Cross-scale coupling method for residual stress and corrosion damage in semiconductor devices

Abstract

The application discloses a kind of semiconductor device residual stress and corrosion damage cross-scale coupling method, including the following steps: semiconductor device is carried out multi-scale experiment, obtains the database including residual stress, corrosion rate and crack propagation rate;The quantitative analysis is carried out to the database obtained, and the damage evolution equation including residual stress and corrosion rate relationship and residual stress and crack propagation rate relationship is constructed;Microscopic corrosion damage variable is obtained based on semiconductor production related theoretical knowledge and introduced into damage evolution equation, and then the cross-scale correlation model for simulation is constructed;The cross-scale correlation model is verified based on the obtained database.The beneficial effects of the application: by establishing the cross-scale failure evolution process between residual stress and corrosion rate and crack propagation rate, the stress corrosion damage evolution mechanism is revealed systematically, and it has important theoretical and practical significance for improving the use reliability and stability of semiconductor device.

Description

Technical Field

[0001] The present application relates to the field of semiconductor technology, and in particular to a cross-scale coupling method for residual stress and corrosion damage in semiconductor devices. Background Art

[0002] Semiconductor photodetectors, key devices for converting optical and electrical signals, play an indispensable role in many fields, including modern optical communications, optical sensing, defense and military, and biomedicine. However, during their manufacturing process, residual stress inevitably builds up within the device due to material processing and heat treatment. Furthermore, in actual service environments, detectors are also subject to various corrosive media. The synergistic effect of residual stress and corrosive media can easily lead to stress corrosion damage, severely impacting the detector's performance and service life. Therefore, in-depth research on the cross-scale coupling mechanism of residual stress and stress corrosion damage in semiconductors is of great theoretical and practical significance for improving the reliability and stability of detectors. Summary of the Invention

[0003] One of the objectives of the present application is to provide a cross-scale coupling method for residual stress and corrosion damage in semiconductor devices that can solve at least one of the defects in the above-mentioned background technology.

[0004] To achieve at least one of the above objectives, the technical solution adopted in this application is: a cross-scale coupling method for residual stress and corrosion damage in semiconductor devices, comprising the following steps:

[0005] S100: Conduct multi-scale experiments on semiconductor devices to obtain a database including residual stress, corrosion rate, and crack growth rate;

[0006] S200: Quantitatively analyze the obtained database and construct damage evolution equations including the relationship between residual stress and corrosion rate and the relationship between residual stress and crack growth rate;

[0007] S300: Based on theoretical knowledge related to semiconductor manufacturing, microscopic corrosion damage variables are obtained and damage evolution equations are introduced to construct a cross-scale correlation model for simulation;

[0008] S400: Validating the cross-scale association model based on the database obtained in step S100.

[0009] Preferably, the construction of the relationship between residual stress and corrosion rate includes the following process: based on the principles of corrosion electrochemistry and mechanics, determining the correlation between the corrosion rate v and the strain energy release rate G under stress; and establishing a relationship equation between residual stress and corrosion rate v through the law of conservation of energy.

[0010] Preferably, the relationship between residual stress and corrosion rate v is expressed as follows:

[0011] ;

[0012] where A represents the area of the region involved in crack propagation, E represents the elastic modulus, and represents the normal stress in the two-dimensional plane, represents the shear stress in the two-dimensional plane, and μ represents the Poisson's ratio, a represents the crack propagation length, and b represents the crack width.

[0013] Preferably, the derivation process of the strain energy release rate G is as follows:

[0014] The residual stress components in the two-dimensional plane are determined, including the normal stress and , and the shear stress ;

[0015] The corresponding strain components and , and the shear strain are calculated based on the obtained residual stress components;

[0016] The specific expression is: , , ;

[0017] The strain energy density u(x, y) in the plane stress state is calculated;

[0018] The specific expression is:

[0019] ;

[0020] The strain energy release rate in the crack propagation area is calculated; ;

[0021] where the strain energy ; .

[0022] Preferably, the construction of the relationship between the residual stress and the crack propagation rate includes the following processes: combining the stress corrosion empirical model, introducing the residual stress factor to modify the stress intensity factor; based on the modified stress intensity factor, the relationship equation between the crack propagation rate and the residual stress is constructed.

[0023] Preferably, the establishment of the equation of the relationship between the residual stress and the crack propagation rate comprises the following processes: based on the empirical model of stress corrosion, a Paris formula of the crack propagation rate with respect to the stress intensity factor is constructed; the residual stress is introduced to establish a relationship between the residual stress and the stress intensity factor; the relationship between the residual stress and the stress intensity factor is substituted into the Paris formula of the crack propagation rate to obtain the equation of the relationship between the crack propagation rate and the residual stress.

[0024] Preferably, the crack propagation rate da / dN and the residual stress The expression of the equation of the relationship under the Paris formula is as follows:

[0025] ;

[0026] wherein C, n and m all represent constants related to the material, represents the stress intensity factor without the residual stress.

[0027] Preferably, in the step S300, the expression of the damage evolution equation of the micro-corrosion damage variable D is as follows:

[0028] ;

[0029] wherein dD / dt represents the change rate of the micro-corrosion damage variable D, k1 and k2 both represent constants related to the material characteristics, and v represents the corrosion rate, represents the residual stress.

[0030] Preferably, when the semiconductor evolves from the micro-corrosion damage to the macro-crack, the micro-corrosion damage variable D reaches a critical value D c ; at this time, the expression of the damage evolution equation is as follows:

[0031] da / dt=k3(D-D c )×da / dN;

[0032] wherein da / dt and da / dN both represent the crack propagation rate, and k3 represents a constant related to the material characteristics.

[0033] Preferably, the step S400 comprises the following processes:

[0034] Different semiconductor materials are selected to perform the residual stress measurement experiment, the corrosion rate test experiment and the crack propagation rate monitoring experiment, and the experimental parameters and the corresponding results are recorded;

[0035] The experimental parameters are substituted into the cross-scale correlation model to output the results;

[0036] Compare the experimental results with the results output by the model; if the error between the two is within the set threshold range, it is determined that the cross-scale correlation model meets the accuracy requirement, otherwise the cross-scale correlation model is optimized based on the experimental results.

[0037] Compared with the prior art, the application has the beneficial effects that:

[0038] By establishing the quantitative relationship between residual stress and corrosion rate and crack propagation rate, introducing a corrosion damage variable to quantify the cross-scale failure evolution process from the accumulation of micro corrosion damage to the macro crack propagation under the influence of residual stress, and systematically revealing the stress corrosion damage evolution mechanism, the application has important theoretical and practical significance for improving the use reliability and stability of semiconductor devices. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 The step flowchart of the application.

[0040] Figure 2 The error diagram of the experimental data and the theoretical data of the corrosion rate in the application.

[0041] Figure 3 The error diagram of the experimental data and the theoretical data of the crack propagation rate in the application. DETAILED DESCRIPTION

[0042] In the following, the application will be further described in conjunction with specific embodiments, and it should be noted that in the description of the present application, the description of the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the application. In the present application, the illustrative description of the above terms should not be understood as necessarily referring to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the present application.

[0043] In the description of the application, it should be noted that for the orientation words, such as the terms "center", "transverse", "longitudinal", "length", "width", "thickness", "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc. indicate the orientation and positional relationship based on the orientation or positional relationship shown in the drawings, which is only for the convenience of describing the application and simplifying the description, and does not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and cannot be understood as limiting the specific protection scope of the application.

[0044] It should be noted that the terms "first", "second" and the like in the specification and claims of the application are used to distinguish similar objects, and do not necessarily have to describe a specific order or chronological order.

[0045] In the present application, unless otherwise expressly specified and limited, the terms "mounting", "connecting", "connecting", "fixing" and the like should be understood broadly, for example, it can be connected, or it can be detachable, or it can be integrated; it can be mechanical connection, or it can be electrical connection; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0046] In the present application, unless otherwise expressly specified and limited, the first feature "on" or "under" the second feature can include that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, the first feature "on", "above" and "above" the second feature includes that the first feature is directly above and obliquely above the second feature, or only indicates that the horizontal height of the first feature is higher than that of the second feature. The first feature "below", "below" and "below" the second feature includes that the first feature is directly below and obliquely below the second feature, or only indicates that the horizontal height of the first feature is less than that of the second feature.

[0047] The terms "include" and "have" in the specification and claims of the application, as well as any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device containing a series of steps or units does not have to be limited to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0048] One of the preferred embodiments of the present application is as follows: Figure 1As shown, a cross-scale coupling method for residual stress and corrosion damage in semiconductor devices includes the following steps:

[0049] S100: Conduct multi-scale experiments on semiconductor devices to obtain a database including residual stress, corrosion rate, and crack growth rate.

[0050] S200: Quantitatively analyze the obtained database and construct a damage evolution equation including the relationship between residual stress and corrosion rate and the relationship between residual stress and crack growth rate.

[0051] S300: Based on theoretical knowledge related to semiconductor manufacturing, microscopic corrosion damage variables are obtained and damage evolution equations are introduced to construct a cross-scale correlation model for simulation.

[0052] S400: Validating the cross-scale association model based on the database obtained in step S100.

[0053] It should be noted that residual stress primarily originates from material processing, such as doping, annealing, and thin-film deposition, which can lead to internal stress in the material. Stress corrosion damage, on the other hand, refers to cracks and damage in materials caused by the combined effects of stress and a corrosive environment, seriously impacting the stability and reliability of semiconductor devices.

[0054] Specifically, in humid, high-temperature, or corrosive environments, the presence of residual stress can increase the material's susceptibility to stress corrosion, leading to rapid crack propagation. Therefore, the interaction between external stress and environmental factors experienced by photodetectors during operation can significantly accelerate their failure. Therefore, a deeper understanding of the coupling mechanism between residual stress and stress corrosion damage is key to improving the performance and reliability of photodetectors.

[0055] Stress corrosion damage is a complex failure mode, usually caused by the combined action of external stress and corrosive media. Its mechanism mainly includes the following aspects: 1. Crack formation and expansion: In a corrosive environment, tiny defects on the surface of the material may become the starting point of cracks, and externally applied stress will accelerate the formation and expansion of cracks. This process involves factors such as the yield strength, tensile strength and stress concentration of the material. 2. Environmental influence: Different corrosive media have a significant impact on stress corrosion damage. For example, chloride ions can reduce the corrosion resistance of the material in a high-salt environment, leading to the formation of cracks. High temperature and high humidity environments will accelerate the process of stress corrosion damage. 3. The particularity of the metal-semiconductor interface: In semiconductor photodetectors, the contact interface between metal and semiconductor is an important area of ​​stress corrosion damage. The stress state of the metal will affect the corrosion behavior of the semiconductor material, forming a complex coupling effect.

[0056] To achieve cross-scale coupling between residual stress and corrosion damage from the microscopic to the macroscopic level, this example establishes a quantitative relationship between residual stress and corrosion rate and crack growth rate. This introduces corrosion damage variables to quantify the effect of residual stress on the cross-scale failure evolution process from microscopic corrosion damage accumulation to macroscopic crack growth, systematically revealing the stress corrosion damage evolution mechanism. Based on multi-scale experiments, a comprehensive database covering residual stress, corrosion rate, and crack growth rate is constructed. The accuracy of the model is verified using experimental data, providing theoretical support for the prediction and protection of stress corrosion in semiconductor photodetectors. This has important theoretical and practical significance for improving the reliability and stability of detectors.

[0057] For ease of understanding, steps S100 to S400 will be described in detail below.

[0058] In this embodiment, the construction of the relationship between residual stress and corrosion rate in step S200 includes the following processes: based on the principles of corrosion electrochemistry and mechanics, determining the correlation between the corrosion rate v and the strain energy release rate G under stress; establishing a relationship equation between residual stress and corrosion rate v through the law of conservation of energy, and quantifying the promoting effect of residual stress on corrosion damage.

[0059] For ease of understanding, the specific derivation process of the relational equation will be described in detail below.

[0060] Specifically, the corrosion rate v can predict the extent of corrosion damage to a material caused by residual stress in a specific corrosive environment, providing a basis for developing protective measures. Assuming that the corrosion rate v is related to the local strain energy release rate G under stress, the law of conservation of energy establishes a relationship between the two: v = kG, where k represents a material-related constant that can be determined experimentally.

[0061] Since k is a known constant, the strain energy release rate G under residual stress will be calculated using mechanical principles. r .

[0062] First, determine the residual stress components. Taking the plate as an example, in the case of two-dimensional plane stress, the residual stress Including normal stress and , and shear stress .

[0063] Then calculate the strain component; according to Hooke's law: stress is equal to the product of elastic modulus and strain. Then, under the two-dimensional plane stress state, the corresponding strain component is calculated based on the obtained residual stress component and , and shear strain The specific expression is: , , ; where E represents the modulus of elasticity, and μ represents the Poisson's ratio.

[0064] Then the strain energy density u(x, y) in the plane stress state is calculated, and the strain energy density u(x, y) represents the strain energy stored in the unit volume of material. In the plane state, the calculation formula of the strain energy density u(x, y) is:

[0065] .

[0066] The strain component formula obtained in the foregoing is brought into the calculation formula of the strain energy density u(x, y), and the following formula can be obtained:

[0067] .

[0068] Finally, the strain energy release rate G r is calculated, and the strain energy release rate G r represents the strain energy released per unit area when the crack expands. For a material containing a crack, it is assumed that the crack expands by , and the strain energy released by the crack is U, and then the following formula is obtained: .

[0069] Given the strain energy density u(x, y) near the crack, the strain energy U released by the crack can be calculated by integrating the crack expansion area. Then the following formula is obtained:

[0070] .

[0071] Where A represents the area of the region involved in the crack expansion.

[0072] For the crack expansion area , the crack expansion length a and the crack width b can be regarded as the product of the crack expansion length a and the crack width b, and then the calculation formula of the strain energy release rate G r can be transformed into:

[0073] .

[0074] Based on G=G r , then the calculation formula of the strain energy release rate G r and the corrosion rate v can be obtained, and the relationship equation expression between the residual stress and the corrosion rate v is as follows:

[0075] .

[0076] In this embodiment, the construction of the relationship between the residual stress and the crack propagation rate in step S200 includes the following process: the residual stress factor is introduced to correct the stress intensity factor based on the stress corrosion empirical model. The relationship equation between the crack propagation rate and the residual stress is constructed based on the corrected stress intensity factor. Specifically, the Paris formula of the crack propagation rate about the stress intensity factor is constructed based on the stress corrosion empirical model. The relationship equation between the residual stress and the stress intensity factor is established by introducing the residual stress. The relationship equation between the crack propagation rate and the residual stress is obtained by substituting the relationship equation between the residual stress and the stress intensity factor into the Paris formula of the crack propagation rate.

[0077] For the convenience of understanding, the specific derivation process of the relationship equation between the crack propagation rate and the residual stress will be described in detail below.

[0078] Firstly, the Paris formula of the crack propagation rate about the stress intensity factor is constructed based on the stress corrosion empirical model as follows:

[0079] .

[0080] wherein da / dN represents the crack propagation rate under the Paris formula, C and n both represent constants related to the material, which can be obtained by experiments, K represents the stress intensity factor.

[0081] Then the residual stress σr is introduced to establish the relationship equation between the residual stress σr and the stress intensity factor K as follows:

[0082] .

[0083] wherein σ0 represents the stress intensity factor without the residual stress, and m represents a constant related to the material, which can be obtained by experiments.

[0084] Finally, the relationship equation between the residual stress σr and the stress intensity factor K is substituted into the Paris formula of the crack propagation rate to obtain the relationship equation between the crack propagation rate da / dN and the residual stress σr under the Paris formula as follows:

[0085] .

[0086] ​​​In this embodiment, the construction of the cross-scale correlation model includes the following process: the relationship equation between residual stress and corrosion rate and the preliminary relationship equation between crack propagation rate and residual stress are substituted into the damage evolution equation and the micro-corrosion damage variable D is introduced to describe the degree of material corrosion damage, forming a cross-scale correlation model from micro-corrosion damage accumulation to macro-crack propagation, to reveal the cross-scale coupling mechanism of residual stress-stress corrosion.

[0087] For the convenience of understanding, the specific construction process of the cross-scale correlation model will be described in detail from the perspective of formula derivation below.

[0088] First, the damage evolution equation is established; since the change rate dD / dt of the corrosion damage variable D is related to the corrosion rate v, and is also affected by the residual stress , the expression of the damage evolution equation of the micro-corrosion damage variable D is as follows:

[0089] .

[0090] Wherein, k1 and k2 represent material property related constants; k1×v(1-D) represents the contribution of corrosion rate to damage evolution, and as corrosion proceeds, damage accumulates, and when damage approaches complete failure (D→1), the rate of damage increase slows down; k2×σ×(1-D) represents the additional promotion of residual stress to damage evolution, and residual stress will accelerate the further damage of the damaged area.

[0091] The calculation formula of the foregoing corrosion rate v is brought into the damage evolution equation, which can further obtain:

[0092] .

[0093] Then, the damage evolution to crack propagation process is analyzed; it is necessary to know that when the corrosion damage reaches a certain degree, the semiconductor device will crack, at this time the damage of the semiconductor device will be converted from the micro level to the macro level. Specifically, when the corrosion damage variable D reaches a critical value D c , it is considered that the micro-corrosion damage begins to evolve into macro-cracks. At this time, the crack propagation rate da / dt is related to the corrosion damage variable D and the residual stress , and the specific relationship expression is as follows:

[0094] da / dt=k3(D-D c )×da / dN.

[0095] Wherein, k3 represents a material property related constant, which can be determined by experiment; the specific value of the critical value D c can be set by the actual needs of those skilled in the art.

[0096] Finally, the construction of the cross-scale correlation model is carried out; it can be understood that when the corrosion damage variable D≤D c , the crack propagation rate is 0; when the corrosion damage variable D>D c , the crack starts to expand, and the expansion rate is related to the degree of damage exceeding the critical value and the crack propagation rate da / dN.

[0097] Based on the above analysis process, by introducing the corrosion rate v and the residual stress correlation formula, and the crack propagation rate da / dN calculation formula into the damage evolution equation, the relationship between damage evolution and crack propagation is established, and a cross-scale parallel model from micro corrosion damage to macro crack propagation can be formed, and the expression of the cross-scale parallel model is as follows:

[0098] .

[0099] In this embodiment, step S400 includes the following processes:

[0100] Different semiconductor materials are selected for residual stress measurement experiments, corrosion rate test experiments and crack propagation rate monitoring experiments, and experimental parameters and corresponding results are recorded.

[0101] The experimental parameters are substituted into the cross-scale correlation model to output the results.

[0102] The experimental results are compared with the results output by the model; if the error between the two is within the set threshold range, it is determined that the cross-scale correlation model meets the accuracy requirement, otherwise the cross-scale correlation model is optimized based on the experimental results.

[0103] In order to facilitate understanding, the database acquisition process of step S100 and the specific process of model verification based on experiments will be described in detail below.

[0104] (1) Residual stress measurement experiment.

[0105] Select semiconductor photodetector and other material samples, and measure the residual stress of different material samples by X-ray diffraction method, and record the size, direction and distribution of residual stress.

[0106] The specific experimental materials and related parameters are shown in the following table:

[0107]

[0108] Experimental method: use an X-ray diffractometer to measure the incident angle (2θ) of the semiconductor device Irradiation angles: 0°, 15°, 30° and 45°, respectively. Crystal surface selection: (220) crystal surface of elemental silicon, Bragg angle θ = 29.16°; (220) crystal surface of germanium, Bragg angle θ = 21.13°; (400) crystal surface of gallium arsenide, Bragg angle θ = 22.54°. Stress The calculation formula is as follows: .

[0109] The experimental data obtained based on the above experimental method are shown in the following table:

[0110]

[0111] (2) Corrosion rate test experiment.

[0112] The material sample is placed in a specific corrosion environment, and the corrosion degree of the material is measured periodically by means of weight loss method, electrochemical impedance spectroscopy and other means, the size and number of pitting pits on the surface of the pipe are observed by microscope and other equipment, the corrosion rate is calculated, and the potential relationship between the corrosion rate and the residual stress is analyzed.

[0113] Unified corrosion environment: 3.5% NaCl solution (neutral salt spray environment, simulating marine atmospheric corrosion). Test method adopts weight loss method and electrochemical impedance spectroscopy; weight loss method: weigh the sample every 24 hours, and calculate the weight loss rate; electrochemical impedance spectroscopy (EIS): test at open circuit potential, frequency range 10 -2 ~10 5 Hz.

[0114] The number and size of pitting pits are observed and recorded by microscope, and the experimental data obtained are shown in the following table:

[0115]

[0116] From the above table, it can be seen that germanium (tensile stress +120 MPa): the highest corrosion rate (0.78 mm / year) and the largest pitting density, indicating that tensile stress accelerates corrosion. Monocrystalline silicon (compressive stress-85 MPa): the lowest corrosion rate (0.14 mm / year), compressive stress inhibits corrosion. Gallium arsenide (compressive stress-150 MPa): the corrosion rate is between the two, which may be due to the better neutral salt spray resistance of the material itself.

[0117] (3) Crack propagation rate monitoring experiment.

[0118] Microscope, acoustic emission monitoring and other equipment are used to observe and record the crack initiation and propagation process of the material under the combined action of stress and corrosion in real time, accurately measure the length, propagation direction and propagation rate of the crack, and establish the relationship between the crack propagation rate and the residual stress and the corrosion degree.

[0119] Experimental conditions: stress loading is uniaxial tensile stress , Yield strength is represented; corrosion environment is 3.5% NaCl solution which is the same as corrosion rate test; monitoring means is in-situ optical microscope (resolution 0.1 μm) and acoustic emission sensor (AE, frequency range 100~500 kHz).

[0120] The experimental data monitored according to the above experimental conditions are shown in the following table:

[0121]

[0122] From the above table, it can be seen that germanium (tensile stress +120 MPa): the crack propagation rate is the fastest (1.0 μm / h), and the stress and corrosion synergistic effect is significant. Monocrystalline silicon (compressive stress-85 MPa): the crack propagation rate is the slowest (0.2 μm / h), and the compressive stress inhibits crack initiation. Gallium arsenide (compressive stress-150 MPa): the propagation rate is moderate, which may be due to the partial offset of the corrosion driving force by the compressive stress.

[0123] (4) Verification of the cross-scale correlation model based on the experimental results.

[0124] The strain energy release rate G of each material in the calculation experiment is substituted into the calculation formula of the corrosion rate v to fit and determine the value of the material constant k in the corrosion rate v=kG. The specific fitting results are: the material constant k corresponding to monocrystalline silicon is 0.0028 mm / (year•MPa•m^{1 / 2}), the material constant k corresponding to germanium is 0.0148 mm / (year•MPa•m^{1 / 2}), and the material constant k corresponding to gallium arsenide is 0.0032 mm / (year•MPa•m^{1 / 2}).

[0125] The material parameters C, n and m in the crack propagation rate da / dN calculation formula are fitted and determined using the crack propagation experimental data. The specific fitting results are: monocrystalline silicon: C=0.05 μm / (h•(MPa•m^{1 / 2})^n), n=1.8, m=0.08; germanium: C=0.02 μm / (h•(MPa•m^{1 / 2})^n), n=2.0, m=0.01; gallium arsenide: C=0.07 μm / (h•(MPa•m^{1 / 2})^n), C=1.9, m=0.09.

[0126] The prediction results based on the cross-scale correlation model are compared with the experimental data.

[0127] For the verification of the corrosion rate, the experimental corrosion rate of single crystal silicon is 0.14 mm / year, the theoretical prediction value is 0.13 mm / year, and the error of the two is -7.1%; the experimental corrosion rate of germanium is 0.78 mm / year, the theoretical prediction value is 0.75 mm / year, and the error of the two is -3.8%; the experimental corrosion rate of gallium arsenide is 0.23 mm / year, the theoretical prediction value is 0.25 mm / year, and the error of the two is 8.7%. Based on the verification results, the error curve diagram as shown in Figure 2 From the figure, it can be seen that the experimental data Experimental values (scatter points) and the theoretical data Theoretical values (solid line) are in good agreement, and the deviation of germanium material is the smallest.

[0128] For the verification of the crack propagation rate, the crack propagation rate da / dt of single crystal silicon is 0.2 μm / h, the theoretical prediction value is 0.22 μm / h, and the error of the two is 10%; the crack propagation rate da / dt of germanium is 1 μm / h, the theoretical prediction value is 0.95 μm / h, and the error of the two is 5%; the crack propagation rate da / dt of gallium arsenide is 0.4 μm / h, the theoretical prediction value is 0.38 μm / h, and the error of the two is 5%. Based on the verification results, the error curve diagram as shown in Figure 3 From the figure, it can be seen that the deviation of single crystal silicon under high stress is slightly larger, but the overall trend of the experimental data Experimental values (scatter points) and the theoretical data Theoretical values (solid line) is consistent.

[0129] The above describes the basic principles, main features and advantages of the present application. Those skilled in the art should understand that the present application is not limited to the above embodiments, and the above embodiments and descriptions in the specification are only the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection claimed by the present application is defined by the appended claims and their equivalents.

Claims

1. A cross-scale coupling method for residual stress and corrosion damage in semiconductor devices, characterized by: The steps include: S100: Conduct multi-scale experiments on semiconductor devices to obtain a database including residual stress, corrosion rate, and crack growth rate; S200: Quantitatively analyze the obtained database and construct damage evolution equations including the relationship between residual stress and corrosion rate and the relationship between residual stress and crack growth rate; S300: Based on theoretical knowledge related to semiconductor manufacturing, microscopic corrosion damage variables are obtained and damage evolution equations are introduced to construct a cross-scale correlation model for simulation; S400: Validating the cross-scale association model based on the database obtained in step S100; The construction of the relationship between residual stress and corrosion rate includes the following process: Based on the principles of corrosion electrochemistry and mechanics, the correlation between the corrosion rate v and the strain energy release rate G under stress is determined; The relationship equation between residual stress and corrosion rate v is established through the law of conservation of energy; The relationship between residual stress and corrosion rate v is expressed as follows: ； Among them, A represents the area involved in crack expansion, E represents the elastic modulus, and represents the normal stress in a two-dimensional plane, represents the shear stress in a two-dimensional plane, μ represents the Poisson's ratio, a represents the crack extension length, b represents the crack width; The construction of the relationship between residual stress and crack growth rate includes the following process: Combined with the empirical model of stress corrosion, the residual stress factor is introduced to correct the stress intensity factor; The relationship equation between crack growth rate and residual stress is constructed based on the modified stress intensity factor; The establishment of the relationship equation between residual stress and crack growth rate includes the following process: Based on the empirical model of stress corrosion, the Paris formula of crack growth rate related to stress intensity factor is constructed; Introduce residual stress and establish the relationship between residual stress and stress intensity factor; Substituting the relationship between residual stress and stress intensity factor into the Paris formula of crack growth rate, the relationship equation between crack growth rate and residual stress is obtained; Crack growth rate da / dN and residual stress The relationship equation expression under the Paris formula is as follows: ； Among them, C, n and m are constants related to the material. Indicates the stress intensity factor when there is no residual stress; In step S300, the damage evolution equation that introduces the micro-corrosion damage variable D is expressed as follows: ； Where dD / dt represents the rate of change of the microscopic corrosion damage variable D, k1 and k2 represent constants related to material properties, and v represents the corrosion rate. represents residual stress; When the semiconductor evolves from microscopic corrosion damage to macroscopic cracks, the microscopic corrosion damage variable D reaches a critical value D c ; At this time, the expression of the damage evolution equation is as follows: da / dt=k3(DD c )×da / dN; Where da / dt and da / dN represent the crack growth rate, and k3 represents a constant related to material properties.

2. The cross-scale coupling method for residual stress and corrosion damage in semiconductor devices according to claim 1, characterized in that: The derivation process of the strain energy release rate G is as follows: Determine residual stress components in a 2D plane, including normal stresses and , and shear stress ; Calculate the corresponding strain components based on the obtained residual stress components and , and shear strain ; The specific expression is: , , ; Calculate the strain energy density u(x, y) under plane stress state; The specific expression is: ; Calculation of crack growth Strain energy release rate under area ; Among them, strain energy ; .

3. The cross-scale coupling method for residual stress and corrosion damage in semiconductor devices according to claim 1, characterized in that: Step S400 includes the following process: Select different semiconductor materials to conduct residual stress measurement experiments, corrosion rate test experiments, and crack growth rate monitoring experiments, and record the experimental parameters and corresponding results; Substitute the experimental parameters into the cross-scale correlation model to output the results; The experimental results are compared with the results output by the model; if the error between the two is within the set threshold range, the cross-scale correlation model is deemed to meet the accuracy requirements; otherwise, the cross-scale correlation model is optimized based on the experimental results.

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