Figure 4 c shows a schematic diagram of the contact stress of a silicon wafer located on the outer side of the large disk under different gap conditions in one embodiment of the present invention.

[0022] Figure 5 a shows a schematic diagram of the motion trajectory of the outer edge point of the silicon wafer in one embodiment of the present invention.

[0023] Figure 5 b shows a schematic diagram of the movement trajectory of the center point of the silicon wafer in one embodiment of the present invention.

[0024] Figure 5 c shows a schematic diagram of the motion trajectory of the inner edge point of the silicon wafer in one embodiment of the present invention.

[0025] Figure 6 a shows a schematic diagram of the movement trajectory of the outer edge point of the silicon wafer in the inner area of ​​the disk in one embodiment of the present invention.

[0026] Figure 6 b shows a schematic diagram of the movement trajectory of the outer edge point of the silicon wafer in the middle area of ​​the large disk in one embodiment of the present invention.

[0027] Figure 6 c shows a schematic diagram of the movement trajectory of the outer edge point of the silicon wafer in the outer area of ​​the disk in one embodiment of the present invention.

[0028] Figure 7 a is a schematic diagram of the thickness distribution curve under the condition that Gap is less than 0 in one embodiment of the present invention.

[0029] Figure 7 b is a schematic diagram of the thickness distribution curve under the condition that Gap is greater than 0 in one embodiment of the present invention.

[0030] Figure 8 The diagram shown is a structural schematic of a simulation system for double-sided polishing removal in one embodiment of the present invention.

[0031] Figure 9 The diagram shows a structural schematic of an electronic terminal according to an embodiment of the present invention. Detailed Implementation

[0032] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0033] It should be noted that in the following description, reference is made to the accompanying drawings, which illustrate several embodiments of the present invention. It should be understood that other embodiments may also be used, and changes in mechanical composition, structure, electrical system, and operation may be made without departing from the spirit and scope of the invention. The following detailed description should not be considered limiting, and the scope of the embodiments of the invention is defined only by the claims of the published patents. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. Spatially related terms, such as “upper,” “lower,” “left,” “right,” “below,” “below,” “lower part,” “above,” “upper part,” etc., may be used herein to illustrate the relationship between one element or feature shown in the figures and another element or feature.

[0034] Throughout this specification, when it is said that a part is "connected" to another part, this includes not only "direct connection" but also "indirect connection" by placing other elements in between. Furthermore, when it is said that a part "includes" a certain constituent element, unless otherwise stated otherwise, it does not exclude other constituent elements, but rather implies that other constituent elements may also be included.

[0035] The terms "first," "second," and "third," etc., used herein are for the purpose of describing various parts, components, regions, layers, and / or segments, but are not limiting. These terms are used only to distinguish one part, component, region, layer, or segment from others. Therefore, the "first part," "component," "region," "layer," or "segment" described below may refer to a "second part," "component," "region," "layer," or "segment" without departing from the scope of this invention.

[0036] Furthermore, as used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context indicates otherwise. It should be further understood that the terms “comprising,” “including,” indicate the presence of the stated feature, operation, element, component, item, kind, and / or group, but do not preclude the presence, occurrence, or addition of one or more other features, operations, elements, components, items, kinds, and / or groups. The terms “or” and “and / or” as used herein are interpreted as inclusive, or mean any one or any combination thereof. Thus, “A, B, or C” or “A, B, and / or C” means “any one of: A; B; C; A and B; A and C; B and C; A, B, and C.” Exceptions to this definition arise only when combinations of elements, functions, or operations are inherently mutually exclusive in some manner.

[0037] This invention provides a simulation method for double-sided polishing removal rate. It analyzes the forces acting on various points on a silicon wafer to obtain the contact pressure at each point. Simultaneously, it analyzes the motion trajectory of each point on the wafer to determine its travel distance within the inner, middle, and outer areas of the polishing pad. Based on the obtained travel distances and contact pressures of each point within the polishing pad, the removal rate at each point is calculated. This invention not only considers the influence of various factors such as the machine tool, pressure, and rotation speed, achieving accurate calculation of the double-sided polishing removal rate, but also offers a simple and efficient calculation method. Furthermore, it provides important guidance and basis for subsequent optimization of DSP processes and the production of highly flattened large silicon wafers.

[0038] The present invention will now be described in detail with reference to the accompanying drawings, so that those skilled in the art can readily implement it. The present invention can be embodied in many different forms and is not limited to the embodiments described herein.

[0039] like Figure 1 A flowchart illustrating a simulation method for double-sided polishing removal volume in an embodiment of the present invention is shown.

[0040] The method includes:

[0041] Step S1: Perform stress analysis on each point on the silicon wafer and obtain the contact pressure at each point on the silicon wafer.

[0042] In one embodiment, the step of performing force analysis on various points on the silicon wafer and obtaining the contact pressure at each point on the silicon wafer includes:

[0043] First, the positions and mechanical parameters of the planetary gear, upper polishing pad, lower polishing pad, polishing head, and wafer are collected. The mechanical parameters include Young's modulus, Poisson's ratio, and density. Among them, Young's modulus and Poisson's ratio are used to calculate the elastic stiffness matrix [K].

[0044] Based on the collected data, a finite element model of solid mechanics is established using CAD software or finite element preprocessing software (such as SolidWorks, ANSYS, Abaqus, etc.). Figure 2 This is a schematic diagram of the geometric structure of a finite element model for solid mechanics. Depending on the machine tool, other components can be added to this model to obtain more accurate results.

[0045] Mesh the finite element model of solid mechanics to generate a finite element mesh. The mesh density and shape will affect the simulation accuracy and computation time. A denser mesh should be used in critical regions (such as contact surfaces) to improve accuracy.

[0046] Based on the actual problem, determine the fixed ends or constraints of the model, and apply volume forces (such as gravity) and external loads (such as polishing pressure). These loads will be used as input parameters to solve the equilibrium equations.

[0047] During the simulation, we used the following governing equations to solve for the forces acting on various points on the silicon wafer:

[0048] The equilibrium equation describes the balance relationship between internal stresses and external loads of an object, specifically expressed as:

[0049]

[0050] Among them, f x and f y Represents the volume force component, ρ is the density, and u and v are the displacements along the x and y directions, respectively.

[0051] The continuity equation, which relates the displacement and stress state inside an object, is specifically expressed as:

[0052] [K]{δ}={Q}; (2)

[0053] Where [K] is the elastic stiffness matrix, {δ} is the nodal displacement vector, and {Q} is the nodal stress vector.

[0054] By comprehensively applying these steps and control equations, we can accurately analyze the contact pressure at various points on the silicon wafer during the polishing process.

[0055] Step S2: Analyze the motion trajectory of each point on the silicon wafer and count the movement distance of each point on the silicon wafer in different areas on the polishing pad.

[0056] In one embodiment, the step of analyzing the motion trajectory of each point on the silicon wafer and calculating the movement distance of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad includes:

[0057] Based on the operating parameters of the double-sided polishing equipment, the motion trajectory of each point on the silicon wafer on the polishing pad is calculated.

[0058] Specifically, during silicon wafer polishing, the formation of the polished surface primarily depends on the relative motion trajectory between the polishing pad and the planetary wheel, or the relative motion trajectory between the polishing pad and the silicon wafer held by the planetary wheel. In actual polishing, the polishing pad and the planetary wheel / wafer can be simplified as two planes undergoing relative planar motion, and their relative motion trajectories are considered to be identical: the motion trajectory of the planetary wheel / wafer relative to the polishing pad is the same as, but in the opposite direction to, the motion trajectory of the polishing pad relative to the planetary wheel / wafer. The calculation method for the motion trajectory of each point on the silicon wafer is as follows:

[0059] Obtain the operating parameters of the polishing equipment, including the inner pin ring angular velocity w, the outer pin ring angular velocity W, the inner pin ring radius r, and the outer pin ring radius R;

[0060] The obtained operating parameters are converted into motion parameters of the planetary wheel in the polishing equipment, namely the planetary wheel's revolution angular velocity Wcenter and its rotation angular velocity Wself;

[0061] W center =(W*R+w*r) / (R+r); (3)

[0062] W self =(W*Rw*r) / (Rr); (4)

[0063] Based on the linkage mechanism model, the time parameter t for forming the motion trajectory of the planetary wheel is set to obtain the orbital angle Acenter and the rotational angle Aself of the planetary wheel:

[0064] A center = W center *t; (5)

[0065] A self = W self *t; (6)

[0066] Next, the polar coordinate system is transformed into a rectangular coordinate system. Assuming the radius of the planetary wheel is L1, the trajectory (x1, y1) of the planetary wheel is obtained:

[0067] x 1 =(r+L 1 )*cos(A center ); (7)

[0068] y 1 =(r+L 1 )*sin(A center ); (8)

[0069] The motion of the silicon wafer on the planetary gear is influenced not only by the planetary gear's revolution and rotation, but also by its own independent trajectory. Assuming the radius of the silicon wafer at its current position is L2, the independent trajectory of that position is (x2, y2):

[0070] x 2 =(L 1 -L 2 )*cos(A center +A self ); (9)

[0071] y 2 =(L 1 -L 2 )*sin(A center +A self ); (10)

[0072] Based on the trajectory of the planetary wheel (x1, y1), the independent trajectory (x2, y2) of the current point of the silicon wafer is superimposed to obtain the trajectory (x3, y3) of the current point of the silicon wafer:

[0073] x 3 = (r+L 1 )*cos(A center )+(L 1 -L 2 )*cos(A center +A self ); (11)

[0074] y 3 =(r+L 1 )*sin(A center )+(L 1 -L 2 )*sin(A center +A self ); (12)

[0075] By following the steps above, we can accurately calculate the trajectory of the silicon wafer at the current point in the polishing equipment.

[0076] The polishing pad is divided into an inner, middle, and outer zone. Since the movement trajectory of each point on the silicon wafer may lie within the inner, middle, and outer zones of the polishing pad, it is necessary to divide the movement trajectory of each point on the silicon wafer into these zones, and then calculate the movement distance of each point within the inner, middle, and outer zones of the polishing pad. The calculation of the movement distance of each point within the inner, middle, and outer zones of the polishing pad can be done in two ways:

[0077] One method involves using Euclidean distance or other suitable distance metrics to calculate the coordinates of the current point's motion trajectory within the inner, middle, and outer areas of the polishing pad. These distances are then summed to obtain the estimated path distance of the current point on the silicon wafer within these areas.

[0078] Another method is to calculate the speed of the current point at different time points based on the trajectory of the current point in the inner, middle and outer areas of the polishing pad, and then integrate the speed of each point in the inner, middle and outer areas to obtain the distance traveled by the point in the inner, middle and outer areas of the polishing pad.

[0079] Step 3: Calculate the removal amount at each point on the silicon wafer based on the movement path of each point on the inner, middle and outer areas of the polishing pad and the contact pressure at each point on the silicon wafer.

[0080] In one embodiment, the step of calculating the removal amount at each point on the silicon wafer based on the movement path of each point on the inner, middle, and outer areas of the polishing pad and the contact pressure at each point on the silicon wafer includes:

[0081] The contact pressure P of the silicon wafer in the inner area of ​​the polishing pad is obtained based on the contact pressure at various points on the silicon wafer. 内 Contact pressure P in the middle zone 中 and the contact pressure P in the outer zone 外 ;

[0082] The distance L traveled by each point on the silicon wafer within the inner area of ​​the polishing pad. 内 The distance L of the central area 中 The distance L of movement in the outer area 外 And the contact pressure P of the silicon wafer on the inner region of the polishing pad. 内 Contact pressure P in the middle zone 中 and the contact pressure P in the outer zone 外 Calculate the removal amount (MRA) at each point on the silicon wafer within the inner area of ​​the polishing pad. 内 MRA removal rate in the middle zone 中 and the removal rate MRA in the outer zone 外 ;

[0083] MRA (Mean Amount Removal) of silicon wafers at various points on the inner area of ​​the polishing pad 内 MRA removal rate in the middle zone 中 and the removal rate MRA in the outer zone 外 Calculate the removal amount (MRA) at each point on the silicon wafer. 总 Specifically, the amount of material removed from each point on the silicon wafer is added together in the inner, middle, and outer areas of the polishing pad to calculate the amount of material removed from that point on the silicon wafer.

[0084] In one embodiment, obtaining the contact pressure of the silicon wafer in the inner, middle, and outer regions of the polishing pad based on the contact pressure at various points on the silicon wafer includes:

[0085] Based on the location of each point on the silicon wafer, the wafer is divided into the inner, middle, and outer areas of the polishing pad. The contact pressure data of each point is classified according to its region, resulting in contact pressure datasets for the inner, middle, and outer areas. These contact pressure data are directly calculated during the simulation process and reflect the mechanical behavior of the silicon wafer when it comes into contact with different areas of the polishing pad during the polishing process.

[0086] Based on the statistical contact pressure dataset of the inner, middle and outer regions, the contact pressure of the silicon wafer on the polishing pad disk in the three regions is calculated, which serves as the contact pressure of each point on the silicon wafer in the three regions.

[0087] For a specific example, the mean value is calculated for the contact pressure dataset of each region. The mean value reflects the average level of contact pressure at all points within that region, and thus serves as the contact pressure for that region.

[0088] In one specific embodiment, the amount of material removed from each point on the silicon wafer within the inner, middle, and outer regions of the polishing pad is calculated based on the travel distance of each point on the silicon wafer within these regions and the contact pressure of the silicon wafer within the inner, middle, and outer regions of the polishing pad. This includes:

[0089] Based on the Preston formula, the amount of material removed from each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad is calculated by the movement path of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad and the contact pressure of the silicon wafer in the inner, middle, and outer areas of the polishing pad.

[0090] The Preston formula, used to describe the relationship between material removal rate and polishing conditions during polishing, is a classic formula. It is typically expressed as MRA = KPV; the material removal amount is calculated by integrating the material removal rate over different time periods, i.e., the Preston formula can be:

[0091] MRA=∫K×P×V t ×dt=K×P×L; (13)

[0092] Where MRA represents the amount of material removed from a point on the silicon wafer within a region of the polishing pad, P represents the contact pressure of the silicon wafer in the corresponding region, L represents the travel distance of that point in the corresponding region, and K is an empirical parameter. The specific value of K may vary depending on the machine and operating conditions. Although different values ​​of K may result in different absolute material removal rates, this formula still provides qualitative results for the amount of material removed at each point, thereby determining the wafer's unevenness, overall profile, edge collapse, etc., and guiding process and machine control.

[0093] Specifically, using the Preston formula, we can calculate the amount of material removed at each point on the silicon wafer in the inner, middle, and outer regions (MRA inner, MRA middle, MRA outer):

[0094] MRA 内 =K×P 内 ×L 内 (14)

[0095] MRA 中 =K×P 中 ×L 中 (15)

[0096] MRA 外 =K×P 外 ×L 外 (16)

[0097] Through the above steps, we can accurately calculate the amount of material removed from each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad, thus providing strong support for optimizing the polishing process and improving polishing quality.

[0098] To better describe the simulation method for the removal amount of double-sided polishing, a specific embodiment will be used for illustration.

[0099] Example

[0100] For double-sided polishing machines, due to differences in the thickness of the polishing pads at different locations and the variations in the thickness direction of the initial incoming silicon wafers, non-uniform gaps will exist between the upper and lower pads. When the pad gaps are uneven, different areas of the silicon wafer experience inconsistent pressure as it passes through different positions, resulting in fluctuations in the removal rate of different areas during silicon wafer polishing. When the pad gaps are uncontrolled, the overall flatness of the silicon wafer will be reduced; therefore, the impact of the upper and lower pad gaps must be studied.

[0101] Based on the simulation method for double-sided polishing removal, we investigated the differences in removal rates at the center and edges of silicon wafers under different upper and lower disk gaps. The calculated results are consistent with the experimental results. The specific calculation settings are as follows.

[0102] First, the gap between the upper and lower plates is defined as the difference in longitudinal distance between the inner and outer sides of the upper and lower plates, and the formula is defined as follows:

[0103] Gap = d in -d out (17)

[0104] To investigate the removal of silicon from the surface during the entire polishing process, we conducted mechanical simulations on silicon wafers located at three different positions: the inner, middle, and outer sides of the large disk. The schematic diagram is shown below. Figure 3 As shown, the positions are W1, W2, and W3 respectively.

[0105] The contact pressure calculation results are as follows Figure 4 As shown in figures a, 4b, and 4c, point 0 represents the edge of the silicon wafer near the center of the planetary wheel. The results show that increasing the gap will increase the pressure in the outer region to some extent, decrease the pressure in the inner region, and keep the pressure in the middle almost unchanged. Therefore, we will further simplify the calculation by dividing the pressure of the entire system into three regions: inner, middle, and outer.

[0106] To determine the difference in removal amount between the center and edge regions of the silicon wafer under different gap conditions, Python was used to calculate and collect the difference in the path relative to the upper polishing pad between the edge and center points of the silicon wafer during the polishing process, as follows: Figure 5 As shown in a, 5b, and 5c; the movement trajectories of the inner edge of the silicon wafer all fall within the inner area of ​​the large disk, the movement trajectories of the center all fall within the center, while the movement trajectories of the outer edge of the silicon wafer pass through the inner, middle, and outer areas, as shown in the partitions. Figure 6 As shown in a, 6b and 6c.

[0107] The path lengths of the outer edge, center, and inner edge points of the silicon wafer are shown in the table below:

[0108] Table 1: Statistics of Distance Length

[0109]

[0110] Based on the calculation results above, the removal rates of silicon wafer edges and center points are shown in the table below:

[0111] Table 2: Removal Rate Statistics under Different Gap Conditions

[0112]

[0113] As shown in the table, the difference in removal amount at the edge and center of the silicon wafer leads to the formation of the uneven surface morphology of the silicon wafer. As the gap increases, the removal amount at the edge of the silicon wafer gradually increases, while the removal amount at the center gradually decreases, thus the surface curve of the silicon wafer gradually becomes convex.

[0114] To verify the impact of gap differences on thickness distribution and flatness, all other process conditions were kept consistent during the experiment. Six rounds of experiments were conducted under two scenarios, with a pressure of 1500 daN and a planetary gear thickness of 779 μm used throughout. In the first scenario (Gap < 0 μm), the values ​​were -17 μm, -20 μm, and -23 μm, respectively; in the second scenario (Gap > 0 μm), the values ​​were 9 μm, 8 μm, and 7 μm, respectively. The initial silicon wafer thickness was 790 μm, and the thickness after polishing was approximately 774.3 μm.

[0115] After polishing, in order to more clearly compare the differences in thickness distribution, the final thickness distribution curve was normalized at a radius of 0 mm, as shown below. Figure 7 As shown in the figure, the thickness distribution reveals that as the gap value increases, the silicon wafer thickness distribution becomes more convex.

[0116] Therefore, this experiment verifies that the gap difference mentioned in the simulation leads to the generation of the silicon wafer's unevenness curve, and also verifies the accuracy of the simulation method.

[0117] Similar to the above embodiments, the present invention provides a simulation control system for double-sided polishing removal amount.

[0118] The following specific embodiments are provided in conjunction with the accompanying drawings:

[0119] like Figure 8 A schematic diagram of a simulation system for double-sided polishing removal volume is shown in an embodiment of the present invention.

[0120] The system includes:

[0121] Force analysis module 1 is used to perform force analysis on various points on the silicon wafer to obtain the contact pressure at each point on the silicon wafer.

[0122] The trajectory analysis and motion path statistics module 2 is used to analyze the motion trajectory of each point on the silicon wafer and to count the motion path of each point on the silicon wafer in the inner, middle and outer areas of the polishing pad.

[0123] The removal amount calculation module 3 is connected to the force analysis module 1 and the trajectory analysis and motion path statistics module 2. It is used to calculate the removal amount of each point on the silicon wafer based on the motion path of each point on the inner, middle and outer areas of the polishing pad and the contact pressure of each point on the silicon wafer.

[0124] Since the implementation principle of the simulation system for the removal amount of double-sided polishing has been described in the foregoing embodiments, it will not be repeated here.

[0125] The simulation method for double-sided polishing removal provided in this invention can be implemented on the terminal side or the server side. For details regarding the hardware structure of the electronic terminal, please refer to [link to relevant documentation]. Figure 9This is a schematic diagram of an optional hardware structure of an electronic terminal 1000 provided in an embodiment of the present invention. The terminal 1000 can be a mobile phone, computer device, tablet device, personal digital processing device, factory back-end processing device, etc. The terminal 1000 includes: at least one processor 1001, a memory 1002, at least one network interface 10010, and a user interface 1009. The various components in the device are coupled together through a bus system 1005. It is understood that the bus system 1005 is used to realize the connection and communication between these components. In addition to a data bus, the bus system 1005 also includes a power bus, a control bus, and a status signal bus. However, for clarity, in... Figure 9 The general will label all buses as bus systems.

[0126] The user interface 1009 may include a monitor, keyboard, mouse, trackball, clicker, button, touchpad, or touch screen.

[0127] It is understood that memory 1002 can be volatile memory or non-volatile memory, or both. Non-volatile memory can be read-only memory (ROM) or programmable read-only memory (PROM), which serves as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM) and synchronous static random access memory (SSRAM). The memories described in the embodiments of this invention are intended to include, but are not limited to, these and any other suitable categories of memory.

[0128] In this embodiment of the invention, the memory 1002 is used to store various types of data to support the operation of the terminal 1000. Examples of this data include: any executable program for operation on the terminal 1000, such as the operating system 10021 and application program 10022; the operating system 10021 contains various system programs, such as the framework layer, core library layer, driver layer, etc., for implementing various basic services and handling hardware-based tasks. The application program 10022 may contain various applications, such as a media player, browser, etc., for implementing various application services. The simulation method for double-sided polishing removal provided in this embodiment of the invention can be included in the application program 10022.

[0129] The methods disclosed in the above embodiments of the present invention can be applied to or implemented by the processor 1001. The processor 1001 may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by the integrated logic circuit of the hardware in the processor 1001 or by instructions in the form of software. The processor 1001 may be a general-purpose processor, a digital signal processor (DSP), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The processor 1001 can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor 1001 may be a microprocessor or any conventional processor, etc. The steps of the accessory optimization method provided in the embodiments of the present invention can be directly reflected as being executed by a hardware decoding processor, or being executed by a combination of hardware and software modules in the decoding processor. The software module may be located in a storage medium, which is located in a memory. The processor reads the information in the memory and combines it with its hardware to complete the steps of the aforementioned method.

[0130] In an exemplary embodiment, the terminal 1000 may be used to execute the aforementioned method by one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), or complex programmable logic devices (CPLDs).

[0131] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented using computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0132] In the embodiments provided in this application, the computer-readable and writable storage medium may include read-only memory, random access memory, EEPROM, CD-ROM or other optical disc storage devices, disk storage devices or other magnetic storage devices, flash memory, USB flash drive, portable hard drive, or any other medium capable of storing desired program code in the form of instructions or data structures and accessible by a computer. Additionally, any connection may be appropriately referred to as a computer-readable medium. For example, if instructions are transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of the medium. However, it should be understood that computer-readable and writable storage media and data storage media do not include connections, carrier waves, signals, or other transient media, but are intended for non-transient, tangible storage media. The disks and optical discs used in the application include compact discs (CDs), laser discs, optical discs, digital multifunction discs (DVDs), floppy disks, and Blu-ray discs, where disks typically copy data magnetically, while optical discs use lasers to copy data optically.

[0133] In summary, the simulation method, system, terminal, and medium for double-sided polishing removal of the present invention analyzes the force on each point on the silicon wafer and obtains the contact pressure at each point; simultaneously, it analyzes the motion trajectory of each point on the silicon wafer to determine its movement path in the inner, middle, and outer areas of the polishing pad; and then calculates the removal amount at each point on the silicon wafer based on the obtained movement paths and contact pressures in the inner, middle, and outer areas of the polishing pad. This invention not only considers the influence of various factors such as the machine tool, pressure, and rotation speed, achieving accurate calculation of the double-sided polishing removal rate, but also offers a simple and efficient calculation method. It also provides important guidance and basis for subsequent optimization of DSP processes and the production of highly flattened large silicon wafers. Therefore, this invention effectively overcomes the various shortcomings of existing technologies and has high industrial application value.

[0134] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A method for simulating the amount of material removed during double-sided polishing, characterized in that, The method includes: Force analysis is performed on various points on the silicon wafer to obtain the contact pressure at each point. The motion trajectory of each point on the silicon wafer was analyzed, and the movement distance of each point on the silicon wafer in the inner, middle and outer areas of the polishing pad was counted. The amount of material removed from each point on the silicon wafer is calculated based on the movement path of each point on the inner, middle, and outer areas of the polishing pad and the contact pressure at each point on the silicon wafer.

2. The simulation method for double-sided polishing removal amount according to claim 1, characterized in that, The stress analysis at various points on the silicon wafer to obtain the contact pressure at each point includes: Based on solid mechanics finite element simulation, the contact pressure at various points on the silicon wafer is obtained according to the positions of the planetary wheel, upper polishing pad, lower polishing pad, polishing head, and wafer, as well as mechanical parameters. Among them, the mechanical parameters include Young's modulus, Poisson's ratio, and density.

3. The simulation method for double-sided polishing removal amount according to claim 1, characterized in that, The analysis of the motion trajectory of each point on the silicon wafer, and the statistical analysis of the movement distance of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad, include: Based on the operating parameters of the double-sided polishing equipment, the motion trajectory of each point on the silicon wafer on the polishing pad is calculated. Based on the motion trajectory of each point on the silicon wafer, the motion path of each point on the silicon wafer in the inner, middle and outer areas of the polishing pad is calculated.

4. The simulation method for double-sided polishing removal amount according to claim 3, characterized in that, The calculation of the movement path of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad, based on the motion trajectory of each point on the silicon wafer, includes: Extract the motion trajectory of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad, and calculate the travel distance of each point in the inner, middle, and outer areas of the polishing pad.

5. The simulation method for double-sided polishing removal amount according to claim 1, characterized in that, The amount of material removed at each point on the silicon wafer is calculated based on the movement path of each point on the inner, middle, and outer areas of the polishing pad and the contact pressure at each point on the silicon wafer, including: The contact pressure of the silicon wafer in the inner, middle and outer areas of the polishing pad is obtained based on the contact pressure at various points on the silicon wafer. The amount of material removed from each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad is calculated based on the movement path of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad and the contact pressure of the silicon wafer in the inner, middle, and outer areas of the polishing pad. The removal amount at each point on the silicon wafer is calculated from the removal amount at each point in the inner, middle, and outer areas of the polishing pad.

6. The simulation method for double-sided polishing removal amount according to claim 4, characterized in that, The method of obtaining the contact pressure of the silicon wafer in the inner, middle, and outer areas of the polishing pad based on the contact pressure at various points on the silicon wafer includes: The contact pressure at points located in the inner, middle, and outer regions of the polishing pad on the silicon wafer was statistically analyzed, and the corresponding contact pressures of the silicon wafer in the three regions were calculated.

7. The simulation method for double-sided polishing removal amount according to claim 4, characterized in that, The removal amount of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad is calculated based on the movement path of each point on the silicon wafer and the contact pressure of the silicon wafer in the inner, middle, and outer areas of the polishing pad. This includes: Based on the Preston formula, the amount of material removed from each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad is calculated by the movement path of each point on the silicon wafer in the inner, middle, and outer areas of the polishing pad and the contact pressure of the silicon wafer in the inner, middle, and outer areas of the polishing pad. The Preston formula is as follows: MRA = K × P × L; Where MRA is the amount of material removed from a point on the silicon wafer in a region on the polishing pad, P is the contact pressure of the silicon wafer in the corresponding region, L is the travel distance of the point in the corresponding region, and K is an empirical parameter.

8. A simulation control system for double-sided polishing removal amount, characterized in that, The system includes: The stress analysis module is used to perform stress analysis on various points on the silicon wafer to obtain the contact pressure at each point on the silicon wafer. The trajectory analysis and motion path statistics module is used to analyze the motion trajectory of each point on the silicon wafer and to count the motion path of each point on the silicon wafer in the inner, middle and outer areas of the polishing pad. The removal amount calculation module is connected to the force analysis module and the trajectory analysis and motion path statistics module. It is used to calculate the removal amount of each point on the silicon wafer based on the motion path of each point on the inner, middle and outer areas of the polishing pad and the contact pressure of each point on the silicon wafer.

9. An electronic terminal, characterized in that, include: One or more memories and one or more processors; The one or more memories are used to store computer programs; The one or more processors are connected to the memory and are used to run the computer program to perform the method as described in claim 7.

10. A computer-readable storage medium, characterized in that, The device contains a computer program that, when executed by one or more processors, performs the method as described in any one of claims 1 to 7.

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