Numerical calculation method for deformation energy of solder layer of semiconductor power device

Abstract

A numerical calculation method for deformation energy of a solder layer of a semiconductor power device comprises the following steps: analyzing stress-strain characteristics of solder under a thermal load, and constructing a constitutive equation; calculating a stress-strain value of the solder layer of the semiconductor power device; calculating a numerical value of deformation energy according to the stress-strain of the solder layer of the semiconductor power device; and analyzing the influence of different factors on the deformation energy. According to the method, a solder layer is taken as a research object, a stress-strain modeling process is given, and the influence of different forms of square wave loss loads on the stress-strain characteristics and deformation energy of the solder layer is evaluated. The calculation method has the characteristics of easy implementation and data visualization.

Description

Technical Field

[0001] The invention relates to the technical field of semiconductor power device life assessment, and in particular to a numerical calculation method for deformation energy of a solder layer of a semiconductor power device. Background Art

[0002] Power electronic systems play an important role in renewable energy generation, motor drive, railway transportation and other fields. Improving the reliability of power electronic systems can meet more stringent safety and cost requirements. Taking IGBT as an example, the complex and harsh electro-thermal-mechanical stress makes the IGBT module one of the devices that is prone to aging and damage in the power electronic system, and the unforeseen failures caused will bring expensive costs. In order to improve the reliability design of the power electronic converter system and integrate the life cycle of the component into the system, the module life model has been increasingly studied. At present, the life model of IGBT is mainly empirical life model and physical life model. Compared with the empirical life model, the physical life model can better reflect the impact of thermal load on the module life from the essence. It first needs to understand the failure and deformation mechanism in order to model the stress and strain inside the power module component. The physical life model includes stress-based, strain-based, damage-based and energy-based life models. Since the energy-based life model can capture the test conditions more accurately, it is considered to be the most convenient. How to obtain the deformation energy of the device through numerical calculation based on the electro-thermal stress of the solder layer of the device, which is most prone to failure, is a technical problem to be solved at present. Summary of the invention

[0003] This paper takes the solder layer as the research object, gives the stress-strain modeling process, proposes a numerical calculation method for the deformation energy of the solder layer of semiconductor power devices, and evaluates the influence of different forms of square wave loss loads on the stress-strain characteristics and deformation energy of the solder layer. The calculation method is easy to implement and has data visualization.

[0004] The technical solution adopted by the present invention is:

[0005] A numerical calculation method for deformation energy of a solder layer of a semiconductor power device comprises the following steps:

[0006] Step 1: Analyze the stress-strain characteristics of solder under thermal load and construct the constitutive equation;

[0007] Step 2: Calculate the stress-strain value of the solder layer of the semiconductor power device;

[0008] Step 3: Calculate the value of deformation energy according to the stress-strain of the solder layer of the semiconductor power device;

[0009] Step 4: Analyze the influence of different factors on deformation energy.

[0010] The step 1 comprises the following steps:

[0011] S1.1: Simplify the two-material components of the welded joint into a spring model:

[0012]

[0013] In the above formula: γ is strain; τ is shear stress; T and T0 are temperature and reference temperature respectively; K is the effective assembly stiffness determined according to the geometry of the solder joint; D is the temperature sensitivity of strain;

[0014] At a given temperature, solder stress and strain exist on a stress reduction line, with stress always tending toward zero.

[0015] S1..2: Based on Hooke's law, the elastic shear behavior is described as:

[0016]

[0017] In the above formula: γ e is the elastic strain; G(T) is the shear modulus, G(T) = G0-G1·(T-273), G0 and G1 are the shear modulus constant and the temperature sensitivity of the shear modulus at 0°C, respectively; T is the temperature in degrees Kelvin.

[0018] The time-independent plastic strain component is expressed as a power-law relation:

[0019]

[0020] In the above formula: γ p is the plastic strain; C P is the plastic strain coefficient; m p is the sensitivity of plastic strain.

[0021] S1..3: Construct Darveaux's constitutive solder model, including initial creep and steady-state creep processes, as shown below:

[0022]

[0023] In the above formula: γ c is the initial creep strain component; t is time; γ T is the transient creep strain; B is the transient creep coefficient; γ s is the steady-state creep strain component; It indicates the dynamic change of transient creep of solder when it enters the steady-state creep stage;

[0024]

[0025] In the above formula: T represents Kelvin temperature; C1, α, n are constant coefficients of corresponding materials; k is Boltzmann constant; Q is creep activation energy;

[0026] In step 2, when the temperature is T1, it is known that the stress-strain state at time t is (γ1, τ1), where γ1 represents the strain at the current temperature T1; τ1 represents the stress at the temperature T1;

[0027] Through the above constitutive equations (2) to (5), under the assumption of a small time step Δt, the stress-strain state (γ2, τ2) at time t+Δt and temperature T2 is obtained, where γ2 represents the strain at temperature T2 and τ2 represents the corresponding stress. Specifically, the following steps are included:

[0028] Step 2.1: Based on the elastic constitutive equation (2), when the stress increases, the increment of the elastic strain component is:

[0029]

[0030] In the above formula: Δγ e The increment of the elastic strain component; Δτ is the stress component.

[0031] According to the differential equation (3), the increment of the plastic strain component Δγ p for:

[0032]

[0033] The slope of the stress-strain curve can be expressed by the stress-strain state, according to the different behavior characteristics of elasticity and plasticity under reverse load.

[0034] When the product of stress and stress increment is less than zero, the slope of the stress-strain curve is equal to the elastic modulus; when the product of the two is greater than zero, its slope consists of the elastic part and the plastic part.

[0035] Therefore, according to equations (6) and (7), the total increment Δγ of the elastic and plastic strain components is ep It is expressed as:

[0036] △γ ep =A·△τ ep (8);

[0037] Among them, Δγ ep is the total increment of the corresponding elastic-plastic stress component, and the coefficient A is:

[0038]

[0039] Where sgn(x) is the sign function; then the elastic-plastic strain component γ caused by temperature at temperature T2 is12 Δγ ep +γ1; elastic-plastic stress component τ caused by temperature at temperature T2 12 is Δτ ep +τ1.

[0040] According to formula (1), the stress reduction line can be used to characterize the relationship between stress and strain:

[0041]

[0042] Where ΔT is the temperature difference change, which is equal to T2-T1; then the combined equation (8) gives τ 12 and γ 12 for:

[0043]

[0044] Step 2.2: According to the creep behavior and stress reduction line, the stress tends to zero. The behavior of the creep component is related to the stress-strain state. When the stress state is positive, the strain increment is greater than zero; when the stress state is negative, the strain increment is less than zero. In addition, the primary creep eventually tends to be constant, and time will be the main part that causes steady-state creep. When only the steady-state creep component is considered, the increment of the creep component can be expressed as: Δγ c =S r ·Δt, where Δt represents the time from temperature T1 to temperature T2; Δγ c γ2-γ 12 , represents the change of creep strain component; S r As shown below:

[0045]

[0046] In the above formula: sgn(x) is the sign function; G(T2) is the shear modulus of the component at temperature T2; T represents the Kelvin temperature; C1, α, n are constant coefficients of the corresponding materials; k is the Boltzmann constant; Q is the creep activation energy;

[0047] Based on the stress reduction line, the relationship between creep stress and strain can be expressed as:

[0048] Where: Δτ c =τ2-τ 12 ,τ2=-K·S r ·△t+τ 12 ;γ2=S r ·△t+γ 12 .

[0049] The zero stress-strain state can be used for the initialization process. It can be used as the new starting value when calculating the stress-strain state (γ2,τ2).

[0050] In step 3, when the solder joint is subjected to cyclic heat load, after several cycles, a closed and stable irregular hysteresis curve can be obtained. The deformation energy can be expressed as the area of ​​the hysteresis curve.

[0051] The stress-strain response moves clockwise under cyclic thermal loading, according to the material's behavior under reversed loading. The maximum and minimum strain values ​​γ can be found max and γ min When the strain changes from γ min Move to Gamma max When the strain is from γ to γ, the stress integral value along the strain direction consists of three parts: A1, B1 and C1 marked in red. A1 with a positive value is part of the hysteresis curve area, while B1 with a negative value and C1 with a positive value do not belong to a certain part of the area. max Move to Gamma min When , the value of the stress integrated along the strain also consists of three parts: A2, B2 and C2 marked in blue. Since the integral direction makes the increment negative, the stress is also negative, so the integral value A2 is positive and is part of the hysteresis curve area. B2 with a positive value and C2 with a negative value do not belong to the area. Since B1 and B2, C1 and C2 coincide, the sum of the integrals of the two parts A1+A2 is the deformation energy. The calculation process is as follows Figure 4 As shown. Among them, N is used to set the threshold value for the calculation process to enter the stable hysteresis curve. n means that the calculation process enters the nth hysteresis half curve.

[0052] In step 4, the square wave power consumption in DC aging is used as the simulation input, and the electrothermal model is established with the thermal impedance of the IGBT. According to the numerical calculation method of steps 1 to 3, the influence of the junction temperature fluctuation and the average junction temperature on the deformation energy is compared. The creep characteristics in the electrothermal model only consider the mid-term steady-state stage;

[0053] a. Influence of junction temperature fluctuation:

[0054] Under the same junction temperature fluctuation, the effect of average junction temperature on deformation energy is much smaller than that of junction temperature fluctuation. Under low junction temperature fluctuation, deformation energy increases with the increase of average junction temperature; under high junction temperature fluctuation, deformation energy decreases with the increase of average junction temperature.

[0055] b. Influence of average junction temperature:

[0056] Under low junction temperature fluctuations, the deformation energy increases with the increase of the average junction temperature; while under high junction temperature fluctuations, the deformation energy decreases with the increase of the average junction temperature.

[0057] The present invention provides a numerical calculation method for the deformation energy of the solder layer of a semiconductor power device, and the technical effects are as follows:

[0058] 1) In step 1 of the present invention, based on the stress reduction line, the stress of the component under the action of temperature is decomposed into an elastic-plastic component that is independent of time and only related to temperature, and a creep component that is related to both temperature and time, providing a basis for the numerical calculation of each stress in the solder layer deformation.

[0059] 2) Step 2 of the present invention provides a strain-stress numerical calculation process based on step 1 through a two-step method. Its characteristic is iterative calculation, that is, based on the temperature at the current moment and the stress and strain of the component at the previous moment, the stress and strain of the component at the current moment are discretely calculated, and the obtained steady-state stress-strain hysteresis curve provides data support for the calculation of deformation energy.

[0060] 3) Step 3 of the present invention provides a numerical calculation process of the deformation energy of the steady-state strain-stress hysteresis curve based on step 2. This method is based on the idea of ​​integration, takes the maximum value of strain as the boundary, and adopts a clockwise cumulative summation method to calculate the area contained in any closed-loop closed curve.

[0061] 4) In step 4 of the present invention, based on the proposed numerical calculation method for deformation energy, the characteristics of the stress-strain curve of the solder layer under temperature fluctuations and average temperature and the corresponding deformation energy change are discussed for the solder layer parts of the power semiconductor device that are prone to failure, and it is verified that the above temperature parameters are the main factors for the failure of the solder layer.

[0062] 5) It can be seen that the present invention can realize the extraction of device deformation energy under different conditions under common numerical calculation software, and provide a method for the numerical calculation of device solder layer deformation energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is the slope of the curve under different stress-strain states.

[0064] Figure 2 This is the flow chart of strain-stress calculation.

[0065] Figure 3 Schematic diagram of deformation energy calculation.

[0066] Figure 4 This is the flow chart of deformation energy calculation.

[0067] Figure 5 It is the stress-strain hysteresis curve of different junction temperature fluctuations when the square wave power consumption period is 50s, the duty cycle is 50%, and the average junction temperature is 50℃.

[0068] Figure 6It is the deformation energy curve under different junction temperature fluctuations and average junction temperature (the influence of temperature fluctuation).

[0069] Figure 7 It is the stress-strain hysteresis curve of different average junction temperatures when the square wave power consumption period is 50s, the duty cycle is 50%, and the junction temperature fluctuates at 50℃.

[0070] Figure 8 It is the deformation energy curve under different junction temperature fluctuations and average junction temperature (the influence of average junction temperature). DETAILED DESCRIPTION

[0071] Principle analysis:

[0072] Studying the stress-strain and deformation energy of an object under thermal load is the basis for evaluating the life of the object based on the energy-based life model. Since the solder layer is one of the most vulnerable components in the IGBT module package failure phenomenon, it can be used as a way to calculate the deformation energy in the energy-based life model. Taking the IGBT module as an example, the solder layer is the part most prone to fatigue failure. The stress it is subjected to mainly includes elastic, plastic and creep stresses, which can be expressed as elastic shear behavior based on Hooke's law, plastic strain model based on power law relationship and Darveaux's creep stress model.

[0073] A numerical calculation method for the deformation energy of the solder layer of a power electronic semiconductor power device, wherein:

[0074] In the numerical calculation method of stress-strain, the strain of the device solder layer involves elastic and plastic components related to temperature and stress, as well as creep components related to time. The basic idea of ​​this calculation method is: first, the elastic and plastic stress-stress components related only to temperature are obtained according to the elastic-plastic constitutive equations and stress-strain isotherms; then, the creep stress-stress components related to time are obtained according to the creep constitutive equations and stress-strain isotherms; finally, the sum of the elastic, plastic and creep stress-stress components is the stress-stress of the device solder layer. The basic process is: first, input the current calculated temperature and time, and extract the stress-stress of the solder layer calculated at the previous moment as an intermediate parameter; secondly, calculate the elastic and plastic stress-stress components at the current moment and current temperature respectively; then take the time step, current temperature and calculated elastic and plastic stress-stress components as input, calculate the creep stress-stress component, and finally, obtain the stress-stress of the solder layer at the current moment and current temperature.

[0075] The basic idea of ​​this method is to directly calculate the deformation energy based on the stress-strain of the solder layer of the device. The maximum and minimum strain values ​​are found according to the stress-strain hysteresis loop, and the closed-loop curve is accumulated and summed from the positive and negative directions to obtain the area formed by the stress-strain hysteresis loop and the deformation energy under the specified conditions. The basic process is:

[0076] Set the threshold for the calculation process to enter a stable hysteresis curve; initialize the calculation process; determine whether the maximum strain value is reached by reading the stress-stress of the solder layer; if the maximum value is reached, determine whether the hysteresis curve enters a stable threshold; if the conditions are met, calculate the energy increment based on the input data to obtain the deformation energy contained in the stress-strain hysteresis loop.

[0077] Example:

[0078] A numerical calculation method for deformation energy of a solder layer of a semiconductor power device comprises the following steps:

[0079] Step 1: Analyze the stress-strain characteristics of solder under thermal load and construct the constitutive equation;

[0080] Step 2: Calculate the stress-strain value of the solder layer of the semiconductor power device;

[0081] Step 3: Calculate the value of deformation energy according to the stress-strain of the solder layer of the semiconductor power device;

[0082] Step 4: Analyze the influence of different factors on deformation energy.

[0083] The step 1 comprises the following steps:

[0084] S1.1: Based on mechanical analysis, the two material components of the welded connection are simplified to a spring model:

[0085]

[0086] In the above formula: γ is strain; τ is shear stress; T and T0 are temperature and reference temperature respectively; K is the effective assembly stiffness determined according to the geometry of the solder joint; D is the temperature sensitivity of strain;

[0087] At a given temperature, solder stress and strain exist on a stress reduction line, with stress always tending toward zero.

[0088] S1.2: Based on Hooke's law, the elastic shear behavior is described as:

[0089]

[0090] In the above formula: γ eis the elastic strain; G(T) is the shear modulus, G(T) = G0-G1·(T-273), G0 and G1 are the shear modulus constant and the temperature sensitivity of the shear modulus at 0°C, respectively; T is the temperature in degrees Kelvin.

[0091] The time-independent plastic strain component is expressed as a power-law relation:

[0092]

[0093] In the above formula: γ p is the plastic strain; C P is the plastic strain coefficient; m p is the sensitivity of plastic strain.

[0094] S1.3: Construct Darveaux's constitutive solder model. Darveaux's constitutive solder model is a comprehensive model, including initial creep and steady-state creep processes, which is specifically expressed as follows:

[0095]

[0096] In the above formula: γ c is the initial creep strain component; t is time; γ T is the transient creep strain; B is the transient creep coefficient; γ s is the steady-state creep strain component; It indicates the dynamic change of transient creep of solder when it enters the steady-state creep stage;

[0097]

[0098] In the above formula: T represents Kelvin temperature; C1, α, n are constant coefficients of corresponding materials; k is Boltzmann constant; Q is creep activation energy;

[0099] In step 2, when the temperature is T1, it is known that the stress-strain state at time t is (γ1, τ1), where γ1 represents the strain at the current temperature T1; τ1 represents the stress at the temperature T1;

[0100] Through the above constitutive equations (2) to (5), under the assumption of a small time step Δt, the stress-strain state (γ2, τ2) at time t+Δt and temperature T2 is obtained, where γ2 represents the strain at temperature T2 and τ2 represents the corresponding stress. Specifically:

[0101] First, assuming that the time-independent elastic and plastic components are the main strain components, the stress occurs instantaneously when the temperature increases from T1 to T2 = T1 + ΔT; then, at temperature T2, the change in stress follows the T2 reduction line to calculate the creep strain component;

[0102] Step 2.1: Based on the elastic constitutive equation (2), when the stress increases, the increment of the elastic strain component is:

[0103]

[0104] In the above formula: Δγ e The increment of the elastic strain component; Δτ is the stress component.

[0105] According to the differential equation (3), the increment of the plastic strain component Δγ p for:

[0106]

[0107] According to the different behavior characteristics of elasticity and plasticity under reverse load, the slope of the stress-strain curve can be expressed by the stress-strain state, such as Figure 1 shown.

[0108] When the product of stress and stress increment is less than zero, the slope of the stress-strain curve is equal to the elastic modulus; when the product of the two is greater than zero, its slope consists of the elastic part and the plastic part.

[0109] Therefore, according to equations (6) and (7), the total increment Δγ of the elastic and plastic strain components is ep It is expressed as:

[0110] △γ ep =A·△τ ep (8);

[0111] Among them, Δγ ep is the total increment of the corresponding elastic-plastic stress component, and the coefficient A is:

[0112]

[0113] Where sgn(x) is the sign function; then the elastic-plastic strain component γ caused by temperature at temperature T2 is 12 is Δγ ep +γ1; elastic-plastic stress component τ caused by temperature at temperature T2 12 is Δτ ep +τ1.

[0114] According to formula (1), the stress reduction line can be used to characterize the relationship between stress and strain:

[0115]

[0116] Where ΔT is the temperature difference change, which is equal to T2-T1; then the combined equation (8) gives τ 12 and γ 12 for:

[0117]

[0118] Step 2.2: According to the creep behavior and stress reduction line, the stress tends to zero. The behavior of the creep component is related to the stress-strain state. When the stress state is positive, the strain increment is greater than zero; when the stress state is negative, the strain increment is less than zero. In addition, the primary creep eventually tends to be constant, and time will be the main part that causes steady-state creep. When only the steady-state creep component is considered, the increment of the creep component can be expressed as: Δγ c =S r ·Δt, where Δt represents the time from temperature T1 to temperature T2; Δγ c γ2-γ 12 , represents the change of creep strain component; S r As shown below:

[0119]

[0120] In the above formula: sgn(x) is the sign function; G(T2) is the shear modulus of the component at temperature T2; T represents the Kelvin temperature; C1, α, n are constant coefficients of the corresponding materials; k is the Boltzmann constant; Q is the creep activation energy;

[0121] Based on the stress reduction line, the relationship between creep stress and strain can be expressed as:

[0122] Where: Δτ c =τ2-τ 12 ,τ2=-K·S r ·△t+τ 12 ;γ2=S r ·△t+γ 12 .

[0123] Typically, a zero stress-strain state can be used for the initialization process. When calculating the stress-strain state (γ2, τ2), it can be used as the new initial value and the next stress-strain state can be calculated similarly. In order to clearly illustrate the stress-strain response under cyclic thermal loading, the calculation process is as follows Figure 2 shown.

[0124] In step 3, when the solder joint is subjected to cyclic heat load, after several cycles, a closed and stable irregular hysteresis curve can be obtained. The deformation energy is expressed as the area of ​​the hysteresis curve. To directly calculate the deformation energy using the hysteresis curve Figure 3 A schematic diagram for calculating deformation energy is given.

[0125] The stress-strain response moves clockwise under cyclic thermal loading, according to the material's behavior under reversed loading. The maximum and minimum strain values ​​γ can be foundmax and γ min When the strain changes from γ min Move to Gamma max When the strain is from γ to γ, the stress integral value along the strain direction consists of three parts: A1, B1 and C1 marked in red. A1 with a positive value is part of the hysteresis curve area, while B1 with a negative value and C1 with a positive value do not belong to a certain part of the area. max Move to Gamma min When , the value of the stress integrated along the strain also consists of three parts: A2, B2 and C2 marked in blue. Since the integral direction makes the increment negative, the stress is also negative, so the integral value A2 is positive and is part of the hysteresis curve area. B2 with a positive value and C2 with a negative value do not belong to the area. Since B1 and B2, C1 and C2 coincide, the sum of the integrals of the two parts A1+A2 is the deformation energy. The calculation process is as follows Figure 4 As shown. Among them, N is used to set the threshold value for the calculation process to enter the stable hysteresis curve. n means that the calculation process enters the nth hysteresis half curve.

[0126] In the step 4, the square wave power consumption in DC aging is used as the simulation input, and the thermal impedance of a certain type of IGBT of Fuji Electric is used to establish an electrothermal model. According to the numerical calculation method of steps 1 to 3, the influence of junction temperature fluctuation and average junction temperature on deformation energy is compared. The creep characteristics in the electrothermal model only consider the mid-term steady-state stage;

[0127] a. Influence of junction temperature fluctuation:

[0128] Figure 5 The stress-strain hysteresis curves of different junction temperature fluctuations are shown when the square wave power consumption cycle is 50s and the duty cycle is 50%, and the average junction temperature is 50℃. When the junction temperature fluctuation increases from 10℃ to 80℃, the area surrounded by stress and strain continues to increase, and the deformation energy continues to increase. The junction temperature fluctuation will cause fatigue degradation of the solder. The deformation energy under different junction temperature fluctuations and average junction temperature is shown in the attached figure. Figure 6 It can be seen that under the same junction temperature fluctuation, the effect of average junction temperature on deformation energy is much smaller than that of junction temperature fluctuation. Under low junction temperature fluctuation, deformation energy increases with the increase of average junction temperature; under high junction temperature fluctuation, deformation energy decreases with the increase of average junction temperature;

[0129] b. Influence of average junction temperature:

[0130] Figure 7 The stress-strain hysteresis curves at different average junction temperatures are shown when the square wave power consumption cycle is 50s and the duty cycle is 50%, and the junction temperature fluctuation is 50°C. Due to the creep behavior of the solder, under the same junction temperature fluctuation, as the average junction temperature increases, the stress of the hysteresis curve decreases and the strain increases. The deformation energy under different junction temperature fluctuations and average junction temperatures is shown in Figure 2. Figure 8Under low junction temperature fluctuation, the deformation energy increases with the increase of average junction temperature; while under high junction temperature fluctuation, the deformation energy decreases with the increase of average junction temperature.

Claims

1. A numerical calculation method for the deformation energy of the solder layer of a semiconductor power device, characterized in that The following steps are involved: Step 1: Analyze the stress-strain characteristics of solder under thermal load and construct the constitutive equation; Step 2: Calculate the stress-strain value of the solder layer of the semiconductor power device; Step 3: Calculate the value of deformation energy based on the stress-strain of the solder layer of the semiconductor power device.

2. The method for numerically calculating the deformation energy of the solder layer of a semiconductor power device according to claim 1, characterized in that: It also includes step 4: analyzing the influence of different factors on deformation energy.

3. The method for numerically calculating deformation energy of solder layer of semiconductor power device according to claim 1, characterized in that: The step 1 comprises the following steps: S1.1: Simplify the two-material components of the welded joint into a spring model: In the above formula: γ is strain; τ is shear stress; T and T0 are temperature and reference temperature respectively; K is the effective assembly stiffness determined according to the geometry of the solder joint; D is the temperature sensitivity of strain; At a given temperature, solder stress and strain exist on the stress reduction line, and the stress always tends to zero; S1.2: Based on Hooke's law, the elastic shear behavior is described as: In the above formula: γ e is the elastic strain; G(T) is the shear modulus, G(T) = G0-G1·(T-273), G0 and G1 are the shear modulus constant and the temperature sensitivity of the shear modulus at 0°C, respectively; T is the temperature in degrees Kelvin; The time-independent plastic strain component is expressed as a power-law relation: In the above formula: γ p is the plastic strain; C P is the plastic strain coefficient; m p is the sensitivity of plastic strain; S1.3: Construct the Darveaux constitutive solder model, including the initial creep and steady-state creep processes, as shown below: In the above formula: γ c is the initial creep strain component; t is time; γ T is the transient creep strain; B is the transient creep coefficient; γ s is the steady-state creep strain component; It indicates the dynamic change of transient creep of solder when it enters the steady-state creep stage; In the above formula: T represents Kelvin temperature; C1, α, n are constant coefficients of corresponding materials; k is Boltzmann constant; Q is creep activation energy.

4. The method for numerically calculating deformation energy of solder layer of semiconductor power device according to claim 3, characterized in that: In step 2, when the temperature is T1, it is known that the stress-strain state at time t is (γ1, τ1), where γ1 represents the strain at the current temperature T1; τ1 represents the stress at the temperature T1; Through the above constitutive equations (2) to (5), under the assumption of a small time step Δt, the stress-strain state (γ2, τ2) at time t+Δt and temperature T2 is obtained, where γ2 represents the strain at temperature T2 and τ2 represents the corresponding stress.

5. The method for numerically calculating deformation energy of solder layer of semiconductor power device according to claim 4, characterized in that: The steps include: Step 2.1: Based on the elastic constitutive equation (2), when the stress increases, the increment of the elastic strain component is: In the above formula: Δγ e The increment of the elastic strain component; Δτ is the stress component; According to the differential equation (3), the increment of the plastic strain component Δγ p for: According to the different behavior characteristics of elasticity and plasticity under reverse load, the slope of the stress-strain curve can be expressed by the stress-strain state; When the product of stress and stress increment is less than zero, the slope of the stress-strain curve is equal to the elastic modulus; when the product of the two is greater than zero, its slope consists of the elastic part and the plastic part; Therefore, according to equations (6) and (7), the total increment Δγ of the elastic and plastic strain components is ep It is expressed as: △γ ep =A·△τ ep (8); Among them, Δγ ep is the total increment of the corresponding elastic-plastic stress component, and the coefficient A is: Where sgn(x) is the sign function; then the elastic-plastic strain component γ caused by temperature at temperature T2 is 12 is Δγ ep +γ1; elastic-plastic stress component τ caused by temperature at temperature T2 12 is Δτ ep +τ1; According to formula (1), the stress reduction line can be used to characterize the relationship between stress and strain: Where ΔT is the temperature difference change, which is equal to T2-T1; then the combined equation (8) gives τ 12 and γ 12 for: Step 2.2: According to the creep behavior and stress reduction line, the stress tends to zero; the behavior of the creep component is related to the stress-strain state; when the stress state is positive, the strain increment is greater than zero; when the stress state is negative, the strain increment is less than zero; in addition, the primary creep eventually tends to be constant, and time will be the main part that causes steady-state creep; when only the steady-state creep component is considered, the increment of the creep component can be expressed as: Δγ c =S r ·Δt, where Δt represents the time from temperature T1 to temperature T2; Δγ c γ2-γ 12 , represents the change of creep strain component; S r As shown below: In the above formula: sgn(x) is the sign function; G(T2) is the shear modulus of the component at temperature T2; T represents the Kelvin temperature; C1, α, n are constant coefficients of the corresponding materials; k is the Boltzmann constant; Q is the creep activation energy; Based on the stress reduction line, the relationship between creep stress and strain can be expressed as: Among them: Dt c For τ2-τ 12 ,τ2=-K·S r ·△t+τ 12 ;γ2=S r ·△t+γ 12 ; The zero stress-strain state can be used for the initialization process; it can be used as the new starting value when calculating the stress-strain state (γ2,τ2).

6. The method for numerically calculating deformation energy of solder layer of semiconductor power device according to claim 1, characterized in that: In step 3, when the solder joint is subjected to cyclic heat load, a closed and stable irregular hysteresis curve can be obtained after several cycles; the deformation energy is expressed as the area of ​​the hysteresis curve.

7. A numerical calculation method for deformation energy of a solder layer of a semiconductor power device according to claim 6, characterized in that: According to the material behavior under reversed loading, the stress-strain response moves clockwise under cyclic thermal loading; the maximum and minimum strain values ​​γ can be found max and γ min ; When the strain changes from γ min Move to Gamma max When the strain direction is γ, the stress integral value along the strain direction consists of three parts: A1, B1 and C1 marked in red; A1 with a positive value is part of the hysteresis curve area, while B1 with a negative value and C1 with a positive value do not belong to a certain part of the area; when the strain changes from γ max Move to Gamma min , the value of the stress integrated along the strain also consists of three parts: A2, B2 and C2 marked in blue; because the integral direction makes the increment negative, the stress is also negative, so the integral value A2 is positive and is part of the hysteresis curve area. B2 with a positive value and C2 with a negative value do not belong to the area; because B1 and B2, C1 and C2 coincide, the sum of the integrals of the two parts A1+A2 is the deformation energy.

8. The method for numerically calculating deformation energy of solder layer of semiconductor power device according to claim 2, characterized in that: In step 4, the square wave power consumption in DC aging is used as the simulation input, and the electrothermal model is established based on the thermal impedance of the IGBT. According to the numerical calculation method of steps 1 to 3, the influence of the junction temperature fluctuation and the average junction temperature on the deformation energy is compared: a. Influence of junction temperature fluctuation: Under the same junction temperature fluctuation, the effect of average junction temperature on deformation energy is much smaller than that of junction temperature fluctuation; under low junction temperature fluctuation, deformation energy increases with the increase of average junction temperature; Under high junction temperature fluctuations, the deformation energy decreases as the average junction temperature increases; b. Influence of average junction temperature: Under low junction temperature fluctuations, the deformation energy increases with the increase of the average junction temperature; while under high junction temperature fluctuations, the deformation energy decreases with the increase of the average junction temperature.

9. A numerical calculation method for stress-strain of solder layer of semiconductor power device, characterized by: The strain of the device solder layer involves elastic and plastic components related to temperature and stress, as well as creep components related to time. First, input the current calculated temperature and time, and extract the stress-stress of the solder layer calculated at the last moment as an intermediate parameter. Secondly, the elastic and plastic stresses-stress components at the current time and temperature are calculated respectively; Then the time step, current temperature and calculated elastic and plastic stress-stress components are taken as input to calculate the creep stress-stress components. Finally, the stress-stress of the solder layer at the current time and temperature is obtained.

10. A method for directly calculating the value of deformation energy based on the stress-strain of the solder layer of a semiconductor power device, characterized in that: Set the threshold for the calculation process to enter a stable hysteresis curve; initialize the calculation process; By reading the stress-stress of the solder layer, it is determined whether the maximum strain value has been reached; If the maximum value is reached, determine whether the hysteresis curve has entered the stable threshold; If the conditions are met, the energy increment is calculated based on the input data to obtain the deformation energy contained in the stress-strain hysteresis loop.

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