Method for measuring kerf width of modified layer in chip package invisible cutting

Abstract

This invention relates to a method for calculating the Kerf width of a stealth dicing modification layer in chip packaging, which overcomes the limitation of existing technologies that cannot use simulation software to calculate the Kerf width of the stealth dicing modification layer. The invention includes the following steps: construction of the physical field and mesh generation; improved setting of the heat source equation; formation of the stealth dicing modification layer; and calculation of the Kerf width of the stealth dicing modification layer. Based on the COMSOL multiphysics simulation platform, this invention establishes a multiphysics coupled model and accurately characterizes the thermal and mechanical processes of melting and resolidification in a specified region inside the wafer material under nanosecond laser action during stealth dicing using temperature and stress fields. Based on the derived stress field, the Kerf width of the modification layer under different laser powers, pulse spacings, and doping concentrations is calculated.

Description

Technical Field

[0001] This invention relates to the fields of laser precision machining and semiconductor material simulation technology, specifically a method for calculating the width of the Kerf layer in a chip packaging stealth cutting modification layer. Background Technology

[0002] In integrated circuit chip packaging processes, traditional laser cutting technology has limitations when precision machining brittle materials such as silicon and silicon carbide. Because it relies on a thermal ablation mechanism, laser energy is difficult to precisely control and localize, resulting in a large heat-affected zone. This easily leads to defects such as microcracks and material chipping, severely impacting cutting quality and device mechanical strength. Research shows that in high-precision memory or chiplet chip manufacturing, edge chipping caused by traditional laser cutting can significantly reduce product yield.

[0003] Laser stealth dicing, as a next-generation processing method, uses lasers to form a modified layer within the material to separate silicon wafers. However, while this technology reduces surface damage, it still faces significant challenges. For example, process optimization heavily relies on experimental trial and error. Determining suitable parameters for pure silicon wafers or novel doped silicon wafer materials often requires numerous dicing experiments, consuming wafer material and accelerating equipment wear. The modified layer, acting as a pre-cutting path for material separation, directly determines the crack initiation location, propagation path, and final wafer separation quality. The width of this modified layer is called the Kerf width. However, because the modified layer is located within the material, its Kerf width is difficult to measure in actual experiments.

[0004] Trial and error are costly and time-consuming in process development. Existing simulation methods, by simplifying the complexity of laser-material interactions, are insufficient to fully address the fundamental problem of process parameter optimization.

[0005] Current laser stealth cutting technology has significant shortcomings in multiphysics simulation modeling. Most models remain at the level of two-dimensional or single-pulse approximation, making it difficult to realistically reflect the cumulative effect of multipulses and the interaction between modified layers.

[0006] Especially for pure silicon wafers and P-type silicon wafers with different doping concentrations, existing simulations lack effective approximate three-dimensional models, making it difficult to study the relationship between process parameters of laser stealth dicing equipment and kerf formation and failure, resulting in an inability to accurately predict modification behavior during actual dicing. Existing models struggle to accurately simulate the effects of doping concentration on the optical and thermal properties of materials, as well as the pulse interaction mechanism under three-dimensional multi-timestep conditions. Traditional laser cutting heat source equations are mostly surface heat sources, used for surface ablation or melting drilling of metals or other plastic materials. Furthermore, because such lasers use high power and irradiation area, they often only consider the linear absorption of Gaussian beam energy by the material, neglecting nonlinearity.

[0007] The heat source equations used in current stealth cutting simulations are based on two-dimensional physical field design. Under two-dimensional physical field, it is impossible to measure the width of the three-dimensional modified Kerf layer located in the material, and most of them only perform one pulse, with the heat source in a fixed position. They are used to study the mechanism of stealth cutting rather than to serve actual production. Summary of the Invention

[0008] The purpose of this invention is to address the deficiency in the prior art that the width of the Kerf layer of the stealth dicing modification layer cannot be calculated using simulation software, and to provide a method for calculating the width of the Kerf layer of the stealth dicing modification layer in chip packaging to solve the above problem.

[0009] To achieve the above objectives, the technical solution of the present invention is as follows:

[0010] A method for calculating the Kerf width of a stealth dicing modification layer in chip packaging includes the following steps:

[0011] 11) Construction of physical fields and mesh generation: Construct three-dimensional solid heat transfer and structural mechanics physical fields based on COMSOL, and generate meshes;

[0012] 12) Improve the setting of the heat source equation: Set the single crystal silicon heat source equation or the P-type silicon heat source equation according to the brittle material to be processed.

[0013] 13) Formation of the invisible cutting modification layer: Based on the COMSOL-initiated heat source equation, transient coupling calculation is performed to form the invisible cutting modification layer. The continuity of the invisible cutting modification layer is determined by the stress distribution around the modified region.

[0014] 14) Calculation of Kerf width of the stealth cutting modified layer: Define the Kerf width according to the derived stress field, and repeatedly measure the Kerf width under different process parameters or doping concentrations to obtain the relationship curve between process parameters or doping concentration and Kerf width.

[0015] The construction of the physical field and the generation of the mesh include the following steps:

[0016] 21) Set fixed laser parameters in the COMSOL simulation process. The fixed laser parameters include pulse interval time, laser pulse width, laser radius, laser beam waist radius, laser wavelength, and laser focal depth. Establish a three-dimensional geometric model based on COMSOL and use the three-dimensional geometric model as the calculation area for laser stealth cutting.

[0017] 22) Add a solid heat transfer physics field to the three-dimensional geometric model and set the initial temperature of the model to 293.15°C. ;

[0018] 23) Set a convective heat flux boundary in the solid heat transfer physical field, where the convective heat transfer coefficient is set to 150. The ambient temperature is set to 297.15 degrees Celsius. ;

[0019] 24) Load a bulk heat source into a solid heat transfer physical field to characterize the deposition process of laser energy inside the material;

[0020] 25) Add solid mechanics physical fields to the three-dimensional geometric model and input the elastic parameters, density parameters and thermophysical parameters of the brittle material to be processed;

[0021] 26) Introduce the thermal expansion effect into the physical field of solid mechanics, and set the coefficient of thermal expansion to be... This is to couple the temperature field results to the stress field calculation;

[0022] 27) Couple the physical field of solid heat transfer with the physical field of solid mechanics, and apply a fixed constraint to the bottom of the material to simulate the clamping state of the bottom surface of the substrate during the processing.

[0023] 28) Set the computational domain to be divided into an outer region and an inner region using a free tetrahedral mesh;

[0024] 29) A sparser mesh is used for the outer layer region, with the maximum cell size set to 0.15 mm, the minimum cell size set to 0.028 mm, the maximum cell growth rate set to 1.6, the curvature factor set to 0.7, and the resolution of narrow regions set to 0.4;

[0025] 210) Locally refined meshing is applied to the inner region, with the maximum cell size set to 0.035 mm, the minimum cell size set to 0.0015 mm, the maximum cell growth rate set to 1.35, the curvature factor set to 0.3, and the resolution of narrow regions set to 0.85, thus completing the physical field construction and mesh generation.

[0026] The setting of the improved heat source equation includes the following steps:

[0027] 31) Set the brittle material to be processed as monocrystalline silicon. The material properties of monocrystalline silicon include thermal conductivity, specific heat capacity, material density, coefficient of thermal expansion, Young's modulus and Poisson's ratio. All parameters that change with temperature, stress or wavelength are called by interpolation function.

[0028] 32) Define the heat source equation for monocrystalline silicon.

[0029] 321) Utilizing the propagation of a Gaussian beam in a brittle material, the mathematical equation for the improved Gaussian beam equation is as follows:

[0030] ,

[0031] in, It is the radial distance from the central axis of the beam. For the initial power density, It is along The axial distance of the beam radius is also known as the laser beam waist radius. For the standard focused beam radius, The energy of the laser beam distribution within the material;

[0032] Determine the radial distance from the beam center axis:

[0033] ,

[0034] in, Represents any computational unit within the geometry. Axis coordinates Represents the y-axis coordinate of any computational unit within the geometric body. This represents the y-axis coordinate of the center of the body heat source. Indicates the x-axis coordinate of the center of the body heat source;

[0035] 322) Determine the location of the heat source:

[0036] , , ,

[0037] Where n is the nth pulse time step, and D is the laser pulse spacing. This represents the z-axis coordinate of the center of the volumetric heat source;

[0038] 323) Determine the laser beam waist radius :

[0039] ,

[0040] in, The wavelength of the laser. Let z be the z-axis coordinate of any computational element within the geometric body. Pi;

[0041] 324) Define the portion of the equivalent laser energy that is effectively absorbed by the material, i.e., the equation for the single-crystal silicon heat source is as follows:

[0042] ,

[0043] in, It is to absorb energy. The single-photon absorption coefficient is... The two-photon absorption coefficient is... For free electron cross section, For free hole cross section, The initial carrier density, The initial electron density, The initial hole density;

[0044] By calling the if function statement, the location of the heat source is discrete over time, activating the generalized heat source of the input physical field. ,

[0045] ,

[0046] in, The pulse width. For pulse period, For the nth pulse time step, This is the default time within the software.

[0047] The setting of the improved heat source equation includes the following steps:

[0048] 41) The brittle material to be processed is defined as P-type doped silicon material;

[0049] 42) For P-type doped silicon materials, define the effective single-photon absorption coefficient. and effective two-photon absorption coefficient ,

[0050] ;

[0051] In the formula, The intrinsic absorption coefficient; The free carrier absorption coefficient;

[0052] ;

[0053] In the formula, , , , , , , , These represent electron charge, laser wavelength, doping concentration, light speed, vacuum dielectric constant, refractive index, effective hole mass, and hole mobility, respectively. Pi;

[0054] ;

[0055] In the formula, , These are the intrinsic two-photon absorption coefficient and the laser incident depth, respectively. For free carrier cross-section;

[0056] 43) Define the heat source equation for the p-type doped silicon material:

[0057] 431) Utilizing the propagation of a Gaussian beam in a brittle material, the mathematical equation for the improved Gaussian beam equation is as follows:

[0058] ,

[0059] in, It is the radial distance from the central axis of the beam. For the initial power density, It is along The axial distance of the beam radius is also known as the laser beam waist radius. For the standard focused beam radius, The energy of the laser beam distribution within the material;

[0060] Determine the radial distance from the beam center axis:

[0061] ,

[0062] in, Represents any computational unit within the geometry. Axis coordinates Represents the y-axis coordinate of any computational unit within the geometric body. This represents the y-axis coordinate of the center of the body heat source. Indicates the x-axis coordinate of the center of the body heat source;

[0063] 432) Determine the location of the heat source:

[0064] , , ,

[0065] in, Let D be the time step of the nth pulse, and D be the laser pulse spacing. This represents the z-axis coordinate of the center of the volumetric heat source;

[0066] 433) Determine the laser beam waist radius :

[0067] ,

[0068] in, The wavelength of the laser. Let z be the z-axis coordinate of any computational element within the geometric body. Pi;

[0069] 434) The portion of the equivalent laser energy effectively absorbed by the material, i.e., the equation for the P-type silicon heat source, is as follows:

[0070] ,

[0071] in, It is energy absorption under the influence of doping. For free electron cross section, For free hole cross section, The initial carrier density, The initial electron density, The initial hole density;

[0072] By calling the if function statement, the location of the heat source is discrete over time, activating the generalized heat source of the input physical field. ,

[0073] ,

[0074] in, The pulse width. For pulse period, For the nth pulse time step, This is the default time within the software.

[0075] The formation of the stealth cutting modification layer includes the following steps:

[0076] 51) In COMSOL, input the laser power and laser pulse spacing, and enable the physics field and mesh;

[0077] 52) Configure the transient solver:

[0078] In the transient separable solution process, the maximum number of field separation iterations was set to 10, and Anderson acceleration technology was enabled; the backward difference formula method was selected as the time integration method, and the principal component perturbation parameter was 1×10. -13 The Bunch-Kaufman principal component selection strategy was adopted, and the principal component perturbation parameter was set to 1×10 in the solution settings for the solid mechanics field. -9Meanwhile, the iterative refinement function was enabled, the maximum number of mesh refinements was set to 15, and the error rate range was 0.5; the total transient solution time was set to 2,000,000 ns, and the time step was set to 10 ns, so as to obtain continuous transient temperature field and stress field evolution results throughout the solution process.

[0079] 53) Start model calculation and activate the heat source controlled by the monocrystalline silicon heat source equation or the P-type silicon heat source equation;

[0080] 54) The heat source generates heat at the first point, and the heat generated by the equivalent laser acting in the material;

[0081] 55) When the material melts, its volume changes. The unmelted area undergoes volume change due to thermal expansion. This volume change generates stress, creating a cracked area around the molten area.

[0082] 56) When the laser pulse ends, the heat source stops heating, the material stops melting and solidifies, the crack zone further expands, forming a complete modified zone cavity;

[0083] 57) The heat source moves to the next position, and steps 54)-56) are repeated to generate the next modified zone pores until the modified zone pores are arranged to form an invisible cutting modified layer;

[0084] 58) Extract the numerical stress distribution around the stealth cutting modified layer.

[0085] 1.5 GPa was used as the stress criterion for brittle fracture and crack initiation in monocrystalline silicon. The effectiveness of the generated invisible cutting modification layer was determined by whether the pores in the modified area were connected by cracks. A test point was set in the middle of the pores in the modified area. The test point was set as the judgment point for whether the cracks between multiple pores in the modified area continued to expand and connect with each other.

[0086] When the stress at the test point is less than 1.5 GPa, it is determined that the cracks between adjacent modified zones cannot be effectively connected and cannot form a complete cutting channel.

[0087] When the stress at the test point is greater than or equal to 1.5 GPa, it is determined that the cracks between adjacent modified zones have effectively extended and merged, forming a continuous and effective invisible cutting modified layer.

[0088] The calculation of the width of the stealth cutting modified layer Kerf includes the following steps:

[0089] 61) Regions in the stress field with stress values ​​greater than or equal to 1.5 GPa are identified as crack regions;

[0090] 62) The pore region formed by the central melting and resolidation and the surrounding crack region are jointly determined as the modified layer region, and the outermost boundary of the surrounding crack region is taken as the boundary of the modified layer.

[0091] 63) Calculate the width of Kerf.

[0092] The calculation of the Kerf width includes the following steps:

[0093] 71) For the heat source controlled by the start-up of the heat source equation of monocrystalline silicon, measure the envelope size of the modified layer boundary in the lateral direction, and define the lateral envelope size as the Kerf width under the process parameters.

[0094] 72) Change the average laser power and repeat steps 61) to 62) to obtain the Kerf width corresponding to different laser powers;

[0095] 73) Change the pulse spacing and repeat steps 61) to 62) to obtain the Kerf width corresponding to different pulse spacings;

[0096] 74) Based on the calculation results under different laser powers and different pulse spacings, generate the relationship curve between process parameters and Kerf width.

[0097] The calculation of the Kerf width includes the following steps:

[0098] 81) For the heat source measurement modification layer boundary in the lateral direction of the heat source control for the start-up of the P-type silicon heat source equation, the lateral envelope size is defined as the Kerf width at this doping concentration.

[0099] 82) Change the doping concentration and repeat steps 61) to 62) to obtain the Kerf width corresponding to different doping concentrations;

[0100] 83) Based on the calculation results of different doping concentrations, generate the relationship curve between doping concentration and Kerf width.

[0101] A computer-readable storage medium storing a computer program, which, when executed by a processor, enables a method for calculating the width of a Kerf layer in a chip package.

[0102] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When executed by the processor, the program enables a method for calculating the width of a Kerf layer in a chip package.

[0103] Beneficial effects

[0104] This invention provides a method for calculating the Kerf width of a modified layer in a chip package during stealth dicing. Compared with existing technologies, this method is based on the COMSOL multiphysics simulation platform. By establishing a multiphysics coupled model, it accurately characterizes the thermal and mechanical processes of melting and resolidification in a specified region inside the wafer material under the action of a nanosecond laser during stealth dicing using temperature and stress fields. Based on the derived stress field, it realizes the calculation of the Kerf width of the modified layer under different laser powers, pulse spacings, and doping concentrations.

[0105] This invention simulates multiple modified layer pores generated by laser translation over a period of time by activating heat sources one by one using an if function. This can be used in actual production to measure the residual stress field around the three-dimensional modified layer and predict the Kerf width of the material after stealth cutting. Using this method, and based on this, the feasible window for predicting power and pulse spacing is determined using the stress at test points between pores and the Kerf width as evaluation indicators. The influence of pulse spacing, power, and cutting depth on the predictable chipping width is also presented, and the optimal parameters obtained are used in the following research.

[0106] Simultaneously, an improved laser energy absorption model incorporating the influence of doping concentration is constructed (corresponding single-photon / two-photon and free carrier absorption to physical quantities such as doping concentration) to explore the effect of doping concentration on the stealth dicing of P-type doped silicon, thereby reducing the number of experiments, lowering costs, and outputting the optimal combination of dicing parameters for different doped materials. Attached Figure Description

[0107] Figure 1 This is a sequence diagram of the method of the present invention;

[0108] Figure 2 This refers to the physical field constructed using COMSOL as described in this invention;

[0109] Figure 3 This is a schematic diagram of the modified layer cutting channel formation process involved in the present invention;

[0110] Figure 4 This is a schematic diagram showing the interconnection conditions and test points of the multiple modified pores involved in this invention;

[0111] Figure 5 This is a schematic diagram illustrating the formation of multiple modified layer pores and the Kerf width involved in this invention;

[0112] Figure 6 This is a graph showing the relationship between power and Kerf width under different pulse intervals involved in this invention.

[0113] Figure 7 This is a graph showing the relationship between power and Kerf width under different doping concentrations involved in this invention. Detailed Implementation

[0114] To provide a better understanding of the structural features and effects achieved by the present invention, a detailed description is provided below, accompanied by preferred embodiments and accompanying drawings:

[0115] like Figure 1 As shown, the method for calculating the Kerf width of the stealth dicing modification layer in chip packaging according to the present invention includes the following steps:

[0116] The first step is to construct the physical field and divide the mesh: such as Figure 2 As shown, a three-dimensional solid heat transfer and structural mechanics physical field is constructed based on COMSOL, and a mesh is generated.

[0117] (1) Set fixed laser parameters in the COMSOL simulation process. The fixed laser parameters include pulse interval time, laser pulse width, laser radius, laser beam waist radius, laser wavelength and laser focal depth; establish a three-dimensional geometric model based on COMSOL and use the three-dimensional geometric model as the calculation area for laser stealth cutting;

[0118] (2) Add a solid heat transfer physical field to the three-dimensional geometric model and set the initial temperature of the model to 293.15°C. ;

[0119] (3) Set up a convective heat flux boundary in the solid heat transfer physical field, where the convective heat transfer coefficient is set to 150. The ambient temperature is set to 297.15 degrees Celsius. ;

[0120] (4) Load a bulk heat source in the solid heat transfer physical field to characterize the deposition process of laser energy inside the material;

[0121] (5) Add solid mechanical physical fields to the three-dimensional geometric model and input the elastic parameters, density parameters and thermal properties of the brittle material to be processed;

[0122] (6) Introduce the thermal expansion effect into the physical field of solid mechanics, and set the coefficient of thermal expansion to be... This is to couple the temperature field results to the stress field calculation;

[0123] (7) Couple the solid heat transfer physical field with the solid mechanical physical field and apply a fixed constraint to the bottom of the material to simulate the clamping state of the bottom surface of the substrate during the processing;

[0124] (8) Set the computational domain to be divided into an outer region and an inner region using a free tetrahedral mesh;

[0125] (9) A sparser grid is used for the outer layer area, with the maximum unit size set to 0.15 mm, the minimum unit size set to 0.028 mm, the maximum unit growth rate set to 1.6, the curvature factor set to 0.7, and the resolution of narrow areas set to 0.4.

[0126] (10) The inner region is locally densified into a mesh, with the maximum unit size set to 0.035 mm, the minimum unit size set to 0.0015 mm, the maximum unit growth rate set to 1.35, the curvature factor set to 0.3, and the resolution of the narrow region set to 0.85. The physical field construction and mesh generation are completed.

[0127] The second step is to improve the setting of the heat source equation: set the single-crystal silicon heat source equation or the P-type silicon heat source equation according to the brittle material to be processed.

[0128] Stealth dicing, as a short-pulse, low-power, small-area discontinuous dicing process, cannot ignore its nonlinear absorption. Furthermore, since it occurs within the material, a bulk heat source is required for heat exchange, and this heat source needs to rapidly dissipate and become effective within a short time. Therefore, after improving the Gaussian beam equation, a nonlinear absorption equation needs to be applied. Simultaneously, the influence of doping concentration must be simulated, and some coefficients in the absorption equation change with doping concentration. Therefore, for doped silicon (P-type silicon), these coefficients also need to be corrected.

[0129] As a first embodiment of the present invention:

[0130] When the brittle material to be processed is set to monocrystalline silicon, the material properties of monocrystalline silicon include thermal conductivity, specific heat capacity, material density, coefficient of thermal expansion, Young's modulus, and Poisson's ratio. All parameters that change with temperature, stress, or wavelength are called using interpolation functions.

[0131] Define the heat source equation for monocrystalline silicon.

[0132] (1) The mathematical equation of the Gaussian beam propagation in brittle materials is as follows:

[0133] ,

[0134] in, It is the radial distance from the central axis of the beam. For the initial power density, It is along The axial distance of the beam radius is also known as the laser beam waist radius. For the standard focused beam radius, The energy of the laser beam distribution within the material;

[0135] Determine the radial distance from the beam center axis:

[0136] ,

[0137] in, Represents any computational unit within the geometry. Axis coordinates Represents the y-axis coordinate of any computational unit within the geometric body. This represents the y-axis coordinate of the center of the body heat source. This represents the x-axis coordinate of the center of the heat source.

[0138] (2) Determine the location of the heat source:

[0139] , , ,

[0140] Where n is the nth pulse time step, and D is the laser pulse spacing. This represents the z-axis coordinate of the center of the heat source.

[0141] (3) Determine the laser beam waist radius :

[0142] ,

[0143] in, The wavelength of the laser. Let z be the z-axis coordinate of any computational element within the geometric body. Pi is the mathematical constant of a circle.

[0144] (4) The portion of the equivalent laser energy effectively absorbed by the material is defined as follows, i.e., the single-crystal silicon heat source equation:

[0145] ,

[0146] in, It is to absorb energy. The single-photon absorption coefficient is... The two-photon absorption coefficient is... For free electron cross section, For free hole cross section, The initial carrier density, The initial electron density, This represents the initial hole density.

[0147] By calling the if function statement, the location of the heat source is discrete over time, activating the generalized heat source of the input physical field. ,

[0148] ,

[0149] in, The pulse width. For pulse period, For the nth pulse time step, This is the default time within the software (no need to define it).

[0150] As a second embodiment of the present invention:

[0151] (1) When the brittle material to be processed is a P-type doped silicon material, the effective single-photon absorption coefficient is set for the P-type doped silicon material. and effective two-photon absorption coefficient ,

[0152] (2) Define the heat source equation for the P-type doped silicon material:

[0153] B1) Utilizing the propagation of a Gaussian beam in a brittle material, the mathematical equation for the Gaussian beam is as follows:

[0154] ,

[0155] in, It is the radial distance from the central axis of the beam. For the initial power density, It is along The axial distance of the beam radius is also known as the laser beam waist radius. For the standard focused beam radius, The energy of the laser beam distribution within the material;

[0156] Determine the radial distance from the beam center axis:

[0157] ,

[0158] in, Represents any computational unit within the geometry. Axis coordinates Represents the y-axis coordinate of any computational unit within the geometric body. This represents the y-axis coordinate of the center of the body heat source. Indicates the x-axis coordinate of the center of the body heat source;

[0159] B2) Determine the location of the heat source:

[0160] , , ,

[0161] Where n is the nth pulse time step, and D is the laser pulse spacing. This represents the z-axis coordinate of the center of the volumetric heat source;

[0162] B3) Determine the laser beam waist radius :

[0163] ,

[0164] in, The wavelength of the laser. Let z be the z-axis coordinate of any computational element within the geometric body. Pi;

[0165] B4) The portion of the equivalent laser energy effectively absorbed by the material, i.e., the equation for the P-type silicon thermal source, is as follows:

[0166] ,

[0167] in, It is energy absorption under the influence of doping. For free electron cross section, For free hole cross section, The initial carrier density, The initial electron density, This represents the initial hole density.

[0168] By calling the if function statement, the location of the heat source is discrete over time, activating the generalized heat source of the input physical field. ,

[0169] ,

[0170] in, The pulse width. For pulse period, For the nth pulse time step, This is the default time within the software (no need to define it).

[0171] The third step is the formation of the invisible cutting modification layer: such as... Figure 3 As shown, transient coupling calculations are performed based on the COMSOL-initiated heat source equation to form an invisible cutting modification layer. The continuity of the invisible cutting modification layer is determined by the stress distribution around the modified region.

[0172] (1) In COMSOL, input the laser power and laser pulse spacing, and enable the physics field and mesh.

[0173] (2) Configure the transient solver:

[0174] In the transient separable solution process, the maximum number of field separation iterations was set to 10, and Anderson acceleration technology was enabled; the backward difference formula method was selected as the time integration method, and the principal component perturbation parameter was 1×10. -13The Bunch-Kaufman principal component selection strategy was adopted, and the principal component perturbation parameter was set to 1×10 in the solution settings for the solid mechanics field. -9 Meanwhile, the iterative refinement function is enabled, the maximum number of mesh refinements is set to 15, and the error rate range is 0.5; the total transient solution time is set to 2,000,000 ns, and the time step is set to 10 ns, so as to obtain continuous transient temperature field and stress field evolution results throughout the solution process.

[0175] (3) Start the model calculation and start the heat source controlled by the monocrystalline silicon heat source equation or the P-type silicon heat source equation.

[0176] (4) The heat source generates heat at the first point, and the heat generated by the equivalent laser in the material.

[0177] (5) The material melts and its volume changes. The unmelted area undergoes volume change due to thermal expansion. The volume change generates stress, which creates a cracked area around the molten area.

[0178] (6) When the laser pulse ends, the heat source stops heating, the material stops melting and solidifies, the crack zone further expands, forming a complete modified zone cavity, such as Figure 4 As shown.

[0179] (7) The heat source moves to the next position and repeats steps (4)-(6) to generate the next modified zone hole until the modified zone holes are arranged to form an invisible cutting modified layer;

[0180] (8) Extract the stress distribution around the outer edge of the invisible cutting modified layer.

[0181] 1.5 GPa was used as the stress criterion for brittle fracture and crack initiation in monocrystalline silicon. The effectiveness of the generated invisible cutting modification layer was determined by whether the pores in the modified area were connected by cracks. A test point was set in the middle of the pores in the modified area. The test point was set as the judgment point for whether the cracks between multiple pores in the modified area continued to expand and connect with each other.

[0182] When the stress at the test point is less than 1.5 GPa, it is determined that the cracks between adjacent modified zones cannot be effectively connected and cannot form a complete cutting channel.

[0183] When the stress at the test point is greater than or equal to 1.5 GPa, it is determined that the cracks between adjacent modified zones have effectively extended and merged, forming a continuous and effective invisible cutting modified layer.

[0184] The fourth step is to calculate the width of the Kerf layer of the stealth cutting modification layer: the Kerf width is defined according to the derived stress field, and the Kerf width is repeatedly measured under different process parameters or doping concentrations to obtain the relationship curve between process parameters or doping concentration and Kerf width.

[0185] (1) Regions with stress values ​​greater than or equal to 1.5 GPa in the stress field are identified as cracked regions, and regions with stress values ​​less than 1.5 GPa in the stress field are identified as non-cracked regions.

[0186] (2) The pore region formed by the central melting and resolidation and the surrounding crack region are jointly determined as the modified layer region, and the outermost boundary of the surrounding crack region is taken as the boundary of the modified layer.

[0187] In the first embodiment of the present invention, when the brittle material to be processed is monocrystalline silicon, the step of calculating the Kerf width is as follows:

[0188] C1) For the heat source controlled by the start-up of the monocrystalline silicon heat source equation, measure the envelope size of the modified layer boundary in the lateral direction, and define the lateral envelope size as the Kerf width under the given process parameters, such as... Figure 5 As shown;

[0189] C2) Change the average laser power and repeat steps (1) to (2) to obtain the Kerf width corresponding to different laser powers;

[0190] C3) Change the pulse spacing and repeat steps (1) to (2) to obtain the Kerf width corresponding to different pulse spacings;

[0191] C4) Based on the calculation results under different laser powers and pulse intervals, generate the relationship curve between process parameters and Kerf width, such as... Figure 6 As shown.

[0192] In the second embodiment of the present invention, when the brittle material to be processed is P-type doped silicon, the step of calculating the Kerf width is as follows:

[0193] D1) For the heat source controlled by the start-up of the P-type silicon heat source equation, measure the envelope size of the modified layer boundary in the lateral direction, and define the lateral envelope size as the Kerf width at this doping concentration.

[0194] D2) Change the doping concentration and repeat steps (1) to (2) to obtain the Kerf width corresponding to different doping concentrations;

[0195] D3) Based on the calculation results for different doping concentrations, generate a curve showing the relationship between doping concentration and Kerf width, such as... Figure 7 As shown.

[0196] In summary, this invention simulates the laser heat source effect during stealth cutting by considering the phase transition of materials, the thermal radiation of the material surface, and the influence of natural convection on the temperature field through a Gaussian heat source and laser energy absorption model. Furthermore, after activating the heat source, a structural mechanics module is used to simulate the thermal stress and material deformation generated in the layer as the heat source changes, simulating the manufacturing process of the modified layer in the pre-selected area stealth cutting technology. The melting zone and crack zone are observed in the temperature and stress fields respectively, and the simulation records the changing trend of the modified zone structure, summarizing its evolution process and the influence of laser power on a single modified zone. By activating the heat source sequentially, the prediction of thermal stress and residual thermal stress under multi-time-step pulses, as well as the influence of the laser effect in later time steps on earlier time steps, is achieved. Multiple modified layer pores generated by laser translation over a period of time are simulated, and the influence of experimental parameters on the measurable Kerf width of the modified layer is studied. As the laser pulse energy gradually increases, the Kerf width generated during laser cutting also gradually widens. As the laser pulse spacing gradually decreases, the Kerf width formed during laser processing gradually widens. Ultimately, a relatively ideal modified layer can be obtained with a power of 3.5W when the laser pulse spacing is 40μm. By establishing a three-dimensionally movable laser-induced Gaussian heat source equation and using spatial / temporal window if-gating to achieve pulse-by-pulse activation, the simulation can realistically reproduce the cumulative process of forming multiple modified region holes and their interconnection into a complete cleavage path within a silicon wafer using multiple time-step, multi-pulse methods. By utilizing the simulation results of stress at test points between holes and Kerf width, the laser power and pulse spacing parameter window required to form a complete cleavage path can be predicted, significantly reducing the need for numerous trial experiments and saving experimental costs. At the same time, the variation of Kerf width with pulse energy and pulse spacing can be calculated, providing a reference for ideal modified layer parameters. Introducing the influence of doping concentration on P-type silicon allows for reliable prediction of Kerf width and power compensation direction under different doping concentrations. This provides a basis for the optimal parameter combination output of stealth cutting processes under different material conditions, improving cutting stability and crack guidance consistency.

[0197] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A method for calculating the width of the Kerf layer in a chip package stealth dicing modification layer, characterized in that, Includes the following steps: 11) Construction of physical fields and mesh generation: Construct three-dimensional solid heat transfer and structural mechanics physical fields based on COMSOL, and generate meshes; 12) Improve the setting of the heat source equation: Set the single crystal silicon heat source equation or the P-type silicon heat source equation according to the brittle material to be processed. 13) Formation of the invisible cutting modification layer: Based on the COMSOL-initiated heat source equation, transient coupling calculation is performed to form the invisible cutting modification layer. The continuity of the invisible cutting modification layer is determined by the stress distribution around the modified region. 14) Calculation of Kerf width of the stealth cutting modified layer: Define the Kerf width according to the derived stress field, and repeatedly measure the Kerf width under different process parameters or doping concentrations to obtain the relationship curve between process parameters or doping concentration and Kerf width.

2. The method for calculating the Kerf width of the stealth dicing modification layer in chip packaging according to claim 1, characterized in that, The construction of the physical field and the generation of the mesh include the following steps: 21) Set fixed laser parameters in the COMSOL simulation process. The fixed laser parameters include pulse interval time, laser pulse width, laser radius, laser beam waist radius, laser wavelength, and laser focal depth. Establish a three-dimensional geometric model based on COMSOL and use the three-dimensional geometric model as the calculation area for laser stealth cutting. 22) Add a solid heat transfer physics field to the three-dimensional geometric model and set the initial temperature of the model to 293.15°C. ; 23) Set a convective heat flux boundary in the solid heat transfer physical field, where the convective heat transfer coefficient is set to 150. The ambient temperature is set to 297.15 degrees Celsius. ; 24) Load a bulk heat source into a solid heat transfer physical field to characterize the deposition process of laser energy inside the material; 25) Add solid mechanics physical fields to the three-dimensional geometric model and input the elastic parameters, density parameters and thermophysical parameters of the brittle material to be processed; 26) Introduce the thermal expansion effect into the physical field of solid mechanics, and set the coefficient of thermal expansion to be... This is to couple the temperature field results to the stress field calculation; 27) Couple the physical field of solid heat transfer with the physical field of solid mechanics, and apply a fixed constraint to the bottom of the material to simulate the clamping state of the bottom surface of the substrate during the processing. 28) Set the computational domain to be divided into an outer region and an inner region using a free tetrahedral mesh; 29) A sparser mesh is used for the outer layer region, with the maximum cell size set to 0.15 mm, the minimum cell size set to 0.028 mm, the maximum cell growth rate set to 1.6, the curvature factor set to 0.7, and the resolution of narrow regions set to 0.4; 210) Locally refined meshing is applied to the inner region, with the maximum cell size set to 0.035 mm, the minimum cell size set to 0.0015 mm, the maximum cell growth rate set to 1.35, the curvature factor set to 0.3, and the resolution of narrow regions set to 0.85, thus completing the physical field construction and mesh generation.

3. The method for calculating the Kerf width of the stealth dicing modification layer in chip packaging according to claim 1, characterized in that, The setting of the improved heat source equation includes the following steps: 31) Set the brittle material to be processed as monocrystalline silicon. The material properties of monocrystalline silicon include thermal conductivity, specific heat capacity, material density, coefficient of thermal expansion, Young's modulus and Poisson's ratio. All parameters that change with temperature, stress or wavelength are called by interpolation function. 32) Define the heat source equation for monocrystalline silicon. 321) Utilizing the propagation of a Gaussian beam in a brittle material, the mathematical equation for the improved Gaussian beam equation is as follows: ， in, It is the radial distance from the central axis of the beam. For the initial power density, It is along The axial distance of the beam radius is also known as the laser beam waist radius. For the standard focused beam radius, The energy of the laser beam distribution within the material; Determine the radial distance from the beam center axis: ， in, Represents any computational unit within the geometry. Axis coordinates This represents the y-axis coordinate of any computational unit within the geometric body. This represents the y-axis coordinate of the center of the body heat source. Indicates the x-axis coordinate of the center of the body heat source; 322) Determine the location of the heat source: ， ， ， Where n is the nth pulse time step, and D is the laser pulse spacing. This represents the z-axis coordinate of the center of the volumetric heat source; 323) Determine the laser beam waist radius : ， in, The wavelength of the laser. Let z be the z-axis coordinate of any computational element within the geometric body. Pi; 324) Define the portion of the equivalent laser energy that is effectively absorbed by the material, i.e., the equation for the single-crystal silicon heat source is as follows: ， in, It is to absorb energy. The single-photon absorption coefficient is... The two-photon absorption coefficient is... For free electron cross section, For free hole cross section, The initial carrier density, The initial electron density, The initial hole density; By calling the if function statement, the location of the heat source is discrete over time, activating the generalized heat source of the input physical field. , ， in, The pulse width. For pulse period, For the nth pulse time step, This is the default time within the software.

4. The method for calculating the Kerf width of the stealth dicing modification layer in chip packaging according to claim 1, characterized in that, The setting of the improved heat source equation includes the following steps: 41) The brittle material to be processed is defined as a P-type doped silicon material; 42) For P-type doped silicon materials, define the effective single-photon absorption coefficient. and effective two-photon absorption coefficient , ； In the formula, The intrinsic absorption coefficient; The free carrier absorption coefficient; ； In the formula, , , , , , , , These represent electron charge, laser wavelength, doping concentration, light speed, vacuum dielectric constant, refractive index, effective hole mass, and hole mobility, respectively. Pi; ； In the formula, , These are the intrinsic two-photon absorption coefficient and the laser incident depth, respectively. For free carrier cross-section; 43) Define the heat source equation for the p-type doped silicon material: 431) Utilizing the propagation of a Gaussian beam in a brittle material, the mathematical equation for the improved Gaussian beam equation is as follows: ， in, It is the radial distance from the central axis of the beam. For the initial power density, It is along The axial distance of the beam radius is also known as the laser beam waist radius. For the standard focused beam radius, The energy of the laser beam distribution within the material; Determine the radial distance from the beam center axis: ， in, Represents any computational unit within the geometry. Axis coordinates This represents the y-axis coordinate of any computational unit within the geometric body. This represents the y-axis coordinate of the center of the body heat source. Indicates the x-axis coordinate of the center of the body heat source; 432) Determine the location of the heat source: ， ， ， in, Let D be the time step of the nth pulse, and D be the laser pulse spacing. This represents the z-axis coordinate of the center of the volumetric heat source; 433) Determine the laser beam waist radius : ， in, The wavelength of the laser. Let z be the z-axis coordinate of any computational element within the geometric body. Pi; 434) The portion of the equivalent laser energy effectively absorbed by the material, i.e., the equation for the P-type silicon heat source, is as follows: ， in, It is energy absorption under the influence of doping. For free electron cross section, For free hole cross section, The initial carrier density, The initial electron density, The initial hole density; By calling the if function statement, the location of the heat source is discrete over time, activating the generalized heat source of the input physical field. , ， in, The pulse width. For pulse period, For the nth pulse time step, This is the default time within the software.

5. The method for calculating the Kerf width of the stealth dicing modification layer in chip packaging according to claim 1, characterized in that, The formation of the stealth cutting modification layer includes the following steps: 51) In COMSOL, input the laser power and laser pulse spacing, and enable the physics field and mesh; 52) Configure the transient solver: In the transient separable solution process, the maximum number of field separation iterations was set to 10, and Anderson acceleration technology was enabled; the backward difference formula method was selected as the time integration method, and the principal component perturbation parameter was 1×10. -13 The Bunch-Kaufman principal component selection strategy was adopted, and the principal component perturbation parameter was set to 1×10 in the solution settings for the solid mechanics field. -9 Meanwhile, the iterative refinement function was enabled, the maximum number of mesh refinements was set to 15, and the error rate range was 0.5; the total transient solution time was set to 2,000,000 ns, and the time step was set to 10 ns, so as to obtain continuous transient temperature field and stress field evolution results throughout the solution process. 53) Start model calculation and activate the heat source controlled by the monocrystalline silicon heat source equation or the P-type silicon heat source equation; 54) The heat source generates heat at the first point, and the heat generated by the equivalent laser acting in the material; 55) When the material melts, its volume changes. The unmelted area undergoes volume change due to thermal expansion. This volume change generates stress, creating a cracked area around the molten area. 56) When the laser pulse ends, the heat source stops heating, the material stops melting and solidifies, the crack zone further expands, forming a complete modified zone cavity; 57) The heat source moves to the next position, and steps 54)-56) are repeated to generate the next modified zone pores until the modified zone pores are arranged to form an invisible cutting modified layer; 58) Extract the numerical stress distribution around the stealth cutting modified layer. 1.5 GPa was used as the stress criterion for brittle fracture and crack initiation in monocrystalline silicon. The effectiveness of the generated invisible cutting modification layer was determined by whether the pores in the modified area were connected by cracks. A test point was set in the middle of the pores in the modified area. The test point was set as the judgment point for whether the cracks between multiple pores in the modified area continued to expand and connect with each other. When the stress at the test point is less than 1.5 GPa, it is determined that the cracks between adjacent modified zones cannot be effectively connected and cannot form a complete cutting channel. When the stress at the test point is greater than or equal to 1.5 GPa, it is determined that the cracks between adjacent modified zones have effectively extended and merged, forming a continuous and effective invisible cutting modified layer.

6. The method for calculating the Kerf width of the stealth dicing modification layer in chip packaging according to claim 1, characterized in that, The calculation of the width of the stealth cutting modified layer Kerf includes the following steps: 61) Regions in the stress field with stress values ​​greater than or equal to 1.5 GPa are identified as crack regions; 62) The pore region formed by the central melting and resolidation and the surrounding crack region are jointly determined as the modified layer region, and the outermost boundary of the surrounding crack region is taken as the boundary of the modified layer. 63) Calculate the width of Kerf.

7. The method for calculating the Kerf width of the stealth dicing modification layer in chip packaging according to claim 6, characterized in that, The calculation of the Kerf width includes the following steps: 71) For the heat source controlled by the start-up of the heat source equation of monocrystalline silicon, measure the envelope size of the modified layer boundary in the lateral direction, and define the lateral envelope size as the Kerf width under the process parameters. 72) Change the average laser power and repeat steps 61) to 62) to obtain the Kerf width corresponding to different laser powers; 73) Change the pulse spacing and repeat steps 61) to 62) to obtain the Kerf width corresponding to different pulse spacings; 74) Based on the calculation results under different laser powers and different pulse spacings, generate the relationship curve between process parameters and Kerf width.

8. The method for calculating the Kerf width of the stealth dicing modification layer in chip packaging according to claim 6, characterized in that, The calculation of the Kerf width includes the following steps: 81) For the heat source measurement modification layer boundary in the lateral direction for the start-up control of the P-type silicon heat source equation, the lateral envelope size is defined as the Kerf width at this doping concentration. 82) Change the doping concentration and repeat steps 61) to 62) to obtain the Kerf width corresponding to different doping concentrations; 83) Based on the calculation results of different doping concentrations, generate the relationship curve between doping concentration and Kerf width.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, enables the implementation of the method for calculating the width of the Kerf layer in a chip package as described in any one of claims 1-8.

10. A computer device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it can implement the method for calculating the width of the Kerf layer in a chip package as described in any one of claims 1-8.

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