DirectFET Thermal Model and Rating Calculator

Application Note AN-1059
DirectFET® Technology
Thermal Model and Rating Calculator
Table of Contents
Page
Introduction............................................................ 2
Equivalent circuits ................................................. 3
Thermal resistance values ............................... 3
Analysis ............................................................ 3
Rating Calculator ................................................... 5
Notes on use .................................................... 5
Rating Calculator inputs ................................... 5
Rating Calculator outputs................................. 5
Types of cooling ............................................... 6
Validation of results ............................................... 6
Model................................................................ 6
Values .............................................................. 7
Thermal resistance values .................................... 8
With equipment chassis or case cooling .......... 8
With no additional DirectFET can cooling ........ 8
Example of use of Rating Calculator................ 9
Summary ............................................................... 9
Appendix A .......................................................... 10
Equation 1 ...................................................... 10
Equation 2a .................................................... 10
Equation 2b .................................................... 10
Appendix B .......................................................... 10
Appendix C .......................................................... 11
Appendix D .......................................................... 11
DirectFET’s thermal properties are fundamentally different from industry-standard, encapsulated power
semiconductors. Its construction encourages heat to disperse from the die in opposite directions,
cooling through both the substrate pad connections (source and gate) and the metal can on top of the
device. The can-to-ambient thermal interface can be maximized by fitting a heat sink.
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AN-1059
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Thermal Model and Rating Calculator
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Introduction
Encapsulated power semiconductors in packages
such as the TO-220 or D-Pak are fairly easy to model
thermally, using only one thermal parameter. The
assumption is that most of the power generated in the
silicon chip travels in one direction. The assumption is
reasonable because the silicon chip is soldered (or
epoxy-attached) to a lead frame that provides the
main cooling path to the environment. Heat flow in the
opposite direction is limited because the die is
insulated with a layer of encapsulation ‘plastic’. The
dissipation of heat from the lead-frame into the
environment is often enhanced by fitting a heat sink.
DirectFET® is fundamentally different. Its construction
encourages heat to disperse from the die in opposite
directions, cooling through both the substrate pad
connections (source and gate) and the metal can on
top of the device. The can-to-ambient thermal
interface can be maximized by fitting a heat sink. The
design of the can also provides a parallel or shunt
thermal path from the can to substrate.
Figure 1 shows the direction of heat flow from a
DirectFET device and an approximate thermal
equivalent circuit for such a device in use.
Measuring the thermal resistance of a DirectFET
device inevitably produces a composite result based
on the temperatures measured at the junction, can or
substrate using the total power dissipated by the
silicon. While this gives the effective thermal
resistance under particular cooling conditions, it does
not give a value that applies under other conditions.
When determining a value for dual-sided cooling
conditions, the most significant factors are the thermal
resistance of the heat sink and substrate. To assess
these correctly, the power flow through each path
must be known. This requires a method of predicting
the proportion of power flow through the paths. The
temperature of the can and the substrate will change
with different levels of can and substrate cooling.
Indeed, it is this feature of DirectFET construction –
which enables cooling from both sides of the silicon
die – that gives the devices their particular benefits.
This application note provides an easy method for
assessing the proportion of power flow from each of a
DirectFET device’s surfaces, so that the appropriate
thermal resistance figures are used and the true rating
is accurately determined.
Tambient
Rth chassis / heat sink
T chassis / heat sink
Rth gap filler
Tcan
Rth junction-can
heat sink
interface material
can heat sink
junction
Tjunction
Rth can-substrate
(can)
Rth junction-substrate
(source)
can (drain)
Tsubstrate
Rth substrate
substrate
gate pad
source pads
Figure 1a Directions of heat flow (indicated by the red arrows)
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Rth heat sink
(substrate attachment,
if present)
Tambient
Figure 1b Approximate thermal equivalent circuit
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Thermal Model and Rating Calculator
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Equivalent circuits
Outline
Can size
R1
R2
R3
Non-PbF devices
Thermal resistance values
With the thermal modeling software available today, it
is possible to predict temperatures at any chosen point
in an entire cooling system. However, many circuit
designers do not have access to such software nor
time to spend on numerous lengthy computations for
each possible set of cooling arrangements.
With this in mind, International Rectifier provides
equivalent thermal resistance values for DirectFET
devices. These can be entered into an online Rating
Calculator that rapidly returns the maximum permitted
power generation by the device in any combination of
substrate and can cooling conditions.
SH
small
1.39
3.47
0.98
SQ
small
1.14
3.47
0.98
ST
small
1.08
2.58
0.98
MN
medium
0.43
0.97
0.80
1.10
MQ
medium
0.99
2.60
MT
medium
0.33
0.97
0.80
MX
medium
0.50
1.50
0.80
PbF devices
Figure 2 shows how the three parameters (R1, R2 and
R3) relate to the physical construction of a DirectFET
device. Their values are derived using a combination
of the dimensions and conductivity of the materials
used in constructing the device.
SH
small
2.96
3.48
0.98
SJ
small
2.05
2.22
0.98
SQ
small
2.43
3.48
0.98
ST
small
2.36
2.58
0.98
MN
medium
0.91
0.97
0.80
MP
medium
2.26
2.58
1.54
MQ
medium
2.07
2.58
1.54
MT
medium
0.71
0.97
0.80
MU
medium
1.91
2.58
1.54
MX
medium
1.04
1.18
0.98
MZ
medium
1.62
0.97
0.80
S1
small
4.18
3.43
1.53
S2
small
2.35
4.55
1.60
Analysis
SB
small
2.68
2.47
1.05
The analysis is carried out on the equivalent thermal
circuit of the DirectFET device (the green circuit in
Figure 3). It also includes the additional cooling
resistance paths to the can and to the substrate (the
black circuits above and below it in Figure 3).
M2
medium
2.09
1.03
1.33
M4
medium
1.27
0.68
0.80
L4
large
1.06
0.56
1.06
L6
large
0.80
0.44
0.56
L8
large
0.65
0.25
0.49
The table at the right shows these equivalent thermal
resistance values for the current range of DirectFET
devices (both lead and lead-free variants).
Thermal resistance RC represents the total thermal
resistance of the path from the surface of the can to
the ambient cooling medium. This must include any
interface resistances resulting from isolation or
mounting materials fitted in this path.
Two options for ratings then become available:
ƒ
For applications where conduction and switching
losses are both significant (such as DC/DC buck
circuits and other high-frequency circuits), the
expression may be arranged to give the maximum
permitted power rating. This is shown in Appendix
A as Equation 2a.
ƒ
For low-frequency applications (say lower than
30–50 kHz), only conduction losses need be
considered and the expression may be arranged
to give the maximum permitted current rating.
This is shown in Appendix A as Equation 2b.
Thermal resistance RS represents the total thermal
resistance of the path from the bottom of the
DirectFET device through the substrate. This may
include a substrate heat sink.
Using the information shown in Figure 3, International
Rectifier has generated an equation that satisfies all
the various power flow constraints. This is shown in
Appendix A as Equation 1. In summary:
TJ = fn (W, TA, α, β, δ, γ, ς, Φ)
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Note: Some International Rectifier data sheets provide more
information about switching power losses. For example,
PD-94574A for the IRF6607 DirectFET:
www.irf.com/product-info/datasheets/data/irf6607.pdf
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thermal
conductive compound
R3
R2
R1
solder
silicon
Rth can-substrate
R3
Tcan
R2
R3
R1
Tsubstrate
gate
footprint
source footprint
Rth junction-can
can
Rth junction-source
mean heat flux
path through can
can footprint
x4 (drain)
source footprint
drain
footprint
Figure 2 Physical realization of parameters R1, R2 and R3
Tambient
TA
W is the total
junction power
W5
Rth can-ambient
W1 through W5
are the individual
branch powers
RC
Tcan
TC
W2
Rth junction-can
R2
W3
W
Rth can-substrate
(can)
Tjunction
TJ
R3
Rth junctionsubstrate (source)
W1
R1
Tsubstrate
Ts
Rth substrate-ambient
RS
W4
Tambient
W=W1+W2
W4=W1-W3
W5=W3+W2
W3=(Ts-Tc)/R3
W4=(Ts-TA)/RS
W=(TC-TA)/RC
basic branch
expressions
TA
Figure 3 Thermal equivalent circuit with basic assumptions
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Thermal Model and Rating Calculator
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Tjunction
Rating Calculator inputs
Rating Calculator
The DirectFET Rating Calculator is available at:
www.irf.com/product-info/hexfet/thermalcalc.html
The Rating Calculator applies the equations from
Appendix A. It uses a simple tabular entry format to
facilitate fast and accurate calculations.
Notes on use
ƒ
For high-frequency applications, use the value
returned for maximum permitted power.
ƒ
For low-frequency applications (where switching
losses are not significant), enter a worst-case
value for RDS(on) and use the value returned for
maximum permitted current.
ƒ
ƒ
Obtain values for the thermal resistance of the
substrate from the manufacturer’s material data
but make sure it is correct for the device footprint,
board thickness and power rating.
Obtain values for the thermal resistance of the
heat sink from the manufacturer’s curves – include
the mounting interface as appropriate.
ƒ
Appendix B gives guidance for applications where
the can is cooled through the chassis or case.
ƒ
Appendix C gives guidance for small and medium
can devices that have no additional heat sinking.
ƒ
Where fan or forced cooling is used, thermal
resistance tends not to vary with power. This
makes it easier to use the Rating Calculator.
ƒ
Where thermal resistance varies considerably with
power, estimate the relative power flow through
the can and substrate. Run the Rating Calculator
and use the result to review the resulting power
flow, checking if thermal resistance values are still
correct for those power levels. If not, adjust the
inputs, repeat the calculation and check the power
flow again. Repeat until the power flows through
the substrate and heat sink align with their thermal
resistances for those flows. Appendix D
demonstrates this procedure.
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Enter:
ƒ
R1, R2 and R3 for the appropriate DirectFET
device from the table on page 3
ƒ
Rth substrate-ambient for the appropriate cooling
conditions and power (estimate the power flows
through this path for the first iteration)
ƒ
Rth heat sink if one is used, taking into account
the cooling conditions and power flow (estimate
the power flows through this path for the first
iteration) – if no heat sink is fitted to the can, enter
the figures for Rth can-ambient from Appendix C.
ƒ
Ambient temperature of the environment
ƒ
Maximum permitted junction temperature
ƒ
The hot RDS(on) of the device – enter this only if a
low-frequency current rating is required.
Rating Calculator outputs
The Rating Calculator returns maximum current or
maximum power. If Rth substrate-ambient or Rth canambient varies significantly with power, adjust the
values to reflect the actual power returned by the
Rating Calculator. Refer to the last of the notes on
using the Rating Calculator (left) and to Appendix D.
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Types of cooling
As stated, one of the main difficulties in making this
calculation is that the thermal resistance of a path
varies with the power passing through it (Figure 4).
This is most relevant for natural-air cooling systems
(represented by the black curve) and least for forcedair cooling systems (represented by the blue curve).
Validation of results
Model
The basic expressions in Equations 2a and 2b
(Appendix A), used for the Rating Calculator, were
verified for mathematical integrity using SIMetrix.
Developed by SIMetrix Technologies (formerly known
as Catena Software Ltd), this mixed-mode circuit
simulation package includes a SPICE simulator.
Thermal resistance
Analogous electrical parameters were used to
represent thermal parameters:
increasing
air flow
0 LMPS
5 LMPS
ƒ
Resistance for Rth
ƒ
Voltage for temperature
ƒ
Current for power
This simulation can be used to demonstrate identical
power flow distributions in DirectFET devices. Figure 5
shows the analogous electrical circuit.
Power
W5 (I5)
Figure 4 Typical thermal resistance characteristics
Rth can-ambient
RC
W2 (I2)
970 m
R2
800 m
W total (Iin)
R3
W3 (I3)
330 m
W1 (I1)
Rth substrate-ambient
R4
RS
Vin
(TJ)
0 V (ambient)
W4 (I4)
0 V (ambient)
Figure 5 Analogous electrical circuit
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Values
Using FloTHERM thermal analysis software from
Mentor Graphics (formerly known as the Flomerics
Group), detailed analyses were generated for
individual elements in the thermal system:
ƒ
Heat sink (with interface compound)
ƒ
Substrate + device
(with insulation on device side – not shown here)
With DirectFET devices mounted on token boards and
placed in a wind tunnel, supportive measurements
were taken with (Figure 6) and without a heat sink.
Figure 6 Device and heat sink on a token board
For a given amount of power generated by the device
under prescribed cooling conditions, effective junction
temperatures were measured using the body diode as
the temperature-sensitive parameter.
ƒ
Substrate + device (with heat sink fitted).
For a flow of 2 linear metres per second (LMPS), the
thermal resistance of these elements was:
ƒ
Heat sink: 40°C/W
ƒ
Device + substrate: 95°C/W
ƒ
Device + substrate + heat sink: 30°C/W
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It was possible to confirm the maximum permitted
power rating for the chosen conditions, within limits of
experimental accuracy, by transferring the following
information to the Rating Calculator:
ƒ
Junction temperature
ƒ
Ambient temperature
ƒ
Expected thermal resistance of the heat sink
(or Rth can-ambient if no heat sink is used).
For any thermal prediction of this sort, the accuracy of
the result depends on the accuracy of the thermal
resistances used for the cooling attachments. That is,
it depends on the figures entered for the substrate to
ambient and for the heat sink (or for the can to
ambient if no heat sink is used).
Appendices B and C suggest thermal resistances for
small and medium can DirectFET devices used with
chassis cooling and no additional heat sink. The usual
approach for obtaining figures for other external
cooling attachments is to consult manufacturers’ data.
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The simulation also shows that aluminum is more
effective than steel for chassis or case cooling. This is
a result of its higher thermal conductivity.
Thermal resistance values
With equipment chassis or case cooling
For popular substrate materials such as FR-4,
polyimide and IMS, suppliers provide thermal
properties. Use these to estimate the thermal
resistance of specific device footprints and board
thicknesses.
With no additional DirectFET can cooling
Many proprietary gap fillers (pads and compounds),
are now reinforced with substances such as boron
nitride. These deliver significant improvements in
thermal conductivity compared with materials of only a
few years ago. There are many suppliers, including
Dow Corning, Bergquist and Thermagon.
Where discrete heat sinks are fitted to DirectFET
devices, the supplier will provide the thermal
resistance. In many applications, however, it is
beneficial and economically sensible to use the
chassis or case to cool both sides of the devices.
With chassis or case cooling, it is more difficult to
estimate the thermal resistance of the path from can to
ambient. As a guide, Appendix B contains the results
of a simulated thermal analysis of nine DirectFET
devices (IRF6603) in a 3 x 3 matrix.
As the can on the device is also the drain contact, it
usually needs to be electrically insulated from the
cooling surface (Figure 6). The insulating pad or
compound also acts as a gap filler, compensating for
any dimensional inconsistencies between the mating
surfaces. The thermal resistance of the material used,
taking into account the area covered and thickness
applied, must be added to the figures in Appendix B.
The flows assumed for the circuit analysis (Figure 3)
show power flowing from the substrate to the can
through the shunting thermal resistance of the can
(R3). This implies that the substrate is hotter than the
can, which is usually true where additional cooling is
used (through heat sinks, chassis or case).
However, without additional cooling, the effective
thermal resistance of the path from the can to ambient
is usually much larger than that of the substrate. The
can then becomes hotter than the substrate, reversing
the power flow. The model automatically resolves this
and heat is transferred from the can to the substrate.
Understanding the implications of this change in
power flow direction is important when designing
circuits for some applications. For example, where
DirectFET devices are located on a substrate with
other components that are dissipating large amounts
of power, applying additional cooling to the cans
provides another channel for power dissipation and
avoids over-burdening the substrate.
Appendix C predicts the probable thermal resistance
in these circumstances. Enter these values into the
Rating Calculator. This is illustrated in the following
example, in the scenario without a can heat sink.
The simulation in Appendix B predicts that the can of
the centrally located device will reach the highest
temperature. This is to be expected because this
device is subjected to the greatest mutual heating
effects from other heat sources.
gap filler – pad or compound
chassis
substrate
Figure 6 Case or chassis cooled DirectFET devices
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Summary
Example of use of Rating Calculator
Using the Rating Calculator for IRF6603 DirectFET
devices mounted on polyimide token boards gives the
following results. Two scenarios are shown, one with
and one without a heat sink fitted to the can.
Can heat sink
Set conditions
Units
With
Without
Max ambient temperature
°C
40
40
Max junction temperature
°C
125
125
Air flow rate
LMPS
2
2
Parameter R1
°C/W
0.33
0.33
Parameter R2
°C/W
0.97
0.97
Parameter R3
°C/W
0.8
0.8
Rth substrate-ambient @ 2 LMPS
(previously determined)
°C/W
95
95
Rth heat sink (including 2°C/W for
mounting/attachment compound)
°C/W
40
—
Rth can-ambient (Appendix C)
°C/W
—
175
RDS(on) for IRF6603 @ 125°C
Vgs=10 V
Ω
4.59e
Max permitted power
W
2.98
1.37
Max permitted current
(for low-frequency operation)
A
25.49
17.31
Substrate power
W
0.89
0.89
Heat sink power
W
2.09
0.48
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-3
4.59e
The thermal performance of DirectFET devices can be
satisfactorily represented by three internal thermal
resistances: R1, R2 and R3.
By entering these parameters into an online Rating
Calculator, with the properties of the thermal paths
through the substrate and can, the maximum
permitted dissipated power can be calculated. For lowfrequency applications, the Rating Calculator also
gives the maximum operating current.
The Rating Calculator enables ratings to be rapidly
assessed and provides an insight into the power flows
within the DirectFET device. Using attachments with
appropriate thermal resistances is essential to achieve
the required cooling, whether through the substrate or
the can. Understanding the proportion of power that
flows through the different paths is essential to select
the optimum combination of can or substrate cooling.
The Rating Calculator is, therefore, a useful aid in
making thermal management decisions for DirectFET
applications.
-3
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Appendix A
Appendix B
This simulation is based on a 3 x 3 matrix of IRF6603
medium can DirectFET devices fitted in an equipment
case with an effective air flow of about 0.5 LMPS (as
shown in Figure B.1).
Equation 1
TJ = (δ*W / (α + β - (δ (γ + ς )) / Φ) ) +TA
where:
α = R3 / (RS*R2)
Rth of each device (°C/W)
Can spacing
β = R3 / (R2*R3+RC*R3+RC*R2)
Case composition
5 mm
10 mm
20 mm
γ = R3 / (RS*R3+RS*R1+R1*R3)
Mild steel (1 mm)
47
38
30
Aluminum (1 mm)
20
17.5
14
ς = R3 / (RC*R1)
δ = (α / γ) – (β* RC*R1) / R3
Note: For small can DirectFET devices, multiply these
results by 2 to reflect the reduced contact area.
Φ = (γ*RS*R2)/R3 - (ς / β)
TJ is the maximum junction temperature
W is the maximum permitted power
metal chassis
or case
TA is the ambient temperature
Equation 2a
W = ((TJ –TA)* (α + β - (δ (γ + ς )) / Φ)) / (δ)
Equation 2b
Where all losses are considered conduction losses:
I = √ [ ((TJ –TA)* (α + β - (δ (γ + ς )) / Φ)) /
(δ * RDS(on) (@ TJ max) ]
where:
I is the low-frequency current rating
RDS(on) is the value at TJ max
substrate with
devices underneath
and cans against
the case or chassis
hottest device
Figure B.1 Devices fitted against the equipment case
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Appendix D
Figures C.1 and C.2 show can-to-ambient thermal
resistance curves for medium and small can
DirectFET devices with no additional heat sinks.
These were simulated devices where the heat flow is
channeled solely through the can surface. These
figures, intended for use in the Rating Calculator,
represent the effective Rth can-ambient only for the
power flow through the surface of the can.
For applications using natural-air cooling, use this
iterative procedure with the Rating Calculator.
DirectFET device:
IRF6603
Maximum ambient temperature: 40°C
Maximum junction temperature: 125°C
4.59 mΩ
RDS(on) @ Tj maximum:
100
500
90
400
300
200
100
0
0
1
0 LMPS
1 LMPS
2
2 LMPS
3
4
3 LMPS Power (W)
80
70
60
50
40
30
0
1
2
Rth substrate-ambient
Figure C.1 Rth can-ambient (medium can)
Thermal resistance (°C/W)
Consider a device mounted on a substrate and fitted
with a heat sink on its can (sample data in Figure D.1).
Thermal resistance (°C/W)
Thermal resistance (°C/W)
Appendix C
3
4
Rth heat sink
5
Power (W)
Figure D.1 Sample thermal resistance curves
First assume that power through the substrate is 1 W
and through the heat sink is twice that at 2 W.
800
Reading from the curves:
Rth substrate-ambient at 1 W = 95°C/W
Rth heat sink at 2 W = 55°C/W
600
400
Running the calculation with these inputs returns:
Substrate power = 0.89 W (96°C/W from the curve)
Heat sink power = 1.53 W (62°C/W from the curve)
200
0
0
1
0 LMPS
1 LMPS
2
2 LMPS
3
4
3 LMPS Power (W)
Figure C.2 Rth can-ambient (small can)
Adjust the inputs to match the curves more closely:
Leave Rth substrate at 95°C/W
Increase Rth heat sink to 57°C/W
Repeating the calculation with these inputs returns:
Substrate power = 0.89 W (96°C/W from the curve)
Heat sink power = 1.48 W (63°C/W from the curve)
Adjust the inputs again:
Leave Rth substrate at 96°C/W
Increase Rth heat sink to 65°C/W
Repeating the calculation with these inputs returns:
Substrate power = 0.88 W (96°C/W from the curve)
Heat sink power = 1.3 W (63°C/W from the curve)
The values entered for thermal resistance are now
very close to those supplied by the the manufacturer.
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