thermal measurements and qualification using the transient method: principles and applications 1...

1Thermal measurements and qualification using the transient method: principles and applications

Thermal measurements and qualification using the transient methodPrinciples and applications

The 21st annual IEEE SEMI-THERM SymposiumFairmont Hotel, San Jose, 13 March 2005

One-day short course by András Poppe

[email protected]

Budapest University of Technology and Economics, Department of Electron Devices

[email protected]


MATHEMATICAL DESCRIPTION OF THERMAL SYSTEMES(distributed linear RC systems)


Introduction

• Linearity is assumed– later we shall check if this assumption was correct

• Thermal systems are– infinite– distributed systems

• The theoretical model is: distributed linear RC system• Theory of linear systems and some circuit theory will be

used

For rigorous treatment of the topic see:

V.Székely: "On the representation of infinite-length distributed RC one-ports", IEEE Trans. on Circuits and Systems, V.38, No.7, July 1991, pp. 711-719

Except subsequent 12 slides no more difficult maths will be used


Introduction • Theory of linear systems

or shortly: tPtWtT )(

= convolution

If the T response to the P excitation is known: tPtTtW 1)(

1 = deconvolution (to be calculated numerically)

dyytPyWtT

0

)()(

Response to any excitation:

t

W(t)

weight function (Green’s function)

W(t)t

(t)

Dirac-delta

(t)


Introduction

If we know the a(t) step-response function, we know everything about the system

the system is fully characterized.

• The h(t) unit-step function is more easy to realize than the (t) Dirac-delta

h(t) a(t),

a(t) is the unit-step response functiont

1

h(t)

t

a(t) thtWta )(

• Theory of linear systems

t

W(t)

weight function (Green’s function)

W(t)t

(t)

Dirac-delta

(t)


• The a(t) unit-step response function is another characteristic function of a linear system.

• The advantage of a(t) the unit-step response function over W(t) weight function is that a(t) can be measured (or simulated) since it is the response to h(t) which is easy to realize.

Step-response

)()( tWtadt

d

t

a(t)

t

W(t)

dyythyWthtWta )()()()()(

dyyWdyythyWta 1)()()()(0


Thermal transient testingh(t) a(t)

The measured a(t) response function is characteristic to the package. The features of the chip+package+environment structure can be extracted from it.


Step-response functions

)/exp(1)( tRta

C

R

CRt

R

n

iii tRta

1

)/exp(1)( C1

R1

C2

R2

Cn

Rn

iii CR t

1

R1

2

R2

n

Rn

If we know the Ri and i values, we know the system.

characteristic values: R magnitude and time-constant

– for a chain of n RC stages:

characteristic values: set of Ri magnitudes and itime-constants

• The form of the step-response function– for a single RC stage:


– for a distributed RC system:

Step-response functions

If we know the R() function, we know the distributed RC system.

n

i 1

0

n

dtRta

0

)/exp(1)()(

n

iii tRta

1

)/exp(1)(

R()

t

1

R1

2

R2

n

Rn

discrete set of Ri and ivalues continuous R(spectrum

characteristic: R(time-constant spectrum:


Discrete RC stages discrete set of Ri and ivalues

Distributed RC system continuous R() function

If we know the R() function, we know the system.

R() is called the time-constant spectrum.

Time-constant spectrum

dtRta

0

)/exp(1)()(

R()


Practical problem • The range of possible time-constant values in thermal

systems spans over 5..6 decades of time– 100s ..10ms range: semiconductor chip / die attach– 10ms ..50ms range: package structures beneath the chip– 50ms ..1 s range: further structures of the package– 1s ..10s range: package body– 10s ..10000s range: cooling assemblies

• Wide time-constant range data acquisition problem during measurement/simulation: what is the optimal sampling rate?


Practical problem (cont.)

Solution: equidistant sampling on logarithmic time scale

Nothing can be seen below the 10s range

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Time [s]

Te

mp

era

ture

ris

e [°

C]

T3Ster Master: Smoothed response

a(t)

t

Measured unit-step response of an MCM shown in linear time-scale


1e-6 1e-4 0.01 1 100 100000

10

20

30

40

50

60

70

Time [s]

Te

mp

era

ture

ris

e [°

C]


Using logarithmic time scale

Instead of t time we use z = ln(t) logarithmic time Details in all time-constant ranges are seen

a(z)

z = ln(t)

Measured unit-step response of an MCM shown in linear time-scale


• Switch to logarithmic time scale: a(t) a(z) where z = ln(t)

a(z) is called*– heating curve or– thermal impedance curve

• Using the z = ln(t) transformation it can be proven that

Step-response in log. time

dzzRzadz

d

0

))exp(exp()()(

*Sometimes Pa(z) is called heating curve in the literature.


• Note, that da(z)/dz is in a form of a convolution integral:

)()()( zwzRzadz

dz

Step-response in log. time

Introducing the function:))exp(exp()( zzzwz

dzwRzadz

dz

0

)()()(

dzzRzadz

d

0

))exp(exp()()(

)()()( 1 zwzadz

dzR z

• From a(z) R(z) is obtained as:


Extracting the time-constant spectrum in practice 1

1e-6 1e-4 0.01 1 100 100000

2

4

6

8

10

12

14

16

18

Time [s]

De

riva

tive

of t

em

p. r

ise

[K/-

]

T3Ster Master: Derivative

VIPER1-2 - Ch. 0

)(zadz

d

Derivative of the thermal impedance

curve

Numerical deconvolution)(1 zwz

1e-6 1e-4 0.01 1 100 100000

10

20

30

40

50

60

Time [s]

Te

mp

era

ture

ris

e [°

C]


VIPER1-2 - Ch. 0

)(za

Measured thermal

impedance curve

1e-6 1e-4 0.01 1 100 100000

2

4

6

8

10

12

14

16

18

Time [s]

Tim

e c

on

sta

nt i

nte

nsi

ty [K

/W/-

]

T3Ster Master: Tau intensity

VIPER1-2 - 0

)(zR

Time-constant spectrum

Numerical

derivation dz

d


)(za Must be noise free, must have high time resolution

(e.g. 200 points/decade)

)(zR False values with small magnitude can be present due to noise enhancement in the procedure. Negative values represent a transfer impedance.

Numerical deconvolution: Bayes-iteration (for driving point impedance only), frequency-domain inverse filtering (both for driving point and transfer impedances)

)(1 zwz

Numerical derivation should be accurate: high order techniques yield better results.

Danger of noise enhancement filtering loss of ultimate resolution in the time-constant spectrum

dz

d

Extracting the time-constant spectrum in practice 2


• The time-constant spectrum gives hint for the time-domain behavior of the system for experts

• Time-constant spectra can be further processed and turned into other characteristic functions

• These functions are called structure functions

Using time-constant spectra


Break!


INTRODUCTION TO STRUCTURE FUNCTIONS


Example: Thermal transient measurementsheating or cooling curves

Network model of a thermal impedance:

Normalized to 1W dissipation: thermal impedance curve

Evaluation: Interpretation of the impedance model: STRUCTURE FUNCTIONS


How do we obtain them?


Structure functions 1• Discretization of R(z) RC network model in Foster canonic

form (instead of spectrum lines, 100..200 RC stages)

Ri=R(i)

i=exp(zi)

Ri

Ci=i/Ri

• A discrete RC network model is extracted name of the method: NID - network identification by deconvolution


Structure functions 2

• The Foster model network is just a theoretical one, does not correspond to the physical structure of the thermal system:

thermal capacitance exists towards the ambient (thermal “ground”) only

• The model network has to be converted into the Cauer canonic form:


• The identified RC model network in the Cauer canonic form now corresponds to the physical structure, but

• This is called cumulative structure function

• it is very hard to interpret its “meaning”

• Its graphical representation helps:

n

iiRR

1

n

iiCC

1



n

iin CC

1

n

iin RR

1

am

bie

nt

jC

thjaR

junction

iC

iR

ambient

Clog

iC

jRiR

Structure functions 4The cumulative structure function is the map of the heat-conduction path:


Cumulative (integral) structure function

differential structure function

Calculate dC/dR:


air


What do structure functions tell us and how?


A hypothetic example for the explanation of the concept of structure functions 1

An ideal homogeneous rod

Ideal heat-sink at Tamb

t

1W

P(t)

1D heat-flow

Rth_tot= L/(A·)

T(z)

z = ln t





L

L A

V = A·L1D heat-flow

Tamb

Cth = V·cv

Rth = L/(A·)





This is the network model of the thermal impedance of the rod

Driving point

Ambient


A hypothetic example for the explanation of the concept of structure functions 4Let us assume L, A and material parameters such, that all element values in the model are 1!

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

There must be a singularity when we reach the ideal heat-sink.

It is very easy to create the cumulative structure function:

y=x – a straight line

n

iiRR

1

n

iiCC

1

Rth_tot

Rth_tot

The location of the singularity gives the total thermal resistance of the structure.


A hypothetic example for the explanation of the concept of structure functions 5Let us assume L, A and material parameters such, that all element values in the model are 1!

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

n

iiRR

1

n

iiCC

1

Rth_tot

n

iiRR

1Rth_tot

dR

dCRK )(

It is also very easy to create the differential structure function for this case. Again, we obtain a straight line:

y=1


A hypothetic example for the explanation of the concept of structure functions 6What happens, if e.g. in a certain section of the structure model all capacitance values are equal to 2?

1

1

1

1

1

1

1

1

1

1

1

2

1

2

1

2

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

n

iiRR

1

n

iiCC

1

double slope

Cumulative structure function

n

iiRR

1

dR

dCRK )(

a peak

Differential structure function

1

2


A hypothetic example for the explanation of the concept of structure functions 7What would such a change in the structure functions indicate?

It means either a change in the

material properties…


A hypothetic example for the explanation of the concept of structure functions 8What would such a change in the structure functions indicate?

… or a change in the geometry …or both


A hypothetic example for the explanation of the concept of structure functions 9What values can we read from the structure functions?


n

iiRR

1

dR

dCRK )(


n

iiRR

1

n

iiCC

1

Cth1 Cth2 Cth3

Cth1

Cth2

Cth3

Thermal capacitance values can be read

Rth1 Rth2 Rth3

Rth1 Rth2 Rth3

Partial thermal resistance values can be read


A hypothetic example for the explanation of the concept of structure functions 10What values can we read from the structure functions?


n

iiRR

1

dR

dCRK )(


n

iiRR

1

n

iiCC

1

V1 V2 V3

V3/cv1

If material is known, volume can be identified.

If material is known, cross-sectional area can be identified.

A1 A2 A1

K2 = A22·cv2·2

K1 = A21·cv1·1

If volume is known, volumetric thermal capacitance can be identified. If cross-sectional area is known, material

parameters (cv·) can be identified.

V2/cv2

V1/cv1


• The differential structure function is defined as the derivative of the cumulative thermal capacitance with respect to the cumulative thermal resistance

• K is proportional to the square of the cross sectional area of the heat flow path.

Structure functions 5 Differential structure function

dR

dCRK )(

2

/)( Ac

Adx

cAdxRK


• Structure functions are direct models of one-dimensional heat-flow – longitudinal flow (like in case of a rod)

• Also, structure functions are direct models of “essentially” 1D heat-flow, such as– radial spreading in a disc (1D flow in polar coordinate system)– spherical spreading– conical spreading– etc.

• Structure functions are "reverse engineering tools": geometry/material parameters can be identified with them

Some conclusions regarding structure functions


In many cases a complex heat-flow path can be partitioned into essentially 1D heat-flow path sections connected in series:

IDEAL HEAT-SINK



IC package assuming pure 1D heat-flow

Cold-plate

BaseChip

Die attachJunction

Die attach: large Rth/Cth ratio

Base: small Rth/Cth ratioGrease: large Rth/Cth ratio

Cold-plate: infinite Cth

Junction: is always in the origin

R

CCumulative structure function:

t

1W

P(t) T(z)

z = ln t

We measure the thermal impedance at the junction......and create its model in form of the cumulative structure function:

Grease

1D heat-flow

Chip: small Rth/Cth ratio


Base

Base

IC package assuming pure 1D heat-flow

R

Differential structure function:

Die attach

Die attach

Chip

Chip

Cold-plate: infinite Cth

Junction

JunctionR

CCumulative structure function:

Die attach interface thermal resistance

The heat-flow path can be well characterized e.g. by partial thermal resistance values

The RthDA value is derived entirely from the junction

temperature transient.

No thermocouples are needed.

Grease

Grease

R

CK


Example of using structure functions: DA testing (cumulative structure functions)

Cold-plate

BaseChip

Die attachJunction

Grease

BaseGrease

Die attach

R

C

Chip

Reference device with good DA

R

C

Cold-plate

BaseChip

Die attachJunction

Grease

Unknown device with suspected DA voids

This change is more visible in the differential structure function.

Copy the reference structure function into

this plot

This increase suggests DA voids

Identify its structure function: Identify its structure function:


Example of using structure functions: DA testing (differential structure functions)

Cold-plate

BaseChip

Die attachJunction

Grease


Cold-plate

BaseChip

Die attachJunction

Grease



this plotBase

RDie attach

Chip

Junction Grease

R

CK

RDie attach

Chip

Junction

Base

Grease

R

CK

Shift of peak: Increased die attach thermal resistance indicates voids


• In case of complex, 3D streaming the derived model has to be considered as an equivalent physical structure providing the same thermal impedance as the original structure.



Cth2

Cth1

Rth1 Rth2

RconstC

12

12 )/ln(

4

1

thth

thth

RR

CCw

Specific features of structure functions for a given way of essentially 1D heat-flow• For “ideal” cases structure functions can be given even

by analytical formulae – for a rod:

– for radial spreading in a disc of w thickness and thermal conductivity:

Section corresponding to

radial heat spreading in a

disk


Accuracy, resolution• Structure functions obtained in practice always differ

from the theoretical ones, due to several reasons:– Numerical procedures

• Numerical derivation• Numerical deconvolution• Discretization of the time-constant spectrum• Limits of the Foster-Cauer conversion

100-150 stages

– Real physical heat-flow paths are never “sharp” • Physical effects that we can try to cope with

– There is always some noise in the measurements– Not 100% complete transient / small transfer effect– In reality there are always parasitic paths (heat-loss) allowing

parallel heat-flow

)(1 zwz

dz

d


Accuracy, resolution• Comparison of the effect of the numerical procedures:

Cumulative structure functions of an artificially constructed Cauer model:

Generated directly from the RC ladder values

Identified from the simulated unit-step response of the RC ladder

0.1

1

10

0 2 4 6 8 10

'cprob3.cum'

Sharp knees become smoother due to the numerical procedures

• Resolution of structure functions in practice is about 1% of the total Rthja of the heat-flow path

SPICEln t

a(t)

NID


• Plateaus correspond to a certain mass of material

• Cth values can be read

• material volume

• dimensions volumetric thermal capacitance

Cth values can be read

Rth values can be read

• Peaks correspond to change in material

• corresponding Rth values can be read

• material cross-sectional area

• cross-sectional area thermal conductivity

Use of structure functions:


Use of structure functions: partial thermal resistances, interface resistance

Rthjc

• Origin = junction, singularity = ambient

• Rthja and partial resistance values

• interface resistance values (difference between two peaks)


Some examples of using structure functions


Measurement of the package/heat-sink interface resistance

Four cases have been investigated:

1. Direct mounting, with heat-conducting grease

2. Direct mounting, without grease

3. Mica, screw strongly tightened

4. Mica, screw medium tightened

We obtain partial thermal resistance values (interface resistance) and properties of the heat-sink


The transient responses:


T3Ster: record=demo11

Curves coincide: transient inside the package - no problem

??

STRUCTURE FUNCTIONS WILL HELP


The structure functions

Inside-package part

See details in: A. Poppe, V. Székely: Dynamic Temperature Measurements: Tools Providing a Look into Package and Mount Structures, Electronics Cooling, Vol.8, No.2, May 2002.



Example: The differential structure function of a processor chip with cooling mount

• The local peaks represent usually reaching new surfaces (materials) in the heat flow path, • their distance on the horizontal axis gives the partial thermal resistances between these surfaces

Intel Ppowered and measured via the chip

Cooling mount

Al2O3 beneath the chip

Chip


Example: FEM model validation with structure functions

Courtesy of D. Schweitzer (Infineon AG), J. Parry (Flomerics Ltd.)

0 1 2 3 4 5 6 70.01

0.1

1

10

100

1000

10000

100000

Rth [K/W]

K [W

2s

/K2

]

T3Ster: differential structure function(s)

Differential structure function - H67Differential structure function - inf_dcp1_simDifferential structure function - flom_dcp1_grid_g2t3

From MEASUREMENT

From FLOTHERM simulation

From ANSYS simulation


Structure functions summary

• Structure functions are defined for driving point thermal impedances only. Deriving structure functions from a transfer impedance results in nonsense.

• Structure functions = thermal resistance & capacitance maps of the heat conduction path.

• Connection to the RC model representation as well as mathematically derived from the heat-conduction equation.

• Exploit special features for certain types of heat-conduction (lateral, radial).


SUMMARY of descriptive functions

• Descriptive functions of distributed RC systems (i.e. thermal systems) are– the a(t) or a(z) step-response functions– the R() time-constant spectrum– the structure functions

• C(R) cumulative

• K(R) differential

• Any of these functions fully characterizes the dynamic behavior of the thermal system

• The step-response function can be easily measured or simulated

• The structure functions are easily interpreted since they are maps of the heat flow path



• Descriptive functions can be used in evaluation of both measurement and simulation results:

• Step-response can be both measured and simulated– Small differences in the transient may remain hidden, that is why other

descriptive functions need to be used

• Time-constant spectra are already good means of comparison– Extracted from step-response by the NID method– Can be directly calculated from the thermal impedance given in the

frequency-domain (see e.g. Székely et al, SEMI-THERM 2000)

• Structure functions are good means to compare simulation models and reality

• Structure functions are also means of non-destructive structure analysis and material property identification or Rth measurement.



• The advanced descriptive functions (time-constant spectra, complex loci, structure functions) are obtained by numerical methods using sophisticated maths.

• That is why the recorded transients– must be noise-free and accurate,– must reflect reality (artifacts and measurement errors should be

avoided),– must have high data density.

since the numerical procedures like– derivation and– deconvolution

enhance noise and errors.Besides compliance to the JEDEC JESD51-1 standard, measurement tools and methods should provide such accurate thermal transient curves.


PART 3APPLICATION EXAMPLESFailure analysis/DA testingStudy of stacked diesPower LED characterizationRthjc measurementsCompact modeling


TESTING OF DIE ATTACH QUALITY basics


Chip carrier (Cu)

pn junction

Heat-sink

Silicon chip

Thermal interface material

Forced air cooling

Die attach solder

Plastic package

Leads

Die attach quality testing The die attach is a key element in the junction-to-ambient heat-conduction path


Detecting voids in the die attach of single die packages

Experimental package samples with die attach voids prepared to verify the accuracy of the detection method based on thermal transient testing

(acoustic microscopic images, ST Microelectronics)

See:

M. Rencz, V. Székely, A. Morelli, C. Villa: Determining partial thermal resistances with transient measurements and using the method to detect die attach discontinuities, 18th Annual IEEE SEMI-THERM Symposium, March 1-14 2002, San Jose, CA,USA, pp. 15-20


Main time-constants of the experimental samples


Measured Zth curves of the average samples

Already distinguishable


Differential structure functions of the experimental samples


The principle of failure detection

• Take a good sample as a reference– Measure its thermal transient– Identify its structure function

• Take sample to be qualified– Measure its thermal transient– Identify its structure function– Compare it with the reference structure function– Locate differences– A difference means a possible failure– If needed, quantify the failure (e.g. increased partial thermal

resistance)


Cold-plate

BaseChip

Die attachJunction

Grease


Cold-plate

BaseChip

Die attachJunction

Grease



this plotBase

RDie attach

Chip

Junction Grease

R

CK

RDie attach

Chip

Junction

Base

Grease

R

CK

Shift of peak: Increased die attach thermal resistance indicates voids

The principle again


TESTING OF DIE ATTACH and SOLDER QUALITY: case studies

A power BJT mount Stacked die packages


Measurement of a power BJT mount: failure analysis

0

5

10

15

20

25

30

35

1e-06 1e-05 0.0001 0.001 0.01 0.1 1 10 100

Tem

pera

ture

ris

e

[Cels

]

Time [s]

miTTT: RECORD=C1DMon Oct 23 22:15:37 2000

"C01d.MR1""C02d.mr1""C03d.mr1""C04d.mr1""C05d.mr1""C06d.mr1"

The measurement setup

The measured transient responses

The transistors are soldered to the Cu platform of the mount Problems: imperfect soldering, chip delamination


T3Ster: differential structure function

The “good” structure function

Rth=3.2 K/W



Die attach delamination inside the package




Imperfect soldering of the package



thermal measurements and qualification using the transient method: principles and applications 1...

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