978-1-61284-736-8/11/$26.00 ©2011 IEEE 208 27th IEEE SEMI-THERM Symposium

Accurate Theta jc Measurement for High Power Packages

Qun Wan and Jesse Galloway Amkor Technology

1900 S Price Rd, Chandler, AZ 85286 Eric.Wan@amkor.com

Abstract

Measuring the case temperature is one of the most challenging measurements for determining the junction-to-case thermal resistance (Theta jc) in high power packages. This is especially true for low Theta jc measurement, in which high power is necessary to control accuracy. Inaccurate case temperature measurement would lead to an inaccurate Theta jc value. This study explores different methods for measuring case temperature and quantifies their impact on Theta jc. A new method of cold-plate protruded thermocouple is proposed and compared with commonly adopted method of lid embedded thermistor both experimentally and numerically. It is found correction is not negligible for low Theta jc measurement in both methods due to the temperature difference between the case surface and the thermal probe location. A standard test jig is also proposed to determine the correction for the cold-plate protruded thermocouple experimentally.

Keywords Theta jc, Thermal resistance, Uncertainty, Accuracy,

Measurement correction, Thermocouple bead, Cold plate, Thermal Test

Nomenclature ��TC Correction for RthC (�C/W) ��TM Correction for RthM (�C/W) �X Uncertainty of a parameter X (unit of parameter X) �jc Theta jc, thermal resistance of IC package (�C/W ) P Heat dissipation from die (W) Rth Theta jc corrected from RthM, same as �jc (�C/W) Rth* Theta jc corrected from RthC, same as �jc (�C/W) RthC Theta jc referenced to cold-plate protruded

thermocouple (�C/W) RthM Theta jc referenced to lid embedded thermistor

(�C/W) T1 Temperature near heater 1 and the bottom of

calorimetry bar (�C) T2 Temperature near case and the top of calorimetry

bar (�C) Tc Case temperature of IC package (�C) Tg Temperature near guard heater (�C) Tj Junction temperature of IC package (�C) TTC Temperature of cold-plate protruded thermocouple

(�C) TTM Temperature of lid embedded thermistor (�C) TTV Thermal Test Vehicle

1. Introduction As the high power semiconductor chips pushes the

computation capacity and same time the power dissipation to a new height, lower resistance material and process are used to lower the thermal resistance from junction to case (Theta jc) so as to maintain the junction temperature under operation limit. Accurate determination of Theta jc through experimental method becomes more difficult as Theta jc value decreases. For small Theta jc measurement, the power dissipation has to be pushed up so as to maintain significant temperature difference between junction and case far from measurement uncertainty. For example, to measure Theta jc = 0.1�C/W, one has to supply power in excess of 100W to produce a temperature difference than can be measured accurately.

Figure 1 from detailed uncertainty analysis in Appendix A shows the relative uncertainty as a decreasing function of both power and Theta jc. It is found that high power is needed to control the relative uncertainty. For example, to measure Theta jc of 0.1 �C/W with uncertainty under 5%, at least 150W heat has to be generated from the die. It is impossible to measure lower Theta jc accurately by low power.

0%

5%

10%

15%

20%

25%

30%

35%

40%

0 30 60 90 120 150P�(W)

%ThetaJC�(Relative�Uncertainty)

ThetaJC=0.5

ThetaJC=0.4

ThetaJC=0.3

ThetaJC=0.2

ThetaJC=0.1

ThetaJC=0.05

ThetaJC increases

Figure 1: Relative Uncertainty of Theta jc Measurement as a Function of Power P (�P=0.5W, �T=0.5�C, refer to Appendix A)

However, high power measurement introduces a new

problem: high heat flux through thermal probe and generate considerable temperature variation within the probe. For example, simulation results in Appendix B show 100W from 9cm2 lid could generate 2.6�C temperature variation within

Wan and Galloway, Accurate Theta jc Measurement for … 27th IEEE SEMI-THERM Symposium

0.5mm diameter K-type thermocouple bead that touches the lid. Thermocouple senses temperature inside the bead instead of the small contacting area with the lid. It is also true for other probes, such as thermistor, that where it senses may not be where it touches. Therefore, it is necessary to compensate the temperature variation within the probe in high power thermal experiment by adding certain correction to the measurement. There are also variations in the installation of each individual probe and the correction is needed for each one. In this paper, we will propose a new Theta jc measurement method of thermocouple installed in cold plate with its bead protruding out to contact the case surface under pressure. Then we will discuss the correction method and how to improve Theta jc measurement.

Let us first review the definition of Theta jc by JEDEC standard and some existing measurement methods. Then we will identify the problem and propose our solution. The thermal resistance, Theta jc, of an IC device is widely known by JEDEC definition [1] the temperature difference between device junction Tj and a specific reference location which in this case is the lid surface, case Tc per unit heat dissipation as shown in Eq. (1).

PTT cj

jc�

��

(1)

Measurements are made usually using steady-state conditions. Although considerable work (e.g. Siegal [2] and Schweitzer [3]) has been published using transient measurements to extract Theta jc, this method has issues, such as lateral heat loss control, to overcome. Study of this paper focuses only on methods of steady state measurement. Power, P, is calculated as the total heat generated by all resistors on the active side of the die. Using four-point Kelvin connection method, it is fairly easy and accurate to measure the heat dissipation from each resistor. Heat loss is also relatively easy to control by proper insulation and configuration of test boards as discussed later. The junction temperature Tj is obtained with high accuracy thermal diodes fabricated among the resistors on the die. They are extremely linear and easy to calibrate [4].

The lid surface (case) temperature Tc, however, is a parameter that is most difficult to measure. Any attempt to measure it, either alters the heat flow path to the external heat sink/cold plate or responds to the cold plate temperature. For high power experiment, correction is needed to compensate the offset from where the probe touches to where it senses. This offset value depends on the test method used, essentially the location of thermal probe. For example, lid embedded thermal probe always senses temperature higher than the true case temperature and leads to smaller Theta jc values while heatsink embedded thermal probe usually predicts larger Theta jc values since it is at cooler location than the true case. Accurate Theta jc data of IC packages are critical to customer applications. Conservative Theta jc data would complicate system level cooling design and increase cost while over-optimistic Theta jc data would risk device junction to operate above limit condition and shorten MTBF (mean time before failure). Hence it is vital to choose right test method with right correction so as to predict accurate Theta jc values.

There are several ways to measure the surface temperature. One of the best ways to do so is to embed a thermal probe in the lid [5]. Since the temperature variation within the metal lid is very small, readings from embedded probe are very close to the surface temperate and it is easy to correct by simple conduction model in simulation as shown in Appendix B.

However, this method of lid embedded thermal probe is not feasible for thin lid or bare die package. It is also a tremendous job for large scale thermal tests to drill a tiny and deep hole and assemble a probe on each individual test vehicle. Since it is one of the best ways to measure Theta jc, we will use it as a reference to evaluate our method proposed later in this paper.

Alternatively, one can solder or glue a thermocouple onto the case surface (lid or bare die) [6]. Good contact is guaranteed by solder or high conductive epoxy. However, same as the lid-embedded method, this method requires installation of thermocouple onto each individual package. Furthermore, a recess has to be machined on the heatsink bottom and there are an inevitable small air gap between the thermocouple and the recess to accommodate tolerances. Hence the thermal path is further altered than the lid embedded method. Mohammed et al. [5] also used a method of thermocouple embedded in heatsink. This method is simple, easy and very good to evaluate the heatsink performance. When utilizing this method to predict Theta values, one must be aware that the outcome is very conservative due to the existence of the low conductive TIM 2 layer which is sandwiched between the case and the heatsink embedded thermocouple. The resulting Theta values also largely depend on the BLT and thermal conductivity of the TIM 2.

There are also some innovated ways to measure case temperature. Gektin et al. [7] utilized fluoroptic probe through a small opening in the heatsink. This optical method excludes EMI-prone metal used in thermocouple and relies on the temperature dependent luminescence decay rate of the phosphor at the probe tip. The probe is made of fragile glass with phosphor encapsulated near the lid contacting tip. Thermal resistance between lid and phosphor should be considered in low Theta jc measurement. Nnebe and Feger [8] used infrared camera to capture the temperature distribution on the lid surface and obtain Theta jc value. Since it is non-contact method, the real case temperature can be captured after careful calibration. However, the opening is so big to accommodate the camera lens that the heat path is completely altered from that in the field application. Schweitzer [9] concluded that Theta jc values depend on the cooling method used. This IR camera method can get a pretty accurate Theta jc values but not applicable to the field application.

In this paper, we will discuss a method of a cold plate embedded thermocouple that touches case surface under pressure to measure case temperature and the associated calibration, correction, and standardization.

Wan and Galloway, Accurate Theta jc Measurement for … 27th IEEE SEMI-THERM Symposium

2. Test Setup and Procedures

2.1. Cold-Plate Protruded Thermocouple and TTV As in the repeatable high accurate measurements

summarized above, it is impractical to embed a thermal probe inside the lid or solder it on the lid for quick and/or large scale thermal test. On the other hand, it is also too conservative and TIM2 dependent to embed a thermal probe in the heatsink/cold plate and flush to the base surface. To combine the advantage of both types of method, it is proposed to embed a 36AWG K-type thermocouple in the cold plate and protrude the bead out of the base surface as shown in Figure 2 below. No lid modification is needed and contact with the lid (case) surface is guaranteed in this method.

thermocouple

Cold Plate

Figure 2: Cold-Plate Protruded Thermocouple

Lid imbedded Thermistor

thermocoupleTIM2 grease

Cold Plate

pressure

Figure 3: Cold-Plate Protruded Thermocouple in Test

Figure 3 shows the cold-plate protruded thermocouple

measuring case temperature. The thermocouple bead protrudes out of the cold plate surface, pushes away TIM 2 grease and keeps contacting the lid surface of thermal test vehicle (TTV) under pressure from either a miniature spring or some elastic material. The TTV selected is similar to what Galloway et al. had used in [11] with lid embedded thermistor as a reference method. Power is generated from 9 resistors on a 130mm2 die and is measured accurately by 4-point Kevin connection. There are 9 thermal diodes on the die to measure the junction temperature and temperature distribution.

2.2. Theta jc Test Fixture

Spacer

Col

d Pl

ate

JED

EC B

oard

Cold Plate

JEDEC

Board

Pressure applied through

pneumatic cylinder

Alignment pin

Alignment pin Figure 4: Theta jc Test Fixture

Thermal performance of TTVs is tested in the Theta jc Test Fixture shown in Figure 4. Two JEDEC standard test boards are aligned by four pins and pressed back to back together onto the cold plate on each side. Back to back configuration creates a symmetrical adiabatic plane between two boards so as to minimize the heat loss through the board. An insulation spacer sandwiched between the backs of two boards further reduces the amount of heat loss.

2.3. Calibration and Test Configuration Calibration is a critical step before powering the test. The

uncalibrated accuracies of thermal probes are usually too low to use in high accuracy thermal tests. For example, the standard tolerance of K-type thermocouple can be as high as 2.2�C [12] before calibration, which is too much to measure the temperature difference of several degrees. Therefore before the test, the thermistors and thermal diodes inside TTVs, and the thermocouples in cold plates are sent to a thermal oven to calibrate against a reference thermistor (calibrated at a high accuracy by NIST) at several temperature points covering the temperature range of the power test. These outcome calibration relationships are used to adjust the raw data from power test later. The accuracies of all the thermal probes are controlled under 0.55�C after calibration.

From preceding thermal test by Galloway et al [11], it is found the Theta jc values of all TTVs fall between 0.15�C/W to 0.25�C/W. Uncertainty analysis in Appendix A shows that power of 70W or higher is needed to achieve 5% or less relative uncertainty. In this study, power dissipation from each TTV is controlled around 72W.

The cold plate inlet temperature is set to 16�C, which is several degrees cooler than ambient temperature. This setting will maintain the mother board temperature close to the ambient and thus minimize heat loss through the mother boards. 20 psi pressure is applied on the TTV to minimize BLT of TIM 2. Other parameters can be found in Table A1 in Appendix B.

3. Test Results

3.1. Design of Experiments (DOE) In this paper, four TTVs are tested in the Theta jc test

fixture, namely Brd #1, Brd #2, Brd #3, and Brd #4. There are two 36 AWG K-type thermocouples installed in two cold plates, namely TC1, and TC2, in the fixture. To test each TTV on every cold plate, a rotation scheme consisting of four tests is designed as shown in Table 1.

Table 1: DOE Rotation Scheme

TC1 TC2 Test 1 Brd #1 Brd #3 Test 2 Brd #3 Brd #1 Test 3 Brd #2 Brd #4 Test 4 Brd #4 Brd #2

Wan and Galloway, Accurate Theta jc Measurement for … 27th IEEE SEMI-THERM Symposium

For repeatability purposes, four rotations have been

completed. Each TTV has been tested 8 times on two cold plates with four times on each cold plate.

3.2. Results and Discussion Theta jc defined by different reference points of each TTV

have been calculated based on the test results. RthM is referenced by the lid embedded thermistor. RthC is referenced by the cold-plate protruded thermocouple.

PTT TMj ��RthM

�(2)

PTT TCj ��RthC

�(3)

Define the correction ��TM for RthM and ��TC for RthC. Thus the respective corrected Theta jc can be expressed as

TM���� RthMRth� (4)

TC���� RthCRth*� (5)

Since Rth* is expected to be smaller than RthC, minus sign is used to keep correction ��TC positive value.

Figure 5 shows RthM, RthC, and the corrected Theta jc Rth and Rth* for four TTVs with standard deviations, which range from 0.007 to 0.015 for RthM, and 0.006 to 0.016 for RthC. As expected, RthC is always larger than RthM since TTC senses cooler temperature than TTM and hence its difference from junction temperature Tj is larger.

Before correction is applied, the difference between RthM and RthC can be as large as 0.017�C/W, which is around 10% of RthM. However, we cannot simply say RthC is 10% less accurate than RthM since RthM needs correction as well. Eq. (A8) in the simulation in Appendix B shows the correction for RthM is ��TM = 0.0092�C/W, which is bigger than the correction for RthC in Eq. (A9), ��TC = 0.0062�C/W. RthC is actually more accurate than RthM. Two bars in the middle of each group in Figure 5 show the corrected Theta jc, Rth and Rth*, with less difference between the two.

0.00

0.05

0.10

0.15

0.20

0.25

TC1 TC2

Brd�#1�Theta�jc�(�C/W)

RthM

Rth

Rth*

RthC

(a)

0.00

0.05

0.10

0.15

0.20

0.25

TC1 TC2

Brd�#2�Theta�jc�(�C/W)

RthM

Rth

Rth*

RthC

(b)

0.00

0.05

0.10

0.15

0.20

0.25

TC1 TC2

Brd�#3�Theta�jc�(�C/W)

RthM

Rth

Rth*

RthC

(c)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

TC1 TC2

Brd�#4�Theta�jc�(�C/W)

RthM

Rth

Rth*

RthC

(d) Figure 5: Theta jc from Different References (RthM: Lid-Embedded Thermistor; Rth: Corrected from RthM; RthC: Cold-Plate Protruded Thermocouple; Rth*: Corrected from RthC) of Four TTVs (Brd # 1 to #4 in (a) to (d))

Table 2 summarizes the deviation of Theta jc by different

reference points from the respective corrected value. In another word, Table 2 shows how much correction is needed with respect to the total Theta jc. RthM needs more than 5% correction and RthC needs more than 3% correction. These

Wan and Galloway, Accurate Theta jc Measurement for … 27th IEEE SEMI-THERM Symposium

values do not seem much because Theta jc of current TTV is around 0.2�C/W. For packages with Theta jc smaller than 0.1�C/W, the corrections for both methods could more than double and become significant.

Table 2: Deviation of Theta jc Referenced by Lid-Embedded Thermistor (RthM) and Cold-Plate Protruded Thermocouple (RthC) from Their Corrected Theta jc (Rth and Rth*)

� (Rth�RthM)/Rth� � (RthC�Rth*)/Rth*�

� TC1� TC2� � TC1� TC2�

Brd�#1� 6.13%� 5.64%� � 4.10%� 3.15%�

Brd�#2� 4.57%� 5.84%� � 3.06%� 3.53%�

Brd�#3� 6.01%� 6.90%� � 3.49%� 4.61%�

Brd�#4� 6.05%� 3.38%� � 3.73%� 2.24%�

Avg� 5.7%� 5.4%� � 3.6%� 3.4%� Another issue is about the robustness of the proposed test

method. In current test, 36AWG thermocouple is used and the correction to theta jc is smaller (0.0062�C/W) due to its small bead size. However, if a thicker and more robust thermocouple, such as 30AWG, is used, diameter of the bead would be twice as big. The proposed method is still valid provided that a larger correction (e.g. 0.026�C/W in Table A2) applies to RthC.

3.3. Standard RthC Correction Test Jig

guard heaterheater1

insulatorTg

calorimetry bar

T2

T1thermocouple

Cold Plate

TIM

(a)

(b)

Figure 6: In-Test Stack-Up (a) and Assembled (b) View of RthC Correction Test Jig

Since TTV with thermistor embedded in lid is not always

available and the simulation results in Appendix B rely on the accurate modeling of thermocouple bead size, shape, and the contact area with the case, a alternative standard test jig is

designed to find out experimentally the correction for RthC as shown in Figure 6. This standard RthC correction test jig can be used in the same Theta jc test fixture in Figure 4 to find out the correction for RthC.

By fine tuning the heat dissipation from the guard heater and approximating the readings from T2 and Tg, the downward heat loss from heater 1 can be minimized close to zero and nearly 100% heat from heat 1 will dissipated through the calorimetry bar. The heat P through the case can also be determined accurately by measuring the temperature drop (T2 - T1) across the precisely machined calorimetry bar, which thermal conductivity is also precisely determined upfront. As shown in Figure 7, case temperature Tc at the top center of the calorimetry bar can be linearly extrapolated by T2 and T1 with respect to their distances from the case.

T

T1

T2

Tc

x1 x20 xDistance x from case

Figure 7: Linear Extrapolation of Case Temperature Tc from T1, T2 and Their Distance from Case

Therefore, utilizing Eqs. (1) and (3) in Eq. (5), the

correction for RthC can be found

PTT TCc

TC�

���� Rth*RthC�

(6)

4. Conclusion In this study, it is found from uncertainty analysis that

high power dissipation is necessary to improve accuracy in low Theta jc measurement. A feasible accurate Theta jc measurement method for high power packages is proposed. With a thermocouple embedded in the cold plate and its bead protruding out, this test method can ensure the contact of the thermocouple bead under pressure on the lid (case) surface without any modification of it. It is also found a correction is needed to adjust Theta jc value referenced by the thermocouple and get the accurate Theta jc. A standard correction test jig is proposed to determine the correction.

Acknowledgments CAD design assistance of standard RthC correction test

jig provided by Cameron Nelson is greatly appreciated. Package assembly assistance provided by Amkor's K1 R&D center is also greatly appreciated.

Wan and Galloway, Accurate Theta jc Measurement for … 27th IEEE SEMI-THERM Symposium

Appendix A. Uncertainty Analysis Kline and McClintock [10] uncertainty analysis shows the

uncertainty �R of a function R = R(x1, x2, …, xn) can be expressed as

�

�

� �

���

�n

ii

ixRR

1

2

��

(A1)

Where �i is the uncertainty of variable xi. Thus the uncertainty ��jc in Eq. (1) can be found as

� � � � � �2221 PTTP jccjjc ������ ���

(A2)

Or relative uncertainty as 222

��

���

�

� �

��

�

� �

��

PP

PT

PT

jc

c

jc

j

jc

jc ���

��

���

(A3)

Where �Tj and �Tc are uncertainties of junction and case temperatures respectively, and �P is the uncertainty of power.

From Eqs. (A2) and (A3), one can find out that increasing P and product �jcP will result in the reduction of uncertainty ��jc. This is especially true for high power package which has very low Theta jc. By calculating ��jc beforehand, the power and accuracy level needed for the experiments can be pre-determined. Figure 1 clearly shows the relative uncertainty of Theta jc as a function of power P and Theta jc. It is found that even for Theta jc = 0.5�C/W, 10W power dissipation can only achieve 15% uncertainty. In low Theta jc test, power should go as high as 150W to achieve 10% uncertainty for Theta jc less than 0.05�C/W.

Appendix B. Thermal Simulation of Temperature Variation within Thermocouple Bead in High Power Test

(a) P

(b)

Figure A1: Isometric (a) and Cross Section (b) Views of Thermal Model

To investigate the heat transfer mechanism of current test setup and the corrections for lid embedded thermistor and cold-plate protruded thermocouple, a 3D thermal simulation model is created in IcePak 12.0 software shown in Figure A1. Uniform heat dissipates into the model through the area of die size from the center region of top boundary. The bottom of the cold plate is maintained at 20�C. All the other boundaries are set adiabatic assuming no heat loss through them.

�TTM = TC – TTM= ��TM� P

TCTTC

TTM

�TTC = TTC – TC= ��TC� P

High conductive epoxy to glue thermistor

Copper lid

Copper cold plate

TIM 2 grease

TC glueThermocouple wireThermocouple bead

Figure A2: Zoomed-in (from broken box in Figure A1(b)) Model Structure of the Thermocouple Installed in the Cold Plate and the Epoxy in Lid

Figure A2 shows the detailed structure of thermocouple

installed in cold plate. The bead is modeled as an R0.25mm sphere with its top overlapping with the lid. A reasonable overlapping interface area is 0.03mm2, which is 15% of the sphere area. Two 36AWG thermocouple wires are modeled into one thicker wire with the cross section area the same as the sum of those of two wires. The complicated wire curvature near the protruding bead is simplified as an L shape bend, which is trivial in the modeling of heat loss through the wires. The model consists of around 67000 nodes, 98 of them are assigned to the tiny spherical bead. Table A1 lists the BOM of the model with parameters of size, material and thermal conductivity.

Table A1: BOM of the Thermal Model

Item Size (mm) Material Thermal Conductivity (W/mK)

Die/Heat source 11.4�11.4 B.C. Lid 42�42�2.25 Copper 388 TM epoxy D0.5�25 Epoxy 3 TIM 2 T0.2 Grease 3 TC bead D0.25 K type 28.8 TC wire R0.09 K type 28.8 TC glue 25.35�0.8�1 Glue 0.14 Cold plate 50�50�5 Copper 388

Figure A3 shows the simulation results for power P =

75W. From the overall view (a) of the isotherm temperature field of the cross section at the package center, the interference of embedding thermistor with epoxy can be found by comparing left and right halves of the temperature

Wan and Galloway, Accurate Theta jc Measurement for … 27th IEEE SEMI-THERM Symposium

field. Although the thermal conductivity difference between epoxy and copper is large (3 to 388), the temperature field does not seem to be affected too much. This might due to the high conductivity of copper that creates small temperature variation across the lid and around the epoxy.

Zoom-in view (b) of the temperature field shows the locations of reference points: TTM at the bottom of epoxy cylinder; Tc at the overlap interface of lid and thermocouple bead; TTC at the coolest bottom of the bead to be conservative.

Detailed view (c) of the thermocouple bead shows 0.47�C difference across the bead for 75W power from the die. This difference could increase as the increase of power, bead size, or decrease of die size.

(a)

(b) (c) Figure A3: Isotherm Plot of Temperature Field of the Cross Section at the Model Center (P=75W). (a) Overall View (b) Zoom-In View (c) Across Thermocouple Bead

By repeating the computation for different power levels,

one can obtain the temperature differences from lid embedded thermistor to case �TTM and from case to cold-plate protruded thermocouple �TTC as defined below.

cTMTM TTT ���

(A4)

TCcTC TTT ���

(A5) Both �TTM and �TTC as a function of power P are shown

in Figure A4. Linear correlation shows that PTTM 0092.0��

(A6) PTTC 0062.0��

(A7) With square of the linear correlation coefficient RSQ = 0.999996 and 0.999846 respectively.

Utilizing Eq. (1) to (5) and (A4) to (A7), one can obtain the corrections for the lid embedded thermistor and the cold-plate protruded thermocouple respectively

0092.0RthMRth ��

����PTTM

TM�

(A8)

0062.0Rth*RthC ��

����PTTC

TC�

(A9)

The constant coefficient �� has the unit of thermal resistance (�C/W). It is actually the offset of thermal resistance from case to the reference point (e.g. thermistor or thermocouple). It apparently depends on specific batch of unit under test, such as the thickness and material of the lid, installation of the thermal probes etc. For low power, high Theta jc package measurement, similar values as Eqs. (A8) and (A9) are negligible. However, for high power, low theta jc packages, these values are significant and cannot be neglected.

�TTM =�0.0092P

�TTC =�0.0062P

00.10.20.30.40.50.60.70.80.91

0 20 40 60 80 100

�T(�C)

Power�(W)

Figure A4: Temperature Differences from Lid-Embedded Thermistor to Case (solid line) and Case to Cold-Pate Protruded Thermocouple (broken line) as a Function of Power

The simulation is also extended to investigate the effect of

larger thermocouples and smaller lid size. Model of 30AWG thermocouple and 30�30�2.25 lid has been simulated at 100W power dissipation. The comparison is shown in Table A2.

Table A2: Effect of Different Sizes of Thermocouples and Lid Size (P=100W)

36AWG TC 30AWG TC Lid Size (mm3) 42�42�2.25 30�30�2.25 Bead size (mm) D0.25 D0.5 Contact Area (mm2) 0.03 0.03 Contact Area/Total Area 15% 3.8% �TTC (�C) 0.62 2.6 ��TC (�C/W) 0.0062 0.026

Wan and Galloway, Accurate Theta jc Measurement for … 27th IEEE SEMI-THERM Symposium

Table A2 shows the effect of different size of thermocouple. Big difference can be found due to the bead size and contact area ratio change. Thus, there are challenges on detail modeling of the thermocouple bead shape and its contact with the case surface under pressure.

References 1. Electronic Industries Association, Integrated Circuit

Thermal Measurement Method –Electrical Test Method, EIA / JEDEC Standard, JESD51-1, 1995 [www.jedec.org].

2. Siegal, B., “An Alternative Approach To Junction-to-case Thermal Resistance Measurements,” Electronics Cooling, May 2001.

3. Schweitzer, Dirk, “Transient Dual Interface Measurement of the Rth-jc of Power Semiconductor Packages,” Electronics Cooling, September, 2010.

4. Sofia, J.W., “Fundamentals of Thermal Resistance Measurement”, Analysis Tech, 1995.

5. Mohammed, R., Xia Yi, R. A. Sahan and Ying-Feng Pang, “Experimental Methodologies for Thermal Design in Silicon Validation Platforms”, Electronics cooling, July 2010.

6. Gondipalli, S., S. Bhopte, B. Sammakia, and V. Calmidi, “Numerical And Experimental Study Of The Effect Of Thermocouple Wire Attachment On Thermal Characterization Of A High Performance Flipchip Package,” IEEE, 2010.

7. Gektin, V., S. Ankireddi, J. Jones, S. Pecavar, and P. Hundt, “Characterizing Bulk Thermal Conductivity And Interface Contact Resistance Effects Of Thermal Interface Materials In Electronic Cooling Applications”, IPack2003-35324, 2003.

8. Nnebe, I, C. Feger, “Drainage-Induced Structural Degradation of Thermal Grease” IBM Research Report, 2007.

9. Schweitzer, D, “The Junction-To-Case Thermal Resistance: A Boundary Condition Dependent Thermal Metric,” 26th IEEE SEMI-THERM Symposium, 2010.

10. Kline, S. J. and F. A. McClintock, “Describing Uncertainties in Single-Sample Experiments,” Mech. Eng., p.3, 1953.

11. Galloway J., S. J. Kim, F. Hamilton, K. Yawaza, M. Adachi, T. Ohde, D. Le, I. Singh, H. Aoki, and E. Hosomi, “Thermal Design of a High Power Multi-Chip Module”, 8th VLSI-PKG-WS (LT), 2008.

12. American Limits of Error ASTM E230-ANSI MC 96.1.