Patent Application
20060086434
The section headings used herein are for organizational purposes only and should not be construed as limiting the subject matter described in the present application.
Modern electronic devices and systems, such as cellular phones, radar systems, high power RF and microwave devices and systems, and imaging systems push current semiconductor device capabilities to their performance limits. Increasing operating speeds and computing power of modern microelectronic devices have given rise to increases in complexity and functionality of the semiconductor structures. Such devices often must dissipate large amounts of heat during normal operation. Consequently, state-of-the art integrated circuit devices often require heat sinks to maintain acceptable operating temperatures. The semiconductor die can be directly attached to a heat sink or can be encased in a ceramic package that protects the die and provides electrical connections.
Common ceramic packages include silicon carbide, aluminum oxide, aluminum nitride, gallium nitride, gallium arsenide, and beryllium oxide. The coefficient of thermal expansion (CTE) of the semiconductor die and the ceramic package are usually matched as closely as possible to avoid thermal cycling induced mechanical stress failures. Thermal cycling arises during power up and power down cycles in combination with resistive heating caused by current flowing in the device.
The semiconductor industry is continually increasing semiconductor die sizes and device densities in order to provide more functions and higher performance to semiconductor devices. The heat generated by these devices continues to increase. Thus, there is a continuing need to develop heat sinks that can dissipate increasing amounts of heat.
The invention, in accordance with preferred and exemplary embodiments, together with further advantages thereof, is more particularly described in the following detailed description, taken in conjunction with the accompanying drawings. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating principles of the invention.
While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art.
It should be understood that the individual steps of the methods of the present invention may be performed in any order and/or simultaneously as long as the invention remains operable. Furthermore, it should be understood that the apparatus of the present invention can include any number or all of the described embodiments as long as the invention remains operable.
Known heat sinks are commonly fabricated from metals, such as copper, molybdenum, tungsten and aluminum. A metal heat sink is often plated with nickel prior to attachment to a ceramic package at an elevated temperature. Alternatively, silver-filled adhesives, or other conductive metal powder-filled adhesives, are sometimes used for bonding.
Choosing a metal or other material for a heat sink often involves a trade-off between desirable and undesirable properties. Some metals, such as aluminum and copper have high thermal conductivity, but have CTEs that are several times greater than that of the ceramic package or semiconductor die. During power cycling of an electronic component, the temperature of the component and the attached heat sink fluctuate significantly. Consequently, such metals cause mechanical stress to the heat sink bonding material during power cycling. The differential expansion of the heat sink relative to the ceramic package or semiconductor die can cause failure of the bond material or cracking of the package or die.
Other metals, such as tungsten and molybdenum, have relatively small CTEs. Although such metals can permit a reliable bond, they have lower thermal conductivity than aluminum or copper substrates and they are difficult to electroplate. Furthermore, tungsten and molybdenum are undesirable for applications that require minimal weight.
Composites of copper and tungsten or of copper and molybdenum have certain advantages over elemental materials. These composites can be made by various methods of powder metallurgy, such as, for example, infiltrating copper into a sintered body of tungsten or molybdenum, or sintering a mixed powder of the two metals. It is difficult, however, to obtain an elongated plate by rolling a sintered ingot of tungsten or molybdenum. Alternatively, metal layers can be joined by cladding or lamination. Cladded and laminated products, however, require precise machining, which is labor-intensive, error-prone, and expensive.
Some heat sinks combine a sintered ceramic with a metal matrix. The fabrication process involves the formation of a ceramic preform, which can be made by, for example, sintering silicon carbide powder. The ceramic preform microstructure typically has a predetermined void volume fraction that is subsequently filled with molten metal, typically aluminum. An aluminum ceramic heat sink can employ copper-based inserts to improve its thermal conductivity. Such heat sinks, however, can be difficult to manufacture and are usually limited in their ability to have a matched CTE with an electronic device.
Other heat sinks are metal matrix composite which include infiltrated inorganic fiber material. Infiltration of fibers has its own limitations, such as, problems with fiber wetting and non-uniform fiber distribution. In addition, molten metal infiltration of fibers under pressure can displace the fibers due to the fiber breakthrough pressure threshold. Furthermore, it is often difficult to control fiber volume fraction, and thus to obtain a desired property of the composite. These factors have limited use of metal matrix fiber composites as heat sinks.
Metal matrix composite (“MMC”) materials that include discontinuous high-modulus graphite fibers that are randomly arranged in-plane at desired volume fractions have significant advantages over many known heat sinks. Such composites are disclosed in U.S. patent application, Ser. No. 10/379,044, filed Mar. 4, 2003, entitled “Discontinuous Carbon Fiber Reinforced Metal Matrix Composite,” which is assigned to the present assignee. The entire application of U.S. patent application Ser. No. 10/379,044 is incorporated herein by reference.
MMC composites enable design of base plates with relatively high thermal conductivity and with CTEs that match the CTEs of common ceramic package materials. It is particularly desirable for such CTE-matching material to have high thermal conductivity in various directions. There currently is a significant need in the electronic thermal management and packaging industry for both heat spreading, which relies on high in-plane thermal conductivity, and heat sinking, which relies on high “z” or through-plane thermal conductivity. The term “in-plane” as used herein refers to the plane parallel to a bonded surface of a heat sink. The term “through-plane” as used herein refers to a direction that is orthogonal to an in-plane surface.
One method of manufacturing a MMC with randomly distributed graphite fibers is disclosed in U.S. patent application Ser. No. 10/379,044. This method includes mixing dry PEG binder material with dry-milled graphite fibers having average length of about 300 microns. The mix is then poured into a mold, pressed, and heated to liquefy the binder. The mix is then chilled to set the binder prior to removal from the die.
The resulting preform is inserted into a pressure infiltration casting mold vessel for metal infiltration and solidification. This process is relatively simple and inexpensive. The fiber distribution obtained with this process is relatively non-uniform and may results in a standard deviation on order of 2 ppm at the volume fraction that resulted in a CTE of 7 ppm/K. Thus, this method may not be suitable for applications requiring particularly close CTE matching. In addition, non-uniform and largely unpredictable fiber distribution may result in warping of plates machined from the casting while processing through the various machining steps or through soldering operations.
Another known method of manufacturing a MMC with randomly distributed graphite fibers is disclosed in U.S. Pat. No. 5,437,921. This method includes dispersing milled fibers in aqueous slurry, which is then poured into a filter vessel. The aqueous slurry is formed into a filter cake under vacuum and then pressed to a desired volume fraction. The filter cake is then dried and pressed to the desired volume fraction. This process, however, is prone to localized non-uniform distribution due to localized flow alignment of milled fibers during pouring and vacuum filtration steps. In addition, the packing density tends to vary with thickness. Furthermore, there are significant variations of CTE. For example, the standard deviation can be 1.25 ppm/K at the average level of CTE at 7 ppm/K.
Yet another known method of manufacturing a MMC with randomly distributed graphite fibers includes incorporating chopped CKD graphite fibers with an average chop length of 25 mm into a paper product. This method is used commercially from Technical Fibre Products of Cumbria in the United Kingdom. The method requires adding a co-polyester fiber, which serves as a binder. The paper product is laid out into a die and then heated to soften the binder fiber. The preform is then pressed to the desired volume fraction. Each ply is rotated through a sequence of orientations to produce a substantially planar isotropic preform. This process results in a lower standard deviation that is about 0.9 ppm/K. However, the process is expensive and the through-plane thermal conductivity is relatively low. In addition, the polyester binder is typically difficult to remove and has relatively a high char yield during the outgasing and preheating operation.
Milled fiber preforms in many known methods of manufacturing a MMC tend to develop preferred orientations when they experience flow alignment. Flow alignment occurs when dry milled fibers are poured into a mold where they exhibit aligned flow that cannot be re-randomized. It is difficult to prevent localized slurry flow and local areas of fiber alignment when vacuum-assisted filtration of filter composites is performed.
The methods and apparatus of the present invention relate to forming metal matrix composite materials having discontinuous high modulus graphite fibers for thermal or structural applications. The methods and apparatus of the present invention can form metal matrix composite containing discontinuous high modulus graphite fibers that are arranged in-plane with a majority of fibers oriented substantially off the basal plane at the desired volume fraction. This material can have predetermined thermal expansion properties that are controllably matched to those of a wide range of materials that are commonly used as electronic substrates. In addition, this material can have relatively high, nearly isotropic thermal conductivity properties.
The spray system 100 includes a slurry input port 102 that receives an aqueous fiber slurry that includes milled graphite fibers in suspension from a slurry source 104. In one embodiment, the slurry source 104 continuously recirculates the aqueous fiber slurry. In some embodiments, a binder is dissolved in the aqueous fiber slurry. A gas pressure input 106 receives pressurized gas, such as pressurized air from a gas source 108. In one embodiment, the gas pressure input 106 is disposed asymmetrically in the spray system 100 in order to promote forming swirling and uniform fan patterns in the spray system 100.
A spray nozzle 110 aspirates the aqueous fiber slurry by mixing the pressurized gas with the aqueous fiber slurry to produce a random stream of fiber cluster droplets 112 that is sprayed through the spray nozzle 110. It is understood that the stream of droplets 112 is not perfectly random. However, each droplet 112 in the stream of droplets contains fiber clusters that have a relatively high degree of randomness relative to the fiber clusters in each of the other droplets 112 in the stream of droplets.
In some embodiments, the aqueous fiber slurry includes a dissolved binder. In other embodiment, the spray deposited mat is sprayed with binder using a second set of spray jets that is down stream from the fiber slurry spray jets (not shown) is used to spray a binder on the aqueous fiber slurry after the aqueous fiber slurry is deposited. A separate nozzle can be used to spray the binder. In yet other embodiments, the aqueous fiber slurry includes the dissolved binder and the spray nozzle 110 or a separate spray nozzle is used to spray additional binder on the deposited aqueous fiber slurry.
In some embodiments, the spray system 100 includes a plurality of spray nozzles. In one particular embodiment, the spray system 100 includes four or five spray nozzles. In some embodiments, the spray nozzle 110 or the plurality of spray nozzles is coupled to a reciprocal scanning mechanism 114 that provides a reciprocal or other motion to the spray nozzle 110. In embodiments that include multiple spray nozzles, the reciprocal scanning mechanism 114 can be coupled to any number of the plurality of spray nozzles to simultaneously scan the spray nozzles. Also, separate and independent reciprocal scanning mechanisms can be coupled to any number of the plurality of spray nozzles to independently scan these spray nozzles. In one embodiment, the width of the spray is in the range of about 3 to 7 inches. In some embodiments, the spray nozzle 110 translates in the Z direction to alter the spay pattern.
A translating filter belt 116 is positioned adjacent to the spray nozzle 110 in the direction of the stream of random fiber cluster droplets 112. A fiber preform mat 118 is positioned on the translating filter belt 116 so that the stream of random fiber cluster droplets 112 is sprayed directly onto the fiber preform mat 118 in a spray area 120 as the fiber preform mat 118 is translated by the translating filter belt 116. The fiber preform mat 118 is a carrier sheet that receives the droplets of random fiber clusters 112. In some embodiments, the fiber preform mat 118 comprises a polymeric non-woven material that can be reusable. The resulting film deposited on the fiber preform mat 118 comprises random fiber clusters. The translating filter belt 116 translates the fiber preform mat 118 relative to the spray nozzle 110. In some embodiments, the translating filter belt 116 translates the fiber preform mat 118 at a constant rate of speed in the longitudinal direction.
A vacuum plenum 122 is positioned under the translating filter belt 116. In the embodiment shown in
In some embodiments, the translating filter belt 116 carrying the fiber preform mat 118 passes through a drying chamber after receiving the fiber cluster droplets. The drying chamber heats and dehumidifies the fiber preform mats. The heating and dehumidification can be accomplished in either a continuous or a discontinuous process. The heat and dehumidification removes moisture, which permanently sets the binder. The filter material is then stripped away from the fiber preform mat 118 to create a fiber preform.
Placing the vacuum plenum 122 a distance away from the spray deposition area 120 allows the fiber cluster droplets 112 to remain on the fiber preform mat 118 for a predetermined time before the excess carrier fluid is removed. The rate of translating the fiber preform mat 118 and the distance between the vacuum plenum 122 and the spray deposition area 120 are important process parameters. For example, the average fiber angular inclination above the basal plan can be controlled by adjusting these process parameters.
One embodiment of the present invention features a method of forming a fiber preform mat. The parameters of the fiber preform mats, such as the angle of inclination above the basal plane, can be changed by varying processing parameters. The method includes forming aqueous fiber slurry comprising milled graphite fibers in suspension. In some embodiments, a binder is dissolved in the aqueous fiber slurry. For example, the carrier fluid can include an easily removable binder material, such as, PEG 8000, dissolved therein. PEG-8000 is commercially available from the Dow Chemical Company under the trade name Carbowax Sentry. The aqueous fiber slurry is aspirated to produce a spray of fiber cluster droplets.
A fiber preform mat 118 is translated in the path of the fiber cluster droplets so that a randomized distribution of fibers is deposited on the fiber preform mat 118. In some embodiments, the fiber preform mat 118 is translated at a constant rate. In some embodiments, a binder is also sprayed onto the fiber preform mat 118.
The milled fibers in the fiber cluster droplets tend to flatten upon impact with the preform mat 118 and during excess carrier fluid removal. The alignment of the milled graphite fibers is specific to the particular volume of each droplet of the aqueous fiber slurry. Each of the droplets sprayed onto the fiber preform mat 118 contains a few fibers and is completely independent of the other droplets. Thus, there is a substantially randomized distribution of fibers deposited onto the fiber preform mat 118.
Excess carrier fluid is extracted from the fiber cluster droplets. In some embodiments, the excess carrier fluid is extracted by reducing the pressure proximate to the preform mat 118. In some embodiments, the excess carrier fluid is extracted by increasing a temperature of the fiber preform mat 118 to remove moisture from the fiber preform mat 118. In some embodiments, the excess carrier fluid is extracted by dehumidifying the fiber preform mat 118 to remove moisture from the fiber preform mat. Any combination of reducing the pressure proximate to the preform mat 118, increasing the temperature of the fiber preform mat 118, and dehumidifying the fiber preform mat 118 can be used to extract the excess carrier fluid.
In some embodiments, the excess carrier fluid is extracted simultaneously with the deposition of the randomized distribution of fibers on the fiber preform mat 118. In other embodiments, the excess carrier fluid is extracted at a predetermined time after the deposition of the randomized distribution of fibers on the fiber preform mat 118 so that the fiber preform mat 118 is exposed to the binder for at least the predetermined time. Once the excess carrier fluid is extracted, and the mats completely dry, the binder is set. The fiber preform mats can then be handled by a technician. The resulting fiber preform mat 118 contains a filter material, which is usually stripped off before additional processing.
One embodiment of the present invention features a method of forming a fiber preform from the fiber preform mat 118. In this embodiment, the filter material is stripped from the fiber preform mat 118 to create a fiber preform. The resulting fiber preform is cut into pieces having the desired dimensions, and these pieces are then stacked into a heating/cooling die that is mounted into a press. The stack is then pressed to the desired volume fraction to obtain the fiber preform. In some embodiments, the temperature of the stack is controlled during pressing. The term “volume fraction” is defined herein as the volume fraction of carbon fiber assuming a density of 2.15 g/cc.
Fibers initially randomized in three dimensions will flatten during the pressing. In some embodiments, the stack is heated during pressing by passing heated air through passages beneath the top and bottom face of the die cavity. The die can be chilled after pressing. For example, the die can be chilled using liquid nitrogen that is piped-through passages beneath the top and bottom face of the die cavity.
The resulting volume fraction of the fiber preform depends upon the number of sheets and the desired final thickness of the fiber preform. In one example, the fiber preform mat 118 was sprayed with a binder containing graphite fiber slurry and dried to result in a volume fraction of approximately 0.23. In order to manufacture a 0.3 volume fraction fiber preform, which is known to have a CTE of 7 ppm/K in Al, a number of mat layers need to be stacked into a mold and pressed to approximately 0.23/0.3 times their initial thickness.
Some physical properties of the fiber preform are determined by the volume fraction. One skilled in the art will appreciate that it is important to maintain a certain thickness uniformity in the resulting fiber preform in order to achieve the desired volume fraction uniformity throughout the entire preform and thus, the desired uniformity in physical properties. In some embodiments, the spray pattern of the nozzle 110 is adjusted in order to maintain the desired uniformity of physical properties of the final preform.
A metal matrix is pressure infiltrated into the pressed fiber preform to form a composite preform. In some embodiments, at least one of Al, Mg, and Cu alloy matrix material is pressure infiltrated into the pressed fiber preform to form the composite preform. In one embodiment, the pressure infiltration is performed using the method described in U.S. Pat. No. 6,148,899, entitled “Methods of High Throughput Pressure Infiltration Casting,” which is assigned to the assignee of the present application. The entire description of U.S. Pat. No. 6,148,899 is incorporated herein by reference.
Composite materials formed using the spray deposition apparatus 100, 200 have a relatively low CTE for a given volume fraction. The CTE of the resulting metal matrix composite can be adjusted by varying parameters, such as the volume fraction of the graphite fibers. The CTE of the resulting metal matrix composite can be matched to various ceramic substrates. For example, when pressurized to the desired volume fraction, the CTE of such composite can be matched to various ceramic and semiconductor materials, such as silicon, silicon carbide, aluminum oxide, aluminum nitride, gallium nitride, gallium arsenide, and beryllium oxide over a range of about 1 to 12 ppm/K.
Composite materials formed using the spray deposition apparatus 100, 200 have discontinuous high modulus graphite fibers arranged in-plane with a majority of fibers oriented substantially off the XY plane. A portion of the fibers in the composite material is oriented randomly off the XY plane. In some experiments using a Cu alloy matrix, a 35% volume fraction was achieved for fiber mats prior to pressing to the desired volume fraction manufactured according to the present invention and the measured distribution in the average angular orientation of the fibers in the Z direction was in the range of about 20 to 30 degrees from the basal plane. In some particular experiments, the average fiber orientation was about 26 degrees from the basal plane.
In other experiments using an Al alloy matrix, a 30% volume fraction was achieved. The measured distribution in the average angular orientation of the fibers in the Z direction in fiber mats manufactured according to the present invention prior to pressing to the desired volume fraction was about 19 degrees. These lower angular distributions were achieved by allowing the fiber cluster droplets 112 to remain on the mat for a period of time prior to removal of the carrier fluid. This allows the fibers to align more nearly parallel to the basal plane.
In other experiments, the fiber cluster droplets 112 were allowed to remain on the fiber preform mat 118 for a predetermined time before the excess carrier fluid was removed as described in connection with
The average fiber angular inclination above the basal plan can be controlled by adjusting process parameters. For example, the average fiber angular inclination above the basal plan can be adjusted by controlling the rate of extracting excess carrier fluid from the fiber cluster droplets. The average fiber angular inclination above the basal plan can also be adjusted by controlling the time between depositing the fiber cluster droplets on the fiber preform mat 118 and the extraction of the excess carrier fluid.
Through-plane thermal conductivity is improved by randomly orienting a significant portion of fibers off the XY plane within a certain range of fiber angles of inclination from the basal plan. In many embodiments, the average fiber angles of inclination from the basal plan for an orientation that is parallel to the XY plane is in the range of about 5 to 45 degrees. In some specific embodiments, the range is between about 15 and 40 degrees. In other specific embodiments, the range is between about 20 and 30 degrees. In yet other specific embodiments, the range is between about 24 and 28. Experiments have shown that composites formed with fibers that are randomly dispersed with fiber angles of inclination from the basal plan of about 26.6 degrees from the basal plane display substantially isotropic thermal conductivity in x, y, and z directions.
The methods and apparatus of the present invention can form numerous types of preforms. There are an almost unlimited number of parameters that can be used to form these preforms. Two examples of fabricating preforms using the methods and apparatus of the present invention are given below. These examples are given to illustrate specific embodiments of the invention and should not be used to limit the scope of the invention in any way. Specifically, these examples should not be used to limit the invention to specific process steps or process parameters.
In the first example, preforms were spray-deposited with slurry containing 300-micron milled graphite fiber DKD and a PEG 8000 binder. An appropriate number of spray deposited performs are loaded into a die. The die is then heated and pressed to a desired thickness that produces the desired volume fraction, which is a 0.3 volume fraction in this example. The die is then clamped and chilled using liquid nitrogen to set the binder. The preforms are then removed and inserted into a confining mold cavity where they are pressure infiltrated with an alloy containing 12.5% Si and 0.3% Mg with the balance being A1 using the pressure infiltration casting process described in US Pat. No. 6,148,899.
It has been previously shown that such composition effectively prevent the formation of Al4C3 during the casting process. See J. A. Cornie, et. al., “Pressure Infiltration Processing of P-55 Graphite Fiber Reinforced Al Alloys, Proceedings of the Symposium on Composites Processing, Microstructures and Properties,” 2nd International Ceramic Sciences and Technology Congress of ACM, Orlando, Fla. Nov. 13, 1990 and Qoing Li and J. Cornie, “Microstructure of the interface and interfiber regions in P-55 reinforced Al alloys manufactured by pressure infiltration casting, Paper D.2.,” Controlled Interphase Structures (ICCI-3), H. Ishida, ed., Elsevier Science Publications, 1990, both publications are incorporated herein by reference. In addition to preventing carbide formation, this alloy melts and solidifies over a narrow temperature range because it is formed near eutectic in composition. Therefore, the alloy is substantially immune from gross macrosegregation during solidification of the casting.
Eight two-inch long by ¼ inch by ¼ inch specimens were removed from the casting in orthogonal directions and tested for thermal expansion. In addition, specimens were removed from the panel to test the thermal conductivity both in-plane and through-plane using flash diffusivity techniques. For comparison, specimens were prepared using a dry mix method that is disclosed in U.S. patent application Ser. No. 10/379,044, filed Mar. 4, 2003, entitled “Discontinuous Carbon Fiber Reinforced Metal Matrix Composite” and tested for thermal expansion and thermal conductivity.
In the second example, the conditions of the first experiment were repeated using a nominal Cu-0.5% Cr matrix alloy. The Cu matrix composite database is less complete, but sufficient data exists to make the same type of comparisons. In this experiment, preforms were spray-deposited with slurry containing milled graphite fiber DKD and a PEG 8000 binder. An appropriate number of spray deposited performs are loaded into a die. The die is then heated and pressed to a desired thickness that produces the desired volume fraction, which is a 0.3 volume fraction in this example. The die is then clamped and chilled using liquid nitrogen to set the binder. The preforms were inserted into a confining mold cavity and pressure infiltrated with an alloy containing Cu-0.5% Cr using the pressure infiltration casting process described in U.S. Pat. No. 6,148,899. The fiber angle of inclination above the basal plane for the preform material was about 25 degrees. Preforms having materials with substantially lower angles of inclination can be produced using the methods of the present invention.
For comparison, specimens were prepared using the Technical Fibre Products available from Cumbria in the United Kingdom as described herein. This method incorporates chopped CKD graphite fibers with an average chop length of 25 mm into a paper product. The chopped CKD fibers have a substantially random distribution in-plane. The resulting preforms were tested for thermal expansion and thermal conductivity and the data is presented in
Shapery's equation for thermal expansion was simplified to assume continuous fibers. The Rule of Mixtures (“ROM”) calculations for thermal conductivity include the fiber angle of inclination above the basal plane and changes of the angle of inclination as a function of compression. However, the ROM calculations were simplified to remove the effects of contact resistance at the fiber-matrix interfaces and at the fiber end interfaces. Consequently, the simplified ROM calculations over-estimate the actual thermal conductivity. The ROM calculations for thermal conductivity that include the fiber angle of inclination above the basal plane and changes of the fiber angle of inclination above the basal plan as a function of compression agree well with the experimental data for preforms with the 19 degree angle of inclination above the basal plane.
The CTE experimental data is considerably above the data calculated using Shapery's equation. The relatively high experimental CTE data may be caused by a large population of fibers below the critical aspect ratio. Poor interface strength may also contribute to the relatively high CTE experimental data. Other experimental data for flat paper derived preforms and for flat spray deposited material are in close agreement with data calculated using Shapery's equation. The CTE experimental data also indicates that the standard deviation for preforms manufactured using the spray deposition methods of the present invention is relatively low (about 0.5 standard deviation), which will lead to a relatively low rejection rate.
The preforms were analyzed to determine why the transverse thermal conductivity measurements where high relative to the in-plane thermal conductivity measurements. Metallographic sections of resin infiltrated preform mats were taken parallel to the basal plane. These sections were polished and photographed in a scanning electron microscope. The length and diameter of 70 fibers were measured and the ratio of the minor-to-major axis of the ellipse was calculated using arc-tangent calculations. Angular deviation from the in plane section were then determined.
While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art, may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
| Number | Date | Country | |
|---|---|---|---|
| 60621274 | Oct 2004 | US |
