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Comparison of transient and static test methods for chip-to-sink thermal interface characterization
ARTICLE IN PRESS Microelectronics Journal 40 (2009) 1379– 1386
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Comparison of transient and static test methods for chip-to-sink thermal interface characterization B. Smith , T. Brunschwiler, B. Michel ¨umerstrasse 4, 8803 Ru ¨ schlikon, Switzerland IBM Research GmbH, Zurich Research Laboratory, Science & Technology, Sa
a r t i c l e in fo
abstract
Article history: Received 30 November 2007 Received in revised form 28 May 2008 Accepted 4 June 2008 Available online 8 August 2008
Accurate thermal interface characterization is essential for high flux microelectronic package design. However, it is increasingly difficult as interfacial bond lines are thinned and thermal interface materials (TIM) evolve to more complex formulations with better performance. This paper compares a static versus transient characterization method targeted at the chip-to-package interface in a test fixture that closely resembles a packaged chip. The static method requires measurements over multiple bond line thicknesses while the transient method yields additional information about the package at the cost of greater numerical complexity, hardware requirements, sensitivity to noise and experimental uncertainty. Both are compared with existing techniques. We conclude that the static method is more generally-applicable while transient is well-suited to rapid characterization of the interface when the rest of the package is well-defined. While both methods are sensitive to the accuracy and resolution of temperature and bondline thickness measurements, the transient technique is additionally sensitive to the relative contribution of the TIM in the full junction-to-ambient thermal path. These points are illustrated through experimental results and compact numerical modeling. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Thermal interface material Transient thermal test Electronics cooling TIM Interface characterization Structure function
1. Introduction Heat diffusion across the interface of two components in an electronic package is a well-studied topic in the thermal packaging field [1,2]. It is fundamental to any package, from conduction-only designs for handheld electronics [3,4] to large datacenters featuring a complex combination of liquid and air fan cooling [5,6]. The thermal interface can account for up to 50% of the total thermal budget in some packages and directly influences product lifetime, performance, reliability, and power consumption. Advanced thermal packages often use metal interfaces [7,8], phase-change materials [9], or thermal interface materials (TIM) made from highly particle-filled materials including greases and adhesives [10]. The optimal TIM for an application is a factor of thermal, mechanical, assembly, and cost considerations but the thermal performance is defined by its thermal resistance, RTH,TIM (K cm2/W). Acoustic mismatch, or the inability to couple the energycarrying phonons of one surface to the interface material is referred to as contact resistance and is one contributor to the overall RTH of the TIM. More significant for the interfaces with
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E-mail address: [email protected] (B. Smith). 0026-2692/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.06.079
bondline thickness (BLT) greater than 1 mm considered here is the resistance to heat diffusion within the TIM, which defines the temperature rise per unit of heat input based on Fourier’s law of heat conduction: q00 ¼ keff
qT ¼ RTH DT qx
(1)
where q00 is heat flux per unit area, keff is the effective thermal conductivity of the medium, T is temperature, and x is length of the medium in the direction of heat propagation. When applied to TIM geometries, RTH reduces to RTH;TIM ¼
BLT keff;TIM
(2)
where keff,TIM is the effective thermal conductivity of the TIM. In this formulation, the direction of heat diffusion is assumed one dimensional, normal to the interface. Therefore, most TIM characterization techniques induce 1-D heat flow and measure the steady or transient temperature gradient through the system to extract RTH,TIM [11–13]. Generally speaking, it is difficult to identify trends in the popularity of the TIM test techniques; rather, each technique has its own niche. Static techniques require the least instrumentation overhead so are well-suited to characterize TIMs with relatively large thermal resistance and BLT. Increased measurement accuracy required for high-keff, small-BLT TIMs begins to marginalize
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this advantage, though, and the cost of high-temporal resolution sampling hardware and advanced data processing software can be justified for transient techniques, especially if they promise faster total test time. Many static test techniques follow ASTM D5470 [14,15], involving four to six temperature sensors placed in-line with the heat flow, half on one side of the interface and half on the other. The discontinuity of the temperature gradient across the interface is attributed to the TIM, and Eq. (1) is used to extract effective conductivity if the BLT is known. The design shown in Fig. 1 is related to this method but more closely resembles an electronic package. A heating element and temperature sensors are fabricated on-chip and TIM placed between chip and heat sink [16]. This layout is advantageous for microelectronics applications because the TIM bondline is formed using the same assembly process and geometry used in the product so any process-dependent effects on RTH,TIM are accounted for. It can be adapted to add and characterize other packaging components like a lid or spreader (Fig. 1b). The thermal resistance of the system in Fig. 1 is defined by the junction temperature of the chip and inlet temperature of the cooler. RTH, TIM is then extracted by either: (1) characterizing the other resistances in the system separately and subtracting them from the measurement to obtain RTH,TIM; or (2) measuring overall RTH for different BLT of the same TIM and associating the
Fig. 1. Schematic of the test fixture with corresponding RC network model describing 1-D heat flow through the TIM: (a) standard heater-cooler arrangement referred to as ‘‘direct attach heat sink’’ and (b) alternative including a spreader or lid also accommodated by the fixture.
derivative of Eq. (2) with respect to BLT to the change in overall system resistance. It is not possible to completely characterize the other components since the performance of the cooler may change over time and, more importantly, contact resistances among the components can vary from one measurement and material to the next. Therefore the second option, referred to as the variable BLT method, is preferred since no additional knowledge of the system is needed. Fig. 2 illustrates this method, plotting the relationship between BLT and RTH for typical TIM material. The TIM’s effective conductivity is the inverse of the slope of the linear fit to this data. While this means that the method is unable to characterize materials with thickness-dependent keff, the conductivity of nearly every TIM material is BLT-independent at the completion of the squeeze process if assembly pressure is larger than other forces (gravity) and the TIM spreads uniformly over the interface. Full discussion follows later but the accuracy of the approach will clearly rely on the R2 value of the linear fit and the uncertainty of RTH and BgLT measurement. Alternately, transient or harmonic methods can isolate the influence of the TIM from the other components in the thermal path [17–20], eliminating error from thermal uncertainties in adjacent components like the cooler. Harmonic and pulse-based transient methods such as 3-omega and laser flash techniques including thermoreflectance have become the standards for thin film thermometry; however, the numerical fitting models and laser heat pulsing required limit their application in a product-like test fixture (Fig. 1), which is preferred for industry relevance. RC analysis using the thermal structure function [21,22], is another candidate as it allows in-package testing of the TIM without multiple BLT measurements or knowledge of the other components in the system. The structure function (SF) is a numerical deconvolution and transformation of the temporal response that can identify the magnitude of thermal resistance and heat capacity of each region in the thermal path, thereby isolating the TIM from the rest of the system. It compiles a sort of complex impedance profile of the heat path from source to sink and associates abrupt changes in the thermal capacitance along the path with material boundaries. That way, the difference in cumulative thermal resistance from one boundary to the next corresponds to the thermal resistance of that component. In the case of the TIM, this data point combined with Eq. (2) and BLT constitute the effective conductivity of the material. Electrical noise and heat spreading outside the 1-D path are significant challenges to the transient analysis with structure functions. Rather than directly interpreting SF, the experimental temporal response can be compared with a numerical model using a Cauer network of thermal RC circuit elements, generally
Fig. 2. Variable BLT static TIM measurement. Circles represent experimental data points (with error bars discussed later), the dashed line is the best fit line through the data. The contribution of each component is labeled and marked by area fill.
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represented by Fig. 1. Both the experimental and numerical data is transformed into the structure function domain and the numerical model fit to experiment to extract RTH,TIM and keff,TIM. The numerical models also provide a sort of idealized, noise-free input to identify the limits over which the SF methods can be used for TIM characterization. Both of these approaches are analyzed in later sections. While thermoreflectance and 3-omega-like methods are established and accurate for a variety of geometries, they are still not suitable in-situ testing of TIM materials in a microelectronics package. Therefore, we focus this work on the static test applied to the setup of Fig. 1, plus the transient method using the same package. The details of the test fixture and data reduction methods of each test are first discussed followed by the presentation of an experimental test case. We discuss the uncertainties and measurement errors of each technique and develop figures of merit for the applicability of the transient test.
2. Experimental setup Fig. 1 shows the experimental fixture schematically and this work will focus on the ‘‘direct attach’’ scheme of Fig. 1a. A pneumatic cylinder (Festo Corp.) presses the IBM-designed thermal chip and chip carrier (ceramic substrate and PWB) to the liquid cooler (Ardex from Atotech, Inc.). A high-performance liquid chiller (Proline series from Lauda) uses a NIST-traceable temperature probe (0.05 1C accuracy) and controller to hold the cooler’s inlet temperature to 25.070.01 1C. The chiller is also used to calibrate the temperature sensors so the estimated maximum error of the temperature measurement is 0.1 1C. Power is measured by an on-chip voltage probe and calibrated 1 O resistor in series with the power supply. A calibrated 612-digit switching multimeter (model 2701 from Keithley Instruments, Inc.) is used to acquire all data so the error of the power measurement should be less than 1%. Setting the power so the total temperature rise of the system is greater than 10 1C ensures that the uncertainty on the temperature measurement is also less than 1% so the total error on power and temperature data acquisition is then close to 1%. Four induction-based displacement sensors with 0.1 mm resolution (Mahr, GmbH, not shown), factory-calibrated to 0.4 mm accuracy, measure BLT by contacting the ceramic substrate 5 mm from each corner of the chip. A zero-BLT reference is taken prior to TIM measurement. The arithmetic average of these four measurements is a very good indication of the average BLT, even though variation in corner-to-corner measurement up to 8 mm is acceptable, owing to the tolerance in the guide rails of the cylinder. Four serpentine resistors, each located in a quadrant of the chip and covering roughly 85% of the chip total area, are fabricated onchip with standard photolithography to apply uniform heat flux to the package. Nine 4-point RTD sensors, each approximately 1 mm2 are deposited over the heaters and are located at the chip’s center, corners, and the center of each quadrant. Heat flux (and therefore temperature) uniformity in the chip worsens as the keff,TIM improves since the heat cannot easily spread laterally in the chip if RTH,TIM+RTH,Si,through plane is less than RTH,Si in plane. Temperature hot spots lie at the center of each of the quad heaters (Thigh) while minimum is at the chip center and corners (Tlow). The temperature profile from hot to cold will follow a parabola as indicated for 1-D radial heat spreading in a cylindrical coordinate system with uniform power generation [23]. This assumption is used to build a temperature map of the chip based on the nine data points. The average temperature of
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the chip (Tave) then follows: T avg ¼ T low þ 0:658ðT high T low Þ
(3)
where the bar above the temperature symbols designates the arithmetic average of all sensors corresponding to the high or low temperature reading (average of all quadrant sensors ¼ T high , for example). In practice, there is little variation in temperature within T high and T low sensor groupings, validating this averaging approach. It then follows that the thermal resistance of the system is RTH ¼
T avg A P
(4) 2
where A is the area (18.3 18.4 mm ) and P is the electrical power through the chip. The ratio T high =T low was measured as high as 1.7 for the best TIMs, despite the 85% coverage of the serpentine heaters so this averaging assumption influences the accuracy of the measurement much more than the uncertainty of the individual data points. An analysis of the effect of temperature averaging and nonuniformities on the TIM characterization follows in later sections. Generally speaking, though, the averaging of the BLT and temperature measurements together ensure that the overall geometry and heat profile of the TIM is captured despite the uncertainties in the product-like test stand. Finally, the cooler is mounted to a force sensor (ME-Messysteme GmbH) to monitor the pressure/force applied during the TIM squeeze process for pressure-actuated BLT control since final BLT is a strong function of applied pressure.
3. Results and analysis This section illustrates the strengths and capabilities of each measurement approach with a case study using a commercially available TIM material with keff,TIM ¼ 5 W/m K reported by the vendor. The material was chosen for its relevance to the industry and high viscosity (easily-controllable BLT). Extending each technique to other TIM materials is also discussed. In both tests, uncertainty of the power and temperature measurements is limited to 1% at all points but grows with decreasing BLT since the displacement sensors are calibrated to 0.4 mm. This leads to o1% error on a 50 mm BLT measurement but up to 10% when BLT ¼ 4.0 mm, for example. The thermal resistance of the parasitic heat paths through the ceramic and the surrounding air were nearly two orders of magnitude higher than the Si–TIM–cooler path, so effectively all the power from the heater is dissipated through the TIM. Temperature nonuniformity within the chip was significant as the bondline thinned below 10 mm (T high =T low approaching 1.35). However, Eq. (3) provides a reasonable estimate of the average temperature of the chip so the actual uncertainty of Tavg is less than the 29% maximum spread in the thermal data. Additionally, the ratio drops below 1.1 for thicker bondlines. Power nonuniformity affects the ability of the setup to resolve spatial nonuniformities in the TIM, but Tavg is a good overall estimate considering the power and BLT data are also composites from multiple discrete measurements. 3.1. Steady state The variable BLT static test yields keff,TIM ¼ 4.8 W/m K with R2 ¼ 0.999 (Fig. 2). The slope fit has an averaging effect so the total uncertainty of the keff,TIM prediction is less than the maximum uncertainty of the data points and additional data points increase the accuracy of the measurement. The relative contributions of the three components illustrated in Fig. 2 and Table 1 are calculated by the vertical axis intercept of
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Table 1 Relative contributions to total RTH BLT (mm)
RTHsystem (Kcm2/W)
% Si
% TIM
% Cooler
54.6 15.2 6.8
0.372 0.288 0.271
13.3 17.2 18.3
30.5 11.0 5.2
56.2 71.8 76.5
the linear data fit plus the analytical estimation of silicon resistance. The remaining resistance, 0.21 K cm2/W, is attributed to the cooler and translates to an effective heat transfer coefficient, h ¼ 48 kW/m2 K. Table 1 also shows the relative contribution of each component in the heat path. There is no fundamental limits on the measurement range of RTH,TIM or the required ratio of RTH,TIM to RTH,system as long as the power is set so the temperature rise across the TIM is significantly greater than the uncertainty of the temperature measurement (0.1 1C). In practice, though, a TIM that accounts for only 5% of RTH,system requires 100 1C junction-to-ambient temperature rise to effect 5 1C rise across the interface (50x the uncertainty of the measurement). These practical limitations prevent measurements when the TIM contributes less than 5%. Similarly, the uncertainty of BLT rises above 10% for BLTo5 mm, decreasing the accuracy of keff,TIM. Nevertheless, the variable BLT static method requires little data processing. It is robust since temporal and spatial averaging of the power and thermal data minimize sensitivity to transient drift and lateral spreading in the chip. The method’s biggest drawback is the need to measure multiple BLTs since precise displacement control is not realistic over a large range (5–100 mm) without the use of artificial means to stop the bondline which can influence keff,TIM. Accuracy of the fit line, and therefore keff, TIM estimate, decreases with range making the method especially difficult for low viscosity TIMs. A single thermal measurement at the final BLT is most attractive and relevant for package design.
Fig. 3. Temporal response to power step for each BLT.
3.2. Transient The transient method uses the same test fixture, heater/sensor chip, and cooler. Fast (o2 ms) power switching, RTD temperature sampling, filtering, and processing are facilitated by Thermal Transient Tester hardware (Micred, Inc.). The system response to a power step (Fig. 3) is recorded with 1 ms resolution at the beginning of the response. This is especially important since the thermal mass of the TIM affects the shape of the response for only approximately 1 s after the load is applied. The uncertainties of the measurement remain the same from the static test, although the spatial averaging of the temperature data is implemented as a scale factor at the end of the structure function calculation. Averaging the temperature data according to Eq. (3) at each time step would distort the actual thermal response along the heat path so one sensor is chosen and RTH is scaled by Eq. (3) after structure function calculation. A sensor on the center of a heater quadrant is used since the response data should be co-located with the heat source for straightforward SF interpretation. The final (maximum) RTH value with respect to BLT reported by the transient technique follows the steady predictions. In fact, the variable BLT technique could also be applied to the final value of the transient data to yield keff,TIM ¼ 4.3 W/m K, within 10% of the steady prediction. Of course, this analysis uses none of the transient or structure function data, but is a good check on the fidelity of both measurements. As shown in Fig. 3, the system responds slightly faster when BLT ¼ 4.2 mm (steeper slope in the 1–100 ms region), corresponding to less thermal mass. Before considering the structure function
Fig. 4. Integral structure function (a) and differential structure function (b) for each BLT.
domain, it is logical to try and extract RTH, TIM directly from these temporal response curves using a slope matching technique. Strong coupling among thermal elements means that the sensitivity of the response curve to any one component is not
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large, however, so the shape of the response in the time domain does not easily yield RTH,TIM. Next, the integral structure functions for each BLT test are computed, shown in Fig. 4a. Previous work [24] discusses influence of numerical parameters of the SF transformation. TIM analysis in microelectronics packages is especially challenging compared to other applications of the transient method since the magnitude of RTH,TIM is less than or comparable to other components and maintaining 1-D heat transfer with thin BLT, high conductivity TIMs is exceedingly difficult. As mentioned, the SF is a kind of thermal history in the RTH domain, plotting the cumulative thermal capacitance of system versus its location in the 1-D heat path from source (RTH ¼ 0) to sink (RTH ¼ RTH,steady). The deconvolution of the high-temporal resolution response (temperature) from the load (power step) results in the time constant spectrum of the system, which is fit to a 1-D Foster network and then transformed to a Cauer network. The Cauer network contains physically realistic thermal RC elements, capturing the load-to-sink response of the system. To analyze the network, the cumulative thermal resistance and capacitance at each point in the network with respect to the origin (RTH ¼ 0) defines the system’s SF-cumulative capacitance plotted against cumulative resistance. The numerical derivative (DSF) identifies material boundaries by highlighting where the SF changes rapidly. Full details, theory, and discussion of the structure function can be found elsewhere [22,25,26]. One interpretation of Fig. 4 is that the plateau around 1 W s/K is the region corresponds to the TIM. The smaller steps toward the end of the path are likely effects of conjugate conduction– convection in the cooler. It then follows that RTH,TIM ¼ 0.15, 0.175, and 0.205 cm2 K/W for the 4.2, 23.7, and 34.2 mm measurements, respectively, based on the length of this plateau on the x-axis. The DSF (Fig. 4b) yields the same information by identifying the peaks instead of the boundaries. However, these data correspond to keff,TIM ¼ 0.28, 1.35, and 1.65 W/m K, respectively, which is much lower than the static test and the vendor data. Uncertainty from the BLT measurement in the 4.2 mm case and the temperature averaging techniques alone cannot explain this deviation. The first step in the SF near the RTH ¼ 0 axis could be enhanced by a synthetic cumulative structure function section to better resolve the location of the step; however, this is also unlikely to account for the 3–5x difference in keff,TIM. Electrical noise from power switching in the early transients and lateral heat spreading are two likely sources of error in the SF analysis. The former can distort the Si–TIM boundary while the later violates the 1-D heat flow assumption of the SF compilation. Strategies to improve heat flux uniformity with conductive inserts or lower-performance coolers tend only to marginalize the overall effect of the TIM, add thermal mass, and reduce the test’s sensitivity to TIM properties. It is possible to isolate the effects of noise and spreading by simulating test data with numerical models and comparing the structure function results to the input of the models. The numerical models are noise-free and based on 1-D heat spreading in a Cauer RC network. They can serve two roles: (1) to identify the range over which the SF analysis is valid for TIM characterization if noise and spreading are not an issue; and (2) to extract the TIM properties by fitting a numerical model to the real experimental data, thereby identifying which peaks/plateaus correspond to actual material boundaries and which are numerical artifacts. The later approach is often employed in thin film thermometry using various analytical and numerical models [27–29]. Each component in the 1-D thermal path is represented by an RC element as shown in Fig. 1. Resistance follows Eq. (2) with the length of the component in the direction of heat flow substituted
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Fig. 5. Comparison between peaks in DSF of simulated data and actual resistance path through the model for three values of RTH,TIM. The magnitude of each component (silicon, TIM, and cooler) is represented by a step in the dashed line. The magnitude RTH,TIM increases as with darker lines.
BLT while thermal capacitance per unit area (C) is defined as C ¼ Cv L
(5)
where Cv is the material’s volumetric heat capacity and L is the length of the component in the direction of heat flow. The resistance and capacitance of the chip is based on published silicon literature and a rough estimate is used for CTIM (the model is insensitive to CTIM for any reasonable value of CvTIM). The cooler is considered a pure resistor: heat capacity is set to zero and 1/RTH,cooler corresponds to h ¼ 4.8 104 W/m2 K (Table 1). Each element is discretized 30 times and solved with commercial software at time steps identical to the experiment. Fig. 5 shows how the peaks in DSF from this simulated data correspond to the actual RTH boundaries in the models. The difference in the location of the boundary (step in the dashed lines) and peak of DSF on the x-axis (arrows) is the difference in RTH at TIM–cooler boundary of the simulated data and the RTH that would be estimated from peak analysis of the DSF. The magnitude of this difference is not constant for all the simulations but changes with the relative influence of RTH,TIM. In general, the accuracy of the DSF peak increases as the TIM’s relative magnitude increases, but the peak becomes indistinguishable with the cooler at the high extreme. This analysis establishes the range where transient structure function analysis of the TIM is valid. It suggests that even if all noise and power nonuniformities were eliminated, there are still limits to the applicability of the SF. Two figures of merit are apparent, both are illustrated in Fig. 6 which quantifies the deviation between the RTH at the TIM–cooler interface of the model and DSF for a large range of RTH,TIM. First, there is good agreement (o10% error) when the TIM is greater than 25% of the total thermal resistance in the system. However, the peak gets pushed close to the end of the thermal path and smeared out when the TIM comprises more than 70% of the total resistance. Second, the location of the peak on the RTH axis determines how well it is resolved in the DSF. This is related to the first figure of merit, but it deals with where in the thermal path the TIM–cooler interface lies, not the magnitude of the TIM itself. The best peak is resolved when TIM–cooler interface is 20% of the total thermal path away from the heater but 30% from the cooler. These studies show that accurate keff,TIM measurements are possible using structure functions with proper test design and very little experimental error or noise. In the framework of Table 1, this applies to TIM for BLT greater than 25 mm. Improved cooler performance would extend the validity of the analysis proportionally, with target of 5–10 mm BLT.
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Fig. 6. Comparison between the location of the peak in the DSF (RTH,peak) and the actual value of the resistance in the numerical model (RTH,actual).
Fig. 8. Cross section of the high-performance liquid cooler revealing the microchannel array (Ardex product literature). Fig. 7. Numerical–experimental match when cooler heat capacity is neglected.
Next, the numerical models are used to extract RTH,TIM from experimental data by fitting the numerical model to the experiment. The formulation of the numerical model remains the same except that RTH,cooler is defined so that the total steady-state RTH of the model matches the experiment: RTH;cooler RTH;chip þ RTH;TIM RTH;experimental
(6)
Fig. 7 shows that ignoring the effective heat capacity of the cooler makes a transient match impossible. Similar mismatch occurs when analyzing the two in the structure function domain. The challenge is then to simulate the conjugate transient heat transfer within the cooler in the 1-D thermal network. Fig. 8 shows a cross section of the cooler geometry. It is clear that a simple 1-D RC model cannot capture the complete phenomena within the microstructure array so the model shown by Fig. 9 describes an approach that is simple and formulaic, avoiding elaborate and/or arbitrary assumptions. The new model has two additional variables: (1) the total heat capacitance of the cooler (Ccooler) and (2) a description of how this capacitance is distributed over the elements (OOM). If the latter is set to 0, all capacitances in the cooler would be equal, but as OOM increases, the capacitances farther from the heat source become relatively larger (however, the sum of the capacitances still equals Ccooler). Physically, this accounts for slow transients late in the response. Introducing two additional unknowns is not ideal from an optimization standpoint but it allows syste-
Fig. 9. schematic of system with modified cooler using N elements.
matic model fitting without knowledge the heat flow within the cooler. With this reformulated model, the transient response can be fit to less than 3.3% average relative error over the full response, shown in Fig. 10, corresponding to keff,TIM ¼ 2.0 W/m K, Ccooler ¼ 106 J/m2 K, and OOM ¼ 105. While this prediction of keff,TIM fits the initial analysis of the SF in Fig. 4, it is still inconsistent with variable BLT analysis and the vendor data. An important consideration, though, is the sensitivity of the modeling to keff,TIM. Fig. 8 shows contours representing the average deviation between experiment and model for a set of model variables. The figure contains the two slices of this 3-D space on the keff,TIM axis that contain the minimum point. The contours in both Fig. 11a and b are nearly parallel to the keff,TIM axis, indicating very low sensitivity of the fit to keff,TIM.
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Fig. 10. Best case experimental–numerical match. Average relative error over the full response time is 3.3%.
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problem for TIM characterization in a product-like fixture and is unlikely that a different cooler would remedy the problem. The insensitivity of the temporal response to TIM is due to the similarity of shape of the temperature rise for varying thermal interfaces (Fig. 3). Another option is to fit the data in the structure function rather than time domain. As illustrated in Fig. 12, though, there is little relationship between the peaks in the experimental and numerical data for any keff,TIM. The noise and spreading effects may influence the location of the ‘‘real’’ peaks corresponding to material boundaries and a matching algorithm using either SF or DSF is not possible. The alternative and more common procedure is to compare the SF of one experiment versus a known sample and associate the shifts in SF (or peaks in DSF) with the differences in the property of interest, rather than taking the absolute value of a plateau in the SF. Applied to the product-like fixture, a robust and repeatable cooler model would eliminate two of the three fitting parameters in the numerical formulation and simplify the fitting technique. However, the cooler performance and system parasitics always vary slightly from test-to-test and these variations could lead to large errors in keff,TIM prediction due to the relative contribution of TIM versus cooler (Table 1). In the broader sense, an accurate cooler model could be easily applied to the steady-state test for the same purpose but with less complexity than transient because the thermal mass of the cooler is not a steady-state parameter. This would again favor the steady-state test for high-performance TIM characterization. As mentioned previously, the transient method is preferred over steady only if it can characterize the film with one measurement. A final consideration is the speed of the transient technique. While the TIM only effects the first few seconds of the response, the full system may take a few minutes to reach steady state, especially for more complicated packages. Recent work on LED assembly characterization [30] demonstrated that the early portion of the structure function is only minimally influenced if the test is stopped prematurely, before the system reaches full steady state. Applied to TIM measurements, it may be adequate to characterize the TIM using only this data instead of the full steady state. This is a promising topic of future transient test development for chip-to-cooler thermal interface characterization.
4. Conclusion
Fig. 11. Average relative error dependence on model variables: (a) keff,TIM vs. Ccooler with OOM fixed at 105 and (b) keff,TIM vs. OOM with Ccooler fixed at 106 J/m2 K.
In fact, any value of keff,TIM can be fit to less than 4% error by manipulating the other variables. Therefore, cooler uncertainty makes the transient fitting technique unreliable. This is a general
The variable BLT technique is robust and accurate in both static and transient TIM characterization schemes. When implemented in a product-like test fixture, it is especially relevant for industrystandard chip-to-cooler TIMs. It is non-ideal, however, since BLT cannot be accurately controlled over a wide range for multiple TIM formulations and is time-consuming. Furthermore, it cannot easily account for thickness-dependent keff,TIM that may lead to inaccurate estimation of keff,TIM at the final BLT. Transient measurements to extract keff,TIM though numerical model fitting are inadequate due to the uncharacterized complexities of heat transfer within the cooler, heat spreading due to spatial nonuniformities in heat flux, and noise in the early transients. However, the technique could enable rapid characterization of the TIM with only one measurement at the mostrelevant (final) BLT. Ongoing work uses numerical analysis to focus on the early transients most affected by TIM. Complementary efforts to reduce experimental signal-to-noise ratio, systematic errors, and thermal resistance of the cooler will increase the sensitivity of the system to TIM properties.
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Fig. 12. DSF of experiment versus best-fit models for varying keff,TIM.
Acknowledgment The authors thank Hugo Rothuizen, Urs Kloter, Ryan Linderman, Evan Colgan, and Paul Seidler for discussions and support. References [1] R. Prasher, Thermal interface materials: historical perspective, status, and future directions, Proc. IEEE 94 (8) (2006). [2] M. Yovanovich, Four decades of research on thermal contact, gap, and joint resistance in microelectronics, IEEE Trans. Components Packag. Technol. 28 (2) (2005). [3] C. Yee, G. Quadir, Z. Zainal, Investigation of steady state and transient thermal management in portable telecommunication products-Part 2, IMAPS J. Microelectron. Packag. 2 (2) (2005) 2005. [4] T. Lee, B. Chambers, K. Ramakrishna, Thermal management of handheld telecommunication products, Electron. Cool. 4 (2) (1998). [5] R. Schmidt, E. Cruz, M. Iyengar, Challenges of data center thermal management, IBM J. Res. Dev. 49 (4/5) (2005). [6] H. Zhang, D. Pinjala, P. Teo, Thermal management of high power dissipation electronic packages from air cooling to liquid cooling, in: Proceedings of the 2003 Electronics Packaging Technology Conference, Singapore, 2003. [7] G. Refai-Ahmed, Z. He, E. Hejan, R. Vincent, T. Rude, D. Van Heerden, Comparison of thermal performance of current high-end thermal interface materials, in: Proceedings of the Interpack 2007, Vancouver, BC, Canada, 2007. [8] F. Hua, C. Deppisch, T. Fitzgerald, Indium as thermal interface material for high power devices, Adv. Microelectron. (2006) 16–17. [9] C.G. Macris, R.G. Ebel, C.B. Leyerle, J.C. Cullough, Phase change metallic alloy TIM2 performance and reliability, in: Proceedings of the Interpack 2007, Vancouver, BC, Canada, 2007. [10] P. Teertstra, Thermal conductivity and contact resistance measurements for adhesives, in: Proceedings of the Interpack 2007, Vancouver, BC, Canada, 2007. [11] J. Tzeng, T. Webber, D. Draqssowski, Technical review on thermal conductivity measurement techniques for thin thermal interfaces, in: Proceedings of the 16th IEEE Semi-Therm, 2000, pp. 174–181. [12] J. Gwinn, R. Webb, Performance and testing of thermal interface materials, in: Proceedings of the THEMES, Santa Fe, NM, USA, 2002, pp. 201–210. [13] R. Aoki, C. Chiu, A testing apparatus for thermal interface materials, in: Proceedings of the 1998 International Symposium on Microelectronics, San Diego, CA, USA, 1998. [14] ASTM D5470: Standard Test Method for Thermal Transmission Properties of Thermally Conductive Electrical Insulation Materials, ASTM International.
[15] D. Kearns, Improving accuracy and flexibility of ASTM D 5470 for high performance thermal interface materials, in: Proceedings of the 19th IEEE Semi-Therm, 2003, pp. 129–133. [16] R. Linderman, T. Brunschwiler, U. Kloter, H. Toy, B. Michel, Hierarchically nested channels for reduced particle stacking and low-resistance thermal interfaces, in: Proceedings of the 23rd IEEE Semi-Therm Symposium, San Jose, CA, 2007, pp. 87–94. [17] D.G. Cahill, K. Goodson, A. Majumdar, Thermometry and thermal transport in micro/nanoscale solid-state devices and structures, Trans. ASME–J. Heat Trans. 124 (2) (2002) 223–241. [18] C. Lasance, T. Murray, D. Saums, M. Rencz, Challenges in thermal interface material testing, in: Proceedings of the 22nd IEEE Semi-therm Symposium, Dallas, TX, USA, 2006, pp. 42–49. [19] E. Bosch, C. Lasance, Accurate measurement of interface thermal resistance by means of a transient method, in: Proceedings of the 16th IEEE Semi-Therm Symposium, San Jose, CA, 2000, pp. 167–173. [20] ASTM E1461: Standard Test Method for Thermal Diffusivity of Solids by the Flash Method, ASTM International. [21] S. Ress, E. Kolla´r, Comparison of various thermal transient measurement methods on a benchmark package, In:, Proceedings of the Sixth Therminic Workshop, Budapest, Hungary, 2000 [22] V. Sze´kely, S. Ress, A. Poppe, S. To¨ro¨k, D. Magyari, Zs Benedek, K. Torki, B. Courtois, M. Rencz, New approaches in the transient thermal measurements, Microelectron. J. 31 (9–10) (2000) 727–734. [23] Y. Cengel, Heat Transfer: A Practical Approach, WCB McGraw-Hill, ISBN 0-07115223-7, 1998. [24] B. Smith, T. Brunschwiler, B. Michel, Utility of transient testing to characterize thermal interface materials, in: Proceedings of the 13th Therminic Workshop, Budapest, Hungary, 2007. [25] V. Sze´kely, M. Rencz, L. Pohl, Novelties in the theory and practice of thermal transient measurements, in: Proceedings of the Seventh Therminic Workshop, Paris, France, 2001. [26] V. Sze´kely, Identification of RC networks by deconvolution: chances and limits, IEEE Trans. Circuits Syst. 45 (3) (1998) 244–258. [27] A. Jacquot, B. Lenior, A. Daucher, M. Stozer, J. Meusel, Numerical simulation of the 3-omega method for measuring the thermal conductivity, J. Appl. Phys. 91 (7) (2002) 4733–4738. [28] G. Chen, P. Hui, Pulsed photothermal modeling of composite samples based on transmission-line theory of heat conduction, Thin Solid Films 339 (1999) 58–67. [29] S. Lang, Laser intensity modulation method (LIMM): review of fundamentals and a new method for data analysis, IEEE Trans. Dielectr. Electr. Insul. 11 (1) (2004) 3–12. [30] P. Szabo, G. Farkas, A. Poppe, M. Rencz, Methodology for the inline die attach characterization of power LEDs, in: Proceedings of the Interpack 2007, Vancouver BC, Canada, 2007.
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Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo
Comparison of transient and static test methods for chip-to-sink thermal interface characterization B. Smith , T. Brunschwiler, B. Michel ¨umerstrasse 4, 8803 Ru ¨ schlikon, Switzerland IBM Research GmbH, Zurich Research Laboratory, Science & Technology, Sa
a r t i c l e in fo
abstract
Article history: Received 30 November 2007 Received in revised form 28 May 2008 Accepted 4 June 2008 Available online 8 August 2008
Accurate thermal interface characterization is essential for high flux microelectronic package design. However, it is increasingly difficult as interfacial bond lines are thinned and thermal interface materials (TIM) evolve to more complex formulations with better performance. This paper compares a static versus transient characterization method targeted at the chip-to-package interface in a test fixture that closely resembles a packaged chip. The static method requires measurements over multiple bond line thicknesses while the transient method yields additional information about the package at the cost of greater numerical complexity, hardware requirements, sensitivity to noise and experimental uncertainty. Both are compared with existing techniques. We conclude that the static method is more generally-applicable while transient is well-suited to rapid characterization of the interface when the rest of the package is well-defined. While both methods are sensitive to the accuracy and resolution of temperature and bondline thickness measurements, the transient technique is additionally sensitive to the relative contribution of the TIM in the full junction-to-ambient thermal path. These points are illustrated through experimental results and compact numerical modeling. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Thermal interface material Transient thermal test Electronics cooling TIM Interface characterization Structure function
1. Introduction Heat diffusion across the interface of two components in an electronic package is a well-studied topic in the thermal packaging field [1,2]. It is fundamental to any package, from conduction-only designs for handheld electronics [3,4] to large datacenters featuring a complex combination of liquid and air fan cooling [5,6]. The thermal interface can account for up to 50% of the total thermal budget in some packages and directly influences product lifetime, performance, reliability, and power consumption. Advanced thermal packages often use metal interfaces [7,8], phase-change materials [9], or thermal interface materials (TIM) made from highly particle-filled materials including greases and adhesives [10]. The optimal TIM for an application is a factor of thermal, mechanical, assembly, and cost considerations but the thermal performance is defined by its thermal resistance, RTH,TIM (K cm2/W). Acoustic mismatch, or the inability to couple the energycarrying phonons of one surface to the interface material is referred to as contact resistance and is one contributor to the overall RTH of the TIM. More significant for the interfaces with
Corresponding author. Tel.: +41 44 724 8775; fax: +41 44 724 8958.
E-mail address: [email protected] (B. Smith). 0026-2692/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.06.079
bondline thickness (BLT) greater than 1 mm considered here is the resistance to heat diffusion within the TIM, which defines the temperature rise per unit of heat input based on Fourier’s law of heat conduction: q00 ¼ keff
qT ¼ RTH DT qx
(1)
where q00 is heat flux per unit area, keff is the effective thermal conductivity of the medium, T is temperature, and x is length of the medium in the direction of heat propagation. When applied to TIM geometries, RTH reduces to RTH;TIM ¼
BLT keff;TIM
(2)
where keff,TIM is the effective thermal conductivity of the TIM. In this formulation, the direction of heat diffusion is assumed one dimensional, normal to the interface. Therefore, most TIM characterization techniques induce 1-D heat flow and measure the steady or transient temperature gradient through the system to extract RTH,TIM [11–13]. Generally speaking, it is difficult to identify trends in the popularity of the TIM test techniques; rather, each technique has its own niche. Static techniques require the least instrumentation overhead so are well-suited to characterize TIMs with relatively large thermal resistance and BLT. Increased measurement accuracy required for high-keff, small-BLT TIMs begins to marginalize
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this advantage, though, and the cost of high-temporal resolution sampling hardware and advanced data processing software can be justified for transient techniques, especially if they promise faster total test time. Many static test techniques follow ASTM D5470 [14,15], involving four to six temperature sensors placed in-line with the heat flow, half on one side of the interface and half on the other. The discontinuity of the temperature gradient across the interface is attributed to the TIM, and Eq. (1) is used to extract effective conductivity if the BLT is known. The design shown in Fig. 1 is related to this method but more closely resembles an electronic package. A heating element and temperature sensors are fabricated on-chip and TIM placed between chip and heat sink [16]. This layout is advantageous for microelectronics applications because the TIM bondline is formed using the same assembly process and geometry used in the product so any process-dependent effects on RTH,TIM are accounted for. It can be adapted to add and characterize other packaging components like a lid or spreader (Fig. 1b). The thermal resistance of the system in Fig. 1 is defined by the junction temperature of the chip and inlet temperature of the cooler. RTH, TIM is then extracted by either: (1) characterizing the other resistances in the system separately and subtracting them from the measurement to obtain RTH,TIM; or (2) measuring overall RTH for different BLT of the same TIM and associating the
Fig. 1. Schematic of the test fixture with corresponding RC network model describing 1-D heat flow through the TIM: (a) standard heater-cooler arrangement referred to as ‘‘direct attach heat sink’’ and (b) alternative including a spreader or lid also accommodated by the fixture.
derivative of Eq. (2) with respect to BLT to the change in overall system resistance. It is not possible to completely characterize the other components since the performance of the cooler may change over time and, more importantly, contact resistances among the components can vary from one measurement and material to the next. Therefore the second option, referred to as the variable BLT method, is preferred since no additional knowledge of the system is needed. Fig. 2 illustrates this method, plotting the relationship between BLT and RTH for typical TIM material. The TIM’s effective conductivity is the inverse of the slope of the linear fit to this data. While this means that the method is unable to characterize materials with thickness-dependent keff, the conductivity of nearly every TIM material is BLT-independent at the completion of the squeeze process if assembly pressure is larger than other forces (gravity) and the TIM spreads uniformly over the interface. Full discussion follows later but the accuracy of the approach will clearly rely on the R2 value of the linear fit and the uncertainty of RTH and BgLT measurement. Alternately, transient or harmonic methods can isolate the influence of the TIM from the other components in the thermal path [17–20], eliminating error from thermal uncertainties in adjacent components like the cooler. Harmonic and pulse-based transient methods such as 3-omega and laser flash techniques including thermoreflectance have become the standards for thin film thermometry; however, the numerical fitting models and laser heat pulsing required limit their application in a product-like test fixture (Fig. 1), which is preferred for industry relevance. RC analysis using the thermal structure function [21,22], is another candidate as it allows in-package testing of the TIM without multiple BLT measurements or knowledge of the other components in the system. The structure function (SF) is a numerical deconvolution and transformation of the temporal response that can identify the magnitude of thermal resistance and heat capacity of each region in the thermal path, thereby isolating the TIM from the rest of the system. It compiles a sort of complex impedance profile of the heat path from source to sink and associates abrupt changes in the thermal capacitance along the path with material boundaries. That way, the difference in cumulative thermal resistance from one boundary to the next corresponds to the thermal resistance of that component. In the case of the TIM, this data point combined with Eq. (2) and BLT constitute the effective conductivity of the material. Electrical noise and heat spreading outside the 1-D path are significant challenges to the transient analysis with structure functions. Rather than directly interpreting SF, the experimental temporal response can be compared with a numerical model using a Cauer network of thermal RC circuit elements, generally
Fig. 2. Variable BLT static TIM measurement. Circles represent experimental data points (with error bars discussed later), the dashed line is the best fit line through the data. The contribution of each component is labeled and marked by area fill.
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represented by Fig. 1. Both the experimental and numerical data is transformed into the structure function domain and the numerical model fit to experiment to extract RTH,TIM and keff,TIM. The numerical models also provide a sort of idealized, noise-free input to identify the limits over which the SF methods can be used for TIM characterization. Both of these approaches are analyzed in later sections. While thermoreflectance and 3-omega-like methods are established and accurate for a variety of geometries, they are still not suitable in-situ testing of TIM materials in a microelectronics package. Therefore, we focus this work on the static test applied to the setup of Fig. 1, plus the transient method using the same package. The details of the test fixture and data reduction methods of each test are first discussed followed by the presentation of an experimental test case. We discuss the uncertainties and measurement errors of each technique and develop figures of merit for the applicability of the transient test.
2. Experimental setup Fig. 1 shows the experimental fixture schematically and this work will focus on the ‘‘direct attach’’ scheme of Fig. 1a. A pneumatic cylinder (Festo Corp.) presses the IBM-designed thermal chip and chip carrier (ceramic substrate and PWB) to the liquid cooler (Ardex from Atotech, Inc.). A high-performance liquid chiller (Proline series from Lauda) uses a NIST-traceable temperature probe (0.05 1C accuracy) and controller to hold the cooler’s inlet temperature to 25.070.01 1C. The chiller is also used to calibrate the temperature sensors so the estimated maximum error of the temperature measurement is 0.1 1C. Power is measured by an on-chip voltage probe and calibrated 1 O resistor in series with the power supply. A calibrated 612-digit switching multimeter (model 2701 from Keithley Instruments, Inc.) is used to acquire all data so the error of the power measurement should be less than 1%. Setting the power so the total temperature rise of the system is greater than 10 1C ensures that the uncertainty on the temperature measurement is also less than 1% so the total error on power and temperature data acquisition is then close to 1%. Four induction-based displacement sensors with 0.1 mm resolution (Mahr, GmbH, not shown), factory-calibrated to 0.4 mm accuracy, measure BLT by contacting the ceramic substrate 5 mm from each corner of the chip. A zero-BLT reference is taken prior to TIM measurement. The arithmetic average of these four measurements is a very good indication of the average BLT, even though variation in corner-to-corner measurement up to 8 mm is acceptable, owing to the tolerance in the guide rails of the cylinder. Four serpentine resistors, each located in a quadrant of the chip and covering roughly 85% of the chip total area, are fabricated onchip with standard photolithography to apply uniform heat flux to the package. Nine 4-point RTD sensors, each approximately 1 mm2 are deposited over the heaters and are located at the chip’s center, corners, and the center of each quadrant. Heat flux (and therefore temperature) uniformity in the chip worsens as the keff,TIM improves since the heat cannot easily spread laterally in the chip if RTH,TIM+RTH,Si,through plane is less than RTH,Si in plane. Temperature hot spots lie at the center of each of the quad heaters (Thigh) while minimum is at the chip center and corners (Tlow). The temperature profile from hot to cold will follow a parabola as indicated for 1-D radial heat spreading in a cylindrical coordinate system with uniform power generation [23]. This assumption is used to build a temperature map of the chip based on the nine data points. The average temperature of
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the chip (Tave) then follows: T avg ¼ T low þ 0:658ðT high T low Þ
(3)
where the bar above the temperature symbols designates the arithmetic average of all sensors corresponding to the high or low temperature reading (average of all quadrant sensors ¼ T high , for example). In practice, there is little variation in temperature within T high and T low sensor groupings, validating this averaging approach. It then follows that the thermal resistance of the system is RTH ¼
T avg A P
(4) 2
where A is the area (18.3 18.4 mm ) and P is the electrical power through the chip. The ratio T high =T low was measured as high as 1.7 for the best TIMs, despite the 85% coverage of the serpentine heaters so this averaging assumption influences the accuracy of the measurement much more than the uncertainty of the individual data points. An analysis of the effect of temperature averaging and nonuniformities on the TIM characterization follows in later sections. Generally speaking, though, the averaging of the BLT and temperature measurements together ensure that the overall geometry and heat profile of the TIM is captured despite the uncertainties in the product-like test stand. Finally, the cooler is mounted to a force sensor (ME-Messysteme GmbH) to monitor the pressure/force applied during the TIM squeeze process for pressure-actuated BLT control since final BLT is a strong function of applied pressure.
3. Results and analysis This section illustrates the strengths and capabilities of each measurement approach with a case study using a commercially available TIM material with keff,TIM ¼ 5 W/m K reported by the vendor. The material was chosen for its relevance to the industry and high viscosity (easily-controllable BLT). Extending each technique to other TIM materials is also discussed. In both tests, uncertainty of the power and temperature measurements is limited to 1% at all points but grows with decreasing BLT since the displacement sensors are calibrated to 0.4 mm. This leads to o1% error on a 50 mm BLT measurement but up to 10% when BLT ¼ 4.0 mm, for example. The thermal resistance of the parasitic heat paths through the ceramic and the surrounding air were nearly two orders of magnitude higher than the Si–TIM–cooler path, so effectively all the power from the heater is dissipated through the TIM. Temperature nonuniformity within the chip was significant as the bondline thinned below 10 mm (T high =T low approaching 1.35). However, Eq. (3) provides a reasonable estimate of the average temperature of the chip so the actual uncertainty of Tavg is less than the 29% maximum spread in the thermal data. Additionally, the ratio drops below 1.1 for thicker bondlines. Power nonuniformity affects the ability of the setup to resolve spatial nonuniformities in the TIM, but Tavg is a good overall estimate considering the power and BLT data are also composites from multiple discrete measurements. 3.1. Steady state The variable BLT static test yields keff,TIM ¼ 4.8 W/m K with R2 ¼ 0.999 (Fig. 2). The slope fit has an averaging effect so the total uncertainty of the keff,TIM prediction is less than the maximum uncertainty of the data points and additional data points increase the accuracy of the measurement. The relative contributions of the three components illustrated in Fig. 2 and Table 1 are calculated by the vertical axis intercept of
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Table 1 Relative contributions to total RTH BLT (mm)
RTHsystem (Kcm2/W)
% Si
% TIM
% Cooler
54.6 15.2 6.8
0.372 0.288 0.271
13.3 17.2 18.3
30.5 11.0 5.2
56.2 71.8 76.5
the linear data fit plus the analytical estimation of silicon resistance. The remaining resistance, 0.21 K cm2/W, is attributed to the cooler and translates to an effective heat transfer coefficient, h ¼ 48 kW/m2 K. Table 1 also shows the relative contribution of each component in the heat path. There is no fundamental limits on the measurement range of RTH,TIM or the required ratio of RTH,TIM to RTH,system as long as the power is set so the temperature rise across the TIM is significantly greater than the uncertainty of the temperature measurement (0.1 1C). In practice, though, a TIM that accounts for only 5% of RTH,system requires 100 1C junction-to-ambient temperature rise to effect 5 1C rise across the interface (50x the uncertainty of the measurement). These practical limitations prevent measurements when the TIM contributes less than 5%. Similarly, the uncertainty of BLT rises above 10% for BLTo5 mm, decreasing the accuracy of keff,TIM. Nevertheless, the variable BLT static method requires little data processing. It is robust since temporal and spatial averaging of the power and thermal data minimize sensitivity to transient drift and lateral spreading in the chip. The method’s biggest drawback is the need to measure multiple BLTs since precise displacement control is not realistic over a large range (5–100 mm) without the use of artificial means to stop the bondline which can influence keff,TIM. Accuracy of the fit line, and therefore keff, TIM estimate, decreases with range making the method especially difficult for low viscosity TIMs. A single thermal measurement at the final BLT is most attractive and relevant for package design.
Fig. 3. Temporal response to power step for each BLT.
3.2. Transient The transient method uses the same test fixture, heater/sensor chip, and cooler. Fast (o2 ms) power switching, RTD temperature sampling, filtering, and processing are facilitated by Thermal Transient Tester hardware (Micred, Inc.). The system response to a power step (Fig. 3) is recorded with 1 ms resolution at the beginning of the response. This is especially important since the thermal mass of the TIM affects the shape of the response for only approximately 1 s after the load is applied. The uncertainties of the measurement remain the same from the static test, although the spatial averaging of the temperature data is implemented as a scale factor at the end of the structure function calculation. Averaging the temperature data according to Eq. (3) at each time step would distort the actual thermal response along the heat path so one sensor is chosen and RTH is scaled by Eq. (3) after structure function calculation. A sensor on the center of a heater quadrant is used since the response data should be co-located with the heat source for straightforward SF interpretation. The final (maximum) RTH value with respect to BLT reported by the transient technique follows the steady predictions. In fact, the variable BLT technique could also be applied to the final value of the transient data to yield keff,TIM ¼ 4.3 W/m K, within 10% of the steady prediction. Of course, this analysis uses none of the transient or structure function data, but is a good check on the fidelity of both measurements. As shown in Fig. 3, the system responds slightly faster when BLT ¼ 4.2 mm (steeper slope in the 1–100 ms region), corresponding to less thermal mass. Before considering the structure function
Fig. 4. Integral structure function (a) and differential structure function (b) for each BLT.
domain, it is logical to try and extract RTH, TIM directly from these temporal response curves using a slope matching technique. Strong coupling among thermal elements means that the sensitivity of the response curve to any one component is not
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large, however, so the shape of the response in the time domain does not easily yield RTH,TIM. Next, the integral structure functions for each BLT test are computed, shown in Fig. 4a. Previous work [24] discusses influence of numerical parameters of the SF transformation. TIM analysis in microelectronics packages is especially challenging compared to other applications of the transient method since the magnitude of RTH,TIM is less than or comparable to other components and maintaining 1-D heat transfer with thin BLT, high conductivity TIMs is exceedingly difficult. As mentioned, the SF is a kind of thermal history in the RTH domain, plotting the cumulative thermal capacitance of system versus its location in the 1-D heat path from source (RTH ¼ 0) to sink (RTH ¼ RTH,steady). The deconvolution of the high-temporal resolution response (temperature) from the load (power step) results in the time constant spectrum of the system, which is fit to a 1-D Foster network and then transformed to a Cauer network. The Cauer network contains physically realistic thermal RC elements, capturing the load-to-sink response of the system. To analyze the network, the cumulative thermal resistance and capacitance at each point in the network with respect to the origin (RTH ¼ 0) defines the system’s SF-cumulative capacitance plotted against cumulative resistance. The numerical derivative (DSF) identifies material boundaries by highlighting where the SF changes rapidly. Full details, theory, and discussion of the structure function can be found elsewhere [22,25,26]. One interpretation of Fig. 4 is that the plateau around 1 W s/K is the region corresponds to the TIM. The smaller steps toward the end of the path are likely effects of conjugate conduction– convection in the cooler. It then follows that RTH,TIM ¼ 0.15, 0.175, and 0.205 cm2 K/W for the 4.2, 23.7, and 34.2 mm measurements, respectively, based on the length of this plateau on the x-axis. The DSF (Fig. 4b) yields the same information by identifying the peaks instead of the boundaries. However, these data correspond to keff,TIM ¼ 0.28, 1.35, and 1.65 W/m K, respectively, which is much lower than the static test and the vendor data. Uncertainty from the BLT measurement in the 4.2 mm case and the temperature averaging techniques alone cannot explain this deviation. The first step in the SF near the RTH ¼ 0 axis could be enhanced by a synthetic cumulative structure function section to better resolve the location of the step; however, this is also unlikely to account for the 3–5x difference in keff,TIM. Electrical noise from power switching in the early transients and lateral heat spreading are two likely sources of error in the SF analysis. The former can distort the Si–TIM boundary while the later violates the 1-D heat flow assumption of the SF compilation. Strategies to improve heat flux uniformity with conductive inserts or lower-performance coolers tend only to marginalize the overall effect of the TIM, add thermal mass, and reduce the test’s sensitivity to TIM properties. It is possible to isolate the effects of noise and spreading by simulating test data with numerical models and comparing the structure function results to the input of the models. The numerical models are noise-free and based on 1-D heat spreading in a Cauer RC network. They can serve two roles: (1) to identify the range over which the SF analysis is valid for TIM characterization if noise and spreading are not an issue; and (2) to extract the TIM properties by fitting a numerical model to the real experimental data, thereby identifying which peaks/plateaus correspond to actual material boundaries and which are numerical artifacts. The later approach is often employed in thin film thermometry using various analytical and numerical models [27–29]. Each component in the 1-D thermal path is represented by an RC element as shown in Fig. 1. Resistance follows Eq. (2) with the length of the component in the direction of heat flow substituted
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Fig. 5. Comparison between peaks in DSF of simulated data and actual resistance path through the model for three values of RTH,TIM. The magnitude of each component (silicon, TIM, and cooler) is represented by a step in the dashed line. The magnitude RTH,TIM increases as with darker lines.
BLT while thermal capacitance per unit area (C) is defined as C ¼ Cv L
(5)
where Cv is the material’s volumetric heat capacity and L is the length of the component in the direction of heat flow. The resistance and capacitance of the chip is based on published silicon literature and a rough estimate is used for CTIM (the model is insensitive to CTIM for any reasonable value of CvTIM). The cooler is considered a pure resistor: heat capacity is set to zero and 1/RTH,cooler corresponds to h ¼ 4.8 104 W/m2 K (Table 1). Each element is discretized 30 times and solved with commercial software at time steps identical to the experiment. Fig. 5 shows how the peaks in DSF from this simulated data correspond to the actual RTH boundaries in the models. The difference in the location of the boundary (step in the dashed lines) and peak of DSF on the x-axis (arrows) is the difference in RTH at TIM–cooler boundary of the simulated data and the RTH that would be estimated from peak analysis of the DSF. The magnitude of this difference is not constant for all the simulations but changes with the relative influence of RTH,TIM. In general, the accuracy of the DSF peak increases as the TIM’s relative magnitude increases, but the peak becomes indistinguishable with the cooler at the high extreme. This analysis establishes the range where transient structure function analysis of the TIM is valid. It suggests that even if all noise and power nonuniformities were eliminated, there are still limits to the applicability of the SF. Two figures of merit are apparent, both are illustrated in Fig. 6 which quantifies the deviation between the RTH at the TIM–cooler interface of the model and DSF for a large range of RTH,TIM. First, there is good agreement (o10% error) when the TIM is greater than 25% of the total thermal resistance in the system. However, the peak gets pushed close to the end of the thermal path and smeared out when the TIM comprises more than 70% of the total resistance. Second, the location of the peak on the RTH axis determines how well it is resolved in the DSF. This is related to the first figure of merit, but it deals with where in the thermal path the TIM–cooler interface lies, not the magnitude of the TIM itself. The best peak is resolved when TIM–cooler interface is 20% of the total thermal path away from the heater but 30% from the cooler. These studies show that accurate keff,TIM measurements are possible using structure functions with proper test design and very little experimental error or noise. In the framework of Table 1, this applies to TIM for BLT greater than 25 mm. Improved cooler performance would extend the validity of the analysis proportionally, with target of 5–10 mm BLT.
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Fig. 6. Comparison between the location of the peak in the DSF (RTH,peak) and the actual value of the resistance in the numerical model (RTH,actual).
Fig. 8. Cross section of the high-performance liquid cooler revealing the microchannel array (Ardex product literature). Fig. 7. Numerical–experimental match when cooler heat capacity is neglected.
Next, the numerical models are used to extract RTH,TIM from experimental data by fitting the numerical model to the experiment. The formulation of the numerical model remains the same except that RTH,cooler is defined so that the total steady-state RTH of the model matches the experiment: RTH;cooler RTH;chip þ RTH;TIM RTH;experimental
(6)
Fig. 7 shows that ignoring the effective heat capacity of the cooler makes a transient match impossible. Similar mismatch occurs when analyzing the two in the structure function domain. The challenge is then to simulate the conjugate transient heat transfer within the cooler in the 1-D thermal network. Fig. 8 shows a cross section of the cooler geometry. It is clear that a simple 1-D RC model cannot capture the complete phenomena within the microstructure array so the model shown by Fig. 9 describes an approach that is simple and formulaic, avoiding elaborate and/or arbitrary assumptions. The new model has two additional variables: (1) the total heat capacitance of the cooler (Ccooler) and (2) a description of how this capacitance is distributed over the elements (OOM). If the latter is set to 0, all capacitances in the cooler would be equal, but as OOM increases, the capacitances farther from the heat source become relatively larger (however, the sum of the capacitances still equals Ccooler). Physically, this accounts for slow transients late in the response. Introducing two additional unknowns is not ideal from an optimization standpoint but it allows syste-
Fig. 9. schematic of system with modified cooler using N elements.
matic model fitting without knowledge the heat flow within the cooler. With this reformulated model, the transient response can be fit to less than 3.3% average relative error over the full response, shown in Fig. 10, corresponding to keff,TIM ¼ 2.0 W/m K, Ccooler ¼ 106 J/m2 K, and OOM ¼ 105. While this prediction of keff,TIM fits the initial analysis of the SF in Fig. 4, it is still inconsistent with variable BLT analysis and the vendor data. An important consideration, though, is the sensitivity of the modeling to keff,TIM. Fig. 8 shows contours representing the average deviation between experiment and model for a set of model variables. The figure contains the two slices of this 3-D space on the keff,TIM axis that contain the minimum point. The contours in both Fig. 11a and b are nearly parallel to the keff,TIM axis, indicating very low sensitivity of the fit to keff,TIM.
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Fig. 10. Best case experimental–numerical match. Average relative error over the full response time is 3.3%.
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problem for TIM characterization in a product-like fixture and is unlikely that a different cooler would remedy the problem. The insensitivity of the temporal response to TIM is due to the similarity of shape of the temperature rise for varying thermal interfaces (Fig. 3). Another option is to fit the data in the structure function rather than time domain. As illustrated in Fig. 12, though, there is little relationship between the peaks in the experimental and numerical data for any keff,TIM. The noise and spreading effects may influence the location of the ‘‘real’’ peaks corresponding to material boundaries and a matching algorithm using either SF or DSF is not possible. The alternative and more common procedure is to compare the SF of one experiment versus a known sample and associate the shifts in SF (or peaks in DSF) with the differences in the property of interest, rather than taking the absolute value of a plateau in the SF. Applied to the product-like fixture, a robust and repeatable cooler model would eliminate two of the three fitting parameters in the numerical formulation and simplify the fitting technique. However, the cooler performance and system parasitics always vary slightly from test-to-test and these variations could lead to large errors in keff,TIM prediction due to the relative contribution of TIM versus cooler (Table 1). In the broader sense, an accurate cooler model could be easily applied to the steady-state test for the same purpose but with less complexity than transient because the thermal mass of the cooler is not a steady-state parameter. This would again favor the steady-state test for high-performance TIM characterization. As mentioned previously, the transient method is preferred over steady only if it can characterize the film with one measurement. A final consideration is the speed of the transient technique. While the TIM only effects the first few seconds of the response, the full system may take a few minutes to reach steady state, especially for more complicated packages. Recent work on LED assembly characterization [30] demonstrated that the early portion of the structure function is only minimally influenced if the test is stopped prematurely, before the system reaches full steady state. Applied to TIM measurements, it may be adequate to characterize the TIM using only this data instead of the full steady state. This is a promising topic of future transient test development for chip-to-cooler thermal interface characterization.
4. Conclusion
Fig. 11. Average relative error dependence on model variables: (a) keff,TIM vs. Ccooler with OOM fixed at 105 and (b) keff,TIM vs. OOM with Ccooler fixed at 106 J/m2 K.
In fact, any value of keff,TIM can be fit to less than 4% error by manipulating the other variables. Therefore, cooler uncertainty makes the transient fitting technique unreliable. This is a general
The variable BLT technique is robust and accurate in both static and transient TIM characterization schemes. When implemented in a product-like test fixture, it is especially relevant for industrystandard chip-to-cooler TIMs. It is non-ideal, however, since BLT cannot be accurately controlled over a wide range for multiple TIM formulations and is time-consuming. Furthermore, it cannot easily account for thickness-dependent keff,TIM that may lead to inaccurate estimation of keff,TIM at the final BLT. Transient measurements to extract keff,TIM though numerical model fitting are inadequate due to the uncharacterized complexities of heat transfer within the cooler, heat spreading due to spatial nonuniformities in heat flux, and noise in the early transients. However, the technique could enable rapid characterization of the TIM with only one measurement at the mostrelevant (final) BLT. Ongoing work uses numerical analysis to focus on the early transients most affected by TIM. Complementary efforts to reduce experimental signal-to-noise ratio, systematic errors, and thermal resistance of the cooler will increase the sensitivity of the system to TIM properties.
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Fig. 12. DSF of experiment versus best-fit models for varying keff,TIM.
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