154
IEEE TRANSACTIONS
ON COMPONENTS,
HYBRIDS, AND MANUFACTURING
TECHNOLOGY,
VOL. CHMT-7. NO. 1. MARCH 1984
Narrow Channel Forced Air Heat Sink
NORMAN GOLDBERG,
A&tract-The
heat transfer between the coolant and the heat sink
contributes a significant fraction of the thermal resistanceof a package. It
has been widely recognized that the heat transfer can be increased by
increasing the area of the .heat sink in contact with the coolant, and
therefore the use of fins is common. Howevei it has not been generally
recognized that for laminar flow in confined channels, the heat transfer
coefficient is inversely proportional to the width of the channel. Narrow
channel forced air heat sinks have been designed, built, and tested. Three
different channel widths, 5,10, and 25 mils, were investigated. The design
of the sinks permit integrated circuits @C’s) on l/2 in centers and printed
circuit (PC) boards on 1 in centers. The measured values of individual heat
sinks with 30 Vmin air flow are 5.5,3.7, and 3.4”C/W for 25,10, and i mil
channel widths, respectively. These values are in good agreement with
calculated values. A 16 chip package with chips on l/2 in centers was
assembled utilizing 10 mil channel width heat sinks. A plenum fitted over
the sinks supplied air to each of the sinks from a single source. The
measured values of thermal resistanceof the four center dies were between
5.3 and 5.9”C/W. If the chips are mounted directly on the sink instead of
on the alumina substrate, the thermal resistance would be reduced by
about 2”C/W.
SENIOR MEMBER,
IEEE
over ambient of the cooled device per unit of power dissipated.
In our package the inte:grated circuit is mounted face up on a
ceramic subs&ate, and the hkat sink is mounted at the: sam,e
position on the other side of the substrate as shown in Fig. 1.l.t
is tionvenient to consider the thermal resistance of the heat sinks
as three resistances in series as described by Tuckerman and
Pease [3] : econd,the resistance due to thermal conduction from
the circuits through the silicon, the silicon to substrate bond,
the ceramic substrate, ,the substrate to heat sink bond, and the
lead-in to the sink; 8,,,,,, the convective resistance, primarily
determined by the heat transfer coefficient between the heat
sink and the coolant fluid; and oheat,the resistance due to the
heating of the fluid as it absorbs energy while flowing through
the sink.
econdis given by
t
8 =-
‘Ond kA
INTRODUCTION
HE AVAILABILITY
of high performance very dense very
large-scale integration (VLSI) will result in significant
improvement in the performance of computer systems. However, in order to fully utilize VLSI, greatly improved heat
removal will be required. In the near future, we must be able to
package a 200 mil x 200 mil size chip that dissipates 10 W. It is
a challenge to cool such a chip even if it is isolated. An array of
these chips, closely packed with a center-to-center spacing of
one-half inch in order to reduce propagation delays, presents an
even more difficult problem. The overall thermal resistance of
the package for each individual chip must be less than 6”C/W to
keep the temperature rise over ambient to less than 60°C.
It is generally assumed that liquid cooling is required to
handle such high power densities [ 11; thefefore, liquid cooling
is generally being utilized in spite of an inherent aversion to
using a liquid within an electrical system because of the
potential damage to the circuits if a leak develops. For example, the IBM thermal conduction module, which is water
cooled, has a thermal resistance of 8.4”C/W [2]. This paper
describes a new compact air-cooled heat sink with the required
thermal resistance. These sinks have been designed, built, and
tested, and it has been demonstrated that they can handle 10 W
chips on l/2 in centers.
T
THEORY
The performance of a heat sink is usually characterized by its
thermal resistance, 0 = AT/P, i.e., the rise in temperature
Manuscript received August 15, 1983; revised November 21, 1983.
The author is with the Sperry Corporation,
P.O. BOX 500, MS ES-134, Blue
Bell, PA 19424.
where t is the thickness of the heat path, k is the thermal
conductivity of the heat path material, and A is the crosssectional area of the heat path. &-“d can be made small by
locating the sink close i:o the heat source and using material with
large thermal conductivity.
The average value of oheatis
1
oheat = -
2PCf
where p is the density of the fluid, c is its specific heat, andf is
the flow rate. &eatcan be reduced by using large flow rates;
8CO””will usually be the dominant component in a higher
performance sink:
eCO””= g
1
where h is the convective heat transfer coefficient and 11 is the
area of the sink in contact with the cooling fluid. It has been
generally recognized ihat this component can be reduced by
increasing the surface area, typically with fins. The importance
of increasing h, the convective- heat transfer coefficient has
received less attention..
The heat transfer coefficient can be calculated from
kf Nu
h=---D
where kf is the thermal conductivity of the fluid and D, the
equivalent diameter of the channel, is given by
D=
4 x flow area wetted perimeter .
0148-641 l/84/0300-0154$01 .OO 0 IEEE 1984
BLDBERG: NARROW CHANNEL
Fig. 1.
FORCED AIR HEAT SINK
Heat sinking mounting.
lr high aspect ratio channels D approximately equals twice
: channel width w. Nu, the Nusselt number, is a dimensions parameter which is essentially defined by the above
uation.
Tuckerman and Pease [3] pointed out that the only way to
:nificantly increase h is by decreasing D. They built a waterDied integral heat sink in a silicon integrated circuit and
monstrated that extremely high power densities circuits
uld be cooled in ‘that way. Our design for an air-cooled device
based on the same principle.
The value of Nu can be calculated exactly for certain
ometries with laminar flow. The flow will be laminar if the
:ynolds number is less than 2100. If the flow is laminar and
ly developed, i.e., invariant along the direction of flow, it
n be shown [41 that Nu = NIL, which is independent of the
w velocity and depends only on the geometry of the channel.
the entrance region where the temperature and velocity vary
th in the direction of the flow and in the direction perpendicuto the flow, the Nusselt number is larger.
[f we assume that Nu has its minimum asymptotic value, the
imates will be conservative; h can be approximated by
kf Nu,
h=-----
2w
Fig. 2.
pointed out in [3], this result is consistent with an intuitive
ldel in which the heat is conducted from the wall to the
idle of the channel and is then carried away by the fluid
w. The smaller the value of w, the greater is the thermal
:dient and, therefore, the greater the heat removal. However
‘row channels increase the resistance to flow. The lower
lit for w is set by the availability of blowers with the required
ssure and flow.
w(1 + o!) w2(1+ CY)
8CO””= ___
=
2zhS2
kfNu,S2z
’
To account for the finite conductivity of the sink, the area is
reduced by a correction factor known as the fin efficiency [5].
The efficiency is given by
tanh N
77=
N
’
If S is much larger than the wall width, N can be approximated
by [31
(+&I”
where k, is the thermal conductivity of the wall. The value of z
is used to set N and thereby 7. For N = 1 the heat removal by the
tins is 76 percent of infinite length fins. For N=2, the heat
removal is 96 percent of infinite length fins. Typically N is set
to a value between 1 and 2. For N= N,,,
z=N,
k,,nw2
~2
~
kf
Nu,
*
(
>
Including the effect of finite conductivity, then
DESIGN
?ig. 2 is a diagram of a narrow channel forced air heat sink.
: square surface which is in contact with the substrate has
esof length S. The channels are of width w and height z, and
wall width is QW.
Theaddition of the narrow channels to the sink multinlv
--r -, the
----
channel forced air heat sink.
area S2 by a factor of 2z/ w( 1 + a) if the heat transfer at the top
and bottom of the channel is neglected. If one assumes infinite
conductivity for the sink material and fully developed laminar
flow, then
N=z (c)“2zz
*
Narrow
0
W(Q
l/2 + a _ l/2)
conv = S2y&(kwkf
Nu,)
1’2
where v. is the fin efficiency for N= NO. For a fixed w, econvis
minimized by (Y = 1; i.e., wall width equal to channel width.
The mean velocity of flow in high aspect ratio channels is u
156
IEEE TRANSACTIONS
ON COMPONENTS.
HYBRIDS, AND MANUFACTURING
TECHNOLOGY,
TABLE I
VALUES FOR HEAT SINKS
= w 2P/ 12~s where P is the pressure and p is the viscosity of
the fluid [3]. The flow rate is
j-z---=
US.2
1 +a
W
(mils)
I/2
w 3PNo
~
12/.&Y”2+cY-“2)
.
Solving for the pressure we have
(a
1
Pressure
(” of H20)
Reynolds
Number
5
4.68
179
10
1.17
358
25
0.19
984
Bconv
(“C/w)
-
0.67
1.60
7.43
l/2+,-1/2),
f = 30 l/mitt,
Since the pressure to achieve the required flow at a fixed w is
also minimized by CY= 1, wall width equal to the channel
width, is the optimum choice.
As a starting point in our design we set
cheat=-=
VOL. CHMT-7, NO. 1, MARC.H 1984
z = 0.5 in.
CALCULATED
TABLE II
VALUES OF THERMAL
RESISTANCE
w(mils)
5
1“C/W.
2PCf
l
l
Withthevalueforairofp
= 1.13 x 10V3g/cm3andc = 1.01
W*s/g”C, f 1; 30 l/min = 1 CFM. The choice of w, which
then fixed the pressure drop through the sink, was guided by the
availability of commercial blowers. A reasonable value for the
pressure is a few inches of water.
In order to evaluate the narrow channel concept, sinks were
made with S = 0.25 in (0.635 cm) and z = 0.5 in (1.27 cm).
Three different values of w were used: 0.005 in (0.0127 cm),
0.010 in (0.0254 cm), and 0.025 in (0.0635 cm). Wall widths
were equal to channel widths. The sinks were made of copper
(k, = 3.91 W/cm”(J). The air fluid fixed k, = 2.85 x 10 -4
W/cm”C and p = 1.99 x 10 -4 g/cm*s.
The sinks were fabricated from flat plate of the appropriate
thickness cut to size. Shims of the same plate at the two ends of
the sink fixed the channel width equal to the wall width. The
ends were bonded by heli-arc welding.
literslmin.)
0 (heat) = -!2ocf (f =30
t
0 (conductivity)
= E
Silicon Chip, t = 0.020”
Alumina Substrate, t =0.030”
Two Bonds
Copper Sink Lead-in, t ~0.20”
Total
e (--C/W)
25
10
0.9
0.9
0.9
2.4
2.4
2.4
0.2
1.7
0.2
0.3 ,
l
0 (convection)
0.7
1.6
7.4
l
f3 (total)
4.0
4.9
10.7
T I”‘3
A flow of 30 l/min with our geometry makes oheat = 0.9”U
W. This flow rate corresponds to an average velocity of 1240
cm/s. The required pressure, the Reynolds number, Re = 2pv
W/P, and Lnv were calculated for the three sinks and are
displayed in Table I. A value of eight was used for Nu, for our
high aspect ratio channels [6]. It should be noted that the
Reynolds numbers are consistent with laminar flow (2100), and
that the required pressures are moderate and readily available.
8 cond is the sum of the thermal resistance through 20 mils of
silicon, 0.2”C/W, through the 30 mil alumina substrate,
1.7”C/W, through the copper lead-in of the sink, 0.3”C/W,
and the two bonds which’ were estimated to be 0.1 “C/W each
resulting in a total of 2.4 “C/W. These calculations are summarized in Table II.
RESULTS
The thermal resistance measurement set-up is shown in Fig.
1. A high-power chip eutectically bonded to a chip carrier was
used as the heat source and temperature sensor. The forward
voltage drop across a previously calibrated diode with fixed
current is a reliable measure of the surface temperature of the
chip. The heat sink was soldered to the other surface of the chip
carrier. The temperature of the chip was measured for powers
from 0 to 10 W with an air flow of 30 l/min, and the results for a
5, 10, and 25 mil channel width sink are shown in Fig. 3.
AIR FLOW = 30 LiterslMin
0
2
4
6
8
IO
POWER (Watts)
Fig. 3.
Temperature
versus power for narrow channel heat sinks with air flow
of 30 l/min.
Measurements were also made at a constant power of 8 W
while varying the air flow rate. Since oheatvaries inverse1.ywith
the flow rate while econdand econvshould be independent of flow
rate, a plot of temperature versus the reciprocal of the flow
should be a straight line. The results are plotted for the 5 m.il
and 10 mil sinks in Fig. 4. The linearity of the data confirms
that the Nusselt number is constant and therefore the temperature profile is effectively fully developed. From these plots,
one can extrapolate to infinite flow and determine 8 for oheat =
0. The results for all the measurements and calculations for 19
are collected in Table III. The measured value of 13are less than
the calculated value in each case. This result is not unexpected
because the calculations assume that the heat is removed only
by the heat sink. In our single chip set-up a significant amount
of heat is removed by natural convection directly and via the
substrate to the ambient air.
q
#OLDBERG: NARROW CHANNEL
157
FORCED AIR HEAT SINK
AIR FLOW
(Liters
per Minute)
30
20
14
I
I
I
e (T/W)
70
Wc(mils)
65
lim f-m
5
2.0
10
2.5
“y/E----‘/
0
.02
.04
l/AIR
Temperature
Fig. 4.
COMPARISON
B(‘CIW)
Calculated
(Liters
versus reciprocal
OF CALCULATED
w
(mils)
FLOW
POWER
= 8 WATTS
.06
.06
.lO
per Minute)-’
of air flow at constant power of 8 W.
TABLE III
AND MEASUREDVALUES
RESISTANCE
(f =30Umin)
Measured
@C/W)
Calculated
OFTHERMAL
(lim f - 00 )
Measured
5
4.0
3.4
3.1
2.0
10
4.9
3.7
25
10.7
5.5
4.0
-
2.5
-
As a more realistic test of the heat sink, 16 chips were
ounted on l/2 in centers on a 2 in x 2 in alumina substrate in
4 ~4 array. A heat sink with 10 mil channels was mounted
rectly under each chip. An air plenum which supplied air
>rna single blower to each of the sinks fits over the sinks. Fig.
rhows two views of the plenum in position.
A fine mesh screen covered the entrance to each sink. The
ded flow resistance of the screen tended to equalize the air
VWthrough each sink. Measurements confirmed that the air
IWthrough each sink was equal to within 10 percent. Fig. 6 is
)hotogiaph of the sink. side of the substrate before the top of
: plenum was attached. Fig. 7 is an overall photograph of the
ip side of the package. To insure low resistance bonds, the
ips were eutectically bonded and the sinks were soldered to
: substrate.
Two test substrates were fabricated. One had only a single
el of metallization so that the power dissipated in each chip
lid not be individually controlled. Also it was necessary to
asure the temperature of the chips with a less precise
rared thermal gun because it was not possible to separately
Lessthe diodes on the chip. ThS! air flow through each sink
s 30 Umin. Our main interest was in the four chips in the
lter of the substrate. The temperature, the power, and the
rmal resistance for each of the four center sites are shown in
. 8. The value of the thermal resistance was generally larger
n for the individually mounted chips as expected but in good
eement with the calculated value of 4.9 ‘C/W.
‘he other test substrate had multilayer metallization which
mitted individual control of the power to each chip as well as
of the more precise diode for temperature measurements.
AIR ENTRANCE
PLENUM
INK
C
SUB&RATE
(a)
AIR PLENUM
AIR SUPPLY
PIPE
\
Fig. 5. (aj Cross-sectional
(b)
view of air plenum mounted on substrate. (b) Plan
view of air plenum mounted on substrate with air supply pipe.
The multilayers added 28 pm of glass dielectric and some gold
to the thermal path. The gold added negligible thermal resistante, but the glass increased Bcond
by about 1.5 “C/W. Measurements were made with 10 W dissipated by each chip and an air
flow
of 30 Urnin through each sink. The temperature and the
158
Fig. 6.
Fig. 7.
Photograph
Photograph
of sink side of test packige.
of chip side of test package with cabling.
OLDBERG: NARROW CHANNEL
159
FORCED AIR HEAT SINK
WIRE
OR TAPE
L---T/+
Fig. 10.
:. 8. Temperature, power, and thermal resistance of four center chips with
air flow of 30 Urnin each on substrate with single level of metalization.
I-
2”
-
Configuration
SINK
for low Bcond.
have a cut-out through which the sink with its pre-mounted and
pretested chip would be inserted. A flange attached to the sink
would provide a stop for inserting the sink as well as a surface
to bond the sink to the substrate.
CONCLUSION
85.7 “C
8.8“CIW
0
CHIP
-
\
86.0 “C
5.9 “C/W
ALUMINA
SUBSTRATE
In summary, a new style compact forced air heat sink has
been designed, fabricated, and tested. It has been shown that
narrow channel heat sinks using air as the cooling fluid can keep
the temperature rise of 10 W chips on l/2 in centers below
60°C (6”C/W). Furthermore, by eliminating the substrate
from the thermal path, thermal resistance can be reduced to
about 3 “C/W.
83.4”C
5.6”CIW
:. 9. Temperature and thermal resistance for four center chips with air flow
‘30 l/min and 10 W power each on substrate with multilayer metalization.
:rmal resistance for the four center chips are shown in Fig. 9.
le values are larger than those made on the substrate with a
oglelevel of metallization because of the extra glass dielectric
m, but the results are in good agreement with the calculated
lues of 6.4”ClW.
A significant improvement in the heat sink can be realized by
:reasing econd.This could be done by removing the substrate
Irn the thermal path. If the chip was bonded directly to the
k, ticondwould be reduced to about 0.6”C/W, 0.2”C for the
.con, 0.1 “C for the bond and 0.3 “C/W for the copper lead-in
%e channels, reducing the calculated value of 19to 3.1 “C/W.
;. 10 shows how that could be done. The substrate would
ACKNOWLEDGMENT
I wish to thank Richard Melcher for the careful assembly of
the test substrates and for assistance in collecting the data, and
Carl Langheim for fabricating thk narrow channel heat sinks. I
am also indebted to Joseph Tomei for his continuous support.
REFERENCES
[l]
T. S. Steele, “Terminal
and cooling
requirements
for LSI packages,”
IEEE Trans. Components, Hybrids, Manufact. Technol., vol.
[2]
[3]
[4]
[5]
[6]
CHMT4,
no. 2, pp. 187-191, June 1981.
S. Oktay and H. C. Kammerer, “A conduction-cooled
module for high
performance LSI devices,” IBM J. Res. Develop., vol. 26, no. 1, pp.
55-60, Jan. 1982.
D. B. Tuckerman and R. F. W. Pease, “High performance heat sinking
for VLSI,”
IEEEEIectron Dev. Letters, vol. EDL-2, no. 5, pp. 126129, May 1981.
W. M. Kays, Convective Heat and Mass Transfer. New York:
McGraw-Hill,
1958.
M. Necate Ozisik, Basic Heat Transfer. New York: McGraw-Hill,
1977.
J. G. Knudson and D. L. Katz, Fluid Dynamics and Heat Transfer.
New York: McGraw-Hill,
1958.