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Thermal measurements and qualification using the transient method: principles and applications 1 Thermal measurements and qualification using the transient method Principles and applications The 21 st 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

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Thermal measurements and qualification using the transient method: principles and applications 2 MATHEMATICAL DESCRIPTION OF THERMAL SYSTEMES (distributed linear RC systems)

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Thermal measurements and qualification using the transient method: principles and applications 3 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

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Thermal measurements and qualification using the transient method: principles and applications 4 Introduction Theory of linear systems or shortly: = convolution If the T response to the P excitation is known: = deconvolution (to be calculated numerically) Response to any excitation: t W(t)W(t) weight function (Green’s function) W(t)W(t) t (t)(t) Dirac-delta (t)(t)

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Thermal measurements and qualification using the transient method: principles and applications 5 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 function t 1 h(t)h(t) t a(t)a(t) Theory of linear systems t W(t)W(t) weight function (Green’s function) W(t)W(t) t (t)(t) Dirac-delta (t)(t)

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Thermal measurements and qualification using the transient method: principles and applications 6 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 t a(t)a(t) t W(t)W(t)

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Thermal measurements and qualification using the transient method: principles and applications 7 Thermal transient testing h(t)h(t)a(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.

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Thermal measurements and qualification using the transient method: principles and applications 8 Step-response functions C R t R C1C1 R1R1 C2C2 R2R2 CnCn RnRn t 11 R1R1 22 R2R2 nn RnRn If we know the R i 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 R i magnitudes and i time-constants The form of the step-response function –for a single RC stage:

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Thermal measurements and qualification using the transient method: principles and applications 9 –for a distributed RC system: Step-response functions If we know the R( ) function, we know the distributed RC system. n n R()R() t 11 R1R1 22 R2R2 nn RnRn discrete set of R i and i values continuous R( spectrum characteristic: R( time-constant spectrum:

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Thermal measurements and qualification using the transient method: principles and applications 10 Discrete RC stages discrete set of R i and i values 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 R()R()

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Thermal measurements and qualification using the transient method: principles and applications 11 Practical problem The range of possible time-constant values in thermal systems spans over 5..6 decades of time –100 s..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?

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Thermal measurements and qualification using the transient method: principles and applications 12 Practical problem (cont.) Solution: equidistant sampling on logarithmic time scale Nothing can be seen below the 10s range a(t)a(t) t Measured unit-step response of an MCM shown in linear time- scale

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Thermal measurements and qualification using the transient method: principles and applications 13 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)a(z) z = ln(t) Measured unit-step response of an MCM shown in linear time- scale

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Thermal measurements and qualification using the transient method: principles and applications 14 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 *Sometimes P a(z) is called heating curve in the literature.

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Thermal measurements and qualification using the transient method: principles and applications 15 Note, that da(z)/dz is in a form of a convolution integral: Step-response in log. time Introducing the function: From a(z) R(z) is obtained as:

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Thermal measurements and qualification using the transient method: principles and applications 16 Extracting the time-constant spectrum in practice 1 Derivative of the thermal impedance curve Numerical deconvolution Measured thermal impedance curve Time-constant spectrum Numerical derivation

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Thermal measurements and qualification using the transient method: principles and applications 17 Must be noise free, must have high time resolution (e.g. 200 points/decade) 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) 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 Extracting the time-constant spectrum in practice 2

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Thermal measurements and qualification using the transient method: principles and applications 18 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

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Thermal measurements and qualification using the transient method: principles and applications 19 Break!

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Thermal measurements and qualification using the transient method: principles and applications 20 INTRODUCTION TO STRUCTURE FUNCTIONS

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Thermal measurements and qualification using the transient method: principles and applications 21 Example: Thermal transient measurements heating or cooling curves Network model of a thermal impedance: Normalized to 1W dissipation: thermal impedance curve Evaluation: Interpretation of the impedance model: STRUCTURE FUNCTIONS

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Thermal measurements and qualification using the transient method: principles and applications 22 How do we obtain them?

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Thermal measurements and qualification using the transient method: principles and applications 23 Structure functions 1 Discretization of R(z) RC network model in Foster canonic form (instead of spectrum lines, RC stages) R i =R( i ) i =exp(z i ) RiRi Ci=i/RiCi=i/Ri A discrete RC network model is extracted name of the method: NID - network identification by deconvolution

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Thermal measurements and qualification using the transient method: principles and applications 24 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:

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Thermal measurements and qualification using the transient method: principles and applications 25 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: Structure functions 3

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Thermal measurements and qualification using the transient method: principles and applications 26 ambient junction ambient Structure functions 4 The cumulative structure function is the map of the heat-conduction path:

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Thermal measurements and qualification using the transient method: principles and applications 27 Cumulative (integral) structure function differential structure function Calculate dC/dR: Structure functions 6 air

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Thermal measurements and qualification using the transient method: principles and applications 28 What do structure functions tell us and how?

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Thermal measurements and qualification using the transient method: principles and applications 29 A hypothetic example for the explanation of the concept of structure functions 1 An ideal homogeneous rod Ideal heat-sink at T amb t 1W P(t)P(t) 1D heat-flow R th_tot = L/(A· ) T(z)T(z) z = ln t

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Thermal measurements and qualification using the transient method: principles and applications 30 A hypothetic example for the explanation of the concept of structure functions 2 Ideal heat-sink at T amb An ideal homogeneous rod LL LL A V = A· L 1D heat-flow T amb C th = V·c v R th = L/(A· )

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Thermal measurements and qualification using the transient method: principles and applications 31 A hypothetic example for the explanation of the concept of structure functions 3 Ideal heat-sink at T amb An ideal homogeneous rod This is the network model of the thermal impedance of the rod Driving point Ambient

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Thermal measurements and qualification using the transient method: principles and applications 32 A hypothetic example for the explanation of the concept of structure functions 4 Let us assume L, A and material parameters such, that all element values in the model are 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 R th_tot The location of the singularity gives the total thermal resistance of the structure.

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Thermal measurements and qualification using the transient method: principles and applications 33 A hypothetic example for the explanation of the concept of structure functions 5 Let us assume L, A and material parameters such, that all element values in the model are 1! R th_tot It is also very easy to create the differential structure function for this case. Again, we obtain a straight line: y=1

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Thermal measurements and qualification using the transient method: principles and applications 34 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? double slope Cumulative structure function a peak Differential structure function 1 2

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Thermal measurements and qualification using the transient method: principles and applications 35 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…

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Thermal measurements and qualification using the transient method: principles and applications 36 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

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Thermal measurements and qualification using the transient method: principles and applications 37 A hypothetic example for the explanation of the concept of structure functions 9 What values can we read from the structure functions? Cumulative structure function Differential structure function C th1 C th2 C th3 C th1 C th2 C th3 Thermal capacitance values can be read R th1 R th2 R th3 R th1 R th2 R th3 Partial thermal resistance values can be read

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Thermal measurements and qualification using the transient method: principles and applications 38 A hypothetic example for the explanation of the concept of structure functions 10 What values can we read from the structure functions? Cumulative structure function Differential structure function V1V1 V2V2 V3V3 V 3 /c v1 If material is known, volume can be identified. If material is known, cross-sectional area can be identified. A1A1 A2A2 A1A1 K 2 = A 2 2 ·c v2 · 2 K 1 = A 2 1 ·c v1 · 1 If volume is known, volumetric thermal capacitance can be identified. If cross-sectional area is known, material parameters (c v · ) can be identified. V 2 /c v2 V 1 /c v1

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Thermal measurements and qualification using the transient method: principles and applications 39 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

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Thermal measurements and qualification using the transient method: principles and applications 40 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

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Thermal measurements and qualification using the transient method: principles and applications 41 In many cases a complex heat-flow path can be partitioned into essentially 1D heat-flow path sections connected in series: IDEAL HEAT-SINK Some conclusions regarding structure functions

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Thermal measurements and qualification using the transient method: principles and applications 42 IC package assuming pure 1D heat-flow Cold-plate Base Chip Die attach Junction Die attach: large R th /C th ratio Base: small R th /C th ratio Grease: large R th /C th ratio Cold-plate: infinite C th Junction: is always in the origin Cumulative structure function: t 1W P(t)P(t) T(z)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 R th /C th ratio

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Thermal measurements and qualification using the transient method: principles and applications 43 Base IC package assuming pure 1D heat-flow Differential structure function: Die attach Chip Cold-plate: infinite C th Junction Cumulative structure function: Die attach interface thermal resistance The heat-flow path can be well characterized e.g. by partial thermal resistance values The R thDA value is derived entirely from the junction temperature transient. No thermocouples are needed. Grease

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Thermal measurements and qualification using the transient method: principles and applications 44 Example of using structure functions: DA testing (cumulative structure functions) Cold-plate Base Chip Die attach Junction Grease Base Grease Die attach Chip Reference device with good DA Cold-plate Base Chip Die attach Junction 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:

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Thermal measurements and qualification using the transient method: principles and applications 45 Example of using structure functions: DA testing (differential structure functions) Cold-plate Base Chip Die attach Junction Grease Reference device with good DA Cold-plate Base Chip Die attach Junction Grease Unknown device with suspected DA voids Copy the reference structure function into this plot Base Die attach Chip Junction Grease Die attach Chip Junction Base Grease Shift of peak: Increased die attach thermal resistance indicates voids

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Thermal measurements and qualification using the transient method: principles and applications 46 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. Some conclusions regarding structure functions

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Thermal measurements and qualification using the transient method: principles and applications 47 C th2 C th1 R th1 R th2 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

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Thermal measurements and qualification using the transient method: principles and applications 48 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

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Thermal measurements and qualification using the transient method: principles and applications 49 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 Resolution of structure functions in practice is about 1% of the total R thja of the heat-flow path SPICE ln t a(t)a(t) NID

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Thermal measurements and qualification using the transient method: principles and applications 50 Plateaus correspond to a certain mass of material C th values can be read material volume dimensions volumetric thermal capacitance C th values can be read R th values can be read Peaks correspond to change in material corresponding R th values can be read material cross-sectional area cross-sectional area thermal conductivity Use of structure functions:

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Thermal measurements and qualification using the transient method: principles and applications 51 Use of structure functions: partial thermal resistances, interface resistance R thjc Origin = junction, singularity = ambient R thja and partial resistance values interface resistance values (difference between two peaks)

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Thermal measurements and qualification using the transient method: principles and applications 52 Some examples of using structure functions

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Thermal measurements and qualification using the transient method: principles and applications 53 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

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Thermal measurements and qualification using the transient method: principles and applications 54 The transient responses: Measurement of the package/heat-sink interface resistance T3Ster: record=demo11 Curves coincide: transient inside the package - no problem ?? STRUCTURE FUNCTIONS WILL HELP

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Thermal measurements and qualification using the transient method: principles and applications 55 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 Measurement of the package/heat-sink interface resistance

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Thermal measurements and qualification using the transient method: principles and applications 56 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 P powered and measured via the chip Cooling mount Al 2 O 3 beneath the chip Chip

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Thermal measurements and qualification using the transient method: principles and applications 57 Example: FEM model validation with structure functions Courtesy of D. Schweitzer (Infineon AG), J. Parry (Flomerics Ltd.) From MEASUREMENT From FLOTHERM simulation From ANSYS simulation

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Thermal measurements and qualification using the transient method: principles and applications 58 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).

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Thermal measurements and qualification using the transient method: principles and applications 59 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

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Thermal measurements and qualification using the transient method: principles and applications 60 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 R th measurement.

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Thermal measurements and qualification using the transient method: principles and applications 61 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.

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Thermal measurements and qualification using the transient method: principles and applications 62 PART 3 APPLICATION EXAMPLES Failure analysis/DA testing Study of stacked dies Power LED characterization R thjc measurements Compact modeling

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Thermal measurements and qualification using the transient method: principles and applications 63 TESTING OF DIE ATTACH QUALITY basics

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Thermal measurements and qualification using the transient method: principles and applications 64 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

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Thermal measurements and qualification using the transient method: principles and applications 65 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, 18 th Annual IEEE SEMI-THERM Symposium, March , San Jose, CA,USA, pp

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Thermal measurements and qualification using the transient method: principles and applications 66 Main time-constants of the experimental samples

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Thermal measurements and qualification using the transient method: principles and applications 67 Measured Z th curves of the average samples Already distinguishable

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Thermal measurements and qualification using the transient method: principles and applications 68 Differential structure functions of the experimental samples

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Thermal measurements and qualification using the transient method: principles and applications 69 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)

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Thermal measurements and qualification using the transient method: principles and applications 70 Cold-plate Base Chip Die attach Junction Grease Reference device with good DA Cold-plate Base Chip Die attach Junction Grease Unknown device with suspected DA voids Copy the reference structure function into this plot Base Die attach Chip Junction Grease Die attach Chip Junction Base Grease Shift of peak: Increased die attach thermal resistance indicates voids The principle again

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Thermal measurements and qualification using the transient method: principles and applications 71 TESTING OF DIE ATTACH and SOLDER QUALITY : case studies A power BJT mount Stacked die packages

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Thermal measurements and qualification using the transient method: principles and applications 72 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

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Thermal measurements and qualification using the transient method: principles and applications 73 T3Ster: differential structure function The “good” structure function R th =3.2 K/W Measurement of a power BJT mount: failure analysis

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Thermal measurements and qualification using the transient method: principles and applications 74 Die attach delamination inside the package T3Ster: differential structure function Measurement of a power BJT mount: failure analysis

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Thermal measurements and qualification using the transient method: principles and applications 75 Imperfect soldering of the package T3Ster: differential structure function Measurement of a power BJT mount: failure analysis

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