A method for constructing an electrothermal coupling model of multi-layer substrate vias considering temperature-dependent parameter changes

Abstract

The method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account temperature-dependent parameter changes provided by the present invention relates to the field of microelectronics technology. It includes: constructing a type lumped parameter equivalent circuit model corresponding to the multi-layer substrate via structure according to the size parameters, material parameters and multi-layer equivalent circuit network cascade mode of the multi-layer substrate via structure; constructing an equivalent thermal circuit model corresponding to the multi-layer substrate via structure according to the size parameters, material parameters and temperature nodes between adjacent layers of the multi-layer substrate via structure; using hardware description language, connecting the type lumped parameter equivalent circuit model and the equivalent thermal circuit model, establishing an electrothermal coupling model of a multi-layer substrate via, and using the electrothermal coupling model of a multi-layer substrate via to obtain the steady-state temperature of the substrate via. In this way, the temperature change of the via can be accurately obtained, and the occupied computing resources are reduced and the computing time is faster.

Description

Technical Field

[0001] The present invention relates to the field of microelectronics technology, and in particular to a method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account temperature-dependent parameter changes. Background Art

[0002] With the miniaturization and increasing integration of the electronics industry, the temperature rise in chip microsystems caused by the electrothermal effect has seriously affected the reliability of devices. Specifically, the power consumption generated during the operation of the integrated circuit will cause the temperature to rise, and the changes in some material parameters with temperature will in turn affect the electrical performance of the integrated circuit. The via structure in the substrate is a key structure for increasing the signal transmission rate between layers of chips and reducing interconnection delays. The temperature rise of the via in the substrate may cause a series of problems such as deterioration of signal integrity and electromagnetic crosstalk. At the same time, excessive local temperature will also lead to increased thermal stress, which seriously affects the reliability of the chip microsystem.

[0003] At present, the modeling of via structures in substrates is usually done by using the finite element method and a single electrical or thermal property analysis to establish the model. It is necessary to assign material properties to the model and perform meshing, add reasonable boundary conditions, and use discrete units to solve the heat conduction equation and Maxwell's equations to obtain the temperature distribution of the model. However, the electrothermal coupling effect is not taken into account in the modeling process, and the changes in the electrical and thermal conductivity of the material caused by power consumption are ignored, so that the temperature of the via obtained in the end deviates from the actual via temperature, resulting in inaccurate temperature changes of the via obtained through the model; using the finite element method to divide a complex three-dimensional model into fine grids often leads to huge degrees of freedom, which requires more computing resources and slows down the calculation speed. Summary of the invention

[0004] The purpose of the embodiment of the present invention is to provide a method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account changes in temperature parameters, thereby solving the problems of inaccurate temperature changes of vias obtained by existing methods, more computing resources occupied, and slow computing speed.

[0005] To solve the above technical problems, the embodiments of the present invention provide the following technical solutions:

[0006] The present invention provides a method for constructing an electrothermal coupling model of a multi-layer substrate via hole considering temperature-dependent parameter changes. The method for constructing an electrothermal coupling model of a multi-layer substrate via hole considering temperature-dependent parameter changes includes:

[0007] According to the size parameters, material parameters and multi-layer equivalent circuit network cascade mode of the multi-layer substrate via structure, the corresponding Lumped parameter equivalent circuit model;

[0008] According to the size parameters, material parameters, and temperature nodes between adjacent layers of the multi-layer substrate via structure, an equivalent thermal circuit model corresponding to the multi-layer substrate via structure is constructed;

[0009] Using hardware description language, The lumped parameter equivalent circuit model and the equivalent thermal circuit model are connected to establish an electrothermal coupling model of multi-layer substrate vias, so as to obtain the steady-state temperature of the substrate vias using the electrothermal coupling model of multi-layer substrate vias.

[0010] Compared with the prior art, the method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account the temperature variation parameters provided by the present invention constructs a multi-layer substrate via structure corresponding to the temperature variation parameters according to the size parameters, material parameters and multi-layer equivalent circuit network cascade mode. The equivalent thermal circuit model of the multi-layer substrate via structure is constructed based on the size parameters, material parameters, and temperature nodes between adjacent layers of the multi-layer substrate via structure. The lumped parameter equivalent circuit model and the equivalent thermal circuit model are connected to establish the electrothermal coupling model of multi-layer substrate vias, so as to obtain the steady-state temperature of the substrate vias using the electrothermal coupling model of multi-layer substrate vias. The lumped parameter equivalent circuit model and the equivalent thermal circuit model are connected to establish the electrothermal coupling model of multi-layer substrate vias. The lumped parameter equivalent circuit model takes into account the change in material conductivity caused by electrical power consumption, and the equivalent thermal circuit model takes into account the change in thermal conductivity caused by electrical power consumption, so that The power consumption of the lumped parameter equivalent circuit model is converted into the heat source input equivalent thermal circuit model, and then the node temperature in the equivalent thermal circuit model is used to update the material parameters, so that the temperature change of the via can be accurately obtained; establish The lumped parameter equivalent circuit model and equivalent thermal circuit model use the size parameters, material parameters, multi-layer equivalent circuit network cascade method and temperature nodes between adjacent layers of the multi-layer substrate via structure, and do not need to divide the multi-layer substrate via structure into fine grids, so that less computing resources are occupied and the calculation speed is faster. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] By reading the detailed description below with reference to the accompanying drawings, the above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily understood. In the accompanying drawings, several embodiments of the present invention are shown in an exemplary and non-limiting manner, and the same or corresponding reference numerals represent the same or corresponding parts, wherein:

[0012] Figure 1A flow chart of a method for constructing an electrothermal coupling model of a multi-layer substrate via considering temperature-dependent parameter changes is schematically shown;

[0013] Figure 2 A schematic diagram of a multi-layer substrate via structure is schematically shown;

[0014] Figure 3 A schematic diagram of an equivalent subcircuit model corresponding to a first single-layer substrate via substructure is schematically shown;

[0015] Figure 4 The schematic diagram of the electric field of the orifice plate capacitance between two metal grounding layers is shown schematically;

[0016] Figure 5 Schematically shows Schematic diagram of the lumped parameter equivalent circuit model;

[0017] Figure 6 Schematically shows the High Frequency Structure Simulator (HFSS) and Comparison of the return loss and reflection coefficient solved by the lumped parameter equivalent circuit model;

[0018] Figure 7 Schematic showing the HFSS and Comparison of insertion loss solved by the lumped parameter equivalent circuit model;

[0019] Figure 8 A schematic diagram schematically shows dividing a multi-layer substrate via structure into a plurality of second single-layer substrate via substructures;

[0020] Fig. 9 A three-dimensional equivalent sub-thermal circuit model corresponding to a second single-layer substrate via sub-structure in a horizontal direction is schematically shown;

[0021] Fig.10 A schematic diagram of the instantaneous temperature at the center of a metal via in an aluminum nitride substrate of an intermediate layer under different convection coefficients is shown;

[0022] Fig.11 A schematic diagram of a multi-layer substrate via electrothermal coupling model is shown schematically. DETAILED DESCRIPTION

[0023] The exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0024] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in the present invention should have the common meanings understood by those skilled in the art to which the present invention belongs.

[0025] The method in the embodiment of the present invention is described in detail below.

[0026] Figure 1 The flowchart of the method for constructing the electrothermal coupling model of the multi-layer substrate via considering the temperature variation parameters in the embodiment of the present invention is schematically shown. Figure 1 As shown, the method may include:

[0027] S101, constructing a multi-layer substrate via structure corresponding to the multi-layer substrate via structure according to the size parameters, material parameters and multi-layer equivalent circuit network cascade method. Lumped parameter equivalent circuit model.

[0028] in, Figure 2 A schematic diagram of a multi-layer substrate via structure is schematically shown, see Figure 2 As shown, the multi-layer substrate via structure includes three layers of aluminum nitride substrates, four layers of metal grounding layers, metal vias and anti-pads. The multi-layer substrate via structure is provided with a first metal grounding layer, a first aluminum nitride substrate, a second metal grounding layer, a second aluminum nitride substrate, a third metal grounding layer, a third aluminum nitride substrate, and a fourth metal grounding layer from top to bottom. An anti-pad is provided between the three layers of aluminum nitride substrates and the four layers of metal grounding layers, and a metal via is provided at the center of the anti-pad. The dimensional parameters of the multi-layer substrate via structure include the thickness of each layer of metal grounding layer, the thickness of each layer of aluminum nitride substrate, the radius of the metal via, the radius of the anti-pad and the height of the metal via. Exemplarily, the thickness of each metal grounding layer The thickness of each layer of aluminum nitride substrate is 20um. The radius of the metal via is 500um. The radius of the anti-pad is 50um The height of the metal via is 150um. The size parameters of the via structure of the multi-layer substrate also include the length and width of the three-layer aluminum nitride substrate, and the length and width of the three-layer aluminum nitride substrate are both 2000um.

[0029] Before step S101 , material parameters of the via structure of the multi-layer substrate may also be obtained.

[0030] The material parameters include the relative dielectric constant of the aluminum nitride substrate, the thermal conductivity of the metal ground layer and the metal via, the thermal conductivity of the aluminum nitride substrate, the constant pressure heat capacity of the metal ground layer and the metal via, the constant pressure heat capacity of the aluminum nitride substrate, the density of the metal ground layer and the metal via, and the density of the aluminum nitride substrate. The material parameters also include the electrical conductivity of the metal ground layer and the metal via.

[0031] The metal material of the four-layer metal grounding layer and the metal vias can be copper, or other materials. The metal material of the four-layer metal grounding layer and the metal vias is not specifically limited here.

[0032] The thermal conductivity of the aluminum nitride substrate, the electrical conductivity of the metal ground layer and the metal via, that is, the electrical conductivity of copper, changes with temperature. The thermal conductivity of the aluminum nitride substrate and the electrical conductivity of copper are expressed as functions that change with temperature. The relative dielectric constant of the aluminum nitride substrate, the thermal conductivity of the metal ground layer and the metal via, the constant-pressure heat capacity of the metal ground layer and the metal via, the constant-pressure heat capacity of the aluminum nitride substrate, the density of the metal ground layer and the metal via, and the density of the aluminum nitride substrate do not change with temperature and are considered constants. See Table 1, which shows the material parameters of the multi-layer substrate via structure. For temperature.

[0033] Table 1 Material parameters of multi-layer substrate via structure

[0034]

[0035] Specifically, according to the size parameters, material parameters and multi-layer equivalent circuit network cascade mode of the multi-layer substrate via structure, the corresponding Lumped parameter equivalent circuit model, including:

[0036] Step A1: Divide the multi-layer substrate via structure into a plurality of first single-layer substrate via sub-structures.

[0037] The multi-layer substrate via structure is divided from the center of the middle metal ground layer to obtain a plurality of first single-layer substrate via substructures, each of which includes a single-layer aluminum nitride substrate, a metal via, and a metal ground layer in contact with the upper and lower surfaces of the single-layer aluminum nitride substrate.

[0038] Step A2: Calculate the parasitic parameters of multiple single-layer substrate via substructures based on the thickness of each metal ground layer, the radius of the metal via, the radius of the anti-pad, the height of the metal via, and the relative dielectric constant of the aluminum nitride substrate, and perform equivalent replacement of multiple first single-layer substrate via substructures based on the parasitic parameters to obtain multiple equivalent subcircuit models corresponding to the multiple first single-layer substrate via substructures.

[0039] The parasitic parameters include parasitic inductance, parasitic capacitance and parasitic resistance. The parasitic resistance includes the parasitic resistance of the metal vias in the first layer of aluminum nitride substrate. , Parasitic resistance of metal vias in the second layer of aluminum nitride substrate , Parasitic resistance of metal vias in the third layer of aluminum nitride substrate The parasitic inductance includes the parasitic inductance of the metal vias in the first layer of aluminum nitride substrate. , Parasitic inductance of metal vias in the second layer of aluminum nitride substrate , Parasitic inductance of metal vias in the third layer of aluminum nitride substrate .

[0040] When high-frequency signals are transmitted in multiple first single-layer substrate via substructures, parasitic inductance, parasitic capacitance and parasitic resistance can be used to perform circuit equivalence on the three-layer aluminum nitride substrate, four-layer metal ground layer, metal via and anti-pad in the multiple first single-layer substrate via substructures, and establish multiple equivalent subcircuit models corresponding to the multiple first single-layer substrate via substructures. Figure 3 A schematic diagram of an equivalent subcircuit model corresponding to a first single-layer substrate via substructure is shown schematically, see Figure 3 As shown in the figure, due to the conductor loss and dynamic current changes in the metal via itself, the role of the metal via can be equivalent to the parasitic inductance of the metal via. and the parasitic resistance of metal vias The parasitic capacitance consists of two parts: the coaxial capacitance between the anti-pad and the metal via. , the plate capacitance between the upper end of the metal via in each layer of aluminum nitride substrate and the upper and lower metal ground layers . Coaxial capacitance between anti-pad and metal via Including the first coaxial capacitor between the anti-pad and the metal via , the second coaxial capacitor between the anti-pad and the metal via , the third coaxial capacitor between the anti-pad and the metal via , the fourth coaxial capacitor between the anti-pad and the metal via The plate capacitance between the upper end of the metal via in each layer of aluminum nitride substrate and the upper and lower metal ground layers Including the plate capacitor between the upper end of the metal via in the first layer of aluminum nitride substrate and the metal ground layer , the plate capacitance between the upper end of the metal via in the third layer of aluminum nitride substrate and the metal grounding layer .

[0041] Parasitic resistance of metal vias The DC resistance at low frequency and AC resistance at high frequencies Composition, parasitic resistance of metal vias It can be expressed as:

[0042] ;

[0043] ;

[0044] ;

[0045] in, is the parasitic resistance of the metal via, is the DC resistance at low frequency, is the AC resistance at high frequency, is the resistivity of the metal via and metal ground layer, is the height of the metal via, is the radius of the metal via, is the signal frequency, is the magnetic permeability in vacuum.

[0046] Parasitic inductance of metal vias Including external inductor and internal inductance , and as the signal frequency increases, the skin effect becomes more and more obvious, making Much smaller than , so the parasitic inductance of the metal via It can be expressed as:

[0047] ;

[0048] in, is the parasitic inductance of the metal via, is the magnetic permeability in vacuum, is the height of the metal via, is the radius of the metal via.

[0049] When the high-frequency signal passes through the first single-layer substrate via substructure, the electromagnetic wave transmission mode changes from transverse electromagnetic wave (TEM) to transverse magnetic wave (TM). Therefore, the parasitic capacitance of the first single-layer substrate via substructure is divided into the coaxial capacitance between the anti-pad and the metal via. And the plate capacitance between the upper end of the metal via in each layer of aluminum nitride substrate and the upper and lower metal ground layers For the coaxial capacitance between the anti-pad and the metal via It can be solved by using the static field method. The calculation formula is:

[0050] ;

[0051] in, is the coaxial capacitance between the anti-pad and the metal via, is the dielectric constant of vacuum, is the thickness of each metal ground layer, is the radius of the anti-pad, is the radius of the metal via.

[0052] Figure 4 The schematic diagram of the electric field of the orifice plate capacitance between two metal grounding layers is shown schematically, see Figure 4 As shown, solve the plate capacitance between the upper end of the metal via and the upper and lower metal ground layers in each layer of aluminum nitride substrate As the operating frequency of the circuit increases, the skin effect causes the charge The charge is almost distributed on the surface of the via, and the quasi-static method can be used for analysis, assuming that the charge at each point on the surface of the metal via is fixed. However, due to the different distances between each point on the surface of the metal via and the metal grounding layer, the charge The direction of the axis is not evenly distributed, but at a very small section of the preset height of the metal via The charge can be considered to be evenly distributed. The distance between the axes is ,by The axis is the center, is the radius of the metal via ( ), according to Gauss's theorem, the preset height is The plate capacitance from the metal via to the metal ground plane for:

[0053] ;

[0054] in, The preset height is The plate capacitance from the metal via to the metal ground plane, is the dielectric constant of vacuum, is the relative dielectric constant of the aluminum nitride substrate, For preset height Angle to the metal ground layer, is the radius of the metal via, is the radius of the anti-pad.

[0055] Divide the upper part of the metal via into The length of each metal via is , the plate capacitance of the upper metal via can be obtained, that is, the plate capacitance between the upper end of the metal via in the first layer of aluminum nitride substrate and the metal ground layer for:

[0056] ;

[0057] in, is the plate capacitance between the upper end of the metal via in the first layer of aluminum nitride substrate and the metal grounding layer, is the dielectric constant of vacuum, is the relative dielectric constant of the aluminum nitride substrate, is the radius of the metal via, is the radius of the anti-pad, is the height of the metal via, For the Segment metal vias, The number of segments divided into the upper part of the metal via.

[0058] The plate capacitance between the upper end of the metal via and the upper and lower metal grounding layers in each layer of aluminum nitride substrate Also includes a plate capacitor between the lower end of the metal via in the first layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the upper end of the metal via in the second layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the lower end of the metal via in the second layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the lower end of the metal via in the third layer of aluminum nitride substrate and the metal grounding layer .

[0059] Calculation of the plate capacitance between the top of the metal via and the metal grounding layer in each other layer of aluminum nitride substrate, and the plate capacitance between the top of the metal via and the metal grounding layer in the first layer of aluminum nitride substrate The calculation is the same.

[0060] According to the calculated parasitic parameters corresponding to each first single-layer substrate via substructure, that is, the first coaxial capacitance between the anti-pad and the metal via , the second coaxial capacitor between the anti-pad and the metal via , the third coaxial capacitor between the anti-pad and the metal via , the fourth coaxial capacitor between the anti-pad and the metal via , parasitic resistance of metal vias in the first layer of aluminum nitride substrate , Parasitic resistance of metal vias in the second layer of aluminum nitride substrate , Parasitic resistance of metal vias in the third layer of aluminum nitride substrate , parasitic inductance of metal vias in the first layer of aluminum nitride substrate , Parasitic inductance of metal vias in the second layer of aluminum nitride substrate , Parasitic inductance of metal vias in the third layer of aluminum nitride substrate , the plate capacitance between the upper end of the metal via in the first layer of aluminum nitride substrate and the metal ground layer , the plate capacitance between the lower end of the metal via in the first layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the upper end of the metal via in the second layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the lower end of the metal via in the second layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the upper end of the metal via in the third layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the lower end of the metal via in the third layer of aluminum nitride substrate and the metal grounding layer , the three-layer aluminum nitride substrate, the four-layer metal ground layer, the metal via and the anti-pad in each corresponding first single-layer substrate via substructure are replaced as a whole to obtain multiple equivalent subcircuit models corresponding to the multiple first single-layer substrate via substructures.

[0061] Step A3: Construct a multi-layer equivalent circuit network based on multiple equivalent subcircuit models and multi-layer equivalent circuit network cascades. Lumped parameter equivalent circuit model.

[0062] in, The lumped parameter equivalent circuit model includes the first coaxial capacitor between the anti-pad and the metal via , the second coaxial capacitor between the anti-pad and the metal via , the third coaxial capacitor between the anti-pad and the metal via , the fourth coaxial capacitor between the anti-pad and the metal via , parasitic resistance of metal vias in the first layer of aluminum nitride substrate , Parasitic resistance of metal vias in the second layer of aluminum nitride substrate , Parasitic resistance of metal vias in the third layer of aluminum nitride substrate , parasitic inductance of metal vias in the first layer of aluminum nitride substrate , Parasitic inductance of metal vias in the second layer of aluminum nitride substrate , Parasitic inductance of metal vias in the third layer of aluminum nitride substrate , the plate capacitance between the upper end of the metal via in the first layer of aluminum nitride substrate and the metal ground layer , the plate capacitance between the lower end of the metal via in the first layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the upper end of the metal via in the second layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the lower end of the metal via in the second layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the upper end of the metal via in the third layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the lower end of the metal via in the third layer of aluminum nitride substrate and the metal grounding layer .

[0063] Figure 5 Schematically shows Schematic diagram of the lumped parameter equivalent circuit model, see Figure 5 As shown, The connection relationship of the lumped parameter equivalent circuit model is: the first coaxial capacitor between the anti-pad and the metal via The plate capacitance between the upper end of the metal via in the first aluminum nitride substrate and the metal grounding layer The parasitic resistance of the metal via in the first layer of aluminum nitride substrate One end of each is connected; the first coaxial capacitor between the anti-pad and the metal via The other end is grounded, and the plate capacitance between the upper end of the metal via in the first layer of aluminum nitride substrate and the metal grounding layer The other end is grounded, and the parasitic resistance of the metal via in the first layer of aluminum nitride substrate The parasitic inductance of the other end and the metal via in the first layer of aluminum nitride substrate One end of the connection; the parasitic inductance of the metal via in the first layer of aluminum nitride substrate The other end, the plate capacitance between the lower end of the metal via in the first layer of aluminum nitride substrate and the metal grounding layer The second coaxial capacitor between one end of the anti-pad and the metal via The plate capacitance between the upper end of the metal via in the second aluminum nitride substrate and the metal grounding layer The parasitic resistance of the metal via in the second layer of aluminum nitride substrate The bottom end of the metal via in the first layer of aluminum nitride substrate is connected to the plate capacitor of the metal ground layer. The other end of the second coaxial capacitor between the anti-pad and the metal via The other end, the upper end of the metal via in the second layer of aluminum nitride substrate and the plate capacitance of the metal ground layer The other end of the metal via in the second layer of aluminum nitride substrate is grounded; The parasitic inductance of the other end of the second aluminum nitride substrate and the metal via The parasitic inductance of the metal via in the second layer of aluminum nitride substrate is connected to one end of The other end, the bottom end of the metal via in the second layer of aluminum nitride substrate and the plate capacitance of the metal ground layer The third coaxial capacitor between one end of the anti-pad and the metal via The plate capacitance between the upper end of the metal via in the third layer of aluminum nitride substrate and the metal ground layer The parasitic resistance of the metal via in the third layer of aluminum nitride substrate The bottom end of the metal via in the second layer of aluminum nitride substrate is connected to the plate capacitor of the metal grounding layer. The other end of the third coaxial capacitor between the anti-pad and the metal via The other end, the upper end of the metal via in the third layer of aluminum nitride substrate and the plate capacitance of the metal ground layer The other end is grounded; the parasitic resistance of the metal via in the third layer of aluminum nitride substrate The parasitic inductance of the other end and the metal via in the third layer of aluminum nitride substrate The parasitic inductance of the metal via in the third layer of aluminum nitride substrate is connected to one end of The other end, the bottom end of the metal via in the third layer of aluminum nitride substrate and the plate capacitance of the metal ground layer The fourth coaxial capacitor between one end of the anti-pad and the metal via The lower end of the metal via in the third layer of aluminum nitride substrate is connected to the plate capacitor of the metal ground layer. The other end of the fourth coaxial capacitor between the anti-pad and the metal via The other ends are grounded.

[0064] To verify The lumped parameter equivalent circuit model is used to compare the scattering parameters (S parameters) obtained by simulation with the simulation results in the commonly used finite element simulation software HFSS. Figure 6 Schematic showing the HFSS and Comparison of the return loss and reflection coefficient solved by the lumped parameter equivalent circuit model. Figure 7 Schematic showing the HFSS and Comparison of insertion loss solved by the lumped parameter equivalent circuit model. Figure 6 To solve the frequency from 0 to 50 GHz, HFSS full-wave simulation and The results of the reflection coefficient (S11) of the return loss solved by the lumped parameter equivalent circuit model are compared. Figure 7 The insertion loss (S21) results of HFSS full-wave simulation and equivalent circuit model solution are compared at solution frequencies of 0~50GHz. Figure 6 and Figure 7 The results show that in the 0~20GHz frequency band, The return loss and insertion loss of the lumped parameter equivalent circuit model are in good agreement with those of the HFSS full-wave simulation. The accuracy of the lumped parameter equivalent circuit model has decreased, but the error of insertion loss is still within 0.05dB, indicating that The lumped parameter equivalent circuit model has higher accuracy.

[0065] S102, constructing an equivalent thermal circuit model corresponding to the multi-layer substrate via structure according to size parameters, material parameters, and temperature nodes between adjacent layers of the multi-layer substrate via structure.

[0066] Specifically, according to the size parameters, material parameters, and the temperature nodes between adjacent layers of the multi-layer substrate via structure, an equivalent thermal circuit model corresponding to the multi-layer substrate via structure is constructed, including:

[0067] Step B1: dividing the multi-layer substrate via structure into a plurality of second single-layer substrate via sub-structures according to the center positions of the two middle metal ground layers.

[0068] Figure 8 A schematic diagram of dividing a multi-layer substrate via structure into a plurality of second single-layer substrate via substructures is schematically shown. According to the center positions of the two middle metal grounding layers, the multi-layer substrate via structure is divided into three second single-layer substrate via substructures.

[0069] Step B2: Calculate the lateral thermal resistance, longitudinal thermal resistance and thermal capacity corresponding to each second single-layer substrate via substructure based on the thickness of each metal ground layer, the thickness of each aluminum nitride substrate, the radius of the metal via, the radius of the anti-pad, the height of the metal via, the thermal conductivity of the metal ground layer and the metal via, the thermal conductivity of the aluminum nitride substrate, the constant-pressure heat capacity of the metal ground layer and the metal via, the constant-pressure heat capacity of the aluminum nitride substrate, the density of the metal ground layer and the metal via, and the density of the aluminum nitride substrate.

[0070] Among them, the lateral thermal resistance includes the lateral thermal resistance of the heat flow through the metal vias and the lateral thermal resistance of the heat flow through the metal vias and diffusing to the aluminum nitride substrate. The longitudinal thermal resistance includes the longitudinal thermal resistance of the heat flow through the metal vias, the longitudinal thermal resistance of the heat flow through the aluminum nitride substrate and the longitudinal thermal resistance of the heat flow through the metal ground layer. The thermal capacitance includes the thermal capacitance of the metal vias, the thermal capacitance of the aluminum nitride substrate and the thermal capacitance of the metal ground layer.

[0071] The longitudinal thermal resistance of heat flow through the metal via includes the longitudinal thermal resistance of heat flow through the upper end of the metal via and the longitudinal thermal resistance of heat flow through the lower end of the metal via. The longitudinal thermal resistance of heat flow through the metal grounding layer includes the longitudinal thermal resistance of heat flow through the upper metal grounding layer and the longitudinal thermal resistance of heat flow through the lower metal grounding layer. The longitudinal thermal resistance of heat flow through the aluminum nitride substrate includes the longitudinal thermal resistance of heat flow through the upper aluminum nitride substrate and the longitudinal thermal resistance of heat flow through the lower aluminum nitride substrate. The thermal capacitance of the metal grounding layer includes the thermal capacitance of the upper metal grounding layer and the thermal capacitance of the lower metal grounding layer.

[0072] The heat in the multiple second single-layer substrate via substructures is mainly generated by the central conductor (i.e., the metal via), and the generated heat diffuses laterally and vertically to the aluminum nitride substrate. Therefore, the aluminum nitride substrate, metal via, and metal grounding layer in the multiple second single-layer substrate via substructures can be modeled separately. In order to reflect the multi-directionality of heat flow and facilitate the connection of thermal circuit nodes between aluminum nitride substrates, the horizontal thermal resistance of the aluminum nitride substrate area and the metal via area is divided into four parts, and the longitudinal thermal resistance is divided into two parts in each horizontal direction. Since the metal grounding layer is thin, its heat mainly diffuses longitudinally, so only the longitudinal thermal resistance of the metal grounding layer is considered. By connecting the adjacent nodes in the three areas of the aluminum nitride substrate, metal via, and metal grounding layer along the direction of heat flow, the equivalent thermal circuit model corresponding to each second single-layer substrate via substructure can be obtained, such as Fig. 9 shown.

[0073] Fig. 9 The three-dimensional equivalent sub-heat circuit model corresponding to the second single-layer substrate via sub-structure in the horizontal direction is schematically shown. Fig. 9 Only one of the four horizontal directions is shown in the figure. The connection relationship of the three-dimensional equivalent sub-thermal circuit model corresponding to the second single-layer substrate via substructure in one horizontal direction is: the longitudinal thermal resistance of the heat flow through the upper end of the metal via The longitudinal thermal resistance of the heat flow through the lower end of the metal via One end of the heat flow through the metal vias lateral thermal resistance One end of the metal via heat capacity One end of the metal via is connected, and the thermal capacity The other end is grounded, and the heat flows through the lateral thermal resistance of the metal via. The other end of the heat flow flows through the longitudinal thermal resistance of the upper aluminum nitride substrate At one end, the heat flow flows through the metal vias and diffuses to the lateral thermal resistance of the aluminum nitride substrate. One end of the aluminum nitride substrate heat capacity The heat flow flows through the longitudinal thermal resistance of the aluminum nitride substrate at the lower end. The heat flow flows through the longitudinal thermal resistance of the aluminum nitride substrate on the upper end. The longitudinal thermal resistance between the other end and the heat flow through the upper metal ground layer One end is connected, and the heat flow flows through the longitudinal thermal resistance of the upper metal ground layer The other end of the metal ground layer has a thermal capacitance of One end is connected to the metal ground layer at the top. The other end is grounded, and the thermal capacitance of the aluminum nitride substrate The other end is grounded, and the heat flows through the longitudinal thermal resistance of the aluminum nitride substrate at the lower end. The longitudinal thermal resistance between the other end and the heat flow through the lower metal ground layer One end is connected, and the heat flow flows through the longitudinal thermal resistance of the metal ground layer at the lower end. The other end and the lower metal ground layer thermal capacitance One end is connected to the metal ground layer at the bottom. The other end is grounded. In the four horizontal directions, the lateral heat flow flows from the metal vias to the aluminum nitride substrate at the same time, and the longitudinal heat flow diffuses in the metal vias, the aluminum nitride substrate and the metal grounding layer at the same time. Therefore, the lateral thermal resistance and the longitudinal thermal resistance in each horizontal direction are in parallel, and the magnitude of the lateral thermal resistance and the longitudinal thermal resistance in each horizontal direction are four times the original; the lateral thermal resistance includes the lateral thermal resistance of the heat flow through the metal vias. , the lateral thermal resistance of heat flow through the metal vias to the aluminum nitride substrate , the longitudinal thermal resistance includes the longitudinal thermal resistance of the heat flow through the upper end of the metal via , the longitudinal thermal resistance of heat flow through the lower end of the metal via , the longitudinal thermal resistance of heat flow through the upper aluminum nitride substrate , the longitudinal thermal resistance of heat flow through the lower aluminum nitride substrate In each horizontal direction, the heat capacity of the metal via 、Heat capacity of aluminum nitride substrate The thermal capacity of the metal grounding layer is one-fourth of the original; the thermal capacity of the metal grounding layer includes the thermal capacity of the upper metal grounding layer , heat capacity of the lower metal ground layer .

[0074] For lateral heat conduction, the heat flow is transferred outward from the metal conductor, namely the metal via, through the aluminum nitride substrate. The lateral thermal resistance of the metal via and the aluminum nitride substrate can be calculated separately.

[0075] The area of ​​the metal via is the heat source generation area. Assuming that the heat is evenly distributed in this area, the lateral thermal resistance of the heat flow through the metal via is The calculation formula is as follows:

[0076] ;

[0077] in, is the lateral thermal resistance of heat flow through the metal via, is the temperature rise, is the heat flow, is the integration radius, is the radius of the metal via, is the height of the metal via, is the thermal conductivity of copper, that is, the thermal conductivity of metal vias and metal grounding layers.

[0078] The outer side of the aluminum nitride substrate is square. Considering that the temperature difference near the outer side of the area is small, the area of ​​the aluminum nitride substrate can be equivalent to a circle to facilitate calculation. The heat flow diffuses through the metal vias to the lateral thermal resistance of the aluminum nitride substrate. The thermal resistance calculation formula is:

[0079] ;

[0080] in, is the lateral thermal resistance of heat flow through the metal vias to the aluminum nitride substrate, is the integration radius, is the thermal conductivity of the aluminum nitride substrate, is the radius of the aluminum nitride substrate after circular equivalent, is the radius of the metal via, is the thickness of each layer of aluminum nitride substrate, is the side length of the aluminum nitride substrate.

[0081] In the vertical direction, the heat flow in the metal via will be transmitted through the metal via, the aluminum nitride substrate, and the metal ground layer. The longitudinal thermal resistance of the heat flow through the metal via , Longitudinal thermal resistance of heat flow through aluminum nitride substrate , the longitudinal thermal resistance of heat flow through the metal ground layer The calculation formula is:

[0082] ;

[0083] ;

[0084] ;

[0085] in, is the longitudinal thermal resistance of heat flow through the metal ground layer, is the temperature rise, is the heat flow, is the thickness of each layer of aluminum nitride substrate, for The direction of the axis, is the thermal conductivity of copper, i.e. the thermal conductivity of metal vias and metal grounding layers, is the radius of the metal via, is the longitudinal thermal resistance of heat flow through the aluminum nitride substrate, is the thermal conductivity of the aluminum nitride substrate, is the side length of the aluminum nitride substrate, is the longitudinal thermal resistance of heat flow through the metal via, is the radius of the anti-pad.

[0086] Longitudinal thermal resistance of heat flow through metal vias The longitudinal thermal resistance of heat flow through the upper end of the metal via , the longitudinal thermal resistance of heat flow through the lower end of the metal via The sum of the longitudinal thermal resistance of the heat flow through the aluminum nitride substrate is the longitudinal thermal resistance of heat flow through the upper aluminum nitride substrate , the longitudinal thermal resistance of heat flow through the lower aluminum nitride substrate The sum of the longitudinal thermal resistance of the heat flow through the metal ground layer is the longitudinal thermal resistance of heat flow through the upper metal ground layer , the longitudinal thermal resistance of heat flow through the lower metal ground layer sum.

[0087] Since the heat capacity is not anisotropic, the heat capacity of metal vias 、Heat capacity of aluminum nitride substrate , heat capacity of metal ground layer The calculation formula is:

[0088] ;

[0089] ;

[0090] ;

[0091] in, is the heat capacity of the metal via, is the height of the metal via, is the constant pressure heat capacity of copper, that is, the constant pressure heat capacity of metal vias and metal grounding layers. is the density of copper, i.e. the density of metal vias and metal grounding layers, is the radius of the metal via, is the heat capacity of the aluminum nitride substrate, is the thickness of each layer of aluminum nitride substrate, is the constant-pressure heat capacity of the aluminum nitride substrate, is the density of the aluminum nitride substrate, is the side length of the aluminum nitride substrate, is the thermal capacity of the metal ground layer, is the thickness of each metal ground layer, is the radius of the anti-pad.

[0092] Metal ground layer thermal capacitance is the thermal capacity of the upper metal ground layer and the thermal capacitance of the lower metal ground layer sum.

[0093] The above calculation of the lateral thermal resistance, longitudinal thermal resistance and thermal capacitance is applicable to the calculation of the lateral thermal resistance, longitudinal thermal resistance and thermal capacitance in each second single-layer substrate via substructure.

[0094] Step B3: construct a three-dimensional equivalent sub-thermal circuit model corresponding to a plurality of second single-layer substrate via sub-structures according to the lateral thermal resistance, the longitudinal thermal resistance and the thermal capacitance.

[0095] Through lateral thermal resistance, longitudinal thermal resistance and thermal capacitance, the three-layer aluminum nitride substrate, four-layer metal ground layer, metal via and anti-pad in multiple second single-layer substrate via substructures are replaced as a whole to obtain a three-dimensional equivalent sub-thermal circuit model corresponding to multiple second single-layer substrate via substructures.

[0096] Step B4: According to the three-dimensional equivalent sub-thermal circuit model, the temperature nodes between adjacent layers of the multi-layer substrate via structure are connected in the four divided horizontal directions to obtain an equivalent thermal circuit model.

[0097] The temperature nodes between adjacent layers may be the temperature nodes at the center of each layer of metal vias and the temperature nodes at the center of each layer of aluminum nitride substrates.

[0098] In order to verify the accuracy of the equivalent thermal circuit model, the finite element simulation results were used as a reference and the equivalent thermal circuit model was compared with the results of the finite element simulation software to verify its accuracy. Fig.10 Schematically shows the instantaneous temperature at the center of the metal via in the aluminum nitride substrate of the middle layer under different convection coefficients, see Fig.10 As shown, the horizontal axis is time and the vertical axis is temperature. In this embodiment, it is assumed that the power consumption of the metal via is 0.5 W, the top surface and four side surfaces of the multi-layer substrate via structure are set as natural convection boundaries, and the bottom convection heat transfer coefficients are set to 3×10 3 and 6×10 3 , in order to simulate different heat dissipation environments, and compare the calculation results of the equivalent thermal circuit model with the simulation results of the multi-physics field simulation software (COMSOL Multiphysics, COMSOL) in the finite element software. Fig.10 is the instantaneous temperature at the center of the via hole in the middle layer substrate under different convection coefficients. It can be seen that the simulation results based on the equivalent thermal circuit model are in good agreement with the simulation results of COMSOL in the finite element software, which verifies the correctness of the equivalent thermal circuit model.

[0099] S103, using hardware description language, The lumped parameter equivalent circuit model and the equivalent thermal circuit model are connected to establish an electrothermal coupling model of multi-layer substrate vias, so as to obtain the steady-state temperature of the substrate vias using the electrothermal coupling model of multi-layer substrate vias.

[0100] The parasitic parameters include parasitic resistance.

[0101] Specifically, using the hardware description language (Verilog-A), The lumped parameter equivalent circuit model and the equivalent thermal circuit model are connected to establish an electrothermal coupling model of multi-layer substrate vias, so as to obtain the steady-state temperature of the substrate vias using the electrothermal coupling model of multi-layer substrate vias, including:

[0102] Step C1: Describe the parasitic resistance, the lateral thermal resistance of the heat flow through the metal vias to diffuse to the aluminum nitride substrate, and the longitudinal thermal resistance of the heat flow through the aluminum nitride substrate using a hardware description language to obtain the corresponding temperature-dependent parasitic resistance and temperature-dependent thermal resistance.

[0103] When current flows through the metal via, it will generate Joule heat. The accumulation of heat causes the temperature to rise, thus affecting the change of material parameters. In this embodiment, the electrical conductivity of copper, i.e. the electrical conductivity of the metal via, and the thermal conductivity of the aluminum nitride substrate will change with temperature. Among them, the change of the electrical conductivity of the metal via affects The parasitic resistance of the metal via in the lumped parameter equivalent circuit model and the change of the thermal conductivity of the aluminum nitride substrate affect the thermal resistance of the aluminum nitride substrate area in the equivalent thermal circuit model.

[0104] Specifically, the parasitic resistance of the metal via in the first layer of aluminum nitride substrate is , Parasitic resistance of metal vias in the second layer of aluminum nitride substrate , Parasitic resistance of metal vias in the third layer of aluminum nitride substrate , described by Verilog-A language, the corresponding temperature-dependent parasitic resistance is obtained. The lateral thermal resistance of the heat flow through the metal vias to the aluminum nitride substrate and the longitudinal thermal resistance of the heat flow through the aluminum nitride substrate are described by Verilog-A language, and the corresponding temperature-dependent thermal resistance is obtained.

[0105] Step C2: In the temperature-variable parasitic resistor, the power consumption output node of the metal via in each layer of the aluminum nitride substrate is used to output the power consumption generated by the temperature-variable parasitic resistor, and the temperature difference between the temperature nodes in the temperature-variable thermal resistor is used to update the temperature-variable thermal resistor to obtain an updated equivalent thermal circuit model.

[0106] The temperature node can be used to obtain the instantaneous temperature of the metal via area in the equivalent thermal circuit model.

[0107] Step C3: Use hardware description language to establish a voltage-controlled current source, in which the power consumption of the power consumption input node is the same as the power consumption generated by the temperature-dependent parasitic resistance.

[0108] When using Verilog-A language to establish a voltage-controlled current source, it is necessary to ensure that the power consumption of the power consumption input node in the voltage-controlled current source is consistent with the power consumption generated by the temperature-dependent parasitic resistance.

[0109] Step C4: Use a voltage-controlled current source to convert the power consumption generated by the temperature-dependent parasitic resistance into a heat source, and input the heat source into the updated equivalent thermal circuit model to establish a multi-layer substrate via electrothermal coupling model, and use the multi-layer substrate via electrothermal coupling model to obtain the steady-state temperature of the substrate via.

[0110] By using a voltage-controlled current source, the power consumption generated by the temperature-dependent parasitic resistance is converted into a heat source, and the heat source is input into the updated equivalent thermal circuit model, which can achieve The electrothermal coupling model of multi-layer substrate vias is established by connecting the new lumped parameter equivalent circuit model and the updated equivalent thermal circuit model.

[0111] Among them, the multi-layer substrate via electrothermal coupling model includes The lumped parameter equivalent circuit model, voltage-controlled current source and updated equivalent thermal circuit model are shown in Figure 2.

[0112] Fig.11 A schematic diagram of a multi-layer substrate via electrothermal coupling model is shown schematically, see Fig.11 As shown, the multi-layer substrate via electrothermal coupling model includes the electrical power consumption output node of the metal via in the first layer of aluminum nitride substrate The first power consumption input node of the voltage controlled current source Connection, electrical power consumption output node of metal via in the second layer aluminum nitride substrate The second power consumption input node of the voltage controlled current source Connection, electrical power consumption output node of metal vias in the third layer of aluminum nitride substrate The third power consumption input node of the voltage controlled current source Connection, heat source input node of the metal via in the first layer of aluminum nitride substrate in the updated equivalent thermal circuit model , and the first heat source output node of the voltage-controlled current source Connection; Heat source input node of the metal via in the second layer of aluminum nitride substrate in the updated equivalent thermal circuit model , and the second heat source output node of the voltage-controlled current source Connection; Heat source input node of the metal via in the third layer of aluminum nitride substrate in the updated equivalent thermal circuit model , and the third heat source output node of the voltage-controlled current source connect; Temperature nodes of metal vias in the first layer of aluminum nitride substrate in the lumped parameter equivalent circuit model Heat source input node with metal vias in the first layer of aluminum nitride substrate connect, Temperature nodes of metal vias in the second layer of aluminum nitride substrate in the lumped parameter equivalent circuit model Heat source input node with metal vias in the second layer of aluminum nitride substrate connect, Temperature nodes of metal vias in the third layer of aluminum nitride substrate in the lumped parameter equivalent circuit model Heat source input node with metal vias in the third layer of aluminum nitride substrate Connection. By connecting the temperature node of the metal via in each layer of the aluminum nitride substrate with the heat source input node of the metal via in each layer of the aluminum nitride substrate, the temperature of each layer of the substrate via in the equivalent thermal circuit model is obtained to update the temperature change parameters.

[0113] In addition, the first coaxial capacitor between one end of the voltmeter, the anti-pad and the metal via The plate capacitance between the upper end of the metal via in the first aluminum nitride substrate and the metal grounding layer The parasitic resistance of the metal via in the first layer of aluminum nitride substrate The other end of the voltmeter, the first coaxial capacitor between the anti-pad and the metal via are connected. The other end, the plate capacitance between the upper end of the metal via in the first layer of aluminum nitride substrate and the metal ground layer The other end of the metal via in the first layer of aluminum nitride substrate is grounded; The parasitic inductance of the other end and the metal via in the first layer of aluminum nitride substrate One end of the connection; the parasitic inductance of the metal via in the first layer of aluminum nitride substrate The other end, the plate capacitance between the lower end of the metal via in the first layer of aluminum nitride substrate and the metal grounding layer The second coaxial capacitor between one end of the anti-pad and the metal via The plate capacitance between the upper end of the metal via in the second aluminum nitride substrate and the metal grounding layer The parasitic resistance of the metal via in the second layer of aluminum nitride substrate The bottom end of the metal via in the first layer of aluminum nitride substrate is connected to the plate capacitor of the metal ground layer. The other end of the second coaxial capacitor between the anti-pad and the metal via The other end, the upper end of the metal via in the second layer of aluminum nitride substrate and the plate capacitance of the metal ground layer The other end of the metal via in the second layer of aluminum nitride substrate is grounded; The parasitic inductance of the other end of the second aluminum nitride substrate and the metal via One end of the connection; the parasitic inductance of the metal via in the second layer of aluminum nitride substrate The other end, the bottom end of the metal via in the second layer of aluminum nitride substrate and the plate capacitance of the metal ground layer The third coaxial capacitor between one end of the anti-pad and the metal via The plate capacitance between the upper end of the metal via in the third layer of aluminum nitride substrate and the metal ground layer The parasitic resistance of the metal via in the third layer of aluminum nitride substrate The bottom end of the metal via in the second layer of aluminum nitride substrate is connected to the plate capacitor of the metal grounding layer. The other end of the third coaxial capacitor between the anti-pad and the metal via The other end, the upper end of the metal via in the third layer of aluminum nitride substrate and the plate capacitance of the metal ground layer The other end is grounded; the parasitic resistance of the metal via in the third layer of aluminum nitride substrate The parasitic inductance of the other end and the metal via in the third layer of aluminum nitride substrate The parasitic inductance of the metal via in the third layer of aluminum nitride substrate is connected to one end of The other end, the bottom end of the metal via in the third layer of aluminum nitride substrate and the plate capacitance of the metal ground layer The fourth coaxial capacitor between one end of the anti-pad and the metal via One end of each of the metal vias in the third layer of aluminum nitride substrate is connected and grounded; the plate capacitor between the lower end of the metal via and the metal grounding layer The other end of the fourth coaxial capacitor between the anti-pad and the metal via The other ends are grounded.

[0114] In this embodiment, the specific steps of realizing the simulation of the multi-layer substrate via electrothermal coupling model are: The temperature-dependent components in the lumped parameter equivalent circuit model and the equivalent thermal circuit model, namely the temperature-dependent parasitic resistor and the temperature-dependent thermal resistor, are described using the Verilog-A language, and the power consumption generated by the temperature-dependent parasitic resistor in the equivalent circuit is defined; then a voltage-controlled current source is built to convert the power consumption generated by the temperature-dependent parasitic resistor into a heat source and transfer it to the corresponding temperature node of the metal via in the equivalent thermal circuit model; the temperature value of the temperature node at the center of the metal via in the equivalent thermal circuit model is transferred back to the A lumped parameter equivalent circuit model is used to update the conductivity and temperature-dependent parasitic resistance of metal vias and metal ground layers. Through simulation and solution, the steady-state temperature of metal vias in different layers can be obtained.

[0115] When solving the simulation, the modified nodal analysis (MNA) method is used for calculation, so that the electrothermal coupling model of the via hole of the multilayer substrate can be realized, and the steady-state temperature of the metal via hole in the multilayer aluminum nitride substrate can be obtained. Currently commonly used circuit simulation software, such as the Hardware Simulation Program with Integrated Circuit Emphasis (HSPICE) and the Advanced Design System (ADS), all have the MNA solving function. In the present invention, the MNA solver provided by ADS is used for solving.

[0116] Furthermore, in order to verify the efficiency and accuracy of the via temperature obtained by the electrothermal coupling model of the via hole of the multi-layer substrate in the present invention. Fig. 9 Taking the multi-layer substrate via electrothermal coupling model shown in the figure as an example, a sinusoidal voltage excitation is applied to the substrate via. The voltage expression on the voltage source in the multi-layer substrate via electrothermal coupling model is:

[0117] ;

[0118] in, is the voltage on the voltage source in the multi-layer substrate via electrothermal coupling model, is the bias voltage, is the oscillation amplitude, is the signal frequency, For time. To set the bias voltage is 0.1V, the oscillation amplitude The value is 0.1V, the initial temperature is 293.15K, the upper surface and four sides of the multilayer substrate via electrothermal coupling model are set to thermal insulation, and the convection coefficient of the lower surface is set to 2000. , to simulate the thermal interaction between the multi-layer substrate via electrothermal coupling model and the surrounding environment. The steady-state temperature of the center point of the metal via calculated by the multi-layer substrate via electrothermal coupling model of the present invention is compared with the simulation result of the finite element software COMSOL. The comparison results are shown in Table 2.

[0119] Table 2 Comparison of computational efficiency and accuracy of different models

[0120]

[0121] As can be seen from Table 2, the method for constructing a multi-layer substrate via electrothermal coupling model considering temperature-dependent parameter changes of the present invention, the steady-state temperature of the center point of the metal via in each layer of the aluminum nitride substrate calculated by the constructed multi-layer substrate via electrothermal coupling model has an average error of only 1.82% compared with the finite element simulation model, and the calculation time is reduced by 40.6%. The multi-layer substrate via electrothermal coupling model obtained by the present invention comprehensively considers the problem of temperature-dependent material parameter changes caused by power consumption, and can quickly obtain the temperature change of the via while ensuring accuracy.

[0122] Based on the above Figure 1 It can be seen from the implementation method that the embodiment of the present invention constructs the corresponding multi-layer substrate via structure according to the size parameters, material parameters and multi-layer equivalent circuit network cascade method of the multi-layer substrate via structure. The equivalent thermal circuit model of the multi-layer substrate via structure is constructed based on the size parameters, material parameters, and temperature nodes between adjacent layers of the multi-layer substrate via structure. The lumped parameter equivalent circuit model and the equivalent thermal circuit model are connected to establish the electrothermal coupling model of multi-layer substrate vias, so as to obtain the steady-state temperature of the substrate vias using the electrothermal coupling model of multi-layer substrate vias. The lumped parameter equivalent circuit model and the equivalent thermal circuit model are connected to establish the electrothermal coupling model of multi-layer substrate vias. The lumped parameter equivalent circuit model takes into account the change in material conductivity caused by electrical power consumption, and the equivalent thermal circuit model takes into account the change in thermal conductivity caused by electrical power consumption, so that The power consumption of the lumped parameter equivalent circuit model is converted into the heat source input equivalent thermal circuit model, and then the node temperature in the equivalent thermal circuit model is used to update the material parameters, so that the temperature change of the via can be accurately obtained; establish The lumped parameter equivalent circuit model and equivalent thermal circuit model use the size parameters, material parameters, multi-layer equivalent circuit network cascade method and temperature nodes between adjacent layers of the multi-layer substrate via structure, and do not need to divide the multi-layer substrate via structure into fine grids, so that less computing resources are occupied and the calculation time is faster.

[0123] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for constructing an electrothermal coupling model of a multi-layer substrate via considering temperature variation parameters, characterized in that: The method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account temperature variation parameters includes: According to the size parameters, material parameters and multi-layer equivalent circuit network cascade mode of the multi-layer substrate via structure, the corresponding A lumped parameter equivalent circuit model is provided, wherein the multi-layer substrate via structure comprises three layers of aluminum nitride substrates, four layers of metal grounding layers, metal vias and anti-pads, the size parameters comprise the thickness of each layer of metal grounding layers, the thickness of each layer of aluminum nitride substrates, the radius of the metal vias, the radius of the anti-pads and the height of the metal vias, and the material parameters comprise the thermal conductivity of the metal grounding layers and the metal vias, the thermal conductivity of the aluminum nitride substrate, the constant-pressure heat capacity of the metal grounding layers and the metal vias, the constant-pressure heat capacity of the aluminum nitride substrate, the density of the metal grounding layers and the metal vias and the density of the aluminum nitride substrate; Constructing an equivalent thermal circuit model corresponding to the multi-layer substrate via structure according to the size parameters, the material parameters, and the temperature nodes between adjacent layers of the multi-layer substrate via structure; Using hardware description language, the The type lumped parameter equivalent circuit model is connected with the equivalent thermal circuit model to establish a multi-layer substrate via electrothermal coupling model, so as to obtain the steady-state temperature of the substrate via by using the multi-layer substrate via electrothermal coupling model; The constructing an equivalent thermal circuit model corresponding to the multi-layer substrate via structure according to the size parameter, the material parameter, and the temperature nodes between adjacent layers of the multi-layer substrate via structure includes: Dividing the multi-layer substrate via structure into a plurality of second single-layer substrate via substructures according to the center positions of the two middle metal ground layers; According to the thickness of each metal ground layer, the thickness of each aluminum nitride substrate, the radius of the metal via, the radius of the anti-pad, the height of the metal via, the thermal conductivity of the metal ground layer and the metal via, the thermal conductivity of the aluminum nitride substrate, the constant-pressure heat capacity of the metal ground layer and the metal via, the constant-pressure heat capacity of the aluminum nitride substrate, the density of the metal ground layer and the metal via, and the density of the aluminum nitride substrate, calculate the lateral thermal resistance, longitudinal thermal resistance and thermal capacity corresponding to each second single-layer substrate via substructure, the lateral thermal resistance includes the lateral thermal resistance of the heat flow flowing through the metal via to diffuse to the aluminum nitride substrate, and the longitudinal thermal resistance includes the longitudinal thermal resistance of the heat flow flowing through the aluminum nitride substrate; Constructing a three-dimensional equivalent sub-thermal circuit model corresponding to the plurality of second single-layer substrate via sub-structures according to the lateral thermal resistance, the longitudinal thermal resistance and the thermal capacitance; According to the three-dimensional equivalent sub-thermal circuit model, temperature nodes between adjacent layers of the multi-layer substrate via structure are connected in four divided horizontal directions to obtain the equivalent thermal circuit model; The multi-layer substrate via structure is constructed according to the size parameters, material parameters and multi-layer equivalent circuit network cascade mode of the multi-layer substrate via structure. Lumped parameter equivalent circuit model, including: Dividing the multi-layer substrate via structure into a plurality of first single-layer substrate via substructures; Calculating parasitic parameters of the plurality of first single-layer substrate via substructures according to the thickness of each metal ground layer, the radius of the metal via, the radius of the anti-pad, the height of the metal via, and the relative dielectric constant of the aluminum nitride substrate, wherein the parasitic parameters include parasitic resistance; The hardware description language is used to The method comprises: connecting a lumped parameter equivalent circuit model of the multilayer substrate via to the equivalent thermal circuit model, establishing an electrothermal coupling model of a multilayer substrate via, and obtaining a steady-state temperature of the substrate via by using the electrothermal coupling model of the multilayer substrate via. The method comprises: The parasitic resistance, the lateral thermal resistance of the heat flow through the metal vias and diffused to the aluminum nitride substrate, and the longitudinal thermal resistance of the heat flow through the aluminum nitride substrate are described by the hardware description language to obtain corresponding temperature-dependent parasitic resistance and temperature-dependent thermal resistance; In the temperature-variable parasitic resistor, the power consumption output node of the metal via in each layer of the aluminum nitride substrate is used to output the power consumption generated by the temperature-variable parasitic resistor, and the temperature difference between the temperature nodes in the temperature-variable thermal resistor is used to update the temperature-variable thermal resistor to obtain an updated equivalent thermal circuit model; Using the hardware description language to establish a voltage-controlled current source, the power consumption of the power consumption input node in the voltage-controlled current source being the same as the power consumption generated by the temperature-dependent parasitic resistor; The voltage-controlled current source is used to convert the electric power consumption generated by the temperature-dependent parasitic resistance into a heat source, and the heat source is input into the updated equivalent thermal circuit model to establish the multi-layer substrate via electrothermal coupling model, and the multi-layer substrate via electrothermal coupling model is used to obtain the steady-state temperature of the substrate via.

2. The method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account temperature-dependent parameter changes according to claim 1, characterized in that: The material parameters also include a relative dielectric constant of the aluminum nitride substrate.

3. The method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account temperature-dependent parameter changes according to claim 2, characterized in that: The multi-layer substrate via structure is constructed according to the size parameters, material parameters and multi-layer equivalent circuit network cascade mode of the multi-layer substrate via structure. Lumped parameter equivalent circuit model, also includes: Performing equivalent replacement on the plurality of first single-layer substrate via substructures according to the parasitic parameters to obtain a plurality of equivalent subcircuit models corresponding to the plurality of first single-layer substrate via substructures; According to the plurality of equivalent subcircuit models and the multi-layer equivalent circuit network cascade mode, the Lumped parameter equivalent circuit model.

4. The method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account temperature-dependent parameter changes according to claim 3, characterized in that: Said The lumped parameter equivalent circuit model includes: the first coaxial capacitor between the anti-pad and the metal via , the second coaxial capacitor between the anti-pad and the metal via , the third coaxial capacitor between the anti-pad and the metal via , the fourth coaxial capacitor between the anti-pad and the metal via , parasitic resistance of metal vias in the first layer of aluminum nitride substrate , Parasitic resistance of metal vias in the second layer of aluminum nitride substrate , Parasitic resistance of metal vias in the third layer of aluminum nitride substrate , parasitic inductance of metal vias in the first layer of aluminum nitride substrate , Parasitic inductance of metal vias in the second layer of aluminum nitride substrate , Parasitic inductance of metal vias in the third layer of aluminum nitride substrate , the plate capacitance between the upper end of the metal via in the first layer of aluminum nitride substrate and the metal ground layer , the plate capacitance between the lower end of the metal via in the first layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the upper end of the metal via in the second layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the lower end of the metal via in the second layer of aluminum nitride substrate and the metal grounding layer , the plate capacitance between the upper end of the metal via in the third layer of aluminum nitride substrate and the metal grounding layer And the plate capacitance between the lower end of the metal via in the third layer of aluminum nitride substrate and the metal ground layer .

5. The method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account temperature-dependent parameter changes according to claim 1, characterized in that: The lateral thermal resistance also includes the lateral thermal resistance of the heat flow through the metal via, the longitudinal thermal resistance also includes the longitudinal thermal resistance of the heat flow through the metal via and the longitudinal thermal resistance of the heat flow through the metal grounding layer, and the thermal capacitance includes the thermal capacitance of the metal via, the thermal capacitance of the aluminum nitride substrate and the thermal capacitance of the metal grounding layer.

6. The method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account temperature-dependent parameter changes according to claim 1, characterized in that: The multi-layer substrate via electrothermal coupling model includes: The type lumped parameter equivalent circuit model, the voltage-controlled current source and the updated equivalent thermal circuit model.

7. The method for constructing an electrothermal coupling model of a multi-layer substrate via taking into account temperature-dependent parameter changes according to claim 1, characterized in that: The multi-layer substrate via electrothermal coupling model includes an electric power consumption output node of a metal via in a first layer of aluminum nitride substrate connected to a first electric power consumption input node of a voltage-controlled current source, an electric power consumption output node of a metal via in a second layer of aluminum nitride substrate connected to a second electric power consumption input node of the voltage-controlled current source, an electric power consumption output node of a metal via in a third layer of aluminum nitride substrate connected to a third electric power consumption input node of the voltage-controlled current source, a heat source input node of a metal via in the first layer of aluminum nitride substrate connected to a first heat source output node of the voltage-controlled current source, a heat source input node of a metal via in the second layer of aluminum nitride substrate connected to a second heat source output node of the voltage-controlled current source, and a heat source input node of a metal via in the third layer of aluminum nitride substrate connected to a third heat source output node of the voltage-controlled current source. The temperature node of the metal via in the first layer of aluminum nitride substrate in the type lumped parameter equivalent circuit model is connected to the heat source input node of the metal via in the first layer of aluminum nitride substrate, The temperature node of the metal via in the second layer of aluminum nitride substrate in the type lumped parameter equivalent circuit model is connected to the heat source input node of the metal via in the second layer of aluminum nitride substrate, The temperature node of the metal via in the third layer of the aluminum nitride substrate in the type lumped parameter equivalent circuit model is connected to the heat source input node of the metal via in the third layer of the aluminum nitride substrate.

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