The 21st annual IEEE SEMI-THERM Symposium

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Thermal measurements and qualification using the transient method Principles and applications
The 21st annual IEEE SEMI-THERM Symposium Fairmont Hotel, San Jose, 13 March 2005 One-day short course by András Poppe Budapest University of Technology and Economics, Department of Electron Devices

MATHEMATICAL DESCRIPTION OF THERMAL SYSTEMES (distributed linear RC systems)

Except subsequent 12 slides no more difficult maths will be used
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 Except subsequent 12 slides no more difficult maths will be used

Response to any excitation:
Introduction Theory of linear systems t d(t) Dirac-delta t W(t) weight function (Green’s function) Response to any excitation: or shortly: = convolution If the T response to the P excitation is known: = deconvolution (to be calculated numerically)

Introduction Theory of linear systems t d(t) Dirac-delta t W(t) weight function (Green’s function) The h(t) unit-step function is more easy to realize than the d(t) Dirac-delta h(t) a(t), a(t) is the unit-step response function t 1 h(t) t a(t) If we know the a(t) step-response function, we know everything about the system the system is fully characterized.

Step-response t a(t) W(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.

Thermal transient testing
h(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
The form of the step-response function for a single RC stage: C R t characteristic values: R magnitude and t time-constant for a chain of n RC stages: C1 R1 C2 R2 Cn Rn t t1 t2 tn characteristic values: set of Ri magnitudes and ti time-constants If we know the Ri and ti values, we know the system.

Step-response functions
for a distributed RC system: n   characteristic: R(t) time-constant spectrum: t R(t) t1 R1 t2 R2 tn Rn discrete set of Ri and ti values continuous R(t) spectrum If we know the R(t) function, we know the distributed RC system.

Time-constant spectrum
Discrete RC stages discrete set of Ri and ti values Distributed RC system continuous R(t) function If we know the R(t) function, we know the system. R(t) is called the time-constant spectrum. t R(t)

Practical problem The range of possible time-constant values in thermal systems spans over 5..6 decades of time 100ms ..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 s range: cooling assemblies Wide time-constant range  data acquisition problem during measurement/simulation: what is the optimal sampling rate?

Practical problem (cont.)
a(t) t Measured unit-step response of an MCM shown in linear time-scale Nothing can be seen below the 10s range Solution: equidistant sampling on logarithmic time scale

Using logarithmic time scale
a(z) Measured unit-step response of an MCM shown in linear time-scale z = ln(t) Details in all time-constant ranges are seen Instead of t time we use z = ln(t) logarithmic time

Step-response in log. time
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 *Sometimes Pa(z) is called heating curve in the literature.

Step-response in log. time
Note, that da(z)/dz is in a form of a convolution integral: Introducing the function: From a(z) R(z) is obtained as:

Extracting the time-constant spectrum in practice 1
Measured thermal impedance curve Numerical derivation Numerical deconvolution Derivative of the thermal impedance curve Time-constant spectrum

Extracting the time-constant spectrum in practice 2
Must be noise free, must have high time resolution (e.g. 200 points/decade) 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 Numerical deconvolution: Bayes-iteration (for driving point impedance only), frequency-domain inverse filtering (both for driving point and transfer impedances) False values with small magnitude can be present due to noise enhancement in the procedure. Negative values represent a transfer impedance.

Using time-constant spectra
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

Break!

INTRODUCTION TO STRUCTURE FUNCTIONS

Example: Thermal transient measurements
heating or cooling curves Normalized to 1W dissipation: thermal impedance curve Evaluation: Interpretation of the impedance model: STRUCTURE FUNCTIONS Network model of a thermal impedance:

How do we obtain them?

Structure functions 1 Discretization of R(z)  RC network model in Foster canonic form (instead of  spectrum lines, RC stages) Ri=R(ti) ti=exp(zi) Ri Ci=ti/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:

Structure functions 3 The identified RC model network in the Cauer canonic form now corresponds to the physical structure, but it is very hard to interpret its “meaning” Its graphical representation helps: This is called cumulative structure function

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

Structure functions 6 Cumulative (integral) structure function
Calculate dC/dR: differential structure function air

What do structure functions tell us and how?

A hypothetic example for the explanation of the concept of structure functions 1
Ideal heat-sink at Tamb T(z) z = ln t An ideal homogeneous rod t 1W P(t) 1D heat-flow Rth_tot= L/(A·l)

A hypothetic example for the explanation of the concept of structure functions 2
An ideal homogeneous rod DL DL A V = A·DL 1D heat-flow Tamb Cth = V·cv Rth = DL/(A·l) Ideal heat-sink at Tamb

A hypothetic example for the explanation of the concept of structure functions 3
An ideal homogeneous rod Driving point Ambient This is the network model of the thermal impedance of the rod Ideal heat-sink at Tamb

A hypothetic example for the explanation of the concept of structure functions 4
Let us assume DL, A and material parameters such, that all element values in the model are 1! 1 Rth_tot The location of the singularity gives the total thermal resistance of the structure. It is very easy to create the cumulative structure function: y=x – a straight line There must be a singularity when we reach the ideal heat-sink.

A hypothetic example for the explanation of the concept of structure functions 5
Let us assume DL, A and material parameters such, that all element values in the model are 1! 1 1 It is also very easy to create the differential structure function for this case. Again, we obtain a straight line: y=1 Rth_tot Rth_tot

A hypothetic example for the explanation of the concept of structure functions 6
What happens, if e.g. in a certain section of the structure model all capacitance values are equal to 2? 1 2 double slope Cumulative structure function a peak Differential structure function 1 2

It means either a change in the material properties…
A hypothetic example for the explanation of the concept of structure functions 7 What would such a change in the structure functions indicate? It means either a change in the material properties…

… or a change in the geometry …or both
A hypothetic example for the explanation of the concept of structure functions 8 What 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 9
What values can we read from the structure functions? Cth1 Cth2 Cth3 Thermal capacitance values can be read Rth1 Rth2 Rth3 Partial thermal resistance values can be read Differential structure function Cumulative structure function

A hypothetic example for the explanation of the concept of structure functions 10
What values can we read from the structure functions? V1 V2 V3 A1 A2 V3/cv1 Differential structure function V2/cv2 K2 = A22·cv2·2 V1/cv1 Cumulative structure function K1 = A21·cv1·1 If material is known, volume can be identified. If material is known, cross-sectional area can be identified. If volume is known, volumetric thermal capacitance can be identified. If cross-sectional area is known, material parameters (cv·) can be identified.

Structure functions 5 Differential structure function
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.

Some conclusions regarding structure functions
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
P(t) T(z) z = ln t We measure the thermal impedance at the junction... Junction Grease Die attach Chip 1D heat-flow Base ...and create its model in form of the cumulative structure function: Cold-plate Cumulative structure function: Cold-plate: infinite Cth Grease: large Rth/Cth ratio Base: small Rth/Cth ratio Junction: is always in the origin Die attach: large Rth/Cth ratio Chip: small Rth/Cth ratio

IC package assuming pure 1D heat-flow
Grease Cold-plate: infinite Cth Base Junction Chip Die attach Cumulative structure function: The heat-flow path can be well characterized e.g. by partial thermal resistance values Differential structure function: Die attach interface thermal resistance The RthDA value is derived entirely from the junction temperature transient. No thermocouples are needed.

Example of using structure functions: DA testing (cumulative structure functions)
Reference device with good DA Cold-plate Base Chip Die attach Junction Grease Unknown device with suspected DA voids Cold-plate Base Chip Die attach Junction Grease Identify its structure function: Identify its structure function: Base Grease Die attach Chip Copy the reference structure function into this plot This change is more visible in the differential structure function. This increase suggests DA voids

Copy the reference structure function into this plot
Example of using structure functions: DA testing (differential structure functions) Reference device with good DA Unknown device with suspected DA voids Cold-plate Base Chip Die attach Junction Grease Cold-plate Base Chip Die attach Junction Grease Shift of peak: Increased die attach thermal resistance indicates voids Base Die attach Chip Junction Grease Die attach Chip Junction Base Grease Copy the reference structure function into this plot

Some conclusions regarding structure functions
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.

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 l thermal conductivity: Cth2 Cth1 Rth1 Rth2 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 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

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 Sharp knees become smoother due to the numerical procedures SPICE ln t a(t) NID Resolution of structure functions in practice is about 1% of the total Rthja of the heat-flow path

Use of structure functions:
Cth values can be read Plateaus correspond to a certain mass of material Cth values can be read material  volume dimensions  volumetric thermal capacitance 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: 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 Ez egy olyan mintapélda, ahol nyilvánvalóvá tesszük, hogy hogyan kell rész hőellenállásokat mérni a T3Sterrel. Azt is látni fogjuk, hogy tulajdonképpen heat-sink jellemzők mérésére is alkalmas az eljárás.

Measurement of the package/heat-sink interface resistance
The transient responses: T3Ster: record=demo11 ?? STRUCTURE FUNCTIONS WILL HELP Curves coincide: transient inside the package - no problem A 4 függvény eleje nyilván megegyezik, hiszen az a belső tranziens. Az elválás utáni rész pontos értelmezése viszont csak a struktúrafüggvénnyel megy.

Measurement of the package/heat-sink interface resistance
The structure functions Inside-package part Hívjuk fel a figyelmet: A négy függvény bal oldala megegyezik - mindaddig, amíg a feltételek változatlanok, vagyis a tokkal bezárólag. A függvényről azt lehet jól leolvasni, hogy a legjobb (közvetlen, zsírozott) esethez képest mennyi az interfaze ellenállás növekmény. Még a közepesen meghúztam/nagyon meghúztam is igen szépen leolvasható. Rá kell itt mutatni, hogy bár ezek a hatások elvileg a teljes hőellenállás mérésével és a 4 esetre való különbségképzéssel is számolhatók, a gyakorlatban ez nem járható, mert a nagy hűtőborda néhány-tized fokos kezdeti állapot különbségei miatt az eredmény elveszne a mérési pontatlanságban. Figyeljük meg: ilyen kezdeti állapot pontatlanság miatt a közepesen/erősen meghúztam a globális hőellenállásban a várakozással éppen ellentétes eredményt adna, míg a parciális hőellenállás mérésben a hiba nem jelentkezik. 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
Intel mP powered and measured via the chip Cooling mount Al2O3 beneath the chip Chip 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

Example: FEM model validation with structure functions
From MEASUREMENT From FLOTHERM simulation From ANSYS simulation Courtesy of D. Schweitzer (Infineon AG), J. Parry (Flomerics Ltd.)

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(t) time-constant spectrum the structure functions CS(RS) cumulative K(RS) 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

SUMMARY of descriptive functions
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.

SUMMARY of descriptive functions
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 3 APPLICATION EXAMPLES Failure analysis/DA testing Study of stacked dies Power LED characterization Rthjc measurements Compact modeling

TESTING OF DIE ATTACH QUALITY basics

Die attach quality testing
The die attach is a key element in the junction-to-ambient heat-conduction path Chip carrier (Cu) pn junction Heat-sink Silicon chip Thermal interface material Forced air cooling Die attach solder Plastic package Leads A 2 csúcs mindkét görbén beazonosítható, de C02 esetén tőle jobbra egy határozott minimumot látunk, és a következő platóig sokkal nagyobb (kb. 2,5-szörös) a hőellenállás, mint C08 esetén. Úgy tűnik tehát, hogy a szerelőlap műanyag bevonatának nőtt meg a hőellenállása. Magyarázatot kapunk erre, ha szemrevételezzük a tranzisztort. A felforrasztási hiba szemmel látható, az ón néhány apró cseppé futott össze. A cseppekbe szaladt forrasz miatt a műanyag valószínűleg nem vezeti a hőt teljes keresztmetszetében, hanem csak a cseppek alatt, így a hőellenállásnak ez az összetevője megnő.

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 , San Jose, CA,USA, pp

Main time-constants of the experimental samples

Measured Zth curves of the average samples

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 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)

Copy the reference structure function into this plot
The principle again Reference device with good DA Unknown device with suspected DA voids Cold-plate Base Chip Die attach Junction Grease Cold-plate Base Chip Die attach Junction Grease Shift of peak: Increased die attach thermal resistance indicates voids Base Die attach Chip Junction Grease Die attach Chip Junction Base Grease Copy the reference structure function into this plot

TESTING OF DIE ATTACH and SOLDER QUALITY: case studies
A power BJT mount Stacked die packages

Measurement of a power BJT mount: failure analysis
The measurement setup The measured transient responses The transistors are soldered to the Cu platform of the mount Problems: imperfect soldering, chip delamination

Measurement of a power BJT mount: failure analysis
T3Ster: differential structure function The “good” structure function Rth=3.2 K/W A függvénygörbe bal oldali vége a chipnek felel meg, a jobb oldali a cold plate-nek. Utóbbi pontot a 4 jelű nyíl mutatja. A kettő között a vízszintes tengelyen leolvasott hőellenállás a chip és a cold plate közötti teljes hőellenállás (jelen esetben 3,2 K/W). A függvény kezdete kissé zajos (cikk-cakkos), de átlag értékként kb. K=0,1 rendelhető hozzá. Ez átszámolva szilícium keresztmetszetre 19,7 mm2 keresztmetszetet ad, ami a teljesítmény tranzisztor chip felületére reális adat. A következő, 1 jelű csúcs a tranzisztor-tok hőkapacitása (azon belül is a tok Cu alaplemezének domináns hőkapacitása). A 2 kisebb csúcs (inkább csak dudor) a szerelőlemezen levő Cu sziget hőkapacitása, míg a 3 csúcs a szerelőlemez hőkapacitása. Ezen pontok behatárolása után leolvashatjuk a rész-hőellenállásokat. Az 1 és 2 pont közötti kb. 0,6 K/W a tranzisztor felforrasztásának hőellenállása. A 2 és 3 pont között a szerelőlemez műanyag bevonatának hőellenállása van, jelenleg kb. 1,3 K/W. Végül a 3 és 4 pontok között a szerelőlemez és a cold plate között megvalósított hőellenállást olvashatjuk le.

Die attach delamination inside the package
Measurement of a power BJT mount: failure analysis Die attach delamination inside the package T3Ster: differential structure function Az 1 minimum C17-nél kb. 0,4 K/W értékkel jobbra tolódva jelenik meg, és a görbe egész további jobb oldali része nagyjából ugyanekkora eltolódást mutat. Ez egyértelműen azt mutatta, hogy a chip és a tok (1-el jelölt) Cu platformja között anomálisan nagy hőellenállás van, vagyis a chip nincs jól felforrasztva a tok belsejében, felvált a platformról! Ez az úgynevezett die attach hiba, ami megbízhatósági szempontból meglehetősen veszélyes.

Measurement of a power BJT mount: failure analysis
Imperfect soldering of the package T3Ster: differential structure function A 2 csúcs mindkét görbén beazonosítható, de C02 esetén tőle jobbra egy határozott minimumot látunk, és a következő platóig sokkal nagyobb (kb. 2,5-szörös) a hőellenállás, mint C08 esetén. Úgy tűnik tehát, hogy a szerelőlap műanyag bevonatának nőtt meg a hőellenállása. Magyarázatot kapunk erre, ha szemrevételezzük a tranzisztort. A felforrasztási hiba szemmel látható, az ón néhány apró cseppé futott össze. A cseppekbe szaladt forrasz miatt a műanyag valószínűleg nem vezeti a hőt teljes keresztmetszetében, hanem csak a cseppek alatt, így a hőellenállásnak ez az összetevője megnő.