INVESTIGATION of DELPHI COMPACT THERMAL MODEL STYLE for MODELING SURFACE-MOUNTED SOFT MAGNETIC COMPOSITE INDUCTOR Eric Monier-Vinard 1*, Valentin Bissuel 1, Cheikh Tidiane Dia 1, 2, Olivier Daniel 1, Najib Laraqi 2 1 2
Thales Global Services, 92360 Meudon La Foret, France Université Paris Ouest, Laboratoire Thermique Interfaces Environnement, 92410 Ville d’Avray, France
* Corresponding Author:
[email protected]
Abstract Recent works on System-In-Package component pointed out that its in-package inductor is the hottest part. It occurs that thermal stresses due to joule heating and magnetic losses can be damaging. The present study focuses on low profile, surfacemounted, Soft Magnetic Composite inductors to define their thermal behaviour and then to propose a guideline to create pertinent models. Results highlight the impact of thermal conductivity of composite core on temperatures and the lack of properties data of iron-resin mixtures. Using mixture model, a calculation of effective thermal conductivity is proposed. To minimize the expensive meshing of the fine detailed simulations and the computation time, a novel Compact Thermal Model for inductor, based on DELPHI methodology, was established. The predictions of CTM model show good agreement, less than 10% of divergence. Further works must be done to really master the coupled interaction of magnetic, joule effect, thermal phenomenon as well as material properties.
1
Introduction
Latest infrared experiments on a DC-DC power module confirmed that its in-package inductor is the most sensitive element and has a major impact on the thermal performances of housing System In Package device. In fact, those very small devices are more and more submitted to high electrical current, for instance 10A. As a consequence, thermal constraints due to inductor losses are going to be more damaging as those encountered for Integrated Circuits. In theory, inductor self-heating regroups joule heating effect and magnetic losses which are respectively generated in a copper coil part and in an iron-resin magnetic structure. The following study focuses on conventional low profile, surface-mounted, composite inductors that are supplied by several manufacturers. The investigation is conducted with the purpose to better master their physical behavior, then to establish an appropriate method to elaborate a set of realistic and relevant models.
2
Devices under investigation
The Integrated Passive Devices (IPD) style is constructed using a wound copper coil which is over-molded by a Soft Magnetic Composite as pictured in figure 1.
Core
Coil
Lead
Figure 1: Constitution style of studied IPD The overall dimensions of the device are 4.7 x 5.2 x 1.5mm3. Its copper solenoid has a diameter of 0.3mm and a total length of 48mm. The maximal operating temperature is usually 125°C but thermal aging phenomena have to be taken into consideration. Thermal aging will drastically increase core losses. In consequence the temperature level of inductor body as well as bottleneck effect at lead-board interface will be magnified Indeed, the heat is mostly drained from the two lateral leads, throughout a couple of areas of 1.15 x 1.5mm2. To mitigate the impact of thermal aging, manufacturers recommend limiting the core losses at a low fraction, 1/3 or less, of the total power.
Thus coil and core loss percentages are respectively fixed at 67% and 33% of the operating power to run the numerical simulations.
3
Assumptions for fine thermal modeling
Realistic detailed numerical models needs to simulate the number of turns of the copper coil and its tortuous geometry buried in a magnetic core.
3.2
Magnetic composite thermal modeling
Soft Magnetic Composite name is dedicated to pressed and heat-treated metal powder components with threedimensional magnetic properties. The magnetic material is composed of iron powder particles combined with epoxy binder that are compacted around the solenoid coil to form the body shape as shown on figure 4.
A detailed description of a solenoid shape reclaims a high meshing capacity to be able to achieve relevant electrothermal simulations, as shown in figure 2.
Figure 4: Cross section of a buried coil in SMC core The value of the effective thermal conductivity (ke) of the core material seems never accurately defined, often a range varying from 1W/m.K to 5W/m.K is provided. extensive meshing
Figure 2: Numerical model of the winding parts The total losses are expressed by manufacturer with a basic assumption of a uniform dissipation applied to inductor volume. That one demonstrates that temperatures and spreading heat paths of both inductor coil and core are unknown as well as the potential failure linked to misapprehended hotspots. 3.1 Copper coil thermal modeling The passage of an electric current of 10A has been simulated through the copper coil solenoid, using Ansys software. The conventional properties of copper coil are: • kc =385W/m.k, its thermal conductivity, • σc= 59,6×106 S·m-1, its electrical conductivity, Figure 3 demonstrates the existence of the overheating zones encounters in the coil element when realistic joule heating phenomena is considered.
Table 1 highlights the significant impact of the core thermal conductivity on the IPD skin temperature when a core volume dissipation of 1Watt is assumed. Table 1: Influence of core material on IPD temperatures Node name
Maximal temperature of IPD device (°C) Coil
Core
Case
Lead
ke = 1W/m.K
112
103
112
99
ke = 2W/m.K
107
101
107
97
ke = 5W/m.K
97
95
97
94
Temperature mappings consider a device that is mounted on JEDEC 2S2P test board [1] in vertical free convection at an ambient temperature of 35°C. The variation of the temperature of the sensitive elements is significant, more than 10°C. Thus, every 10°C reduction results in a doubled lifetime, or on the opposite, in accelerated failure occurrence. Moreover, for all cases, the body temperature will exceed 125°C if the maximal operating ambient is 85°C. It appears that the lack of knowledge of thermal material and magnetic properties is a major issue to establish a relevant thermal model. Using Maxwell mixture relationship (1), an effective thermal conductivity of 2.1W/m.K was determined for the composite core material.
(
k p + 2⋅ k m + 2⋅ V f ⋅ k p − k m k e = k m⋅ k + 2⋅ k − V ⋅ k − k m f p m p
(
)
)
(1)
Figure 3: Joule heating effect for U=0V and I=10A And similar maximal temperature is observed, deviation is lower than 2°C if a coil volume dissipation is assumed.
The three parameters were fixed respectively to: • Vf =0.637, the maximum fraction to which a volume can be filled with randomly packed spheres,
• kp =74W/m.K (particle), the thermal conductivity of iron powder, • km=0.345W/m.K (matrix), the thermal conductivity of polyester resin. The effective thermal conductivity is mainly dependent on the matrix material; the previous value can be divided per two if epoxy resin is used, for instance.
Main issue of IPD model reduction was to define properly the isothermal external surfaces to match the asymmetric heat flow paths. Figure 6 displays a set of external surfaces which has been determined to adequately fit the DTM and CTM temperatures and heat flow rates predictions. Top middle
Moreover electro-magnetic simulations are mandatory to validate the hypothesis of uniform volumetric core losses.
Leads
Top inner
Top outer
Bottom
These ones are planned using Maxwell 3D from Ansys for finer understanding of magnetic phenomenon.
4
Definition of inductor behavioral model
Sides
A fine representation will be hard to keep at overpopulated board level so Compact Thermal Model approach is mandatory for mastering IPD thermal behaviour. The creation of DELPHI style CTM [1] [2] of IPD was led according to the following assumptions:
• creation of two distinct coil and core nodes to apply magnetic and copper wire losses, • boundary conditions set is completed by random set of power dissipation apply on both junction nodes [4-7],
Figure 6: Inductor DELPHI style network concept Some areas of the top surface are not anymore square or rectangular. So, circular or annular shapes have to be used to build a compliant thermal model. Table 2 summarizes the resistor set that composes the "best of art" compact model of the studied component.
Table 2: Thermal network of the inductor device Node name
• subdivisions of the external surfaces [8]. Figure 5 presents the new style of two-source thermal network which is generated from our reduction process flow. TTO
TTM
SIDES
TS
TTI
TOP
QCOIL
“Junction” Internal nodes
QCORE BOTTOM
External surface nodes
TB
TL
LEADS
Figure 5: Inductor DELPHI style network concept The two-sources (S) thermal resistances network, is built from a wide set of DELPHI [4-8] or JEDEC-JESD15-4 [1] boundary conditions (BC), applied successively on all external surfaces of the model, which is completed by the superposition principle; (S number +1) x BC number.
Thermal resistor matrix (°C/W) Coil
Core
Top inner
Bottom
-
Coil
-
23.5
-
Top inner
21.3
222.7
56.2
-
Top middle
123.1
96.9
-
-
Top outer
-
20.3
-
-
Bottom
-
24.4
-
-
Leads
50
76.7
-
230
Sides
-
59.8
-
251.4
Its fitting score, depending on heat flow rates and temperatures balance, is 0.981 (perfect correlation is 1). The concept of Delphi style CTM extended to inductor device appears to be an appropriate solution to supply an efficient reduced model, our primary concern.
5
Comparison of both thermal models
The analysis of Compact Thermal Model prediction demonstrates that a low discrepancy, below 5%, can be obtained with the purpose to monitor the maximum coil and average core temperatures and then to detect potential ageing damage.
Then a Genetic Algorithm fitting technique [3] [4-8] allows us to determine the best network candidate that properly matches heat flow rates and temperatures of the realistic model, for all its sensitive parts and its external surfaces.
Temperature results of table 3 consider a device mounted on 2S2P test board in vertical free convection at an ambient temperature of 35°C.
By this way, the deducted network is according to the DELPHI concept of Boundary Condition Independent.
Similar temperature agreements are noticed for top inner, top outer, bottom, sides or leads nodes.
Table 3: DTM versus CTM temperature on 2S/2P board Temperature prediction of both models
Node name
PLOSS (W)
TDTM (°C)
TCTM (°C)
∆T/ TDTM
Coil
0.666
106.8
106.6
0.1%
Core
0.333
101.0
99.1
2.9%
The analysis highlights that the temperatures of both inductor coil and core have to be mastered to prevent fast ageing phenomena. It appears that the material thermal and magnetic properties have a major impact on the realistic thermal model.
Thus, the deducted multiple heating sources DELPHI model style adequately correlate the physical behaviour of all diverse heat paths of the component, our purpose.
A two-source compact thermal model of the inductance device based on DELPHI style methodology using superposition principle and a genetic algorithm fitting technique is proposed.
6
This one allows minimizing the expensive meshing of the fine detailed thermal model and its computation time, such as those of conventional IC components.
Relevance of compact modeling approach
In usual thermal analysis, the compact thermal models are used on equivalent single orthotropic layer which summarizes the complex board multi-layer architecture by a simple lumped model. In fact, few authors really describe the performance of their compact thermal models for a board design which has only a thin single upper copper trace.
However, complementary simulations and experiments have to be performed to fix material properties in order to assess the quality of the realistic and the behavioural models.
Literature [1]
In this condition, 2R CTM models or equivalent block models has to be rejected to evaluate the temperature encountered by the device under investigation. The proposed model has been checked on a simple copper trace PWB having a width of 2mm and a thickness of 35µm. Both component leads are soldered on a couple of 1.6mm x 2mm foot print areas, as described in figure 7.
[2]
[3]
Copper trace
[4]
Board JEDEC 1S/0P
Figure 7: Inductance mounted on 1S/0P PCB [5]
Due to the low thermal conductivity of the board, the power dissipation has been divided per 2. Table 4: DTM versus CTM temperature on 1S/0P board Temperature prediction of both models
Node name
PLOSS (W)
TDTM (°C)
TCTM (°C)
∆T/ TDTM
Coil
0.335
107.7
107.5
0.1%
Core
0.165
104.9
103.8
1.6%
The deducted DELPHI thermal compact model allows us to predict the key temperatures of IPD device for various board designs with a discrepancy lower than 5%.
7
Summary
It occurs that low profile surface-mounted inductors are more and more submitted to harsh operating conditions. As a consequence, thermal stress effects due to joule heating and magnetic losses could be a potential failures cause as those encountered for IC components.
[6]
[7]
[8]
JEDEC standard: - JESD51-7: High Effective Thermal Conductivity Test Board for Leaded Surface Mount Packages, February 1999. - JESD15-4: DELPHI Compact Thermal Model guideline, October 2008. Clements J.M, Lasance, Two Benchmarks for the study of Compact Thermal Modelling Phenomena, Phillips Research Laboratories, Parthiban A., Kankanhally N.S., Ishak A.A., Determination of Thermal Compact Model via Evolutionary Genetic Optimization Method, IEEE Transactions on components and packaging technologies, June 2005 E. Monier-Vinard, V. Bissuel, P. Murphy, O. Daniel, J. Dufrenne “Thermal modelling of the emerging multichip packages”, 12th EUROSIME conference, 2010, Bordeaux, France. E. Monier-Vinard, V. Bissuel, P. Murphy, O. Daniel, J. Dufrenne “DELPHI style compact modeling for multichip package including its bottom board area based on genetic algorithm optimization”, ITHERM conference, 2010, Las Vegas USA. E. Monier-Vinard, M. Brizoux, A Grivon, W. Maia, O. Daniel, V. Bissuel, “Impact of PCB via and micro-via structure on component thermal performances”, 16th THERMINIC workshop, 2010, Barcelona, Spain. E. Monier-Vinard, M. Brizoux, A Grivon, V. Bissuel, F. Pires, “Impact of PCB via and micro-via structure on component thermal performances”, Journal of Electronic Packaging Vol.133, Iss.3 September 2011. E. Monier-Vinard, C. Dia, V. Bissuel, O. Daniel, “DELPHI style compact modeling by means of genetic algorithms of System in Package devices using composite sub-compact thermal models dedicated to model order reduction”, ITHERM conference, 2012 San diego, USA.
