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Estimation of thermal parameters of the enclosed electronic package system by using dynamic thermal response
Mechatronics 19 (2009) 1034–1040
Contents lists available at ScienceDirect
Mechatronics journal homepage: www.elsevier.com/locate/mechatronics
Technical note
Estimation of thermal parameters of the enclosed electronic package system by using dynamic thermal response Jung-Kyun Kim a, Wataru Nakayama b, Yoshimi Ito c, Sang-mo Shin a, Sun-Kyu Lee a,* a
Ultraprecision Machine System Lab., Dept. of Mechatronics, Gwangju Institute of Science and Technology, 261 Cheomdan gwagiro(Oryoung-dong), Buk-gu, Gwangju 500-712, Republic of Korea b ThermTech International, 920-7 Higashi Koiso, Oh-Iso Machi, Kanagawa 255-0004, Japan c Tokyo Institute of Technology, 2-12-1-I1-41, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
a r t i c l e
i n f o
Article history: Received 22 January 2008 Accepted 26 June 2009
Keywords: Electro-thermal system Dynamic thermal network model Time-variant thermal parameters Thermal contact resistance
a b s t r a c t A methodology for modeling and simulating the electro-thermal behavior of an enclosed electronic package is presented and validated. The electro-thermal model is constructed using system dynamics. The system model, in which the electrical and the thermal domain are combined, is presented. The developed model describes the dynamic thermal behavior system that was an electronic device in the test enclosure. An effective way to identify the thermal parameters of the system, especially the thermal contact resistance, is suggested. In detail, the new method for thermal resistance identification is based on the temperature difference behavior between the component and the air temperature inside the enclosure. Based on the proposed model, either the variation of the heat source or the ambient temperature can be estimated. Simulated results were in good agreement with the measured temperature in the transient state accompanying with the variation of the environment. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Modeling and simulating electronic packaging systems has long been a popular issue, especially when the electronic package is enclosed [1]. One problem with this subject has to do with the identification of the complex structure with variations in the transient state [2,3]. Most network simulation programs using FEM and FDM require a great deal of computing time for compute the system in a transient state; especially the model is composed of time-invariant system parameters [4]. In this paper, an approach is proposed to develop an electro-thermal model of an enclosed electronic package that takes into account time-variant parameters under the dynamic variations of the environment. Bond graph modeling [5,6] is an attraction means of modeling dynamic physical systems [7–9]. It is a language based on power exchanges within a system model where the structure of the system model is shown graphically [10]. One of its most interesting advantages is that it is an efficient method to represent analytical models graphically in complicated cases in which multiple energy domains (i.e. mechanical, electrical, hydraulic, thermal, magnetic) are coupled [11–15]. For example, Garcia et al. introduced a methodology for modeling and simulating the electro-thermal behavior of power semiconductor switching devices using bond graph * Corresponding author. Tel.: +82 62 970 2388; fax: +82 62 970 2384. E-mail address: [email protected] (S.-K. Lee). 0957-4158/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2009.06.013
modeling [10,16,17]. This model shows good consistency with measurements of the junction temperature response in a steady state as well as in a transient state [10,16,17]. The main purpose of this paper is to build a model that describes the thermal response of enclosed electronic devices or package systems in a control box. Using the proposed electro-thermal model, it is possible to predict the thermal response according to the operating conditions, the thermal deformation of components, and the reliability of component bonding in an effort to provide a guideline for designing an electronic package system. The proposed model is one in which an electrical domain is combined with a thermal domain. This model was tested and validated by comparing with measured data in the transient sate accompanying with dynamic variations of the environment. It is also possible to estimate the variation of the thermal resistance of the system from the dynamic temperature response. 2. Test set-up The test set-up for the modeling of an enclosed electronic package system is shown in Fig. 1. The electronic device is placed inside the test chamber. In the electronic package, heater was implanted. The size of heater was 13.5 mm square and 470 lm thick. A forward biased diode was used for monitoring the temperature of heater through the measurement of a temperature sensitive parameter. To accurately measure the temperature of heater, the
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Nomenclature T temperature (K) DT AB temperature difference between A and B (K) C thermal capacitance (J/K) R thermal resistance (K/W) heat flow rate (W) Q0 Q heat (J) I current input on the electronic device (A) V voltage input on the electronic device (V) Subscripts Amb ambient air
Heater Chip Test air Case Ins air Elec Load
electronic device heater chip surface test chamber air test chamber case surface insulation chamber air electro-thermal heater resistance external pressure loading part
diode was located at the center of the heater surface. The thermal test chip was placed on top of the heater surface and it composed of copper and the size was 28 mm square and 520 lm thick. Four cooling fans were placed inside the wall to ensure the temperature uniformity inside the chamber at each corner of the chamber. The fans provide variation of heat transfer rate of the air through the speed changes. The test chamber was placed inside an insulation chamber to minimize the influence of any fluctuation of the surrounding air. In particular, several cooling fans were placed on the wall of the insulation chamber to exhaust insulation chamber air continually to ambient. The temperatures of the chip surface, test chamber air, test chamber case surface, and insulation chamber air were measured using thermocouples. 3. System modeling A model for the enclosed electronic package system is presented using a bond graph model. The overall heat flow in the electronic package system, including the heat generation of the electronic device heater through chip surface, the test chamber air, the test chamber case surface, and the insulation chamber air is illustrated in Fig. 2. The bond graph language is based on the representation of power flow. Two variables, effort and flow are associated with each bond. The product of these variables is always equal to the power in power bond graphs. The causal stroke (causality) denotes the direction of the effort variable [17]. Fig. 3a depicts the entire system in which the thermal model is coupled with the electrical model. Solid lines depict the power bond graph in the electrical domain, in which the effort variable and the flow variable represent the voltage and current, respectively. On the other hand, the dotted lines show pseudo bond graph in the thermal domain, in which the effort variable and the flow variable represent the temperature and the heat flow rate, respectively, [18]. The 0-junction represents a power continuous connection of elements at which the sum of the flows on all ports is zero and the efforts on all ports are equal (no energy storage, dissipation or
Fig. 2. The overall heat flow in the electronic package system.
Fig. 3. System modeling (a) bond graph model of electro-thermal system (b) electrical equivalent circuit of the electro-thermal system.
Fig. 1. Test set-up for the enclosed electronic package.
generation), while the thermal node point which has thermal capacitance ‘C’ in the thermal domain. The 1-junction represents a power continuous connection of elements at which the sum of the efforts on all ports is zero and the flows on all ports are equal,
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while the heat flow path connected to the thermal resistance ‘R’ existed between each node in the thermal domain. The thermal resistance involves conductive, convective, irradiative and thermal contact resistance. The dynamic behavior of thermal system is often expressed by the thermal impedance. The thermal impedance of a system can be modeled by combining two elements, the thermal resistance and the thermal capacitance. The thermal impedance model can be represented by a lumped RC-network [19– 24]. The electrical equivalent circuit of an electro-thermal system is shown in Fig. 3b. As the bond graph modeling is applied for the transient behaviors, in order to make the thermal model approximately, substructures and element size should be determined carefully on the consideration of thermal diffusivity, Fourier number or Biot number in the system. In the electronic package, internal resistance of the chip is 0.0017 K/W (e: 0.520 mm, S: 784 mm2, k: 401 W/mK) and the external resistance is 1.21 K/W (convective resistance: 2.0 K/ W, radiative resistance: 182.73 K/W, contact resistance: 3.14 K/ W). The Biot number is 0.0013, which is much lower than unity. Therefore, assumption of uniform temperature of the chip is legitimate. The thermal diffusivities of the heater and the chip are 0.8 104 m2/s and 1.12 104 m2/s, respectively, and the diffusion times of the heater and the chip are 0.0028 s and 0.0024 s, respectively. The characteristic time in transient state was determined with consideration of diffusion time. The electronic device heater generates heat flow via ‘Joule heating’ with a constant current input and converts electrical energy input to thermal output. The conversion of electrical power dissipation into heat in the electro-thermal heater is modeled in bond graph by a 2-port R-field with one electrical port and one thermal port. The power flows of the electro-thermal heater resistance flows only from the electrical port to the thermal port and never the other way around. Fig. 4 shows the electro-thermal model for a heater as a switch bond graph R-filed and its constitutive relations.Fig. 5 illustrates a part of a bond graph model that is connected with the thermal resistance (R) component and thermal capacitance (C) in the thermal domain. In the figure, the dashed arrows with the number 1, 2, and 3 represent identical bonds, and e and f with identical bond subscripts denote the flow and effort values. The relationship between the neighbored elements with respect to the Q 05 can be constitute by
e3 e7 e2 e4 e6 e8 Q 05 ¼ f5 ¼ f4 f6 ¼ f3 f7 ¼ ¼ R3 R7 R3 R7 e1 e5 e5 e9 1 Q1 Q5 1 Q5 Q9 ¼ ¼ R3 C 1 C 5 R7 C 5 C 9 R3 R7
Fig. 4. Switch bond graph R-filed and its constitutive relations.
ð1Þ
Since bond graph can be interpreted into state-space equation, using the constitutive equation relations associated with bond graph in Fig. 3a, Q 07 ; Q 011 ; Q 015 ; Q 019 can be found:
Q0 ¼ A Q þ B u
ð2Þ
where
2
3 Q 07 6 Q0 7 6 7 Q 0 ¼ 6 11 7; 4 Q 015 5 2 6 6 6 A¼6 6 4 2
Q 019 C71R9
1 C 11 R9
0
0
1 C 7 R9
C 111R9 C111R13
1 C 15 R13
0
0
1 C 11 R13
C 151R13 C 151R17
1 C 19 R17
0
1 C 15 R17
C191R17 C 191R20
0 3
7 7 7 7 7 5
Q 06
6 0 7 6 7 B¼6 7 4 0 5 0 In the modeling, various elements, nodes, sub-units or signals can be inserted or extracted, and then the system produces dynamic response, transient thermal behaviors and system equations. Here, time-variant thermal parameters (thermal dependence of the electrical resistance and temperature fluctuations of ambient air) are represented by the external signal flows in this bond graph model. Those will be explained in the next sections. 4. Identification of thermal parameters For design purposes, at this point it is now necessary to find the numerical values of the thermal components of the thermal network. Fig. 6 shows a typical temperature change response and temperature difference response between each element for the enclosed electronic package system with constant 150 mA current input. In the thermally enclosed system, it is difficult to define a specific steady state of temperature response because the temperature of the elements inside the chamber varies slightly due to heat accumulation or exterior ambient variation as shown in Fig. 6a. The emitted heat from the heating elements to the air becomes accumulated inside the enclosure and the temperature response of each element is strongly affected by the enclosed air temperature. The thermal dependent character of electro-thermal heater resistance makes also temperature increase slightly. Fig. 6b shows a temperature difference response between each element and the air temperature inside the enclosure. The temperature differences keep constant values like steady state after about twenty minutes. The new method for thermal resistance identification for the element inside the enclosure is based on the temperature difference response. The relationship of the temperature difference with the thermal resistance and heat flow input is expressed in Eq. (4). Thus, the thermal resistance (RChipTest air ) can be obtained easily. All temperatures are relative to the initial state temperature (T Amb ), i.e.
DT Chip ¼ T Chip T Amb DT Chip DT Test
Fig. 5. Bond graph model in thermal domain.
3
air
¼ RChipTest
ð3Þ air
Q0
ð4Þ
It is necessary to determine the value of the heat flow rate (Q 0 ) input on the electronic device. The heat flow rate can be found using the known values of the current input on the electronic device heater and the electro-thermal heater resistance. This is expressed in Eq. (5). When the electronic device was operated at a constant
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DT Case DT Ins air ¼ RCaseIns DT Case DT Ins RCaseIns air ¼ I2 RElec
air air
Q0
ð12Þ ð13Þ
It is also difficult to define the thermal resistance values by only using steady state temperature increment in the variation of heat convection inside the enclosure system or in the variation of thermal contact resistance, induced by the variation of contact pressure. Hence, a new idea is needed to identify the thermal parameters on the basis of transient temperature response. It is possible to identify the value of the thermal resistances in a transient state using the fitted curve of temperature difference response between each node. In this study, polynomial least square method was used for the curve fitting algorithm. Fig. 7 shows temperature difference response between the electronic device heater and the chip surface and the fitted curve of temperature difference response. Temperature difference response was calculated through the measured temperature response on the electronic device heater and the chip surface.The thermal capacitance of each component can be identified from the value of the transient slope (S) at t = 0 from the temperature rise curve [17,25]. Fig. 8 shows the electronic device heater temperature response. The relationship of the heat flow rate with resistance, and thermal capacitance is expressed by Eq. (14)
Fig. 6. Comparison between (a) temperature change response and (b) temperature difference response.
150 mA current input, the temperature increment of the chip surface was measured as 27.5 K, the maximum temperature increment of bottom substrate surface of the electronic package was 2.4 K and the average temperature increment of bottom substrate surface was under 1 K. Since electronic package board material, FR-4, has a lot lower thermal conductivity value (0.3 W/mK) than the chip material (401 W/mK). Heat losses of the heater towards external air through the bottom substrate were considered negligible. Thus, the thermal resistance (RChipTest air ) can be obtained easily.
Q 0 ¼ I2 RElec RChipTest
air
DT Chip DT Test ¼ I2 RElec
Fig. 7. Temperature difference between the electronic device heater and the chip surface and its fitted curve.
ð5Þ air
ð6Þ
In the same way, other thermal resistance (RHeaterChip ; RTestCase ; andRCaseIns air ) values can be obtained using Eq. (7)–(13) consecutively.
DT Heater ¼ ðRHeaterChip þ RChipTest air Þ Q 0 þ DT Test DT Heater ¼ RHeaterChip Q 0 þ DT Chp DT Heater DT Chip RHeaterChip ¼ I2 RElec DT Test air DT Case ¼ RTest airCase Q 0 DT Test air DT Case RTest airCase ¼ I2 RElec
air
ð7Þ ð8Þ ð9Þ ð10Þ ð11Þ Fig. 8. Temperature rise on the electronic device heater (step response).
1038
Q ðtÞ0 ¼
J.-K. Kim et al. / Mechatronics 19 (2009) 1034–1040
1 Q ðtÞ þ RElec I2 RHeaterChip C Heater
ð14Þ
The relationship of the temperature increment with the work and thermal capacitance is expressed by Eq. (15)
DT Heater ¼
1 Q ðtÞ C Heater
ð15Þ
The transient slope (Sheater ) of the system above at t ¼ 0, corresponding to DT_ Heater (0) is expressed as:
DT_ Heater ð0Þ ¼ SHeater ¼
1 C Heater
Q ðtÞ0 ¼
I2 RElec C Heater
ð16Þ
From Eq. (16), the value of the thermal capacitance of the electronic device heater (C heater ) can be determined by measuring SHeater . 5. Simulation results In this section, simulation results are presented with a comparison of the experimented data. Fig. 9a shows the temperature rise at the constant current input on the electronic device heater. In this case, the thermal resistance was identified using the temperature incremental value. As is shown, the simulation results are fairly different from the measured data in the transient state. These discrepancies are caused by the identification of the thermal resistance, which is determined from the steady state temperature with a constant heat input.
However, since the heater resistance varies with its temperature. Heat input on the electronic device continuously change with the resistance of heater even applying constant current input. It is necessary to identify the resistance variation of heater with temperature. The relationship between resistance of heater and temperature is identified as per EIA/JEDEC standard no. 51-1 [26]. Fig. 10 shows the calibration curve of electronic package heater resistance with temperature and the relationship is expressed by Eq. (17) at this experiment. Fig. 9b shows the results with consideration of thermal dependence of the electrical resistance on the modeling
RElecther ¼ 110:003 þ 0:1678 T Heater
ð17Þ
However, there still exist some discrepancies at the inflection zone by the thermal resistance identification method using temperature incremental values. Thus, by adapting the suggested thermal resistance identification method using from Eqs. (3)–(13), simulation results are shown in Fig. 11. The results are in good agreement, and less temperature differences between the simulated and the measured temperature response is shown. Through the comparison of the inflection zone in Fig. 9b with that in Fig. 11, the new thermal resistance identification method is a better approach for measuring the temperature. The temperature
Fig. 10. Calibration curve of electronic package heater resistance with temperature.
Fig. 9. Comparison of the temperature response between simulation and experiment (a) by using the identified thermal resistance based on the steady state temperature (b) by using the identified thermal resistance based on the steady state temperature and the heat input variation.
Fig. 11. Comparison of the temperature response between simulation and experiment using the thermal resistance based on the temperature difference and the heat input variance.
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response of this improved identification method follows the pattern of upward trend temperature well; however, it has a temperature deviation of less than 0.8° for the as final instance. For a more accurate simulation, it is necessary to consider the temperature variation of the insulation chamber air. As the new method for thermal resistance identification uses the temperature difference between each node, the temperature of the insulation chamber air is a basis for all other nodes, as the ground is a basis for other node point voltages in an electrical analogy. The temperature shows fluctuations following the trend of the ambient air. Using a least square technique through the measured temperature curve, the variation of the insulation chamber air temperature can be included in the model, and comparisons between the measurement and the simulation results are shown in Fig. 12. Excellent coincidences are obtained after adopting the thermal dependence of the heater resistance, the temperature fluctuations of ambient air and the temperature differences between each element. 6. Validation of the system modeling In this section, the electro-thermal bond graph model was validated when the system has time-variant thermal parameters such as heat convection and thermal contact resistance. Fig. 13 shows a case the effect of a convection change. An electronic device was operated at a constant current input, and cooling fan speed inside test chamber was switched from 0.7 m/s to 1.5 m/s. Fig. 13a shows effects on the temperature response of each node in the existence of variations in the convection condition with cooling fan air speed. Fig. 13b shows a comparison of fan air speed and the simulated thermal resistance between the test chamber air and the case surface. With increases in the velocity of the fan cooler speed, the thermal resistance between the chip surface and the test chamber internal air, calculated from simulation results, decreases from 6.3 K/W to 6.0 K/W. Validation of the contact pressure variation was also performed. Fig. 14 shows the experimental set-up with an electronic device and external pressure variation apparatus. Applying pressure on the electronic device was regulated using a bolt screw-type handler and was measured using a load cell simultaneously. With a constant current input on the electronic device heater, the temperature of each node point (electronic device heater, chip surface, and pressure loading part) was measured when applying a pressure change. The electronic device was operated at a constant 150 mA current input and the applied pressure varied from a selfweight value to 0.06 MPa. Fig. 15a shows the comparison of the temperature response while changing the pressure. As external pressure is applied to the electronic device, the thermal contact
Fig. 13. Simulation results and validation curves with a constant 150 mA current input and with variations of the internal air flow (a) simulation results and measured temperature curves (b) thermal resistance between the internal air and the test chamber case from simulation results and the cooling fan air speed.
Fig. 14. Experimental set-up of external pressure variation.
Fig. 12. Comparison of the temperature response.
resistance between the electronic package heater and the chip decreases, therefore, it makes temperature decrease of heater and
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of the system induced by thermal boundary conditions such as environment or contact pressure. Acknowledgments This work was supported by the Korea Science and Engineering Foundation (KOSEF) NRL Program grant funded by the Korea government (MEST) (No. R0A-2008-000-10065-0) and in part supported by the Research Center for Biomolecular Nanotechnology at GIST. References
Fig. 15. Simulation results and validation curves with a constant 150 mA current input and with variations of the applied external pressure (a) simulation results and measured temperature curves (b) thermal resistance between the electronic device heater and chip surface from simulation results and external pressure variation curve.
chip surface. This phenomenon can be verified by comparing with external pressure variation along with the thermal resistance between the electronic device heater and the chip surface, as shown in Fig. 15b. The thermal resistance between the electronic package heater and the chip surface, calculated from simulation results decreases from 2.55 K/W to 2.35 K/W while the thermal resistance increases from 2.35 K/W to 2.5 K/W after the release of the external pressure. It is possible to estimate the variation of the thermal resistance on the system from the dynamic temperature response induced by the variation of the convection condition or the contact pressure. 7. Conclusions A new method of modeling and simulating the electro-thermal behavior of enclosed electronic packages is proposed and validated. An electrical model was coupled with a thermal model in a complete system model such that the joule heat caused by the operation of the device changes directly according to the device temperature. Thermal resistance identification using the temperature difference between each node in the transient state is presented and verified by comparisons of the temperature response between the measurement data and the simulation results. The simulated temperature response based on the proposed method well agreed with the measured one. This model also can be extended to estimate the variation of the thermal resistance
[1] Szekely V. A new evaluation method of thermal transient measurement results. Microelectron J 1997;28:277–92. [2] Lee SK, Kyryu M, Shinno H, Ito Y. Thermal behavior of machine tool spindle system based on the thermal closed-loop concept (remedies for thermal deformation by using the high-speed spindle adapter). Trans JSME 1991;57(538):295–301. [3] Kim SI, Cho JW. Thermal characteristic analysis of a high-precision centerless grinding machine for machining ferrules. Int J Precision Eng Manuf 2007;8(1):32–7. [4] Kim SK. Object-oriented development of a computer code for inverse heat conduction problems. Int J Precision Eng Manuf 2007;8(1):59–65. [5] Paynter HM. Analysis and design of engineering systems. Cambridge: MIT Press; 1961. [6] Karnopp D, Rosenberg R. Analysis and simulation of multiport systems. Cambridge: MIT Press; 1968. [7] Karnopp D, Margolis Donald L, Rosenberg Ronald C. System dynamics: a unified approach. 2nd ed. New York: John Wiley & Sons, Inc.; 1990. [8] Granda JJ. New developments in bond graph modeling software tools: the computer aided modeling program CAMP-G and MATLAB. In: Proceedings of the IEEE international conference on systems, man, and cybenetics. Orlando, Florida, USA; 1997. p. 1542–7. [9] Granda JJ. The role of bond graph modeling and simulation in mechatronics systems – an integrated software tool: CAMP-G, MATLAB-SIMULINK. Mechatronics 2002;12:1271–95. [10] Garcia J, Dauphin-Tanguy G, Rombaut, C. Electrothermal bond graph model for semiconductor switching devices. In: Proceedings of the APEC’96 conference. San Jose; 1996. p. 258–63. [11] Thoma JU. Bond graphs for thermal energy transport and entropy flow. J Franklin Inst-Eng Appl Math 1971;292:109–20. [12] Pal SK, Linkens DA. Temperature distribution in steel during hot rolling: pseudo-bond graph view. Simul Modell Practice Theory 2002;10:69–85. [13] Granda JJ, Tang Shaoqing. Computer simulation of heat transfer models using a pseudo bond graph network. Trans Soc Comput Simul 1988;5(4): 265–83. [14] Kim SM, Lee SK. Prediction of thermo-elastic behavior in a spindle-bearing system considering bearing surroundings. Int J Machine Tools Manuf 2001;41:809–31. [15] Zhao Su, Kim TH, Kim WS, Lee SK. Modeling of an electromagnetically actuated spindle system considering bidirectional bearing compliance. In: Proceedings of the 3rd ICMIT, Chongqing, China; 2005. p. 262. [16] Garcia J, Dauphin-Tanguy G, Rombaut C. Bond graph modeling of thermal effects in switching devices. In: Proceedings of the SCS conference ICBGM’95, Las Vegas, USA; 1995. p. 145–50. [17] Garcia J, Dauphin-Tanguy G, Rombaut C. Modeling and simulating the dynamic electrothermal behavior of power electronic circuits using bond graphs. In: Proceedings of the IEEE annual power electronics specialists conference; 1996. p. 1641–7. [18] Gawthrop PJ. Thermal modelling using mixed energy and pseudo bond graphs. In: Proceedings of the institution of mechanical engineers part I – journal of systems and control engineering, vol. 213; 1999. p. 201–16. [19] Paschkis Victor. Analog methods. In: Handbook of heat transfer. USA: MacGraw-Hill; 1973. p. 1–31. [20] Szekely Vladimir, Rencz Marta. Thermal dynamics and the time constant domain. IEEE T CPMT 2000;23(3):587–94. [21] Hopkins T, Cognetti C, Tiziani R. Designing with thermal impedance. SEMITHERM IV. San Diego, CA, USA; 1988. p. 55–61. [22] Dumele Heidi, Troltzsch Uwe, Horn Michael. Thermal impedance modeling of a temperature dependent resistance. In: Proceedings of the SICE annual conference. Japan: Kagawa University; 2007. p. 2424–7. [23] Christianens F, Beyne E. Transient thermal modeling and characterization of a hybrid component. In: Proceedings of the 46th electronic components and technology conferences, Orlando, USA; 1996. p. 154–64. [24] Skibinski GL, Sethares WA. Thermal parameter estimation using recursive identification. IEEE Trans Power Electron 1991;6(2):228–39. [25] Sueur C, Dauphintanguy G. Bond graph approach to multitime scale systemsanalysis. J Franklin Inst-Eng Appl Math 1991;328:1005–26. [26] EIA/JESD 51-1. Integrated circuits thermal measurement method – electrical test method (single semiconductor device); 1995.
Contents lists available at ScienceDirect
Mechatronics journal homepage: www.elsevier.com/locate/mechatronics
Technical note
Estimation of thermal parameters of the enclosed electronic package system by using dynamic thermal response Jung-Kyun Kim a, Wataru Nakayama b, Yoshimi Ito c, Sang-mo Shin a, Sun-Kyu Lee a,* a
Ultraprecision Machine System Lab., Dept. of Mechatronics, Gwangju Institute of Science and Technology, 261 Cheomdan gwagiro(Oryoung-dong), Buk-gu, Gwangju 500-712, Republic of Korea b ThermTech International, 920-7 Higashi Koiso, Oh-Iso Machi, Kanagawa 255-0004, Japan c Tokyo Institute of Technology, 2-12-1-I1-41, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
a r t i c l e
i n f o
Article history: Received 22 January 2008 Accepted 26 June 2009
Keywords: Electro-thermal system Dynamic thermal network model Time-variant thermal parameters Thermal contact resistance
a b s t r a c t A methodology for modeling and simulating the electro-thermal behavior of an enclosed electronic package is presented and validated. The electro-thermal model is constructed using system dynamics. The system model, in which the electrical and the thermal domain are combined, is presented. The developed model describes the dynamic thermal behavior system that was an electronic device in the test enclosure. An effective way to identify the thermal parameters of the system, especially the thermal contact resistance, is suggested. In detail, the new method for thermal resistance identification is based on the temperature difference behavior between the component and the air temperature inside the enclosure. Based on the proposed model, either the variation of the heat source or the ambient temperature can be estimated. Simulated results were in good agreement with the measured temperature in the transient state accompanying with the variation of the environment. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Modeling and simulating electronic packaging systems has long been a popular issue, especially when the electronic package is enclosed [1]. One problem with this subject has to do with the identification of the complex structure with variations in the transient state [2,3]. Most network simulation programs using FEM and FDM require a great deal of computing time for compute the system in a transient state; especially the model is composed of time-invariant system parameters [4]. In this paper, an approach is proposed to develop an electro-thermal model of an enclosed electronic package that takes into account time-variant parameters under the dynamic variations of the environment. Bond graph modeling [5,6] is an attraction means of modeling dynamic physical systems [7–9]. It is a language based on power exchanges within a system model where the structure of the system model is shown graphically [10]. One of its most interesting advantages is that it is an efficient method to represent analytical models graphically in complicated cases in which multiple energy domains (i.e. mechanical, electrical, hydraulic, thermal, magnetic) are coupled [11–15]. For example, Garcia et al. introduced a methodology for modeling and simulating the electro-thermal behavior of power semiconductor switching devices using bond graph * Corresponding author. Tel.: +82 62 970 2388; fax: +82 62 970 2384. E-mail address: [email protected] (S.-K. Lee). 0957-4158/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2009.06.013
modeling [10,16,17]. This model shows good consistency with measurements of the junction temperature response in a steady state as well as in a transient state [10,16,17]. The main purpose of this paper is to build a model that describes the thermal response of enclosed electronic devices or package systems in a control box. Using the proposed electro-thermal model, it is possible to predict the thermal response according to the operating conditions, the thermal deformation of components, and the reliability of component bonding in an effort to provide a guideline for designing an electronic package system. The proposed model is one in which an electrical domain is combined with a thermal domain. This model was tested and validated by comparing with measured data in the transient sate accompanying with dynamic variations of the environment. It is also possible to estimate the variation of the thermal resistance of the system from the dynamic temperature response. 2. Test set-up The test set-up for the modeling of an enclosed electronic package system is shown in Fig. 1. The electronic device is placed inside the test chamber. In the electronic package, heater was implanted. The size of heater was 13.5 mm square and 470 lm thick. A forward biased diode was used for monitoring the temperature of heater through the measurement of a temperature sensitive parameter. To accurately measure the temperature of heater, the
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Nomenclature T temperature (K) DT AB temperature difference between A and B (K) C thermal capacitance (J/K) R thermal resistance (K/W) heat flow rate (W) Q0 Q heat (J) I current input on the electronic device (A) V voltage input on the electronic device (V) Subscripts Amb ambient air
Heater Chip Test air Case Ins air Elec Load
electronic device heater chip surface test chamber air test chamber case surface insulation chamber air electro-thermal heater resistance external pressure loading part
diode was located at the center of the heater surface. The thermal test chip was placed on top of the heater surface and it composed of copper and the size was 28 mm square and 520 lm thick. Four cooling fans were placed inside the wall to ensure the temperature uniformity inside the chamber at each corner of the chamber. The fans provide variation of heat transfer rate of the air through the speed changes. The test chamber was placed inside an insulation chamber to minimize the influence of any fluctuation of the surrounding air. In particular, several cooling fans were placed on the wall of the insulation chamber to exhaust insulation chamber air continually to ambient. The temperatures of the chip surface, test chamber air, test chamber case surface, and insulation chamber air were measured using thermocouples. 3. System modeling A model for the enclosed electronic package system is presented using a bond graph model. The overall heat flow in the electronic package system, including the heat generation of the electronic device heater through chip surface, the test chamber air, the test chamber case surface, and the insulation chamber air is illustrated in Fig. 2. The bond graph language is based on the representation of power flow. Two variables, effort and flow are associated with each bond. The product of these variables is always equal to the power in power bond graphs. The causal stroke (causality) denotes the direction of the effort variable [17]. Fig. 3a depicts the entire system in which the thermal model is coupled with the electrical model. Solid lines depict the power bond graph in the electrical domain, in which the effort variable and the flow variable represent the voltage and current, respectively. On the other hand, the dotted lines show pseudo bond graph in the thermal domain, in which the effort variable and the flow variable represent the temperature and the heat flow rate, respectively, [18]. The 0-junction represents a power continuous connection of elements at which the sum of the flows on all ports is zero and the efforts on all ports are equal (no energy storage, dissipation or
Fig. 2. The overall heat flow in the electronic package system.
Fig. 3. System modeling (a) bond graph model of electro-thermal system (b) electrical equivalent circuit of the electro-thermal system.
Fig. 1. Test set-up for the enclosed electronic package.
generation), while the thermal node point which has thermal capacitance ‘C’ in the thermal domain. The 1-junction represents a power continuous connection of elements at which the sum of the efforts on all ports is zero and the flows on all ports are equal,
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while the heat flow path connected to the thermal resistance ‘R’ existed between each node in the thermal domain. The thermal resistance involves conductive, convective, irradiative and thermal contact resistance. The dynamic behavior of thermal system is often expressed by the thermal impedance. The thermal impedance of a system can be modeled by combining two elements, the thermal resistance and the thermal capacitance. The thermal impedance model can be represented by a lumped RC-network [19– 24]. The electrical equivalent circuit of an electro-thermal system is shown in Fig. 3b. As the bond graph modeling is applied for the transient behaviors, in order to make the thermal model approximately, substructures and element size should be determined carefully on the consideration of thermal diffusivity, Fourier number or Biot number in the system. In the electronic package, internal resistance of the chip is 0.0017 K/W (e: 0.520 mm, S: 784 mm2, k: 401 W/mK) and the external resistance is 1.21 K/W (convective resistance: 2.0 K/ W, radiative resistance: 182.73 K/W, contact resistance: 3.14 K/ W). The Biot number is 0.0013, which is much lower than unity. Therefore, assumption of uniform temperature of the chip is legitimate. The thermal diffusivities of the heater and the chip are 0.8 104 m2/s and 1.12 104 m2/s, respectively, and the diffusion times of the heater and the chip are 0.0028 s and 0.0024 s, respectively. The characteristic time in transient state was determined with consideration of diffusion time. The electronic device heater generates heat flow via ‘Joule heating’ with a constant current input and converts electrical energy input to thermal output. The conversion of electrical power dissipation into heat in the electro-thermal heater is modeled in bond graph by a 2-port R-field with one electrical port and one thermal port. The power flows of the electro-thermal heater resistance flows only from the electrical port to the thermal port and never the other way around. Fig. 4 shows the electro-thermal model for a heater as a switch bond graph R-filed and its constitutive relations.Fig. 5 illustrates a part of a bond graph model that is connected with the thermal resistance (R) component and thermal capacitance (C) in the thermal domain. In the figure, the dashed arrows with the number 1, 2, and 3 represent identical bonds, and e and f with identical bond subscripts denote the flow and effort values. The relationship between the neighbored elements with respect to the Q 05 can be constitute by
e3 e7 e2 e4 e6 e8 Q 05 ¼ f5 ¼ f4 f6 ¼ f3 f7 ¼ ¼ R3 R7 R3 R7 e1 e5 e5 e9 1 Q1 Q5 1 Q5 Q9 ¼ ¼ R3 C 1 C 5 R7 C 5 C 9 R3 R7
Fig. 4. Switch bond graph R-filed and its constitutive relations.
ð1Þ
Since bond graph can be interpreted into state-space equation, using the constitutive equation relations associated with bond graph in Fig. 3a, Q 07 ; Q 011 ; Q 015 ; Q 019 can be found:
Q0 ¼ A Q þ B u
ð2Þ
where
2
3 Q 07 6 Q0 7 6 7 Q 0 ¼ 6 11 7; 4 Q 015 5 2 6 6 6 A¼6 6 4 2
Q 019 C71R9
1 C 11 R9
0
0
1 C 7 R9
C 111R9 C111R13
1 C 15 R13
0
0
1 C 11 R13
C 151R13 C 151R17
1 C 19 R17
0
1 C 15 R17
C191R17 C 191R20
0 3
7 7 7 7 7 5
Q 06
6 0 7 6 7 B¼6 7 4 0 5 0 In the modeling, various elements, nodes, sub-units or signals can be inserted or extracted, and then the system produces dynamic response, transient thermal behaviors and system equations. Here, time-variant thermal parameters (thermal dependence of the electrical resistance and temperature fluctuations of ambient air) are represented by the external signal flows in this bond graph model. Those will be explained in the next sections. 4. Identification of thermal parameters For design purposes, at this point it is now necessary to find the numerical values of the thermal components of the thermal network. Fig. 6 shows a typical temperature change response and temperature difference response between each element for the enclosed electronic package system with constant 150 mA current input. In the thermally enclosed system, it is difficult to define a specific steady state of temperature response because the temperature of the elements inside the chamber varies slightly due to heat accumulation or exterior ambient variation as shown in Fig. 6a. The emitted heat from the heating elements to the air becomes accumulated inside the enclosure and the temperature response of each element is strongly affected by the enclosed air temperature. The thermal dependent character of electro-thermal heater resistance makes also temperature increase slightly. Fig. 6b shows a temperature difference response between each element and the air temperature inside the enclosure. The temperature differences keep constant values like steady state after about twenty minutes. The new method for thermal resistance identification for the element inside the enclosure is based on the temperature difference response. The relationship of the temperature difference with the thermal resistance and heat flow input is expressed in Eq. (4). Thus, the thermal resistance (RChipTest air ) can be obtained easily. All temperatures are relative to the initial state temperature (T Amb ), i.e.
DT Chip ¼ T Chip T Amb DT Chip DT Test
Fig. 5. Bond graph model in thermal domain.
3
air
¼ RChipTest
ð3Þ air
Q0
ð4Þ
It is necessary to determine the value of the heat flow rate (Q 0 ) input on the electronic device. The heat flow rate can be found using the known values of the current input on the electronic device heater and the electro-thermal heater resistance. This is expressed in Eq. (5). When the electronic device was operated at a constant
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DT Case DT Ins air ¼ RCaseIns DT Case DT Ins RCaseIns air ¼ I2 RElec
air air
Q0
ð12Þ ð13Þ
It is also difficult to define the thermal resistance values by only using steady state temperature increment in the variation of heat convection inside the enclosure system or in the variation of thermal contact resistance, induced by the variation of contact pressure. Hence, a new idea is needed to identify the thermal parameters on the basis of transient temperature response. It is possible to identify the value of the thermal resistances in a transient state using the fitted curve of temperature difference response between each node. In this study, polynomial least square method was used for the curve fitting algorithm. Fig. 7 shows temperature difference response between the electronic device heater and the chip surface and the fitted curve of temperature difference response. Temperature difference response was calculated through the measured temperature response on the electronic device heater and the chip surface.The thermal capacitance of each component can be identified from the value of the transient slope (S) at t = 0 from the temperature rise curve [17,25]. Fig. 8 shows the electronic device heater temperature response. The relationship of the heat flow rate with resistance, and thermal capacitance is expressed by Eq. (14)
Fig. 6. Comparison between (a) temperature change response and (b) temperature difference response.
150 mA current input, the temperature increment of the chip surface was measured as 27.5 K, the maximum temperature increment of bottom substrate surface of the electronic package was 2.4 K and the average temperature increment of bottom substrate surface was under 1 K. Since electronic package board material, FR-4, has a lot lower thermal conductivity value (0.3 W/mK) than the chip material (401 W/mK). Heat losses of the heater towards external air through the bottom substrate were considered negligible. Thus, the thermal resistance (RChipTest air ) can be obtained easily.
Q 0 ¼ I2 RElec RChipTest
air
DT Chip DT Test ¼ I2 RElec
Fig. 7. Temperature difference between the electronic device heater and the chip surface and its fitted curve.
ð5Þ air
ð6Þ
In the same way, other thermal resistance (RHeaterChip ; RTestCase ; andRCaseIns air ) values can be obtained using Eq. (7)–(13) consecutively.
DT Heater ¼ ðRHeaterChip þ RChipTest air Þ Q 0 þ DT Test DT Heater ¼ RHeaterChip Q 0 þ DT Chp DT Heater DT Chip RHeaterChip ¼ I2 RElec DT Test air DT Case ¼ RTest airCase Q 0 DT Test air DT Case RTest airCase ¼ I2 RElec
air
ð7Þ ð8Þ ð9Þ ð10Þ ð11Þ Fig. 8. Temperature rise on the electronic device heater (step response).
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Q ðtÞ0 ¼
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1 Q ðtÞ þ RElec I2 RHeaterChip C Heater
ð14Þ
The relationship of the temperature increment with the work and thermal capacitance is expressed by Eq. (15)
DT Heater ¼
1 Q ðtÞ C Heater
ð15Þ
The transient slope (Sheater ) of the system above at t ¼ 0, corresponding to DT_ Heater (0) is expressed as:
DT_ Heater ð0Þ ¼ SHeater ¼
1 C Heater
Q ðtÞ0 ¼
I2 RElec C Heater
ð16Þ
From Eq. (16), the value of the thermal capacitance of the electronic device heater (C heater ) can be determined by measuring SHeater . 5. Simulation results In this section, simulation results are presented with a comparison of the experimented data. Fig. 9a shows the temperature rise at the constant current input on the electronic device heater. In this case, the thermal resistance was identified using the temperature incremental value. As is shown, the simulation results are fairly different from the measured data in the transient state. These discrepancies are caused by the identification of the thermal resistance, which is determined from the steady state temperature with a constant heat input.
However, since the heater resistance varies with its temperature. Heat input on the electronic device continuously change with the resistance of heater even applying constant current input. It is necessary to identify the resistance variation of heater with temperature. The relationship between resistance of heater and temperature is identified as per EIA/JEDEC standard no. 51-1 [26]. Fig. 10 shows the calibration curve of electronic package heater resistance with temperature and the relationship is expressed by Eq. (17) at this experiment. Fig. 9b shows the results with consideration of thermal dependence of the electrical resistance on the modeling
RElecther ¼ 110:003 þ 0:1678 T Heater
ð17Þ
However, there still exist some discrepancies at the inflection zone by the thermal resistance identification method using temperature incremental values. Thus, by adapting the suggested thermal resistance identification method using from Eqs. (3)–(13), simulation results are shown in Fig. 11. The results are in good agreement, and less temperature differences between the simulated and the measured temperature response is shown. Through the comparison of the inflection zone in Fig. 9b with that in Fig. 11, the new thermal resistance identification method is a better approach for measuring the temperature. The temperature
Fig. 10. Calibration curve of electronic package heater resistance with temperature.
Fig. 9. Comparison of the temperature response between simulation and experiment (a) by using the identified thermal resistance based on the steady state temperature (b) by using the identified thermal resistance based on the steady state temperature and the heat input variation.
Fig. 11. Comparison of the temperature response between simulation and experiment using the thermal resistance based on the temperature difference and the heat input variance.
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response of this improved identification method follows the pattern of upward trend temperature well; however, it has a temperature deviation of less than 0.8° for the as final instance. For a more accurate simulation, it is necessary to consider the temperature variation of the insulation chamber air. As the new method for thermal resistance identification uses the temperature difference between each node, the temperature of the insulation chamber air is a basis for all other nodes, as the ground is a basis for other node point voltages in an electrical analogy. The temperature shows fluctuations following the trend of the ambient air. Using a least square technique through the measured temperature curve, the variation of the insulation chamber air temperature can be included in the model, and comparisons between the measurement and the simulation results are shown in Fig. 12. Excellent coincidences are obtained after adopting the thermal dependence of the heater resistance, the temperature fluctuations of ambient air and the temperature differences between each element. 6. Validation of the system modeling In this section, the electro-thermal bond graph model was validated when the system has time-variant thermal parameters such as heat convection and thermal contact resistance. Fig. 13 shows a case the effect of a convection change. An electronic device was operated at a constant current input, and cooling fan speed inside test chamber was switched from 0.7 m/s to 1.5 m/s. Fig. 13a shows effects on the temperature response of each node in the existence of variations in the convection condition with cooling fan air speed. Fig. 13b shows a comparison of fan air speed and the simulated thermal resistance between the test chamber air and the case surface. With increases in the velocity of the fan cooler speed, the thermal resistance between the chip surface and the test chamber internal air, calculated from simulation results, decreases from 6.3 K/W to 6.0 K/W. Validation of the contact pressure variation was also performed. Fig. 14 shows the experimental set-up with an electronic device and external pressure variation apparatus. Applying pressure on the electronic device was regulated using a bolt screw-type handler and was measured using a load cell simultaneously. With a constant current input on the electronic device heater, the temperature of each node point (electronic device heater, chip surface, and pressure loading part) was measured when applying a pressure change. The electronic device was operated at a constant 150 mA current input and the applied pressure varied from a selfweight value to 0.06 MPa. Fig. 15a shows the comparison of the temperature response while changing the pressure. As external pressure is applied to the electronic device, the thermal contact
Fig. 13. Simulation results and validation curves with a constant 150 mA current input and with variations of the internal air flow (a) simulation results and measured temperature curves (b) thermal resistance between the internal air and the test chamber case from simulation results and the cooling fan air speed.
Fig. 14. Experimental set-up of external pressure variation.
Fig. 12. Comparison of the temperature response.
resistance between the electronic package heater and the chip decreases, therefore, it makes temperature decrease of heater and
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of the system induced by thermal boundary conditions such as environment or contact pressure. Acknowledgments This work was supported by the Korea Science and Engineering Foundation (KOSEF) NRL Program grant funded by the Korea government (MEST) (No. R0A-2008-000-10065-0) and in part supported by the Research Center for Biomolecular Nanotechnology at GIST. References
Fig. 15. Simulation results and validation curves with a constant 150 mA current input and with variations of the applied external pressure (a) simulation results and measured temperature curves (b) thermal resistance between the electronic device heater and chip surface from simulation results and external pressure variation curve.
chip surface. This phenomenon can be verified by comparing with external pressure variation along with the thermal resistance between the electronic device heater and the chip surface, as shown in Fig. 15b. The thermal resistance between the electronic package heater and the chip surface, calculated from simulation results decreases from 2.55 K/W to 2.35 K/W while the thermal resistance increases from 2.35 K/W to 2.5 K/W after the release of the external pressure. It is possible to estimate the variation of the thermal resistance on the system from the dynamic temperature response induced by the variation of the convection condition or the contact pressure. 7. Conclusions A new method of modeling and simulating the electro-thermal behavior of enclosed electronic packages is proposed and validated. An electrical model was coupled with a thermal model in a complete system model such that the joule heat caused by the operation of the device changes directly according to the device temperature. Thermal resistance identification using the temperature difference between each node in the transient state is presented and verified by comparisons of the temperature response between the measurement data and the simulation results. The simulated temperature response based on the proposed method well agreed with the measured one. This model also can be extended to estimate the variation of the thermal resistance
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