An integrated circuit package transient electro-thermal simulation method based on field-circuit cooperation

Abstract

The application provides an integrated circuit package transient electro-thermal simulation method based on field-circuit cooperation, comprising the following steps: based on the electromagnetic field and circuit characteristics of the integrated circuit package, respectively adopting the discontinuous Galerkin method and the improved node analysis method to construct electromagnetic field and circuit discrete equations; constructing electromagnetic field-circuit joint equations, solving electromagnetic field distribution and port voltage and current, and calculating electromagnetic field loss and device power consumption; taking the electromagnetic field loss and device power consumption as heat sources, respectively adopting the finite element method and the compact thermal model to construct thermal field and thermal circuit discrete equations; constructing thermal field-thermal circuit joint equations, solving temperature distribution and device junction temperature, and updating material parameters and device parameters based on temperature; solving at each time according to a preset time step, and finally obtaining complete electro-thermal transient response. The application unifies electromagnetic field-circuit coupling, thermal field-thermal circuit coupling and electromagnetic-thermal coupling in a transient simulation framework, and effectively improves the calculation efficiency of integrated circuit package electro-thermal multi-physical field simulation.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation and computation technology, and more specifically, to a method for simulating transient electrothermal processes in integrated circuit packaging based on field-circuit coordination. Background Technology

[0002] With the continuous improvement of integrated circuit operating frequencies, interconnect densities, and package integration, traditional circuit-based simulation methods struggle to accurately describe the electromagnetic field effects in conductors, dielectrics, interconnect structures, and the packaging environment under high-frequency conditions. Especially in applications such as high-speed interconnects, RF packaging, and on-chip and package-level power distribution networks, electromagnetic field distribution directly affects port response, signal integrity, and device operating states. Therefore, it is necessary to combine electromagnetic field solutions with external circuit solutions to conduct field-circuit co-simulation.

[0003] On the other hand, increased packaging integration density leads to a significant increase in system power density. Electromagnetic losses and device power consumption accumulate continuously within a limited space, easily causing localized temperature rise. Increased temperature not only alters material properties such as conductivity, dielectric parameters, and thermal conductivity, but also causes drift in the equivalent parameters of semiconductor devices, further affecting circuit response and electromagnetic field distribution. Therefore, a clear bidirectional coupling relationship exists between the electromagnetic field, circuit, thermal field, and thermal path.

[0004] Existing multiphysics simulation methods typically focus on either electromagnetic-circuit co-simulation or electromagnetic-thermal co-simulation separately. While a few methods can achieve electromagnetic-circuit-thermal coupled solutions, they often fail to fully incorporate the coupling relationship between external circuits and equivalent thermal paths, determined by both power consumption and temperature, into a unified transient framework. This makes it difficult to comprehensively characterize the loss-temperature feedback mechanisms in integrated circuits and packages. Furthermore, directly using commercial software for electromagnetic and temperature field-circuit co-simulation transient solutions incurs high computational costs per time step, hindering the optimization and iterative design of complex structures.

[0005] Therefore, how to accurately establish the coupling relationship between electromagnetic field, circuit, thermal field and equivalent thermal path, while improving transient analysis efficiency, is a technical problem that urgently needs to be solved in multiphysics simulation of integrated circuits and packages. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination. By embedding an electromagnetic field circuit model based on the discontinuous Galerkin method and an improved node analysis method, as well as a thermal field circuit model based on the finite element method and a compact thermal model, into a unified transient electromagnetic-thermal field circuit co-simulation framework, high computational accuracy is achieved while significantly improving simulation efficiency.

[0007] The technical solution of this invention is as follows:

[0008] A transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination includes the following steps:

[0009] Based on the electromagnetic field and circuit characteristics of integrated circuit packaging, discrete equations of electromagnetic field and circuit are constructed using the discontinuous Galerkin method and the improved node analysis method, respectively.

[0010] Construct the electromagnetic field-circuit joint equation, solve for the electromagnetic field distribution, port voltage and current, and calculate the electromagnetic field loss and device power consumption;

[0011] Electromagnetic field loss and device power consumption are used as heat sources, and the discrete equations of thermal field and thermal path are constructed using the finite element method and compact thermal model, respectively.

[0012] Construct a joint equation for the thermal field and thermal path, solve for the temperature distribution and device junction temperature, and update the material parameters and device parameters based on the temperature.

[0013] The solution is obtained by solving the problem step by step according to the preset time step, and finally the complete electrothermal transient response is obtained.

[0014] Preferably, in the step of constructing discrete equations for electromagnetic fields and circuits based on the electromagnetic field and circuit characteristics of integrated circuit packaging using the discontinuous Galerkin method and the improved nodal analysis method, the steps for constructing discrete equations for electromagnetic fields and circuits include:

[0015] The first step is to spatially discretize Maxwell's equations using the discontinuous Galerkin method and then time-discretize them using the frog-jumping difference strategy to obtain the discrete matrix equations of the electromagnetic field.

[0016] The second step involves using an improved nodal analysis method to establish the lumped circuit equations, and combining this with a first-order backward difference strategy to discretize the time, thus obtaining the discrete circuit matrix equations.

[0017] Preferably, the steps of constructing the electromagnetic field-circuit joint equation, solving for the electromagnetic field distribution, port voltage and current, and calculating electromagnetic field loss and device power consumption specifically include:

[0018] The first step is to establish a joint electromagnetic field-circuit equation based on the coupling constraint relationship between the electric field and current density in the electromagnetic field and the port voltage and port current.

[0019] The second step is to solve the electromagnetic field-circuit joint equations obtained in the first step to obtain the electromagnetic field distribution and port voltage and current.

[0020] The third step is to calculate the electromagnetic field loss based on the electromagnetic field distribution obtained in the second step, and to calculate the device power consumption based on the port voltage and current obtained in the second step.

[0021] Preferably, in the step of using electromagnetic field loss and device power consumption as heat sources, and constructing discrete equations for the thermal field and thermal path using the finite element method and compact thermal model respectively, the steps for constructing discrete equations for the thermal field and thermal path include:

[0022] The first step is to model the thermal path of the compact thermal model using the bulk-surface thermal resistance method;

[0023] The second step involves using electromagnetic field loss as the heat source of the thermal field and device power consumption as the heat source of the thermal path. The finite element method is used to spatially discretize the heat conduction equation, and a first-order backward difference strategy is combined to perform time discretization, resulting in the discrete equations of the thermal field and thermal path.

[0024] Preferably, the step of constructing the joint equation of thermal field and thermal path, solving for the temperature distribution and device junction temperature, and updating the material parameters and device parameters based on the temperature specifically includes:

[0025] The first step is to construct and solve the joint equations of thermal field and thermal path to obtain the temperature distribution and the junction temperature of the device in the compact thermal model;

[0026] The second step is to update the temperature-affected material and device parameters based on the temperature results obtained in the first step.

[0027] Preferably, in the step of solving the problem step by step according to a preset time step to finally obtain the complete electrothermal transient response, the time step solution loop advances along the time axis one time at a time to capture and record the electromagnetic field and temperature field responses at each time step.

[0028] Compared with existing technologies, this invention transforms the computationally complex three-dimensional electrothermal multiphysics field coupling simulation into a field-circuit collaborative simulation through port interaction by constructing a collaborative model of physical space fields (electromagnetic field, thermal field) and lumped networks (circuit, thermal path). This effectively reduces the computational complexity of transient simulation and significantly shortens the electrothermal coupling simulation time of integrated circuit packaging while ensuring accuracy. Attached Figure Description

[0029] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments, which is accompanied by the accompanying drawings:

[0030] Figure 1 This is a flowchart of the transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination according to the present invention;

[0031] Figure 2 This is a schematic diagram of a compact thermal model;

[0032] Figure 3 This is a geometric schematic diagram of a typical printed circuit board in a specific embodiment;

[0033] Figure 4 This is a transient response curve of the port voltage in a specific embodiment;

[0034] Figure 5 This is a transient response curve of the device junction temperature in a specific embodiment. Detailed Implementation

[0035] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0036] Specifically, this invention provides a transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination, such as... Figure 1 As shown, the method includes the following steps:

[0037] S1: Based on the electromagnetic field and circuit characteristics of integrated circuit packaging, discrete equations of electromagnetic field and circuit are constructed using the discontinuous Galerkin method and the improved node analysis method, respectively.

[0038] Specifically, in step S1, the steps for constructing the discrete equations of the electromagnetic field and the circuit are as follows:

[0039] Step S11: Spatial discretization of Maxwell's equations is performed using the discontinuous Galerkin method, and temporal discretization is performed using the leapfrog difference strategy, resulting in the discrete matrix equation of the electromagnetic field:

[0040]

[0041] as well as

[0042]

[0043] in, Where is the dielectric constant. Let be the magnetic permeability, e represent the electric field, h represent the magnetic field, and M and S be the mass matrix and stiffness matrix, respectively. and Let C be the flux matrix, and let C represent the loss-related terms. and For port-related terms, the superscripts i and j represent the i-th unit and its adjacent j-th unit, and the subscript n represents the... time.

[0044] Step S12: The improved nodal analysis method is used to establish the lumped circuit equations, and the time is discretized using a first-order backward difference strategy to obtain the circuit discrete matrix equations:

[0045]

[0046] Where G is the admittance matrix. and This represents the connection matrix between the device and the source. The controlled matrix representing the source; and These are the node voltage and node current vectors, respectively. Represents the current vector of a nonlinear device. The current vector is generated by the adjoint model of capacitors and inductors; and These represent the vectors of independent voltage sources and independent current sources, respectively. This is the voltage vector of the lumped port.

[0047] S2: Construct the electromagnetic field-circuit joint equation, solve for the electromagnetic field distribution, port voltage and current, and calculate the electromagnetic field loss and device power consumption;

[0048] Specifically, in step S2, the electromagnetic field circuit co-simulation steps are as follows:

[0049] Step S21, based on the electric field in the electromagnetic field and current density vector Coupling constraints with port voltage and port current:

[0050]

[0051] as well as

[0052]

[0053] in, Represents the unit vector at the lumped port. Let i be the vector basis function of element i. This is the width of the lumped port. Using the formula... and By combining the discrete equations of the electromagnetic field with the discrete equations of the circuit, a joint equation of electromagnetic field-circuit is constructed.

[0054] Step S22: Solve the electromagnetic field-circuit joint equation obtained in S21 to obtain the electromagnetic field distribution and port voltage and current;

[0055] Step S23: Calculate the electromagnetic field loss based on the electromagnetic field distribution obtained in S22, and calculate the device power consumption based on the port voltage and current obtained in S22.

[0056] S3: Electromagnetic field loss and device power consumption are used as heat sources, and the discrete equations of thermal field and thermal path are constructed by finite element method and compact thermal model respectively.

[0057] Specifically, in step S3, the steps for constructing the discrete equations of the thermal field and thermal path are as follows:

[0058] Step S31, use the bulk-surface thermal resistance method to model the compact thermal model (e.g., Figure 2 Perform thermal path modeling (as shown);

[0059] Step S32: Taking electromagnetic field loss as the heat source of the thermal field and device power consumption as the heat source of the thermal path, the finite element method is used to spatially discretize the heat conduction equation, and a first-order backward difference strategy is combined for time discretization to obtain the discrete equations of the thermal field and thermal path:

[0060]

[0061] in, Represents a temperature vector. and These are the mass matrix and the stiffness matrix, respectively. For heat source related terms, the subscript n indicates the nth term. time.

[0062] S4: Construct the joint equation of thermal field and thermal path, solve for the temperature distribution and device junction temperature, and update the material parameters and device parameters based on the temperature;

[0063] Specifically, in step S4, the thermal field-path co-simulation steps are as follows:

[0064] Step S41: Construct and solve the joint equation of thermal field and thermal path to obtain the temperature distribution and the junction temperature of the device in the compact thermal model;

[0065] Step S42: Based on the temperature results obtained in S41, update the material parameters and device parameters affected by temperature.

[0066] S5: Solve step by step according to the preset time step to finally obtain the complete electrothermal transient response.

[0067] Specifically, in step S5, the time-stepping solution loop advances sequentially along the time axis to capture and record the electromagnetic and temperature field responses at each moment.

[0068] Based on the simulation method of the present invention described above, a specific embodiment is calculated.

[0069] The following is in conjunction with the accompanying drawings, Figure 3The transient electrothermal simulation of a circuit board containing integrated circuit packaging, as shown below, provides a further detailed description of the implementation of the technical solution. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this invention.

[0070] This embodiment is a circuit board containing an integrated circuit package, and its three-dimensional geometry is as follows: Figure 3 As shown, a current injection excitation is applied to excitation port a. Its waveform is a Gaussian pulse with an amplitude of 1000 A and a rise time of 5 ns. The integrated circuit package on the circuit board is characterized using a dual thermal resistance model. The conductivity of the printed circuit board and the equivalent parameters of the diodes are both functions of temperature. The total simulation time is set to 30 ns, and the total number of time steps is 600,000.

[0071] To verify the computational accuracy of the method of this invention, simulations were performed using the method of this invention and the commercial software COMSOL for comparative analysis. The transient response of the port voltage is as follows: Figure 4 As shown, the transient response of the device junction temperature is as follows: Figure 5 As shown in the figure. The results show that the voltage and junction temperature response characteristics obtained by the method of the present invention are highly consistent with the reference results, with a relative error of only 0.065% for voltage and a relative error of as low as 0.019% for junction temperature, fully demonstrating the accuracy of the method of the present invention. To verify the efficiency of the method of the present invention, the transient simulation time of the method of the present invention and COMSOL were statistically analyzed. The average simulation time of the method of the present invention per time step is only 40 ms, compared with the 119 ms required by COMSOL, achieving a 3-fold acceleration in computation.

[0072] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination, characterized in that, The method includes the following steps: Based on the electromagnetic field and circuit characteristics of integrated circuit packaging, discrete equations of electromagnetic field and circuit are constructed using the discontinuous Galerkin method and the improved node analysis method, respectively. Construct the electromagnetic field-circuit joint equation, solve for the electromagnetic field distribution, port voltage and current, and calculate the electromagnetic field loss and device power consumption; Electromagnetic field loss and device power consumption are used as heat sources, and the discrete equations of thermal field and thermal path are constructed using the finite element method and compact thermal model, respectively. Construct a joint equation for the thermal field and thermal path, solve for the temperature distribution and device junction temperature, and update the material parameters and device parameters based on the temperature. The solution is obtained by solving the problem step by step according to the preset time step, and finally the complete electrothermal transient response is obtained.

2. The transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination according to claim 1, characterized in that, In the steps of constructing discrete equations for electromagnetic fields and circuits based on integrated circuit packaging using the discontinuous Galerkin method and the improved nodal analysis method, the steps for constructing discrete equations for electromagnetic fields and circuits include: The first step is to spatially discretize Maxwell's equations using the discontinuous Galerkin method and then time-discretize them using the frog-jumping difference strategy to obtain the discrete matrix equations of the electromagnetic field. The second step involves using an improved nodal analysis method to establish the lumped circuit equations, and combining this with a first-order backward difference strategy to discretize the time, thus obtaining the discrete circuit matrix equations.

3. The transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination according to claim 1, characterized in that, The steps of constructing the electromagnetic field-circuit joint equation, solving for the electromagnetic field distribution, port voltage and current, and calculating electromagnetic field loss and device power consumption specifically include: The first step is to establish a joint electromagnetic field-circuit equation based on the coupling constraint relationship between the electric field and current density in the electromagnetic field and the port voltage and port current. The second step is to solve the electromagnetic field-circuit joint equations obtained in the first step to obtain the electromagnetic field distribution and port voltage and current. The third step is to calculate the electromagnetic field loss based on the electromagnetic field distribution obtained in the second step, and to calculate the device power consumption based on the port voltage and current obtained in the second step.

4. The transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination according to claim 1, characterized in that, The step of constructing discrete equations for the thermal field and thermal path using electromagnetic field loss and device power consumption as heat sources, respectively, employing the finite element method and a compact thermal model, includes the following steps: The first step is to model the thermal path of the compact thermal model using the bulk-surface thermal resistance method; The second step involves using electromagnetic field loss as the heat source of the thermal field and device power consumption as the heat source of the thermal path. The finite element method is used to spatially discretize the heat conduction equation, and a first-order backward difference strategy is combined to perform time discretization, resulting in the discrete equations of the thermal field and thermal path.

5. The transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination according to claim 1, characterized in that, The steps of constructing the joint equation of thermal field and thermal path, solving for the temperature distribution and device junction temperature, and updating material and device parameters based on temperature specifically include: The first step is to construct and solve the joint equations of thermal field and thermal path to obtain the temperature distribution and the junction temperature of the device in the compact thermal model; The second step is to update the temperature-affected material and device parameters based on the temperature results obtained in the first step.

6. The transient electrothermal simulation method for integrated circuit packaging based on field-circuit coordination according to claim 1, characterized in that, In the step of solving the problem step by step according to a preset time step to finally obtain the complete electrothermal transient response, the time step solution loop advances along the time axis one time at a time to capture and record the electromagnetic field and temperature field responses at each time step.

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