LA PREVISIONE DELLA TEMPERATURA MASSIMAIN UN DISPOSITIVO DI POTENZA : PROGRAMMI FEM

MARC-MENTAT , ANSYS , FLOW-THERM

LA PREVISIONE DELLA TEMPERATURA MASSIMAIN UN DISPOSITIVO DI POTENZA : APPROSSIMAZIONE ROZZA

LA PREVISIONE DELLA TEMPERATURA MASSIMAIN UN DISPOSITIVO DI POTENZA : SOLUZIONE INTERMEDIA

DJOSER ANALYTICAL THERMAL SIMULATOR FOR MULTILAYER ELECTRONIC STRUCTURES.

Steady-state thermal simulator based on analyticalrelationships.

Working for multi-layer mountings (step-pyramid) withhomogeneous layers

It requires 2-D uniform mesh instead of 3-D

GOAL :

1. Accuracy within 1% with respect to FEM analysis2. Faster and more easily programmable than FEM

MODEL CHARACTERISTICSMODEL CHARACTERISTICS

PIRAMIDE A GRADONI DEL RE DJOSER(Sakkara, III Dinastia)

Rapid and reliable thermal characterization of planarelectronic mountings, from device to printed boardsto be used instead of Finite Elements Programs

High power inverter module (IRCI)Naked chip hybrid medium

power circuit (R.I.CO.)

APPLICATIONSAPPLICATIONS

APPLICATIONSAPPLICATIONS

THICK FILMWATER FLOWSENSORS

STRONGLYCONVECTIVE B.C.

APPLICATIONSAPPLICATIONS

POWER BOARDS THERMAL ANALYSIS

DC-DC BOARD DJOSER ANALYSIS

DC-DC BOARD DJOSER ANALYSIS

87.3 °C

h* = 37.85 W/°C m2.

THERMAL CHARACTERIZATION OF POWER LED COUPLING TO IMS SUBSTRATE

APPLICATIONSAPPLICATIONSCHARACTERIZATION OF THERMAL PROPERTIES OF THE IMS SUBSTRATEINSULATING LAYER

0 ,4 5 0

0 ,4 7 5

0 ,5 0 0

0 ,5 2 5

0 ,5 5 0

0 ,5 7 5

0 ,6 0 0

0 ,4 2 50 ,4 0 0

0,434631

0 , 3 5

0 , 4 0

0 , 4 5

0 , 5 0

0 , 5 5

0 , 6 0

0 , 6 5

3 ,5 3 ,7 3 ,9 4 ,1 4 ,3 4 ,5 4 ,7 4 ,9 5 ,1 5 ,3 5 ,5R E S I S T E N Z A T E R M I C A S T R U T T U R A (° C / W )

COND

UCIB

ILITA

' TER

MICA

ISOL

ANTE

VALORESPERIMENTALE

APPLICATIONSAPPLICATIONS

ACCURATE DESIGN OF PROPER FINNED DISSIPATOR

Pd = H A* (Ts – To) = H* A (Ts – To)

ELECTRO-THERMAL APPLICATIONSELECTRO-THERMAL APPLICATIONS

CHARACTERIZATION OF THE HOT SPOT IN POWER BJT

EMITTERBASE

COLLECTOR

ELECTRO-THERMAL APPLICATIONSELECTRO-THERMAL APPLICATIONS

REAL ELECTRO-THERMAL BEHAVIOR OF METAL INTERCONNECTIONSFOR HIGH CURRENT.

Temperature

Power density

STRUCTURE

FUTURE DEVELOPEMENTSFUTURE DEVELOPEMENTS

THESIS: THERMO-MECHANICAL SIMULATION OF POWER PACKAGES

To HEAT SINK

Ta ENVIRONMENT

Ta Ta

Ta

To

Ta

To ToTo

BOTTOM HEAT SINK (To)and ENVIRONMENT (Ta)TEMPERATURES

MODEL PROPERTIESMODEL PROPERTIES

P(x,y) : 2-D POWER SOURCESON THE TOP SURFACES

MODEL PROPERTIESMODEL PROPERTIES

MODEL PROPERTIESMODEL PROPERTIES

P*(x,y) : 2-D POWER SOURCESON THE BOTTOM SURFACES(if the lower contact resistance exists)

R* CONTACT THERMAL RESISTANCE (mm °C/W)2

MODEL PROPERTIESMODEL PROPERTIES

hi

hi

hi

CONVECTION ON TOP SURFACES(with different coefficents per layer)

MODEL PROPERTIESMODEL PROPERTIES

MODEL PROPERTIESMODEL PROPERTIES

hi

hi hi

hi

hi

hi

CONVECTION ON LATERAL WALLS(with different coefficents per layer, per side)

INSULATING OR PASSIVATING LAYERS(with different thermal properties)

MODEL PROPERTIESMODEL PROPERTIES

SINGLE LAYER MODELSINGLE LAYER MODEL

R*z

INCOMING THERMAL FLUX

BOTTOM TEMPERATURE DISTRIBUTION

KNOWNVARIABLES

SINGLE LAYER MODELSINGLE LAYER MODEL

R*z OUTGOING THERMAL FLUX

TOP TEMPERATURE DISTRIBUTION

UNKNOWNVARIABLES

MULTI - LAYER SOLUTIONMULTI - LAYER SOLUTION

11 2 1 1

12 1 2 2 2 3

22 3 2 2

23 2 3 3 3 4

33 4 3 3

34 3 4 4 4 0

*

*

*

*

*

*

ˆq̂ (x,y) ( T , P ,P )ˆ ˆ ˆˆT (x,y) (q ,T ,P ,P ,T )

ˆq̂ (x,y) ( T , P , P )ˆ ˆ ˆˆT (x,y) (q ,T ,P ,P ,T )

ˆq̂ (x,y) ( T , P , P )ˆ ˆ ˆˆT (x,y) (q ,T ,P ,P ,T )

f

g

f

g

f

g

=

=

=

=

=

=

q0=0T2

T3

T5 = HEAT SINK (To)

T4

q1q2

q3

T1

STACK OF LAYERS System of integral equations

LyLx

i j i j n m n mn 1 m 1 x yA 0 0

1F(x ,y ) G (x ,y |x,y)dx dy C (n,m) X(β x)Y(μ y) F(x ,y ) X(β x )Y(μ y )dx dy L L

∞ ∞

= =

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′⋅ = ⋅∑ ∑∫ ∫ ∫ ∫

TEMPERATUREor FLUX

ALGEBRIC FORMULATIONALGEBRIC FORMULATION

LyLx

i j i j n m n mn 1 m 1 x yA 0 0

1F(x ,y ) G (x ,y |x,y)dx dy C (n,m) X(β x)Y(μ y) F(x ,y ) X(β x )Y(μ y )dx dy L L

∞ ∞

= =

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′⋅ = ⋅∑ ∑∫ ∫ ∫ ∫

TEMPERATUREor FLUX

N

n,m k k k kk 1

B (x ,y ) F(x ,y )=

⋅∑(xk,yk)

ALGEBRIC FORMULATIONALGEBRIC FORMULATION

(Depending on the squaring method chosen,Rectangular or Cavalieri - Simpson)

LyLx

i j i j n m n mn 1 m 1 x yA 0 0

1F(x ,y ) G (x ,y |x,y)dx dy C (n,m) X(β x)Y(μ y) F(x ,y ) X(β x )Y(μ y )dx dy L L

∞ ∞

= =

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′⋅ = ⋅∑ ∑∫ ∫ ∫ ∫

TEMPERATUREor FLUX

N

n,m k k k kk 1

B (x ,y ) F(x ,y )=

⋅∑(xk,yk)

ALGEBRIC FORMULATIONALGEBRIC FORMULATION

(Depending on the squaring method chosen,Rectangular or Cavalieri - Simpson)

N

ij k k k kk 1

φ (x ,y |x,y) F(x ,y )=

∑ijA

F(x ,y ) G (x ,y |x,y)dx dy′ ′ ′ ′ ′ ′⋅∫ ∫

THEREFORE

IN PRACTICE ….IN PRACTICE ….

1° STEP:Solving the algebric system = Knowledge of temperature andflux values in the 2-D cells (xk , yk)j

(xk , yk)j

2° STEP:Using this set of values andthe same algebric equations,temperature and flux canbe evaluated everywhere inthe solid (x,y,z).

( ) ( ) ( )

( ) ( ) ( )( ) ( )

J k k k k k kJ J+1 J J

k k k k k kJ J+1 J+1J J+1

k k k kJ+1 J+2

*

*

ˆq̂ (x,y,z) f T x ,y , P x ,y , P x ,y

ˆq̂ x ,y ,T x ,y , P x ,y ,T̂ (x,y,z) g

ˆ, P x ,y ,T x ,y

= =

PLASTIC-EPOXSILICONMETAL (k = 100)

To = 20 °CTa = 0 °C

EXAMPLE (ADIABATIC B.C.)EXAMPLE (ADIABATIC B.C.)

PLASTIC-EPOXSILICONMETAL (k = 100)

To = 20 °CTa = 0 °C

EXAMPLE (ADIABATIC B.C.)EXAMPLE (ADIABATIC B.C.)

ADIABATIC TEMP. MAPS

PLASTIC-EPOXSILICONMETAL (k = 100)

To = 20 °CTa = 0 °C

EXAMPLE (ADIABATIC B.C.)EXAMPLE (ADIABATIC B.C.)

TEMP. COMPARISON ALONG THE X-AXES

EXAMPLE (CONVECTIVE B.C.)EXAMPLE (CONVECTIVE B.C.)

SAMPLE A: TOP CONVECTION SAMPLE B: WEST and SOUTH CONVECTION

TOP SILICON

TOP PLASTIC

TEMP. RELATIVE ERRORS(REFERENCE Nnm =180)

n

m

Nnm

Nnm

SQUARE EIGENVALUES SET

ACCURACY (Number of eigenvalues)ACCURACY (Number of eigenvalues)

Accuracy depends on : Nnm : the number of eigenvalues used for the series calculation.

ACCURACY (Density of 2-D cells)ACCURACY (Density of 2-D cells)

Accuracy depends on : the density of cells at the layer interfaces

TEMP. RELATIVE ERRORS(REFERENCE Dc =100 mm-2)

EXPERIMENTAL VALIDATIONON BUILT MULTY-LAYERSTRUCTURES

Comparison between DJOSERmaps and thermoghaphic images

EXPERIMENTAL VALIDATIONON INDUSTRIAL POWERELECTRONIC CIRCUIT

MOTORBIKE ELECTRICAL REGULATORBy MITSUBA EUROPE (Pisa, Italy)

CONCLUSIONSCONCLUSIONS

DJOSER:

Steady-state thermal simulation tool NOT general purpose(thermal vias, metal bumps, ball-grid arrays cannot be modeled)with a complicate mathematics.

BUT

It was designed to be used by customers instead of FEM programs because of its speed (2-D uniform meshing, reduced variable number.., fully automatic model construction)for standard mounting configurations of power devices and systems.

AND OVERALL…

It does not require any specific cultural background by the operator.

…IN OTHER WORDS…IN OTHER WORDS

FERRARI is alwaysthe best

..but sometimesalso something less may be useful!

(From the movie “Vacanze Romane”)