Analog device, thermal equivalent circuit manufacturing method, and data structure

Abstract

Embodiments provide a simulation device useful for verifying a temporal change in thermal characteristics of a semiconductor device, a thermal equivalent circuit production method, and a data structure. The simulation device (1) of an embodiment includes a storage device (20) that stores data related to a thermal equivalent circuit of a semiconductor device, and an estimation device (30) that estimates a temporal change in thermal characteristics of the semiconductor device using the data. The thermal equivalent circuit includes a first thermal equivalent circuit that corresponds to an upper surface side portion of the semiconductor device, and a second thermal equivalent circuit that is connected to the first thermal equivalent circuit and corresponds to a lower surface side portion of the semiconductor device.

Description

[0001] [Related Applications]

[0002] This application relates to the priority of Japanese Patent Application No. 2021-152306 (filed on September 17, 2021). This application incorporates the entire contents of the basic application by reference to that basic application. Technical Field

[0003] The embodiments of the present invention relate to analog devices, methods for fabricating thermal equivalent circuits, and data structures. Background Technology

[0004] In the development of semiconductor devices, a process is performed to verify the time-dependent changes in the thermal properties of the designed semiconductor device. This verification is, for example, conducted using a simulation device. Summary of the Invention

[0005] Embodiments of the present invention provide a simulation apparatus, a method for fabricating a thermal equivalent circuit, and a data structure useful for verifying the time-dependent changes in the thermal characteristics of semiconductor devices.

[0006] The simulation apparatus of the embodiment includes: a storage device for storing data related to the thermal equivalent circuit of a semiconductor device; and an estimation device for using the data to estimate the time-dependent changes in the thermal characteristics of the semiconductor device. The thermal equivalent circuit includes: a first thermal equivalent circuit corresponding to a lower surface portion of the semiconductor device; and a second thermal equivalent circuit connected to the first thermal equivalent circuit and corresponding to an upper surface portion of the semiconductor device. Attached Figure Description

[0007] Figure 1 This is a block diagram illustrating an example of the hardware structure of a storage system implemented in this way.

[0008] Figure 2 This is a cross-sectional view showing an example of a semiconductor device.

[0009] Figure 3 This is a circuit diagram illustrating an example of the thermal equivalent circuit of an implementation method.

[0010] Figure 4 It is a graph showing the time-varying thermal characteristics of a semiconductor device estimated using a simulation device according to the implementation method.

[0011] Figure 5 It is a graph showing the time-varying thermal properties of a semiconductor device calculated using the finite element method for thermal fluid analysis.

[0012] Figure 6 It is a graph showing the time-varying changes of other thermal properties of a semiconductor device estimated using the simulation device of the embodiment.

[0013] Figure 7 It is a graph showing the time-varying thermal properties of other semiconductor devices calculated using the finite element method for thermal fluid analysis.

[0014] Figure 8 This is a graph showing the time-varying thermal characteristics of a semiconductor device under heat dissipation and adiabatic conditions estimated using a comparative example simulation device.

[0015] Figure 9 This is a flowchart illustrating the sequence of the first method for fabricating the thermal equivalent circuit in the implementation embodiment.

[0016] Figure 10 This is a flowchart illustrating the sequence of the second fabrication method for the thermal equivalent circuit of the embodiment.

[0017] Figure 11 This is a diagram showing the data structure of the thermal equivalent circuit used in the simulation device of the implementation method. Detailed Implementation

[0018] The embodiments are described below with reference to the accompanying drawings.

[0019] Figure 1 This is a block diagram illustrating an example of the hardware structure of the simulation device 1 in the implementation method.

[0020] The simulation device 1 estimates the time-dependent change (transient thermal response) of the thermal characteristics of the designed semiconductor device through calculation. In addition to estimating the time-dependent change of the thermal characteristics of the designed semiconductor device through calculation, the simulation device 1 can also estimate the electrical characteristics of the designed semiconductor device through calculation.

[0021] like Figure 1 As shown, the simulation device 1 includes an input device 10, a storage device 20, an estimation device 30, and an output device 40.

[0022] Input device 10 is a device for inputting information such as the type of semiconductor device and the values ​​of its thermal parameters. Input device 10 may include, for example, a keyboard 11 and a mouse 12. The type of semiconductor device may be, for example, an integrated circuit device using MOSFETs as basic components or an integrated circuit device using diodes as basic components. Thermal parameters may include, for example, the temperature of the atmosphere in which the semiconductor device is used (ambient temperature) and the power consumption of the semiconductor device.

[0023] The storage device 20 stores data, programs, etc. in a readable manner. In this embodiment, the storage device 20 stores data (hereinafter referred to as thermal circuit data) 21 related to the thermal equivalent circuit of the semiconductor device and data (hereinafter referred to as numerical data) 22 related to the values ​​of thermal parameters input from the input device 10 in a readable manner.

[0024] In estimating the time-dependent changes in the thermal characteristics and electrical characteristics of a semiconductor device, the storage device 20 stores, in addition to storing thermal circuit data in a readable manner, data related to the electrical equivalent circuit of the semiconductor device in a readable manner.

[0025] Storage device 20 includes, for example, a magnetic storage device or a semiconductor storage device. A magnetic storage device is, for example, a hard disk drive. A semiconductor storage device is, for example, a non-volatile semiconductor device. A non-volatile semiconductor device is, for example, a solid-state drive (SSD) with NAND flash memory. Alternatively, PRAM (Phase Change Random Access Memory), ReRAM (Resistive Random Access Memory), or FeRAM (Ferroelectric Random Access Memory) devices may be used instead of SSDs.

[0026] The estimation device 30 is an apparatus for estimating the time-dependent changes in the thermal characteristics of a semiconductor device through simulation (computation). The estimation device 30 includes an arithmetic unit 31 that performs the aforementioned calculations. The arithmetic unit 31 includes, for example, a CPU (central processing unit). The arithmetic unit 31 uses thermal circuit data 21 and numerical data 22 read from the storage device 20, as well as the simulation program (illustrated), to estimate the time-dependent changes in the thermal characteristics of the designed semiconductor device through calculations.

[0027] The program required for the simulation (the simulation program) is stored in the simulation device 1 in a readable manner. For example, the simulation program is stored in the storage device 20 in a readable manner.

[0028] In addition, if the estimation device 30 includes a storage device (not shown), the simulation program can also be stored in the storage device in a readable manner.

[0029] Furthermore, the program can also be stored in a readable manner in an external storage device that can be connected to the simulation device 1.

[0030] Simulation programs, for example, are SPICE (Simulation Program with Integrated Circuit Emphasis). These programs are available, for example, via the Internet.

[0031] The output device 40 is a device that outputs the time-varying changes (simulation results) of the thermal characteristics of the semiconductor device estimated by the estimation device 30 in a manner that can be observed by the naked eye. The output device 40 includes, for example, a display 41 and a printer 42.

[0032] Alternatively, the output device 40 may not be included as part of the simulation device 1. In this case, an output device that can be connected to the simulation device 1 is prepared when outputting simulation results.

[0033] Next, an example of a semiconductor device targeted as analog device 1 will be described. Figure 2 This is a cross-sectional view showing an example of semiconductor device 2.

[0034] Semiconductor device 2 includes a first frame 51, a semiconductor chip 52, a second frame 53, and a molding resin 54. The semiconductor chip 52 is sealed by the first frame 51, the second frame 53, and the molding resin 54. The semiconductor chip 52 may include, for example, automotive-grade semiconductor devices or power semiconductor devices. An example of an automotive-grade semiconductor device is an automotive MOSFET. An example of a power semiconductor device is a power diode. The first frame 51 and the second frame 53 are made of, for example, copper.

[0035] Figure 3 This is a circuit diagram illustrating an example of the thermal equivalent circuit 3 of an embodiment of the semiconductor device 2.

[0036] The thermal equivalent circuit 3 includes: a first thermal equivalent circuit 61 of the Cauer type and a second thermal equivalent circuit 62 of the Cauer type connected thereto.

[0037] The first thermal equivalent circuit 61 represents the thermal equivalent circuit corresponding to the lower surface side portion of the semiconductor device 2. Figure 2 In one example, the lower surface portion of the semiconductor device 2 includes a lower surface of the semiconductor chip 52, a first frame 51 below the lower surface of the semiconductor chip 52, and a molding resin 54 in contact with the first frame 51.

[0038] The first thermal equivalent circuit 61 includes a first resistor R1, a second resistor R2, a third resistor R3, a fourth resistor R4, a first capacitor C1, a second capacitor C2, a third capacitor C3, and a fourth capacitor C4.

[0039] The left terminal of the first resistor R1 is connected to terminal Tj. Terminal Tj is supplied with a current corresponding to the power consumption of the semiconductor device 2. Figure 3 Reference numeral 60 in the figure indicates a current source corresponding to the power consumption. The terminal to the right of the fourth resistor R4 is connected to terminal Tc1. Terminal Tc1 is subjected to a voltage corresponding to the surface temperature (casing temperature) of the lower surface of the first frame 51.

[0040] like Figure 3 As shown, a second resistor R2 and a third resistor R3 are connected in series between the first resistor R1 and the fourth resistor R4.

[0041] The first resistor R1 corresponds to the thermal resistance of the lower surface portion of the semiconductor chip 52. The second resistor R2 corresponds to the thermal resistance of the first frame 51 below the lower surface of the semiconductor chip 52. The third resistor R3 corresponds to the thermal resistance of the molding resin 54 in contact with the first frame 51. In addition, the fourth resistor R4 corresponds to the thermal resistance used for adjusting the impedance between terminal Tc1 and terminal Ta without heat input or output from the lower surface of the semiconductor device 2.

[0042] The left terminal of the first resistor R1 is connected to the upper terminal of the first capacitor C1. The upper terminal of the second capacitor C2 is connected to the connection point between the first resistor R1 and the second resistor R2. The upper terminal of the third capacitor C3 is connected to the connection point between the second resistor R2 and the third resistor R3. The upper terminal of the fourth capacitor C4 is connected to the connection point between the third resistor R3 and the fourth resistor R4.

[0043] Additionally, the lower terminals of the first capacitor C1, the second capacitor C2, the third capacitor C3, and the fourth capacitor C4 are connected to terminal Ta. A voltage corresponding to the temperature of the atmosphere surrounding the semiconductor device 2 (ambient temperature) is applied to terminal Ta.

[0044] The first capacitor C1 corresponds to the thermal capacitance of the lower surface of the semiconductor chip 52. The second capacitor C2 corresponds to the thermal capacitance of the first frame 51 under the lower surface of the semiconductor chip 52. The third capacitor C3 corresponds to the thermal capacitance of the molding resin 54 in contact with the first frame 51. The fourth capacitor C4 is a thermal capacitor used for adjusting the impedance between terminal Tc1 and terminal Ta without heat input or output from the lower surface of the semiconductor device 2.

[0045] The second thermal equivalent circuit 62 represents the thermal equivalent circuit corresponding to the upper surface side portion of the semiconductor device 2. Figure 2 In the example, the upper surface side portion of the semiconductor device 2 includes the upper surface of the semiconductor chip 52, the second frame 53 on the upper surface of the semiconductor chip 52, and the molding resin 54 on the second frame 53.

[0046] The second thermal equivalent circuit 62 includes a fifth resistor R5, a sixth resistor R6, a seventh resistor R7, an eighth resistor R8, a fifth capacitor C5, a sixth capacitor C6, a seventh capacitor C7, and an eighth capacitor C8.

[0047] The left terminal of the fifth resistor R5 is connected to terminal Tj. The right terminal of the eighth resistor R8 is connected to terminal Tc2. A voltage corresponding to the surface temperature (casing temperature) of the upper surface of the molding resin 54 is applied to terminal Tc2.

[0048] like Figure 3 As shown, a sixth resistor R6 and a seventh resistor R7 are connected in series between the fifth resistor R5 and the eighth resistor R8.

[0049] The left terminal of the fifth resistor R5 is connected to the upper terminal of the fifth capacitor C5. The upper terminal of the sixth capacitor C6 is connected to the connection point between the fifth resistor R5 and the sixth resistor R6. The upper terminal of the seventh capacitor C7 is connected to the connection point between the sixth resistor R6 and the seventh resistor R7. The upper terminal of the eighth capacitor C8 is connected to the connection point between the seventh resistor R7 and the eighth resistor R8.

[0050] In addition, the lower terminals of the fifth capacitor C5, the sixth capacitor C6, the seventh capacitor C7, and the eighth capacitor C8 are connected to terminal Ta.

[0051] The fifth resistor R5 corresponds to the thermal resistance of the upper surface portion of the semiconductor chip 52. The sixth resistor R6 corresponds to the thermal resistance of the second frame 53 on the upper surface of the semiconductor chip 52. The seventh resistor R7 corresponds to the thermal resistance of the molding resin 54 on the second frame 53. The eighth resistor R8 is a thermal resistance used to adjust the impedance between terminal Tc2 and terminal Ta without heat input or output from the upper surface of the semiconductor device 2.

[0052] The fifth capacitor C5 corresponds to the thermal capacitance of the upper surface of the semiconductor chip 52. The sixth capacitor C6 corresponds to the thermal capacitance of the second frame 53 on the upper surface of the semiconductor chip 52. The seventh capacitor C7 corresponds to the thermal capacitance of the molding resin 54 on the second frame 53. The eighth capacitor C8 is a thermal capacitor used for adjusting the impedance between terminal Tc2 and terminal Ta without heat input or output from the upper surface of the semiconductor device 2.

[0053] The number of resistors and capacitors constituting the first thermal equivalent circuit 61 and the number of resistors and capacitors constituting the second thermal equivalent circuit 62 depend on the construction of the semiconductor device being simulated. Generally, the more complex the structure, the more resistors and capacitors are used.

[0054] Figure 4 This is a graph showing the time-varying thermal characteristics of the semiconductor device 2 estimated using simulation device 1 (simulation results).

[0055] Curve a represents the change in thermal characteristics over time when heat is dissipated from the lower surface of the semiconductor device 2, which is either the lower surface or the upper surface of the semiconductor device 2. The lower surface of the semiconductor device 2 is the lower surface of the first frame 51. The upper surface of the semiconductor device 2 is the upper surface of the molding resin 54. Hereinafter, heat dissipation from the lower surface of the semiconductor device 2 will be referred to as lower surface heat dissipation.

[0056] Curve b represents the change in thermal characteristics over time when heat is dissipated from the lower surface and the upper surface of the semiconductor device 2. Hereinafter, heat dissipation from the upper surface of the semiconductor device 2 will be referred to as upper surface heat dissipation.

[0057] Curve c represents the change in thermal characteristics over time when heat is dissipated from both the lower and upper surfaces of semiconductor device 2. Hereinafter, heat dissipation from both the lower and upper surfaces of semiconductor device 2 will be referred to as double-surface heat dissipation.

[0058] Figure 5 This is a graph showing the time-varying thermal properties of the semiconductor device 2 calculated through thermal fluid analysis (analysis results). Thermal fluid analysis can be performed, for example, using the finite element method, finite volume method, or finite difference method. Figure 5 The change in thermal properties over time shown is called the transition thermal resistance or transition thermal response. Additionally, it is possible to obtain the results through actual measurements. Figure 5 The results show the same changes in thermal properties over time.

[0059] Curve a' represents the change in thermal characteristics of semiconductor device 2 with heat dissipation on its lower surface over time. Curve b' represents the change in thermal characteristics of semiconductor device 2 with heat dissipation on its upper surface over time. Curve c' represents the change in thermal characteristics of semiconductor device 2 with heat dissipation on both surfaces over time.

[0060] from Figure 4 and Figure 5 From the following, we can see that: When heat is dissipated from the lower surface, the simulated curve a is approximately consistent with the analytical curve a'. When heat is dissipated from the upper surface, the simulated curve b is approximately consistent with the analytical curve b'. When heat is dissipated from both surfaces, the simulated curve c is approximately consistent with the analytical curve c'. Therefore, in the cases of heat dissipation from the lower surface, the upper surface, and both surfaces, it can be said that simulation device 1 has the required estimation accuracy in estimating the time-varying thermal characteristics of the designed semiconductor device.

[0061] Thus, since the simulation device 1 can accurately estimate the time-dependent changes in the thermal characteristics of heat dissipation in both one-dimensional and two-dimensional directions, it can be said that the simulation device 1 is useful for verifying the time-dependent changes in the thermal characteristics of semiconductor devices.

[0062] If simulation device 1 is used, it is possible to verify the time-dependent changes in thermal characteristics of the lower surface, the upper surface, and any combination of the time-dependent changes in thermal characteristics of both surfaces.

[0063] According to this embodiment, it is not necessary to prepare dedicated simulation devices for estimating the time-varying thermal characteristics of the lower surface heat dissipation, the time-varying thermal characteristics of the upper surface heat dissipation, or the time-varying thermal characteristics of both surfaces heat dissipation. Therefore, the cost required for simulation devices can be reduced.

[0064] Figure 6 It is a graph showing the time-varying changes (simulation results) of other thermal properties of semiconductor device 2 estimated using simulation device 1.

[0065] exist Figure 6 In the diagram, curve d represents the change in the thermal properties of semiconductor device 2 over time when there is heat exchange from the lower and upper surfaces (heat dissipation state). Conversely, curve e represents the change in the thermal properties of semiconductor device 2 over time when there is no heat exchange from the lower and upper surfaces (insulation state).

[0066] Figure 7 This represents the time-dependent changes in other thermal properties of semiconductor device 2, calculated using thermal fluid analysis of FEM (analysis results).

[0067] exist Figure 7 In the figure, curve d' represents the change of thermal characteristics of semiconductor device 2 over time in the heat dissipation state, and curve e' represents the change of thermal characteristics of semiconductor device 2 over time in the adiabatic state.

[0068] from Figure 6 and Figure 7 It can be seen that, under heat dissipation conditions, the simulation result curve d is approximately consistent with the analytical result curve d'. Furthermore, under adiabatic conditions, the simulation result curve e is approximately consistent with the analytical result curve e'. Based on this, it can be said that, under both heat dissipation and adiabatic conditions, simulation device 1 possesses the required estimation accuracy in estimating the time-varying thermal characteristics of the designed semiconductor device.

[0069] Thus, since the simulation device 1 can accurately estimate the thermal characteristics over time under heat dissipation conditions and adiabatic heat dissipation conditions, it can be said that the simulation device 1 is useful for verifying the thermal characteristics of semiconductor devices over time.

[0070] Figure 8 This is a graph showing the time-varying thermal characteristics (simulation results) of the semiconductor device 2 under the estimated heat dissipation and adiabatic conditions using the simulation device of the comparative example.

[0071] The difference between the simulation device in the comparative example and the simulation device in this embodiment is that it uses a [device / device] from [other source]. Figure 3 The thermal circuit data of the thermal equivalent circuit shown in the thermal equivalent circuit 3 is omitted after omitting the fourth resistor R4, the fourth capacitor C4, the eighth resistor R8, and the eighth capacitor C8 (the thermal resistance and thermal capacitance of the final stage).

[0072] exist Figure 8 In the diagram, curve d” represents the change in the thermal properties of semiconductor device 2 over time in the heat dissipation state. Curve e” represents the change in the thermal properties of semiconductor device 2 over time in the adiabatic state.

[0073] from Figure 7 and Figure 8 The following can be observed: Under heat dissipation conditions, the simulated curve d” is roughly consistent with the analytical curve d’. However, under adiabatic conditions, the simulated curve e” is inconsistent with the analytical curve e’.

[0074] In the implementation method, the reason why the simulation results and analytical results under adiabatic conditions are roughly consistent is as follows.

[0075] This is because, in this embodiment, by adding the fourth resistor R4, the fourth capacitor C4, the eighth resistor R8, and the eighth capacitor C8, the impedance between terminal Tc1 and terminal Ta increases during the transition. The fourth resistor R4 and the fourth capacitor C4 do not affect the impedance between terminal Tc1 and terminal Ta when the system is stable. Furthermore, the eighth resistor R8 and the eighth capacitor C8 do not affect the impedance between terminal Tc2 and terminal Ta when the system is stable.

[0076] The value of one of the fourth resistor R4 and the eighth resistor R8 can sometimes be approximately zero. In this case, one of the fourth resistor R4 and the eighth resistor R8 can be omitted. However, if the fourth resistor R4 is omitted, the first thermal equivalent circuit 61 is not of the Caul type. Furthermore, if the eighth resistor R8 is omitted, the second thermal equivalent circuit 62 is not of the Caul type.

[0077] Figure 9 This is a flowchart illustrating the steps of the first fabrication method for the thermal equivalent circuit 3.

[0078] First, the thermal characteristics of the semiconductor device 2 with heat dissipation on the lower surface are obtained over time (hereinafter referred to as the thermal characteristics over time), the thermal characteristics of the semiconductor device 2 with heat dissipation on the upper surface are obtained over time (hereinafter referred to as the thermal characteristics over time), and the thermal characteristics of the semiconductor device 2 with heat dissipation on both surfaces are obtained over time (hereinafter referred to as the thermal characteristics over time) (step S1).

[0079] The time-dependent changes in the first to third thermal properties are obtained through simulation or actual measurement. Alternatively, a portion of the time-dependent changes in the first to third thermal properties can be obtained through actual measurement, while the remaining thermal properties can be obtained through simulation. Furthermore, when the time-dependent changes in thermal properties are obtained through actual measurement, it is preferable to eliminate the influence of the measurement environment from the measurement results.

[0080] Next, a first thermal equivalent circuit 61 and a second thermal equivalent circuit 62 connected thereto are fabricated (step S2). Furthermore, if it is not necessary to reproduce the time-dependent changes in thermal characteristics under adiabatic conditions, resistors R4 and R8, and capacitors C4 and C8 are not required.

[0081] Next, the process proceeds to determine the values ​​of resistors R1 to R4 and capacitors C1 to C4 in the first thermal equivalent circuit 61, and the resistance values ​​of resistors R5 to R8 and the capacitance values ​​of capacitors C5 to C8 in the second thermal equivalent circuit 62 (step S3). Additionally, when it is not necessary to reproduce the time-dependent changes in thermal characteristics under adiabatic conditions, the resistance values ​​of resistors R1 to R3, the capacitance values ​​of capacitors C1 to C3, the resistance values ​​of resistors R5 to R7, and the capacitance values ​​of capacitors C5 to C8 are determined.

[0082] Step S2 is performed as follows. The values ​​of resistors R1 to R8 and capacitors C1 to C9 are determined such that the first difference between the time-dependent change in the thermal characteristics of the lower surface portion of the semiconductor device 2 calculated using the first thermal equivalent circuit 61 and the second thermal equivalent circuit 62 and the time-dependent change in the first thermal characteristic converges to a predetermined first range; the second difference between the time-dependent change in the thermal characteristics of the upper surface portion of the semiconductor device 2 calculated using the first thermal equivalent circuit 61 and the second thermal equivalent circuit 62 and the time-dependent change in the second thermal characteristic converges to a predetermined second range; and the third difference between the time-dependent changes in the thermal characteristics of the lower and upper surface portions of the semiconductor device 2 calculated using the first thermal equivalent circuit 61 and the second thermal equivalent circuit 62 and the time-dependent change in the third thermal characteristic converges to a predetermined third range.

[0083] The first range, second range, and third range are determined according to the thermal characteristics (specifications) required by the semiconductor device 2. Furthermore, the values ​​of resistors R1 to R8 and capacitors C1 to C9 are preferably determined such that the first difference is close to the lower limit of the first range, the second difference is close to the lower limit of the second range, and the third difference is close to the lower limit of the third range.

[0084] Figure 10 This is a flowchart illustrating the steps of a second fabrication method for the thermal equivalent circuit 3. In this second fabrication method, the time-dependent change in the second thermal characteristic (heat dissipation characteristics of the upper surface) is not used. This second fabrication method is used, for example, when it is not necessary to fabricate a thermal equivalent circuit capable of reproducing the heat dissipation characteristics of the upper surface.

[0085] First, the time-dependent changes of the first thermal characteristic and the time-dependent changes of the third thermal characteristic are obtained (step S1a).

[0086] Next, a thermal equivalent circuit including a first thermal equivalent circuit 61 and a second thermal equivalent circuit 62 connected thereto is fabricated (step S2a).

[0087] Next, the values ​​of resistors R1 to R8 and capacitors C1 to C9 are determined in such a manner that the time-dependent change in the thermal characteristics of the lower surface side portion of the semiconductor device 2 calculated using the first thermal equivalent circuit 61 and the second thermal equivalent circuit 62 converges to a predetermined first range, and the third difference between the time-dependent change in the thermal characteristics of the lower surface side and the upper surface side portion of the semiconductor device 2 calculated using the first thermal equivalent circuit 61 and the second thermal equivalent circuit 62 converges to a predetermined third range.

[0088] Figure 11 This is a diagram representing the data structure 4 of the thermal equivalent circuit 3 used in the simulation device 1.

[0089] As described above, the thermal equivalent circuit 3 includes: a first thermal equivalent circuit 61 corresponding to the upper surface side portion of the semiconductor device 2; and a second thermal equivalent circuit 62 connected to the first thermal equivalent circuit 61 and corresponding to the lower surface side portion of the semiconductor device 2. The data structure 4 includes first circuit data D1 related to the first thermal equivalent circuit 61 and second circuit data D2 related to the second thermal equivalent circuit 62.

[0090] Several embodiments of the present invention have been described, but these embodiments are given by way of example and are not intended to limit the scope of the invention. These new embodiments can be implemented in various other ways, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included within the scope and spirit of the invention, and are included within the scope of the invention as described in the claims and its equivalents.

Claims

1. A method for fabricating a thermal equivalent circuit, comprising: The first step involves obtaining the time-dependent change of a first thermal characteristic of the semiconductor device when heat dissipation occurs from the lower surface of the semiconductor device, the time-dependent change of a second thermal characteristic of the semiconductor device when heat dissipation occurs from the upper surface of the semiconductor device, and the time-dependent change of a third thermal characteristic of the semiconductor device when heat dissipation occurs from both the lower and upper surfaces of the semiconductor device. The second step involves fabricating a first thermal equivalent circuit and a second thermal equivalent circuit. The first thermal equivalent circuit includes a plurality of first resistors and a plurality of first capacitors and corresponds to the lower surface of the semiconductor device. The second thermal equivalent circuit is connected to the first thermal equivalent circuit, includes a plurality of second resistors and a plurality of second capacitors, and corresponds to the upper surface of the semiconductor device. as well as The third step involves determining the resistance values ​​of the plurality of first resistors, the capacitance values ​​of the plurality of first capacitors, the resistance values ​​of the plurality of second resistors, and the capacitance values ​​of the plurality of second capacitors in the following manner: The method is as follows: the difference between the time-varying change of the thermal characteristics of the semiconductor device, calculated using the first thermal equivalent circuit and the second thermal equivalent circuit under the condition that heat is dissipated from the lower surface of the semiconductor device, and the time-varying change of the first thermal characteristic converges within a predetermined range. The difference between the time-varying thermal characteristics of the semiconductor device, calculated using the first and second thermal equivalent circuits under the condition that heat dissipation occurs from the upper surface of the semiconductor device, and the time-varying thermal characteristics of the second thermal characteristic, converges within a predetermined range, and... The difference between the time-varying thermal characteristics of the semiconductor device and the time-varying thermal characteristics of the third thermal characteristic, calculated using the first thermal equivalent circuit and the second thermal equivalent circuit, is such that the difference converges within a predetermined range when heat is dissipated from the lower and upper surfaces of the semiconductor device.

2. The method for fabricating the thermal equivalent circuit according to claim 1, wherein, In the first process, the acquisition of the time-dependent change in the second thermal property is omitted.

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