Three-dimensional microsystem temperature calculation method considering thermal capacity change of transient thermal analysis model

Abstract

The invention discloses a three-dimensional microsystem temperature calculation method considering thermal capacity change of a transient thermal analysis model. The method comprises the following steps: extracting anisotropic equivalent thermal conductivity of a substrate of a TCV array embedded in a three-dimensional microsystem; wherein a plurality of chips are arranged on the substrate; obtaining a first anisotropic transient thermal analysis model corresponding to a single chip in the three-dimensional microsystem according to the anisotropic equivalent thermal conductivity; superposing the first anisotropic transient thermal analysis models of the plurality of chips to obtain a second anisotropic transient thermal analysis model; and gradually updating the heat capacity value of the second anisotropic transient thermal analysis model in a plurality of continuous time periods to obtain a final anisotropic transient thermal analysis model corresponding to the last time period, and obtaining the final transient temperature of the three-dimensional microsystem according to the final anisotropic transient thermal analysis model. According to the method, the temperature of the three-dimensional microsystem is calculated, the relation between the heat capacity value of the chip and the temperature is considered, and the method has high precision and short calculation time.

Description

Technical Field

[0001] The invention belongs to the field of microelectronic technology, and in particular relates to a temperature calculation method for a three-dimensional microsystem taking into account the heat capacity change of a transient thermal analysis model. Background Art

[0002] Today, with the rapid development of electronic technology, three-dimensional microsystems have become a revolutionary progress in the semiconductor field with their excellent integration capabilities and performance improvement. However, as three-dimensional microsystems develop in the direction of miniaturization, multi-function and high speed, the number of chips in the microsystem continues to increase, and the power of the chip itself is also increasing. If the heat in the system cannot be dissipated in a timely and effective manner, it will cause the local temperature in the system to rise sharply, which may cause problems such as increased thermal stress, chip warping or deformation, thereby increasing the probability of electronic device failure. Therefore, how to design a heat dissipation solution for a three-dimensional microsystem has become an urgent problem to be solved. At present, the main heat dissipation methods can be divided into active heat dissipation and passive heat dissipation. Although active heat dissipation has a better heat dissipation effect, this method occupies a large volume and is difficult to integrate into a three-dimensional microsystem with a high integration density. Therefore, passive heat dissipation solutions based on heat dissipation through-hole arrays are more concerned.

[0003] At present, many related studies have developed thermal modeling methods for three-dimensional microsystems containing heat dissipation through-hole arrays: the first is the finite element method, which divides the actual physical model of the three-dimensional microsystem into a finite number of simple geometric units, and establishes a corresponding mathematical model in each unit to approximately solve the entire physical problem; the second is the thermal resistance network model, which uses the thermoelectric analogy method and establishes a thermal resistance topological network method to analyze the steady-state and transient temperature distribution of the three-dimensional microsystem; the third is the thermal analysis model, which uses the separation of variables method to solve the Fourier series form of the steady-state and transient temperature fields, and requires the Fourier coefficients to be determined through initial conditions and boundary conditions.

[0004] However, the above thermal analysis methods have some limitations. Method 1 usually requires a large number of grids to be divided, which is time-consuming in model construction and simulation calculations; the error of method 2 will increase with the increase in the number of chips; the transient thermal analysis model of method 3 is not yet perfect, and there is a certain gap between the modeling effect and the actual heat dissipation effect. Therefore, a time-saving and more accurate thermal modeling method for three-dimensional microsystems is urgently needed. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a three-dimensional microsystem temperature calculation method considering the heat capacity change of a transient thermal analysis model.

[0006] The technical problem to be solved by the present invention is achieved through the following technical solutions: In a first aspect, the present invention provides a method for calculating the temperature of a three-dimensional microsystem taking into account the heat capacity change of a transient thermal analysis model, the method comprising: S1. extracting anisotropic equivalent thermal conductivity of a substrate of a TCV array embedded in a three-dimensional microsystem; wherein a plurality of chips are arranged on the substrate; S2. Obtaining a first anisotropic transient thermal analysis model corresponding to a single chip in the three-dimensional microsystem according to the anisotropic equivalent thermal conductivity; S3, superimposing the first anisotropic transient thermal analysis models of the plurality of chips to obtain a second anisotropic transient thermal analysis model; S4. Successively update the heat capacity value of the second anisotropic transient thermal analysis model in multiple consecutive time periods to obtain a final anisotropic transient thermal analysis model corresponding to the last time period, and obtain a final transient temperature of the three-dimensional microsystem according to the final anisotropic transient thermal analysis model.

[0007] Optionally, S2 includes: S21, obtaining an initial anisotropic transient thermal analysis model corresponding to a single chip in the three-dimensional microsystem according to the anisotropic equivalent thermal conductivity; S22, obtaining a first control equation and a first boundary condition corresponding to a steady-state part, and a second control equation, an initial condition, and a second boundary condition corresponding to a transient part according to the initial anisotropic transient thermal analysis model; S23, obtaining a steady-state temperature rise according to the first control equation and the first boundary condition; S24, obtaining a transient temperature rise according to the second control equation, the initial condition and the second boundary condition; S25, combining the steady-state temperature rise and the transient temperature rise to obtain a first anisotropic transient thermal analysis model corresponding to a single chip of the three-dimensional microsystem.

[0008] Optionally, the anisotropic equivalent thermal conductivity is expressed as follows: ; ; ; in, is the equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, is the equivalent thermal conductivity of the substrate along the Z direction in the three-dimensional coordinate system, is the first part equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, is the second part equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, , is the thermal conductivity of Cu in the substrate, is the thermal conductivity of AlN in the substrate, , , , , is the first volume fraction, is the second volume fraction, is the volume fraction of Cu in the substrate, is the volume fraction of AlN in the substrate, is the radius of the TCV in the TCV array, is the spacing between adjacent TCVs in the TCV array, .

[0009] Optionally, S4 includes: S41, calculating a plurality of time nodes of each time period in the plurality of continuous time periods; S42, calculating the initial average temperatures corresponding to the last two time nodes of the first time period according to the second anisotropic transient thermal analysis model; S43. According to the initial average temperature, the estimated temperatures corresponding to the middle moments of the remaining time periods are obtained in sequence, and the heat capacity value of the second anisotropic transient thermal analysis model is updated according to the estimated temperatures, until the second anisotropic transient thermal analysis model corresponding to the last time period is obtained as the final anisotropic transient thermal analysis model, and the final transient temperature is obtained according to the final anisotropic transient thermal analysis model.

[0010] Optionally, S43 includes: S431, in each remaining time period, obtain an estimated temperature corresponding to the middle moment of the current time period according to the average temperature of the previous time period; S432, updating the heat capacity value of the second anisotropic transient thermal analysis model in the current time period according to the estimated temperature to obtain an updated second anisotropic transient thermal analysis model; S433, calculating the transient temperature of the current time period and the average temperatures corresponding to the last two time nodes of the current time period according to the updated second anisotropic transient thermal analysis model; S434, using the temperature correction item to perform temperature correction on the transient temperature and the average temperature of the current time period to obtain a corrected transient temperature and a corrected average temperature of the current time period; S435. If the current time period is the last time period, the updated second anisotropic transient thermal analysis model corresponding to the current time period is used as the final anisotropic transient thermal analysis model, and the corrected transient temperature corresponding to the current time period is used as the final transient temperature; if the current time period is not the last time period, return to S431.

[0011] Optionally, the estimated temperature corresponding to the middle moment of the current time period is expressed as follows: ; in, represents the estimated temperature, Indicates the sequence number of the time period. , Indicates the preset number of thermal capacity updates. represents the calculation time of each time period, , Indicates the total calculation time. Indicates The average temperature at the last time node in the time period, Indicates The average temperature of the second-to-last time node in the time period, Represents the time step.

[0012] Optionally, the temperature correction term is expressed as follows: ; in, represents the temperature correction term, Indicates The transient temperature at the last time node in a time period, Indicates The transient temperature at the first time node in a time period.

[0013] In a second aspect, the present invention provides a three-dimensional microsystem temperature calculation device considering the heat capacity change of a transient thermal analysis model, the device comprising: A thermal conductivity extraction module, used to extract the anisotropic equivalent thermal conductivity of a substrate of a TCV array embedded in a three-dimensional microsystem; wherein a plurality of chips are arranged on the substrate; A first model acquisition module, used for obtaining a first anisotropic transient thermal analysis model corresponding to a single chip in the three-dimensional microsystem according to the anisotropic equivalent thermal conductivity; A second model acquisition module, configured to superimpose the first anisotropic transient thermal analysis models of the plurality of chips to obtain a second anisotropic transient thermal analysis model; The temperature calculation module is used to successively update the heat capacity value of the second anisotropic transient thermal analysis model in multiple consecutive time periods to obtain a final anisotropic transient thermal analysis model corresponding to the last time period, and obtain the final transient temperature of the three-dimensional microsystem according to the final anisotropic transient thermal analysis model.

[0014] The technical solution provided by the embodiments of the present invention may have the following beneficial effects: In the above technical scheme, the final anisotropic transient thermal analysis model constructed by the present invention can realize the extraction of the temperature and peak temperature of any point in the three-dimensional microsystem; and when establishing the anisotropic transient thermal analysis model, the relationship between the heat capacity value and temperature of the chip in the three-dimensional microsystem is considered. Compared with the current existing technology that does not consider the temperature-dependent characteristics of heat capacity in the transient thermal analysis model of the three-dimensional microsystem, resulting in unsatisfactory modeling effect, the temperature calculated by the present invention using the final anisotropic transient thermal analysis model is more accurate and the calculation time is greatly reduced.

[0015] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of a three-dimensional microsystem temperature calculation method considering the heat capacity change of a transient thermal analysis model provided by an embodiment of the present invention.

[0017] Figure 2 It is a schematic structural diagram of a three-dimensional microsystem provided by an embodiment of the present invention.

[0018] Figure 3 It is a schematic diagram of a temperature field provided by an embodiment of the present invention.

[0019] Figure 4 It is a schematic diagram of a relative error of a temperature field provided by an embodiment of the present invention.

[0020] Figure 5 It is a block diagram of a three-dimensional microsystem temperature calculation device considering the heat capacity change of a transient thermal analysis model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0021] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0022] Figure 1 is a flow chart of a method for calculating the temperature of a three-dimensional microsystem taking into account the heat capacity change of a transient thermal analysis model provided by an embodiment of the present invention. Figure 1 As shown, the method comprises the following steps: S1. Extracting the anisotropic equivalent thermal conductivity of a substrate of a TCV array embedded in a three-dimensional microsystem; wherein a plurality of chips are arranged on the substrate.

[0023] In this embodiment, the three-dimensional microsystem includes a substrate and a plurality of chips arranged on the substrate. The chip serves as a heat source. Each chip is fixed to the substrate by welding. A TCV (Through Ceramic Via) is provided on the substrate. The heat dissipation via is filled with Cu. The material of the substrate may be AlN.

[0024] In a specific example, Figure 2 : is a schematic diagram of the structure of a three-dimensional microsystem provided by an embodiment of the present invention, the three-dimensional microsystem includes four chips C1, C2, C3 and C4, and 36 heat dissipation through holes are arranged on the substrate. The structural parameters of the three-dimensional microsystem include substrate length, substrate width, substrate thickness, chip length, chip width, chip thickness, heat dissipation through hole radius, adjacent through hole spacing and center point coordinates between adjacent chips.

[0025] For example, Figure 2 Taking the three-dimensional microsystem shown in FIG. 1 as an example, its structural parameters can be shown in Table 1.

[0026] Table 1

[0027] In S1, the anisotropic equivalent thermal conductivity of the substrate of the TCV array embedded in the three-dimensional microsystem is extracted, including: obtaining the anisotropic equivalent thermal conductivity according to the structural parameters of the three-dimensional microsystem, which is expressed as follows: ; ; ; in, is the equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, is the equivalent thermal conductivity of the substrate along the Z direction in the three-dimensional coordinate system, is the first part equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, is the second equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, , is the thermal conductivity of Cu in the substrate, is the thermal conductivity of AlN in the substrate, , , , , is the first volume fraction, is the second volume fraction, is the volume fraction of Cu in the substrate, is the volume fraction of AlN in the substrate, is the radius of the heat dissipation vias in the TCV array, is the spacing between adjacent heat dissipation vias in the TCV array, .

[0028] S2. Obtain a first anisotropic transient thermal analysis model corresponding to a single chip in a three-dimensional microsystem according to the anisotropic equivalent thermal conductivity.

[0029] Optionally, S2 may include: S21. Obtaining an initial anisotropic transient thermal analysis model corresponding to a single chip in a three-dimensional microsystem according to anisotropic equivalent thermal conductivity; S22, obtaining a first control equation and a first boundary condition corresponding to a steady-state part, and a second control equation, an initial condition, and a second boundary condition corresponding to a transient part according to an initial anisotropic transient thermal analysis model; S23, obtaining a steady-state temperature rise according to the first control equation and the first boundary condition; S24, obtaining a transient temperature rise according to the second control equation, the initial condition and the second boundary condition; S25. Combining the steady-state temperature rise and the transient temperature rise to obtain a first anisotropic transient thermal analysis model corresponding to a single chip of the three-dimensional microsystem.

[0030] In the above S21, the initial anisotropic transient thermal analysis model of the three-dimensional microsystem obtained according to the anisotropic equivalent thermal conductivity includes: (1) Construct the control equation of the three-dimensional microsystem, which is expressed as follows: ; in, Indicates temperature rise, is the transient temperature at any point on the substrate, is the ambient temperature; is the anisotropic thermal diffusivity of the substrate along the X direction in the three-dimensional coordinate system, is the anisotropic thermal diffusivity of the substrate along the Y direction in the three-dimensional coordinate system, is the anisotropic thermal diffusivity of the substrate along the Z direction in the three-dimensional coordinate system, is the coordinate of the substrate along the X direction in the three-dimensional coordinate system, is the coordinate of the substrate along the Y direction in the three-dimensional coordinate system, is the coordinate of the substrate along the Z direction in the three-dimensional coordinate system, Indicates time; (2) Establish the overall initial conditions: ; in, express The corresponding temperature rise when (3) Model the heat source area of ​​the chip on the upper surface of the substrate to meet the heat flux boundary conditions, as shown below: ; in, is the chip power of the chip on the surface of the substrate; (4) Model the other areas on the upper surface of the substrate to meet the adiabatic boundary conditions, as shown below: ; (5) The lower surface of the substrate is modeled to meet the convective heat transfer boundary conditions, which is expressed as follows: ; in, is the convective heat transfer coefficient; (6) Model the other surfaces that satisfy the adiabatic boundary conditions as follows: ; ; Anisotropic heat diffusion is modeled as follows: ; ; in, , is the average density of the three-dimensional microsystem, is the average heat capacity of the three-dimensional microsystem, which can be calculated by the mass fraction of each material in the three-dimensional microsystem; Thus, the modeling of the initial anisotropic transient thermal analysis model of the three-dimensional microsystem is completed.

[0031] In S22, the first control equation corresponding to the steady-state part obtained according to the initial anisotropic transient thermal analysis model is expressed as follows: ; Accordingly, the first boundary condition corresponding to the steady-state part obtained according to the initial anisotropic transient thermal analysis model includes: (1) The chip heat source area on the substrate surface satisfies the heat flux boundary condition, which is expressed as follows: ; (2) The other areas on the upper surface of the substrate meet the adiabatic boundary conditions, which are expressed as follows: ; (3) The lower surface of the substrate satisfies the convective heat transfer boundary conditions, which are expressed as follows: ; (4) Other surfaces satisfy the adiabatic boundary conditions, which are expressed as follows: ; .

[0032] In S23, the steady-state temperature rise is obtained according to the first control equation and the first boundary condition corresponding to the steady-state part, which is expressed as: (1); in, , , , L and W are the length and width of the substrate, is the hyperbolic cosine function, is the hyperbolic sine function, , , , , , , and is the Fourier coefficient of the steady-state part, expressed as follows: ; ; ; ; ; ; ; ; in, is the horizontal coordinate of the chip center, is the vertical coordinate of the chip center, represents the Fourier coefficient A and B The proportional relationship, , and The expression is: ; ; ; in, is the hyperbolic tangent function.

[0033] In S22, the second control equation corresponding to the transient part obtained according to the initial anisotropic transient thermal analysis model is expressed as follows: ; The initial conditions corresponding to the transient part are expressed as follows: ; in, for Transient temperature rise when The second boundary conditions corresponding to the transient part obtained according to the initial anisotropic transient thermal analysis model include: (1) The lower surface of the substrate satisfies the convective heat transfer boundary conditions, which are expressed as follows: ; (2) Other surfaces satisfy the adiabatic boundary conditions, which are expressed as follows: ; ; ; In S24, the transient temperature rise is obtained according to the second control equation, the initial condition and the second boundary condition corresponding to the transient part, which is expressed as: (2); in, is the characteristic value, , , and are the Fourier coefficients of the transient part.

[0034] Eigenvalue This is consistent with the transcendental equation: ; Among them, select The range is 1, 2, ..., 5, To meet the first five non-negative solutions of the above transcendental equation, the Fourier coefficients of the transient part are expressed as follows: ; ; ; ; in, ; Therefore, in S25, the steady-state temperature rise represented by equation (1) and the transient temperature rise represented by equation (2) are combined to obtain the first anisotropic transient thermal analysis model corresponding to a single chip in the three-dimensional microsystem, which is expressed as follows: ; S3. Superimposing the first anisotropic transient thermal analysis models of multiple chips to obtain a second anisotropic transient thermal analysis model.

[0035] Specifically, the first anisotropic transient thermal analysis models of multiple chips are superimposed to obtain a second anisotropic transient thermal analysis model, which is expressed as follows: ; in, Indicates The first anisotropic transient thermal analysis model corresponding to the chip, is the total number of chips, Represents the second anisotropic transient thermal analysis model.

[0036] S4. Successively update the heat capacity value of the second anisotropic transient thermal analysis model in multiple consecutive time periods to obtain a final anisotropic transient thermal analysis model corresponding to the last time period, and obtain a final transient temperature of the three-dimensional microsystem according to the final anisotropic transient thermal analysis model.

[0037] Optionally, S4 may include: S41, calculating multiple time nodes in each time period in multiple continuous time periods; S42, calculating the initial average temperatures corresponding to the last two time nodes of the first time period according to the second anisotropic transient thermal analysis model; S43. According to the initial average temperature, the estimated temperatures corresponding to the middle moments of the remaining time periods are obtained in turn, and the heat capacity value of the second anisotropic transient thermal analysis model is updated according to the estimated temperatures, until the second anisotropic transient thermal analysis model corresponding to the last time period is obtained as the final anisotropic transient thermal analysis model, and the final transient temperature is obtained according to the final anisotropic transient thermal analysis model.

[0038] Specifically, in S41, by setting the initial temperature to the ambient temperature , the number of heat capacity updates is , the total time is calculated as , the time step is , use these parameters to obtain the calculation time of each time period in multiple consecutive time periods , the corresponding time node is ,in, .

[0039] In S42, the initial transient temperature of the first time period is solved according to the second anisotropic transient thermal analysis model. This is used for subsequent calculation of temperature correction items and to calculate the initial average temperature of the last two time nodes. and , the average temperature can be estimated using the temperature at the center of the three-dimensional microsystem.

[0040] S43 may include: S431, in each remaining time period, obtain an estimated temperature corresponding to the middle moment of the current time period according to the average temperature of the previous time period; S432, updating the heat capacity value of the second anisotropic transient thermal analysis model in the current time period by estimating the temperature, to obtain an updated second anisotropic transient thermal analysis model; S433, calculating the transient temperature of the current time period and the average temperatures corresponding to the last two time nodes of the current time period according to the updated second anisotropic transient thermal analysis model; S434, using the temperature correction item to perform temperature correction on the transient temperature and the average temperature of the current time period to obtain a corrected transient temperature and a corrected average temperature of the current time period; S435. If the current time period is the last time period, the updated second anisotropic transient thermal analysis model corresponding to the current time period is used as the final anisotropic transient thermal analysis model, and the corrected transient temperature corresponding to the current time period is used as the final transient temperature; if the current time period is not the last time period, return to S431.

[0041] It can be understood that the estimated temperature corresponding to the middle moment of the current time period is obtained according to the average temperature of the previous time period, and the estimated temperature is used to update the heat capacity value of the second anisotropic transient thermal analysis model of the current time period. The estimated temperature corresponding to the middle moment of the current time period is calculated as follows: ; in, represents the estimated temperature, Indicates the sequence number of the time period. , Indicates the preset number of thermal capacity updates. represents the calculation time of each time period, , Indicates the total calculation time. Indicates The average temperature at the last time node in the time period, Indicates The average temperature of the second-to-last time node in the time period, Represents the time step.

[0042] Solve the current time period (second time period) according to the updated second anisotropic transient thermal analysis model Transient temperature of , and calculate the average temperature of the last two time nodes of the current time period and ; The temperature correction term is expressed as follows: ; in, represents the temperature correction term, Indicates The transient temperature at the last time node in a time period, Indicates The transient temperature of the first time node in the time period; when calculating the temperature correction term, the transient temperature of the first time node in the first time period is also the initial transient temperature .

[0043] The corrected temperatures are: ; ; ; in, For the The corrected transient temperature corresponding to each time period is and For the The corrected average temperatures corresponding to the last two time nodes in a time period.

[0044] If the current time period is the last time period, the updated second anisotropic transient thermal analysis model corresponding to the current time period is used as the final anisotropic transient thermal analysis model, and the corrected transient temperature corresponding to the current time period is used as the final transient temperature; if the current time period is not the last time period, return to S431.

[0045] In one embodiment, Figure 3 is a schematic diagram of a temperature field provided by an embodiment of the present invention, Figure 4 is a schematic diagram of a relative error of a temperature field provided by an embodiment of the present invention, Figure 2 As an example, the three-dimensional microsystem shown in the figure has the same structural parameters as those in Table 1. When the power consumption of chips C1, C2, C3 and C4 in the three-dimensional microsystem is 0.8W, 0.8W, 4.2W and 4.2W respectively, the temperature of the three-dimensional microsystem considering the heat capacity change of the transient thermal analysis model is calculated as follows: Figure 3 As shown. Taking the finite element simulation results as a reference, the relative error of the surface temperature field on the substrate is calculated as follows Figure 4 shown.

[0046] The final anisotropic transient thermal analysis model in the present invention is compared with other models. The comparison results are shown in Table 2. Among them, model 1 is a finite element simulation model, model 2 is an anisotropic transient thermal analysis model without considering the change of heat capacity, and model 3 is the final anisotropic transient thermal analysis model in the present invention. The comparison data are the temperature and peak temperature of each chip in the three-dimensional microsystem at the 10th second calculated by each model.

[0047] Table 2

[0048] As can be seen from Table 2, the final anisotropic transient thermal analysis model constructed by the present invention taking into account the change in heat capacity has an average error of only 0.84% ​​in the temperature of each chip at the 10th second compared with the finite element simulation; the average error of the peak temperature of the three-dimensional microsystem at the 10th second obtained is only 0.74% compared with the finite element simulation, and the calculation time is 0.43s. The anisotropic transient thermal analysis model that does not consider the change in heat capacity has high calculation efficiency because it does not consider the relationship between the heat capacity and temperature of each material in the microsystem, and the calculation process is relatively simple. Compared with the anisotropic transient thermal analysis model that does not consider the change in heat capacity, the model of the present invention greatly improves the calculation accuracy while ensuring high calculation efficiency. However, in actual working conditions, the temperature will gradually increase after the system is working, and the use of the anisotropic transient thermal analysis model that does not consider the change in heat capacity to predict the temperature will further increase the error.

[0049] The final anisotropic transient thermal analysis model constructed by the present invention can realize the extraction of the temperature and peak temperature of any point in the three-dimensional microsystem; and when establishing the anisotropic transient thermal analysis model, the relationship between the heat capacity value and the temperature of the chip in the three-dimensional microsystem is considered. Compared with the current existing technology that does not consider the temperature-dependent characteristics of heat capacity in the transient thermal analysis model of the three-dimensional microsystem, resulting in unsatisfactory modeling effect, the temperature calculated by the present invention using the final anisotropic transient thermal analysis model is more accurate and the calculation time is greatly reduced.

[0050] Figure 5 is a block diagram of a three-dimensional microsystem temperature calculation device considering the heat capacity change of a transient thermal analysis model provided by an embodiment of the present invention, such as Figure 5 As shown, the device 500 includes: The thermal conductivity extraction module 501 is used to extract the anisotropic equivalent thermal conductivity of the substrate of the TCV array embedded in the three-dimensional microsystem; wherein a plurality of chips are arranged on the substrate; A first model acquisition module 502 is used to obtain a first anisotropic transient thermal analysis model corresponding to a single chip in a three-dimensional microsystem according to anisotropic equivalent thermal conductivity; A second model acquisition module 503 is used to superimpose the first anisotropic transient thermal analysis models of multiple chips to obtain a second anisotropic transient thermal analysis model; The temperature calculation module 504 is used to update the heat capacity value of the second anisotropic transient thermal analysis model in a plurality of consecutive time periods, obtain a final anisotropic transient thermal analysis model corresponding to the last time period, and obtain a final transient temperature of the three-dimensional microsystem according to the final anisotropic transient thermal analysis model.

[0051] Optionally, the first model acquisition module 502 includes: S51. Obtaining an initial anisotropic transient thermal analysis model corresponding to a single chip in a three-dimensional microsystem according to anisotropic equivalent thermal conductivity; S52, obtaining a first control equation and a first boundary condition corresponding to a steady-state part, and a second control equation, an initial condition, and a second boundary condition corresponding to a transient part according to an initial anisotropic transient thermal analysis model; S53, obtaining a steady-state temperature rise according to a first control equation and a first boundary condition corresponding to the steady-state part; S54, obtaining a transient temperature rise according to a second control equation, an initial condition, and a second boundary condition corresponding to the transient part; S55. Combine the steady-state temperature rise and the transient temperature rise to obtain a first anisotropic transient thermal analysis model corresponding to a single chip of the three-dimensional microsystem.

[0052] Alternatively, the anisotropic equivalent thermal conductivity is expressed as follows: ; ; ; in, is the equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, is the equivalent thermal conductivity of the substrate along the Z direction in the three-dimensional coordinate system, is the first part equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, is the second equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, , is the thermal conductivity of Cu in the substrate, is the thermal conductivity of AlN in the substrate, , , , , is the first volume fraction, is the second volume fraction, is the volume fraction of Cu in the substrate, is the volume fraction of AlN in the substrate, is the radius of the TCV in the TCV array, is the spacing between adjacent TCVs in the TCV array, .

[0053] Optionally, the temperature calculation module 504 includes: S61, calculating multiple time nodes in each time period in multiple continuous time periods; S62, calculating the initial average temperatures corresponding to the last two time nodes of the first time period according to the second anisotropic transient thermal analysis model; S63. According to the initial average temperature, the estimated temperatures corresponding to the middle moments of the remaining time periods are obtained in turn, and the heat capacity value of the second anisotropic transient thermal analysis model is updated according to the estimated temperatures, until the second anisotropic transient thermal analysis model corresponding to the last time period is obtained as the final anisotropic transient thermal analysis model, and the final transient temperature is obtained according to the final anisotropic transient thermal analysis model.

[0054] Optionally, S63 may include: S631, in each remaining time period, obtain an estimated temperature corresponding to the middle moment of the current time period according to the average temperature of the previous time period; S632, updating the heat capacity value of the second anisotropic transient thermal analysis model in the current time period by estimating the temperature, to obtain an updated second anisotropic transient thermal analysis model; S633, calculating the transient temperature of the current time period and the average temperatures corresponding to the last two time nodes of the current time period according to the updated second anisotropic transient thermal analysis model; S634, using the temperature correction item to perform temperature correction on the transient temperature and the average temperature of the current time period to obtain a corrected transient temperature and a corrected average temperature of the current time period; S635. If the current time period is the last time period, the updated second anisotropic transient thermal analysis model corresponding to the current time period is used as the final anisotropic transient thermal analysis model, and the corrected transient temperature corresponding to the current time period is used as the final transient temperature; if the current time period is not the last time period, return to S431.

[0055] Optionally, the estimated temperature corresponding to the middle moment of the current time period is expressed as follows: ; in, represents the estimated temperature, Indicates the sequence number of the time period. , Indicates the preset number of thermal capacity updates. represents the calculation time of each time period, , Indicates the total calculation time. Indicates The average temperature at the last time node in the time period, Indicates The average temperature of the second-to-last time node in the time period, Represents the time step.

[0056] Optionally, the temperature correction term is expressed as follows: ; in, represents the temperature correction term, Indicates The transient temperature at the last time node in a time period, Indicates The transient temperature at the first time node in a time period.

[0057] It should be noted that the terms "first", "second", etc. are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention.

[0058] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0059] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art can understand and implement other changes to the disclosed embodiments by viewing the drawings and the disclosed content. In the description of the present invention, the term "comprising" does not exclude other components or steps, "one" or "an" does not exclude multiple situations, and "multiple" means two or more, unless otherwise clearly and specifically limited. In addition, certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0060] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A three-dimensional microsystem temperature calculation method considering the heat capacity change of transient thermal analysis model, characterized in that: The method comprises: S1. extracting anisotropic equivalent thermal conductivity of a substrate of a TCV array embedded in a three-dimensional microsystem; wherein a plurality of chips are arranged on the substrate; S2. Obtaining a first anisotropic transient thermal analysis model corresponding to a single chip in the three-dimensional microsystem according to the anisotropic equivalent thermal conductivity; S3, superimposing the first anisotropic transient thermal analysis models of the plurality of chips to obtain a second anisotropic transient thermal analysis model; S4. Successively update the heat capacity value of the second anisotropic transient thermal analysis model in multiple consecutive time periods to obtain a final anisotropic transient thermal analysis model corresponding to the last time period, and obtain a final transient temperature of the three-dimensional microsystem according to the final anisotropic transient thermal analysis model.

2. The three-dimensional microsystem temperature calculation method considering the heat capacity change of the transient thermal analysis model according to claim 1 is characterized in that: S2, including: S21, obtaining an initial anisotropic transient thermal analysis model corresponding to a single chip in the three-dimensional microsystem according to the anisotropic equivalent thermal conductivity; S22, obtaining a first control equation and a first boundary condition corresponding to a steady-state part, and a second control equation, an initial condition, and a second boundary condition corresponding to a transient part according to the initial anisotropic transient thermal analysis model; S23, obtaining a steady-state temperature rise according to the first control equation and the first boundary condition; S24, obtaining a transient temperature rise according to the second control equation, the initial condition and the second boundary condition; S25, combining the steady-state temperature rise and the transient temperature rise to obtain a first anisotropic transient thermal analysis model corresponding to a single chip of the three-dimensional microsystem.

3. The three-dimensional microsystem temperature calculation method considering the heat capacity change of the transient thermal analysis model according to claim 1 is characterized in that: The anisotropic equivalent thermal conductivity is expressed as follows: ； ； ； in, is the equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, is the equivalent thermal conductivity of the substrate along the Z direction in the three-dimensional coordinate system, is the first part equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, is the second part equivalent thermal conductivity of the substrate along the X and Y directions in the three-dimensional coordinate system, , is the thermal conductivity of Cu in the substrate, is the thermal conductivity of AlN in the substrate, , , , , is the first volume fraction, is the second volume fraction, is the volume fraction of Cu in the substrate, is the volume fraction of AlN in the substrate, is the radius of the TCV in the TCV array, is the spacing between adjacent TCVs in the TCV array, .

4. The three-dimensional microsystem temperature calculation method considering the heat capacity change of the transient thermal analysis model according to claim 1 is characterized in that: S4, including: S41, calculating a plurality of time nodes of each time period in the plurality of continuous time periods; S42, calculating the initial average temperatures corresponding to the last two time nodes of the first time period according to the second anisotropic transient thermal analysis model; S43. According to the initial average temperature, the estimated temperatures corresponding to the middle moments of the remaining time periods are obtained in sequence, and the heat capacity value of the second anisotropic transient thermal analysis model is updated according to the estimated temperatures, until the second anisotropic transient thermal analysis model corresponding to the last time period is obtained as the final anisotropic transient thermal analysis model, and the final transient temperature is obtained according to the final anisotropic transient thermal analysis model.

5. The three-dimensional microsystem temperature calculation method considering the heat capacity change of the transient thermal analysis model according to claim 4 is characterized in that: S43, including: S431, in each remaining time period, obtain an estimated temperature corresponding to the middle moment of the current time period according to the average temperature of the previous time period; S432, updating the heat capacity value of the second anisotropic transient thermal analysis model in the current time period according to the estimated temperature to obtain an updated second anisotropic transient thermal analysis model; S433, calculating the transient temperature of the current time period and the average temperatures corresponding to the last two time nodes of the current time period according to the updated second anisotropic transient thermal analysis model; S434, using the temperature correction item to perform temperature correction on the transient temperature and the average temperature of the current time period to obtain a corrected transient temperature and a corrected average temperature of the current time period; S435. If the current time period is the last time period, the updated second anisotropic transient thermal analysis model corresponding to the current time period is used as the final anisotropic transient thermal analysis model, and the corrected transient temperature corresponding to the current time period is used as the final transient temperature; if the current time period is not the last time period, return to S431.

6. The three-dimensional microsystem temperature calculation method considering the heat capacity change of the transient thermal analysis model according to claim 5 is characterized in that: The estimated temperature corresponding to the middle moment of the current time period is calculated as follows: ； in, represents the estimated temperature, Indicates the sequence number of the time period. , Indicates the preset number of thermal capacity updates. represents the calculation time of each time period, , Indicates the total calculation time. Indicates The average temperature at the last time node in the time period, Indicates The average temperature of the second-to-last time node in the time period, Represents the time step.

7. The three-dimensional microsystem temperature calculation method considering the heat capacity change of the transient thermal analysis model according to claim 6 is characterized in that: The temperature correction term is calculated as follows: ； in, represents the temperature correction term, Indicates The transient temperature at the last time node in a time period, Indicates The transient temperature at the first time node in a time period.

8. A three-dimensional microsystem temperature calculation device considering the heat capacity change of transient thermal analysis model, characterized in that: The device comprises: A thermal conductivity extraction module, used to extract the anisotropic equivalent thermal conductivity of a substrate of a TCV array embedded in a three-dimensional microsystem; wherein a plurality of chips are arranged on the substrate; A first model acquisition module, used for obtaining a first anisotropic transient thermal analysis model corresponding to a single chip in the three-dimensional microsystem according to the anisotropic equivalent thermal conductivity; A second model acquisition module, configured to superimpose the first anisotropic transient thermal analysis models of the plurality of chips to obtain a second anisotropic transient thermal analysis model; The temperature calculation module is used to successively update the heat capacity value of the second anisotropic transient thermal analysis model in multiple consecutive time periods to obtain a final anisotropic transient thermal analysis model corresponding to the last time period, and obtain the final transient temperature of the three-dimensional microsystem according to the final anisotropic transient thermal analysis model.

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