Trans-scale coupling method for residual stress and corrosion damage of semiconductor device

Abstract

The invention discloses a cross-scale coupling method for residual stress and corrosion damage of a semiconductor device, and the method comprises the following steps: carrying out the multi-scale experiment of the semiconductor device, and obtaining a database comprising the residual stress, the corrosion rate and the crack growth rate; carrying out quantitative analysis on the obtained database, and constructing a damage evolution equation comprising a relationship between residual stress and corrosion rate and a relationship between residual stress and crack growth rate; the method comprises the following steps: obtaining microscopic corrosion damage variables based on semiconductor manufacturing related theoretical knowledge, introducing a damage evolution equation, and further constructing a cross-scale correlation model for simulation; and verifying the cross-scale correlation model based on the obtained database. The method has the beneficial effects that the stress corrosion damage evolution mechanism is systematically revealed by establishing the cross-scale failure evolution process among the residual stress, the corrosion rate and the crack growth rate, and the method has important theoretical and practical significance for improving the use reliability and stability of semiconductor devices.

Description

Technical Field

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

[0002] As a key device for realizing the mutual conversion between optical signals and electrical signals, semiconductor photodetectors play an indispensable role in many fields such as modern optical communication, optical sensing, national defense and military, and biomedicine. However, during its manufacturing process, due to processes such as material processing and heat treatment, residual stress will inevitably be generated inside the device. At the same time, in the actual service environment, the detector will also be affected by various corrosive media, and the synergistic effect of residual stress and corrosive media is extremely likely to cause stress corrosion damage, seriously affecting the performance and service life of the detector. Therefore, in-depth study of the cross-scale coupling mechanism of residual stress-stress corrosion damage in semiconductors has important theoretical and practical significance for improving the reliability and stability of detectors. Summary of the Invention

[0003] One of the purposes of this application is to provide a cross-scale coupling method for residual stress and corrosion damage of semiconductor devices that can solve at least one defect in the above background art.

[0004] To achieve at least one of the above purposes, the technical solution adopted in this application is: a cross-scale coupling method for residual stress and corrosion damage of semiconductor devices, including 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: Conduct quantitative analysis on the obtained database to 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: Obtain microscopic corrosion damage variables based on relevant theoretical knowledge of semiconductor manufacturing and introduce them into the damage evolution equation, and then construct a cross-scale correlation model for simulation;

[0008] S400: Verify the cross-scale correlation 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 corrosion electrochemistry and mechanics principles, determine the correlation between corrosion rate v and strain energy release rate G under stress; establish a relationship equation between residual stress and corrosion rate v through the law of conservation of energy.

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

[0011]

[0012] Among them, A represents the area of the region involved in crack propagation, E represents the elastic modulus, and σ xx and σ yy represent the normal stress in the two-dimensional plane, σ xy represents the shear stress in the two-dimensional plane, μ represents the Poisson's ratio, Δa 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] Determine the residual stress components in the two-dimensional plane, including the normal stresses σ xx and σ yy , and the shear stress σ xy ;

[0015] Calculate the corresponding strain components ε xx and ε yy , and the shear strain γ xy ;

[0016] The specific expressions are: ε xx =(σ xx -μσ yy ) / E, ε yy =(σ yy -μσ xx ) / E, γ xy =2σ xy (1 + μ) / E;

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

[0018] The specific expression is: u(x, y)=(σ xx ε xx +σ yy ε yy+ σ xy γ xy ) / 2 = [σ2xx + σ2yy - 2μσ xx σ yy + 2(1 + μ)σ2xy] / 2E;

[0019] Calculate the strain energy release rate G = ΔU / ΔA for the area of crack propagation ΔA;

[0020] Among them, the strain energy ΔA = Δa × b.

[0021] Preferably, the construction of the relationship between residual stress and crack growth rate includes the following process: combining the stress corrosion empirical model, introducing the residual stress factor to correct the stress intensity factor; constructing the relationship equation between crack growth rate and residual stress based on the corrected stress intensity factor.

[0022] Preferably, the establishment of the relationship equation between residual stress and crack growth rate includes the following process: based on the stress corrosion empirical model, constructing the Paris formula for crack growth rate with respect to stress intensity factor; introducing residual stress to establish the relationship between residual stress and stress intensity factor; substituting the relationship between residual stress and stress intensity factor into the Paris formula for crack growth rate to obtain the relationship equation between crack growth rate and residual stress.

[0023] Preferably, the relationship equation expression of crack growth rate da / dN and residual stress σ r under the Paris formula is as follows:

[0024] da / dN = C(ΔK0 + m×σ r ) n ;

[0025] where C, n, and m all represent constants related to the material, and ΔK0 represents the stress intensity factor without residual stress.

[0026] Preferably, in step S300, the expression of the damage evolution equation introducing the microscopic corrosion damage variable D is as follows:

[0027] dD / dt = k1×v(1 - D) + k2×σ r ×D;

[0028] where dD / dt represents the change rate of the microscopic corrosion damage variable D, k1 and k2 both represent constants related to material properties, v represents the corrosion rate, and σ r represents the residual stress.

[0029] Preferably, when the semiconductor evolves from microscopic corrosion damage to macroscopic crack, the microscopic corrosion damage variable D reaches the critical value D c ; at this time, the expression of the damage evolution equation is as follows:

[0030] da / dt = k3(D - D c )×da / dN;

[0031] where da / dt and da / dN both represent crack growth rates, and k3 represents a constant related to material properties.

[0032] Preferably, step S400 includes the following process:

[0033] Select different semiconductor materials for residual stress measurement experiments, corrosion rate test experiments, and crack growth rate monitoring experiments, and record the experimental parameters and corresponding results;

[0034] Substitute the experimental parameters into the cross-scale correlation model for result output;

[0035] 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 requirements, otherwise, optimize the cross-scale correlation model based on the experimental results.

[0036] Compared with the prior art, the beneficial effects of this application are as follows:

[0037] By establishing a quantitative relationship between residual stress, corrosion rate, and crack growth rate, introducing a corrosion damage variable to quantify the cross-scale failure evolution process of residual stress on the accumulation of microscopic corrosion damage to macroscopic crack growth, and systematically revealing the stress corrosion damage evolution mechanism, it has important theoretical and practical significance for improving the use reliability and stability of semiconductor devices. Brief Description of the Drawings

[0038] Figure 1 It is a schematic diagram of the step flow of this application.

[0039] Figure 2 It is a schematic diagram of the error between the experimental data and the theoretical data of the corrosion rate in this application.

[0040] Figure 3 It is a schematic diagram of the error between the experimental data and the theoretical data of the crack growth rate in this application. Detailed Description of the Embodiments

[0041] Next, in combination with the specific embodiments, this application will be further described. It should be noted that in the description of this specification, the descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic descriptions 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 the different embodiments or examples described in this specification.

[0042] In the description of the present application, it should be noted that for orientation terms, such as the terms "center", "lateral", "longitudinal", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc., which indicate the orientation and positional relationship are based on the orientation or positional relationship shown in the drawings. This is only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and should not be construed as limiting the specific protection scope of the present application.

[0043] It should be noted that the terms "first", "second", etc. in the description and claims of the present application are used to distinguish similar objects and do not necessarily need to describe a specific order or sequence.

[0044] In the present application, unless otherwise clearly defined and limited, the terms "installed", "connected", "connected to", "fixed", etc. should be understood in a broad sense. For example, it can be a connection, a detachable connection, or integrated; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements or the interaction relationship between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0045] In the present application, unless otherwise clearly defined and limited, the first feature being "on" or "under" the second feature may include the direct contact between the first and second features, or may include the situation where the first and second features are not in direct contact but in contact through other features between them. Moreover, the first feature being "above", "over" and "on" the second feature includes that the first feature is directly above and obliquely above the second feature, or merely indicates that the horizontal height of the first feature is higher than that of the second feature. The first feature being "under", "beneath" and "under" the second feature includes that the first feature is directly below and obliquely below the second feature, or merely indicates that the horizontal height of the first feature is lower than that of the second feature.

[0046] The terms "comprising" and "having" in the description and claims of the present application, and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0047] One preferred embodiment of the present application, as Figure 1 shown, a cross-scale coupling method for residual stress and corrosion damage of semiconductor devices, comprising the following steps:

[0048] S100: Conduct multi-scale experiments on semiconductor devices to obtain a database including residual stress, corrosion rate and crack growth rate.

[0049] S200: Quantitatively analyze the obtained database and construct the damage evolution equation including the relationship between residual stress and corrosion rate and the relationship between residual stress and crack growth rate.

[0050] 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.

[0051] S400: verifying the cross-scale association model based on the database obtained in step S100.

[0052] It should be known that residual stress mainly comes from the material processing, such as doping, annealing and thin film deposition, which will lead to the generation of internal stress in the material. Stress corrosion damage refers to the cracks and damage of the material under the combined action of stress and corrosion environment, which seriously affects the stability and reliability of semiconductor devices.

[0053] Specifically, in a humid, high temperature or corrosive environment, the presence of residual stress will increase the stress corrosion sensitivity of the material, leading to rapid crack expansion. Therefore, during the operation of the photodetector, the interaction between external stress and environmental factors will significantly accelerate its failure. Therefore, a deep understanding of the coupling mechanism of residual stress and stress corrosion damage is the key to improving the performance and reliability of photodetectors.

[0054] Stress corrosion damage is a complex failure mode, usually caused by the combined effect 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 the crack, and the externally applied stress will accelerate the formation and expansion of the crack. 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 effect 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.

[0055] To achieve the cross-scale coupling of residual stress and corrosion damage from the microscale to the macroscale, in this embodiment, by establishing a quantitative relationship between residual stress, corrosion rate, and crack propagation rate, a corrosion damage variable is introduced to quantify the cross-scale failure evolution process of residual stress on the accumulation of microscale corrosion damage to macroscale crack propagation, and the stress corrosion damage evolution mechanism is systematically revealed. Based on multi-scale experiments, a comprehensive database covering residual stress, corrosion rate, and crack propagation rate is constructed. The accuracy of the model is verified using experimental data, providing theoretical support for the prediction and prevention of stress corrosion in semiconductor photodetectors, which has important theoretical and practical significance for improving the reliability and stability of the detectors.

[0056] For ease of understanding, the steps S100 to S400 will be described in detail below.

[0057] In this embodiment, the construction of the relationship between residual stress and corrosion rate in step S200 includes the following process: Based on corrosion electrochemistry and mechanics principles, the correlation between corrosion rate v and the strain energy release rate G under stress is determined; through the law of conservation of energy, a relationship equation between residual stress and corrosion rate v is established to quantify the promoting effect of residual stress on corrosion damage.

[0058] For ease of understanding, the specific derivation process of the relationship equation will be described in detail below.

[0059] Specifically, the corrosion rate v can predict the degree of corrosion damage caused by residual stress in a specific corrosion environment, providing a basis for formulating protection measures. Assuming that the corrosion rate v is related to the local strain energy release rate G under stress, a relationship between the two is established through the law of conservation of energy. The specific relationship formula is: v = kG; where k represents a constant related to the material and can be obtained through experimental measurement.

[0060] Since k can be regarded as a known constant, the strain energy release rate G under the action of residual stress will be calculated below through mechanics principles. r 。

[0061] First, determine the residual stress components. Taking a plate as an example, in the case of two-dimensional plane stress, the residual stress σ r includes the normal stress σ xx and σ yy , as well as the shear stress σ xy (σ xy = σ yx ).

[0062] Then calculate the strain components; according to Hooke's law: stress is equal to the product of the elastic modulus and strain. Then, in the two-dimensional plane stress state, based on the obtained residual stress components, the corresponding strain components ε xx and ε yy, and shear strain γ xy . The specific expressions are: ε xx =(σ xx -μσ yy ) / E, ε yy =(σ yy -μσ xx ) / E, γ xy =2σ xy (1 + μ) / E; where E represents the elastic modulus and μ represents Poisson's ratio.

[0063] Then calculate the strain energy density u(x, y) under plane stress state. The strain energy density u(x, y) represents the strain energy stored in the material per unit volume. In the plane state, the calculation formula for the strain energy density u(x, y) is:

[0064] u(x, y)=(σ xx ε xx +σ yy ε yy+ σ xy γ xy ) / 2.

[0065] Substitute the previously obtained strain component formula into the calculation formula for the strain energy density u(x, y), and we can get:

[0066] u(x, y)=[σ²xx + σ²yy - 2μσ xx σ yy +2(1 + μ)σ²xy] / 2E.

[0067] Finally, calculate the strain energy release rate G r ; The strain energy release rate G r represents the strain energy released when the crack propagates per unit area. For a material containing a crack, assuming the crack propagates by an area of ΔA and the released strain energy is ΔU, then: G r =ΔU / ΔA.

[0068] Given that the strain energy density near the crack is u(x, y), the released strain energy ΔU can be calculated by integrating over the crack propagation region. Then:

[0069]

[0070] where A represents the area of the region involved in crack propagation.

[0071] For the crack propagation area ΔA, it can be regarded as the product of the crack propagation length Δa and the crack width b. Then the calculation formula for the strain energy release rate G r can be transformed into:

[0072]

[0073] Based on G=G r , then the combined strain energy release rate G r And the calculation formula of corrosion rate v, the relationship between residual stress and corrosion rate v can be obtained as follows:

[0074]

[0075] In this embodiment, the construction of the relationship between residual stress and crack growth rate in step S200 includes the following process: In combination with the stress corrosion empirical model, the residual stress factor is introduced to correct the stress intensity factor. The relationship equation between the crack growth rate and the residual stress is constructed based on the corrected stress intensity factor. Specifically, based on the stress corrosion empirical model, the Paris formula of the crack growth rate with respect to the stress intensity factor is constructed. Residual stress is introduced to establish the relationship between residual stress and stress intensity factor. The relationship between residual stress and stress intensity factor is substituted into the Paris formula of crack growth rate to obtain the relationship equation between crack growth rate and residual stress.

[0076] For ease of understanding, the specific derivation process of the relationship equation between crack growth rate and residual stress will be described in detail below.

[0077] First, based on the stress corrosion empirical model, the Paris formula for crack growth rate regarding the stress intensity factor is constructed as follows:

[0078] da / dN=C(ΔK) n .

[0079] Among them, da / dN represents the crack growth rate under the Paris formula, C and n are constants related to the material and can be obtained by experimental measurement, and ΔK represents the stress intensity factor.

[0080] Then the residual stress σ is introduced r , establish the residual stress σ r The relationship with the stress intensity factor ΔK is as follows:

[0081] ΔK=ΔK0+m×σ r .

[0082] Among them, ΔK0 represents the stress intensity factor when there is no residual stress, and m represents a constant related to the material, which can be obtained by experimental measurement.

[0083] Finally, the residual stress σ r Substituting the relationship between the stress intensity factor ΔK and the crack growth rate into the Paris formula, we can get the crack growth rate da / dN and the residual stress σ rThe relational equation expression under the Paris formula is as follows:

[0084] da / dN = C(ΔK0 + m×σ r ) n 。

[0085] In this embodiment, the construction of the cross-scale correlation model includes the following process: substituting the relational equation between residual stress and corrosion rate and the preliminary relational equation between crack growth rate and residual stress into the damage evolution equation and introducing the microscopic corrosion damage variable D to describe the degree of material corrosion damage, forming a cross-scale correlation model from microscopic corrosion damage accumulation to macroscopic crack growth to reveal the cross-scale coupling mechanism of residual stress-stress corrosion.

[0086] For the convenience of understanding, the specific construction process of the cross-scale correlation model will be elaborated in detail from the perspective of formula derivation below.

[0087] First, establish the damage evolution equation; 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 σ r , the expression of the damage evolution equation introducing the microscopic corrosion damage variable D is as follows:

[0088] dD / dt = k1×v(1 - D) + k2×σ r ×D.

[0089] Among them, both k1 and k2 represent constants related to material properties; k1×v(1 - D) represents the contribution of the corrosion rate to damage evolution. As corrosion progresses, damage accumulates, and when the damage approaches complete failure (D → 1), the rate of damage increase slows down; k2×σ r ×D represents the additional promotion effect of residual stress on damage evolution, and residual stress will accelerate the further damage of the damaged area.

[0090] Substituting the foregoing calculation formula of the corrosion rate v into the damage evolution equation, we can further obtain:

[0091]

[0092] Then, analyze the process from damage evolution to crack growth; it should be noted that when the corrosion damage reaches a certain level, the semiconductor device will crack, and at this time, the damage of the semiconductor device will be transformed from the microscopic level to the macroscopic level. Specifically, when the corrosion damage variable D reaches a critical value D c , it is considered that the microscopic corrosion damage begins to evolve into macroscopic cracks. At this time, the crack growth rate da / dt is related to the corrosion damage variable D and the residual stress σ r , and the specific relational expression is as follows:

[0093] da / dt = k3(D - D c ) × da / dN.

[0094] Wherein, k3 represents a constant related to material properties and can be obtained through experimental determination; the specific value of the critical value D c can be set according to the actual needs of those skilled in the art.

[0095] Finally, a cross-scale correlation model is constructed; it can be understood that when the corrosion damage variable D ≤ D c , the crack growth rate is 0; when the corrosion damage variable D > D c , the crack begins to expand, and the expansion rate is related to the degree of damage exceeding the critical value and the crack growth rate da / dN.

[0096] Based on the above analysis process, by introducing the correlation formula between the corrosion rate v and the residual stress σ r , and the calculation formula of the crack growth rate da / dN into the damage evolution equation, the relationship between damage evolution and crack propagation is established, and a cross-scale parallel model from microscopic corrosion damage to macroscopic crack expansion can be formed. The expression of this cross-scale parallel model is as follows:

[0097]

[0098] In this embodiment, step S400 includes the following process:

[0099] 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.

[0100] Substitute the experimental parameters into the cross-scale correlation model for result output.

[0101] 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 requirements, otherwise, optimize the cross-scale correlation model based on the experimental results.

[0102] For the convenience of understanding, the following will describe in detail the process of obtaining the database in step S100 and the specific process of model verification based on experiments.

[0103] (1) Residual stress measurement experiment.

[0104] Select material samples such as semiconductor photodetectors, and use X-ray diffraction method to measure the residual stress of different material samples, and record the magnitude, direction, and distribution of the residual stress.

[0105] The specific experimental materials and related parameters are shown in the following table:

[0106] Experimental method: The semiconductor device was irradiated with X-ray diffractometer at incident angles (ψ) of 0°, 15°, 30° and 45° respectively. Crystal plane selection: For single crystal silicon: (220) crystal plane, Bragg angle θ = 29.16°; for germanium: (220) crystal plane, Bragg angle θ = 21.13°; for gallium arsenide: (400) crystal plane, Bragg angle θ = 22.54°. The stress σ calculation formula is used as follows:

[0107] The experimental data obtained based on the above experimental method are shown in the following table:

[0108] (2) Corrosion rate test experiment.

[0109] The material samples were placed in a specific corrosion environment, and the corrosion degree of the materials was regularly measured by means of weight loss method, electrochemical impedance spectroscopy, etc. The pitting pit size, quantity, etc. on the surface of the pipe were observed through equipment such as microscopes, the corrosion rate was calculated, and the potential relationship between the corrosion rate and the residual stress was analyzed.

[0110] Uniform corrosion environment: The solution used was 3.5% NaCl solution (neutral salt spray environment, simulating marine atmospheric corrosion). The test methods used were weight loss method and electrochemical impedance spectroscopy; Weight loss method: The samples were weighed every 24 hours to calculate the weight loss rate; Electrochemical impedance spectroscopy (EIS): Tested at open circuit potential, frequency range 10 -2 ~10 5 Hz.

[0111] The pitting pit quantity and size were observed and recorded through microscopes, and the experimental data obtained are shown in the following table:

[0112] It can be seen from the above table that for germanium (tensile stress +120 MPa): the corrosion rate is the highest (0.78 mm / year), and the pitting density is the largest, indicating that tensile stress accelerates corrosion. For single crystal silicon (compressive stress -85 MPa): the corrosion rate is the lowest (0.14 mm / year), and compressive stress inhibits corrosion. For gallium arsenide (compressive stress -150 MPa): the corrosion rate is between the two, probably because the material itself has good resistance to neutral salt spray.

[0113] (3) Crack propagation rate monitoring experiment.

[0114] Using equipment such as microscopes and acoustic emission monitors, observe and record in real time the process of crack initiation and propagation in materials under the combined action of stress and corrosion, accurately measure the crack length, propagation direction, and propagation rate, and establish the relationship between the crack propagation rate, residual stress, and corrosion degree.

[0115] Experimental conditions: Uniaxial tensile stress σ = 0.8σ s , σ s is used to represent the yield strength; the corrosion environment uses the same 3.5% NaCl solution as in the corrosion rate test; the monitoring methods use an in-situ optical microscope (resolution 0.1μm) and an acoustic emission sensor (AE, frequency range 100 - 500kHz).

[0116] The experimental data monitored according to the above experimental conditions are shown in the following table:

[0117] It can be seen from the above table that for germanium (tensile stress +120 MPa): the crack propagation rate is the fastest (1.0 μm / h), and the synergistic effect of stress and corrosion is significant. For single-crystalline silicon (compressive stress -85 MPa): the crack propagation rate is the slowest (0.2 μm / h), and the compressive stress inhibits crack initiation. For gallium arsenide (compressive stress -150 MPa): the propagation rate is medium, probably because the compressive stress partially offsets the corrosion driving force.

[0118] (4) Verify the cross-scale correlation model based on the experimental results.

[0119] Calculate the strain energy release rate G of each material in the experiment and substitute it into the calculation formula of the corrosion rate v for fitting to determine the value of the material constant k in v = kG. The specific fitting results are: for single-crystalline silicon, the material constant k = 0.0028 mm / (year·MPa·m^{1 / 2}); for germanium, the material constant k = 0.0148 mm / (year·MPa·m^{1 / 2}); for gallium arsenide, the material coefficient k = 0.0032 mm / (year·MPa·m^{1 / 2}).

[0120] Use the crack propagation experimental data to fit and determine the material parameters C, n, and m in the crack propagation rate da / dN calculation formula. The specific fitting results are: for single-crystalline silicon: C = 0.05 μm / (h·(MPa·m^{1 / 2})^n), n = 1.8, m = 0.08; for germanium: C = 0.02 μm / (h·(MPa·m^{1 / 2})^n), n = 2.0, m = 0.01; for gallium arsenide: C = 0.07 μm / (h·(MPa·m^{1 / 2})^n), C = 1.9, m = 0.09.

[0121] Compare the prediction results based on the cross-scale correlation model with the experimental data.

[0122] For the verification of the corrosion rate, the experimental corrosion rate of single-crystalline silicon is 0.14 mm / year, and the theoretical prediction value is 0.13 mm / year. The error between the two is -7.1%; the experimental corrosion rate of germanium is 0.78 mm / year, and the theoretical prediction value is 0.75 mm / year. The error between the two is -3.8%; the experimental corrosion rate of gallium arsenide is 0.23 mm / year, and the theoretical prediction value is 0.25 mm / year. The error between the two is 8.7%. Based on this verification result, construct a schematic diagram of the error curve as shown in Figure 2 Figure. It can be seen from the figure that the experimental data Experimental values (scattered points) and the theoretical data Theoretical values (solid line) are in good agreement, and the deviation of germanium material is the smallest.

[0123] For the verification of the crack growth rate, the experimental value of the crack growth rate da / dt of single-crystalline silicon is 0.2 μm / h, and the theoretical prediction value is 0.22 μm / h. The error between the two is 10%; the experimental value of the crack growth rate da / dt of germanium is 1 μm / h, and the theoretical prediction value is 0.95 μm / h. The error between the two is 5%; the experimental value of the crack growth rate da / dt of gallium arsenide is 0.4 μm / h, and the theoretical prediction value is 0.38 μm / h. The error between the two is 5%. Based on this verification result, construct a schematic diagram of the error curve as shown in Figure 3 Figure. It can be seen from the figure that the deviation of single-crystalline silicon under high stress is slightly larger, but the overall trend of the experimental data Experimental values (scattered points) and the theoretical data Theoretical values (solid line) is the same.

[0124] 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 by the above embodiments. What is described in the above embodiments and the specification is only the principle of the present application. Without departing from the spirit and scope of the present application, the present application will have various changes and improvements, and these changes and improvements fall within the scope of the present application claimed. The scope of protection required 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 of semiconductor devices, characterized in that It includes the following steps: S100: Conduct multi-scale experiments on semiconductor devices to obtain a database including residual stress, corrosion rate, and crack propagation rate; S200: Conduct quantitative analysis on the obtained database to construct damage evolution equations including the relationship between residual stress and corrosion rate and the relationship between residual stress and crack propagation rate; S300: Obtain microscopic corrosion damage variables based on relevant theoretical knowledge of semiconductor manufacturing and introduce them into the damage evolution equations, and then construct a cross-scale correlation model for simulation; S400: Verify the cross-scale correlation model based on the database obtained in step S100.

2. The cross-scale coupling method for residual stress and corrosion damage of a semiconductor device according to claim 1, wherein The construction of the relationship between residual stress and corrosion rate includes the following process: Based on corrosion electrochemistry and mechanics principles, determine the correlation between corrosion rate v and strain energy release rate G under stress; Establish a relationship equation between residual stress and corrosion rate v through the law of conservation of energy.

3. The cross-scale coupling method for residual stress and corrosion damage of the semiconductor device according to claim 2, wherein, The expression of the relationship equation between residual stress and corrosion rate v is as follows: Among them, A represents the area of the region involved in crack propagation, E represents the elastic modulus, σ xx and σ yy represent the normal stress in the two-dimensional plane, σ xy represents the shear stress in the two-dimensional plane, μ represents the Poisson's ratio, Δa represents the crack propagation length, and b represents the crack width.

4. The cross-scale coupling method for residual stress and corrosion damage of a semiconductor device according to claim 3, wherein The derivation process of strain energy release rate G is as follows: Determine the residual stress components in a two-dimensional plane, including the normal stresses σ xx and σ yy , and the shear stress σ xy ; Calculate the corresponding strain components ε xx and ε yy , as well as the shear strain γ xy ; The specific expressions are: ε xx =(σ xx -μσ yy ) / E, ε yy =(σ yy -μσ xx ) / E, γ xy =2σ xy (1 + μ) / E; Calculate the strain energy density u(x, y) in the plane stress state; The specific expression is: u(x, y) = (σ xx ε xx + σ yy ε yy+ σ xy γ xy ) / 2 = [σ²xx + σ²yy - 2μσ xx σ yy + 2(1 + μ)σ²xy] / 2E; Calculate the strain energy release rate G = ΔU / ΔA for the area of crack propagation ΔA; Among them, strain energy 5. The cross-scale coupling method for residual stress and corrosion damage of the semiconductor device according to claim 1, wherein The construction of the relationship between residual stress and crack propagation rate includes the following process: Combine the stress corrosion empirical model and introduce the residual stress factor to correct the stress intensity factor; Construct a relationship equation between crack propagation rate and residual stress based on the corrected stress intensity factor.

6. The cross-scale coupling method for residual stress and corrosion damage of a semiconductor device according to claim 5, wherein The establishment of the relationship equation between residual stress and crack propagation rate includes the following process: Based on the stress corrosion empirical model, construct the Paris formula for crack propagation rate regarding the stress intensity factor; Introduce residual stress and establish a relationship equation between residual stress and stress intensity factor; Substitute the relationship equation between residual stress and stress intensity factor into the Paris formula for crack propagation rate to obtain the relationship equation between crack propagation rate and residual stress.

7. The cross-scale coupling method for residual stress and corrosion damage of a semiconductor device according to claim 6, wherein The crack growth rate da / dN and the residual stress σ r The relational equation expression under the Paris formula is as follows: da / dN = C(ΔK0 + m×σ r ) n ; Among them, C, n, and m all represent constants related to the material, and ΔK0 represents the stress intensity factor without residual stress.

8. The cross-scale coupling method for residual stress and corrosion damage of the semiconductor device according to claim 1, characterized in that In step S300, the expression of the damage evolution equation introducing the microscopic corrosion damage variable D is as follows: dD / dt = k1 × v(1 - D) + k2 × σ r × D; where dD / dt represents the change rate of the microscopic corrosion damage variable D, k1 and k2 both represent material property-related constants, v represents the corrosion rate, and σ r represents the residual stress.

9. The cross-scale coupling method for residual stress and corrosion damage of the semiconductor device according to claim 8, wherein When the semiconductor evolves from microscopic corrosion damage to macroscopic cracks, the microscopic corrosion damage variable D reaches the critical value D c ; At this time, the expression of the damage evolution equation is as follows: da / dt = k3(D - D c ) × da / dN; Among them, da / dt and da / dN both represent crack propagation rate, and k3 represents a constant related to material properties.

10. The cross-scale coupling method for residual stress and corrosion damage of a semiconductor device 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 propagation rate monitoring experiments, and record the experimental parameters and corresponding results; Substitute the experimental parameters into the cross-scale correlation model for result output; 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 considered that the cross-scale correlation model meets the accuracy requirements, otherwise optimize the cross-scale correlation model based on the experimental results.

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