Freescale Semiconducto Thermal Analysis of Semiconductor Systems User Manual
Freescale Semiconductor, Inc.
White Paper
Thermal Analysis of
Semiconductor Systems
Contents
1 Introduction ................................................................................................................................ 2
2 Definitions and Basic Principles ................................................................................................. 3
2.1 Definitions ............................................................................................................................ 3
2.2 Basic Principles ................................................................................................................... 3
2.3 Transient Thermal Response ............................................................................................... 5
2.4 Convection and Radiation ................................................................................................... 6
3 Differences between Electrical and Thermal Domains .............................................................. 8
4 Thermal Rating ........................................................................................................................... 9
4.1 Thermal Resistance Ratings ................................................................................................ 9
4.2 JEDEC Test Methods and Ratings .................................................................................... 10
4.3 Thermally Enhanced Circuit Boards .................................................................................. 12
4.4 Transient Thermal Response Ratings ................................................................................ 15
5 Ramifications of High Operating Temperature ......................................................................... 18
6 Thermal Circuits ....................................................................................................................... 20
7 Thermal Modeling Software ..................................................................................................... 24
7.1 Uses of Thermal Modeling Software ................................................................................. 24
7.2 Thermal Modeling Software Options ................................................................................. 26
8 Empirical Analysis Techniques ................................................................................................. 28
9 Optimizing the Thermal Environment ....................................................................................... 30
10 Appendices............................................................................................................................. 32
10.1 Appendix A—List of JESD51 Series Publications ........................................................... 32
10.2 Appendix B—Thermal Properties of Common Semiconductor Packaging Materials .... 33
11 References.............................................................................................................................. 34
1 Introduction
Designing a cost competitive power electronics system requires careful
consideration of the thermal domain as well as the electrical domain.
Over designing the system adds unnecessary cost and weight; under
designing the system may lead to overheating and even system failure.
Finding an optimized solution requires a good understanding of how to
predict the operating temperatures of the system’s power components
and how the heat generated by those components affects neighboring
devices, such as capacitors and microcontrollers.
No single thermal analysis tool or technique works best in all
situations. Good thermal assessments require a combination of
analytical calculations using thermal specifications, empirical analysis
and thermal modeling. The art of thermal analysis involves using all
available tools to support each other and validate their conclusions.
This white paper first presents the basic principles of thermal systems
and then describes some of the techniques and tools needed to
complete such an analysis. Power devices and low lead count
packages are the primary focus, but the concepts herein are general
and can be applied to lower power components and higher lead count
devices such as microcontrollers.
2 Definitions and Basic Principles
2.1. Definitions
A good way to begin a study of a domain is to familiarize oneself
with its definitions, nomenclature and notations. The terms used for
thermal analysis vary somewhat throughout the industry. Some of
the most commonly used thermal definitions and notations are:
T
Temperature at reference point “A”
A
Junction temperature, often assumed to be
T
J
constant across the die surface
T
or T
C
Package temperature at the interface between the
Case
package and its heatsink; should be the hottest
spot on the package surface and in the dominant
thermal path
ΔT
Temperature difference between reference points
AB
“A” and “B”,
q Heat transfer per unit time (Watts)
Power dissipation, source of heat flux (Watts)
P
D
The term “Junction Temperature”
The term junction temperature became commonplace in the early
days of semiconductor thermal analysis when bipolar transistors and
rectifiers were the prominent power technologies. Presently the term is
reused for all power devices, including gate isolated devices like power
MOSFETs and IGBTs.
Using the concept “junction temperature” assumes that the die’s
temperature is uniform across its top surface. This simplification
ignores the fact that x-axis and y-axis thermal gradients always exist
and can be large during high power conditions or when a single die has
multiple heat sources. Analyzing gradients at the die level almost always
requires modeling tools or very special empirical techniques.
H Heat flux, rate of heat flow across a unit area (J·m-
2
·s-1)
Thermal resistance between reference points “A” and
R
QAB
“B”, or R
R
Junction to moving air ambient thermal resistance
QJMA
Junction to case thermal resistance of a packaged
R
QJC
THAB
component from the surface of its silicon to its
thermal tab, or R
Junction to ambient thermal resistance, or R
R
QJA
C
Thermal capacitance between reference points “A”
QAB
and “B”, or C
THAB
THJC
THJA
ºC or K Degrees Celsius or degrees Kelvin
Transient thermal impedance between reference
Z
QAB
points “A” and “B”, or Z
THAB
Most of the die’s thickness is to provide mechanical support for the
very thin layer of active components on its surface. For most thermal
analysis purposes, the electrical components on the die reside at the
chip’s surface. Except for pulse widths in the range of hundreds of
microseconds or less, it is safe to assume that the power is generated
at the die’s surface.
3Thermal Analysis of Semiconductor SystemsFreescale Semiconductor, Inc.
2.2. Basic Principles
The basic principles of thermal analysis are similar to those in the
electrical domain. Understanding one domain simplifies the task
of becoming proficient in the other. This is especially clear when
we consider thermal conduction. The two other thermal transport
mechanisms are discussed later.
Each domain has a “through” and an “across” variable, as shown in
Figure 1 and Table 1. The through variable can be thought of as the
parameter that flows from one reference point to another. Current is
the through variable for the electrical domain and power is the through
variable in the thermal domain.
The across variable can be thought of as the variable that forces
the flow of current or heat. In each domain the forcing function is a
difference in potential; in one domain it’s temperature and in the other
it’s voltage.
Both systems have a resistance that impedes the flow of the through
variable.
Given the duality of the two systems, it is no surprise that the
fundamental equations of the domains are similar. This is illustrated
most clearly when we see that each system has an “Ohm’s Law”, as is
shown in Table 1.
Figure 1—Fundamental Relationships in the Electrical and Thermal Domains
4 Freescale Semiconductor, Inc.Thermal Analysis of Semiconductor Systems
Table 1—Basic Relationships in the Electrical and
Thermal Domains
Electrical Domain Thermal Domain
Variable Symbol Units Variable Symbol Units
Through Variable Current I Amperes or Coulombs/s Power or Heat Flux P
D
Watts or Joules/s
Across Variable Voltage V Volts Temperature T ºC or K
Resistance Electrical Resistance R Ohms Thermal Resistance R
Capacitance Electrical Capacitance C Farads or Coulombs/V Thermal Capacitance C
“Ohm’s Law” ΔV
= VA – VB = I * R
AB
AB
ΔTAB = TA – TB = PD * R
(derived from Fourier’s Law)
QAB
Q
ºC/W or K/W
Joules/ºC
QAB
From the relationships above,
ΔT
= (TJ – TA) = PD R
JA
QJA
we can easily derive the often used equation for estimating junction
temperature:
T
= TA + (PD R
J
) (Eq. 1)
QJA
For example, let’s assume that:
R
P
T
= 30ºC/W
QJA
= 2.0W
D
= 75ºC
A
Then, by substitution:
T
= TA + (PD R
J
T
= 75ºC + (2.0W * 30ºC/W)
J
T
= 75ºC + 60ºC
J
T
= 135ºC
J
QJA
)
A cautionary note is in order here. The thermal conductivities of some
materials vary significantly with temperature. Silicon’s conductivity, for
example, falls by about half over the min-max operating temperature
range of semiconductor devices. If the die’s thermal resistance is
a significant portion of the thermal stackup, then this temperature
dependency needs to be included in the analysis.
2.3. Transient Thermal Response
Of course, the duality extends to transient as well as steady state
conditions. The existence of capacitance in both domains results in
thermal RC responses like those we are familiar with in the electrical
domain. The basic relationships follow.
Thermal time constant is equal to the thermal R-C product, that is:
t
= RQ CQ (Eq. 2)
Q
Thermal capacitance is a function of the temperature rise associated with
a given quantity of applied energy. The equation for thermal capacitance
is:
CQ = q t/ΔT (Eq. 3)
where:
q = heat transfer per second (J/s)
t = time (s)
ΔT = the temperature increase (ºC)
Thermal capacitance is also a function of mechanical properties. It is
the product of a material’s specific heat, density, and volume:
C
= c d V (Eq. 4)
Q
where:
c = specific heat (J kg
d = density (kg/m
V = volume (m
-1 K-1
)
3
)
3
)
Furthermore, the temperature of a thermal RC network responds to a
step input of power according to:
ΔT
AB
= R
QAB PD
(1 - e
(-t/t)
) (Eq. 5)
5Thermal Analysis of Semiconductor SystemsFreescale Semiconductor, Inc.
2.4. Convection and Radiation
Conduction is only one of three possible thermal transport
mechanisms. In addition to conduction, the other mechanisms are
radiation and convection. In fact, these other transport mechanisms
often become the predominant ones as heat exits a module.
Radiation and convection are clearly more complex thermal transport
mechanisms than conduction, and we will see that in their governing
equations. Consider first convection, which occurs when a solid
surface is in contact with a gas or liquid at a different temperature. The
fluid’s viscosity, buoyancy, specific heat and density affect the heat
transfer rate from the solid’s surface to the fluid. The surface’s area and
its orientation (i.e., horizontal or vertical) as well as the shape of the
volume in which the fluid is free to circulate are additional factors. And,
having the greatest effect is whether the system uses forced air (fan
cooling) or natural convection.
Although convective behavior is quite complex, its descriptive equation
is relatively simple and can be expressed as:
q = k A ΔT (Eq. 6)
where:
q = heat transferred per unit time (J/s)
k (or h) = convective heat transfer coefficient of the process
-2
(W m
ºC-1)
A = heat transfer area of the surface (m
2
)
ΔT = temperature difference between the surface and the bulk
fluid (ºC)
mechanism. But at the module level, because of the much larger
surface area and the heat transfer’s dependence on the 4th power
of temperature, radiation can play a much more important role.
Nevertheless, for larger objects thermal radiation is often accounted for
by including its effect in a general thermal resistance value. But since
radiation is a strong function of temperature, this practice is acceptable
only over a modest range of module and ambient temperatures or
when the module and ambient temperatures are nearly the same.
Applying three different and sometimes complex thermal transport
mechanisms to a complex thermal circuit creates a system that cannot
be evaluated by simple and inexpensive tools. Often the only feasible
approach is to model a thermal circuit with tools created for that
purpose and validate that model with empirical testing.
The convection coefficient, k, can be determined empirically, or it can
be derived from some thermal modeling programs. It changes, for
example, with air speed when a fan is used, with module orientation or
with fluid viscosity.
Radiation is a completely different process and augments the other
two transport mechanisms. Quantifying heat transferred by radiation
is complicated by the fact that a surface receives as well as emits
radiated heat from its environment. “Gray Body” (vs. “Black Body”)
radiation is the more general condition and its governing formula is:
4
q = e s A (T
4
- T
) (Eq. 7)
h
c
where:
q = heat transfer per unit time (W)
e = emissivity of the object (one for a black body)
s = Stefan-Boltzmann constant = 5.6703*10
A = area of the object (m
T
= hot body absolute temperature (K)
h
T
= cold surroundings absolute temperature (K)
c
2
)
-8
(W m-2 K-4)
Exercising Equation 7 shows that for geometries and temperatures
typical of semiconductor packages, radiation is not a primary transport
6 Freescale Semiconductor, Inc.Thermal Analysis of Semiconductor Systems
3 Differences between Electrical and Thermal Domains
Leadframe
Exposed Pad
Standard SOIC
Thermally Enhanced
Considering how the electrical and thermal domains differ is a good
way to avoid some common misconceptions and misunderstandings.
One key difference between the domains is that in the electrical
domain the current is constrained to flow within specific circuit
elements, whereas in the thermal domain heat flow is more diffuse,
emanating from the heat source in three dimensions by any or all of
the three thermal transport mechanisms. In electrical circuit analysis
current is limited to defined current paths and that allows us to use
lumped circuit elements, such as resistors, capacitors, etc. But in
the thermal domain the thermal path is not so constrained, so using
lumped elements is not as appropriate. Even in relatively simple
mechanical systems, defining lumped thermal components is often an
exercise in estimation, intuition and tradeoffs. We want to use lumped
elements to model our thermal systems, but we must remember that to
do so we’ve made many simplifying assumptions.
A second major difference is that coupling between elements is usually
a more prominent behavior in the thermal domain. Isolating devices in
electrical circuits is usually easier than isolating elements in thermal
4 Thermal Ratings
4.1. Thermal Resistance Ratings
Now let’s investigate how these basic thermal relationships affect
manufacturers’ thermal resistance specifications. For a given package
style, for example the SOIC, thermal performance can vary substantially
depending on the package’s internal construction and how the system
extracts heat from the package leads or its body. Figure 2 shows
that the standard SOIC’s leadframe floats within the package’s mold
compound, so there is no direct low impedance thermal path from the
die to that package’s surface. Heat generated in the die readily travels
into the leadframe, but then it struggles to move through the mold
compound to the package surface and through the wirebonds to its
leads. Even though heat travels only a short distance, the package’s
thermal resistance is high due to the mold compound’s high thermal
resistivity and the wirebonds’ very small cross sectional area.
The portion of the leadframe on which the die is placed is called
the “die paddle,” or “flag.” The package’s thermal performance can
be enhanced substantially by improving the thermal path from the
paddle to the package’s surface. One way to do this is to stamp the
networks. Therefore, good thermal models usually employ thermal
coupling elements, while many electrical circuits do not require them.
The tools to model complex systems are quite different between
the domains. Electrical circuit analysis tools, such as SPICE, can be
used for thermal circuits of lumped elements, but such tools are not
appropriate for assessing how heat flows in a complex mechanical
assembly.
The test and evaluation tools differ as well. You can’t clamp a “heat flux
meter” around a thermal element to monitor how much power passes
through it. For thermal analysis infrared cameras and thermocouples
replace oscilloscopes and voltage probes.
Even though the domains have their differences, they are likely to
be interdependent. A prime example is the temperature dependence
of a power MOSFET’s on-resistance, which increases by 70 to 100
percent as the temperature increases from 25ºC to 150ºC. The higher
on-resistance increases power dissipation, which elevates temperature,
which increases on-resistance, and so on.
leadframe so that some of the leads are directly connected to the die
paddle (flag). This allows heat to flow relatively unimpeded through the
“thermally enhanced” leads and onto the PCB. Another approach is
to expose the die paddle at the bottom (or top) of the package. This
structure yields a much more direct thermal path and vastly improves
the device’s thermal performance.
Since the primary thermal path differs with modifications in the
package construction, each variation merits its own thermal reference
points and, therefore, its unique thermal resistance specifications.
Table 2 contains thermal resistance ratings of two devices with
essentially the same die. Both use a version of the 32-lead, fine-pitch,
wide-body SOIC. One version has an enhanced leadframe (the two
centermost leads on each side of the package are directly connected
to the die pad), and the other has an exposed pad on the IC’s belly.
Their internal construction and how they are typically mounted on a
PCB are shown in Figure 3.
Figure 2—Cross Sections of standard and exposed pad SOICs
7Thermal Analysis of Semiconductor SystemsFreescale Semiconductor, Inc.
Table 2—Typical Thermal Resistance Specifications
Standard
Optimum T
lead
reference
Some leads may be
attached to the leadframe
Exposed Pad
Optimum T
case
reference point
circuit board
Thermal Ratings Symbol Value Unit
Thermal Resistance
Junction to Case
Junction to Lead
Junction to Ambient
32 lead SOIC Case 1324-02
R
QJC
R
QJL
R
QJA
Standard
18
70
Exposed pad
32 lead SOIC Case 1437-02
1.2
-
71
ºC/W
Figure 3—Cross Sections of standard and exposed pad SOICs
For the standard SOIC the primary path for heat flux is laterally through
the wirebonds and the mold compound, into the leads and then
vertically into the board. For the exposed pad package the path is
much more direct; heat passes vertically through a broad cross section
from the top of the die through the silicon, through the die attach
are most appropriate for devices whose primary thermal path is
through an exposed thermal tab, not through the leads. The moral of
the story is that the user should carefully note the reference points
used for a device’s thermal resistance specifications and correctly
apply those specifications to the application.
material, through a leadframe and another solder layer then into the
circuit board. The difference in thermal paths between the two options
is in the tens of ºC/W.
Semiconductor manufacturers are adept at specifying their devices’
thermal performance. But users want more. They want to know
what performance they can expect when the device is used as
However, the alert reader will note that the junction to ambient thermal
resistances of the two SOIC package options is essentially the same
even though one is clearly thermally superior. How is this possible? The
reason is that each device is characterized on a worst case board, that
is, one that has minimum heatsinking on the board. Without measures
to disperse heat, the advantage of the exposed pad package is lost.
But the important point here is that each device merits its own thermal
rating based on its primary thermal path. The standard SOIC merits
intended, that is, mounted to a board and possibly attached to a
heatsink. Unfortunately, thermal performance depends strongly on
how the device is mounted and used, and there is a vast array of
possibilities. So there is no single set of test conditions for a universally
applicable characterization. In order to provide some characterization,
manufacturers specify thermal behavior for worst case mounting
conditions or conditions typical of the application. Users must relate
the test data and specifications to their particular thermal environment.
a junction-to-lead specification, whereas the exposed pad device
requires a junction-to-case rating. Junction-to-case ratings, therefore,
8 Freescale Semiconductor, Inc.Thermal Analysis of Semiconductor Systems
Loading...