Boundary Condition Independence of Cauer RC … Condition Independence ,, , of Cauer RC Ladder ......

Nanotechnology Conference and Expo NanotechWorkshop on Compact Modelling

Santa Clara, CA, USA, June 18-21, 2012

Boundary Condition Independence , , , ,

of Cauer RC Ladder Compact Thermal Modelsp

Marcin JANICKI, Tomasz TORZEWICZ, Zbigniew KULESZA, Andrzej NAPIERALSKI

Department of Microelectronics and Computer Science, Technical University of ŁódźWólczańska 221/223, 90-924 Lodz, Poland

e-mail: [email protected]

Technical University of ŁódźDepartment of Microelectronics and Computer Science

Presentation Plan

Generation of RC ladder compact thermal d lmodels thermal transient recording time constant spectrum thermal structure functions

Experimental investigation internal package structure identification thermal interface characterization cooling effectiveness assessment


Conclusions

RC Ladder Compact Thermal Models- DELPHI compact thermal models

(JEDEC JESD15-4) are generated in a complex way and their elementsin a complex way and their elements do not have any physical significance

- RC ladder models are more convenient for many practical engineering applications,e.g. for prediction of junction temperature in electro-thermal simulations

- RC ladder models might have physically significant model elements when generatedin a proper way employing the NetworkIdentification by Deconvolution method


RC Ladder Compact Thermal Modelsgeneration of accurate RC ladder models requires good quality

transient temperature measurements recorded on the logarithmically equidistant time scale hence allowing the identification of all thermal

time constants ranging from microseconds to hours


RC Ladder Compact Thermal Models


RC Ladder Compact Thermal Modelsthe thermal time constant spectrum identified after the deconvolution

represents a system in the form of distributed RC Foster ladder which cannot be physically correct because it implies the infinite speed

of temperature response propagation throughout the system


RC Ladder Compact Thermal Modelsthe Foster RC ladder needs to be converted to its Cauer counterpart

which could be physically correct, but for a large number of RC stages the conversion is numerically unstable


RC Ladder Compact Thermal Modelsafter the conversion to the RC Cauer ladder it is possible to construct cumulative thermal structure functions reflecting the entire heat flow

path from the junction to the ambient


RC Ladder Compact Thermal Models

cumulative differential


structure function

RC Ladder Compact Thermal Modelsour approach is to discretize the heat flow path into individual regions already at the stage of the time constant spectrum and then to convert it to the Cauer form which is a more numerically stable operation and

it can be done in a simple spreadsheet

the discretisation should be done at the locations of the minima in the time constant spectra which correspond to the change of a material

in a heat flow path


Experimental ResultsCASE 1

Dual SiC power diode in TO-247 package

Considered cooling configurations:

-still air cooling-package submerged in a recipient with water-device with a loosely attached multifinned heat sink-device with a tightly attached multifinned heat sink


Experimental Results

1E+2in air in water loose sink tight sink

1E+1se [K

]

1E+0pera

ture

ris

1E+0

Tem

p

1E-11E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 1E+4

Time [s]

d d h tiTechnical University of Łódź

Department of Microelectronics and Computer Science

recorded heating curves

Experimental Results1E+5

in air in water loose sink tight sink

1E+2

1E+3

1E+4

1E 1

1E+0

1E+1

Cth

[J/K

]

1E-1

1E+0

1E-3

1E-2

1E-1

1E 4

1E-3

1E-2

1E-40 5 10 15 20 25 30 35 40

Rth [K/W]

1E-40 1 2 3

l ti t t f tiTechnical University of Łódź


cumulative structure functions


1E+1

in air in water loose sink tight sink

1E+0

1E-2

1E-1

R[K

/W]

1E-3

R

1E-41E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 1E+4

[s]

ti t t tTechnical University of Łódź


time constant spectra

Experimental Resultsin air

(s) R (K/W) C (J/K) 2.87E-04 6.19E-01 4.64E-04 9 81E-03 1 73E+00 5 67E-03

- individual RC stages correspond to real heat flow path

9.81E 03 1.73E+00 5.67E 038.04E+00 4.72E+00 1.71E+00 5.62E+01 3.14E+01 1.79E+00

in water (s) R (K/W) C (J/K)

- improved cooling forces 1D heat flowand reduces temperature setting time

- possible estimation of package2.79E-04 6.95E-01 4.01E-046.19E-03 1.50E+00 4.13E-03 1.61E+01 5.05E+00 3.19E+00 1.42E+03 8.53E+00 1.67E+02

loose sink

possible estimation of packageor heat sink heat capacity

- assessment of thermal interfaceresistance or heat transfer coefficient(s) R (K/W) C (J/K)

2.81E-04 6.36E-01 4.42E-04 5.07E-03 1.47E+00 3.46E-03 1.11E+01 2.39E+00 4.62E+00 6 54E+02 3 45E+00 1 89E+02

resistance or heat transfer coefficient

6.54E+02 3.45E+00 1.89E+02tight sink

(s) R (K/W) C (J/K) 2.86E-04 6.87E-01 4.17E-04 2.69E-03 1.05E+00 2.57E-03


8.06E-01 7.92E-01 1.02E+007.76E+02 4.09E+00 1.90E+02


SiC power diodes in TO-220 packages

Considered cooling configuration:

-still air cooling with a tightly attached multifinned heat sink

adapted from M. Janicki, M. Zubert, A. Napieralski, “Generation of reduced thermal models of electronic systems from transient thermal response”, Proc. 12th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems EuroSimE, 18-20 April, 2011, Linz, Austria, pp. 1-4.


y p pp


121314

D1 - MESD2 - MESD1 SIM

89

1011

e ris

e (K

)D1 - SIMD2 - SIM

4567

empe

ratu

re

0123Te

1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2

Time (s)

d d h tiTechnical University of Łódź


recorded heating curves


1E+3

1E+4)

D1D2

1E+0

1E+1

1E+2

itanc

e (J

/K) D2

1E-2

1E-1

1E+0

rmal

cap

aci

l ti t t f ti1E-5

1E-4

1E-3

Ther

cumulative structure functions0.0 1.0 2.0 3.0 4.0 5.0

Thermal resistance (K/W)



cumulative structure function

Experimental Results0.25

W)

D1D2

0.15

0.20st

ance

(K/W D2

0.10

herm

al re

sis

0.00

0.05Th

1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 1E+3

Time constant (s)




Experimental ResultsDiode 1

R C (s) (K/W) (J/K)

7.58E-04 8.62E-01 8.79E-04 1.72E-03 2.04E+00 8.44E-04 2 40E 01 9 24E 01 2 60E 012.40E-01 9.24E-01 2.60E-014.75E+00 4.32E-01 1.10E+01 6.21E+01 5.84E-01 1.06E+02

Diode 2Diode 2 R C

(s) (K/W) (J/K) 1.85E-04 2.50E-01 7.39E-043.32E-03 1.73E+00 1.92E-03 2.10E-01 7.86E-01 2.67E-01 4.98E+00 4.32E-01 1.15E+01


5.66E+01 5.05E-01 1.12E+02


Power amplifier in a 12-pin SIP packageConsidered cooling configurations:Considered cooling configurations:

-still air cooling with a loosely or tightly attachedltifi d h t i kmultifinned heat sink

-forced air cooling at different air velocity

adapted from M. Janicki, J. Banaszczyk, B. Vermeersch; G. De Mey, and A. Napieralski, “Generation of reduced thermal models of electronic systems from time constant spectra of transient temperature responses” Microelectronics Reliability Vol 51


transient temperature responses , Microelectronics Reliability, Vol. 51, Issue 8, August 2011, pp. 1351-1355, ISSN 0026-2714.

Experimental Resultsloose -mes tight-mes grease-mesloose -sim tight-sim grease-sim

50

60

70

e (K

)

30

40

50

pera

ture

ris

10

20

Tem

p

01E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 1E+4

Time (s)

d d liTechnical University of Łódź


recorded cooling curves

Experimental Results0 m/s-mes 1.5 m/s-mes 3 m/s-mes0 m/s-sim 1.5 m/s-sim 3 m/s-sim

40

50

se (K

)

20

30

pera

ture

ris

0

10Tem

p

01E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 1E+4

Time (s)

d d liTechnical University of Łódź


recorded cooling curves


1.0E+6loose tight grease

1.0E+31.0E+41.0E+5

1.0E+01.0E+11.0E+2

Cth

[J/K

]

1 0E 41.0E-31.0E-21.0E-1

1.0E-40 1 2 3 4 5 6 7 8

Rth [K/W]




Experimental Results1.0E+6

0.00 m/s 1.50 m/s 3.00 m/s

1.0E+3

1.0E+4

1.0E+5

1.0E+0

1.0E+1

1.0E+2

Cth

[J/K

]

1.0E-3

1.0E-2

1.0E-1

1.0E-40 1 2 3 4 5 6

Rth [K/W]





1.4

loose tight grease

1.0

1.2

1.4W

]

0.6

0.8

Rth

[K/W

0.0

0.2

0.4

0.01.0E-3 1.0E-2 1.0E-1 1.0E+0 1.0E+1 1.0E+2 1.0E+3

Time constant [s]





0.350.00 m/s 1.50 m/s 3.00 m/s

0.25

0.30

0.15

0.20

Rth

[K/W

]

0 00

0.05

0.10

0.001.0E-3 1.0E-2 1.0E-1 1.0E+0 1.0E+1 1.0E+2 1.0E+3

Time constant [s]




Experimental Resultsgrease tight loose

(s) R (K/W) C (J/K) (s) R (K/W) C (J/K) (s) R (K/W) C (J/K)( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

6.52 E-3 6.65 E-1 9.81 E-3 6.83 E-3 7.11 E-1 9.62 E-3 6.27 E-3 6.90 E-1 9.09 E-3

7.58 E-2 4.62 E-1 1.64 E-1 8.43 E-2 5.17 E-1 1.63 E-1 8.20 E-2 4.94 E-1 1.66 E-1

2 88 E+0 5 04 E-1 5 71 E+0 3 06 E+0 1 01 E-1 3 05 E+0 5 28 E+0 1 85 E+0 2 85 E+02.88 E+0 5.04 E 1 5.71 E+0 3.06 E+0 1.01 E 1 3.05 E+0 5.28 E+0 1.85 E+0 2.85 E+0

5.02 E+2 4.46 E+0 1.12 E+2 5.09 E+2 4.37 E+0 1.16 E+2 5.25 E+2 4.32 E+0 1.21 E+2

0.0 m/s 1.5 m/s 3.0 m/s

( ) R (K/W) C (J/K) ( ) R (K/W) C (J/K) ( ) R (K/W) C (J/K)(s) R (K/W) C (J/K) (s) R (K/W) C (J/K) (s) R (K/W) C (J/K)

8.50 E-3 9.63 E-1 8.83 E-3 8.23 E-3 8.70 E-1 9.46 E-3 7.56 E-3 8.27 E-1 9.15 E-3

7.48 E-2 4.01 E-1 1.87 E-1 6.96 E-2 4.27 E-1 1.63 E-1 6.85 E-2 4.14 E-1 1.66 E-1

2.91 E+0 5.03 E-1 5.77 E+0 2.86 E+0 4.52 E-1 6.34 E+0 2.82 E+0 4.08 E-1 6.91 E+0

3.91 E+2 3.30 E+0 1.18 E+2 1.58 E+2 1.36 E+0 1.16 E+2 1.04 E+2 8.91 E-1 1.16 E+2


Conclusions & Future Tasks logarithmically equidistant sampling of system thermal response

is the key issue in the identification of system time constant spectra; l h ll ti t t i l d d i d d th l d lonly when all time constants are included in reduced thermal models

the entire heat flow path from the junction to the ambient is properly characterized

opposed to the blind pole matching, the proposed method for the generation of reduced thermal models from time constant spectra allows for the physical interpretation of individual model elementallows for the physical interpretation of individual model element values

resulting reduced RC ladder thermal models of a system predict accurately junction temperature in dynamic states and they can be easily included in standard electrical simulators


Conclusions & Future Tasks conversion from Foster to Cauer network performed for a limited

number of RC stages is more numerically stable

generally Cauer RC ladder models are not boundary condition independent but not significant changes of boundary conditions can be taken into account without the necessity to regenerate thecan be taken into account without the necessity to regenerate the entire model

the NID method is developed based on a linear circuit theory thusspecial care must be taken when large temperature gradients occur

in future research both temperature and boundary condition dependence of RC ladder model elements should be investigateddependence of RC ladder model elements should be investigated in more detail



Boundary Condition Independence of Cauer RC … Condition Independence ,, , of Cauer RC Ladder ......

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