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Fundamentals of Thermal Resistance Measurement

Dr. John W. Sofia

1995

Analysis Tech

(781)245-7825

FAX (781)246-4548

email: [email protected]


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PART 1: Technical Background

1.1 Introduction

The Analysis Tech Thermal Analyzers are complete test systems for semiconductor

component thermal characterization. These systems offer extensive selections of testcapabilities accessed via user-friendly menus and forms. The range of applicationextends from laboratory research to production screening.

Part 1 deals with the scientific background of experimental methods and analysesrelated to the thermal characterization of packaged semiconductor devices, commonly

referred to as "components".

Thermal characterization of a semiconductor device (component) is the

determination of the temperature response of the semiconductor circuit junctionsdue to internal self-heating. This internal self-heating is a byproduct of electricalcurrent flow in the electronic device during operation; the heat generatedelevates the temperature in the semiconductor junctions. It conducts from the

junction area through the die, through the package, and eventually into the localambient. This flow of heat is governed by the laws of thermodynamics and theprinciples of heat transfer. Accordingly the temperature within the package is

the highest in the heat generating junctions on the semiconductor die. It is thistemperature elevation of the semiconductor junctions that drives the need forthermal characterization of packaged semiconductors since higher

semiconductor junction temperatures are associated with reduced operating life.

[Kraus, et. al., 1983]

Device heat generation is concentrated in a small region in the semiconductor die fromwhich it diffuses outward into the package where it becomes progressively less

concentrated. Stated another way, the heat flux density is greatest in the heat

generating region of the semiconductor. As the energy moves further and further from

the semiconductor, heat flux densities are lower and the temperature elevations aresmaller. This general pattern is a central theme in all component heat dissipation.

From the perspective of the entire electronics cooling network, the component is thecritical, initial link for all heat leaving the die. As such, the component exhibits heat flux

densities that are many orders of magnitude higher than in any other area of thecooling network. At the component level, minute differences in package design,material selection, and quality of manufacture can have enormous impacts on junctionoperating temperatures and time-to-failure. The technological trend toward

progressively increasing heat flux densities and the necessity to control junctiontemperatures creates the need for component characterization.


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The focal point of component thermal characterization is the control of junctiontemperatures. Since semiconductor reliability is adversely affected by higher junctionoperating temperatures, the determination of junction temperature is essential to

developing electronic systems free from thermally induced failures.

1.2 Thermal Resistance

The primary goal of thermal engineering in electronics-cooling is the reduction or

control of operating junction temperatures. The measurement of component thermal

resistance is a common approach to junction temperature determination given a set of

environmental conditions and the component power dissipation. Thermal resistanceprovides a simple and convenient means for estimating junction temperatures.

Thermal resistance is analogous to electrical resistance. Electrical resistance iscomputed as the difference in voltage between two points divided by the electrical

current flowing between them. This analogy is based on the fundamental similaritybetween voltage and temperature, current conduction and heat conduction: Electricalconduction occurs in response to a voltage difference; heat conduction occurs in

response to a temperature difference. This is a popular analogy due the generalfamiliarity of electric conduction in wires.

One shortcoming of the electrical analogy is that it suggests familiar networks such asone-dimensional current flow in wires between discrete components. The conduction

of heat in electronic components is rarely so simple since it is significantly three-dimensional with spatially distributed thermal resistances and heat capacitances. Thisdifference tends to make the electrical analogy lead to a one-dimensional interpretation

of an inherently three dimensional phenomena. The precise definition of thermalresistance is key to its correct measurement and application.

Thermal Resistance is defined as the difference in temperature between two

closed isothermal surfaces divided by the total heat flow between them. It

further requires that all of the heat which flows through one surface also flowsthrough the other and that no net thermal energy accumulation occurs in the

volume between the surfaces. It should be noted that these "surfaces" are notphysical, solid surfaces but rather imaginary surfaces of constant temperature.Defining Tj and Tx as the hot and cold isothermal surface temperatures,

respectively, and the total heat flow rate between them as P, the thermalresistance between them is

RT T

Pjx

j x=

(Equ. 1)


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The units of thermal resistance in electronic applications are C / Watt. If massflow occurs across these isothermal surfaces, there must be no net mass

accumulation within the volume enclosed between the two surfaces since thatwould comprise an accumulation of thermal energy in the form of mass heatcapacity. Likewise, there can also be no net thermal accumulation due to latent

heat that may result from phase change effects.

In addition to being surfaces of constant temperature, isothermal surfaces experience

heat flow in a perpendicular direction. Lines drawn parallel to the heat flow are called"heat-flux-lines". Each line is a heat flow (flux) path, each leading from the component

junction to the environment. Taken together, these lines form a map-like network ofpaths for heat flowing from the component. The heat flux network provides a means forillustrating and visualizing heat flow. Isothermal surfaces do not intersect but rather

form "nests" of concentric, closed volumes around a heat source. Isotherm nests andheat-flux-networks are directly related: a complete description of either one contains allthe information necessary to construct the other since heat conducts perpendicular to

isotherms and parallel to heat-flux-lines. A complete heat flux network describes indetail the three dimensional conduction of heat from a component's hot core to itsperipheral surfaces.

Isothermal surfaces are uniquely defined by size and shape. Thermal resistance isisotherm specific: changing the size or shape of the isothermal surfaces used in

Equation (1) will change the computed thermal resistance. Alternatively, thermalresistance is specific to the heat flux network; any alteration will change the thermalresistance.

To avoid confusion, it is important to distinguish the difference between thermal

resistance and thermal resistivity.

Thermal Resistivity is defined as the ratio of thermal gradient to the heat flux

density for a one-dimensional heat conduction. Thermal resistivity is thereciprocal of thermal conductivity and is a material property indicating the

resistance of the material to thermal conduction. Alternatively, resistivity is anindication of thermal insulative quality. To understand resistivity and itsmeasurement, envision two parallel isothermal surfaces, T1 and T2 separated

by a uniform layer of material of thickness with thickness x. If the heat flux perunit area is defined as q, the resistivity of the material separating the isothermal

surfaces is

r

T T

x

q=

(Equ. 2)


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For electronic cooling applications thermal resistivity is expressed in units ofCmeter / Watt. The reciprocal of resistivity, conductivity, is more commonly used

and indicated by the symbol "k".

Thermal resistivity is a material property and is not affected by the geometry of the

thermal flux network in which the material is used. By contrast, thermal resistance is afunction of material resistivities and geometry. Thermal resistivity is used for evaluatingthe thermal quality of a materials for use in component packaging applications.

Thermal resistance is a figure of merit for evaluation of the thermal transport capabilityof component packaging.

1.3 Electrical Junction Temperature Measurement

The measurement of junction temperatures is essential for evaluating thermal

performance for design, application and manufacture of semiconductor components.

The electrical method for junction temperature measurement is a widely used methodtoday. It is a direct, non-contact technique since it utilizes the junction itself as thetemperature sensor. Although methods such as infrared and liquid crystal sensing[Azar, 1991] can be used to measure junction temperatures, their application is limited

to junctions that are directly visible. In contrast, the electrical method is a directtechnique that can be performed at-a-distance without an introduced sensor using onlythe electrical-temperature properties of semiconductor junctions. It is used extensively

for direct component characterization measurements.

The electrical method is a popular technique for measuring junction temperatures in

electronic components spanning the entire power and function spectrum of the

electronics industry. The most common implementation of the method uses the forwardvoltage drop of a junction as the temperature sensitive parameter and is variously

known as the "diode-forward-drop" method or the "Vbe" technique from originalapplications with power diodes and bipolar power transistors. The method wasimplemented soon after the invention of semiconductor electronics and continues to be

used extensively used throughout the industry. In the integrated circuit industry, it isused to thermally characterize functional components as well as "dummy" thermal testcomponents made by substituting standard thermal test dice for functional dice.

Although the diode forward voltage is the most commonly used temperature sensitiveparameter (TSP), other parameters can also be used depending on the specific device

under test. An excellent reference on the electrical method is contained in reference[Oettinger, F.F., Blackburn, D.L., 1990].

The electrical method of junction temperature measurement is based on a temperatureand voltage dependency exhibited by all semiconductor diode junctions. Thisrelationship can be measured and used to compute the semiconductor junction

temperatures in response to power dissipation in the junction region.


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Voltage-temperature relationships are an intrinsic electro-thermal property of

semiconductor junctions. These relationships are characterized by a nearlylinear relationship between forward-biased voltage drop and junctiontemperature when a constant forward-biased current is applied. This constant

current is called the "sense current" (also "measurement current"). Figure 1illustrates the concept of measuring this voltage versus junction temperaturerelationship in for a diode junction; Figure 2 shows a graph of the resulting data.

The relationship can be expressed mathematically as in the calibratingrelationship,

T m V T j f= +(Equ. 3)

The slope, "m" (deg C/volt) and the temperature ordinate-intercept, "T0" areused to quantify this straight line relationship. The reciprocal of the slope is

often referred as the "K factor" expressed in units of mV/C. In this case, Vfisthe "temperature sensitive parameter" (TSP). The slope and intercept aredevice specific and are collectively referred to as the "calibration parameters".

Figure 1: Illustration of bath method for measurement of temperature sensitive

parameter


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Figure 2: Illustration of temperature sensitive parameter plot

Two other concepts that are central to the electrical are defined below.

Sense Junction is the junction through which the sense current passes. The

temperature sensitive parameter (TSP) and calibrating parameters are specificto the sense current and sense junction.

Device calibration is the procedure for determining the calibration parameters

of slope and temperature intercept. This voltage/temperature relationship mustbe individually measured for each distinct die and sense junction to be tested.

For semiconductor junctions, the temperature/voltage slope of the calibrating straightline is always negative, i.e., the forward conduction voltage decreases with increasing

junction temperature. The temperature intercept is always positive and is theoretically

the temperature at which the semiconductor junction forward-voltage becomes zero.Once the slope and intercept have been determined, the junction is calibrated for use

as a temperature sensor. The voltage generated in response to the applied sensecurrent can then be used to compute the junction temperature using the calibrating

relationship (Equ. 3).


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If a collection of identical parts were calibrated, and the calibration parameters werecompared, the temperature/voltage slopes would be quite consistent although theintercepts would generally exhibit a range of variation typical of the specific part

examined. When plotted as in Figure 3, the calibration lines would be parallel but withdifferent intercepts. This leads to a generally accepted and useful rule when using the

diode voltage TSP: device calibration must be performed for each new die type testedto establish the temperature/voltage slope. The temperature intercept can be computedfor identical parts which were not calibrated by using one measured voltage-temperature data point. This situation dramatically reduces the number of components

that must be calibrated.

Figure 3: Illustration of device calibrations from a group of "identical parts"

Some specific points should be mentioned in regard to the electrical method forjunction temperature measurement when utilizing the diode voltage TSP:

a) True junction diodes are sufficiently linear to use the above first order,

straight line equation for calibration (Equ. 3).

b) Shotkey diodes (which are really "half-diodes", see glossary) may require an

interpolation between sufficiently closely spaced points for a similar level of

accuracy (see item "d" below).


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c) Device calibration is current-specific; specific calibration parameters cannot

be used for other sense current values.

d) Device calibration data can be used in tabular form with linear interpolation

applied rather tan converted to calibration equations such as Equ. 3 and Equ.4.

The "transistor saturation voltage" is another temperature sensitive parameter (TSP)

that can be used for electrical junction temperature sensing. Its characteristics aresimilar to the diode forward voltage. For testing certain types of devices, the diodevoltage TSP cannot be used due to the absence of an electrically accessible diode.

Such parts include IGBTs and some darlington transistors. The transistor saturationvoltage is defined as the voltage across the main current terminals of a 3-terminaldevice in response to a fixed, small sense current while the control terminal is held fully

"on". The voltage versus temperature data fits the linear equation format (Equ. 3) used

for the diode-junction temperature sensing. The gate-turn-on voltage [Oettinger, F.F.,Blackburn, D.L., 1990] is another possible TSP for testing of IGBTs and MOSFETs.

Unlike other TSPs, this TSP requires junction calibration of each and every device tobe tested.

1.4 Device Calibration Technique

1.4.1 Performing Device Calibrations

Device calibration is the procedure of measuring data pairs of junction temperature

versus junction voltage due to the imposed sense current. These measurements areperformed under unpowered, thermal equilibrium conditions so that the junction and

case temperature are nearly equal. Once the electrical connections for the selectedtemperature sensitive junction have been completed, device calibration entails:

a) selection of the sense current levelb) establishment of thermal equilibrium between the component and a stable-

temperature environment

c) measurement of the component case (junction) temperature and temperaturesensitive voltage

d) alteration of the environment temperature and repeating steps b through d

During calibration, the device is unheated except for the heat generated by the sense

current which is generally insignificantly small. When the component is immersed inthe constant temperature environment, any point on the component case will eventuallyreach the same temperature as the component junction. Under these conditions, the

component is said to be in thermal equilibrium with its surrounding environment.


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Measurement of the forward voltage and the associated case temperature comprisesone data point for construction of the calibration relationship.

This procedure must be performed for at least two sufficiently spaced temperaturessince at least two points are required for a straight line calibrating relationship (Equ. 3).

Although two points are the minimum required, a far superior technique is performedusing 5-20 data pairs spaced in equal temperature increments. The calibrationparameters are then determined by a best-fit straight line using least-squares linearregression. Often, the only indication that a particular sense junction on an active die

is unsuitable for junction temperature sensing lies in the non-linearity of the calibration.Since any two points define a straight line, such non-linearity is totally masked whenusing the two-point calibration. The use of multiple temperature points for calibration

also provides a dramatic increase in the accuracy of the calibration in the same mannerthat sample averaging decreases the level of random error associated with a singlesample.

1.4.2 Sense Current Level Selection

The selection of the sense current is the first step for device calibration. The selectionof this current is limited by a number of factors although within a fairly wide range, theprecise selection is not critical. Generally, the best sense current is the smallest one

which does not encroach on any of the limiting factors discussed below. Once thesense current has been chosen and the device calibration performed, the calibrationparameters are specific to the junction and the sense current level. Sense current

selections typically range from 0.1 to 50 milliamps.

Lower limit - conduction: The sense current must be sufficiently large toestablish conduction in the body of the junction rather than just superficial

surface leakage conduction. Generally, 0.1 milliamp is the lower limit of theselection range for the smallest junctions tested. Typically, the larger the

junction, the higher this lower limit becomes.

Upper limit - thermal: Ideally, a sense current generates no internal heating in

the diode junction. In reality, diode current flows of any magnitude generatesome heating; therefore the ideal sense current is the one that generates the

smallest amount of self-heating. For example, if the sense current is 10

milliamps and the forward voltage is 0.6 volts, the power dissipation is 0.006Watts or 6 milliwatts. This apparently insignificantly small amount of heating is

focused exclusively on the sensed junction and causes some temperature rise.Ultimately this heating contributes to an error in the final computation of junctiontemperature. Based on this, two conclusions can be drawn:


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a) Given a particular junction, smaller sense currents generate less self-heating error.

b) Given a particular sense current, larger sense junctions experience

smaller the temperatures rises and thus less self-heating error.

Although self-heating errors are generally quite small, properly conducted testprocedures can further reduce this potential problem. (See "recalibration" in thefollowing section "Calibration Environments")

Lower Limit - electrical: All semiconductor junctions have parasitic electrical

capacitances in parallel connection with them. These capacitances cause thediode voltage readings to "lag" the temperature readings whenever voltage ortemperature changes occur during thermal testing. Although such changes are

quite slow during calibration, during thermal testing, the sense current mustcharge or discharge these capacitances as the junction temperature/voltagechanges. This charging/discharging utilizing a fixed current requires time in

proportion to the size of the parasitic capacitance. Larger sense currentsrequire less time since they offer faster charge/discharge rates. Generally,larger, more capacitive junctions will test better with larger sense currents. (See

Active Dice underDevice Types and Test Methods)

The most commonly used sense current throughout the industry is 1 milliamp. Mosttesting on integrated circuits, functional and thermal dice, is performed with a 1

milliamp sense current. Other common selections are 10 and 20 milliamps for largerpower devices.

1.4.3 Thermal Equilibrium in Calibration

As stated previously, unpowered, steady-state, thermal equilibrium of the component in

the calibration environment is required for convergence of the junction and casetemperatures. This necessitates a waiting period, the duration of which depends on:

a) the heat capacity of the componentb) the thermal resistance between the component junction and the environment

medium

The product of a resistance and a capacitance yields a time parameter, i.e., the "RC"time constant of the pair. The linear combination of a resistance "R" and a capacitance

"C" will reach 99.3% of final equilibrium in a duration equal to 5 times the "RC" timeconstant.

In practice, the heat capacity and thermal resistance are never known prior tocalibration. Therefore other less precise methods are used to estimate the onset of


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thermal equilibrium. Although the rate of change in the case temperature can be usedto estimate equilibrium, the waiting interval is usually extended to the point where thereis no doubt that equilibrium has been reached. Clearly, there is a significant benefit in

choosing a medium that offers a small thermal resistance to the component-under-calibration to minimize the waiting interval.

1.4.4 Calibration Environments

Two types of stable temperature environments are commonly used for device

calibration: liquid baths and ovens. The function of the device calibration environmentis to provide stable temperature surroundings which will quickly reach equilibrium withthe component, and to provide a convenient means of controlling that stable

temperature.

The bath liquid must be a dielectric (electrical insulator) and capable of withstanding

temperatures up to about 150 C without boiling. Flouro-chloro carbon liquids andcommon mineral oil are typical choices. The liquid must be circulated or stirred toenhance temperature uniformity and increase the liquid-to-component heat transfercoefficient. This allows the device to reach equilibrium with the liquid quickly. The bath

must have some means of temperature control and regulation. This control should belinear and free from cyclic variations. The component should be suspended in the bathand should not contact the bath walls or the liquid surface. The thermocouple used for

sensing the case temperature should be soldered to the component leads. This willensure maximum mechanical stability and accurate sensing of the junction temperature.

The oven technique may require the use of a significant heat sink to stabilize the rapid

fluctuations of air in the oven as the heating elements cycle on and off. Forcedconvection should be utilized on the heat sink and the component must be attached to

the heat sink with an excellent thermal bond. Again, the thermocouple used for sensingthe case temperature should be soldered to the component leads or otherwise wellgrounded to the internal bulk temperature of the component. Some ovens offer more

optimal controllers utilizing short-duration time-proportioning algorithms to minimize thecyclic variations inherent in the common banded-hysteresis "bang-bang" controller.These oven controllers offer significantly better conditions for calibration, so a smaller

device heat sink may be used.

The bath technique offers some advantages based on the following considerations.Since the chosen sense current will not cause significant self-heating, the ambient and

junction temperatures will become nearly equal after a sufficiently long thermal

"soaking" interval in the constant temperature environment. The length of this intervalis determined by the heat capacity of the component and the thermal resistancebetween the component and the environment, liquid or air. Since a circulated liquid

has an order of magnitude lower fluid-to-solid thermal resistance than oven-circulated


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air, the time required for the thermal "soaking-equilibrium" in the bath is less than one-tenth that of an oven for equivalent accuracy. The use of a heat sink in the oven cansomewhat reduce this difference. Alternatively, the bath method is somewhat more

messy and generally less suitable for non-hermetic packages. In summary, bothmethods will ultimately produce the same results if each offers a suitably constant

environment temperature and sufficient soaking time is allowed.

Once a device has been calibrated using the diode voltage TSP, calibration parametersfor identical parts are adjusted for part-to-part variations by using a single temperature-

voltage data point. This procedure is often referred as "recalibration". It makes use ofthe fact that identical parts calibrate with a uniform slope and only vary in thetemperature intercept (Equ. 3). Referring to Figure 4, the intercept can be computed by

simply allowing the component to reach unpowered steady state equilibrium at roomtemperature and then measuring the sense voltage and case temperature. This onedata point combined with the calibrated slope for an identical component permits the

corrected computation of the temperature intercept. Once a part has been calibrated,

recalibration on identical parts is usually a sufficient substitute for a full devicecalibration on every identical part tested. One point recalibration is effective for the

diode voltage TSP and transistor saturation voltage but not for the gate-turn-on TSP.

Figure 4: Illustration of one-point recalibration method


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When a device calibration is performed using the diode voltage TSP, the calibratingparameters apply to a specific junction on a specific die. The slope applies to all

identical junctions of the type calibrated; the temperature intercept only applies to theactual die calibrated but can be established with a one-point recalibration procedure.

When a previously calibrated die is mounted in different packages, the calibration neednot be repeated. Care should be taken to ensure that the correct electrical connectionsare bonded out for the chosen sense parameter each time the die is used in a differentpackage. If device calibrations are correctly performed, it does not matter in what

package a calibrated die is mounted; a given diode on a given die will have the samecalibration regardless of the package.

1.5 Application of Thermal Resistance Concepts

According to the definition, Equ. 2, thermal resistance is specific to the chosen

isothermal surfaces, specified by size and shape. Practically, it would be quite difficultto specify an isothermal surface that does not correspond to a physical surface bydescribing its particular size and shape. Even if such a description could be provided,

it would be nearly impossible to utilize such information in a real-world test situation.

The application of thermal resistance measurement to electronic component

applications requires a practical perspective in addition to an understanding of thebasic definition. Thermal resistance is generally based on junction temperature (hotterisotherm), with a variety of different forms spawned from the selection of the reference

temperature (colder isotherm). Thermal resistances are frequently cited as thermal

resistance, junction-to-,Rjx

, or

jx, where would be

substituted with such typical temperature sites as:a) local ambient air temperature

b) specific site on the component casec) specific site on a component leadd) other well defined reference site

It is instructive to compare the theoretical definition with the practical application ofthermal resistance. Each of the above varieties of thermal resistance implies a pair of

isothermal surfaces. The "junction" is considered to be tightly enclosed by an

infinitesimal, "hot", isothermal surface through which all of the internally generated heatis dissipated. Provided the same junction is used for all measurements of thermalresistance on a particular component, this "hot" isothermal surface is well defined andconstant.

The "cold" isothermal surface, the reference isothermal surface, is much moreproblematic. Each of the above reference temperature sites is a physically defined


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location without regard to the shape and size of the isothermal surfaces in theimmediate vicinity. Under any precisely defined set of cooling conditions, eachreference site corresponds to one point on a particular, vaguely specified, isothermal

surface. Under different component cooling conditions, heat flows from the componentin a different pattern of paths and forms different the isothermal surfaces. (Note:

isothermal surfaces are defined by size and shape) Since no practical method existsfor specifying the shape and size of these isothermal surface, the above thermalresistances, based on fixed reference sites, require complete specification of thecomponent cooling conditions. Expressed simply, any thermal resistance based on

physically fixed temperature sites is specific to the cooling conditions under which themeasurements are taken. Thermal resistances measured under significantly differentcooling conditions are simply different measured parameters.

Junction-to-local-ambient thermal resistance typically exhibits appreciable variationwith the velocity of the air flow on the component. Natural convection is influenced by

the orientation of the component and its power dissipation; forced convection is

affected by the local air pressure gradient. The isothermal surfaces in the vicinity ofthe component are specifically linked to the type of thermal resistance measured. For

example, the isothermal surfaces in natural convection cooling are dramaticallydifferent than those in forced convection. Therefore, junction-to-ambient thermalresistance measurements must include specifications of the air flow conditions.

Junction-to-case thermal resistances are likewise specific to the cooling conditions

implemented during measurement. The case temperature is usually measured at aspecific accessible site on the outside of the component case, most often, the hottestpoint on the case. The temperature difference between the junction and the case is

dramatically affected by variations in heat flux network for the junction. Factors such as

heat dissipation from adjacent components, nearby materials and thermal pathways,power level, air flow, and component mounting can radically affect the junction-to-case

thermal resistance. Components with a wide variety of cooling-condition alternativeswill likewise offer a wide variety of thermal resistances. Conversely, componentsdesigned for strictly defined cooling configurations with little variation in the overall heat

flow patterns will have few meaningful thermal resistance varieties.

Junction-to-case thermal resistances are often mistaken for fixed parameters that are

independent of the specific heat flow configuration. This stems from the misconceptionthat junction-to-case thermal resistance is solely a function of the component packageand does not depend on the cooling environment imposed when the thermal resistance

is measured. Despite plentiful evidence to the contrary, this erroneous attitude persiststoday.

Integrated circuits are a good example of components which typically experience awide variety of heat flow patterns. Some of the primary paths typically include:


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a) case directly into the board holding the componentb) case directly into the airc) case-to-leads and into board holding the component

Additional cooling parameters include adjacent component heating of the board and the

local air flow. Each set of cooling conditions prescribes a different, defined thermalresistance.

By contrast, some components with integral metal plates which are always cooled by

attachment to a significant heat sink have few primary heat flow paths and few coolingvariations. Component packages of the type TO220, TO202, and TO247 are goodexamples of this. These packages are specifically intended to be used with a

significant heat sink. Nearly all of the heat that leaves the junction exits the componentthrough the integral cooling plate regardless of the specific application. For thisreason, there are very few varieties of thermal resistances for these components.

In summary, thermal resistances must be reported with precise descriptions of thecooling conditions and the power dissipations that were used during the measurement.

This description should ideally be as simple as possible yet sufficiently accurate toenable detailed reconstruction of the test configuration.

1.5.1 Thermocouple Measurements

Thermocouples are generally used to measure thermal resistance reference

temperatures. Ideally, the reference temperature measurement should be non-invasive, i.e., report the same site-temperature as that which existed prior to the

installation of the thermocouple. This goal is never perfectly achieved sincethermocouples inherently involve contact measurement. Some heat conductioninvariably occurs in the thermocouple, thus wicking the heat away and cooling the

reference site. This error elevates the temperature difference between the referenceand the junction and yields a thermal resistance value which is chronically too high.This error is most acute when measuring case temperatures of components fabricated

of low thermal conductivity (high resistivity) packaging materials compared to theconductivity of the thermocouple wire. For example, if high conductivity 30 gaugethermocouple wire (type T) is used to measure a typical plastic integrated circuit case

temperature, the error can be as high as 40% of the difference between the ambientand the actual case temperature depending on the means of thermocouple attachment.

Although precise error predictions are not practical, the following recommendations

generally apply:

a) Wire thermocouples should be no larger than 30 gauge, preferably, 36

gauge.


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b) Type K offers the lowest wire-conductivity and thus the lowest conductionerror but requires additional adhesive attachment; type T offers solderable-attachment although with a higher level of conduction error.

c) The use of wire thermocouples should be limited to measurement of metaland highly conductive surfaces; use laminated thin-foil type thermocouples

for surfaces of low conductivity materials.d) Larger thermocouples are desirable for measurement of bulk air

temperatures where the averaging affect of the heat capacitance in the beadcan stabilize unwanted fluctuations.

e) Test systems utilizing temperature sensitive phosphor technology providethermocouple-like measurement with very low conductivity contact-fibers.

f) Infrared temperature sensors can be used effectively for the measurement of

non-conductive surface temperatures. These devices avoid the errorsassociated with thermocouple heat wicking effects.

1.5.2 Specific Thermal Resistance Measurement Methods

Standard environmental specifications for measurement of junction-to-case and

junction-to-ambient thermal resistances are available as Military Standards, SEMIPackaging Standards and JEDEC Industrial Standards. Such standards offer avaluable means of technical communication and documentation. When applying such

industry standard methods, critical examination must be exercised to independentlyevaluate the validity of the recommended methods. Some "standards" have been laterfound to be deeply flawed based on the underlying physical principles or tainted by the

effects of commercial bias in the standards creation process. There is no substitute fora critical investigation of any unfamiliar method regardless of how widely recognized or

standardized. Care should always be taken to ensure that the method employedgenerates data which is useful for the intended purpose.

The following example underscores the caution must be exercised before embracingany "standard" method. SEMI Standards, G30-88 and G43-87, discuss the use ofliquid bath environments for junction-to-case measurements. These specious methods

measure junction-to-case thermal resistance by suspending the component in anagitated fluid. According to the method, the high thermal conductivity of the fluidcombined with the agitation effectively creates infinite heat sinking conditions and

thereby assures that the entire surface of the case will be isothermal. Any cautiousimplementation of this method quickly reveals that the component is far from isothermaland that the fluid selection (within the range of specification) and degree of agitation

dramatically affect the resulting measurement. These methods do not sufficientlyspecify the essential liquid cooling parameters but rather rely on fictitious infinite heatsinking. Such bogus "standards" illustrate the hazards of assuming that a standard

method is technically sound.


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Another popular junction-to-case thermal resistance measurement standard is found inMil Std 883, method 1012 as well as SEMI Std G30-88. Here the integrated circuitcomponent is thermally grounded to a very significant heat sink so that almost all of the

heat flows directly into the heat sink. The case temperature is usually the surfacetemperature of the component that is in contact with the heat sink. The resulting

junction-to-case thermal resistance value is quite valid and repeatable since the heatflow patterns and cooling conditions are well specified. This variety of junction-to-casethermal resistance is directly applicable to components which are cooled in thismanner, i.e., by heat sink attachment in the same manner as the test configuration. But

for components which are not intended to be cooled in this way, this technique provideswildly elevated thermal resistances that are nearly useless for predicting the operating

junction temperatures in their intended applications.

Much of the latest standards work has been by JEDEC. JEDEC committees haverecently generated a number of new standardized methods for component thermal

characterization including JESD51-1 and JESD52-2. As these "standards" are new,

their technical merit, and overall quality has yet to be demonstrated. As with allunfamiliar methods, a cautious, skeptical application approach is warranted. These

standards are available from Global Engineering Documents, 800-854-7179.

1.6 Delivery of DC heating power

Test procedures for component characterization generally utilize steady state, DCcurrent to heat the semiconductor component. The reason for this is that thermal

resistance measurement requires steady-state thermal equilibrium which in turnrequires constant heat dissipation for a sufficient period of time. The heating power

dissipated in a component is computed as the product of the current flow through thecomponent times the voltage difference between the in-flowing and out-flowing currentleads. With the voltage expressed in volts and the current expressed in amps, the

product is expressed in Watts.

P I V Vin out =

(Equ 5)

For a thermal test die (see glossary), the heat dissipating element may be a pure

resistance. When dealing with a linear resistor, the voltage, current, and resistance

are governed by Ohm's law:

V I R=(Equ 6)

Current flow through any resistor generates heat. This is also true of the wires which

carry power to the device. Lead wires have a finite resistance and generate a voltage


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difference between any two points when current flows through them. This in turngenerates some internal heating of the wires; the magnitude of which is likewisecomputed as the current flow times the voltage difference. Although the heat

dissipation in the lead wires is usually a fraction of the heat dissipated in thecomponent under test, it should not be included as part of the heat dissipation in the

component when total power dissipation is computed for thermal resistancemeasurement. This error can be easily avoided by measuring the voltage differenceacross the component at the points where the current actually enters and leaves thedie. This method is called a "Kelvin connection" or a "four-wire connection".

Figure 5 illustrates the two-wire connection with its attendant power measurementerror. Figure 6 illustrates the four-wire connection. In the four-wire method, the leads

which serve to deliver the heating current are often called the "force" connections; theleads which serve to measure the voltage are called "sense" or "voltage sense"connections. In all cases of thermal characterization of components, the voltage

sensing leads and the current delivery leads should be joined at a site which is as close

to the actual die as possible to minimize the error in power computation due to lossesin the power delivery wires.

Figure 5: Illustration of 2 wire power measurement with attendant error


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Figure 6 Illustration of 4 wire power measurement

A four-wire connection measurement is sometimes used on the junction temperature

sensing connections. The concept here is that voltage difference across thetemperature sensing junction should not include the voltage drops across the wireswhich carry the sense current to the sense junction. Using Ohms law, if the total round-

trip resistance of the sense-junction lead-wires is Rl and the sense current is Is, thevoltage drop in the lead wires, Vs is

V R Is l s=(Equ 7)

The following is an example using typical-to-high range numbers:

lead wire resistance: .06 ohms per foot

lead wire length (round trip): 10 feetsense current: 10 milliamp

computed lead voltage drop = .006 volts

Although the case can be made that voltages of this magnitude are significant whenmeasuring junction temperatures electrically, the fact often overlooked is that the sensecurrent voltage drops in the leads are essentially constants that are simply nulled out

when the electrical method is properly implemented. The inconvenience of using four-wire connection for the sense junction voltage must be weighed against the minimalbenefits after considering these points:


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a) If a device is calibrated using sense current lead-lengths approximately thesame as those intended for thermal resistance testing, the sense voltagedrop in the leads is inherently included in the device calibration parameters.

b) If all thermally characterized devices utilize one-point recalibration to adjustfor variations in the temperature intercept within a collection of identical

components, variations in lead length between that used for devicecalibration versus device characterization will be nulled out.

c) The variation in lead electrical resistance with temperature is insignificant.

Based on the above, the four-wire technique is generally confined to connections forheating power delivery.

1.7 Control of Heating Power

The method used to control the heating power delivered to the component under test is

specific to the type of die being tested. For this consideration, components are dividedinto two categories: two-terminal and three-terminal devices.

The category of two-terminal devices includes diodes, thyristors (SCRs, TRIACs, etc.),and thermal test dice. These devices exhibit essentially one power dissipation for any

specified supply voltage orcurrent. The voltage and the current cannot be

independently selected. At any given power dissipation, these devices possess a

nearly fixed ratio between the applied voltage and the current flow, much like Ohmslaw. The ratio is "nearly" fixed since the voltage/current ratio varies somewhat as afunction of the die temperature. If a fixed heating current is established in a previously

unpowered two-terminal component, the power dissipation will progressively change

until a steady die temperature is reached. These variations can be generalized forspecific types of power control for specific device types:

Fixed Heating Current in Two Terminal Devices:

Thermal Test Die - Increasing temperature leads to increasing voltage

drop and thus increasing power dissipation with temperature.

Diodes and thyristors - Increasing temperature leads to decreasing

voltage drop and thus decreasing power dissipation with temperature

Fixed Heating Voltage in Two Terminal Devices:

Thermal Test Die - Increasing temperature leads to decreasing current

flow and thus decreasing power dissipation with temperature.

Diodes and thyristors - Increasing temperature leads to increasing

current flow and thus increasing power dissipation with temperature.


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In summary, as die temperatures increase, thermal dice experience highervoltage/current ratios while diodes and thyristors experience lower ratios. These

voltage/current ratio variations typically range from 10% to 50% for a 100 C change indie temperature. The power dissipation will thus vary by a comparable amount over the

course of a test when using either fixed-voltage or fixed-current power control. Whenthermally characterizing two-terminal devices, the power dissipation cannot becontrolled to a specified level using a fixed heating voltage or heating current. Although

application of a fixed voltage or current will eventually result in constant powerdissipation and establishment of thermal equilibrium, the final value of the heating

power will not be controlled to a pre-selected level. The Thermal Analyzer powercontrol options can be used to establish a controlled constant wattage without junctiontemperature dependency.

The category of three-terminal devices includes bipolar transistors, MOSFETs, junctionFETs, and IGBTs. The functional design of these devices permits the heating voltage

and current to be simultaneously specified independently. Each of these devices hasone pair of terminals which essentially carry all of the power and a third terminal whichacts to control the operating voltage/current ratio device. By design, these devicespermit a small voltage or current to control much larger voltages and currents, and

essentially control the voltage/current operating point of the device. This amplifiedcontrol behavior of three-terminal devices also exhibits significant temperaturedependency in much the same manner as two-terminal devices. Despite this, the

capability to select the heating voltage and current independently is a powerful assetwhen thermally characterizing three-terminal devices. Again, the Thermal Analyzerpower control capabilities eliminate these temperature dependencies of power control.

1.8 Device Types and Test Methods

This section covers the application of the electrical test method to a variety offunctional device categories. These categories are determined by the electrical designof the die utilized in the specific component under test.

1.8.1 Thermal Test Die

Thermal test dice are specifically designed for thermal characterization of integratedcircuit packages. These dice are available in a variety of sizes and can be mountedinto any desired package to create a thermal test vehicle. They have become popular

for package characterizations including related thermal enhancements. Thermal dicehave been designed to offer electrically independent power dissipation and electricalmeasurement of junction temperature. The thermal die test method is illustrated

schematically in Figure 7. Thermal dice offer accurate thermal characterization with a


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minimum of measurement hardware. The basic concepts of device calibration, junctiontemperature measurement, power delivery, and wattage control are direct application ofthe concepts presented previously. The sense diode voltage can be directly measured

with a voltmeter and the associated junction temperature computed (Equ. 3) usingpredetermined calibrating parameters. The Thermal Analyzer provides comprehensive

test capabilities for thermal dies.

Figure 7: Illustration of thermal test die test method concept

Care must be taken to ensure that the thermal test die size corresponds the intendedfunctional die application. The die attachment may also be different for the thermal die

versus the active die since one is a prototype process and the other a production

process. Any component characterizations utilizing thermal test dice should include aspecification of the thermal test die size and the type of die attachment.

1.8.2 Active Dice

Active or functional dice are often used as the ultimate test for component thermalcharacterization. The primary feature that distinguishes active die from thermal die isthat heat dissipation is not electrically independent from temperature sensing and that

the die is designed to perform an electrical function other than providing convenientjunction temperature reporting. This requires that the otherwise continuous heating

power be interrupted for the measurement of the junction temperature. The process ofperiodically interrupting the heating power to measure the sense junction voltage isbest presented with some standard definitions. This process is automatically

performed by the Thermal Analyzer.

Temperature sampling interval is the period of time when the heating power

has been interrupted and the sense current has been applied to the sensed


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junction. The temperature sensitive voltage is measured during this interval.During the temperature sampling interval, the junction cools passively until theheating power is restored. When properly executed, the cooling is minimal and

can be further reduced to negligible levels with rapid data acquisition. Onetemperature sampling interval is required for each junction temperature reading.

The temperature sampling interval is very small compared to the heating interval(less than 0.01%).

Heating Interval is the period of time when the heating power is being delivered

to the component under test. Active dice are tested with a succession of heating

intervals and temperature sampling intervals. During thermal resistance testing,the heating intervals are much longer than the temperature sampling intervals;the heating duty-cycle approaches 100% and thereby essentially satisfies

requirement of steady, fixed heat dissipation for thermal resistancemeasurement.

The end of the heating interval corresponds with the beginning of the temperaturesampling interval and visa versa. Although the objective of the temperature samplinginterval is to measure the junction temperature at the instant the heating interval ends,

some junction cooling does occur during the temperature sampling interval. Threeapproaches are used to minimize the impact of junction cooling from the instant ofpower interruption until the temperature sensitive voltage has been acquired:

a) minimize the duration of the temperature sampling interval to minimizejunction cooling

b) perform rapid sampling of the temperature sensitive voltagec) extrapolate back to the instant of power interruption to overcome the effects

of junction cooling and electrical switching transients

These techniques will be discussed below with additional details on the temperature

sampling process. Junction temperature measurement on active dice is a uniqueprocedure with special requirements which include:

a) rapidly switching the heating power offb) switching the sense current onc) measuring the temperature sensitive parameter

d) switching the heating power back on again

Unlike thermal die testing, special purpose electrical switching hardware is required to

perform this operation such as that contained within the Analysis Tech ThermalAnalyzer. In addition, there is a wide variety of specific requirements for temperaturesensing and power control to match the diversity of active dice. Commercially available

test systems offer such specialized test functionality with convenient software


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interfaces for testing all types of semiconductor components, active as well as thermaldice.

Heating Power

Time

Figure 8: Graphic illustration of the heating and measurement intervals

The test procedure for testing a rectifier diode provides an excellent example of somecommon issues associated with application of the electrical method to active die

testing. Figure 9 schematically illustrates the electrical test method for a rectifier diode.Here the diode serves as both the heat dissipator as well as the temperature sensor.

During the heating interval, the diode is powered with a controlled heating current.Since diodes have a very small voltage/current ratio when operating in heavy forwardconduction mode, control of the power dissipation via current control is far less

"delicate" than a comparable voltage control. In addition, diode power dissipation viacurrent control is inherently stable whereas the counterpart via voltage control is not.This is because of the change in diode power dissipation as a function of junction

temperature. As previously stated, diode power dissipation decreases with increasingjunction temperature under fixed current heating whereas dissipation increases withtemperature under fixed voltage control. Thus voltage control has a tendency toward

"thermal runaway" where the diode temperature spirals higher and higher, positivelyreinforcing with higher and higher wattage.

Heating Interval

Measurement Interval


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Figure 9: Illustration of diode test method concept

The junction temperature measurement interval is of critical importance when makingthermal measurements on active dice. When the heating interval ends, the heatingpower is abruptly terminated and the sense current is applied. Ideally, this process

would occur instantaneously in zero time. In reality there are a number of factors whichcause deviation from this ideal. First, the switching process tends to stimulateelectrical transients which vary in magnitude depending on the device tested. The

most common electrical transient is caused by the parasitic electrical capacitance that

exists across any junction. Figure 10 illustrates this situation for the case of therectifier diode. In this case this capacitance must be electrically discharged from the

higher voltage (apparent lower temperature) associated with the passage of the heatingcurrent to the lower voltage associated with sense current. During this recharginginterval, the electrical transients dominate the sense junction voltage samples and

which thus project inaccurate junction temperatures. Although the electronic switchingcircuits within the Thermal Analyzer reduce the duration of the electrical transients,

ultimately, temperature-dependent diode sense voltages can only be measured afterthe switching transients have died out. This waiting interval is often called the"measurement delay interval".


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Figure 10: Typical electrical transient for rectifier diode

Measurement delay interval is the initial portion of temperature samplinginterval between the instant of heating power interruption and acquisition of thefirst valid, temperature dependent voltage reading. This interval always beginsat the instant of power interruption and lasts until the electrical switching

transients have subsided. The typically range is from 0 to 500 microsecondsand tends to be higher for larger junctions. It is specific to the functionalcategory of the active die as well as the part type designation. The

determination of the correct measurement delay interval is quite critical: If tooshort, the junction temperature will be spurious; if too long, excessive junctioncooling will occur. In addition, the correct measurement delay interval is often

junction temperature sensitive. The determination of the correct interval is

discussed below.

Review of the event sequence for the active-die test method:

a) The heating power is interrupted at the end of the heating interval.b) The electrical transients are "waited out" during the measurement delay

interval.


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c) Sampling of the temperature sensitive voltage is performed for the remainderof the temperature sampling interval.

d) Heating power is resumed at the end of the temperature sampling interval.

The recommended approach for acquiring the desired junction temperature at the

instant of heating power interruption utilizes repetitive sampling for the remainingduration of the temperature sampling interval. [Oettinger, F.F., Blackburn, D.L., 1990]Typical sampling rates range from 50 to 200 kilohertz (5 to 20 microsecond samplingperiod) for 10 to 30 samples. The Analysis Tech Thermal Analyzers utilize up to 10

kilohertz reading rates at 25 or more samples. The temperature sensitive voltages arethen converted into junction temperature readings (Equ 3). Since the junction coolsduring the temperature sampling interval, extrapolation should be utilized to determine

the junction temperature at the instant of power interruption. This extrapolationbecomes critical for longer measurement delay intervals. The process of extrapolationalso improves sample accuracy since the random noise present in the sense voltage

readings will be averaged-out.

The extrapolation can use normal linear methods or a linear extrapolation using a

square root transformation of time [Oettinger, F.F., Blackburn, D.L., 1990]. TheAnalysis Tech Thermal Analyzers utilizes sampling both before and after the end of themeasurement delay interval for optimal perspective on the transient electrical activity.

Figures 10, 11, and 12 illustrate some typical sampling intervals with a variety ofelectrical transients. It is seldom difficult to recognize transient-corrupted temperature

data when examining samples spanning the entirety of a sufficiently long temperaturesampling interval.


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Figure 11: Electrical transient from MOSFET

Figure 12: No electrical transient exhibited from signal diode


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1.9 Standard Test Methods

Standard methods have been developed for applying the electrical method of junction

temperature measurement to a variety of different functional device categories, i.e.,bipolar transistor, rectifier, and MOSFET. A resource for these methods is MIL STD750C, 3100 series methods.

Devices can be divided into two categories for thermal testing: two-terminal and three-

terminal. The issues and differences in powering these two device types have alreadybeen covered in the section on Delivery of Heating Power. The junction-temperaturesensing is somewhat specific to the functional device type. Table #1 provides an

overview of the temperature sensitive parameters used for various device types. Adetailed description of these methods are available in the MIL Std 750C, 3100 seriesmethods.

Device Family Temperature Sensitive Parameter

diode, rectifier, SCR, TRIAC diode V

integrated circuit, thermal test die die sensing diode V

integrated circuit, functional die substrate isolation diode sensed and

powered or

sense diode voltage and functionalpowering

bipolar transistor, NPN base-to-emitter or base-to-collector diode V

bipolar transistor, PNP emitter-to-base or collector-to-base diode V

MOSFET (N channel) source-to-drain diode V or gate turn-on V

MOSFET (P channel) drain-to-source diode V or gate turn-on V

darlington transistor base-to-emitter diode or

saturation VIGBT saturation V or

gate turn-on V

Table #1: Temperature Sensitive Parameter Listing for Various Device Types


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1.9.1 Integrated Circuits

Integrated circuit components can be thermally characterized using a functional die orby substituting a thermal test die. Active die testing can be quite simple despite thepotentially complex functionality and high lead counts that integrated circuits may

present. The simplest technique utilizes the substrate isolation diode that is present onmost (although not all) integrated circuit dice. The substrate isolation diode iselectrically accessed by reverse biasing the power and ground pins and can be used

as both the heat dissipator and sense junction. This technique is the same as theprocedure for testing rectifier diodes. The die heating is not concentrated but rather is

quite uniform much like that of the thermal test die. The advantage of using substrateisolation diode testing on active dice is that the die size and die attachment is identicalto the final production components. This is often not true when a thermal test die is

substituted for the active die. A difference in either die size or attachment can cause adiscrepancy between component characterization data with the thermal test die versusthat with an active die. The disadvantage of using the substrate isolation diode method

or the thermal test die method is that the heat dissipation pattern on the die can bequite different from that which exists during functional operation of the integratedcircuit. This difference can yield higher junction temperature in actual operation of

functional dies than that predicted by thermal testing.

1.10 Component Thermal Impedance

This section deals with the topic of transient, non-equilibrium, component

characterization. Consideration of transient effects is required in applications where

the component never reaches steady state during the course of operation. Forexample, the components in some small on-board missile applications experience no

more than 100 seconds of intended operation. Characterization of components atsteady state is not useful for such situations.

Characterization of component transient behavior can also reveal aspects of internaldevice construction. It can be used to perform non-destructive testing for dieattachment quality and to delineate the effective thermal performance of component

construction details.

Further, transient component characterization can be used to predict the performanceof components in response to non-steady, irregular, or cyclic heating waveforms.


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1.10.1 Transient and Steady State

When a component is unpowered and at thermal equilibrium with the ambientenvironment, its temperature is uniform throughout. When a constant level of power isabruptly applied to the component and held constant for long period of time, the

component temperature undergoes a transition from an initially unpowered equilibriumcondition to a new, final powered steady state equilibrium condition.

Steady state thermal equilibrium is the condition where the previous

temperature of the component no longer influences the present temperaturedisposition of the component. At thermal equilibrium, the only variables thatcontrol the temperature of the component are the fixed power dissipation and the

thermal environment; when both of these are constant for a sufficient period oftime, the part approaches thermal equilibrium. Prior to equilibrium, thecomponent is considered to be in thermal transition or a transient thermal state.

At thermal equilibrium, time becomes an irrelevant parameter. Once equilibrium

has been reached, the duration of previous heating is not needed to predict thetemperature of the component.

During a transient thermal condition, the temperatures within the component package

are changing toward a new thermal equilibrium. Thermal resistance can only bemeasured at equilibrium conditions. The physical reason for this is the existence ofthermal mass or heat capacitance that is present in all matter. These capacitances are

distributed throughout the body of a component and must be thermally "charged" todifferent temperatures when a component makes a thermal transition from oneequilibrium condition to another. This thermal "charging" via heat flow requires time.

The definition of thermal resistance requires the same total heat flow across both of the

two isothermal surfaces. This can only occur when all of the heat capacitancesbetween the two isothermal surfaces have stopped changing temperature and have

reached equilibrium. The greater the heat capacity of the package contained betweenthe isothermal surfaces, the longer the transient period until the onset of thermalequilibrium.

Prior to thermal equilibrium, the attempted computation of thermal resistance yieldsthermal impedance.

Thermal impedance is defined as the difference in temperature between two

isothermal surfaces divided by the heat flow entering the hotter of the twosurfaces. Thermal impedance at thermal equilibrium is synonymous with thermal

resistance. Thermal impedance must specify the powering condition andduration whereas thermal resistance is only defined at thermal equilibrium.These "surfaces" are not physical, solid surfaces but rather imaginary surfaces

of constant temperature. Defining Tj and Tx as the hot and cold isothermalsurface temperatures respectively and the total heat flow rate entering the


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isothermal surface at temperature Tj as P, the thermal impedance between thesesurfaces is

ZT T

Pjx

j x=

(Equ 8)

The units of thermal impedance are C / Watt.

Thermal impedance is simply thermal resistance without the condition of equal heat fluxacross both isotherms. This inequality occurs when heat capacitances between theisothermal surfaces are storing heat energy prior to thermal equilibrium.

The thermal impedance concept is analogous to electrical impedance. Electrical

impedances include resistances and reactances, i.e., capacitors and inductances.Reactances only manifest themselves during periods of transition. Once electricalsteady state has been reached, only the presence of resistance is apparent. This

situation is precisely analogous to thermal impedances although electrical inductors

have no thermal analog.

As an example to illustrate the difference between thermal resistance and thermalimpedance, consider a device that is in unpowered thermal equilibrium with the ambient

air at 25 C. Beginning at a time defined as "time = 0", a constant power of 3 Watts isinitiated.

After 5 seconds, the temperature of the part is measured at 35 C. and power continues

to be applied for a total of 3000 seconds. The junction-to-ambient thermal impedancefor this part would be computed and stated as:

Power Duration,

t (sec) Power (watts) T (C) Tamb (C)

Z a @ t

(C/watt)

5 3 35 25 3.33

15 3 49 25 8.00

30 3 55 25 10.00

1000 3 60 25 11.66

2000 3 61 25 12.00

3000 3 61 25 12.00

Table 2: Example data for definition of thermal impedance and resistance

and

Rja = 12.00 C/Watt (@ equilibrium)


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Clearly, by the time the component has been powered for 2000 seconds, it has reachedsteady state and therefore the impedance at 2000 seconds is actually the thermalresistance of the component. In summary for any given power level, selected

temperature references, and cooling environment, a component can have an unlimitednumber of thermal impedances but can have only one thermal resistance for any set of

selected isothermal surfaces.

Figure 13 illustrates component junction-to-ambient thermal impedance versus heatingduration after a step change in power dissipation. Theoretically, equilibrium requires

an infinite heating duration, although for all practical purposes, equilibrium begins after5 or 6 times the longest thermal time constant of the system enclosed between the twoisothermal surfaces. Collectively, the thermal impedance data taken during transient

response to a step-change in power is often called "heat characterization" or "heatingcurve," since a plot of the data plot details the heating of the device.

Figure 13: Example of linear-time heating characterization plot


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Heating Characterization is the complete response of a component to a step-

heating condition. It defines the relationship of thermal impedance to heating

duration and contains a complete signature of the thermal behavior of the deviceranging from transient to steady state. When properly analyzed, the data can beused to predict the operation of the device under any set of operating power

conditions.

Heating characterization also provides valuable insights into the cross sectional

disposition of thermal resistances and capacitances within the component. Insummary, the transient thermal data contained in a heating characterization can offer a

wealth of insight into the thermal performance of a component. (See following paper onSynthetic Models in Heating Characterization.) Figure13 presents a heatingcharacterization plot of impedance versus heating duration in response to a heating

power step. The X-axis is a linear time axis where zero is the instant of step-initiationand the Y-axis is the component impedance. The longest duration of this heatingcharacterization is 1000 seconds. A very large portion of this plot presents equilibrium

data. Figure 14 presents the same heating characterization data plotted using a log-time. When plotted in this manner, the curve

Figure 14: Example of log-time heating characterization


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exhibits plateaus or ripples which are associated with the internal thermal capacitances

and resistances of the package. The bulk of the log-time plot presents non-equilibriumdata. This example illustrates a useful fact regarding the selection of time axes for

plotting heating characterization data. The linear time axis provides a much betterpresentation of equilibrium data; the log time axis presents a more detailedpresentation of the short duration, transient, non-equilibrium thermal data. Sinceheating characterization focuses on the transient data, the log-time plot is universally

accepted for heating curves.

Figures15 and 16 each present a comparison of two heating curves. Figure 15

contains the heating characterization for two plastic packages, one with an internalheat spreader pad and one without the spreader. Comparing the data starting from theshortest duration, the curves progressively diverge as the duration increases. After

about 4 seconds, the curves track parallel to each other at a fixed impedance

difference. This is indicative of a thermal difference quite close to the die.

Figure 15: Heating curve comparison for two plastic packages


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Figure 16 presents a comparison of heating curves for the same part in natural andforced convection. Here the curves coincide up to about 10 seconds duration and then

begin to diverge. This is indicative of a thermal difference which is quite far from thedie.

Figure 16: Heating curve comparison for a device in natural and forced

convection

Examination of the overall heating characterization profile of a component indicateswhere the most significant thermal resistances lie with respect to the die. Components

with heating curves which rise sharply for short durations have most of their internal

thermal resistance close to the die; such a component would benefit most from thermalimprovements which are close the die, i.e., the die attachment. Alternatively,

components which have heating curves that rise sharply for long durations can benefitmost by thermal enhancements to the heat transfer at the outer surface of the package,i.e., increased air flow or heat sinking. In this manner, interpretation of heating

characterizations can provide an excellent source of direction for thermal performanceenhancement efforts.


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1.11 Heating Characterization Measurements

Conceptually, heating characterization begins with a component in an unpowered

equilibrium condition. Ideally, the power-step begins when the component heating-power is instantaneously elevated to the specified level and then held constant for theduration required to ensure complete thermal equilibrium. The junction - reference

temperature difference climbs steadily from its initial value to the final equilibrium valueas the heating-step progresses. During this heating power step, the temperature of the

junction-to-reference temperature difference is measured continuously. Thecomponent impedance is computed as the instantaneous difference between the

junction and the reference temperature divided by the power level. For a number of

practical reasons, the implementation of the heating characterization divergessignificantly from this basic concept.

In the single-step heating characterization, the junction temperature rises are quitesmall shortly after the commencement of the heating step. As the heating progresses,the temperatures differences increase and eventually reach a maximum at equilibrium.

Since the fundamental errors associated with the measurement of junction temperature

rises are not tolerance ratios but rather a fixed error level expressed in C,measurement errors will tend to overwhelm the small temperature rise data early in theheating pulse. As the heating progresses and temperatures rise, the relative

significance of these fixed errors will subside to manageable levels. Thus, the singlestep response heating characterization will suffer from massive errors for the shortduration impedances and minimal errors for long duration impedances and thermal

resistance. One solution is to use a higher heating power level throughout the step.

This marginally improves the measurement errors and would be restricted by themaximum power and junction temperature limits of the component. The fundamental

problem with the idealized, fixed power, single step heating response is that theheating power is limited to the steady state DC power limit.

Another problem with the ideal heating characterization concept is that only thermaldice can be continuously powered while simultaneously being measured for junctiontemperature. All active non-thermal dice require fixed duration interruption in the

heating power for the measurement of the junction temperature. For short durationimpedances, these power interruptions comprise a significant "duty cycle" factor and an

unacceptable deviation from the requirement of continuous heating at a fixed level. Asthe heating duration progresses, the off-power intervals become insignificant as aproportion of the heating duration.

For these reasons, heating characterization for components with active, non-thermaldice is performed using a sequence of single pulses which are successively delivered

at reduced power levels as the pulse duration increases. After each pulse, the


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component impedance can be computed for that particular heating duration as thetemperature difference rise at the end of the pulse divided by the pulse power level.The heating curve is then composed by collecting the impedances, one from each

pulse. After each pulse, the component must be allowed to passively cool to nearly itsoriginal unpowered equilibrium state. When the pulse wattages are chosen to generate

a uniform temperature rise for all heating durations, the impedance measurementsexhibit a uniform accuracy throughout the heating characterization. In the interest ofreducing the total time required for a heating characterization, longer heating durationscan be performed in the idealized, fixed-power level approach. When performing

heating characterization with a respect a reference temperature which is assumed to befixed, i.e., ambient air temperature, care should be taken to ensure that the referencetemperature does not inadvertently "drift" during the heating characterization. Such a

"drift" would generate systemic errors in the resultant data. Alternatively the referencetemperature can be monitored with a thermocouple to eliminate such errors.

1.11.1 Interpreting Heating Characterizations

The heating step-response curve of Figure 14 illustrates typical characteristics worth

noting. The variations in slope with shallow "plateaus" are a common, although notuniversal, manifestation. Each ripple in the heating step-response indicates anequilibrium condition in the distributed network of thermal resistances and capacitances

at a particular depth of the component with respect the outer portions of the package.The final plateau is reached when all of the intermediate levels of the componentpackage are near thermal equilibrium on the extreme right of the plot. Recalling that an

exponential function exceeds 95% of its final value after 3 exponential time constantshave elapsed, each of the points of inflection correspond to approximately three-times

one of the inherent internal thermal time constants of the component packagingconfiguration.

The heating characterization represents a type of cross sectional view of the internalthermal resistances and capacitances of a component as depicted. To appreciate thisfact, it is helpful to envision the flow of heat in the component beginning at the instant

that the power-step commences: As heat spreads through the die, it begins to enterthe die attachment region. The small heat capacitance of the die region and the highheat flux density present causes a significant increase in the die temperature with only

a small accumulation of heat energy. Thus initial temperature rises are almost entirelygoverned by thermal spreading in the die region; the short duration impedances areoverwhelmingly representative of the heat flux network in the die region. The mass of

the component package, with its larger heat capacitance, responds after further heatingand sufficient energy accumulates to alter its temperature. The larger the heatcapacitance associated with a thermal resistance, the longer the heating duration

before its influence will be manifested. Thus heating curve data plots depict thedisposition of internal thermal resistances as a function of distance from the die -


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effectively a thermal resistance cross section of the component [Sofia, J.W.,1995, D.L.Blackburn, 1975, D.L. Blackburn, F.F. Oettinger, 1974, C. Neugebauer, [et al.], 1986].

1.11.2 Impedance Testing

As the duration of heating characterization continues, the component approachesequilibrium as the measured impedances approach the steady state thermal resistance.

At equilibrium, the thermal resistance embodies all of the distributed, constituentthermal resistances elements between the two designated reference temperature sites.

For heating durations less than that required for thermal equilibrium, those thermalresistances are partially reflected in the associated impedances as a function of theheating duration: The longer the heating duration, the greater the proportion of the

thermal resistances between the reference sites that will be included in the associatedthermal impedance. Based on this, pre-equilibrium heating durations can be chosen toselectively exclude the outer portions of a component. Essentially, an impedance

measurement can be "tuned" to probe a particular internal component interface byselecting the correct heating duration. Such tests are specific and highly sensitive tothe thermal performance of the component package-depth of interest.

One of the most popular applications of "tuned" impedance measurement is the dieattachment test. [F.F. Oettinger, R.L. Gladhill, 1973] This test is also referred to as the

"power pulse" test. The objective is to evaluate the thermal resistance of themechanical/thermal bond between the die-attachment and the package. Since most ofthe heat dissipated from a die is first conducted through the die-attachment, evaluation

of the thermal integrity of the die-attachment is crucial to ensuring good thermalperformance. If the die-attachment is incomplete or defective and thus offers a poor

heat-conduction path from the chip to the chip-package, the packaged semiconductordevice will operate with higher junction temperatures and thus have a shortened lifeexpectancy.

The die attachment test does not approach thermal equilibrium but is a totally transient,non-equilibrium test. Typical heating durations range from 10 to 200 milliseconds. The

test begins by heating the component with a short, precisely controlled pulse causingrapid heating of the die without substantially heating the package into which it ismounted. At the end of the heating pulse the chip temperature rise is determined and

the impedance computed. When the pulse duration has been correctly chosen, theimpedance measured reflects the thermal resistance of the package from the dieoutward to slightly beyond the die attachment. The local ambient is used as the implicit

reference temperature although, since this temperature does not change during the testand the device is assumed to be at unpowered thermal equilibrium prior to the test, theimpedance is simply the difference in junction temperature before and after the power

pulse. The peak junction temperature rise above the starting temperature is stronglycontrolled by the thermal resistance of the die attachment. Voids or defects in the


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attachment will result in reduced thermal conduction and higher chip temperatures.The short duration of the power pulse required for die attachment testing is ideallysuited to screening production lots of devices for acceptable thermal die-attachment.

It should be noted that the pulse power in die-attachment tests is often significantly

higher than the steady state, DC power level limit. Such augmented power levels offersignificantly higher temperature rises than the DC limit and thereby improves themeasurement accuracy of the test.

In a similar manner, longer heating duration pulses can be used to test internalcomponent-interface layers. The testing of header attachments is a good example ofthis. Here the pulse duration can range from 50 to 500 milliseconds. This test

effectively determines the quality of the header attachment but is also affected by thequality of the die attachment since the longer pulse measures the thermal resistancefrom the die through the die attachment, the header, an