Fundamentals of Thermal Resistance Measurement
Dr. John W. Sofia
1995
Analysis Tech
(781)245-7825
FAX (781)246-4548
email: info@analysistech.com
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 test
capabilities accessed via user-friendly menus and forms. The range of application
extends from laboratory research to production screening.
Part 1 deals with the scientific background of experimental methods and analyses
related 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 junctions
due to internal self-heating. This internal self-heating is a byproduct of electrical
current flow in the electronic device during operation; the heat generated
elevates the temperature in the semiconductor junctions. It conducts from the
junction area through the die, through the package, and eventually into the local
ambient. This flow of heat is governed by the laws of thermodynamics and the
principles of heat transfer. Accordingly the temperature within the package is
the highest in the heat generating junctions on the semiconductor die. It is this
temperature elevation of the semiconductor junctions that drives the need for
thermal 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 from
which 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 are
smaller. This general pattern is a central theme in all component heat dissipation.
From the perspective of the entire electronics cooling network, the component is the
critical, 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 the
cooling network. At the component level, minute differences in package design,
material selection, and quality of manufacture can have enormous impacts on junction
operating temperatures and time-to-failure. The technological trend toward
progressively increasing heat flux densities and the necessity to control junction
temperatures creates the need for component characterization.
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The focal point of component thermal characterization is the control of junction
temperatures. Since semiconductor reliability is adversely affected by higher junction
operating 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 resistance
provides a simple and convenient means for estimating junction temperatures.
Thermal resistance is analogous to electrical resistance. Electrical resistance is
computed as the difference in voltage between two points divided by the electrical
current flowing between them. This analogy is based on the fundamental similarity
between voltage and temperature, current conduction and heat conduction: Electrical
conduction occurs in response to a voltage difference; heat conduction occurs in
response to a temperature difference. This is a popular analogy due the general
familiarity of electric conduction in wires.
One shortcoming of the electrical analogy is that it suggests familiar networks such as
one-dimensional current flow in wires between discrete components. The conduction
of heat in electronic components is rarely so simple since it is significantly threedimensional with spatially distributed thermal resistances and heat capacitances. This
difference tends to make the electrical analogy lead to a one-dimensional interpretation
of an inherently three dimensional phenomena. The precise definition of thermal
resistance 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 flows
through the other and that no net thermal energy accumulation occurs in the
volume between the surfaces. It should be noted that these "surfaces" are not
physical, 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 thermal
resistance between them is
Tj − Tx
Rjx =
P
(Equ. 1)
3
The units of thermal resistance in electronic applications are °C / Watt. If mass
flow occurs across these isothermal surfaces, there must be no net mass
accumulation within the volume enclosed between the two surfaces since that
would comprise an accumulation of thermal energy in the form of mass heat
capacity. 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 of
paths for heat flowing from the component. The heat flux network provides a means for
illustrating and visualizing heat flow. Isothermal surfaces do not intersect but rather
form "nests" of concentric, closed volumes around a heat source. Isotherm nests and
heat-flux-networks are directly related: a complete description of either one contains all
the information necessary to construct the other since heat conducts perpendicular to
isotherms and parallel to heat-flux-lines. A complete heat flux network describes in
detail the three dimensional conduction of heat from a component's hot core to its
peripheral surfaces.
Isothermal surfaces are uniquely defined by size and shape. Thermal resistance is
isotherm specific: changing the size or shape of the isothermal surfaces used in
Equation (1) will change the computed thermal resistance. Alternatively, thermal
resistance is specific to the heat flux network; any alteration will change the thermal
resistance.
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 the
reciprocal of thermal conductivity and is a material property indicating the
resistance of the material to thermal conduction. Alternatively, resistivity is an
indication of thermal insulative quality. To understand resistivity and its
measurement, envision two parallel isothermal surfaces, T1 and T2 separated
by a uniform layer of material of thickness with thickness x. If the heat flux per
unit area is defined as q, the resistivity of the material separating the isothermal
surfaces is
T −T
x
r=
q
(Equ. 2)
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For electronic cooling applications thermal resistivity is expressed in units of °C
meter / 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 a
function of material resistivities and geometry. Thermal resistivity is used for evaluating
the thermal quality of a materials for use in component packaging applications.
Thermal resistance is a figure of merit for evaluation of the thermal transport capability
of 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 method
today. It is a direct, non-contact technique since it utilizes the junction itself as the
temperature 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 direct
technique that can be performed at-a-distance without an introduced sensor using only
the 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 forward
voltage drop of a junction as the temperature sensitive parameter and is variously
known as the "diode-forward-drop" method or the "Vbe" technique from original
applications with power diodes and bipolar power transistors. The method was
implemented soon after the invention of semiconductor electronics and continues to be
used extensively used throughout the industry. In the integrated circuit industry, it is
used to thermally characterize functional components as well as "dummy" thermal test
components made by substituting standard thermal test dice for functional dice.
Although the diode forward voltage is the most commonly used temperature sensitive
parameter (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 temperature
and voltage dependency exhibited by all semiconductor diode junctions. This
relationship can be measured and used to compute the semiconductor junction
temperatures in response to power dissipation in the junction region.
5
Voltage-temperature relationships are an intrinsic electro-thermal property of
semiconductor junctions. These relationships are characterized by a nearly
linear relationship between forward-biased voltage drop and junction
temperature when a constant forward-biased current is applied. This constant
current is called the "sense current" (also "measurement current"). Figure 1
illustrates the concept of measuring this voltage versus junction temperature
relationship in for a diode junction; Figure 2 shows a graph of the resulting data.
The relationship can be expressed mathematically as in the calibrating
relationship,
Tj = m Vf + T
(Equ. 3)
The slope, "m" (deg C/volt) and the temperature ordinate-intercept, "T0" are
used 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, Vf is
the "temperature sensitive parameter" (TSP). The slope and intercept are
device 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 specific
to 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 must
be individually measured for each distinct die and sense junction to be tested.
For semiconductor junctions, the temperature/voltage slope of the calibrating straight
line 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 sense
current 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 were
compared, the temperature/voltage slopes would be quite consistent although the
intercepts 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 with
different 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 tested
to establish the temperature/voltage slope. The temperature intercept can be computed
for identical parts which were not calibrated by using one measured voltagetemperature 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 for
junction 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 are
similar to the diode forward voltage. For testing certain types of devices, the diode
voltage TSP cannot be used due to the absence of an electrically accessible diode.
Such parts include IGBTs and some darlington transistors. The transistor saturation
voltage is defined as the voltage across the main current terminals of a 3-terminal
device 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 to
be 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 are
performed under unpowered, thermal equilibrium conditions so that the junction and
case temperature are nearly equal. Once the electrical connections for the selected
temperature sensitive junction have been completed, device calibration entails:
a) selection of the sense current level
b) establishment of thermal equilibrium between the component and a stabletemperature environment
c) measurement of the component case (junction) temperature and temperature
sensitive 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 in
the constant temperature environment, any point on the component case will eventually
reach 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 comprises
one data point for construction of the calibration relationship.
This procedure must be performed for at least two sufficiently spaced temperatures
since 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 performed
using 5-20 data pairs spaced in equal temperature increments. The calibration
parameters are then determined by a best-fit straight line using least-squares linear
regression. 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 when
using 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 manner
that sample averaging decreases the level of random error associated with a single
sample.
1.4.2 Sense Current Level Selection
The selection of the sense current is the first step for device calibration. The selection
of this current is limited by a number of factors although within a fairly wide range, the
precise 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 the
sense current has been chosen and the device calibration performed, the calibration
parameters 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 to
establish conduction in the body of the junction rather than just superficial
surface leakage conduction. Generally, 0.1 milliamp is the lower limit of the
selection 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 generate
some 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 0.006
Watts 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 junction
temperature. Based on this, two conclusions can be drawn:
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a) Given a particular junction, smaller sense currents generate less selfheating 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 test
procedures can further reduce this potential problem. (See "recalibration" in the
following section "Calibration Environments")
Lower Limit - electrical: All semiconductor junctions have parasitic electrical
capacitances in parallel connection with them. These capacitances cause the
diode voltage readings to "lag" the temperature readings whenever voltage or
temperature changes occur during thermal testing. Although such changes are
quite slow during calibration, during thermal testing, the sense current must
charge or discharge these capacitances as the junction temperature/voltage
changes. This charging/discharging utilizing a fixed current requires time in
proportion to the size of the parasitic capacitance. Larger sense currents
require less time since they offer faster charge/discharge rates. Generally,
larger, more capacitive junctions will test better with larger sense currents. (See
Active Dice under Device Types and Test Methods)
The most commonly used sense current throughout the industry is 1 milliamp. Most
testing on integrated circuits, functional and thermal dice, is performed with a 1
milliamp sense current. Other common selections are 10 and 20 milliamps for larger
power 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 case
temperatures. This necessitates a waiting period, the duration of which depends on:
a) the heat capacity of the component
b) 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" time
constant.
In practice, the heat capacity and thermal resistance are never known prior to
calibration. 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 used
to estimate equilibrium, the waiting interval is usually extended to the point where there
is 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-undercalibration 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 environment
is to provide stable temperature surroundings which will quickly reach equilibrium with
the 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 and
common mineral oil are typical choices. The liquid must be circulated or stirred to
enhance temperature uniformity and increase the liquid-to-component heat transfer
coefficient. 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 be
linear and free from cyclic variations. The component should be suspended in the bath
and 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 will
ensure 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. Forced
convection 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 sensing
the case temperature should be soldered to the component leads or otherwise well
grounded to the internal bulk temperature of the component. Some ovens offer more
optimal controllers utilizing short-duration time-proportioning algorithms to minimize the
cyclic 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 interval
is determined by the heat capacity of the component and the thermal resistance
between 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 onetenth that of an oven for equivalent accuracy. The use of a heat sink in the oven can
somewhat reduce this difference. Alternatively, the bath method is somewhat more
messy and generally less suitable for non-hermetic packages. In summary, both
methods 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 parameters
for identical parts are adjusted for part-to-part variations by using a single temperaturevoltage data point. This procedure is often referred as "recalibration". It makes use of
the fact that identical parts calibrate with a uniform slope and only vary in the
temperature intercept (Equ. 3). Referring to Figure 4, the intercept can be computed by
simply allowing the component to reach unpowered steady state equilibrium at room
temperature and then measuring the sense voltage and case temperature. This one
data 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 device
calibration 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 calibrating
parameters 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 the
actual die calibrated but can be established with a one-point recalibration procedure.
When a previously calibrated die is mounted in different packages, the calibration need
not be repeated. Care should be taken to ensure that the correct electrical connections
are bonded out for the chosen sense parameter each time the die is used in a different
package. 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 same
calibration 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 difficult
to specify an isothermal surface that does not correspond to a physical surface by
describing 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 the
basic definition. Thermal resistance is generally based on junction temperature (hotter
isotherm), 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-<reference x>,Rjx, or θjx, where <reference x> would be
substituted with such typical temperature sites as:
a)
b)
c)
d)
local ambient air temperature
specific site on the component case
specific site on a component lead
other well defined reference site
It is instructive to compare the theoretical definition with the practical application of
thermal 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 heat
is dissipated. Provided the same junction is used for all measurements of thermal
resistance on a particular component, this "hot" isothermal surface is well defined and
constant.
The "cold" isothermal surface, the reference isothermal surface, is much more
problematic. 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 the
immediate vicinity. Under any precisely defined set of cooling conditions, each
reference site corresponds to one point on a particular, vaguely specified, isothermal
surface. Under different component cooling conditions, heat flows from the component
in a different pattern of paths and forms different the isothermal surfaces. (Note:
isothermal surfaces are defined by size and shape) Since no practical method exists
for specifying the shape and size of these isothermal surface, the above thermal
resistances, based on fixed reference sites, require complete specification of the
component cooling conditions. Expressed simply, any thermal resistance based on
physically fixed temperature sites is specific to the cooling conditions under which the
measurements are taken. Thermal resistances measured under significantly different
cooling conditions are simply different measured parameters.
Junction-to-local-ambient thermal resistance typically exhibits appreciable variation
with 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 of
the component are specifically linked to the type of thermal resistance measured. For
example, the isothermal surfaces in natural convection cooling are dramatically
different than those in forced convection. Therefore, junction-to-ambient thermal
resistance 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 a
specific accessible site on the outside of the component case, most often, the hottest
point 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 alternatives
will likewise offer a wide variety of thermal resistances. Conversely, components
designed 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 misconception
that junction-to-case thermal resistance is solely a function of the component package
and does not depend on the cooling environment imposed when the thermal resistance
is measured. Despite plentiful evidence to the contrary, this erroneous attitude persists
today.
Integrated circuits are a good example of components which typically experience a
wide variety of heat flow patterns. Some of the primary paths typically include:
15
a) case directly into the board holding the component
b) case directly into the air
c) 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 thermal
resistance.
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 cooling
variations. Component packages of the type TO220, TO202, and TO247 are good
examples 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 component
through the integral cooling plate regardless of the specific application. For this
reason, there are very few varieties of thermal resistances for these components.
In summary, thermal resistances must be reported with precise descriptions of the
cooling conditions and the power dissipations that were used during the measurement.
This description should ideally be as simple as possible yet sufficiently accurate to
enable 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 noninvasive, i.e., report the same site-temperature as that which existed prior to the
installation of the thermocouple. This goal is never perfectly achieved since
thermocouples inherently involve contact measurement. Some heat conduction
invariably occurs in the thermocouple, thus wicking the heat away and cooling the
reference site. This error elevates the temperature difference between the reference
and 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 the
conductivity of the thermocouple wire. For example, if high conductivity 30 gauge
thermocouple 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 ambient
and 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 conduction
error but requires additional adhesive attachment; type T offers solderableattachment although with a higher level of conduction error.
c) The use of wire thermocouples should be limited to measurement of metal
and 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 bead
can stabilize unwanted fluctuations.
e) Test systems utilizing temperature sensitive phosphor technology provide
thermocouple-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 errors
associated 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, SEMI
Packaging Standards and JEDEC Industrial Standards. Such standards offer a
valuable means of technical communication and documentation. When applying such
industry standard methods, critical examination must be exercised to independently
evaluate the validity of the recommended methods. Some "standards" have been later
found 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 for
a critical investigation of any unfamiliar method regardless of how widely recognized or
standardized. Care should always be taken to ensure that the method employed
generates data which is useful for the intended purpose.
The following example underscores the caution must be exercised before embracing
any "standard" method. SEMI Standards, G30-88 and G43-87, discuss the use of
liquid bath environments for junction-to-case measurements. These specious methods
measure junction-to-case thermal resistance by suspending the component in an
agitated fluid. According to the method, the high thermal conductivity of the fluid
combined with the agitation effectively creates infinite heat sinking conditions and
thereby assures that the entire surface of the case will be isothermal. Any cautious
implementation of this method quickly reveals that the component is far from isothermal
and that the fluid selection (within the range of specification) and degree of agitation
dramatically affect the resulting measurement. These methods do not sufficiently
specify the essential liquid cooling parameters but rather rely on fictitious infinite heat
sinking. 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 in
Mil Std 883, method 1012 as well as SEMI Std G30-88. Here the integrated circuit
component 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 surface
temperature 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 heat
flow patterns and cooling conditions are well specified. This variety of junction-to-case
thermal resistance is directly applicable to components which are cooled in this
manner, 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 provides
wildly 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 have
recently 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 all
unfamiliar 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, DC
current to heat the semiconductor component. The reason for this is that thermal
resistance measurement requires steady-state thermal equilibrium which in turn
requires 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 the
component times the voltage difference between the in-flowing and out-flowing current
leads. With the voltage expressed in volts and the current expressed in amps, the
product is expressed in Watts.
P = I
Vin − Vout
(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
18
difference between any two points when current flows through them. This in turn
generates some internal heating of the wires; the magnitude of which is likewise
computed 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 the
component under test, it should not be included as part of the heat dissipation in the
component when total power dissipation is computed for thermal resistance
measurement. This error can be easily avoided by measuring the voltage difference
across the component at the points where the current actually enters and leaves the
die. This method is called a "Kelvin connection" or a "four-wire connection".
Figure 5 illustrates the two-wire connection with its attendant power measurement
error. 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; the
leads 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 losses
in the power delivery wires.
Figure 5: Illustration of 2 wire power measurement with attendant error
19
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 the
temperature sensing junction should not include the voltage drops across the wires
which carry the sense current to the sense junction. Using Ohms law, if the total roundtrip resistance of the sense-junction lead-wires is Rl and the sense current is Is, the
voltage drop in the lead wires, Vs is
V s = Rl
Is
(Equ 7)
The following is an example using typical-to-high range numbers:
lead wire resistance:
lead wire length (round trip):
sense current:
.06 ohms per foot
10 feet
10 milliamp
computed lead voltage drop = .006 volts
Although the case can be made that voltages of this magnitude are significant when
measuring junction temperatures electrically, the fact often overlooked is that the sense
current voltage drops in the leads are essentially constants that are simply nulled out
when the electrical method is properly implemented. The inconvenience of using fourwire connection for the sense junction voltage must be weighed against the minimal
benefits after considering these points:
20
a) If a device is calibrated using sense current lead-lengths approximately the
same as those intended for thermal resistance testing, the sense voltage
drop in the leads is inherently included in the device calibration parameters.
b) If all thermally characterized devices utilize one-point recalibration to adjust
for variations in the temperature intercept within a collection of identical
components, variations in lead length between that used for device
calibration 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 for
heating 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 divided
into 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 or current. 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 Ohms
law. The ratio is "nearly" fixed since the voltage/current ratio varies somewhat as a
function 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 for
specific 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.
21
In summary, as die temperatures increase, thermal dice experience higher
voltage/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 in
die 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. When
thermally characterizing two-terminal devices, the power dissipation cannot be
controlled 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 power
dissipation and establishment of thermal equilibrium, the final value of the heating
power will not be controlled to a pre-selected level. The Thermal Analyzer power
control options can be used to establish a controlled constant wattage without junction
temperature dependency.
The category of three-terminal devices includes bipolar transistors, MOSFETs, junction
FETs, and IGBTs. The functional design of these devices permits the heating voltage
and current to be simultaneously specified independently. Each of these devices has
one pair of terminals which essentially carry all of the power and a third terminal which
acts to control the operating voltage/current ratio device. By design, these devices
permit a small voltage or current to control much larger voltages and currents, and
essentially control the voltage/current operating point of the device. This amplified
control behavior of three-terminal devices also exhibits significant temperature
dependency in much the same manner as two-terminal devices. Despite this, the
capability to select the heating voltage and current independently is a powerful asset
when thermally characterizing three-terminal devices. Again, the Thermal Analyzer
power 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 of
functional device categories. These categories are determined by the electrical design
of 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 integrated
circuit packages. These dice are available in a variety of sizes and can be mounted
into any desired package to create a thermal test vehicle. They have become popular
for package characterizations including related thermal enhancements. Thermal dice
have been designed to offer electrically independent power dissipation and electrical
measurement of junction temperature. The thermal die test method is illustrated
schematically in Figure 7. Thermal dice offer accurate thermal characterization with a
22
minimum of measurement hardware. The basic concepts of device calibration, junction
temperature measurement, power delivery, and wattage control are direct application of
the concepts presented previously. The sense diode voltage can be directly measured
with a voltmeter and the associated junction temperature computed (Equ. 3) using
predetermined 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 intended
functional 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 a
specification 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 thermal
characterization. The primary feature that distinguishes active die from thermal die is
that heat dissipation is not electrically independent from temperature sensing and that
the die is designed to perform an electrical function other than providing convenient
junction temperature reporting. This requires that the otherwise continuous heating
power be interrupted for the measurement of the junction temperature. The process of
periodically interrupting the heating power to measure the sense junction voltage is
best 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
23
junction. The temperature sensitive voltage is measured during this interval.
During the temperature sampling interval, the junction cools passively until the
heating power is restored. When properly executed, the cooling is minimal and
can be further reduced to negligible levels with rapid data acquisition. One
temperature 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 resistance
measurement.
The end of the heating interval corresponds with the beginning of the temperature
sampling interval and visa versa. Although the objective of the temperature sampling
interval is to measure the junction temperature at the instant the heating interval ends,
some junction cooling does occur during the temperature sampling interval. Three
approaches are used to minimize the impact of junction cooling from the instant of
power interruption until the temperature sensitive voltage has been acquired:
a) minimize the duration of the temperature sampling interval to minimize
junction cooling
b) perform rapid sampling of the temperature sensitive voltage
c) 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 unique
procedure with special requirements which include:
a)
b)
c)
d)
rapidly switching the heating power off
switching the sense current on
measuring the temperature sensitive parameter
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 Thermal
Analyzer. In addition, there is a wide variety of specific requirements for temperature
sensing and power control to match the diversity of active dice. Commercially available
test systems offer such specialized test functionality with convenient software
24
interfaces for testing all types of semiconductor components, active as well as thermal
dice.
Heating Interval
Heating Power
Measurement Interval
Time
Figure 8: Graphic illustration of the heating and measurement intervals
The test procedure for testing a rectifier diode provides an excellent example of some
common 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 forward
conduction mode, control of the power dissipation via current control is far less
"delicate" than a comparable voltage control. In addition, diode power dissipation via
current 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 increasing
junction temperature under fixed current heating whereas dissipation increases with
temperature under fixed voltage control. Thus voltage control has a tendency toward
"thermal runaway" where the diode temperature spirals higher and higher, positively
reinforcing with higher and higher wattage.
25
Figure 9: Illustration of diode test method concept
The junction temperature measurement interval is of critical importance when making
thermal measurements on active dice. When the heating interval ends, the heating
power 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 which
cause deviation from this ideal. First, the switching process tends to stimulate
electrical 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 the
rectifier diode. In this case this capacitance must be electrically discharged from the
higher voltage (apparent lower temperature) associated with the passage of the heating
current to the lower voltage associated with sense current. During this recharging
interval, the electrical transients dominate the sense junction voltage samples and
which thus project inaccurate junction temperatures. Although the electronic switching
circuits within the Thermal Analyzer reduce the duration of the electrical transients,
ultimately, temperature-dependent diode sense voltages can only be measured after
the switching transients have died out. This waiting interval is often called the
"measurement delay interval".
26
Figure 10: Typical electrical transient for rectifier diode
Measurement delay interval is the initial portion of temperature sampling
interval between the instant of heating power interruption and acquisition of the
first valid, temperature dependent voltage reading. This interval always begins
at the instant of power interruption and lasts until the electrical switching
transients have subsided. The typically range is from 0 to 500 microseconds
and tends to be higher for larger junctions. It is specific to the functional
category of the active die as well as the part type designation. The
determination of the correct measurement delay interval is quite critical: If too
short, the junction temperature will be spurious; if too long, excessive junction
cooling 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.
27
c) Sampling of the temperature sensitive voltage is performed for the remainder
of 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 remaining
duration 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 sampling
period) 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 are
then converted into junction temperature readings (Equ 3). Since the junction cools
during the temperature sampling interval, extrapolation should be utilized to determine
the junction temperature at the instant of power interruption. This extrapolation
becomes critical for longer measurement delay intervals. The process of extrapolation
also 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]. The
Analysis Tech Thermal Analyzers utilizes sampling both before and after the end of the
measurement delay interval for optimal perspective on the transient electrical activity.
Figures 10, 11, and 12 illustrate some typical sampling intervals with a variety of
electrical transients. It is seldom difficult to recognize transient-corrupted temperature
data when examining samples spanning the entirety of a sufficiently long temperature
sampling interval.
28
Figure 11: Electrical transient from MOSFET
Figure 12: No electrical transient exhibited from signal diode
29
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 STD
750C, 3100 series methods.
Devices can be divided into two categories for thermal testing: two-terminal and threeterminal. The issues and differences in powering these two device types have already
been covered in the section on Delivery of Heating Power. The junction-temperature
sensing is somewhat specific to the functional device type. Table #1 provides an
overview of the temperature sensitive parameters used for various device types. A
detailed description of these methods are available in the MIL Std 750C, 3100 series
methods.
Device Family
diode, rectifier, SCR, TRIAC
integrated circuit, thermal test die
integrated circuit, functional die
bipolar transistor, NPN
bipolar transistor, PNP
MOSFET (N channel)
MOSFET (P channel)
darlington transistor
IGBT
Temperature Sensitive Parameter
diode V
die sensing diode V
substrate isolation diode sensed and
powered or
sense diode voltage and functional
powering
base-to-emitter or
base-to-collector diode V
emitter-to-base or
collector-to-base diode V
source-to-drain diode V or
gate turn-on V
drain-to-source diode V or
gate turn-on V
base-to-emitter diode or
saturation V
saturation V or
gate turn-on V
Table #1: Temperature Sensitive Parameter Listing for Various Device Types
30
1.9.1 Integrated Circuits
Integrated circuit components can be thermally characterized using a functional die or
by substituting a thermal test die. Active die testing can be quite simple despite the
potentially complex functionality and high lead counts that integrated circuits may
present. The simplest technique utilizes the substrate isolation diode that is present on
most (although not all) integrated circuit dice. The substrate isolation diode is
electrically 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 the
procedure 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 substrate
isolation diode testing on active dice is that the die size and die attachment is identical
to 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 a
discrepancy between component characterization data with the thermal test die versus
that 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 be
quite different from that which exists during functional operation of the integrated
circuit. 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. For
example, the components in some small on-board missile applications experience no
more than 100 seconds of intended operation. Characterization of components at
steady state is not useful for such situations.
Characterization of component transient behavior can also reveal aspects of internal
device construction. It can be used to perform non-destructive testing for die
attachment quality and to delineate the effective thermal performance of component
construction details.
Further, transient component characterization can be used to predict the performance
of components in response to non-steady, irregular, or cyclic heating waveforms.
31
1.10.1 Transient and Steady State
When a component is unpowered and at thermal equilibrium with the ambient
environment, its temperature is uniform throughout. When a constant level of power is
abruptly applied to the component and held constant for long period of time, the
component temperature undergoes a transition from an initially unpowered equilibrium
condition 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 temperature
disposition of the component. At thermal equilibrium, the only variables that
control the temperature of the component are the fixed power dissipation and the
thermal environment; when both of these are constant for a sufficient period of
time, the part approaches thermal equilibrium. Prior to equilibrium, the
component 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 the
temperature 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 be
measured at equilibrium conditions. The physical reason for this is the existence of
thermal 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" to
different temperatures when a component makes a thermal transition from one
equilibrium 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 capacitances
between the two isothermal surfaces have stopped changing temperature and have
reached equilibrium. The greater the heat capacity of the package contained between
the isothermal surfaces, the longer the transient period until the onset of thermal
equilibrium.
Prior to thermal equilibrium, the attempted computation of thermal resistance yields
thermal impedance.
Thermal impedance is defined as the difference in temperature between two
isothermal surfaces divided by the heat flow entering the hotter of the two
surfaces. Thermal impedance at thermal equilibrium is synonymous with thermal
resistance. Thermal impedance must specify the powering condition and
duration 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 isothermal
surface temperatures respectively and the total heat flow rate entering the
32
isothermal surface at temperature Tj as P, the thermal impedance between these
surfaces is
Tj − Tx
Zjx =
P
(Equ 8)
The units of thermal impedance are °C / Watt.
Thermal impedance is simply thermal resistance without the condition of equal heat flux
across both isotherms. This inequality occurs when heat capacitances between the
isothermal 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 electrical
steady 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 thermal
impedance, 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 is
initiated.
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 impedance
for this part would be computed and stated as:
Power Duration,
t (sec)
5
15
30
1000
2000
3000
Power (watts)
3
3
3
3
3
3
Tj (°°C)
35
49
55
60
61
61
Tamb (°°C)
25
25
25
25
25
25
Zja @ t
(°°C/watt)
3.33
8.00
10.00
11.66
12.00
12.00
Table 2: Example data for definition of thermal impedance and resistance
and
Rja = 12.00 °C/Watt (@ equilibrium)
33
Clearly, by the time the component has been powered for 2000 seconds, it has reached
steady state and therefore the impedance at 2000 seconds is actually the thermal
resistance of the component. In summary for any given power level, selected
temperature references, and cooling environment, a component can have an unlimited
number 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 heating
duration after a step change in power dissipation. Theoretically, equilibrium requires
an infinite heating duration, although for all practical purposes, equilibrium begins after
5 or 6 times the longest thermal time constant of the system enclosed between the two
isothermal surfaces. Collectively, the thermal impedance data taken during transient
response to a step-change in power is often called "heat characterization" or "heating
curve," since a plot of the data plot details the heating of the device.
Figure 13: Example of linear-time heating characterization plot
34
Heating Characterization is the complete response of a component to a stepheating condition. It defines the relationship of thermal impedance to heating
duration and contains a complete signature of the thermal behavior of the device
ranging from transient to steady state. When properly analyzed, the data can be
used 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. In
summary, 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 on
Synthetic Models in Heating Characterization.) Figure13 presents a heating
characterization 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-initiation
and the Y-axis is the component impedance. The longest duration of this heating
characterization is 1000 seconds. A very large portion of this plot presents equilibrium
data. Figure 14 presents the same heating characterization data plotted using a logtime. When plotted in this manner, the curve
Figure 14: Example of log-time heating characterization
35
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-equilibrium
data. This example illustrates a useful fact regarding the selection of time axes for
plotting heating characterization data. The linear time axis provides a much better
presentation of equilibrium data; the log time axis presents a more detailed
presentation of the short duration, transient, non-equilibrium thermal data. Since
heating 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 internal
heat spreader pad and one without the spreader. Comparing the data starting from the
shortest 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
36
Figure 16 presents a comparison of heating curves for the same part in natural and
forced 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 the
die.
Figure 16: Heating curve comparison for a device in natural and forced
convection
Examination of the overall heating characterization profile of a component indicates
where 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 thermal
improvements which are close the die, i.e., the die attachment. Alternatively,
components which have heating curves that rise sharply for long durations can benefit
most 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 performance
enhancement efforts.
37
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 heatingpower is instantaneously elevated to the specified level and then held constant for the
duration required to ensure complete thermal equilibrium. The junction - reference
temperature difference climbs steadily from its initial value to the final equilibrium value
as the heating-step progresses. During this heating power step, the temperature of the
junction-to-reference temperature difference is measured continuously. The
component 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 diverges
significantly from this basic concept.
In the single-step heating characterization, the junction temperature rises are quite
small 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 the
heating pulse. As the heating progresses and temperatures rise, the relative
significance of these fixed errors will subside to manageable levels. Thus, the single
step response heating characterization will suffer from massive errors for the short
duration 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 the
maximum power and junction temperature limits of the component. The fundamental
problem with the idealized, fixed power, single step heating response is that the
heating power is limited to the steady state DC power limit.
Another problem with the ideal heating characterization concept is that only thermal
dice can be continuously powered while simultaneously being measured for junction
temperature. All active non-thermal dice require fixed duration interruption in the
heating power for the measurement of the junction temperature. For short duration
impedances, these power interruptions comprise a significant "duty cycle" factor and an
unacceptable deviation from the requirement of continuous heating at a fixed level. As
the heating duration progresses, the off-power intervals become insignificant as a
proportion of the heating duration.
For these reasons, heating characterization for components with active, non-thermal
dice 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
38
component impedance can be computed for that particular heating duration as the
temperature 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 its
original unpowered equilibrium state. When the pulse wattages are chosen to generate
a uniform temperature rise for all heating durations, the impedance measurements
exhibit a uniform accuracy throughout the heating characterization. In the interest of
reducing the total time required for a heating characterization, longer heating durations
can be performed in the idealized, fixed-power level approach. When performing
heating characterization with a respect a reference temperature which is assumed to be
fixed, i.e., ambient air temperature, care should be taken to ensure that the reference
temperature does not inadvertently "drift" during the heating characterization. Such a
"drift" would generate systemic errors in the resultant data. Alternatively the reference
temperature 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 not
universal, manifestation. Each ripple in the heating step-response indicates an
equilibrium 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 component
package 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 constants
have elapsed, each of the points of inflection correspond to approximately three-times
one of the inherent internal thermal time constants of the component packaging
configuration.
The heating characterization represents a type of cross sectional view of the internal
thermal resistances and capacitances of a component as depicted. To appreciate this
fact, 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 enter
the die attachment region. The small heat capacitance of the die region and the high
heat 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 entirely
governed by thermal spreading in the die region; the short duration impedances are
overwhelmingly representative of the heat flux network in the die region. The mass of
the component package, with its larger heat capacitance, responds after further heating
and sufficient energy accumulates to alter its temperature. The larger the heat
capacitance associated with a thermal resistance, the longer the heating duration
before its influence will be manifested. Thus heating curve data plots depict the
disposition of internal thermal resistances as a function of distance from the die 39
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 approaches
equilibrium as the measured impedances approach the steady state thermal resistance.
At equilibrium, the thermal resistance embodies all of the distributed, constituent
thermal resistances elements between the two designated reference temperature sites.
For heating durations less than that required for thermal equilibrium, those thermal
resistances are partially reflected in the associated impedances as a function of the
heating duration: The longer the heating duration, the greater the proportion of the
thermal resistances between the reference sites that will be included in the associated
thermal impedance. Based on this, pre-equilibrium heating durations can be chosen to
selectively exclude the outer portions of a component. Essentially, an impedance
measurement can be "tuned" to probe a particular internal component interface by
selecting the correct heating duration. Such tests are specific and highly sensitive to
the thermal performance of the component package-depth of interest.
One of the most popular applications of "tuned" impedance measurement is the die
attachment 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 the
mechanical/thermal bond between the die-attachment and the package. Since most of
the 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 thermal
performance. 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 semiconductor
device will operate with higher junction temperatures and thus have a shortened life
expectancy.
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 causing
rapid heating of the die without substantially heating the package into which it is
mounted. 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, the
impedance measured reflects the thermal resistance of the package from the die
outward 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 test
and the device is assumed to be at unpowered thermal equilibrium prior to the test, the
impedance is simply the difference in junction temperature before and after the power
pulse. The peak junction temperature rise above the starting temperature is strongly
controlled by the thermal resistance of the die attachment. Voids or defects in the
40
attachment will result in reduced thermal conduction and higher chip temperatures.
The short duration of the power pulse required for die attachment testing is ideally
suited 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 offer
significantly higher temperature rises than the DC limit and thereby improves the
measurement accuracy of the test.
In a similar manner, longer heating duration pulses can be used to test internal
component-interface layers. The testing of header attachments is a good example of
this. 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 the
quality of the die attachment since the longer pulse measures the thermal resistance
from the die through the die attachment, the header, and the header attachment,
respectively. A test of this type does not comprise a good indicator of header
attachment unless a previous test for die attachment has been performed.
In production environments, large quantities of devices can be "screened" for die
attachment. The results of this screening can be represented as a histogram. Figure
17 presents an example of this type of evaluation. The shape of these curves is often a
bell curve with an extended "hot-foot" as shown in the figure. This type of analysis
helps to determine production consistency and provides the basis for enhancement of
thermal quality of manufacture.
Figure 17: Sample histogram of die-attachment test results
41
The topic of heating characterization is also discussed in SEMI Std G46-88.
1.11.3 Further Applications of Heating Characterization
A heating characterization contains all of the information needed to accurately predict
the behavior of the component to any non-steady heating condition. A technique for
synthesizing dynamic models comprised of discrete thermal resistances and
capacitances has been developed for improved physical insight. [Sofia, 1995] These
models provide three significant benefits:
a) delineation of effective internal package thermal resistances and time
constants
b) delineation of the best "target" for package thermal enhancement efforts and
estimate of probable results
c) simulation of the behavior of the device to non-steady or cyclic powering
conditions.
These component dynamic models can be used to simulate the thermal performance in
response to power conditions other than the simple step. Arbitrary power waveforms
can be specified as the input to the synthetic model. The resulting simulation can
completely detail the thermal performance of the device. Figure 18 presents a typical
simulation using square-wave heating power over a range duty cycles.
42
Figure 18: Sample of square-wave impedance simulation
Arbitrary heating waveforms can be utilized when expressed in step-wise
approximation. This simulation technique essentially involves a superposition in time of
a sequence of power steps that, when added together, produce the desired heating
waveform. Since the response of the component to a single heating step is known,
superimposing the responses of the individual steps comprising the desired heating
waveform produces the desired response. This technique is called "temporal
superposition". It can be applied to simulate the thermal response of any component
for any arbitrary heating waveform, transient or steady-state, based on the information
contained in the standard heating characterization.
1.12 Thermal Resistance Methods for Hybrids/Multi-Chip Components
1.12.1 Introduction
Thermal resistance characterizations of electronic packages having multiple heat
sources are unique and can often pose problems, particularly for the thermal test
43
engineer. Such packages are typified by multi-chip packages or hybrid electronic
assemblies. Such components possess multiple dice in close proximity with
independent heat dissipations. The fundamental effect that differentiates these
components from the single die packages is that each die heats the adjacent dice and
the relative heat dissipation of the dice may independently be a function of the
component operation.
The following discussion covers the method of thermal resistance characterization in
multi-chip components. The underlying theory of linear superposition is briefly
discussed followed by the matrix method of thermal resistance formulation.
1.12.2 Method of Linear Superposition
The physics of heat transfer is expressed by the general heat-conduction equation and
governs the temperature distribution and the conduction heat flow in a solid having
uniform physical properties. The Laplace transformation theory that can be used to
solve this differential equation includes the superposition theorem, the Duhamel
integral theorem, as part of its formulation. The idea of superposition is that known
heat conduction solutions for specific heat transfer problems can be superimposed to
yield valid solutions for more complex problems of interest. This principle of linear
superposition of heat conduction solutions is an extremely powerful tool which can be
applied to thermal testing.
As a simple example of linear superposition, consider the hypothetical case of onedimensional heat conduction in a bar. Here, the bar contains two internal heat sources
and is insulated everywhere except at the ends where a fixed temperature is imposed.
The temperature distribution within this bar is shown in Figure 19A, where only a single
heat source is operating. With a different heat source operating, a second solution can
be easily generated as shown in Figure 19B. Using the method of linear superposition,
the solution for the bar with the two heat sources operating simultaneously can be
created by simply adding the temperature fields and the heat fluxes. This
superimposed solution is shown in Figure 19C which was created by summing the
temperature rises from each single source solution.
44
Figure 19 A, B, C: Illustraion of superposition concept
This is a powerful technique since it allows simple, single heat source temperature
fields to be superimposed to generate solutions for more complex problems which are
relatively difficult to solve by direct approach. It is most accurate for application which
are dominated by conduction. The method of superposition can be conveniently
expressed through a matrix method of thermal resistance formulations for multiple heat
source thermal problems.
45
1.12.3 Superposition Method for Thermal Resistance
The method of linear superposition can easily be applied to thermal resistance
characterization and measurement of components with multiple, independent heat
sources where the heat transfer is dominated by solid conduction.
Consider the case of the linear bar conduction shown in Figure 18. Physically, this
example represents a bar with internally embedded heat sources. The sides of the bar
are insulated such that heat can only escape the bar from the uninsulated end faces
which are both exposed to an infinite heat sink of temperature T0. The reference
temperature for this simple example is the infinite heat sink temperature, i.e., Tref = T0.
Superimposing Figures 18A and 18B, the temperature of point 1 equals the
temperature rise of point 1 with only the heat source at point 1 operating plus the
temperature rise of point 1 with only the heat source at 2 operating. This is expressed:
T = T −T + T −T +T
T = T −T + T
−T +T
where the single-source temperatures are defined:
T11 = temperature of point 1 with heating from point 1
T22 = temperature of point 2 with heating from point 2
T12 = temperature of point 1 with heating from point 2
T21 = temperature of point 2 with heating from point 1
and the superimposed temperatures are :
T1 = temperature of point 1 due to heat from both point 1 & point 2
T2 = temperature of point 2 due to heat from both point 1 & point 2
This superposition solution can be similarly expressed in terms of thermal resistances:
R =
T −T
Q
where all thermal resistances here are from the heat source "junctions" to the reference
temperature, Tref or T0. Here R11 is the thermal resistance of point 1 due to heating at
point 1. These thermal resistance manipulations can be cast in matrix form for
convenience. This yields a 2 by 2 matrix, R , for our case of two heat sources:
46
R 11 R 12
R 21 R 22
R
Q1
T1− T 0
=
Q2
T 2− T0
Equ. 9
Q = ∆T
Equ. 10
The general thermal resistance description of a component having 'N' heat sources is
an N-by-N matrix, R . The heat dissipation of each source is formed into a column
matrix, Q The differences between the source temperatures and the reference
temperature also form a column matrix, ∆Τ , where with the elements of the array are
equal to Ti - Tref, for i = 1 to N. With the thermal resistance matrix determined, the
temperature of each source can be calculated from the above matrix equation (Equ. 10)
based on the principle of superposition.
It should be noted that R12 and R21 are equal when the selected reference
temperature is equally sensitive to the heat fluxes from each of the heat sources.
Conversely, the reference temperature should not be more sensitive to the heat flux
from any particular heat source due to its proximity to reference temperature site.
When this condition is satisfied, the R matrix is a symmetrical matrix. This is a very
desirable condition from the perspective of component characterization.
In regard to the selection of a reference temperature site, the degree of matrix
symmetry is a good indicator of the desirability of candidate reference temperature
sites. Usually the local ambient or the average heat sink temperature is the best
selection for the reference temperature site. Since the local ambient air temperature is
nearly equally influenced by each of the heat sources. An average heat sink reference
temperature is ideally influenced by the total heat flux of all of the nodes and not the
proximity of any particular heat source(s). This issue should be considered when
selecting the reference temperature site for multi-chip modules (MCMs). When the
matrix must be symmetric (as in the case of the ambient reference temperature)
averaging the elements can be use to create a symmetric matrix. In cases where the
mattrix is known to be symmetric as is the case isothermal ambient reference
temperature, non-equal symmetric elements should be replaced by their average value.
This correctly averages out random measurement errors.
This superposition technique is extremely useful for effective thermal resistance
characterization of multi-chip modules, hybrid devices, or any components having
multiple heat sources. The method simply requires that for each independent heat
source present, one test must be performed. During each test, junction temperatures
for all dice must be measured.
47
1.12.4 Limitations and Sources of Error
The method of superposition may be used effectively over a wide range of problems.
Random errors are always present but these can be quantified by test repetition and
analysis of the sensitivity of the final results to such errors. There are however some
situations which may cause significant systematic errors:
a) radiation effects: When radiation becomes a significant means of heat
transfer (greater than 5 to 10 % of the total heat transfer) superposition will
begin to generate systematic errors. The reason is that radiation heat
transfer has fourth power dependency on temperature, hence, is not
superimposable.
b) temperature variations in material properties: These are nonlinearities
which are not superimposable. To minimize these non-linear effects, all
single source tests should be performed at peak temperatures close to those
expected in the superimposed solution.
c) transport by convection: Natural convection generates a nonsuperimposable non-linearity since the convective action depends on the
total amount of heat dissipated leading to buoyancy. Convection affects
components that are down-stream of the heated component(s). Fluid
dynamic effects are often non-linear and thus can create systematic errors
for superposition method.
1.13 Component Characterization Method Summary
The following list comprises the primary steps for component characterization.
Device Calibration
a) Determine the electrical connections for the temperature sensitive
parameter (TSP).
b) Select the sense current and calibration environment.
c) Perform calibration to determine the calibration relationship for the
TSP.
Thermal Resistance Testing
a) Determine the means to heat the component with DC power.
b) Determine the reference temperature site and the means to measure
it.
c) Fixture the component in the desired test thermal environment.
d) Allow the component to reach unpowered equilibrium with the
environment.
e) Measure the sense voltage and compute the unpowered junction
temperature.
48
f) Compare the junction temperature with the environment temperature
and correct temperature intercept if necessary (one-point
recalibration).
g) Begin heating the component.
h) Check the junction temperature readings to ensure the correct value
for the measurement delay interval to avoid spurious electrical noise.
i) When powered thermal equilibrium has been reached, report the
thermal resistance based on the final power level, measured reference
temperature, and junction temperature (computed using the
recalibrated calibration parameters).
Thermal Impedance Testing
a) Perform thermal resistance first to establish steady state power limits
and stable DC power conditions.
b) Let component reach unpowered equilibrium in test environment.
c) Determine the desired duration of heating .
d) Determine the desired power level for sufficient temperature rise.
e) Deliver the desired power pulse and determine the junction
temperature rise. Be sure that the correct value for the measurement
delay interval is used to avoid spurious electrical noise.
f) Compute thermal impedance based on the temperature rise and the
power level delivered.
g) If performing a heating characterization, repeat steps b) - f) for another
combination of duration and power level.
1.14 References
Azar, K., Benson, J. R., Manno, V., "Liquid Crystal Imaging for Temperature
Measurement of Electronic Devices" Seventh IEEE SEMI-THERM Symposium pp 2329, 1991
Blackburn, D.L., "An Electrical Technique for the Measurement of the Peak Junction
Temperature of Power Transistors", 13th Annual Proceedings Reliability Physics, '75,
IEEE 75CH0931-6PHY, pp. 142-145, 1975
Blackburn, D.L., Oettinger, F.F., "Transient Thermal Response Measurements of Power
Transistors," IEEE Power Electronics Specialists Conference (PESC), 1974 Record,
June 1974, pp 140-148
"Circuit-Performance and Thermal Resistance Measurements" (3100 Series) MIL-STD750C, February, 1993
49
Kraus, A.D., Bar-Cohen, A., Thermal Analysis and Control of Electronic Equipment,
McGraw Hill, 1983, ch. 1
C. Neugebauer, [et al.], Thermal Response Measurements for Semiconductor Devices,
New York: Gordon & Breach Science Publications, 1986, ch. 4, 5, 6
Oettinger, F.F., Blackburn, D.L. Thermal Resistance Measurements, NIST Special
Publication 400-86 from Series on Semiconductor Measurement Technology, July,
1990
Oettinger, F.F., Gladhill, R.L., "Thermal Response Measurements for Semiconductor
Device Die Attachment Evaluation," International Electronic Device Meeting Technical
Digest (IEDM), 1973, pp. 47-50
Sofia, J.W., "Analysis of Thermal Transient Data with Synthesized Dynamic Models for
Semiconductor Devices", IEEE Transactions on Components, Packaging, and
Manufacturing Technology Part A (CPMT), Volume 18, March 1995, pp 39-47
50