CN113254868A - Data analysis method for transient thermal test of semiconductor device - Google Patents

Data analysis method for transient thermal test of semiconductor device Download PDF

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CN113254868A
CN113254868A CN202110759313.5A CN202110759313A CN113254868A CN 113254868 A CN113254868 A CN 113254868A CN 202110759313 A CN202110759313 A CN 202110759313A CN 113254868 A CN113254868 A CN 113254868A
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equation
formula
model
thermal
transient thermal
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罗亚非
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Weifang Advanced Photoelectric Chip Research Institute
Lu'ou Zhizao Shandong High End Equipment Technology Co ltd
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Weifang Advanced Photoelectric Chip Research Institute
Lu'ou Zhizao Shandong High End Equipment Technology Co ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N25/00—Investigating or analyzing materials by the use of thermal means
    • G01N25/20—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Abstract

The application discloses a data analysis method for transient thermal test of a semiconductor device, which comprises the following steps: step one, establishing a first-level RthCmodel by adopting a thermal resistance and heat capacity model; secondly, transient thermal response calculation of the semiconductor product is carried out by using a multi-level RthCth model; and step three, performing convolution operation processing on the data by adopting an RthCth model. Has the following advantages: the problems that the data for numerical analysis cannot be directly provided and a mathematical model for transient simulation cannot be provided on the physical structure of a tested device cannot be corresponded are solved.

Description

Data analysis method for transient thermal test of semiconductor device
Technical Field
The invention discloses a data analysis method for transient thermal test of a semiconductor device, and belongs to the technical field of transient thermal test of semiconductor devices.
Background
In recent years, with the development of new energy industries, the usage amount of semiconductors, especially power semiconductor products, is greatly increased, and the layout of related industries is more incorporated into fourteen-five plans in China. At present, the demand of the market of China for power semiconductors reaches the scale of hundreds of billions of yuan, and the annual growth rate of the demand exceeds 10 percent.
In the technical aspect, the power semiconductor generates a large amount of heat when in use, and the power semiconductor must ensure that the temperature of a chip does not exceed an upper limit value of about 150 degrees, otherwise the power semiconductor cannot work, which brings a great challenge to the thermal design of a power semiconductor product.
A large number of investigations have shown that, among the causes of failure of all electronic devices, the excess temperature (poor heat dissipation) accounts for 55%, whereas above the power semiconductor this proportion reaches more than 70%.
In the design cost of the current electronic products, particularly power electronic products (such as an inverter of a driving motor, a high-power supply and the driving current of respective heavy electric machinery), the thermal design reaches about 30%, in the manufacturing cost of the products, the cost of parts and materials for heat dissipation also rises year by year, reaches more than 20%, and even reaches more than 50% in some special applications.
The problem of how to perform thermal testing is firstly solved for scientific and effective semiconductor thermal design. Before 1995, thermal testing of electronic products only used temperature probes such as thermocouples to measure the surface temperature of components, but the method is simple and low in cost, but has large errors (the common error is more than +/-5 ℃), and the chip temperature which is most concerned by thermal designers cannot be measured (because the chip is packaged in a shell and cannot be touched), so that the method only can carry out the most rough estimation and cannot provide effective experimental data.
After 1995, the JEDEC published a standard method for directly measuring the temperature of a semiconductor device, by which the temperature of a chip can be directly measured through a pin connection without damaging the device and the measurement accuracy is improved to a high accuracy of ± 0.1 ℃, and this set of standards has rapidly become popular in the field of electronic product design.
But the next question is how to perform the thermal structure analysis. The over-high temperature of the chip is caused by over-high heat productivity on one hand and insufficient capability of a chip packaging structure, a heat conduction material and a heat dissipation device on the other hand. Because the driving force required to be provided is larger and larger, the heat productivity of the chip is always increased, and it is not shown that the heat productivity is reduced, and the only solution here is to improve the heat dissipation capability of the chip packaging structure, the heat conduction material and the heat dissipation apparatus, and the heat dissipation capability must be improved along with the increase of the heat productivity of the chip. In this context, thermal design of semiconductor products requires the ability to analyze heat dissipation structures other than chips, in addition to accurately measuring the chip temperature.
The united states standardization organization of the electronics industry also provides a guidance on how to analyze the heat dissipation structure of a semiconductor device, and this method is to perform a transient thermal test on a chip and analyze the heat dissipation structure outside the chip by measuring the transient response of the temperature of the chip.
The method obtains a curve (horizontal axis time and vertical axis temperature) of temperature change along with time, the curve reflects the information of the heat dissipation structure of the semiconductor device to a certain extent in the physical principle, but the data form of the temperature VS time is very non-intuitive, the human brain is difficult to directly understand, and the data cannot be directly corresponding to a specific structure or material in a physical space, so that the effective structural analysis cannot be carried out.
The current industry development provides constantly increased requirement to semiconductor product thermal design, but product designers just also can't carry out accurate analysis to specific engineering product problem owing to can't obtain effectual heat radiation structure data, need finally find the heat dissipation solution and need pay out very huge time cost and economic cost, can't effectively ensure the heat-sinking capability of the product of design simultaneously, just also can't ensure the quality and the reliability of product.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a data analysis method for transient thermal test of a semiconductor device, which solves the problems that the data analysis method cannot be corresponding to the physical structure of the tested device, the data for numerical analysis cannot be directly provided, and a mathematical model for transient simulation cannot be provided, so that the measurement result is more visual and understandable, quantitative analysis can be performed, and the mathematical model for simulation calculation can be generated.
In order to solve the technical problems, the invention adopts the following technical scheme:
a data analysis method for transient thermal testing of a semiconductor device comprises the following steps:
step one, establishing a first-level RthCmodel by adopting a thermal resistance and heat capacity model;
secondly, transient thermal response calculation of the semiconductor product is carried out by using a multi-level RthCth model;
and step three, performing convolution operation processing on the data by adopting an RthCth model.
Further, the specific mathematical model of the first-order rthchth model established in the first step is as follows:
the change of the temperature difference delta T between the heat source temperature and the environment temperature along with time is the transient thermal response of the system, and the mathematical model is solved to obtain a formula 1 to a formula 3;
Figure 288151DEST_PATH_IMAGE001
formula 1;
Figure 290742DEST_PATH_IMAGE002
formula 2;
Figure 345285DEST_PATH_IMAGE003
formula 3;
the product of Rth and Cth in the exponential term, which is referred to as the time constant of the thermal structure of the semiconductor product, is denoted by the symbol τ and has a unit of seconds.
Further, the calculation formula of the transient thermal response calculation in the second step is as follows:
Figure 103026DEST_PATH_IMAGE004
equation 5;
Figure 875810DEST_PATH_IMAGE005
equation 6.
Further, the specific process of the convolution operation processing in the third step is as follows:
step 1, carrying out logarithmic processing on time and time constant terms;
Figure 416512DEST_PATH_IMAGE006
equation 7;
Figure 591142DEST_PATH_IMAGE007
equation 8;
step 2, performing partial differential calculation on the time item on the time axis;
Figure 457467DEST_PATH_IMAGE008
equation 9;
in the step 3, the step of,
Figure 514284DEST_PATH_IMAGE009
sign substitution;
Figure 124257DEST_PATH_IMAGE010
equation 10.
By adopting the technical scheme, compared with the prior art, the invention has the following technical effects:
1. the method has the advantages that the measurement result is more visual and understandable, the original transient thermal test original data are curves of temperature changing along with time, the original transient thermal test original data are obscure and unintelligible, the characteristics of the tested sample cannot be visually analyzed, the characteristics of the tested sample are clearly reflected after the transient thermal test original data are changed into the time constant frequency spectrum, and the data analysis difficulty is greatly reduced.
2. The quantitative analysis can be carried out, in the time constant frequency spectrum, the characteristic of the measured sample is reflected as a peak on a certain time constant, and the quantitative analysis can be carried out on the measured sample through the position and the height of the peak.
3. The method can generate a mathematical model for simulation calculation, and after discretization processing is carried out on the time constant spectrum, a one-dimensional mathematical model of the RthCt can be generated for later-stage simulation calculation.
Drawings
In order to more clearly illustrate the detailed description of the invention or the technical solutions in the prior art, the drawings that are needed in the detailed description of the invention or the prior art will be briefly described below. Throughout the drawings, like elements or portions are generally identified by like reference numerals. In the drawings, elements or portions are not necessarily drawn to scale.
FIG. 1 is a schematic diagram showing the structure of a first-stage thermal resistance-heat capacity model according to the present invention;
FIG. 2 is a schematic diagram showing a multi-stage thermal resistance and heat capacity model according to the present invention;
FIG. 3 is a graph showing transient thermal test results for a thermal structure having a thermal resistance of 1K/W and a thermal capacity of 1J/W according to the present invention;
FIG. 4 is a graph showing the results of Rth (ζ) calculated according to the present invention;
FIG. 5 is a three-level heat grid model diagram of the present invention in the form of raw data of transient heat test results;
FIG. 6 is a graph of a three-stage heat grid model under Rth (ζ) results in accordance with the present invention;
FIG. 7 is a graph of a thermal structure of the present invention using a data analysis method of the present invention;
FIG. 8 is a graph of the thermal resistance component of the present invention using the data analysis method of the present invention;
FIG. 9 is a graph of Rth (ζ) of the mathematical processing results including actual Rth and Cth values of each stage of the grid in the mathematical model according to the present invention.
Detailed Description
Embodiment 1, as shown in fig. 1, a data analysis method for transient thermal testing of a semiconductor device includes the steps of:
step one, adopting a thermal resistance and heat capacity model in the figure 1 to perform mathematical modeling of a first-level RthCmodel.
The change of the temperature difference delta T between the heat source temperature and the environment temperature along with the time is the transient thermal response of the system, and the mathematical model is solved to obtain the formula 1 to the formula 3.
Figure 887814DEST_PATH_IMAGE001
Formula 1;
Figure 190619DEST_PATH_IMAGE002
formula 2;
Figure 672416DEST_PATH_IMAGE003
formula 3;
the product of Rth and Cth in the exponential term, which is referred to as the time constant (in seconds) of the thermal structure of the semiconductor product, is denoted by the symbol τ. Since the time constant τ depends only on the physical properties (thermal resistance and heat capacity) of the thermal structure itself, and is independent of the input, it can be used as a parameter for proving the thermal structure.
Step two, in the actual product, only one-level RthCmodel cannot be used for complete demonstration, and the transient thermal response calculation of the semiconductor product is carried out by using the multi-level RthCmodel, as shown in FIG. 2.
The transient thermal response calculation formulas at this time are formula 5 and formula 6.
Figure 882818DEST_PATH_IMAGE004
Equation 5;
Figure 766460DEST_PATH_IMAGE005
equation 6;
considering the continuity of the actual physical world, the discrete summation is changed into a continuous integral expression, and the change from summation to integral requires high mathematical tools such as Taylor expansion.
Thirdly, performing convolution operation processing on the data by adopting an RthCth model:
step 1, carrying out logarithmic processing on time and time constant terms;
Figure 974588DEST_PATH_IMAGE006
equation 7;
Figure 943681DEST_PATH_IMAGE007
equation 8;
step 2, performing partial differential calculation on the time item on the time axis;
Figure 895456DEST_PATH_IMAGE008
equation 9;
in the step 3, the step of,
Figure 695922DEST_PATH_IMAGE009
sign substitution;
Figure 340530DEST_PATH_IMAGE010
equation 10.
Comparative analysis
FIG. 3 shows transient thermal test results for a thermal structure having a thermal resistance of 1K/W and a thermal capacity of 1J/W. From this result, it is difficult to directly obtain the parameters of the corresponding rthcht model.
Fig. 4 shows the calculated corresponding Rth (ζ) result, and it can be seen that a very distinct peak is formed at the counterpart of 1s, so that the time constant τ =1s of the thermal structure can be conveniently and accurately known, and the heat capacity value Cth = τ/Rth =1J/W can be conveniently and accurately obtained.
In the case of the three-level heat grid model, in the original data form of the transient heat test result, it can be said that the data analysis cannot be performed as shown in fig. 5, but in the Rth (ζ) result, it can be clearly seen that the thermal structure is composed of the three-level heat grid model, and the time constants of each level are respectively as shown in fig. 6: the thermal resistance values of each stage are basically the same at 0.0001 second, 0.01 second and 1 second, so that the total thermal resistance value is 1/3 and is 1K/W respectively.
The effect is more evident by comparing the actual data shown in fig. 7 and 8, and it can be clearly seen that the thermal structure has three significant thermal resistance characteristics around τ =10-2 seconds, 1 second, 10 seconds, and then has a significant thermal resistance component around 0.01 seconds.
The set of analysis method is established on the basis of an RthCth heat grid mathematical model
As shown in fig. 9, Rth (ζ) as a result of the mathematical processing includes actual Rth and Cth values of each stage of the mesh in the mathematical model, as shown in equation 11:
Figure 531340DEST_PATH_IMAGE011
equation 11.
Finally, only Rth (zeta) needs to be discretized, the discretization mathematical methods are various and can be selected at will, the discretization density can be set according to user requirements, and thermal transient simulation requirements can be met generally from dozens of levels to dozens of levels.
The thermal transient simulation result performed by using the model has high consistency with the actual test result.
The description of the present invention has been presented for purposes of illustration and description, and is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to practitioners skilled in this art. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.

Claims (4)

1. A data analysis method for transient thermal test of a semiconductor device is characterized by comprising the following steps: the method comprises the following steps:
step one, establishing a first-level RthCmodel by adopting a thermal resistance and heat capacity model;
secondly, transient thermal response calculation of the semiconductor product is carried out by using a multi-level RthCth model;
and step three, performing convolution operation processing on the data by adopting an RthCth model.
2. The method of claim 1, further comprising the step of:
the specific mathematical model of the first-level RthCmodel established in the first step is as follows:
the change of the temperature difference delta T between the heat source temperature and the environment temperature along with time is the transient thermal response of the system, and the mathematical model is solved to obtain a formula 1 to a formula 3;
Figure 526791DEST_PATH_IMAGE001
formula 1;
Figure 630882DEST_PATH_IMAGE002
formula 2;
Figure 941778DEST_PATH_IMAGE003
formula 3;
the product of Rth and Cth in the exponential term, which is referred to as the time constant of the thermal structure of the semiconductor product, is denoted by the symbol τ and has a unit of seconds.
3. The method of claim 1, further comprising the step of:
the calculation formula of the transient thermal response calculation in the second step is as follows:
Figure 477932DEST_PATH_IMAGE004
equation 5;
Figure 915473DEST_PATH_IMAGE005
equation 6.
4. The method of claim 1, further comprising the step of:
the specific process of the convolution operation processing in the third step is as follows:
step 1, carrying out logarithmic processing on time and time constant terms;
Figure 190466DEST_PATH_IMAGE006
equation 7;
Figure 723078DEST_PATH_IMAGE007
equation 8;
step 2, performing partial differential calculation on the time item on the time axis;
Figure 125241DEST_PATH_IMAGE008
equation 9;
in the step 3, the step of,
Figure 685797DEST_PATH_IMAGE009
sign substitution;
Figure 882424DEST_PATH_IMAGE010
equation 10.
CN202110759313.5A 2021-07-06 2021-07-06 Data analysis method for transient thermal test of semiconductor device Pending CN113254868A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114091292A (en) * 2022-01-24 2022-02-25 鲁欧智造(山东)高端装备科技有限公司 Semiconductor transient thermal test result analysis method

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Publication number Priority date Publication date Assignee Title
CN103823170A (en) * 2012-11-16 2014-05-28 闽南师范大学 Novel method for measuring thermal resistance of power-type LED integration module
CN112364591A (en) * 2020-09-16 2021-02-12 南京航空航天大学 SiC MOSFET junction temperature real-time dynamic prediction method and voltage detection circuit

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103823170A (en) * 2012-11-16 2014-05-28 闽南师范大学 Novel method for measuring thermal resistance of power-type LED integration module
CN112364591A (en) * 2020-09-16 2021-02-12 南京航空航天大学 SiC MOSFET junction temperature real-time dynamic prediction method and voltage detection circuit

Non-Patent Citations (1)

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Title
董宇航: ""基于瞬态响应的LED热阻测试原理及算法研究"", 《中国优秀硕士学位论文全文数据库》 *

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Publication number Priority date Publication date Assignee Title
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