Simulation analysis method for multi-physics coupling performance of flexible electronic device

Abstract

The invention provides a flexible electronic device multi-physics field coupling performance simulation analysis method, and relates to the technical field of flexible electronics. Firstly, a geometric model of the flexible electronic device is constructed; the geometric model comprises a three-layer assembly structure of an electronic chip, an adhesive layer and a flexible PCB layer, and an interconnection structure; setting electromagnetic-thermal-mechanical field coupling parameters of the geometric model; then, grid division is conducted on the geometric model through a finite element method, and the grid division precision of the area where the interconnection structure is located is higher than that of other areas; building a multi-physics field coupling model according to the geometric model and set coupling parameters; applying load and boundary conditions to the model, wherein the load and boundary conditions comprise a current source, a heat generation load, a convection heat dissipation boundary condition and a mechanical constraint condition; and simulating the working state of the flexible electronic device under the action of multi-physics field coupling in the multi-physics field coupling model to obtain a simulation result. According to the method, the performance and the failure mechanism of the flexible electronic device under the multi-physics field coupling effect can be effectively predicted.

Description

Technical Field

[0001] The present invention belongs to the technical field of flexible electronics, and specifically relates to a method for simulating and analyzing the multi-physical field coupling performance of flexible electronic devices. Background Art

[0002] With the rapid development of flexible electronics technology, flexible electronic devices have been widely used in fields such as wearable devices, intelligent sensors, and flexible displays. Flexible electronic devices usually consist of electronic chips, adhesive layers, and flexible PCB layers, and achieve electrical connection through interconnect structures (such as bumps, filling adhesives, or solders). However, flexible electronic devices face complex multi-physical field coupling problems in practical applications, such as the interaction of electric fields, thermal fields, and mechanical fields, and these coupling effects have a significant impact on their performance and reliability.

[0003] The existing technology for analyzing the performance of flexible electronic devices mainly relies on experimental tests and single-physical field analysis. Experimental tests are difficult to implement under the coupling action of multiple physical fields, and it is difficult to accurately measure multiple physical quantities. Traditional single-physical field analysis methods cannot comprehensively reflect the complex behavior of flexible electronic devices under actual working conditions, especially when the multi-physical field coupling effect is significant. For example, the Joule heating effect generated under the action of an electric field will cause the temperature to rise, which in turn affects the mechanical properties and electrical characteristics of the material; while the thermal expansion or contraction caused by temperature changes will generate thermal stress, further affecting the mechanical stability of the device.

[0004] In addition, the interconnect structures of flexible electronic devices usually use heterogeneous materials, and their geometric characteristics have large non-uniformities, which are prone to becoming stress concentration regions and key parts of failure. Therefore, traditional analysis methods cannot effectively predict the performance and failure mechanism of flexible electronic devices under the coupling action of multiple physical fields, and it is difficult to meet the requirements of design optimization and reliability assessment of flexible electronic devices. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the technical problem to be solved by the present invention is to provide a method for simulating and analyzing the multi-physical field coupling performance of flexible electronic devices.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A method for simulating and analyzing the multi-physical field coupling performance of flexible electronic devices, comprising the following steps:

[0008] Step 1: Construct a geometric model of the flexible electronic device, and the geometric model includes an electronic chip, an adhesive layer, a flexible PCB layer, and an interconnect structure;

[0009] Step 2: Set the electromagnetic-thermal-mechanical field coupling parameters of the geometric model, including the mechanical parameters, electrical parameters, and thermal parameters of the material; the mechanical parameters include the elastic modulus and Poisson's ratio, the electrical parameters include the conductivity, and the thermal parameters include the thermal conductivity and the coefficient of thermal expansion;

[0010] Step 4: Build a multi-physical field coupling model according to the geometric model and the electromagnetic-thermal-mechanical field coupling parameters; the multi-physical field coupling model includes an electrostatic field model, a solid heat transfer model, and a solid mechanics model, and simultaneously considers the electromagnetic-thermal coupling characteristics and the electromagnetic-thermal-mechanical coupling characteristics;

[0011] Step 6: Apply loads and boundary conditions to the multi-physical field coupling model, including current sources, heat generation loads, convective heat dissipation boundary conditions, and mechanical constraint conditions;

[0012] Step 6: Simulate the working state of the flexible electronic device under the action of multi-physical field coupling in the multi-physical field coupling model to obtain the simulation results.

[0013] Further, the current continuity equation of the electrostatic field model is:

[0014]

[0015] where φ is the electric potential, Γ D is the Dirichlet boundary, is the electric potential on the Dirichlet boundary, ρ E (t) is the charge density, is the rate of change of the charge density with time, ▽·(σ▽φ) is the divergence of the current density, ▽ is the gradient operator, and σ is the conductivity;

[0016] The relationship between the heat flux density and the temperature gradient of the solid heat transfer model is shown by the following formula:

[0017]

[0018] where q x , q y , and q z are the heat flux densities in the x, y, and z directions respectively, λ is the thermal conductivity of the material, respectively represent the temperature gradients in the x, y, and z directions, and T is the temperature;

[0019] The solid mechanics model is: when the temperature changes, the material will generate strain due to thermal expansion or contraction, and the thermal strains in the length and diameter directions are expressed as:

[0020]

[0021] where ε lis the thermal strain in the length direction, ε d is the thermal strain in the diameter direction, α t is the coefficient of thermal expansion of the material, t1 is the current temperature, t0 is the reference temperature, Δl and Δd are the thermal expansion amounts in the length and diameter directions respectively;

[0022] The relationship between stress and strain is shown in the following formula:

[0023] s - s0 = C:(ε - ε0 - ε inel )(15)

[0024] In the formula, s is the stress tensor, s0 is the initial stress, ε0 is the initial strain, ε inel is the final strain, C is the elastic tensor, is the strain tensor, is the displacement gradient.

[0025] Furthermore, the electromagnetic-thermal coupling characteristics are described by the following formula:

[0026] p = |J| 2 / σ (16)

[0027] In the formula, p is the Joule heat power density, J is the current density;

[0028] The electromagnetic-thermal-mechanical coupling characteristics are described by the following formula:

[0029]

[0030] In the formula, σ ij is the stress tensor, is the externally applied force, u i is the displacement vector, μ D is the damping coefficient, ∈ ij is the strain tensor, is the elastic strain component, is the thermal strain component, is the elastic stress part in the stress tensor, D ijkl is the fourth-order elastic tensor, is the elastic strain in other directions, ΔT is the temperature change, α is the coefficient of thermal expansion, δ ij is the Kronecker delta function, is the displacement value set on the Dirichlet boundary, is the stress boundary Γ σ is the stress value applied on it, is the stress on the boundary Γ σ on it.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] By constructing a geometric model of a flexible electronic device, setting the electromagnetic-thermal-mechanical fields of the geometric model, building a multi-physics field coupling model based on the constructed geometric model and the set coupling parameters, and applying corresponding loads and boundary conditions in the model, the complex behavior of the flexible electronic device under the coupling action of multi-physics fields can be comprehensively considered, and its performance can be analyzed comprehensively and accurately, providing an effective technical means for the design optimization and reliability evaluation of flexible electronic devices. Description of the Drawings

[0033] Figure 1 is the overall flowchart;

[0034] Figure 2 is the geometric model diagram of the flexible electronic device;

[0035] Figure 3 is the dimension diagram of the geometric model;

[0036] Figure 4 is the dimension diagram of the interconnect structure;

[0037] Figure 5 is the diagram showing the relationship between the Young's modulus of the polyimide material and temperature;

[0038] Figure 6 is the diagram showing the relationship between the Young's modulus of the underfill and temperature;

[0039] Figure 7 is the diagram showing the relationship between the Poisson's ratio of the polyimide material and temperature;

[0040] Figure 8 is the diagram showing the relationship between the Poisson's ratio of the underfill and temperature;

[0041] Figure 9 is the mesh division result diagram of the geometric model;

[0042] Figure 10 is the schematic diagram of the charge density distribution of the interconnect structure;

[0043] Figure 11 is the schematic diagram of the current density distribution of the interconnect structure;

[0044] Figure 12 is the schematic diagram of the electric potential density distribution of the interconnect structure;

[0045] Figure 13 is the schematic diagram of the temperature distribution of the flexible electronic device;

[0046] Figure 14 is the schematic diagram of the cut-off point position;

[0047] Figure 15 is the schematic diagram of the electric potential and temperature changes at the cut-off point;

[0048] Figure 16 It is a schematic diagram of the temperature change at the cut-off point when considering and not considering the material temperature change;

[0049] Figure 17 It is a schematic diagram of the von Mises stress and volume strain at the cut-off point changing with temperature. Specific implementation manners

[0050] The following provides specific embodiments in conjunction with the attached drawings. The specific embodiments are only used to introduce the technical solutions of the present invention in detail and do not limit the protection scope of this application.

[0051] The present invention provides a simulation analysis method for the multi-physical field coupling performance of flexible electronic devices, including the following steps:

[0052] Step 1: Construct a geometric model of the flexible electronic device, and the geometric model includes an electronic chip, an adhesive layer, a flexible PCB layer, and an interconnection structure.

[0053] In this step, three-dimensional modeling technology can be used to construct a geometric model based on the actual flexible electronic manufacturing technology. For example, a software tool (such as COMSOL Multiphysics) can be used for modeling, and the influence of different processes on the geometric structure can be considered during the modeling process; for example, a three-layer component structure composed of an adhesive layer, an electronic chip, and a flexible PCB layer is constructed, and its geometric model is shown in Figure 2 , the geometric model includes underfill (i.e., the adhesive layer), an ultra-thin chip (i.e., the electronic chip), contact pads (for connecting the chip and the flexible PCB, i.e., the interconnection structure), conductive bumps (i.e., the adhesive layer), and FPCB (that is, the flexible PCB layer). The dimensions of the geometric model are shown in Figure 3 , the chip size can be 4 mm × 4 mm × 0.05 mm, the flexible PCB size can be 35 mm × 35 mm × 0.055 mm, and the thickness between the two can be 0.035 mm.

[0054] The geometric characteristics of the interconnection structure (such as bumps, filling glue, or solder, etc.) are also finely modeled to ensure the accuracy of the model. The interconnection structure in the flexible electronic device is the main component that bears deformation and is very fragile. Therefore, the failure of the flexible PCB interconnection is the key factor for the failure of electronic devices and is also the main object of simulation. The model of the interconnection structure is shown in Figure 4 , the diameter of the chip-side pad is 24 μm and the thickness is 8 μm, the diameter of the flexible PCB-side pad is 50 μm and the thickness is 8 μm, and the diameter of the bump is 45 μm and the thickness is 35 μm.

[0055] Step 2: Set the electromagnetic-thermal-mechanical field coupling parameters of the geometric model;

[0056] In this step, the coupling parameters include the mechanical parameters of the material (such as elastic modulus, Poisson's ratio), electrical parameters (such as conductivity), and thermal parameters (such as thermal conductivity, coefficient of thermal expansion); Table 1 gives the electrical, thermal, and mechanical parameters of some materials.

[0057] Table 1 Electrical, Thermal, and Mechanical Parameters of Materials

[0058]

[0059] Figure 5 It shows the relationship between the Young's Modulus of Polyimide (PI for short) material and temperature. The Young's Modulus is an important parameter to measure the rigidity of a material, indicating the ability of the material to resist deformation in the elastic deformation stage. Generally, as the temperature increases, the Young's Modulus of the material decreases, indicating a weakening of the material's rigidity. In flexible electronic devices, polyimide is often used as a flexible substrate material.

[0060] Figure 6 It shows the relationship between the Young's Modulus of the die bond adhesive and temperature. The die bond adhesive is usually used for filling between the chip and the flexible PCB, playing the roles of mechanical support and heat conduction. This figure reflects the change of the Young's Modulus of the filling adhesive material in the temperature range from 0°C to 350°C. Similar to polyimide, the Young's Modulus of the filling adhesive also decreases with the increase of temperature. In the multi-physical field coupling analysis, the change of the Young's Modulus of the filling adhesive will affect the overall mechanical properties of the flexible electronic device, especially the mechanical stability when the temperature changes. For example, the decrease of the Young's Modulus may cause the device to be more prone to deformation or failure at high temperatures.

[0061] Figure 7 It shows the relationship between the Poisson's Ratio of polyimide material and temperature. The Poisson's Ratio is a parameter to measure the relationship between the transverse deformation and the longitudinal deformation of a material when it is stressed. When the material is under tension, the Poisson's Ratio represents the ratio of transverse contraction to longitudinal elongation. This figure shows the change of the Poisson's Ratio of polyimide material in the temperature range from 0°C to 350°C. The change of the Poisson's Ratio will affect the deformation behavior of the material under multi-axial stress conditions. In flexible electronic devices, the change of the Poisson's Ratio of polyimide needs to be considered in the mechanical analysis, especially when analyzing the deformation and reliability of the device under complex stress conditions.

[0062] Figure 8Shows the relationship between the Poisson's ratio of the underfill and temperature. Similar to polyimide, the Poisson's ratio of the underfill also reflects the relationship between its transverse and longitudinal deformations when stressed. This figure shows the change in the Poisson's ratio of the underfill material in the temperature range from 0 °C to 350 °C. In flexible electronic devices, the change in the Poisson's ratio of the underfill will affect its mechanical behavior during temperature changes. For example, during thermal expansion or contraction, the change in the Poisson's ratio may lead to uneven stress distribution between the underfill and surrounding materials (such as chips or flexible PCBs), thereby affecting the reliability of the device.

[0063] Step 3: Mesh the geometric model in the finite element analysis software; among them, the meshing accuracy of the area where the interconnect structure is located is higher than that of the remaining areas;

[0064] Use finite element analysis software (such as COMSOL Multiphysics) to mesh the geometric model. During the establishment of the geometric model, special attention should be paid to the interconnect area between the chip and the flexible PCB. This area usually uses heterogeneous materials to connect to each other, and the geometric characteristics have large non-uniformities. For example, the bump material has a low resistivity, but its mechanical strength is usually poor and it is easy to crack or peel in the stress concentration area; while the underfill material has a high mechanical strength, but its conductivity is not as good as that of the solder joint material, which is easy to cause excessive concentration of local current density; therefore, refine the mesh of the interconnect area where the interconnect structure is located to improve the accuracy of the model. Specifically, a multi-scale modeling method can be adopted to establish independent local models for different areas of the interconnect interface respectively, and the average element quality reaches 0.635. This refined meshing technology can ensure the description ability of local complex areas and meet the needs of flexible electronic multi-physics field simulation. The schematic diagram of the meshing is as Figure 9 shown.

[0065] Step 4: Build a multi-physics field coupling model based on the constructed geometric model and the set coupling parameters;

[0066] In this step, in the simulation software, combine the geometric model and parameters to build a multi-physics field coupling model; the multi-physics field coupling model includes an electrostatic field model, a solid heat transfer model, and a solid mechanics model, etc. The coupling relationship between each physical field can also be considered during the building process.

[0067] The electrostatic field model (the current module is a steady-state DC model, solving the time-varying electromagnetic field distribution), the solid heat transfer model (based on the three-dimensional isotropic heat conduction differential equation), and the solid mechanics model (considering the strain and stress caused by thermal expansion) together constitute the multi-physics field coupling model, which is used to analyze the performance of flexible electronic devices under the coupling action of multi-physics fields.

[0068] The current continuity equation of the electrostatic field model is:

[0069]

[0070] In the formula, φ is the electric potential, and Γ D is the Dirichlet boundary, is the electric potential on the Dirichlet boundary, and ρ E (t) is the charge density, is the rate of change of the charge density with time, ▽·(σ▽φ) is the divergence of the current density, ▽ is the gradient operator, and σ is the conductivity.

[0071] The current continuity equation is used to describe the distribution law of the current in the electric field. By solving this equation, the current density distribution and the electric potential distribution inside the flexible electronic device can be obtained. It can be known through simulation that the current flows from the chip end to the ground plane of the flexible PCB end, the current density is concentrated at the contact position between the chip end pad and the bump, and the charge density distribution is shown in Figure 10 , and the current density distribution is shown in Figure 11 , and the electric potential density distribution is shown in Figure 12 .

[0072] The relationship between the heat flux density and the temperature gradient of the solid heat transfer model is shown in Equation (2):

[0073]

[0074] In the formula, q x , q y , and q z are the heat flux densities in the x, y, and z directions respectively, λ is the thermal conductivity of the material, represent the temperature gradients in the x, y, and z directions respectively, and T is the temperature;

[0075] Assume that the heat flow rate flowing into the left side of the microelement along the x direction is Φ x , and the area of the left side is dydz, then its heat flux density is expressed as:

[0076]

[0077] Therefore, the heat flow rate Φ x+dx flowing out of the right side of the microelement, and the area of the right side is also dydz, then its heat flux density is expressed as:

[0078]

[0079] Then, the net heat flow rate ΔΦ x obtained by the microelement in the x direction is calculated by the following formula:

[0080]

[0081] where \(dxdydz\) is the volume of the infinitesimal element;

[0082] Similarly, the net heat fluxes obtained by the infinitesimal element in the \(y\) and \(z\) directions are respectively:

[0083]

[0084] The change in the internal energy of the infinitesimal element depends on its mass, specific heat capacity, and the rate of change of temperature with time, which is expressed mathematically as:

[0085]

[0086] where \(\Delta U\) is the change in the internal energy of the infinitesimal element, \(\rho\) is the density, \(c\) is the specific heat capacity, and \(t\) is the time;

[0087] According to the law of conservation of energy, the net heat obtained by the infinitesimal element is equal to the increase in the internal energy of the infinitesimal element with time; the total net heat flux \(\Delta\varPhi\) obtained by the infinitesimal element per unit time is the sum of the net heat fluxes in the three directions, so there is:

[0088] \(\Delta\varPhi=\Delta\varPhi\) x +\(\Delta\varPhi\) y +\(\Delta\varPhi\) z (9)

[0089] From the law of conservation of energy, the general form of the transient heat conduction differential equation can be obtained as:

[0090]

[0091] In the multi - physical coupling analysis of surface - mounted integrated circuits on flexible PCBs, the materials are all isotropic, that is, the thermal conductivity \(\lambda\) is set as a constant, then the unsteady heat conduction differential equation can be obtained as shown in the following equation (11);

[0092]

[0093] When the volume of the infinitesimal element is extremely small, its density and the heat generation per unit volume are constant, then the mass and heat of the infinitesimal element are expressed as:

[0094] \(m = \rho V=\rho\Delta x\Delta y\Delta z\) (12)

[0095] \(G = gV = g\Delta x\Delta y\Delta z\) (13)

[0096] where \(m\) is the mass of the infinitesimal element, \(V\) is the volume of the infinitesimal element, \(\Delta x\), \(\Delta y\), \(\Delta z\) respectively represent the infinitesimal length elements in the \(x\), \(y\), \(z\) directions, \(G\) is the heat of the infinitesimal element, and \(g\) is the heat generated per unit volume.

[0097] In this embodiment, it is assumed that the initial temperature of the model and the ambient reference temperature are both T = 293.15 K, that is, the room temperature is 20 °C. When the flexible electronics generate heat, they will dissipate heat to the surrounding air. However, the space around the flexible electronics is large, and the change in the ambient reference temperature caused by the ultra-thin chip energized and heated is extremely small and can be ignored. The heat dissipation of the flexible electronics to the air is called convective heat dissipation, and the heat dissipation process can be considered a boundary condition of heat conduction. According to the above differential function, iterative calculations are performed to obtain the temperature distribution of the integrated circuit surface-mounted on the flexible PCB, as shown in Figure 13 shown. In practical applications, flexible electronic devices are usually regarded as isotropic materials, so a three-dimensional isotropic heat conduction differential equation is used for modeling. By solving this equation, the temperature distribution and heat flux density distribution inside the flexible electronic device can be obtained.

[0098] The solid mechanics model is as follows: When the temperature changes, the material will generate strain due to thermal expansion or contraction. The thermal strains in the length and diameter directions are expressed as:

[0099]

[0100] In the formula, ε l is the thermal strain in the length direction, ε d is the thermal strain in the diameter direction, α t is the thermal expansion coefficient of the material, t1 is the current temperature, t0 is the reference temperature, and Δl and Δd are the thermal expansion amounts in the length and diameter directions respectively;

[0101] The relationship between stress and strain is shown in the following formula:

[0102] s - s0 = C:(ε - ε0 - ε inel )(15)

[0103] In the formula, s is the stress tensor, s0 is the initial stress, ε0 is the initial strain, ε inel is the final strain, C is the elastic tensor, is the strain tensor, is the displacement gradient.

[0104] In this embodiment, the flexible electronic device will generate thermal strain and thermal stress when the temperature changes, and these stresses will affect the mechanical properties and reliability of the device. For example, in the simulation, the Young's modulus and Poisson's ratio of polyimide (PI) and underfill change with temperature. By introducing the relationship between thermal strain and stress, the mechanical response of the flexible electronic device under temperature change can be analyzed. This embodiment provides an important basis for studying the mechanical properties and reliability of the device, and helps to predict and prevent failure problems caused by thermal stress.

[0105] Step Five: Apply loads and boundary conditions to the multi-physical field coupling model;

[0106] The load and boundary conditions include current sources, heat generation loads, convective heat dissipation boundary conditions, and mechanical constraint conditions. The parameters of the load and boundary conditions can be set according to the actual working conditions. The load and boundary conditions in this embodiment are as follows:

[0107] Current source: A current of 1 A flows through the conducting pin.

[0108] Heat generation load: Assuming the chip power is 1 W, the heat generation rate is calculated to be 62500 W / m 2 ;

[0109] Convective heat dissipation boundary condition: The surface heat transfer coefficient is 10 W / (m 2 ·K), and the external temperature is 25 °C.

[0110] Mechanical constraint condition: Fixed constraints are applied to the four corners at the bottom of the flexible PCB.

[0111] Step 6: Simulate the working state of the flexible electronic device under the action of multi-physical field coupling in the multi-physical field coupling model to obtain the simulation results;

[0112] In this step, use finite element analysis software for iterative solution to simulate the working state of the flexible electronic device under the action of multi-physical field coupling and output the simulation results. The simulation results can include the distribution of electric field, temperature field, stress field, etc.

[0113] Specifically, for example, through finite element analysis software, the current density distribution and electric potential distribution of the flexible electronic device under the action of a current source can be simulated: In the interconnect structure of the flexible electronic device, the current flows from the chip end to the flexible PCB ground plane. Through simulation, it can be observed that the current density is concentrated at the contact position between the chip end pad and the bump (as Figure 11 shown). This current density distribution reflects the electric field state of the device during operation, helps analyze the current conduction path and possible electrical failure points. The simulation can also calculate the electric potential distribution in different regions to verify the uniformity or non-uniformity of the electric field, thereby evaluating the electrical performance of the device.

[0114] Simulate the heat distribution, temperature field, and heat dissipation path generated during the operation of the flexible electronic device: When the chip is powered on and generates heat, the simulation can calculate the temperature distribution inside and around the chip (as Figure 13 shown). For example, when the chip power is 1 W, the heat generation rate calculated by the power and chip area is 62500 W / m 2 , and the simulation results show that the temperature in the heat source area is relatively high and gradually decreases towards the surrounding. Calculate the relationship between the heat flux density and the temperature gradient through Fourier's law of heat conduction, observe the heat conduction path from the high-temperature region to the low-temperature region, and analyze the heat dissipation efficiency and thermal management performance.

[0115] Simulate the stress and strain distributions generated in flexible electronic devices under the coupling action of multiple physical fields, and evaluate their mechanical stability: When the temperature changes, due to the different thermal expansion coefficients of different materials, thermal stress will be generated in flexible electronic devices. The simulation can calculate the stress distribution inside the device, such as the stress concentration areas at the interconnect structure and the flexible PCB interface. By analyzing the stress and strain distributions, potential mechanical failure points during device operation can be predicted, such as solder joint cracking and interconnect structure peeling.

[0116] Analyze the failure mechanism of flexible electronic devices under the coupling action of electro-thermal-mechanical multiple physical fields: In the case where there are defects in the interconnect structure (such as mounting voids or misalignments), the simulation can simulate the impact of these defects on device performance. For example, mounting voids will lead to uneven current density distribution and local temperature rise, which will accelerate the mechanical failure of materials. For interconnect misalignment, the simulation can analyze its impact on electrical connection performance, such as increased contact resistance and signal transmission interruption, and at the same time, the mechanical stress changes caused by misalignment can also be observed.

[0117] Simulate the response of flexible electronic devices under dynamic operating conditions, such as their performance under different operating frequencies or temperature changes: At low operating frequencies (such as 125 kHz), the simulation can analyze the electromagnetic compatibility issues of flexible electronic devices and identify the impact of low-frequency interference on device performance. During the temperature change process, the dynamic response of the device can be observed through simulation, such as the impact of changes in material parameters (such as conductivity and Young's modulus) on device performance when the temperature rises.

[0118] In this embodiment, a geometric model of the flexible electronic device is constructed, the parameters of the geometric model are set, and based on the constructed geometric model and the set parameters, a multi-physical field coupling model is built. By applying corresponding loads and boundary conditions in the multi-physical field coupling model, the complex behavior of the flexible electronic device under the coupling action of multiple physical fields can be comprehensively considered, and its performance can be analyzed comprehensively and accurately, providing an effective technical means for the design optimization and reliability evaluation of flexible electronic devices.

[0119] The multi-physical field coupling model also includes electro-magnetic-thermal coupling characteristics, which are used to analyze the Joule heat effect generated when current passes through a conductor in a flexible electronic device and the impact of temperature change on conductivity; the electro-magnetic-thermal coupling characteristics involve the Joule heat power density generated when current passes through a conductor as shown in Equation (16):

[0120] p = |J| 2 / σ (16)

[0121] In the formula, p is the Joule heat power density and J is the current density.

[0122] In this embodiment, when actually solving the multi-physical field coupling problem, different coupling relationships need to be considered. According to the coupling interaction relationship, the coupling relationship can be divided into unidirectional coupling and bidirectional coupling. The multi-physical field finite element model of the flexible PCB surface-mounted integrated circuit mainly includes the coupling relationships among the mechanical field, the electric field, and the temperature field. The main physical phenomena among them are the electro-thermal effect, thermal stress, and thermal expansion. The coupling effects among these physical fields will affect the material parameters, physical field variables, and calculation results in each single physical field. According to the position where the current density is concentrated in the simulation results, cut-off points are selected in the flexible electronic interconnection structure, such as Figure 14 the cut-off point position in, to study the mechanism of the multi-physical field coupling effect and analyze the reasons for the deformation failure of the flexible interconnection structure.

[0123] When the flexible electronic device is working, current will flow through the conductor interconnection structure, and the work done by the current is converted into heat energy, which causes the temperature of the flexible electronics to rise. Due to the uneven temperature distribution and the thermal expansion mismatch of different material structures, thermal strain and thermal stress will be generated in the flexible electronics, thus affecting the fatigue performance of the flexible electronics. In fact, the electro-thermal effect is the main reason for the multi-physical field interaction in the flexible electronics. In order to analyze the influence of the multi-physical field interaction on the reliability of the flexible electronics, it is first necessary to conduct an in-depth analysis of the electro-thermal effect of the flexible structure. Therefore, in this section, by applying a current load to the flexible electronics in the multi-physical field finite element model, the electro-thermal effect is generated in the conductor, and the current density distribution and temperature distribution in the structure are calculated, and the influence of the electro-thermal effect on the physical properties and reliability of the flexible PCB surface-mounted integrated circuit structure is analyzed.

[0124] First, the electro-thermal performance results of the flexible electronics in the multi-physical field coupling process are obtained as Figure 15 shown, which shows the variation of the electric potential and temperature with the progress of time. The change of the electromagnetic field is at the microsecond level or even shorter, and in the transient simulation results, the electric potential and temperature change in the same trend within 300 ms, and the electric potential and temperature stop changing at the same time node of 260 ms. This is because there is a bidirectional coupling relationship between the electric field (current field) and the temperature field in the flexible electronic structure. In the electro-thermal bidirectional coupling process, the interconnection structure is regarded as a pure resistive conductor. According to Joule's law, all the work done by the current is converted into heat. According to the heat conduction law, the Joule heat acts as a heat source to cause the temperature of the flexible structure to rise, thus forming a temperature field in the flexible electronics. When the signal exists in the internal interconnection structure of the electronics, the Joule heat power density generated by it can be expressed by the above formula (18).

[0125] Since the resistivity of the interconnection conductor has an obvious temperature dependence, the temperature change will change the resistivity of the conductor, affect the current density distribution of the conductor, and thus affect the electric field in the flexible electronics. Therefore, in Figure 15Among them, the electric potential is affected by temperature and changes with temperature. To further reflect the difference between electro-thermal bidirectional coupling and unidirectional coupling, within 0 - 100 ms with a sharp temperature rise, the cases of considering and not considering material temperature change were calculated for the flexible electronic model respectively, as Figure 16 shown. The temperature at the cut-off point rises with the occurrence of electro-thermal coupling. As can be seen from Figure 16 , there are differences in the response results between considering and not considering the temperature change characteristics of the material. In particular, the conductivity of the material decreases with the increase of temperature, and the reduction of the conductivity ability leads to a more intense Joule heat effect. Therefore, as time goes by, with heat accumulation and temperature increase, the temperature difference between the two cases becomes larger. This result also proves the effectiveness of the simulation modeling of the electromagnetic-thermal bidirectional coupling effect.

[0126] In flexible electronic devices, Joule heat is generated when current passes through a conductor. This thermal effect will cause the temperature to rise, which in turn affects the conductivity of the material. For example, in the simulation, the Joule heat power density generated when current passes through the interconnect structure can be used as a heat source to cause the temperature of the device to rise. Considering the electromagnetic-thermal coupling characteristics can analyze the Joule heat effect generated when current passes through a conductor in a flexible electronic device and the influence of temperature change on conductivity, providing theoretical support for a deeper understanding of the interaction between the electric field and the thermal field, and further improving the comprehensiveness and accuracy of the simulation analysis.

[0127] The multi-physics field coupling model also includes electromagnetic-thermal-mechanical coupling characteristics for analyzing the thermal stress caused by temperature change in flexible electronic devices; the calculation formula for thermal stress is as follows:

[0128]

[0129] In the formula, σ ij is the stress tensor, is the externally applied force, u i is the displacement vector, μ D is the damping coefficient, ∈ ij is the strain tensor, is the elastic strain component, is the thermal strain component, is the elastic stress part in the stress tensor, D ijkl is the fourth-order elastic tensor, is the elastic strain in other directions, ΔT is the temperature change, α is the thermal expansion coefficient, δ ij is the Kronecker delta function, is the displacement value set on the Dirichlet boundary, is the stress value applied on the stress boundary Γ σ , is the stress value applied on the boundary Γ σThe stress on

[0130] In this embodiment, due to the different coefficients of thermal expansion and elastic parameters of different structural materials, temperature changes cause thermal strain in flexible electronics, thereby affecting the deformation of the flexible PCB under mechanical loads. The temperature change caused by the deformation is extremely small. If it is ignored, there is a one-way coupling relationship between the temperature field and the mechanical field. In the simulation results, this is reflected in the change of von Mises stress and volume strain at the cut-off point within 0-200 ms as the temperature rises, as Figure 17 shown. It can be seen from the figure that the equivalent stress and volume strain change linearly with temperature, and the stress and strain are no longer proportional to the temperature. This is because the force on the structure is not simply determined by thermal strain, but also needs to consider the influence of thermal expansion and temperature gradient between different structures and different materials on stress and strain.

[0131] Where the present invention is not described is applicable to the prior art.

Claims

1. A simulation analysis method for the multi-physical field coupling performance of a flexible electronic device, characterized in that, The method includes the following steps: Step 1: Construct a geometric model of the flexible electronic device, where the geometric model includes an electronic chip, an adhesive layer, a flexible PCB layer, and an interconnection structure; Step 2: Set the electromagnetic-thermal-mechanical field coupling parameters of the geometric model, including the mechanical parameters, electrical parameters, and thermal parameters of the materials; the mechanical parameters include the elastic modulus and Poisson's ratio, the electrical parameters include the conductivity, and the thermal parameters include the thermal conductivity and the coefficient of thermal expansion; Step 4: Based on the geometric model and the electromagnetic-thermal-mechanical field coupling parameters, build a multi-physics field coupling model; the multi-physics field coupling model includes an electrostatic field model, a solid heat transfer model, and a solid mechanics model, and simultaneously considers the electromagnetic-thermal coupling characteristics and the electromagnetic-thermal-mechanical coupling characteristics; Step 5: Apply loads and boundary conditions to the multi-physics field coupling model, including current sources, heat generation loads, convective heat dissipation boundary conditions, and mechanical constraint conditions; Step 6: Simulate the working state of the flexible electronic device under the multi-physics field coupling effect in the multi-physics field coupling model to obtain the simulation results.

2. The simulation analysis method for the multi-physical field coupling performance of the flexible electronic device according to claim 1, wherein The current continuity equation of the electrostatic field model is: where φ is the electric potential, Γ D is the Dirichlet boundary, is the electric potential on the Dirichlet boundary, ρ E (t) is the charge density, is the rate of change of the charge density with time, is the divergence of the current density, is the gradient operator, and σ is the conductivity; The relationship between the heat flux density and the temperature gradient of the solid heat transfer model is shown by the following formula: where q x , q y , and q z are the heat flux densities in the x, y, and z directions respectively, λ is the thermal conductivity of the material, represent the temperature gradients in the x, y, and z directions respectively, and T is the temperature; The solid mechanics model is: When the temperature changes, the material will generate strain due to thermal expansion or contraction, and the thermal strains in the length and diameter directions are expressed as: where ε l is the thermal strain in the length direction, ε d is the thermal strain in the diameter direction, α t is the coefficient of thermal expansion of the material, t1 is the current temperature, t0 is the reference temperature, and Δl and Δd are the thermal expansion amounts in the length and diameter directions, respectively; The relationship between stress and strain is shown by the following formula: s - s0 = C:(ε - ε0 - ε inel )(15) where s is the stress tensor, s0 is the initial stress, ε0 is the initial strain, ε inel is the final strain, C is the elastic tensor, is the strain tensor, is the displacement gradient.

3. The multi-physical field coupling performance simulation analysis method for flexible electronic devices according to claim 1 or 2, characterized in that, The electromagnetic-thermal coupling characteristics are described by the following formula: p = |J| 2 / σ(16) In the formula, p is the Joule heat power density, and J is the current density; The electromagnetic-thermal-mechanical coupling characteristics are described by the following formula: Where, σ ij is the stress tensor, is the externally applied force, u i is the displacement vector, μ D is the damping coefficient, ij is the strain tensor, is the elastic strain component, is the thermal strain component, is the elastic stress part in the stress tensor, D ijkl is the fourth-order elastic tensor, is the elastic strain in other directions, ΔT is the temperature change, α is the thermal expansion coefficient, δ ij is the Kronecker delta function, is the displacement value set on the Dirichlet boundary, is the stress boundary Γ σ is the stress value applied on it, is the stress on the boundary Γ σ ​

Images