In modern day highperformance machines, the burden of cooling
has shifted from the systems level to the component level [Tumm89].
This has been brought about by the increasing heat density at
the chip level as evident by the power dissipation numbers of
recent commercial highperformance microprocessors shown in Table
61. The heat flux of most of the highperformance microprocessors
is greater than 10 W/cm^{2}. The FRISC/G package dissipates
about 220 W with an average heat flux of 10.47 W/cm^{2}.
Devices 


 
DEC Alpha 21264  0.35m CMOS  15,200,000  
Intel Pentium Pro  0.35µm BiCMOS  5,500,000  
IBM PowerPC620  0.5m CMOS  6,900,000  
UltraSPARC II  0.35m CMOS  5,400,000  
PARISC 8000  0.5µm CMOS  3,900,000  
MIPS R10000  0.35µm CMOS  6,800,000  
Exponential X704  0.5µm BiCMOS  2,700,000  
FRISC/G  GaAs HBTs  301642 
The temperature that directly affects chip operation is the device junction temperature. This affects the chip reliability as it is inversely proportional to the product of the junction temperature and the time spent at that temperature [Serg95][Cohe94]. The functionality may vary too as the gate delay figures are typically valid only over a limited range of temperature. System noise margin is also compromised because current and voltage levels depend on temperature at the drivers and receivers [Poon95]. Power consumption in dense areas  such as register files, cache blocks, and ALU  leads to nonuniform temperature distribution giving rise to local hot spots. If one region operates at a much lower temperature than the other, voltage swings need to be adjusted to meet design margins. Therefore, squeezing maximum performance out of a microprocessor requires that all of the regions on the microprocessor be tuned to perform compatibly [Fitc94]. If these temperature variations are not known, the designs are made overconservative with a loss of performance. Therefore identification of thermal problems and thermal management becomes critical for highperformance circuits.
The gain of the HBT transistors goes down with an increase in temperature, unlike the homojunction bipolar transistors, resulting in a slowdown of the transistors [Wald92]. Interestingly, this is in conflict with the goal of higher integration unless the devices consume less power with a resulting lower total chip power. Otherwise, the temperature increase will offset the speed advantages gained through reduction of interconnection parasitics. The available HBT SPICE models show the opposite effect as they were modeled along the homojunction bipolar devices. Therefore, SPICE's internal temperature parameter, which is for silicon homojunction bipolar devices was not used in circuit simulations. Though SPICE device models were available at several temperatures, the most reliable and extensively tested model worked at only 25C. Therefore, all the designs were simulated with the 25C model and the important requirement on the cooling structure of the package was to keep the device junction temperature at 25C.
Silicon's thermal conductivity is about three times that of GaAs at room temperature and is inversely proportional to temperature increases while the thermal conductivity of GaAs decreases with temperature by a power of 1.25 [Roes88]. Therefore, hot spots are more likely to form on GaAs surfaces compared to Si at same power densities. Some researchers have devised CAD tools to layout GaAs ICs keeping the temperature effects in mind [Vold95]. Though, for designers working on highperformance designs, the result of such tools has not been an overriding factor [Fitc94]. Typically, a postprocessing step is used to make minor rearrangements for thermal integrity such as moving a big resistor away from a device. As we go to higher heat flux a thermal engineering approach is more suitable than simple post layout thermal management. Due to a reduced performance from process based penalties, FRISC/G designers couldn't apply power reduction techniques to the chips and most of the power reduction was obtained by powering down bidirectional pads between primary and secondary cache.
The powering down of pads brought the power dissipation of the package from a maximum of 270 W to 220 W with the maximum power density on a chip at 18 W/ cm^{2}. The effect of this power density on the device junction temperatures was modeled for different HBT devices to determine the worst case junction temperature rise. A layout guide was also generated to help in device level floorplanning and minimize the effect of mutual heating. The device temperature models were based on the methods available in literature [Smit91][Poul91] and were verified against measured results [Wald92].
Thermal management and design has always been an integral part of mainframes and supercomputer [Cohe93] designs. These machines are generally large and can afford elaborate cooling schemes. On the other hand, processors geared towards personal or workstation type computing applications can't afford the associated cost of a complex cooling system. Since FRISC/G was targeted towards a workstation type environment a demonstration aircool system was set as a goal. Therefore, the basic heat dissipation structure required the attachment of the package to a big enough aircooled heat sink. This became possible by the donation of a low thermal resistance heat sink, capable of dissipating 600 W  800 W with a low form factor, by IBM [Knic91].
Since the device junction temperature needed to be kept at 25C some form of cooling was still required. One of the most attractive option was the incorporation of semiconductor cooling elements in the form of thermoelectric coolers. This reduced the demands on the ambient cooling and provided fine control on the chip temperatures with low noise. The resulting cooling arrangement, along with the boundary conditions, has the structure shown in Figure 6.1. The rest of the chapter is organized as follows:
The processor dissipates power in the current switches used for
logic, emitter followers used for driving long onchip interconnections,
memory circuits used for temporary storage, and the driverreceiver
circuits used for offchip communication. Table 63 shows the
power requirements of all the chips. The computational core of
one decoder and four datapath chips dissipates close to 64 W.
The primary cache memory and the cache controllers spend an additional
205 W of power.
ID  
DP (4)  
CC (2)  
CR (16)  
Deskew  
Total 
ID  
DP  
CC  
CR  
DSK  
Total 
One major component of this dissipation in all the chips is the
power expended in the clock drivers, clock buffers, address drivers,
and the superbuffers used to drive large capacitances. The increased
capacitance required additional power in the already "hot"
drivers to maintain speed. The circuit blocks dissipating most
of the heat are shown in Table 64 with the pie distribution shown
in Figure 6.3.
L1L2 Drivers/Receivers  1024  50.5 
Core Drivers  312  13.0 
Regfile Blocks  4  8.0 
Cache RAM Blocks  64  128.0 
Tag RAM Blocks  4*  8.0 
Boundary Scan  23  21.0 
Core logic + receivers  39.44  
Core Drivers/Receivers  4.46  
Other (Terminators)  Counted with drivers/receivers above  
Total  272.4 
*only 12 columns out of a possible 32 are used here.
One important fact indicated in Table 64 is the power consumed
by the communication between the first and second level of cache.
This is due to more than a thousand signals for data exchange
between L1 and L2 cache sustaining a data rate of 8 GB/s between
L1 cache and CPU core. This type of bandwidth was essential to
keep a high throughput and the price was in terms of increased
power.
A decision was made not to implement L1  L2 interface on the demonstration prototype because they were not needed to run test programs. These driver/receiver pairs have been powered down on the present system saving 50 W in power dissipation. Currently, the proposed system dissipates about 220 W of power. The modified power dissipation numbers are given in Table 65 and the pie distribution is shown in Figure 6.4. Table 66 provides the area and power distribution numbers for the subpackages. The silicon  or GaAs efficiency of the complete package is
showing the high packing density achieved in this design. The
areas are given in mm^{2}.
Power [W]  Power Density [W/cm^{2}]  
ID  12.0  18.1  
DP (4)  13.0 x 4  16.4  
CC (2)  12.6 x 2  15.9  
CR (16)  8.0 x 16  12.5  
Deskew  4.0  11.1  
Total  221.2   
Module 


 
MCM1  48.0  10.42  
MCM2  120.2  10.38  
MCM3  53.0  10.89  
Total  221.2   
One major constraint on this design was the requirement to keep
the device junctions at room temperature. The measurement of peak
junction temperature is very difficult [Anho95] and the spice
models are mostly verified against an average junction temperature
[Wald92]. Since the area occupied by the devices is very small
compared to the area occupied by the wires the heat flux on the
surface of the chip is highly nonuniform as shown in Table 67.



 
Instruction Decoder  7358  66.12  
Datapath  9785  79.05  
Cache RAM  14300  64.4  
Cache Controller  13172  78.85  
4004* (10 µm)  2300  12  40%  
Pentium Pro** (0.35 µm)  5,500,000  195  7.25% 
*PMOS, **CMOS (device area approximated by 21 x [minimum design
rule].
Thus, an assumption of uniform heat flux on the surface, also
known as the parallel plate case [Poul91], can lead to an overoptimistic
thermal design. The nominal thickness of a GaAs wafer is about
25 mil (625 µm) and individual dies are thinned down to reduce
the thermal resistance of the die. The thermal resistance presented
by a die is not a strong function of its thickness as most of
the heat is generated in a very small area at the top of the die.
The heat is spread out from a device to cooler points on the surface
or back of the chip as shown in Figure 6.5.
The already low thermal conductivity of GaAs decreases  as much as 30% in the 25C125C range  leading to a self heating of the device [Smit91]. Similarly if two or more devices are located close together, their temperature fields interact and the temperature at any point is given by a superposition of the two fields. This effect, called proximity heating, can also increase the device temperature requiring even more cooling to operate the device at a given junction temperature.
Usually, the chip can work within a relatively wide temperature range unlike wire delays which have a rather narrow range available to maximize performance. Therefore the conventional tools are configured to minimize wire delays and the temperature problem is fixed later by external cooling [Fitc94]. This is not true everywhere in the circuit as the highly congested memory cells may need to tradeoff temperature with capacitance and speed for reliable operation especially if the device degrades at higher temperatures.
Determining temperature distribution on a chip is a complex problem,
akin to capacitance determination, due to multitude of nonregular
heat sources and conductive geometries. This removes the possibility
of getting any closed form analytical solution and all the methods
 finite element, finitedifference, seriessummation  use some
kind of empirical approximation due to the problem of using up
excessive memory. Next section describes the thermal models for
an HBT device which estimate maximum junction temperatures at
different power levels and at different die thicknesses.
The temperature is highly peaked where the power is dissipated in a transistor. As mentioned before, it is very difficult to measure the peak temperature because of its high nonuniformity. Most of the measured results and spice models are based on an average temperature [Wald92]. Therefore the device resistance needs to be modeled and verified against measured results. The basis of most of the modeling in the literature is the assumption that the heat flow problem can be separated from the calculation of the device's electrical characteristics. Thus, instead of solving 3 or more coupled differential equations  Poisson, current continuity, and heat flow  in 3D space extending to the back of the substrate we solve just the temperature problem in 3dimensions and weakly couple the two equations through the thermal impedance parameter, and use linear thermal coefficients for the electrical and physical parameters [Anho95].
The heat flow equation is
where k is the thermal conductivity of the medium in W/mK, T is the temperature at a point in K and P is the power generated per unit volume in W/m^{3}. This equation can be solved analytically or numerically but most of the methods assume a temperature independent thermal conductivity k [Poul91]. GaAs thermal conductivity depends on temperature and can be expressed as
[6. 2]
Various authors have provided different values of n varying from 0.85 to 1.41 [Anho95]. We assume n = 1.25 which gives a reasonable approximation [Blak82]. With n = 1.25 the thermal conductivity of GaAs at 300 K is 44 W/mK.
The temperature dependent conductivity of GaAs can be changed into a temperature independent variable by applying the Kirchoff's integral transformation [Smit86]. With this transformation, we can reduce equation (6.1) and equation (6.2) to a constant k equation by applying the following equation to obtain a pseudo temperature [Poul91].
[6. 3]
Here T_{0} is the chip backside temperature. The real temperature rise then can be obtained by using the following transformation after solving for :
[6. 4]
This reduces equation (6.1) to the familiar Poisson equation
[6. 5]
There are several methods in the literature to solve the Poisson equation and the most relevant one here is the solution for a point or hemispherical source on the surface of a semiinfinite medium. Assuming that the temperature field is distributed twodimensionally on the surface of the chip with no heat loss to either the back of the die or from the top surface, the temperature can be written as [Holm81]
[6. 6]
Here T is the temperature at a point away from a source, with power P, by a distance r. Superposition is used to calculate temperature rise due to multiple sources. On the surface of a die, equation (6.5) can be rewritten as
[6. 7]
where z is normal to the die surface. If we apply the boundary condition of a constant chip backside temperature, there are no known closed form solutions [Poul91]. This problem can be circumvented by using series summation methods such as the method of images [Daws93] where for every power source, another negative power source is placed at twice the chip thickness below the top source. This is followed by another positive source at three times the thickness of the chip, and so on, so that the temperature at any point on the surface due to the original source is given by the sum of a series of sources with alternating signs. This method suffers from an excessive computation requirement for a usually multisource chip and the series takes a long time to converge.
Other solution methods are programs employing finiteelement and
finitedifference calculations requiring a lot of memory and are
very slow for even simple structures. Floating points programs
such as QuickCAP [Rlc94] can also be applied to solve this equation
but a suitable version was not available. Instead, the following
approach was used to model the device temperature rise and other
effects readily and was shown to be conforming to measured results.
The approach is based on [Smit86] and [Poul91] and is a hybrid
of finiteelement and analytical solutions.
Step 1
Previous research [Anho95] has shown that most of the power in an HBT is dissipated below the emitter and the power density is nearly independent of the position beneath the emitter. This conforms to the fact that in an HBT the current and fields are vertical. Therefore, for the worst case analysis, the heat source can be approximated as a rectangular plate having the dimensions of an emitter stripe. The current density in the emitter can be as high as 1000A/mm^{2}.
Step 2
Equation (6.6) for a point source can be integrated in two dimensions to model a rectangular source. This results in the following expression from [Smit86] for the temperature at any point (x,y) with the source of dimension L x W centered at (x_{0},y_{0}).
[6. 8]
where,
, and
Step 3
Now add the effects of a finite chip thickness, dieattach layers and chip edges. [Poul91] determined that for chip thickness larger than the source dimensions the temperature distribution, with infinite thickness assumption, should be multiplied by e^{r/H} to obtain the temperature at the desired point. This factor was determined by comparing the results with finitedifference and seriessummation simulators. Therefore, the temperature at the point (x,y) can be given as
[6. 9]
The contribution due to the dieattach layers, such as epoxy for FRISC/G chips, can be determined using the above expression by assuming two layers with the same conductivity and is given from [Poul91] for the sake of completeness:
[6. 10]
where k_{1} and h_{1} refer to the chip conductivity and thickness and k_{2 }, h_{2} refer to the dieattach layer. This expression is valid when
[6. 11]
Step 4
Use superposition to add up the contribution of multiple sources.
Step 5
Model the standard devices used in FRISC/G and compare them with the published experimental results.
This algorithm was followed to develop a program in MATLAB [Math92],
a popular matrix based package, to simulate the temperature distribution
on top of HBT transistors with different size emitters. Table
68 and Figure 6.7 give the worst case power dissipation situations
in the FRISC/G design. The 3input AND gate shown in Figure 6.7
shows level2 and level3 transistors, Q4 and Q6 respectively,
dissipating 5.1 mW and 7.9 mW in the ON state. The other transistors
in the same pair still dissipate 2.8 mW maximum.







 
Level 1  1.15  0.5  0.575  1.2  1.38  2  2.3  1.15  2.0  2.3 
Level 2  1.4  0.5  0.7  1.2  1.68  2  2.8  5.1  2.0  5.1 
Level 3  1.4  0.5  0.7  1.2  1.68  2  2.8  7.9  2.0  7.9 
Figure 6.7: A 3input AND gate
displaying bias variations in level 1, level 2, and level 3 devices
at 2 mA.
All the devices used in the design were modeled for temperature
rise and the results were used to determine the maximum temperature
rise in the package. Current/area and total power dissipation
are two main indicators of the maximum temperature rise on a device.
These two numbers were higher on the transistors than on the schottky
diodes and the resistors. Therefore, the results for only the
transistors are presented in the following sections. There are
three types of gates in the design  high/medium/low power. These
devices consume  on an average  2.8 mW, 1.2 mW, and 0.7 mW respectively
as given is Table 68. In a real circuit these devices switch
between on and off states, and therefore their average power dissipation
is lower. Still, to get a fair idea about the maximum temperature
rise, 2.8 mW power dissipation was assumed in all the Q1 devices.
Q3 transistors are assumed to dissipate 12.6 mW (4.2 mW/finger).
The standard Q1, also known as Q1430, having an emitter stripe
area of 1.4 µm x 3.0 µm was simulated by varying device
power dissipation values at a chip thickness of 600 µm, and
was compared with the published measured results [Wald92]. This
device was analyzed to gain confidence in the device temperature
modeling due to the availability of experimental results. Figure
6.8 shows the comparison between the simulated and measured average
temperatures. The simulated average temperature, averaged over
the emitter area, matches the measured temperature within 10%.
Figure 6.8: Comparison of
modeled and measured [Wald92] average temperatures for a Q1 Device
(1.4 µm x 3.0 µm Emitter) at different device power
dissipation values (t_{die }= 600µm, t_{epoxy}
= 50µm).
Figure 6.9 and Figure 6.10 show the temperature distribution due to Q1430 from different angles. The average temperature rise on this device is 10C at the worst case power dissipation values encountered in the current designs. These transistors were later abandoned in favor of Q1217 transistors which are described in the next section.
Figure 6.9: Temperature
distribution for a Q1430 with P = 2.8 mW, t_{die }= 600
µm, t_{epoxy} = 50 µm, T_{peak} = 16.2C,
and T_{avg }= 9.48C.
Figure 6.10: 2D surface plot of temperature variation for
a Q1430 device with P = 2.8 mW, t_{die }= 600 µm,
t_{epoxy} = 50 µm, T_{peak} = 16.2C, and
T_{avg} = 9.48C.
Figure 6.11: Temperature distribution on top of the die surface
for a Q1217 device with P = 2.8 mW, t_{die }= 75 µm,
t_{epoxy }= 25 µm, T_{max }= 23.6C, and
T_{avg}
= 13.03C.
Q1217 device was designed to increase the switching speed of the
Q1430 device by increasing the current density in the emitter
at the same power. This was accomplished by reducing the emitter
size [Camp97]. This, in turn, increased the device temperature
rise from about 10C in Q1430 to 13.03C, as shown in Figure 6.11.
Figure 6.12 shows the lateral temperature distribution from the
center of the device. All the Q1430 devices have been replaced
by this device in the layouts. Therefore, the temperature rise
over this device at the maximum power dissipation conditions was
taken as an important design constraint for the thermal design
of the package.
Figure 6.12: Twodimensional
numerical simulation of the temperature rise on a Q1217 transistor
with distance from the center of the transistor with P = 2.8 mW,
t_{die }= 75 µm, T_{max }= 23.6C, and
T_{avg}
= 13.03C.
Another interesting problem was the variation in temperature with
respect to die thickness. Figure 6.13 shows the temperature increase
by varying device power and die thickness. The device temperature
goes up by at least 80C at a device power dissipation of 20 mW
and an almost zero thickness. The results of a simulation of temperature
rise at a constant device power of 2.8 mW and varying die thickness
are shown in Figure 6.14. Due to the small power generation area
the total thermal resistance of the device doesn't change too
much until the die is very thin. Therefore the die needs to be
lapped to at least 75 µm. Figure 6.15 shows the same kind
of temperature variation with different device power and thickness
values.
Figure 6.13: Variation of
surface temperature with device power and die thickness for Q1217
device.
Figure 6.14: Variation of temperature with die thickness at device power of 2.8 mW for a Q1217 transistor.
Figure 6.15: Temperature
variation with varying die thickness at different device powers
for a Q1217 transistor.
Figure 6.16: Temperature distribution for a Q1226 device with
P = 4.2 mW, t_{die }= 75 µm, t_{epoxy }=
25 µm, T_{peak }= 28.19C, T_{avg }= 16.05C.
Q1226 is a long emitter device used in the register files and cache blocks when the switching current required was a little more than 2 mA. The resulting temperature rise is higher than the temperature rise on a standard Q1217 device. Since this device has been used only in a few places it is not a cause of concern. The temperature peak on this device is sharper than the temperature peak on Q1217 due to an increase in emitter stripe area at the same current density. Since all these devices are used in pairs, one of them is off at any time and therefore the device has enough surrounding area so that it doesn't affect any other device's temperature field.
Figure 6.17: Q3 device with each finger dissipating 4.2 mW,
at I = 3 mA in each finger, with t_{die} = 600 µm,
T_{max} = 21.86C, and T_{avg}= 15.32C.
Q3 devices are three emitter devices which drive large loads. These devices have mostly been used in address drivers in memory or in offchip drivers requiring high power. These devices can sink a maximum of 12 mA of current but, on an average, have been used at 9 mA levels. The current density is lower than a Q1217 device and the temperature rise is slightly more than a standard Q1 device. Each finger carries 4.2 mW and the temperature distribution is shown in Figure 6.17 and Figure 6.18.
Figure 6.18: Variation of
average and peak temperatures for a Q3 transistor at a power level
of 4.2 mW/finger. The emitter stripe area is 1.2 µm x 5.0
µm.
Another important fact evident from Figure 6.17 is that local
heating effects do not interact even within the narrow confines
of a device where we see three individual peaks of equal heights.
Therefore, even in a dense device array such as register file
the effects of mutual heating are minimal and the junction temperature
depends, primarily, on the power dissipation of the device itself.
This effect is also more pronounced due to the lower thermal spreading
capability of GaAs material.
Simulations were done to find out the minimum distance to keep the temperature rise on either device under control. The FRISC/G chips employ differential logic with devices placed in pairs. This meant that one of the device is off and the other one is on at any time. For a worst case analysis two different current switches were placed very close with two ON devices put side by side. This was simulated at the maximum power levels by varying the distance between them. The results for Q1217, Q1226, and Q3 are shown in Figure 6.20, Figure 6.21, Figure 6.22, and Figure 6.23. The emitter pitch and minimum device distances are illustrated in Figure 6.19.
Figure 6.20: Design guide
for specifying the minimum distance between two Q1217 devices
of different current switches, with one device fixed at (0,0)
and the other moved along (X,0) with P = 2.8 mW, t_{die }=
75 µm.
Figure 6.21: Average junction
temperature increase with one Q1217 device fixed at (0,0) and
the other positioned at (x,y) with P = 2.8 mW, and t_{die}
= 75 µm.
Figure 6.22: Distance vs.
temperature rise for two Q1226 devices with t_{die }=
75 µm, t_{epoxy }= 25 µm, and P = 4.2 mW.
Figure 6.23: Distance vs. temperature rise for two Q3 devices, t_{die }= 75 µm, t_{epoxy }= 25 µm, and P=4.2 mW.
All the results presented so far were obtained by simulating one
or two devices in an isolated environment. The thermal environment
on a real chip is much more complex and a device can heat up due
to the addition of mutual heating effects from a number of devices
much farther away. Therefore, to simulate the worst case temperature
rise, an array of Q1217 devices was simulated with all the devices
dissipating power. Due to the slow speed of simulation, an array
size of 1.6 mm x 1.3 mm was simulated by replicating heat sources
at W_{x} and W_{y} pitch as shown in Figure 6.24.
This size was more than sufficient as mutual heating effects decrease
exponentially once the devices are further apart than the maximum
die thickness of 600 µm. There are few higher density placements
possible that are not legal due to design rule restrictions. The
simulation results are shown in Figure 6.25 with the temperature
peaking at the junctions.
The temperature increase over the chip due to mutual heating and field coupling is shown in Figure 6.26 and Figure 6.27. The big device array was simulated at different die thicknesses to determine the optimum thickness keeping in mind its handling. The 11 data points in Figure 6.28 took 240 hours to simulate and indicated a maximum temperature rise of 18.4C at a die thickness of 75 µm. This decided the die thickness and the maximum temperature difference across it to be considered in the thermal structure design. A summary of all the device level simulations and resulting thermal impedances is given in Table 69.
Device 


 
Q1430  1.4 x 3.0  16.2  9.48  3.30  
Q1217  1.2 x 1.7  23.6  13.03  12 µm  4.65 
Q1226  1.2 x 2.6  28.19  16.05  15 µm  5.73 
Q3  3 x 1.2 x 5.0  21.86  15.32  18 µm  5.47 
Consideration of all the factors discussed earlier results in the following design guide for managing the thermal integrity of a chip.
A standard thermoelectric cooler (TEC) consists of a number of thermocouples, made of n and p type legs  connected electrically in series, and thermally in parallel  between two ceramic plates. When a current is sent through it, a temperature difference is generated across its two face plates due to peltier effect [Gold95]. The TECs have been used successfully in applications where space and weight are at a premium such as space based electronics [Vand95]. Therefore, one way to increase the cooling ability of the FRISC/G package is by incorporating a TEC between the package and the heat sink. Peltier coolers increases the efficiency of a heat sink by increasing its base temperature. They are also very useful in dealing with the hot spot problem, effectively pumping the heat away from the center of a chip. For example, the register files are very hot and located almost in the center of the package and can use this heat pumping ability to cool the FRISC/G module.
Good thermoelectric materials are good electrical conductors but poor thermal conductors. They also possess large Seebeck coefficients. This is represented by a figure of merit called z given as
[6. 12]
where, is the Seebeck coefficient in V/C, is the electrical conductivity in mhos/m, k is the thermal conductivity in W/mK and the units of z are K^{1}. , , k, and z are strong functions of temperature. z determines the maximum temperature difference possible with a thermocouple made of a set of materials. The standard active material used for thermoelectric coolers is bismuth telluride based alloys and the theoretical maximum z which can be obtained with this material is in the range 3  4 K^{1} depending on the average temperature of operation [Gold86]. The maximum available in a commercial product is about 2.7 by several manufacturers. z varies with temperature and therefore, zT, where T is the absolute temperature, is also used as a figure of merit at a temperature T. At present the highest zT which can be obtained is close to 1 for SiGe at 1050 K as compared to the theoretical maximum possible of 1.75 at 1050K [Rowe95].
The efficiency of a thermoelectric converter depends upon the temperature difference across which it operates, the average temperature of operation, and its figure of merit. There are three main categories of materials which are popular for thermoelectric applications in different temperature ranges [Rowe95]. These are given in Table 610.
Commercial ratings are typically specified over vacuum operating conditions or under dry N_{2} atmosphere. Typically, the specifications are derated by upto 25% for operation under standard atmospheric conditions due to parasitic losses. Another specification of importance is the maximum temperature inside a TEC. The standard modules are assembled with solder that melts at 138C. Therefore, the maximum operating temperature should be well below this melting temperature. A good value is 80C. The TECs can be mounted using solder, adhesives, or compression methods. Large TECs are not recommended to be soldered to a heat sink as the stresses developed across the thermocouples due to the temperature difference across their hot and cold surfaces may crack them.
Material  Figure of Merit Ranking  Temperature range 
Bismuth Telluride and its alloys  1  450 K (max) 
Lead Telluride based alloys  2  1000 K 
Silicon germanium  3  1300 K 
There are five types of effects taking place inside a TEC peltier, seebeck, thomson, joule, and fourier. Peltier, seebeck, and thomson effects are reversible but not the joule heating and fourier heat conduction. Therefore, a thermoelectric cooler rejects more heat on the hot side than it can absorb on the cold side. This puts a limit on the amount of possible cooling depending on the heat dissipation capacity on the hot side. Peltier effect is proportional to the current while joule heating is proportional to the square of current. Therefore above an optimum current value, joule heating effect dominates over the peltier cooling effect and the device starts losing its efficiency. Since one requirement of this design was to keep it aircooled with the available heatsinks it was necessary to find a cooler solution within a 600 W range.
The best commercially available thermoelectric material in the temperature range of 120C to 230C is a pseudobinary alloy of bismuth, tellurium, selenium, and antimony,  (Bi,Sb)_{2}(Te,Se)_{3}  also, referred to as bismuth telluride [Marl95]. The highest reported figure of merit is about 4x10^{3} K^{1 }for this material [Seel72] though the commercially available devices have a figure of merit of about 2.67x10^{3} K^{1}. All the good thermoelectric materials, such as bismuth telluride, are semiconductors and a thermocouple can be obtained by joining a ptype and an ntype element. When a direct current is passed from the n to the p element, cooling takes place at the cold junction, while reversing the current direction generates heat at the same junction. The normal temperature range of operation of FRISC/G is well within the range of bismuth telluride, and therefore, parameters of this material were used in the design equations described in this section.
The following equations are based on [Krau83][Gold95][Marl95]
to illustrate the theory used in determining the cooler specifications
and have been reformulated to incorporate the factors employed
by commercial manufacturers. Figure 6.29 shows the schematic of
a TEC with only one thermocouple. The two legs of the thermocouple
are made of a ptype element, with resistivity _{p}, thermal
conductivity k_{p}, and Seebeck coefficient _{p},
and an ntype element, with resistivity _{n}, thermal
conductivity k_{n}, and Seebeck coefficient _{n}.
The area and length of the p and ntype elements are A_{p},
L_{p}, and A_{n}, L_{n} respectively.
Assuming T_{h} and T_{c} as the hot and cold junction temperatures of the thermocouple we can define T_{ave} and T as and, [6. 13]
Geometric factor, G, of these thermoelectric element is defined as
[6. 14]
The overall resistance, thermal conductance, and Seebeck coefficient of the thermocouple is given as
[6. 15]
[6. 16]
and, [6. 17]
The figureofmerit (FOM) of this thermocouple can now be defined as
[6. 18]
whereas z was the FOM for a material. Given a material, the highest value of Z is desired for maximum performance and it reaches that value when the denominator, KR, in the previous equation is minimized. KR is minimized when [6. 19]
Due to the flat nature of the top and bottom surface of a TEC
L_{p} = L_{n}. In this temperature range and k
are also comparable for both pand ntype materials and therefore
A_{p}=A_{n} [Gold95]. This also makes
G_{p}=G_{n}.
Therefore, p and n type legs can now be described with a single
set of parameters and will not be distinguished in the equations.
The new Z is given by, [6. 20]
When a current I is sent through the couple, it develops a voltage across the couple which is equal to the sum of the Seebeck voltages and the ohmic drop in the couple, i.e., [6. 21]
The power supplied to the couple is or, [6. 22]
The heat absorbed at the cold junction is reduced by two sources  Joule heat and the fourier heat. The net heat absorbed at the cold junction is then equal to the peltier heat at the cold junction minus the sum of resistive heat loss (assumed half of total resistive loss at each junction) and the heat conducted from the hot junction to the cold junction. This is given as [6. 23]or, [6. 24]
The total heat rejected by the couple on the hot side is [6. 25]
The coefficient of performance (COP), , of the couple is defined as the ratio of the heat withdrawn to the applied power. Hence, [6. 26]
can be maximized by applying the optimum current I_{0}. Differentiating with respect to I_{0} and equating it to zero we get the following I_{0} [6. 27]
Thus, the optimum current through a couple for a given average temperature and temperature difference depends solely on its bulk material properties ( and Z) and its geometrical properties (G). The coefficient of performance at the optimum current can be simplified to [6. 28]
The goal is to minimize total heat rejected on the hot side for a given q_{C}, T, and area. For a given material, maximizing G maximizes the optimum current and satisfies the minimum heat rejection constraints. Currently, couples with a range of G values are available from commercial manufacturers such as MELCOR Corporation [Eem95] and the maximum G available from MELCOR is 1.179. The problem in increasing G is the low yields in getting bigger area and shorter length pellets. Anything shorter or bigger also requires a high current source which can be impractical to obtain at such a low voltage.
The commercial modules are specified by four temperature dependent
parameters  I_{max}, V_{max}, T_{max},
and Q_{cmax}. These parameters are always specified at
a hot side temperature, T_{h}, of 25C. I_{max}/G
is unaffected by T_{h} and is about 5x10^{3}
A/m. The parameters of the couples made by MELCOR and other manufacturers
are given in Table 612 and Table 612.
Parameter  Minimum  Maximum 
Size  1.8 mm x 3.4 mm  62 mm x 62 mm 
H  2.45 mm  5.8 mm 
Q_{cmax}  0.2 W  125 W 
I_{max}  0.8 A  60 A 
V_{max}  0.4 V  15.4 V 
N  4  127 
T_{max}  67C  
G  0.016  1.179 
Surface Finish  Lapped  1 mil 
Item  Value (T = 296K) 
_{n}  2x10^{4} V/C 
_{p}  2x10^{4} V/C 
_{n}  1.0x10^{3 cm} 
_{p}  1.0x10^{3 cm} 
K_{n}  1.5x10^{2} W/cm.K 
K_{p}  1.5x10^{2} W/cm.K 
Z  2.67x10^{3} K^{1} 
The TECs with a maximum G of 1.179 are available with a surface area of 55 mm x 55 mm and contains 31 couples. Four of these TEC can be mounted on top of the heat sink which has a mounting area of 12.75 cm x 12.75 cm. Figure 6.30 shows an engineering drawing of this TEC with relevant dimensions and parameters.
Figure 6.30: CP 53106L from
MELCOR with I_{max }= 60 A, Q_{max} = 125 W,
V_{max} = 3.75 V, T_{max }= 67C, and number of
couples N = 31.
Table 612 gives the material parameters at 296 K. The temperature dependent variation in the parameters is given by the equations below as specified by MELCOR Corporation.(T_{ave}) = ( 22224.0 + 930.6 T_{ave } 0.9905 T_{ave}^{2 }) x 10^{9} V/C [6. 29](T_{ave}) = ( 5112.0 + 163.4 T_{ave }+ 0.6279 T_{ave}^{2 }) x 10^{8} cm [6. 30]k(T_{ave}) = ( 62605.0  277.7 T_{ave }+ 0.4131 T_{ave}^{2 }) x 10^{6} W/cm.K [6. 31]
To take the heat sink and the contact resistance into account,
T can be substituted by [6. 32]
This makes the equation for q_{c} iterative as the hot plate temperature depends on the temperature rise of the heat sink which in turn depends on the heat rejected by the cooler. Therefore, the TEC equations were analyzed independently of the heat sink resistance, for the amount of cooling possible with a given cooler.
All the equations provided above were input into a spreadsheet
with the parameters of the chosen TEC  CP 53106L. From the
initial modeling of the device and package thermal resistance,
the temperature rise of the junction relative to the TEC cold
face was about 25C. This suggested the temperature range at the
TEC cold face (Tc) to be 0C  10C to keep the device junction
(Tj) in the 25C  35C range. The temperature of the hot face (Th)
depended on the resistance of the external heat sink and the resistance
of the bond between the heat sink and the cooler. Since Th was
still unknown, the total amount of heat rejected for different
values of (TcTh) was calculated. The plots for three different
cold side values  in the 0C10C range  are shown in Figure 6.31.
The plots have a parabolic shape and show that for every delta
T value there are two possible values of the input current or
power. The cooler is run at the minimum value of the two currents
to minimize the rejected heat. The left half of the plot is detailed
in Figure 6.32. These values are further given in Table 613 for
calculation purposes. Shaded rows in Table 613 provide a few
operating points for cooler operation keeping in mind the cooling
required for the package.
Figure 6.31: Plot of delta T vs. heat rejected at cold side temperature T_{c }= 0C, 5C, and 10C, and input heat Qc =220 W.
Figure 6.32: Delta T vs.
heat rejected at cold side temperature Tc = 0C, 5C, and 10 C,
and input heat Qc = 220 W.




0  
5  
10  
15  
20  
25  
30  
35  
40  
45 
The heat sink [Knic91] is rated at 600 W capacity at 150 CFM air flow at room temperature with a thermal resistance of 0.041 °C/W. This can be bumped to 700 W750 W by increasing the air flow and/or lowering the ambient temperature. It has a top mounting area of 127.5 mm x 127.5 mm of aluminum and a fin area of 1m^{2}. The full assembly has a plenum and a blower to pull air through the heat sink. Thus, the maximum cooling possible with the selected thermoelectric cooler, keeping the possible heat dissipation capacity of the heat sink in mind, is about 35C when the cooler rejects about 725 W. The actual operation point will depend on the ambient temperature and the total resistance from cooler hot side to ambient air and is determined later.
Several things can be done to increase performance of these coolers. Normally, they are made with alumina face plates. To increase the thermal spreading capability of the face plates and lower the overall resistance, other options are aluminum nitride, and beryllia plates. These devices need DC power for operation. Linear or switching power supplies are available for these applications. The power supplies should have a low ripple present at the power supply output. MELCOR recommends limiting this ripple to less than 10% to contain the performance loss less than 1%. One fact to note in this design is the inadequacy of a multistage cooler. Multistage units can improve the coefficient of performance but they need more surface area on the hot side which was not possible in this case. Multistage cooling is useful for achieving larger temperature differences. Another idea is to use a TEC as a heat spreader by assembling elements with different values of G with the higher values of G in the center where most of the heat is being absorbed and lower values of G in the outer areas where little heat is being absorbed.
The major heat conduction path is vertically downward in the package, from the back side of the chips, as shown in Figure 6.33. There is negligible power conducted from the top of the chip through the polyimide and copper wires to the ambient and will be ignored for the purpose of making conservative design decisions. A possible scheme of assembling this package is illustrated in Figure 6.34 with the thermal interfaces between different blocks shown in bold lines.
This arrangement shows a first level assembly of chips on three
separate substrates and placement of the combined module on a
heat spreader. The heat spreader spreads the heat on top of a
2x2 thermoelectric cooler array mounted on top of a heat sink.
The problem is lowering the interfacial thermal resistance and
matching the thermal coefficients of expansion across different
interfaces. The constraint of maintaining the repair/rework capability
of the modules and matching the coefficients of expansion removed
the possibility of soldering at all the interfaces. The design
matrix for dieattach is given in Table 614.
Die Attach  Thermal Conductivity  Rework  Comments 
Epoxy  Low  Difficult  Compliant 
Thermoplastics  Low  Yes  Compliant 
Solder  High  No 

Substrate  Thermal Conductivity [W/m·K]  TCE
[10^{6}/C]  Sizes Available
 
Alumina (96%)  20  6.8  4 x 4 x 0.3  
AlN  250  4.3  4 x 4 x 0.3  
AlSiC  160  6.59  4 x 4 x 0.3  
Diamond  1200  23  4 x 4 x 1 mm 
The heat from the AlN substrate is spread on top of the thermoelectric cooler array using a heat spreader. The substrate needs to be placed on top of this spreader using a reworkable interface. The thermoelectric cooler array is mounted on top of Al heat sink using a reworkable and pliant material. Selection of this material is described later in the section on thermal calculation. Thus, the resistance to the heat flow comprises of the thermal resistance offered by the chip, epoxy, shims, epoxy, AlN, thermal interface, heat spreader, thermal interface, thermoelectric cooler, thermal interface, and the heatsink. The selection of the heat spreader and this interface material is done in the next section.
The thermoelectric cooler array requires a uniform loading on
its top face. This is accomplished by placing a heat spreader
between the package and the cooler to spread the heat out on all
sides of the package. Threedimensional modeling is required for
determining this spreading resistance. In case of simple geometries
a good correlation can be obtained on the basis of spreading angles.
The spreading resistance increases with increasing thermal conductivity
as shown in Figure 6.35 [Kuhl92]. As shown in Figure 6.36, the
heat dissipated by the package is spread out using a heat spreader
with a maximum base dimensions equal to the area of the cooler.
The spreading angles for common substrate materials and the dimension
of some of the possible heat spreaders with the resulting temperature
difference across them are given in Table 616.






 
Al  220  23  56  39  26.3  
AlN  250  4.3  62  39  20.7  
Cu  398  17  70  39  14.2 
The temporary nature of the testing process required a thermal
interface which would provide high thermal conductivity, good
compliance to both microscopic and macroscopic irregularities,
ease of application, and reworkability. Some options with their
advantages and disadvantages are given in Table 617.
Thermal Interface  Advantages  Disadvantages 
Solder 


Epoxy 


Thermal Grease 


Thermal pads 


Commercially available thermal pads were looked at as a possible
medium as their thermal conductivity is as good as thermal grease
and they are able to conform to irregular surfaces. Using these
pads also removes the problem of handling greases. These pads
are characterized better by their thermal impedance values. In
addition to a material's ability to conduct heat, this quantity
also denotes the material's ability to conform to irregular surfaces
minimizing contact resistance. Some of the commonly available
materials are given in Table 618. Tpli205 (a trademark of Thermagon)
is a conformable elastomeric material and provides a low thermal
impedance at a clamping pressure of 10 psi. Since it doesn't need
any phase changing temperature for best operation it was selected
over other thermal pads.
Name 

 
KonDux™ (Aavid)  graphite based  
Softface™ (Bergquist)  supplied on a polyester film; can be transferred using hot stamping  
HiFlow™ (Bergquist)  filled polymer;dries at 27C;flows at 43C;low pressure operation  
QPad3™ (Bergquist)  pressure sensitive, graphite imbedded in a polymer matrix,  
Thermflow T705™
(Chomerics) 
 thin, dry film; softens at 50C;  
Tpli205™ (Thermagon)  0.125 mm thickness; elastomer 
The schematic of the whole thermal structure is given in Figure 6.37 with the thermal resistance values in Table 619. Instruction decoder chip is assumed for chip level resistor calculations due to it being the chip with highest power density. Onedimensional heat flow is assumed through the thin epoxy, shim, and the substrate layers. Aluminum is assumed as a heat spreader. The module is covered with thermal insulation to stop a feedback of heat from the cooler's hot plate to cold plate and transfer of heat from ambient to the module.




 
R1(Chip+Epoxy)*  100  7.6x8.7  18.4 *  1.53  
R2 (Silvar Shim)  250  7.6x8.7  0.18  0.024  
R3 (Epoxy:841LMI)  25  7.6x8.7  1.15  0.096  
R4 (AlN)  895  2101  0.37  0.0017  
R5 (Tpli205)  125  2101  4.75  0.0215  
R6 (Heat Spreader)  26300  12100  3.70  0.0166  
R7 (ESP7359)**  100  12100  0.157  0.00071  
Total (Heat input = 221.2 W)  28.7 
*  From device level simulations **ESP7359  Diamond Epoxy from AI Technology.
Therefore, the temperature rise on top of the cooler is 28.7 C.
The heat sink is attached to the cooler with ESP7359 (diamond
filled epoxy) as shown in Figure 6.38. The desired degrees of
freedom are the ability to independently vary both the temperature
difference across the cooler plates and the ambient temperature.
Fixing the temperature difference across the cooler plates demands
a particular ambient temperature due to a finite resistance between
the cooler hot face and the ambient. Hence, there is only degree
of freedom available in this case. Table 620 gives the ambient
temperature needed to obtain a particular cold side temperature.
The most promising numbers are those with high enough ambient
temperatures and low enough cold side temperatures. The best operating
points to keep the junction temperature in the range of 25C 
40C are shown as shaded rows. The entire thermal network with
the junction temperature at 28.7C is shown in Figure 6.39. An
isometric view of the proposed assembly of the structure is shown
in Figure 6.40.







AutoTherm, a finite element analysis tool to thermally characterize
PCBs and multichip modules [Ment91], was used to model the temperature
distribution on the chip surface and modeling the package, and
heat spreader together. This tool has been reported to be accurate
to within 56% [Wolf91]. Uniform heat flux assumption over chip
surfaces give the temperature distribution shown in Figure 6.41.
The maximum temperature rise is about 25C over the base temperature.
Since the power densities are not uniform on the chips, a nonuniform
power density distribution was modeled with the register files
and the cache blocks dissipating more heat than the logic blocks.
The resulting temperature distribution is shown in Figure 6.42
with a maximum temperature of 27 C.
Figure 6.42 : Temperature
distribution on top of the chips: nonuniform case (Max temp =
27 C).
There are several ways of arranging the external cooling required for this package. Figure 6.43 shows a couple of such configurations based on [Naka86]. Configuration (a) is possible in CII due to its use of liquid cooling in room airconditioners. Configuration (b) is possible at GE facilities.
The TCE mismatches of the materials in this structure are minimized
to prevent failure due to thermally induced forces and stresses
during assembly. Since the structure will operate in a 30  40
C window near room temperature the temperature excursions are
not going to be of too much magnitude. Still, there is a chance
of fatigue failure due to thermal cycling.
The chip temperature can be measured by several methods such as
measuring the voltage drop across an onchip diode, liquid crystal
thermography, or by infrared imaging [Tumm89]. All these methods
have their own limitations and do not have a high resolution suitable
for submicron features on a chip. Most of the temperature spike
is in the emitter region and it falls sharply as we move away
from the emitter. Diode drops can be used to indicate the average
temperature near a junction. They can be calibrated by pulse
measurements,
so they don't heat up, with the chip turned off and later pulsing
them again with the chip turned on. The diode can also be made
to estimate the temperature by dissipating the same amount of
power and employing rapid fire measurements. On the other hand
the chip temperature can also be determined by measuring the temperature
at several points on the support structure of the package and
reverse calculating the temperature on the chip surface. For this
several Ktype thermocouples are attached with thermally conducting
epoxy to the heat sink and thermoelectric coolers.
The temperature presents another limitation in designs with increased heat flux as the devices operate in a limited temperature range [Ryma89]. More modeling effort is needed on the device temperature variations and the peak junction temperature. It will be more and more important due to the sensitivity of gate delays to temperature. The design of an appropriate cooling system for the package was challenging in terms of the required constraint of aircooling and cost. Peltier junction based coolers can provide the requisite assistance to these aircooled packages. Increasing the power requirements of a chip will increase the total cost of a computer due to its increasing cooling costs. This is why optimal circuit designs that keep power dissipation to a minimum are increasingly more important.