CROSS REFERENCE TO RELATED APPLICATION
This application claims the benefit of priority to U.S. Provisional Patent Application Ser. No. 60/829,753, filed Oct. 17, 2006, entitled ELECTROTHERMAL INTERFACE MATERIAL ENHANCER, incorporated herein by reference.
The United States government may have rights to certain aspects of this invention as a result of funding from Air Force Research Lab Grant No. FA8750-04-D-2409.
FIELD OF THE INVENTION
This invention pertains to flexible structures having nanostructures attached to a surface, and in particular to deformable thermal and electrical interface materials using multiwalled carbon nanotubes.
BACKGROUND OF THE INVENTION
Electrical contacts are vital elements in many engineering systems and applications at the macro, micro, and nano scales. Reliability and functionality of electrical contacts can often be a limiting design factor. A major portion of electrical contact resistance comes from the lack of ideal mating between surfaces. Primary causes of this problem involve the mechanical properties of the surfaces and surface roughness. When two surfaces are brought together, the actual contact area may be much smaller than the apparent contact area. The contact between two surfaces can actually be thought of as the contact of several discrete points in parallel, referred to as solid spots or α-spots. Thus, only the α-spots act as conductive areas and can be a small percentage of the total area.
Since their discovery, carbon nanotubes (CNTs) have been studied intensively throughout many communities in science and engineering. Several researchers have reported on the mechanical, electrical, and thermal properties of individual single-wall carbon nanotubes (SWNTs). The electrical properties of SWNTs are affected by the chirality of the SWNTs to the degree that the SWNTs can exhibit metallic or semiconducting electrical conductivity. The electrical transport properties of a single SWNT are a well studied subject. It has been shown that for ballistic transport and perfect contacts, a SWNT has a theoretical resistance of 6.45 KΩ, which is half of the quantum resistance h/2e2. In MWCNTs, each layer within the MWCNT can have either a metallic or semi-conducting band structure depending on its diameter and chirality. Due to this variation among layers, the net electrical behavior of a MWCNT is typically metallic and a wide range of resistance values, e.g., from 478Ω to 29 KΩ, have been reported.
The use of an individual MWCNT may not be low enough to reduce contact resistance at an interface significantly. However, by using an array of MWCNTs as an interfacial layer, it is expected that numerous individual contact spots and contact area enlargement can create current flow paths through each contact, thus reducing overall resistance. An additional advantage to using CNTs is that they can tolerate high current densities. Therefore a MWCNT layer can be a potential solution to the reliability and functionality issues faced at electrical interfaces.
Various embodiments of the present invention present novel and nonobvious apparatus and methods for improved structural, electrical, and thermal interfaces.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1A is a schematic diagram of a photoacoustic (PA) test apparatus.
FIG. 1B is a schematic representation of a nanoparticle assembly according to one embodiment of the present invention.
FIG. 1C is a schematic representation of a nanoparticle assembly according to another embodiment of the present invention.
FIG. 2 is a comparison of contact resistance between a bare Cu—Cu Interface and a Cu-MWCNT-Cu Interface.
FIG. 3 depicts a classification of the Contact Surface.
FIG. 4a is a typical contact configuration of a bare Cu—Cu contact.
FIG. 4b shows a contact resistance reduction by parallel contacts created by MWCNTs according to one embodiment of the present invention.
FIG. 5 shows SEM images according to one embodiment of the present invention of a CNT array synthesized on a Si substrate on a silicon substrate. (a) A 30°-tilted plane, top view of the vertically oriented and dense CNT array. The array height is estimated to be 15 μm. The CNT array has a part across the top of the image that helps illustrate the uniformity of growth. (b) An image with higher magnification showing individual CNTs. CNT diameters range from 15-60 nm.
FIG. 6 shows SEM images according to one embodiment of the present invention of a CNT array synthesized on a Cu sheet according to one embodiment of the present invention. (a) Cross-section view of the vertically oriented and dense CNT array. The array height is estimated to be approximately 20 μm; the inset shows the CNT array grown on a 1 cm tall Cu bar. (b) An image with higher magnification showing individual CNTs. The CNT diameters range from 15-60 nm.
FIG. 7 is a schematic representation of a system for preparing apparatus according to one embodiment of the present invention.
FIG. 8 is a schematic representation of different analytical models of the inventive sample assemblies during PA measurement. (a) The CNT array is not considered a layer in the PA model, but rather as a contributor to the interface resistance between the Si wafer and the Ag foil, RSi—Ag. (b) The CNT array is considered a layer in the PA model; therefore, the component resistances, RSi—CNT and RCNT-Ag, and the thermal diffusivity of the CNT array can be estimated. (c) The CNT arrays are not considered as layers in the PA model, but rather as contributors to the interface resistance between the Si wafer and the Cu sheet, RSi—Cu. (d) The CNT arrays are considered as layers in the PA model; therefore, the component resistances, RSi-CNT, RCNT-CNT, and RCNT-Cu, and the thermal diffusivity of each CNT array can be estimated.
FIG. 9 show phase shift as a function of modulation frequency for CNT interfaces under 0.241 MPa of pressure. (a) Lumped one-sided interface fitting results. The mean-square deviation is 0.5° in phase shift. (b) Resolved one-sided interface fitting results. The mean-square deviation is 0.5° in phase shift. (c) Lumped two-sided interface fitting results. The mean-square deviation is 0.9° in phase shift. (d) Resolved two-sided interface fitting results. The mean-square deviation is 0.3° in phase shift. The two-sided fitting data is typical of measurements at each pressure.
FIG. 10 shows thermal resistance as a function of pressure for a two-sided CNT interface (RSi-CNT-CNT-Cu) measured with the PA method and the 1-D reference bar method according to one embodiment of the present invention.
FIG. 11 is a schematic representation of an apparatus according to one embodiment of the present invention.
FIG. 12 is a schematic representation of an apparatus according to another embodiment of the present invention.
FIG. 13 is a schematic representation of an apparatus and method according to another embodiment of the present invention.
FIG. 14 is a schematic representation of an apparatus and method according to another embodiment of the present invention.
FIG. 15 is a schematic representation of an apparatus and method according to another embodiment of the present invention.
FIG. 16 shows CNT arrays synthesized on both sides of a 10 μm thick CU foil according to another embodiment of the present invention. The density is ˜108 CNTs/mm2. Both CNT arrays are approximately 50 μm in height and the average CNT diameter is approximately 20 nm.
FIG. 17 Thermal resistances of bare foil interfaces, Rfoil and CNT/foil interfaces, RCNT/foil, as a function of contact pressure.
FIG. 18 Thermal circuit for the CNT/foil interface. The local resistances sum to give RCNT/foil.
FIG. 19 Thermal resistance between the two free surfaces of the samples. For the bare foil, the resistance is the same as Rfoil. For the CNT/Foil the resistance is the sum of the two free CNT tip interface resistances.
FIG. 20 CNT arrays synthesized on both sides of aluminum foil according to another embodiment of the present invention. The insert is a higher magnification SEM image that illustrates the CNT diameters in the array.
FIG. 21 Resistive network for the aluminum foil/CNT interface.
FIG. 22 is an exploded schematic representation of an apparatus according to another embodiment of the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
For the purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiments illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, such alterations and further modifications in the illustrated device, and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates.
The present invention pertains to nanoparticles that are deposited on at least one side of a flexible, easily deformable substrate. The substrate with attached nanoparticles can then be placed in contact with the interface of a device. The easily deformable substrate permits the substrate and nanoparticles to closely conform to irregularities on the surface of the object. By virtue of this intimate contact of the nanoparticles with the object, an interface is formed with improved properties due to the presence of the nanoparticles and an apparatus prepared according to various embodiments of the present invention include improvements in one, some, or all of the following properties: increased thermal conductance, reduced electrical resistance, absorption of electromagnetic radiation, increased efficiency in converting electromagnetic radiation to heat, and mechanical support. This list of properties provided by the nanoparticles is by way of example only, and is not an exhaustive list.
In one embodiment of the present invention, a plurality of thermally conductive nanoparticles are grown or otherwise adhered to a thin, readily deformable substrate, such as a flexible sheet of any solid material, including a foil of metal, and further including foil of noble metal. The side of the substrate or foil with nanoparticles is placed in contact with a heat source, such as a package containing an integrated circuit. Because of their small size and the easy deformation of the foil, the nanoparticles readily occupy many surface irregularities of the package. Thus, the heat transmitted through the wall of the package is more effectively spread into the foil. The heat transfer to the foil can be removed by convection or by phase change if a phase change material is placed in contact with the nanoparticles, or if another object is placed in contact with the foil, through conduction.
In another embodiment of the present invention, nanoparticles are placed on both sides of a substrate that is plastically deformable with small amounts of pressure.
In one embodiment, this member is placed inbetween a source of heat and a sink for heat, such as between an integrated circuit package and a finned heat exchanger. Since the member plastically deforms under light pressure, it readily adapts to irregularities on the adjacent surfaces of the integrated circuit package and finned heat exchanger. Further, the nanoparticles will fill in some surface voids and small irregularities and any adjacent surface. Therefore, heat is more effectively transferred out of the heat source and more effectively transferred into the heat sink.
In some embodiments, the nanoparticles are multiwalled carbon nanotubes (MWCNTs). Although an individual MWCNT has an electrical resistance measured in thousands of ohms, by arranging a high density of MWCNTs on surface of the member, the overall resistance is greatly reduced, since the MWCNTs act as resistances in parallel.
In yet other embodiments of the present invention, the MWCNTs are exposed to an electromagnetic field that preferentially aligns the MWCNTs during deposition and formation. In one embodiment, the MWCNTs are arranged such that the central axes of the tubes are substantially perpendicular to the surface to which they are attached. However, the present invention is not so limited and contemplates other directions of alignment.
In yet another embodiment, a plurality of nanoparticles is deposited on a thin, metallic, easily deformable substrate and used as a shield from electromagnetic interference (EMI). This member can be placed at the mating interface between electrical components or housings. As one example, an electrically conductive metallic foil having a plurality of vertically aligned MWCNTs on opposing sides is placed between a lid of an electronics housing and the base of the electronics housing. This foil easily conforms to irregularities in the adjoining surfaces, and both: (1) enhances the housing's blockage of external and internal EMI; and (2) reduces the electrical resistance between the lid and the base.
In yet another embodiment, the ability of MWCNTs to convert electromagnetic energy to heat is utilized to provide localized heating of a component subjected to an electromagnetic field. As one example, a member populated with MWCNTs can be placed at an interface where two thermosetting plastic materials come into contact. When the assembly of the plastic materials and nanopopulated member is subjected to a microwave field, the MWCNTs cause the thermoset joint to heat and fuse into a structural joint.
In one embodiment of the invention there is a product to be used to reduce the thermal (electrical) interface resistance between two connecting devices such as an electronic component and a heat sink (another electrical component). The invention includes a metal foil with dense carbon nanotube (CNT) arrays directly synthesized on the surface of both sides. Under moderate applied pressure, the metal foil deforms to the shape of the interface and the CNTs act to produce a plurality of thermally (electrically) conductive surface to surface contact spots which in effect increases the real contact area in the interface and reduces the resistance of the interface to heat conduction and electrical flow. The invention can also be used with existing commercial, wax-based phase change materials (PCM) to enhance the stability of the PCM in the interface and to produce increased thermal conduction through the PCM.
Various embodiments of the present invention pertain to an apparatus that can be inserted, with or with out the addition of a phase change material, between a processor chip or an integrated circuit (IC) device and a heat sink to allow the chips or IC devices to operate at lower temperatures.
Various embodiments of the present invention pertain to an apparatus that can be inserted between an electrical device and a connecting electrical device to allow electricity to pass between the devices with lowered resistance.
Various embodiments of the present invention produce a thermal and or electrical interface resistance lower than other removable interface materials. The invention does not require CNT synthesis on the devices to be interfaced, which allows for scalable production and implementation with existing thermal (electrical) systems. When used without the PCM the embodiment of the invention is dry so it will be stable in the interface over continued use. When used with the PCM the embodiment of the invention acts to hold the PCM in the interface, increasing the stability of the PCM in the interface while enhancing thermal conduction through the PCM.
n some embodiments, dense CNT arrays are directly synthesized on both sides of metal foil to form a material that is dry, highly conductive, and conformal to an interface. In yet other embodiments, wax based phase change material is combined with the CNT arrays on the foil which enhances the thermal conductivity of the wax and discourages the wax from running out of the interface in its liquid phase. The enhancement of CNT arrays can be added to any existing interface without the need to synthesize CNTs on the interfaced devices (which can be destroyed by the temperatures required for CNT growth and limits scalability).
The use of an N-series prefix for an element number (NXX) refers to an element that is the same as the non-prefixed element (XX), except as shown and described. The use of the suffix prime after an element number (XX′) refers to an element that is the same as the non-suffixed element (XX) except as shown and described.
Referring to FIG. 1B, a nanoparticle assembly 20 is shown according to one embodiment of the present invention and fabricated with three metal layers 50, 52, and 54, including Ti, Al, and Ni, respectively, (thickness: 30 nm, 10 nm, and 6 nm respectively) deposited on the one side of a copper substrate 30 using electron-beam evaporation. Preferably, assembly 20 is adapted and configured to be easily separable as an assembly, such that it can be handled as a separate component. Although various specific quantities (spatial dimensions, materials, temperatures, times, force, resistance, etc.), such specific quantities are presented as examples only, and are not to be construed as limiting. The Ti layer 50 promotes adhesion of MWCNT 40 to the copper substrate 30. The Al layer 52 acts as a “buffer” layer to enhance the CNT growth with the Ni catalyst 54 that provides seed sites for CNT growth.
Although various materials are described herein, the present invention also contemplates usage of other materials. For example, some embodiments of the present invention utilize a central substrate comprising at least in part aluminum, platinum, gold, nickel, iron, tin, lead, silver, titanium, indium, or copper. Further, yet other embodiments of the present invention comprise the use of an adhesive layer comprising at least in part titanium or chromium. Yet other embodiments of the present invention include a buffer material comprising at least in part aluminum, indium, lead, or tin. Yet other embodiments of the present invention utilize a catalyst layer 54 comprising cobalt, iron, nickel, or palladium.
The CNTs were grown on this substrate surface by a microwave plasma enhanced chemical vapor deposition (PECVD) process. The feed gases were H2 and CH4. The flow rates of H2 and CH4 were 72 and 8 sccm respectively. The H2 plasma was maintained under a microwave power of 150 W. The process temperature was 800° C., and the growth time was 20 min.
Referring to FIG. 1C, a nanoparticle assembly 20′ is shown according to another embodiment of the present invention. Assembly 20′ includes the nanoparticle assembly 20 previously described, and includes a mirror image structure on the opposite side of central substrate 30′. Central substrate 30′ further includes an adhesive layer 50′ to promote adhesion of the CNTs to substrate 30′. A buffer layer 52′ of aluminum is deposited on adhesive layer 50. A catalyst layer 54′ is deposited on buffer layer 52′. A plurality 40′ of carbon nanotubes are grown from catalytic layer 54′.
A schematic of a resistance measurement test setup is shown in FIG. 1A. While subjecting the MWCNT-enhanced Cu substrate 30 to compressive loading using a Cu probe, electrical resistance change was monitored by a multimeter (Hewlett Packard 3478A). To precisely measure small resistance changes, a four wire (point) measurement scheme was adopted. This method eliminates wire connection resistance and thereby permits pure contact resistance measurement at the interface. The probe material was also chosen to be Cu in order to match the properties of the Cu substrate. The probe tip area is much smaller in dimension than the substrate so that multiple measurements can be made with each specimen by changing the probing location. To make the probe, the end of a copper nail was polished flat using a polisher (Buheler ECOMET V) and Al2O3 powder (size: 9 to 1 μm). The polished copper probe tip was observed by optical microscope (Olympus BX60), and the image was digitized using software (Golden Software Diger 2.01) to measure the apparent surface area of the probe tip to be 0.31 mm2.
A small-scale mechanical testing machine (Bose Endura ELF 3200) was used to control the probe displacement and to measure the interaction force between the probe and MWCNT-enhanced Cu substrate surface. The position of the probe tip was adjusted toward the sample surface while monitoring the position of the probe tip through a CCD camera. Starting from this non-contacting position (infinite electrical resistance) the probe was displaced downward slowly in 1.0 μm increments until first measurable electrical resistance was observed. This location was set to be the initial position (Z=0 μm) of the probe, and the probe tip was subsequently moved downward by 1.0 μm increments. At each step of displacement, contact resistance and force data were recorded. When the resistance displayed a trend close to a constant value, the probe descent was stopped. The probe was then moved upward (reverse direction) in 1.0 μm increments while measuring the contact resistance and force until electrical contact was lost (infinite resistance).
The measurements were conducted at two different locations on the same specimen surface, referred to as Test 1 and Test 2. The resistance ranged from a maximum value of 108Ω to a minimum value of 4Ω. As the probe was lowered, resistance decreased.
In Test 1, the position corresponding to the first finite resistance value is identified as initial electrical contact position (Z=0 μm). The resistance did not change significantly until the probe moved downward past Z=7 μm. At Z=11 μm, the first measurable reaction force was observed. The electrical resistance then reduced significantly to a steady value of 4Ω with increased probe movement. Note that between the initial position (Z=0 μm) and Z=11 μm, there was no measurable force but electrical contact was maintained (finite resistance was measured).
In Test 2, the distance between the initial position (Z=0 μm) and the first measurable force position (Z=18 μm) is longer than that of Test 1. This can be attributed to the resolution limits of the load cell and contact characteristics between the probe and MWCNT layer. In the beginning of contact, a relatively smaller number of MWCNT touch the probe tip and thus the force is in the range below the 0.001 N resolution of the load cell.
Resistance measured while the probe moved upward (reverse process) for the first several steps (from Z=20 μm to Z=14 μm for Test 1 and from Z=28 μm to Z=24 μm for Test 2) showed similar or slightly higher values at corresponding positions of the downward measurement. However, the resistance did not increase to an infinite value when the probe passed the position from where contact force between two surfaces dropped to zero (Z=13 μm for Test 1 and Z=23 μm for Test 2). Electrical contact is maintained even past the initial position (Z=0 μm), up to Z=−7 μm for Test 1 and to Z=−1 μm for Test 2. This trend is opposite to that observed for the bare Cu—Cu contact. Also, step-like features of resistance change are evident during both downward and upward movements of the probe. These features are thought to be the result of van der Waals forces.
The overall trend of force change is more linear than the control case. The average stiffness during downward movement (0.173×106 N/m for Test 1 and 0.123×106 N/m for Test 2) is approximately two times higher than the initial stiffness of the bare Cu—Cu contact (0.067×106 N/m).
The differences in the measured resistance and force between Test 1 and Test 2 are attributed to the global-scale variations of the MWCNT layer. The density and morphology of the MWCNT layer generally varies at different probing locations. Also the sensitivity of the electrical resistance measurements affects how one defines the initial electrical contact position. However, it is notable that after the probe registers a measurable force, the trends of contact resistance versus force for both tests are found to closely overlap each other, as shown in FIG. 2.
From the previous results, it is clear that the MWCNT layer played a key role reducing electrical resistance and increasing stiffness. A comparison of the bare Cu—Cu contact and the Cu-MWCNT-Cu contact is shown in FIG. 2. For the same apparent contact area the Cu-MWCNT-Cu interface showed a minimum resistance of 4Ω while the Cu—Cu interface showed a minimum resistance of 20Ω. An 80% reduction in resistance was observed under small compressive loading when MWCNTs are used as an interfacial material between Cu surfaces. The average stiffness of the Cu-MWCNT-Cu contact is approximately two times larger than that of the bare Cu—Cu contact.
The mechanism of contact resistance reduction due to the presence of the MWCNT layer 40 can be explained by two phenomena: (i) enlargement of real contact area through numerous parallel contacts, (ii) electrical junctions between CNTs combined with compressive loading. Although CNTs can carry large current densities, it is known that by simply placing a single CNT on a metal electrode, the contact resistance was observed to be in the 103Ω to 106Ω range. Also the minimum resistance between a single CNT and a metal contact can be on the order of 103Ω. However macroscopic contact resistance can be reduced by using a MWCNT layer containing numerous individual MWCNTs that create parallel paths. Note that only a portion of the apparent contact surface which is indicated as Ac (α-spots) in FIG. 3 participates in electrical conduction. In the case of the Cu-MWCNT-Cu contact, CNTs significantly increase the size of Ac (α-spots). While this contact situation is very complicated, it can be simplified conceptually. As depicted in FIG. 4, the gap between two contacting members (see FIG. 4a) is filled with MWCNTs thereby increasing the contact area (see FIG. 4b) via numerous parallel electrical contact paths.
Resistance reduction is also possible though electrical junctions made between CNTs. The MWCNTs on the substrate\'s surface exhibit a random configuration with no preferential direction. These create electrical junctions among adjacent CNTs to reduce the contact resistance. Other researchers suggest that contact resistance vary widely depending upon the relative orientation of two CNT surfaces and the level of compressive loading on the junction. When two contacting CNTs are in the A-A configuration it is called “in registry” which exhibits lower contact resistance than the A-B configuration (“out of registry”). For example, in the case of an “in registry” junction, the resistance is 2.05 MΩ for rigid tubes. If compressive force is applied on this junction, the resistance is reduced to 121 KΩ. In real cases, the junction resistance likely falls between the lower and the higher resistances. Therefore it is believed that the ensemble of the numerous contacts and junctions created during the probe movement dictate the macroscopic contact resistance.
For the Cu-MWCNT-Cu interface, the force increased almost linearly when the Cu probe moved downward. However for the bare Cu—Cu contact, the force did not increase in a steady manner and was less than that of the Cu-MWCNT-Cu contact. Note that if the load bearing area is increased, then the force will increase accordingly. Thus it can be concluded that MWCNT layer is also effective in enlarging the load bearing area.
In yet another embodiment of the present invention, CNT array samples were grown on Si (Ra=0.01 μm and Rz=0.09 μm, calculated by ASME B46.1-2002) and Cu (Ra=0.05 μm and Rz=0.5 μm, calculated by ASME B46.1-2002) surfaces with a tri-layer (Ti/Al/Ni) catalyst configuration by direct synthesis with microwave plasma-enhanced chemical vapor deposition (PECVD) employing H2 and CH4 feed gasses. Si and Cu were chosen as growth substrates in order to assemble an interface that is representative of a common heat sink-processor chip interface. Similar to the work of Xu and Fisher, the thicknesses of Ti, Al, and Ni metal layers were 30 nm, 10 nm, and 6 nm respectively. The working pressure of the PECVD chamber was 10 torr, the sample stage temperature was 800° C., and the microwave plasma power was 150 W. The volumetric flow rates of H2 and CH4 were 72 sccm and 8 sccm respectively, and the growth period was approximately 20 minutes.
FIG. 5a shows a 30°-tilted plane, top view of the CNT array synthesized on Si. The array height is approximately 15 μm. CNT diameters for the array on the Si wafer range from 15-60 nm (FIG. 5b). FIG. 6 shows that, with identical catalyst preparation, the CNT array synthesized on a Cu sheet is very similar to the array on the Si wafer. The array height is approximately 20 μm (FIG. 6a), and the CNT diameters also range from 15-60 nm (FIG. 6b).
A CNT array was grown on a Cu block, which protruded into the plasma and had sharp edges, in a prior study (inset of FIG. 6a). The block acted like an antenna to concentrate the plasma energy around its corners and edges. This plasma concentration had a strong etching effect on the CNT growth surface. By comparison, the height and density of the array on the Cu sheet is greatly improved because the plasma did not concentrate on the sheet during CNT growth.
The CNT density, determined by counting CNTs in a representative area of a scanning electron microscope (SEM) image, was approximately 6×108 CNT/mm2. Assuming an average CNT diameter of approximately 30 nm, an approximate CNT volume fraction of 42% can be calculated by assuming the CNTs are circular tubes of uniform height that are packed in vertical alignment. Some embodiments of the present invention contemplate volume fractions of about 30 percent to 50 percent. Considering the lower porosities in comparison with fullerenes, multi-walled CNTs should possess a mass density between that of fullerenes, 1900 kg/m3 and graphite, 2210 kg/m3. Thus, by assuming a multi-walled CNT mass density of approximately 2060 kg/m3, the effective mass density of all the CNT arrays (including effects of void space) in this work is estimated to be approximately 865 kg/m3.
For some of the test specimens prepared according to one embodiment of the present invention, a photoacoustic technique was used to measure resistance. In photoacoustic (PA) measurements a heating source, normally a laser beam, is periodically irradiated on a sample surface. The acoustic response of the gas above the sample is measured and related to the thermal properties of the sample. The PA phenomenon was first explained by Rosencwaig and Gersho, and an analytic solution of the PA response of a single layer on a substrate was developed. A more general analytic solution derived by Hu et al. that explains the PA effect in multilayered materials is used in this study. A review of the PA technique was given by Tam, and the technique has been used successfully to obtain the thermal conductivity of thin films. The PA technique has also been used to measure the resistance of atomically bonded interfaces, for which resistances were orders of magnitude less than the resistances measured in this study. The use of the PA technique for the measurement of thermal resistance of separable (non-bonded) interfaces has not been found in the literature. Also, the use of the PA technique with a pressurized acoustic chamber and sample has not been found in the literature.
A schematic of the experimental setup is shown in FIG. 7. A fiber laser operating at a wavelength of 1.1 μm is used as the heating source. Laser power is sinusoidally modulated by an acoustic-optical modulator driven by a function generator. For this study, the modulation frequency ranges from 300-750 Hz. The output power of the laser is approximately 350 mW in the modulation mode. After being reflected and focused, the laser beam is directed onto the sample mounted at the bottom of the PA cell. The PA cell is pressurized by flowing compressed He as shown in FIG. 7, thus providing a uniform average pressure on the sample surface. The PA cell pressure is adjusted using a flow controller and is measured by a gauge attached to the flow line. The test pressures are chosen to span a range of pressures commonly applied to promote contact between a heat sink and a processor chip. A microphone, which is built into the PA cell, senses the acoustic signal and transfers it to a lock-in amplifier, where the amplitude and phase of the acoustic signal are measured. A personal computer, which is connected to the GPIB interface of the lock-in amplifier and function generator, is used for data acquisition and control of the experiment.
For the one-sided CNT interface prepared according to one embodiment of the present invention, Ag foil (Ra=0.06 μm and Ra=0.4 μm, calculated by ASME B46.1-2002) forms the top of the sample, while for the two-sided CNT interface according to another embodiment of the present invention the side of the Cu sheet not coated by the CNT array is the effective top of the sample. The sample structures according to various embodiments of the present invention are shown schematically in FIG. 8. To prepare the samples for PA measurements, an 80 nm top layer of Ti was deposited by electron beam deposition, thus allowing for the Ti film to absorb the same amount of laser energy as the Ti film on the reference sample during measurements. The Ag foil (hard, Premion® 99.998% (metals basis); Alfa Aesar, Inc.) was 25 μm thick, and the Cu sheet (Puratronic® 99.9999% (metals basis); Alfa Aesar, Inc.) was 50 μm thick to allow for high sensitivity to the total interface resistance of the one-sided and two-sided CNT interfaces, respectively. The Si wafers (double-side polished and <1 0 0> orientation; Universitywafer.com) were 565 μm thick to ensure that the layer is thermally thick. Although particular thicknesses of silver and copper foil for the substrate have been shown and described, the present invention is not so limited, and contemplates the use of foil as thick as about 0.1 millimeters. Further, although various purities of silver and copper have been described, the present invention is not so constrained and contemplates the use of foils with significantly more impurities that are cheaper and more commercially available.
The one-sided CNT interface sample has an upper and lower measurement limit of ˜100 mm2·K/W and ˜0.1 mm2·K/W, respectively. The two-sided CNT interface sample has an upper and lower measurement limit of ˜35 mm2·K/W and ˜0.4 mm2·KAN respectively. The use of the hard, 25 μm-thick Ag foil in the one-sided CNT sample instead of the 50 μm-thick Cu sheet allows for greater measurement sensitivity to the expected interface resistance values. Cu sheets less than 50 μm thick can improve measurement sensitivity as well; however, reduction in interface resistance resulting from the sheet\'s surface conformability (deformation between asperities) are to be carefully considered in such a case.
In general, the range of measurable resistances expands as the ratio of the thermal penetration depth to thickness increases for the top substrate (Ag and Cu in this work). The upper measurement limit results when the sample\'s effective thermal penetration depth is insufficient for allowing heat to pass through the interface and into the Si substrate; in this limit the interface is thermally thick. The lower measurement limit results when the sample\'s effective thermal penetration depth is much larger than the ‘resistive thickness’ of the interface; in this limit the interface is thermally thin. For the frequency range and sample configurations of this study a 1-D heat diffusion analysis is applicable because the largest in-plane thermal diffusion length in the layered one-sided CNT sample, 1/aAg=0.43 mm, and two-sided CNT sample, 1/aCu=0.35 mm, are much less than the laser beam size (approximately 1 mm×2 mm).37
A reference or calibration sample is used for PA measurements in order to characterize signal delay due to the time needed for the acoustic wave to travel from the sample surface to the microphone and acoustic resonance in the cell (resonance was not experienced for the cell in the frequency range of this study). A 565 μm-thick Si wafer with a top 80 nm layer of Ti, deposited by electron beam deposition, was used as the reference sample (for uniformity, Ti was deposited on the reference and test samples at the same time).
The reference was tested with the PA cell pressurized at different levels, including the pressure levels at which the samples were tested. According to PA theory, phase shift is independent of cell pressure, while amplitude is proportional to cell pressure. However, the signal delay may be pressure-dependent for both phase shift and amplitude. The composition of the cell gas can change the nature of the cell signal delay as well. Air, N2, and He were observed to cause different signal delay responses. Of these gases, He produced the highest signal to noise ratio, which is expected because the thermal conductivity of He is approximately an order of magnitude higher than that of air or N2. He was therefore used as the cell gas for this work. The thermal diffusion length in the He filled PA cell, 1/aHe=0.46 mm (at atmospheric pressure), is much less than the PA cell radius (4 mm) which supports the assumptions of the PA model.
Using the PA technique, the thermal resistance of a one-sided CNT interface (Si-CNT-Ag) has been measured at 0.241 MPa, and the thermal resistance of a two-sided CNT interface (Si—CNT-CNT-Cu) has been measured as a function of pressure. The PA technique has also been used to measure the component resistances of the CNT interfaces and the thermal diffusivities of the CNT arrays. All CNT interface measurements were performed at room temperature. After testing, the interfaces were separated, and the CNT coverage on the Cu and Si substrates was observed visually to match the pre-test condition. This resiliency is the result of the strong anchoring of the arrays to their substrates enabled by the tri-layer catalyst.
FIG. 9 illustrates the fitted phase shift results at 0.241 MPa for the CNT interface samples. FIGS. 9a, 9b, 9c, and 9d, correspond to FIGS. 8a, 8b, 8c, and 8d, respectively. To establish a benchmark for the accuracy of the PA technique, a commercial PCM (Shin-Etsu 25×25 mm thermal pad; Shin-Etsu Chemical Co., Ltd.) interface (Si—PCM-Cu) was tested. The PCM changes phase at 48° C. and has a reported resistance of 22 mm2·K/W for a 50 μm-thick layer. A resistance of 20 mm2·K/W was measured with the PA technique for an approximate interface temperature of 55° C. and pressure of 0.138 MPa, which is in good agreement with the manufacturer\'s published value.
One-sided CNT interface results are shown in Table 1, and two-sided CNT interface results are illustrated in FIG. 10 and displayed in detail in Table 2. The resistances at CNT-substrate interfaces (and CNT-CNT interface for the two-sided interface) and the intrinsic conductive resistance of the CNT arrays are grouped into the measured total interface resistances, RSi—Ag and RSi—Cu. This lumping approach has no effect on the measured results because during each measurement the laser energy penetrates deep enough to completely pass through RSi—Ag and RSi—Cu and into the Si substrate.