CHARACTERIZING JUNCTION-TO-CASE THERMAL RESISTANCE AND ITS IMPACT ON
END-USE APPLICATIONS
Jesse E. Galloway, Siddharth Bhopte, Cameron Nelson
Amkor Technology
1900 S. Price Rd.
Chandler, Arizona 85286
Email: jessg@amkor.com
ABSTRACT
High power packages require a low junction-to-case thermal
resistance (Theta jc) to achieve target junction temperatures.
Theta jc is a metric used to compare package-to-package
relative thermal performance. It is also used in two-resistor
models to predict thermal performance under system level
conditions. This study shows that the commonly used Theta jc
definition does not correctly track package junction
temperatures in actual end-use applications nor does it serve as
a reliable metric for comparing package-to-package
performance. When spreading resistance in the lid is taken
into account, the modified Theta jc definition overcomes some
of the shortfalls found with the standard Theta jc calculation.
Lastly, a simplified thermal interface resistance model is
presented as a more accurate alternative to the one resistor
Theta jc and the multi-resistor Delphi models.
dimensional conduction analysis to estimate the maximum
junction temperature expected during system operation.
θ JC =
(1)
P
The purpose of this paper is to demonstrate that thermal
analyses or thermal performance metrics based on Theta jc
data may lead to inaccurate prediction of the junction
temperature. Tacitly implied in the Theta jc definition is the
one-dimensional conduction assumption. One dimensional
conduction requires that the junction and case nodes be
isothermal. Neither the die nor the lid are isothermal.
Additional discussion on the limitations of the Theta jc
resistance is presented by Bar Cohen et al. [1].
Ta
θ sa
Ts
θ cs
KEY WORDS: Theta jc, TIM, FEA, experimental,
Tc
NOMENCLATURE
P
T
T j − Tc
θ jc
Power (W)
Temperature (C)
Tj
Figure 1. One-dimension heat flow.
Greek symbols
θ
Resistance (C/W)
Subscripts
||
Parallel
1D
One-dimensional
a
Ambient
J
Maximum junction
C
Case
s
Heat sink
INTRODUCTION
High power electronic packages rely on a low thermal
resistance path between the active surface of the die and the
case. The case is designed to spread the heat over a larger
area than the die. It may be a copper slug as in the case of an
exposed pad wire bond package or a large copper lid as in the
case of flip chip ball grid array (FCBGA) style package.
Theta jc, θjc, is the most common metric used to define the
junction to case thermal resistance, see equation (1). Package
vendors supply this metric on their component data sheets.
Thermal engineers often use Theta jc along with a one-
ANALYSIS OF HEAT FLOW PATHS
A package with a lower Theta jc should produce lower
junction temperature for the same TIM II and external heat
sink. This will not necessarily follow when the accepted
definition for Theta jc is employed. To illustrate this point, a
finite element model (FEA) of a flip chip ball grid array
(FCBGA) style package was analyzed. Figure 2 indicates that
heat flow is three-dimensional due to the lateral spreading in
lid and external heat sink. The majority of the heat (greater
that 90% for most packages with an external heat sink) flows
from the active side of the die, through the thermal interface
material at the first interface layer (TIM I) and into the lid.
Heat then flows through the TIM II layer into the external heat
sink.
TIM II
External Heat Sink
Lid
Figure 2. Heat flow paths in a FCBGA package.
TIM I
TIM II
spreading resistance was performed by dividing the package
and heat sink shown in Figure 3 into five concentric regions,
see Figure 5. Heat flow channels were determined as lines
drawn perpendicular to isotherms.
T (C)
The model used to predict heat flow paths in this study is
shown in Figure 3. The body was 45mm x 45mm with a
17.8mm x 17.8mm die. Heat (125W) was applied to the nodes
on the active die surface (bottom side). A fixed uniform heat
transfer coefficient (10,000W/mm2) was applied to the top
surface of the cold plate to simulate the removal of heat from a
water cooled cold plate with supply water at 25C. Four
different conditions were simulated: (1) copper cold plate with
a 0.5mm copper lid, (2) copper cold plate with a 1.0mm
copper lid, (3) aluminum cold plate with a 0.5mm copper lid,
(4) aluminum cold plate with a 1.0mm copper lid.
70
65
60
55
50
45
40
35
30
25
1.0 mm Lid
Die
0
5
10
15
70
Die
Lid
Adhesive
Substrate
Solder
Balls
T (C)
Mother
Board
50
45
40
35
30
25
0
The temperature profiles predicted at a cross-section through
the center of the package are shown for the 1.0mm lid package
in Figure 4(a) and for the 0.5mm lid in Figure 4(b). In both
cases the external heat sink has a copper base. Contrary to
expectations, the Theta jc for the 0.5mm lid is lower than the
1.0mm lid. However the junction temperature for the 0.5mm
lid package was approximately 6C higher compared to the
1.0mm lid package. Thicker lids spread heat away from the
die yielding more uniform temperatures at the die and lid. The
0.5mm lid has a 19C temperature variation in a region above
the die whereas the 1.0mm lid has 15C temperature variation.
Both packages have similar Theta jc. However, further away
from the die, the affect of a thinner lid impedes the conduction
of heat creating greater temperature range in the lid. A
summary of the Theta jc and Theta ja resistances for the cases
previously discussed are provided in Table 1. The highest
total resistance, θja, was predicted for the 0.5mm lid with the
aluminum heat sink.
5
(C/W)
0.069
0.065
0.068
0.34
0.30
0.37
0.31
0.17
0.15
0.18
0.15
* Calculated using equation (2)
One cannot expect Theta jc, which is based on two
temperatures taken at the center of the package, to properly
represent the three-dimensional conduction resistance in the
die, TIM I layer and lid. A more detailed investigation of the
10
15
20
25
r (mm)
4(b)
0.5mm Lid
1.0mm Lid
4(c)
Figure 4(a) 1.0mm lid, Theta jc = 0.069C/W, 4(b) 0.5mm lid,
Theta jc = 0.066C/W, 4(c) heat flow contour plots.
Table 1. Theta jc and Theta ja summary.
Cold Plate
Cu
Al
Lid Thick (mm)
0.50
1.0
0.5
1.0
θ jc
HtSnk
55
Figure 3. FEA model geometry.
*
Lid
60
Lid
θ ja (C/W)
25
0.5mm Lid
65
0.066
20
4(a)
Die
θ jc (C/W)
HtSnk
r (mm)
TIM I
Cold Plate
Lid
Figure 5(a)
1
2
4
3
5
HTSNK
TIM II
Lid
TIM I
T1
T2
Q1
Q2
Die
T3
Q3
T4
Q4
T5
Q5
5(b)
Figure 5(a) Temperature isotherms in die and 1.0mm thick lid.
5(b) Heat flow paths.
2.0
Cu HtSnk, 0.5mm Lid
Cu HtSnk, 1.0mm Lid
Theta jc|Local (C/W)
1.8
1.6
Al HtSnk, 0.5mm Lid
Al HtSnk, 1.0mm Lid
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1
2
3
4
5
6(a)
2.0
Cu HtSnk, 0.5mm Lid
Cu HtSnk, 1.0mm Lid
1.8
1.6
Theta cs (C/W)
The heat flow from each region (1-5) was modeled by a
resistor between the die and top surface of the cold plate. The
local resistance was calculated as the difference between the
average die and heat sink temperatures, for the respective heat
channel zone, divided by one fifth of the total power. The size
of each concentric zone on the lid was determined iteratively
by selecting a radius for the five zones that equally divided the
total power. Local Theta jc resistance, calculated using
averaged die and lid temperatures for each zone, are plotted in
Figure 6(a). Theta jc increases slightly moving from the
center towards the edge of the die. There is a bigger
difference in local Theta jc for the fifth zone. The 1.0mm lid
produced lower local Theta jc values. The next resistor in the
one-dimensional heat flow path is the case-to-sink resistance,
Theta cs, see Figure 6(b). It includes the spreading resistance
in the cold plate. The 1.0mm lid with copper cold plate
provides the lowest Theta cs for all cases simulated. The last
resistor in the one-dimensional path is the sink-to-ambient.
This resistance is inversely proportional to the area of the
concentric circle for the zone. The impact of the thicker lid
increases the spread area at the cold plate top surface, see
Figure 6(c). Lastly, summing up the individual contributions
of Theta jc, Theta cs and Theta ca yields the local Theta ja for
each zone. As expected the thicker lid produces the lowest
Theta ja, see Figure 6(d).
Al HtSnk, 0.5mm Lid
Al HtSnk, 1.0mm Lid
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1
2
3
4
5
6(b)
2.0
Cu HtSnk, 0.5mm Lid
Cu HtSnk, 1.0mm Lid
1.8
1.6
Al HtSnk, 0.5mm Lid
Al HtSnk, 1.0mm Lid
Theta sa (C/W)
There are more precise methods for predicting the spreading
resistance in lids, see for example Lee [2]. However, the point
made here is that the current method for predicting or
measuring Theta jc may be improved by taking into account
spreading resistance in the lid. The approached outlined in
this section would be difficult to implement into an
experimental system due to the difficulty of measuring case
temperature at multiple locations.
1.4
1.2
1.0
simulations.
The modified Theta jc reported here,
θ jc
,
properly accounts for the lid thickness affects as shown in
Table 2. Unlike the one point case temperature method for
computing Theta jc, the averaged case temperature method
using equation (2) predicts a lower average Theta jc,
θ jc
, as
the lid thickness is increased from 0.5mm to 1.0mm.
θ jc =
1
T j − 0.5 * (Tc ,center + Tc ,edge )
P
[
]
0.8
0.6
0.4
0.2
0.0
1
2
3
4
5
6(c)
2.0
Cu HtSnk, 0.5mm Lid
Cu HtSnk, 1.0mm Lid
1.8
Theta ja|Local (C/W)
A more simplified approach in characterizing the spreading
resistance is possible experimentally by measuring the case
temperature at two different locations, at the center and at a
second location at the edge of the lid, see Figure (7). The case
temperature could then be taken as an average between the
center and at the off center location, see equation (2). A
similar method was suggested by Liang [3] for calculating an
equivalent Theta jc, called Gamma jc, based on numerical
Al HtSnk, 0.5mm Lid
Al HtSnk, 1.0mm Lid
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
(2)
0.0
1
2
3
4
5
6(d)
Figure 6(a). Local junction-to-case resistance, 6(b) local caseto-sink resistance, 6(c) local sink-to-ambient resistance, 6(d)
local sink to ambient resistance.
Tc, center
Tc, edge
the resistance is expected to be lower in the center. Wei et al.
[7] provided a model that related the effective conductivity as
a function of strain. Over a 30% increase in resistance was
measured at the die edges compared to the center
Figure 7. Two location case temperature method.
EXPERIMENTAL METHODS USED TO EXTRACT
TIM PROPERTIES
In the previous section, attention was focused on developing a
definition for Theta jc that could be reported as a single
number in a package characterization data sheet. The
traditional Theta jc definition, equation (1), does not account
for the effect of lid thickness. Measuring the case temperature
at a center and edge locations provides a means for tracking
lid thickness effects. A Delphi style resistor network [4] can
do a better job in accounting for lid spreading affects but is
limited by having a single isothermal junction temperature.
Yet there are other parameters that also impact Theta jc that
should be included in detailed simulations. These include
variations in bond line thickness (BLT) as a function of
location (thicker in the corners), warpage of lid, power maps
and variations in material properties due to aging or dry
affects along the outer regions of the TIM I. A one resistor
model cannot account for these effects.
There are two distinctly different needs for reporting Theta jc.
One is a requirement for supplying a number in
characterization data sheets. The second need is to provide
accurate thermal models used in system level simulations.
One should not limit modeling approaches by the need for
supplying a number in a data sheets. As a consequence in the
second part of this study, the modeling approach will not focus
on the overall Theta jc but rather developing localized
resistance model for TIM I materials using experimental data
and a FEA model. The spreading resistance in silicon and the
copper lid may be modeled easily using FEA software since
their properties are known. It is the uncertainty in TIM
resistance and BLT that creates difficulties in characterizing
FCBGA packages. When it comes to predicting junction
temperatures for high power die with detailed power maps, a
simplified resistor model will not suffice. A method is given
in this section for extracting the TIM resistance. Once known,
it may be deployed in a simplified FEA model to predict the
junction temperature in system level simulations.
TIMs used in FCBGA applications tend to be made from a
low modulus matrix (e.g. silicone) filled with a higher
conductivity material such as silver, alumina or aluminum.
Since the die backside is curved (due to the mismatch between
the thermal expansion coefficient of silicon and substrate) the
TIM must undergo a tensile strain on edges of the die and a
compressive strain in the center Wakharkar et al. [5]. A
highly magnified view of a TIM I material is shown in Figure
8. The BLT plays a strong role in the determining the TIM I
resistance Yan et al. [6]. In the center region filler-to-filler
contact is more predominate than along the die edges. Hence
Copper Lid
TIM I
Silicon Die
Figure 8. cross section view (100X) of TIM I layer.
Experimental measurements made from a 45mm body
FCBGA, with 7.6mm, 12.7mm and 17.8mm thermal test, were
used to extract the thermal resistance of TIM I layers. Each
package was instrumented with heaters and temperature
sensors evenly distributed across the die active surface. Die
temperatures along with the case temperature (measured at the
center of the top surface of the lid) were used to provide
boundary conditions for a FEA model shown in Figure 3. The
heat transfer coefficient applied to the top surface of the cold
plate is adjusted to produce the same case temperature as
measured for the same input power to the heaters. The
thermal interface material local resistance (i.e. for a given x,y
location) is adjusted to produce the same junction temperature
as measured. Thus the local resistance may be mapped based
on experimental measurements and FEA simulations.
The thermal test die was manufactured as a tile array having a
unit cell of 2.54mm x 2.54mm. Each cell has 4 different
diodes. the 17.8mm x 17.8mm die is formed as a 7x7 array.
Hence a total of 196 temperature sensors are available to read
temperatures across the die.
Power is supplied at two
resistors in each cell as shown by the heat flux boundary
condition in Figure 9(a). A boundary condition of 125W was
applied to the 17.8mm x 17.8mm die with the cold plate set to
a temperature of 25C. The case temperature was measured at
the center of the lid. Experimental die temperature data was
reported as a temperature difference (difference between local
die temperature and case temperature) as a function of x and y
location, see Figure 9(b). Using the FEA model, predicted
temperatures were forced to match experimental temperatures
by adjusting the local TIM I resistance. Temperature
difference predictions for the same conditions are shown in
Figure 9(c).
A comparison of the model with experimental data for the
7.6mm, 12.7mm and 17.8mm die are shown in Figure 10. The
TIM I resistance model was able to accurately model the
experimentally measured temperature difference.
10
17.8mm die
8
Data
Simulation
6
Tj – Tc (C)
The variation of the resistance of the TIM I material is shown
in Figure 11. The lowest resistance is measured at the center
of the package corresponding to thinnest bond line. Towards
the edge of the package, the resistance increased due to an
increase in the bond line thickness.
4
2
0
-2
-4
-6
0
2
4
6
8
10
12
r (mm)
Figure 10(a)
10
12.7mm die
Figure 9(a)
Data
Simulation
8
Tj – Tc (C)
6
4
2
0
-2
-4
-6
0
2
4
6
8
10
12
r (mm)
Figure 10(b)
Figure 9(b)
10
7.6mm die
Data
8
Simulation
Tj – Tc (C)
6
4
2
0
-2
-4
-6
Figure 9(c)
0
2
4
6
8
10
12
r (mm)
Figure 9(a) Heat flux boundary conditions for a 17.8mm die.
9(b) Experimentally measured temperature difference.
9(c) FEA model predicted temperature difference.
Figure 10(c)
Figure 10. Experimental temperature difference compared to
FEA model. 10(a) 17.8mm die. 10(b) 12.7mm die. 10(c)
7.6mm die
APPLYING TIM RESISTANCE DATA TO SYSTEM
LEVEL SIMULATIONS
Acknowledgments
The support of Amkor’s A4 and K4 labs are appreciated.
References
[1] Bar Cohen A., R. Eliasi and T. Elperin, “θjc
characterization of chip packages – Justifications,
limitations and future”, presented at the IEEE 5th annual
Semi-Therm Conference, 1989.
Summary & Conclusions
The traditional center point case temperature measurement
method was unable to distinguish the difference in Theta jc for
0.5mm and 1.0mm thick lid packages. An alternative
approach, based on an averaged case temperature model was
shown to accurately predict the dependency of Theta jc on lid
thickness.
A simplified model using a localized TIM I
resistance correlation was proposed to improve the accuracy
without greatly increasing the complexity of system level
thermal models.
[4] JESD 15-4, "DELPHI Compact Thermal Model
Guideline, October, 2008.
Theta TIM(r) / Theta TIM (r=0)
A system level model may be constructed from basic cuboids
or blocks consisting of silicon having the same length, width
and thickness as the production die, a detailed power map, a
TIM I resistance model as a function of (x,y) location, a lid of
the same length, width and thickness as the production lid and
a TIM II resistance model as a function of (x,y) location,
bump/underfill layer and a substrate. This model, shown in
Figure 12, represents a reduced order model of an actual
FCBGA making its implementation into system level models
manageable. Since the majority of heat flows through the lid,
the primary factor affecting its accuracy is the TIM I material
model.
1.6
1.5
[2] Lee. S, S. Song, V. Au and K.P. MoranASME/JSME
Thermal Engineering Conference: Volume 4, ASME
1995, pp. 199-206.
[3] Liang H.S., Discussion during JEDEC JESD51 thermal
standards meeting, San Jose, 2006.
[5] Wakharkar V, C. Matayabas, E. Lehman, R. Manepalli, M.
Renavikar, S. Jayaraman, and V. LeBonheur, “Materials
technologies for thermomechanical management of
organic packages”, Intel Technology Journal, Vol. 9,
Issue 4., pp. 309-323, 2005.
[6] Wei X., K. Marston and K. Sikka, “Thermal modeling for
warpage effects in organic packages”, Thermal and
Thermomechanical Phenomena in Electronic Systems,
2008. ITHERM 2008. 11th Intersociety Conference on
Thermal and Thermomechanical Phenomena in Electronic
Systems, pp. 310-314, 2008.
1.4
1.3
1.2
Die = 7.6mm
1.1
Die = 12.7mm
Die = 17.8mm
1.0
0
2
4
6
8
10 12 14 16
r (mm)
Figure 11. Variation of TIM resistance as a function of radius
from die center.
RTIMII (x,y)
RTIMI (x,y)
Power map
Figure 12. Thermal model for FCBGA TIM I and TIM II as
function of (x,y) coordinate.
[7] Yan Z., Z. Zhang and M. Touzelbaev, “Impact of
temperature-dependent die warpage on TIM1 thermal
resistance in field condition”. Semiconductor Thermal
Measurement and Management Symposium, pp. 285-291,
SEMI-THERM 2009.