Full opinion text
OPINION MCKELVIE, District Judge. This is a patent case. Plaintiff CFMT, Inc. is the owner and assignee of U.S. Patent No. 4,911,761 (“the ’761 patent”). The ’761 patent discloses a process and apparatus for drying surfaces, such as the surfaces of semiconductor wafers. Plaintiff CFM Technologies, Inc. is the exclusive licensee of the ’761 patent. CFM Technologies, Inc. is the parent and sole shareholder of CFMT, Inc. Defendant Steag Microtech, Inc. (“Steag”) sells a “Marangoni Dryer” within the United States that is used to dry semiconductor wafers. On July 10, 1995, plaintiffs (collectively “CFMT”) filed a complaint alleging that defendant Steag has infringed one or more claims of the ’761 patent, either literally or under the doctrine of equivalents. On July 31, 1995, Steag filed an answer denying infringement and asserting several affirmative defenses. These defenses include that the claims of the ’761 patent are invalid for anticipation and obviousness, that the claims are invalid because the claimed invention was on sale or in public use more than one year prior to the date of application, and that the patent is unenforceable due to CFMT’s inequitable conduct during the patent prosecution. On November 24, 1997, the court held a hearing in accordance with Markman v. Westview Instruments, Inc., 517 U.S. 370, 116 S.Ct. 1384, 134 L.Ed.2d 577 (1996), to construe disputed claims of the ’761 patent. On December 2 through 11, 1997, the court held a jury trial on the issues of infringement, validity, and unenforceability. On December 12, 1997, the jury returned its verdict. The jury found that operation of Steag’s Marangoni dryer literally infringes claims 1, 8, 17, and 22 (“the asserted claims”) of the ’761 patent, that Steag has actively induced users of the Marangoni Dryer to infringe on the asserted claims, and that Steag has contributorily infringed those claims. The jury also found that Ste-ag failed to establish that the asserted claims are invalid. Finally, the jury found that Steag failed to show that the ’761 patent is unenforceable due to inequitable conduct. The jury awarded CFMT damages of $3,105,000.00. During trial, Steag moved for judgment as a matter of law (“JMOL”) on the issues of infringement, validity, and unenforceability. On December 26, 1997, Steag renewed its motion for JMOL. Alternatively, Steag moved for a new trial. On December 29, 1997, CFMT moved for treble damages and a finding that the case is “exceptional” under 35 U.S.C. § 285. This is the court’s decision on those motions. I. FACTUAL AND PROCEDURAL BACKGROUND The court draws the following facts from the pre-trial order and the testimony and evidence presented at trial. A. Computer Chip Manufacturing Modern computers, and many everyday appliances, use “computer chips.” Computer chips contain miniature electronic circuits. A computer chip consists of a sliver of silicon (“a semiconductor wafer”), a surrounding case that protects the silicon, and wires that extend from the silicon and enable the computer chip to interact with the equipment in ■which it is used. Computer chip manufacture takes place in a process with three major steps. In the first step, a wafer of pure silicon is produced. Next, this wafer goes to a “wafer fabrication” plant. Finally, the manufacturer mounts the wafer in a case and attaches wires to it. The patent in suit relates to the second step — wafer fabrication. In wafer fabrication, the manufacturer imprints circuitry onto the silicon wafer. The manufacturer imprints these circuits by shooting light images onto the wafer, much like a photograph is shot onto film. Between each photographic shot, the manufacturer performs various processing steps. These processing steps often include applying chemicals to the wafer (“wet processing”) for etching, cleaning, or developing. The processing also adds different layers and coatings to the wafer between each photographic shot. Wafer fabrication usually takes two to three months to complete, and results in a semiconductor wafer. During wafer fabrication, the wafers can often be exposed to contaminants and airborne particles. This contamination can be detrimental to the microscopic circuits which the wafer fabrication process creates. As the process adds layers and coatings to the wafer, contaminants can become trapped in the semiconductor. Thus, between each chemical processing step, the wafers must be washed and dried in a way that reduces the chances that any impurities or chemical residue are left on the wafer surfaces. During this rinsing and drying process, a premium is placed on not only producing a clean and dry wafer, but doing so in a way that reduces the chances of streaking or water marks. Water streaks and water marks can interfere with the semiconductor’s circuits in the same way that contaminants do. Rapid drying methods are preferred, since allowing water to simply evaporate into the air from the wafer surfaces can leave these streaks and marks. Conventionally, semiconductor wafers were dried by the use of a spin-rinser-dryer, which uses centrifugal force to throw water off of the wafers. This process, however, subjects the wafers to mechanical stress, and may allow contamination or the buildup of static electric charges on the wafer surfaces. Electric charges attract contaminants when the wafers are exposed to the air. B. CFMT In 1984, Christopher McConnell and Roger Carolin started a company called CFM Technologies. McConnell and Carolin knew each other from Harvard University, where they attended business school together. McConnell had a degree in chemical engineering, and Carolin had a degree in electrical engineering. They decided to form a company to develop and market an apparatus for chemical processing of semiconductor wafers. The two co-founders began developing a “process flow vessel” for this chemical processing. They used the basement in McConnell’s father-in-law’s house in Pennsylvania as their office. In the summer of 1984, after Carolin decided to move to Florida, McConnell hired Alan Walter. Walter is a chemical engineer whom McConnell met while working before he enrolled in business school. Walter and McConnell continued to develop chemical processing equipment. They eventually developed a process that they termed the “Full Flow” process. C. The ’532 Patent On August 13,1985, Walter and McConnell applied for a patent on the Full Flow process. The PTO issued U.S. Patent No. 4,778,532 (“the ’532 patent”) to McConnell and Walter on October 18,1988. CFM Technologies is listed as the assignee of the ’532 patent. The ’532 patent is entitled “Process and Apparatus for Treating Wafers With Process Fluids.” The ’532 patent discloses the Full Flow method for cleaning and wet processing semiconductor wafers. It describes an apparatus that pumps fluids into the enclosed vessel where the wafers remain stationary. It explains that the system allows fluids (gases or liquids) to flow past the wafers “sequentially and continuously.” The apparatus then drains the fluids out the bottom as new fluid comes in the top for rinsing or drying. The specification lists as advantages of this system the reduced contamination risk (since the wafers do not move from one place to another), the increased control over the flow of chemicals and the amount of time that the wafers are exposed to those chemicals, and the safety to users (since the system is enclosed). The ’532 patent specification describes a drying method that it calls “chemical drying.” In chemical drying, a “drying fluid” drives the rinsing fluid off of the wafers, and then a “predried gas, preferably an inert gas such as nitrogen” evaporates the drying fluid. The specification lists isopropanol (IPA), which is similar to rubbing alcohol, as the preferred drying fluid. At trial, McConnell described the way that he and Walter developed the IPA drying process that they claimed in the ’532 patent. He explained that he had worked in labs where chemists dried test tubes and beakers by dousing them with alcohol, shaking them off, and then putting them in racks. He claimed that this had always produced very clean, dry beakers and test tubes. He testified that alcohol facilitates drying because it reduces the surface tension of water, thus causing water droplets to run off of surfaces instead of clinging to them. He explained that he and Walter designed the system so that IPA vapor came into the chamber as the water drained out. The IPA would condense on the wafer surfaces and cause the water to run off. They would then purge the chamber with nitrogen. He testified that “the whole thing [was] dry and actually very clean.” It looked “really good” and produced “terrific wafers.” D. The Full Flow System CFMT began its marketing efforts for the Full Flow system in 1986. CFMT often referred to the system’s drying method as one of its strengths. For instance, CFMT put together a brochure (“the 1986 brochure”) entitled “Full Flow Semiconductor Wet Processing.” Under the section headed “Wafer Drying,” the brochure claimed that CFMT “has developed an extremely clean and simple drying technique based on isopropyl alcohol.” It described the drying process as follows: After the wafers have completed their pri- or wet processing steps, but while the wafers are still completely immersed in ultra-pure water, filtered IPA vapor is introduced to the top of the wafer vessel and a drain is opened out the bottom. As the system drains, IPA vapors flow in, replacing the water. The brochure lists the lack of “particle generation,” the lack of “streaking or staining,” and “very fast drying” as benefits of the Full Flow drying method. It claims that wafers “emerge bone-dry from the drying step” and have “exceptionally low particle counts.” On October 16, 1986, CFMT announced in a press release (“the Rodel press release”) that it had “joined forces” with Rodel Products Corporation (“Rodel”) to market the Full Flow system. The Rodel press release states that the system takes wafers “to complete dryness.” It also states that “the wafers never move until they emerge clean and dry.” The Rodel press release claims the Full Flow system is “more effective in controlling particles than other automated units.” CFMT announced the production of the Full Flow system in the February 1987 issue of a trade magazine called Semiconductor International (“the 1987 advertisement”). The 1987 advertisement describes a process that brings semiconductor wafers “to complete dryness” using isopropanol vapors. The advertisement claims that the system allows “more effective control of particles.” E. The Beta Test With Texas Instruments In late 1986, through its connections with Rodel, CFMT reached an agreement with Texas Instruments (“T.I”) to run a “beta program” at TI’s Sherman, Texas plant. The program required CFMT to ship a Full Flow vessel to TI before receiving payment. TI agreed to purchase the equipment if it met certain performance criteria. CFMT shipped out a Full Flow vessel to TI on December 23,1986. In early 1987, it shipped out additional subsystems to TI. CFMT employees, including McConnell and Walter, took turns visiting TI in order to help set up the system and to take part in the testing of the equipment. In 1987, CFMT sent out a “Technical and Marketing Report — 1986” to its investors. The report does not bear a date on it, but appears to have been sent out in early 1987, since it refers to the February advertisement in Semiconductor International as having come out “recently.” The report summarizes the progress the company made in 1986, and its plans for 1987. The report describes CFMT’s relationship with Rodel, and the beta program agreement with TI. The report notes that while “[ijnitial TI data are encouraging,” there are still “high risks” and that “Full Flow technology has yet to produce a single wafer confirmed commercially clean.” In a letter to a CFMT investor on May 15, 1987, McConnell writes that the “Full Flow wet processor has performed admirably during its maiden voyage at Texas Instruments.” He claims that TI officials had described the “beta-test start-up [as] one of the smoothest that they have ever witnessed.” He states that CFMT had made “dramatic strides in hardware enhancements for the isopropanol vapor drying system,” but notes that there was still a “nagging problem with the center-most wafers in the vessel.” At trial, both McConnell and Walter explained that the results at TI at first appeared good — the same as they were in CFMT’s factory in Pennsylvania. However, McConnell testified that TI eventually looked at the wafer surfaces with a “particle scanner.” A particle scanner is an instrument that uses a laser to detect very small particles. McConnell testified that, upon looking at the wafers through a particle scanner, TI and CFMT discovered that results were “terrible.” They found hundreds of particles on what had appeared to be clean wafers. Walter testified that when TI discovered this “dirty wafers” problem, they first assumed that the equipment just needed to be cleaned out. CFMT and TI checked each of the connections, replaced some valves, and flushed the entire system with ultra-pure water for several days. This cleansing procedure decreased particle count, but did not eliminate the problem. Walter testified that, in April 1987, after several weeks of analysis, he concluded that there was a problem with the drying step in the Full Flow process. Walter and McConnell each testified about the analyses they performed on the Full Flow system to determine how they might alter the drying process so that it did not leave particles on the wafers. Walter testified that he wanted to alter the pressure of the IPA as it entered the chamber. In May, 1987, he replaced the Teflon valve that fed IPA into the chamber with a stainless steel valve, so that it could withstand a pressure drop. A May 28, 1987 memorandum titled “IPA Drying Experimental Program” written by McConnell lists several experiments and tests that CFMT wanted to perform on the drying process. It lists different parameters that CFMT would vary, such as “warm vs. cold nitrogen dilution,” “different water temperatures,” “solvent variations,” and “hardware variations.” One of the headings in the memorandum is “Runs in Full-Scale Clear Vessel.” Walter testified that in June 1987, McConnell sent him a clear vessel at TI so that he could actually watch the drying process. He described this experience as “nirvana.” He was able to watch the process for the first time as it happened, and he saw “all these droplets of rain coming down and ... all this condensation.” After running more tests with the particle scanner, Walter concluded that there was a correlation between water droplets left on the wafers and the particles they discovered on the wafers after the drying process. Walter testified that he began varying the speed at which the vessel drained. He varied the temperature of the rinse water. He also reduced the number of wafer carriers in the chamber, so that they were not stacked. He explained that higher carriers drip onto lower ones, leaving water droplets on the lower wafers. On July 1, 1987, Walter sent a fax to Joan Koppenbrink, CFMT’s salesperson at Rodel. He states that CFMT has “eliminated streaking on bottom wafers, and ... have consistent particle counts on the top and bottom wafers for several of the runs. The optimum conditions appear to be with the valve between 1/3 and 2 turns open.” The second page of the fax is a chart that plots “Linear flowrate” on the x-axis and “Drops from the first carrier” on the y-axis. Walter testified that he measured the number of drops by simply counting how many droplets he could see falling from the wafers as the vessel drained. Walter plotted several lines on the chart, for different water temperatures. The chart shows that the number of drops approach zero when the flow rate is at about 2.0 inches per minute, and the water temperature is 90 degrees Celsius. On the top of the chart, it indicates that Walter was introducing the IPA to the chamber at a pressure of 22 to 30 pounds per square inch, and then reducing it to very low pressure. He testified that this drop in pressure created “a very dry vapor.” Walter testified that by the summer of 1987 “we had [the problem] licked and we were getting good results.” McConnell testified that they had a “big breakthrough in ... June [of 1987].” By slowing the rate of descent, and controlling vapor pressure and water temperature, the process eliminated condensation on the wafers. On April 20, 1988, McConnell and Walter applied for a patent on this process, and the PTO eventually issued the ’761 patent. F. The ’761 Patent The PTO issued the ’761 patent on March 27,1990. It is entitled “Process and Apparatus for Drying Surfaces.” The patent lists CFM Technologies Research Associates as its assignee. On December 30, 1992, CFM Technologies assigned the ’761 patent to CFMT, Inc., and CFMT Inc. made CFM Technologies the exclusive licensee of the ’761 patent. CFMT asserts that use of Steag’s Maran-goni dryer infringes claims 1, 8, 17, and 22. These claims read as follows: 1. A method for drying surfaces of objects which are suspended in a rinsing fluid comprising providing a drying vapor, replacing said rinsing fluid with said drying vapor by directly displacing said rinsing fluid from said surfaces with said vapor at such a rate that substantially no liquid droplets are left on the surfaces after replacement of the rinsing fluid with drying vapor. 8. A method according to claim 1 wherein said drying vapor is purged from said surfaces by introducing a dry, inert, non-con-densable gas after replacement of said rinsing fluid. 17. A method according to claim 1 wherein substantially no rinsing fluid or drying vapor is removed by evaporation of liquid droplets. 22. A method according to claim 1 wherein said objects are semiconductor wafers. In its “Background” section, the ’761 specification describes the conventional spin-rinser-drier. It also refers to the newer methods using “steam or chemical drying of wafers,” and specifically mentions the drying method in the ’532 patent as an example. It explains that in methods such as the one disclosed in the ’532 patent, there are “two steps. First, the rinsing fluid, preferably water is driven off the wafers and replaced by a nonaqueous drying fluid. Second, the nonaqueous drying fluid is evaporated using a predried gas.” The specification goes on to describe the claimed invention. It explains that, in the ’761 process, CFMT believes it “to be important that the downward velocity of the [rinsing fluid] be controlled at a relatively slow rate.” It notes that descent rates of one to four inches per minute have been found to be satisfactory, but that rates of over five inches per minute “yield poor results.” The specification also recommends using “warmer vessel temperatures.” The specification states that “it is preferred that the drying vapor be miscible with water and form a minimum boiling azeotrope with water, isopropanol being a particularly preferred drying vapor.” A substance is miscible with another when it can be freely mixed with that substance in any proportion. An azeotrope is a mixture of two substances in such a proportion that they do not separate when boiled. The specification goes on to recommend that the drying vapor be “substantially pure and either saturated or preferably superheated, and the surfaces should be heated to a temperature near to but preferably below that of the drying vapor prior to contact.” The specification notes that “this may result in some condensation of vapor on the surfaces, and too much condensation should be avoided, [but] it has been found that preheating to above the temperature of the drying vapor yields poorer results.” The specification explains that one of the surfaces in which the drying fluid condenses is the surface of the rinsing fluid. This condensation forms a “distinctive drying fluid layer” that is “more than one half inch in thickness in some cases.” At trial, McConnell testified that CFMT prefers to run the process so that this IPA layer forms on top of the rinsing fluid. He stated that CFMT believes “it makes the [process] more robust.” That is, it facilitates cleaning and drying by trapping particles and letting the water pull them down as it drains off of the wafer. The specification explains the way in which CFMT believes its drying process works. It explains that “it is believed that the method of the invention involves a physical pushing by the vapor or pulling by the liquid surface, resulting in direct displacement by vapor for liquid raither than an evaporation of liquid droplets.” G. Marketing of Full Flow System CFMT has marketed and sold Full Flow equipment, incorporating the ’761 drying process, since 1987. McConnell testified that the company charges between $2 million and $3 million per unit, and has sold almost 200 units around the world. Pam McCardell, CFMT’s vice president of North American sales, testified that the Full Flow system won the 1995 Best Product Award from Semiconductor International. McCardell also testified that all Full Flow systems now use the direct displacement drying method described in the ’761 patent. Roger Carolin testified that the drying step is a fundamental part of any cleaning process, and that the ’761 patent is the most important patent that CFMT owns. McConnell described the ’761 patent as the “crown jewel” of the company. However, McConnell admitted on cross that when CFMT attempted to sell a stand-alone dryer using the ’761 technology, it was a “short-lived effort,” and that CFMT was only able to sell three such units. H. The Steag Marangoni Dryer On February 21, 1990, a Dutch company called N.V. Philips’ Gloeilampenfabrieken (“Philips”) filed a patent application in the European Patent Office. Philips is a large company that manufactures electronic equipment. On September 14,1994, the European Patent Office issued Publication number 0-385-536-B1 (“the Philips patent”). The Philips patent claims a “method of treating substrates, in which the latter are immersed for some time in a bath containing a liquid and are then taken therefrom so slowly that practically the whole quantity of liquid remains in the bath.” On April 7, 1993, before the Philips patent issued, Philips entered an agreement (“the Philips-Steag Agreement”) with Steag Lami-narflow-Prozesstechnik GmbH (“Laminar-flow”). Under the Philips-Steag Agreement, Philips transferred the “know-how” for the design and development of the drying equipment described in the Philips patent. On May 31,1995, Philips entered into an amended agreement with Steag Microtech GmbH Donaueschingen (“Donaueschingen”), indicating that Laminarflow had transferred its rights and obligations under the Philips-Ste-ag Agreement to Donaueschingen, and that Philips consented to this transfer. Donaues-chingen is a subsidiary of Steag Industrie AG, which is the sole shareholder of defendant Steag. Donaueschingen, using the Philips technology, eventually developed equipment for the process it calls “Marangoni drying.” Steag’s president, Johannes Brinkmann, testified at trial that Steag buys its Marangoni dryers from Donaueschingen, which in turn pays a royalty to Philips for each dryer it sells. At trial, An-Ti Chai testified as an expert for Steag. Chai received a Ph.D. in physics from Kansas State University in 1968. He has spent the last 20 years working for NASA at the Lewis Research Center. He has focused on the study of “microgravity fluids and microgravity material science.” His experience with wafer processing is limited to work he did with solar cells from 1976 to 1980. Chai described the process that Steag uses in its Marangoni dryer. This process takes place in a drying chamber. There is a lid over the chamber, but Chai explained that it is “not tightly sealed. It is open to the environment.” At the bottom of the chamber is a rinse bath (fresh deionized water) in a tank. Wafers are in a carrier above the rinse bath. First, the Marangoni dryer lowers the wafers into the rinse bath. The tank feeds water in from the bottom, so that water is constantly overflowing the sides of the tank. Next, the dryer introduces a gaseous mixture that is 2.5% IPA and 97.5% nitrogen through the lid on top of the chamber, so that it fills the space above the rinse bath. The Marangoni dryer then uses a thin knife blade to push the wafers up out of the water from below. The knife blade pushes the wafers at a slow and steady rate. Chai stated that this rate was “approximately two inches per minute.” The dryer then drains the rinse tank and blows nitrogen gas into the chamber to purge whatever vapor remains. Finally, the wafers are removed. I. The Lawsuit On July 10, 1995, CFMT filed a complaint in this court, alleging that Steag has infringed one or more claims of the ’761 patent, either literally or under the doctrine of equivalents. CFMT filed an amended complaint on September 29, 1995, adding Do-naueschingen as a defendant. Steag filed an answer to the amended complaint on October 16, 1995. In its answer to the amended complaint, Steag denies infringement and asserts that the ’761 patent is invalid and unenforceable. On April 28, 1997, the court dismissed CFMT’s claims against Donaues-chingen for. lack of personal jurisdiction. J. Claim Construction On November 24, 1997, the court held a hearing in accordance with Markman v. Westview Instruments, Inc., 517 U.S. 370, 116 S.Ct. 1384, 134 L.Ed.2d 577 (1996) to construe disputed terms in the claims of the ’761 patent. The court issued an opinion construing disputed terms on November 25, 1997. The court found that the language in the asserted claims requiring that the wafers be “suspended” in a rinsing fluid means that they are “hung or upheld, so as not to fall or sink.” The court found that “drying vapor” means “a vapor that facilitates the removal of liquid from a surface.” The court also found that the term “directly displacing” means “replacing with no intervening substance.” K. The Trial On December 2 through December 11, 1997, the court held a jury trial on the issues of infringement, validity, and unenforceability. 1. Infringement On the issue of the Steag dryer’s infringement of the ’761 patent, CFMT presented testimony from Charles R. Helms and Srini Raghavan. Helms is a professor of electrical engineering at Stanford University, where he runs a large research program in the area of semiconductor technology, surface chemistry, and surface physics. Raghavan is a professor of material science and engineering at the University of Arizona in Tuscon. He teaches classes in surface chemistry. Both Helms and Raghavan went through each element of the asserted claims, and testified that the drying method practiced in Steag’s Marangoni dryer performs all of the steps in claims 1, 8, 17, and 22 of the ’761 patent. Helms testified that he had looked at the ’761 patent, and had studied the Steag dryer by reading documents and brochures, watching a Steag videotape, and witnessing the Steag dryer in person. CFMT played a videotape that Steag had produced, showing the Steag dryer and explaining how it works. Helms testified that Steag’s process would not work without IPA, which he claimed helps force water off of the wafers like a' “chemical squeegee.” Raghavan testified that he had read documents describing Steag’s dryer, had watched a videotape of the process, and had read articles and papers on Marangoni drying. He testified that as he understands the language in the ’761 patent, the Steag dryer infringes. An-Ti Chai testified for Steag on the issue of infringement. Chai testified that the Mar-angoni dryer dries wafers by using the “Mar-angoni effect.” He first explained that liquid molecules attract each other and create a “surface tension” at the liquid’s surface. He next explained that the Marangoni effect is the phenomenon where fluid flows from areas with weak surface tension to areas with strong surface tension. Chai testified that, in the Steag process, the IPA vapor introduced with nitrogen dissolves into the surface of the rinse bath. As IPA dissolves in water, it reduces the surface tension of the water. Chai explained that the IPA does not dissolve uniformly along the rinse bath surface. As the wafer breaks the surface of the water, it pulls up some water that sticks to the wafer. The water surface ramps up towards the wafer. This curvature of water is called a “meniscus.” Chai testified that as the IPA vapor dissolves into the water, the IPA concentration will be higher in the meniscus than it is in the areas further away from the wafer, because the meniscus is very thin in the area close to the wafer, but is thicker as one moves away from the wafer. The thicker layer of water disperses the IPA more quickly than the thin meniscus does. Thus, Chai testified that the greater IPA concentration in the water near the wafer will reduce the surface area to a greater extent than it will for areas away from the wafer, and the Marangoni effect will draw water away from the wafer. Chai also explained that the water overflow in the rinse tank prevents the IPA from building up. This helps to flush the IPA from the rinse bath, so that the Marangoni effect can continue to pull water away from the wafer surface. Chai testified that, in his opinion, the Ste-ag process does not infringe the ’761 patent for several reasons. First, the Steag process does not dry wafers that are “suspended,” because the Steag process actually lifts the wafers out of the rinsing fluid, and does not simply hold them up. Second, Chai testified that the IPA/nitrogen mixture that Steag uses does not qualify as a “drying vapor.” He explained that the nitrogen is not a vapor, and the IPA does not facilitate drying, but simply induces the Marangoni flow. Third, he testified that the Steag process does not involve the direct displacement of rinsing fluid with drying vapor. He reiterated that the Marangoni effect was the mechanism that dries the wafers in Steag’s process. He explained that the level of the rinsing fluid does not change during the Steag drying process. He stated that the only displacement that occurs is water for the wafer solid (as the wafer is drawn out of the water, water fills in the space that the wafer once filled), and wafer solid for IPA vapor and nitrogen gas (as the wafer rises from the rinse bath, it fills space that the gas once filled). Finally, Chai testified that he had seen the Steag dryer work effectively while raising the wafers at a speed of over 20 inches per minute. He pointed out that the ’761 patent specification described lift rates of between 1 and 4 inches per minute. Helms and Raghavan were both asked about the role of the Marangoni effect in Steag’s drying process. Helms testified that he does not believe the Marangoni effect is a major reason that the Steag dryer works. However, he testified that even if the Maran-goni effect were the dominant mechanism in the drying achieved by the Steag dryer, his opinion regarding infringement would not change, because the IPA vapor still “directly displaces” the rinsing fluid. Raghavan similarly testified that he did not believe that the “directly displaces” language precludes a dryer that uses the Marangoni effect from infringing the ’761 patent’s claims. 2. Invalidity On Steag’s affirmative defense that the ’761 patent is invalid, Steag offered the testimony of Paul Neitzel. Neitzel is a professor at the Georgia Institute of Technology, in the school of mechanical engineering. He received a Ph.D. in fluid dynamics from Johns Hopkins in 1979. He testified that he had studied the prosecution histories and patents for the ’761 patent and the ’532 patent, as well as other pieces of prior art. Neitzel testified that CFMT’s 1986 brochure for the Full Flow process, published almost two years before April 20, 1988, when CFMT filed the application for the ’761 process, fully describes the drying process claimed in the ’761 patent. He pointed to the brochure’s description of the drying process, which states that “filtered IPA vapor is introduced to the top of the wafer vessel” and that “IPA vapors flow in, replacing the water.” He also pointed to the brochure’s claim that the system produces “no particle generation” and “no streaking or staining.” Neitzel went through each element of claims 1, 8, 17, and 22 of the ’761 patent, and explained how each was disclosed in the 1986 brochure. Neitzel also testified that the advertisement for the Full Flow machine in the February 1987 issue of Semiconductor International describes the ’761 process. Neitzel also testified that several pieces of prior art rendered the ’761 process obvious to one of ordinary skill in the art at the time that CFMT filed its patent application. He specifically referenced four patents. These are: (1) U.S. Patent No. 4,816,081 (“the Meh-ta patent”); (2) U.S. Patent No. 4,722,752 (“the Steck patent”); (3) U.S. Patent No. 4,736,760 (“the Coberly patent”); and (4) U.S. Patent No. 4,643,774 (“the Kishida patent”). CFMT does not dispute that each of these patents qualifies as prior art to the ’761 patent, as each bears an application date more than one year prior to April 20, 1988. a.The Mehta patent The Mehta patent is entitled “Apparatus and Process for Static Drying of Substrates.” Mehta filed the patent application on February 17, 1987, and the Patent and Trademark Office (“the PTO”) issued the Mehta patent on March 28,1989. It discloses a process for drying semiconductor wafers, in which the wafers are held “in a static position to avoid the generation of undesired particulate.” The Mehta process involves positioning the wafers in a chamber, and then filling this chamber with processing fluid. A “vacuum valve” pulls all gas out of the chamber. Then another “vacuum assisted” drain valve is opened, and as the processing fluid drains out, “clean dry inert gas” is introduced from the top. The patent’s abstract claims that this draining step “assures that any droplets remain with the draining fluid so that the [wafers] emerge dry.” The patent specification explains that the inert gas can be “clean ah’, argon or, preferably, nitrogen.” The specification describes the “preferred drain rate” as one gallon per minute. Neitzel calculated this rate to be between 2.1 and 3.7 inches per minute. In the “Background of the Invention” section, the patent specification describes other types of drying equipment. It mentions that some systems use an “IPA dryer,” and describes it as a dryer that involves “immersing the wafers in a liquid/gaseous bath of IPA .” The specification explains that “alcohol may leave organic residue remaining on the surface of the wafer as it evaporates.” The specification describes this as an “unacceptable drawback.” b. The Steck patent The Steck patent is entitled “Apparatus and Method for Rinsing and Drying Silicon Wafers.” Steck applied for the patent on January 16, 1986, and the PTO issued the Steck patent on February 2, 1988. It discloses a method for drying silicon wafers by raising them slowly out of the rinsing solution, so that “the water surface tension at the surface of the water bath evenly and effectively draws off water from the rising surfaces of the wafers.” The patent calls for the wafers to be submerged in a tank filled with hot, deionized water. The wafers rest in a “cassette” (a wafer carrier). Water feeds into the bottom of the tank, so that the water is constantly overflowing the top of the tank. This overflow creates a skimming action on the water surface, which removes particles as they are washed off the wafers. The patent claims a “novel, vertical lift mechanism” that slowly lifts the wafers and the cassette out of the rinsing fluid, so that there is no contact between the cassette and the wafer at the point where the wafer crosses the surface of the water. Above the tank, the process can include a “filtered, laminar flow of clean, dry air.” The patent specification explains that when the wafers are pulled from the water so that “the wafer is in contact with no other object, the water is drawn uniformly from the wafers and the surface of the wafer rising above the water will be dry.” The specification indicates that the rate of removal of the wafers should be “about two inches per minute.” c. The Coberly patent The Coberly patent is entitled “Apparatus for Cleaning, Rinsing and Drying Substrates.” Coberly filed the patent application on September 15, 1986, and the PTO issued the Coberly patent on April 12, 1988. It claims a method for rinsing wafers and then removing them from the rinsing tank “at a slow, controlled rate” so as to “avoid the need for a dryer independent of the rinse tank.” The patent discloses an apparatus that cleans the wafers in one tank (by using “me-gasonie energy”) and then moves the wafers from the cleaning tank to a rinsing tank. The patent specification explains that the process can take place in a controlled environment, in which a “laminar flow system of hepifiltered air” is used. The patent specification also indicates that the typical rate of ascent of the wafers, as they are withdrawn from the rinsing tank, requires between 1 and 15 minutes to achieve total removal. The specification explains that two factors in the patented method help produce dry wafers. First, the rinsing fluid in the Coberly method is supposed to be heated, to between 60 and 100 degrees centigrade. The specification explains that the heated fluid will have a lower surface tension, and thus will not adhere to the wafers very strongly as they rise out of the rinsing fluid. Second, the cleaning process in the Coberly method uses a solution containing ammonium hydroxide, hydrogen peroxide, and water. The specification claims that this solution adheres to the wafer surfaces, and then facilitates the flushing away of water molecules from the wafer surface when it is immersed in rinsing fluid. The combination of lower surface tension and the cleaning solution results in the wafers emerging from the rinsing fluid without any water on them. d. The Kishida patent The Kishida patent is entitled “Method of Washing and Drying Substrates.” Kishida filed the patent application on April 17,1985, and the PTO issued the Kishida patent on February 17, 1987. It discloses a method in which equipment oscillates the objects to be dried as it pulls them out of the wash liquid, and then sprays a stream of “drying gas such as air” on the wafers. The patent specification indicates that in its preferred embodiment, the equipment draws the wafers out of the wash liquid at a speed of 1.5 to 4.2 centimeters per minute. Neitzel calculated this to be equivalent to .59 to 1.7 inches per minute. e. Neitzel’s conclusion After describing each of the patents discussed above, Neitzel concluded that a person of ordinary skill in the art at the time that CFMT filed the ’761 application would have found the method disclosed in the ’761 patent obvious in light of the prior art. He explained that the slow rate of wafer ascent and the use of surface tension for drying disclosed in the ’761 patent was also disclosed in the Mehta, Steck, Coberly, and Kishida patents. He further explained that the use of IPA was disclosed in the Full Flow 1986 brochure and in the ’532 patent, and that the Mehta patent referred to IPA dryers. 3. Unenforceability On its defense that CFMT engaged in inequitable conduct, Steag called Eugene Rzucidlo to the stand to explain PTO procedures to the jury. Rzucidlo worked in the PTO from 1970 to 1985, and has worked as a patent attorney since 1985. He explained that during the prosecution of the ’761 patent, CFMT did not present the patent examiner with a copy of the 1986 Full Flow brochure, the Semiconductor International advertisement from February of 1987, the CFMT press release from late 1986 announcing CFMT’s relationship with Rodel, or any documents referring to the transaction with TI in December, 1986. On cross, Rzucidlo admitted that the patent examiner was aware of the ’532 patent during the patent prosecution. When Rzucidlo testified on direct that thé ’532 patent was not prior art to the ’761, the court sustained CFMT’s objection, and instructed the jury to disregard that testimony. U- Willfulness CFMT argued at trial that Steag not only infringes the ’761 patent, but that the infringement is willful. CFMT presented evidence at trial as to how Steag learned about the ’761 patent, how Steag investigated the possibility that the Marangoni dryer might infringe the ’761 patent, and what Steag did after learning about and analyzing the patent. CFMT read portions from the deposition testimony of Dana Scranton, a former Steag, employee. While working at Steag in late 1994, Scranton heard a rumor that CFMT was preparing to sue Steag for infringement of a patent it owned. Scranton testified that he told Brinkmann, who was then the controller of Steag and is now its president, about the rumors he had heard. Scranton asked George Stradar, an attorney for Steag, to find copies of CFMT’s patents and to send copies to Scranton. Stradar in turn called Charles Mueller, a patent attorney, to find the CFMT patents. In a December 5, 1994 letter from Stradar to Scranton, Stradar indicates that he is sending the CFMT patents to Scranton. Stradar also informs Scranton that he only authorized Mueller to find the patents, but not so spend time analyzing them. Scranton testified that he looked at the CFMT patents, chose the ’761 patent as most relevant to Steag’s products, and read it. Scranton testified that he discussed it with Brinkmann, but told him that there “doesn’t seem to be any concern that there’s an infringement.” In March or April of 1995, Scranton heard another rumor that CFMT was preparing to sue, and then “decided it was not prudent to trust my judgment, but rather [decided] to seek expert counsel.” Scranton wrote a letter to Stradar, dated April 25, 1995, indicating that Brinkmann had authorized him to tell Mueller to study the CFMT patents and to render an opinion on whether Steag infringes. On the same day, April 25, 1995, Mueller wrote a letter back to Scranton asking for information on the Steag process that he needed in order to render an opinion on infringement. On June 1, 1995, Mueller wrote to Scranton again, asking for this same information. On June 2, Scranton sent Mueller the requested information. On June 28, 1995, Mueller sent a letter to Stradar, enclosing his letter opinion stating that in his opinion the Steag process does not infringe the claims in the ’761 patent and the other 11 CFMT patents that he had studied. Mueller opines that the Steag process does not infringe the ’761 patent because the Steag dryer lifts wafers through the liquid-vapor interface, while in the ’761 patent “moving or handling of wafers is not required, and the structure of the vessel ... would not allow any wafer movement or handling.” Steag continued to sell and market Marangoni dryers. 5. Damages Both sides offered expert testimony on the damages that the jury should award if it determined that Steag’s dryer infringes, that the claims of the ’761 patent are valid, and that the patent is enforceable. Russell Parr testified for CFMT. Parr received an M.B.A. from Rutgers University in 1980. He testified that a hypothetical negotiation between CFMT and Steag, at the time that Steag began selling its Marangoni dryers, would have resulted in CFMT charging Steag a royalty rate of 9%, and that CFMT would have expected this rate to be applied to the total sales revenues that Steag received from sale of stand-alone Marangoni dryers, as well as sales of full “wet benches” (wet processing equipment that includes a Marangoni dryer as one of its components). He explained that CFMT would have believed that each sale of a Steag wet bench with the Marangoni dryer would mean that CFMT had lost a potential sale for the entire Full Flow system. Parr calculated the damages due to CFMT as $9.9 million. For Steag, David Urey testified. Urey graduated from George Washington University with a law degree in 1964. He worked for eighteen years for U.S. Steel, recently renamed USX Corporation, as a patent and licensing attorney. Urey testified that, in his opinion, the reasonable royalty that would have resulted from the hypothetical negotiation between CFMT and Steag would have been about 1 to 2%. Urey testified that the royalty rate should only be applied to sales revenues for stand-alone dryers, and the Marangoni dryer component of the wet bench, since those are the actual devices in which drying takes place. He calculated the maximum damages that CFMT should receive to be about $414,000. At trial, Steag’s sales numbers from the sale of Marangoni dryer became a point of dispute between the parties. After Parr testified for CFMT as to his calculations of Steag sales, which he determined from sales sheets that Steag had produced during discovery, Steag called Brinkmann to the stand. Brinkmann testified that Parr had incorrectly calculated Steag’s sales totals, because he misunderstood the Steag sales sheets and had double-counted some Steag sales. CFMT objected to Brinkmann’s testimony, and argued that Steag had not produced sufficient information for CFMT to calculate sales, and furthermore had improperly failed to notify CFMT about Parr’s double-counting before trial. The court ordered the parties to draft a jury instruction that used CFMT’s sales revenues number, and stated that the court would reduce this number, if necessary, as a matter of post-trial relief. The parties drafted a jury instruction, and the court read it to the jury at the close of evidence. The court instructed the jury that if it found that damages should be awarded, and that the reasonable royalty rate should be applied to sales of stand-alone dryers and the Marango-ni dryer component of the full wet bench; the sales revenues are $20,700,000. If the jury found the reasonable royalty rate should be applied to sales of the stand-alone dryers and the full wet bench, the sales revenues are $110,140,282. 6. The Jury’s Verdict At trial, along with the issues of infringement and validity, the court submitted the question of whether CFMT had engaged in inequitable conduct to the jury. However, the court indicated to the parties that it would treat the jury’s verdict on the issue of unenforeeability as an advisory verdict, and that the court would ultimately resolve the issue. On December 12, 1997, the jury returned its verdict. The jury found that operation of Steag’s Marangoni dryer literally infringes claims 1, 8, 17, and 22 of the ’761 patent. The jury also found that the Marangoni dryer infringes each element of each of the asserted claims under the doctrine of equivalents. The jury found that Steag has actively induced users of the Marangoni dryer to infringe, and that Steag has contributorily infringed, the asserted claims. The jury rejected Steag’s contentions that the claims of the ’761 patent are invalid and that the patent is unenforceable. The jury awarded CFMT $3,105,000, and indicated that it used a royalty rate of 15% to arrive at the damages amount. Finally, the jury found that Steag’s infringement of the ’761 patent was willful. On December 15, 1997, the court wrote to counsel for both parties. The court indicated that it would delay entering an order directing the clerk to enter judgment for CFMT, since the court still needed to resolve the issue of unenforceability, and the amount of damages owed by Steag was still subject to revision upon post-trial motion. The court stated that it would refrain from ordering the clerk to enter judgment until it had resolved post-trial motions. L. Post-Trial Motions At the close of CFMT’s evidence, at the close of its own evidence, and again after CFMT’s rebuttal case, Steag moved for judgment as a matter of law on the issues of infringement, invalidity, and unenforceability. On December 26, 1997, Steag renewed its motion, and moved in the alternative for a new trial. On December 29, 1997, CFMT moved for the court to award treble damages pursuant to its authority under 35 U.S.C. § 284, and to award attorney’s fees pursuant to its authority under 35 U.S.C. § 285. II. DISCUSSION A. What is the Standard For Granting Judgment as a Matter of Law? Federal Rule of Civil Procedure 50(a) provides that the court may determine an issue against a party where “there is no legally sufficient evidentiary basis for a reasonable jury to find for that party on that issue.” See also Gomez v. Allegheny Health Servs. Inc., 71 F.3d 1079, 1083 (3d Cir.1995), cert. denied, 518 U.S. 1005, 116 S.Ct. 2524, 135 L.Ed.2d 1049 (1996) (describing standard as “whether there is evidence upon which a reasonable jury could properly have found its verdict”). Rule 50(b) provides that “[i]f, for any reason, the court does not grant a motion for judgment as a matter of law made at the close of all the evidence, the court is considered to have submitted the action to the jury subject to the court’s later deciding the legal questions raised by the motion.” Rule 50(b) also requires that the movant actually renew its request for judgment as a matter of law within 10 days of the entry of judgment. When a party chooses to renew its motion and challenge a jury’s verdict, the court must assess the sufficiency of the evidence supporting the verdict. In performing this assessment, the court must draw all reasonable inferences from the evidence in the light most favorable to the non-movant. Perkin-Elmer Carp. v. Computervision Corp., 732 F.2d 888, 893 (Fed.Cir.), cert. denied, 469 U.S. 857, 105 S.Ct. 187, 83 L.Ed.2d 120 (1984); Richardson-Vicks Inc. v. Upjohn Co., 122 F.3d 1476, 1479 (Fed.Cir.1997); Gomez, 71 F.3d at 1083. The court may not determine the credibility of witnesses, and it may not “substitute its choice for that of the jury between conflicting elements of the evidence.” Perkin-Elmer, 732 F.2d at 893. B. Did the Jury Properly Find That Ste-ag Literally Infringes the Asserted Claims of the ’761 Patent? 1. How must the court determine whether CFMT sufficiently established infringement? To determine whether Steag is entitled to judgment as a matter of law on the issue of literal infringement, the court must first construe the claims of the patent, and then must compare the claims to the accused device. See Texas Instruments Inc. v. United States Int’l Trade Comm’n, 988 F.2d 1165, 1171 (Fed.Cir.1993). In this comparison the court must first determine if all the claim elements, as construed, are present in the device. Id. 2. Does Steag’s process use a “drying vapor”? Steag argues that no reasonable jury could conclude from the evidence that its process uses a “drying vapor,” as required in each of the asserted claims. The court defined drying vapor in its claim construction opinion to mean “a vapor that facilitates the removal of liquid from a surface.” Steag argues that the court should reject the jury’s finding that use of the Steag dryer literally infringes the claims of the ’761 patent, and grant judgment as a matter of law for Steag. Steag’s Marangoni dryer uses a mixture that is 2.5% IPA and 97.5% nitrogen. Steag points out that the ’761 patent specification teaches that nitrogen gas is a foreign gas that should be excluded from the system, and contends that this precludes a jury from finding that Steag’s process uses a drying vapor. Steag also points to the testimony of its expert, An-Ti Chai, who testified that the IPA vapor used in the Steag process does not facilitate drying, but simply induces the Marangoni flow. CFMT counters that Steag’s process clearly uses IPA vapor, and that there was an abundance of evidence that this vapor “facilitated” the drying process. Helms testified for CFMT that the IPA vapor in the Steag process is a drying vapor, and creates a “chemical squeegee” effect on the wafer surface. In fact, even Chai’s testimony supports CFMT’s position. He did not testify that the IPA vapor prevented drying — he stated that the IPA induced a Marangoni flow, and admitted that the Marangoni dryer would not work without this IPA vapor. Thus, despite his testimony to the contrary, he essentially admitted that the IPA vapor facilitates drying. Chai disputed Helms’s explanation of why the Steag dryer works but not whether it works. Since the parties’ experts agree that the IPA vapor in Steag’s dryer facilitates drying, the court finds that the dryer uses a drying vapor. 3.Does Steag’s process “directly displace” rinsing fluid unth drying vapor? Steag next argues that no reasonable jury could conclude that the Marangoni dryer involves a process where drying vapor “directly displaces” rinsing fluid, as required in the asserted claims. The court defined “directly displacing” in its claim construction opinion to mean “replacing with no intervening substance.” Steag offers three arguments to support its claim that its process does not involve direct displacement. First, it argues that the Marangoni dryer actually lifts the wafers during drying, while the ’761 process calls for the wafers to stay stable. Steag argues that the drying vapor and the rinsing fluid do not actually change locations. Instead, Steag claims that as the wafer moves out of the rinse bath, rinsing fluid takes the place that used to be taken by the wafer, and the wafer takes the place that used to be taken by drying vapor. Thus, the only “displacement” is fluid for solid and solid for vapor. Second, Steag argues that as the IPA vapor contacts the rinsing fluid, a layer of IPA condenses into liquid form on the surface of the rinsing fluid. Thus, Steag argues that even if one were to consider displacement from the perspective of the wafer, each portion of the wafer first has rinsing fluid displaced by IPA liquid, and then IPA liquid is displaced by the IPA vapor. Again, Steag argues, there is no direct displacement of rinsing fluid by drying vapor — there is an intermediate step involving IPA liquid. Finally, Steag argues that its process does not use direct displacement, because the vapor in the Steag system does not push the water from the wafer surfaces. Steag argues that its system dries through the Marangoni effect, and that this is not the same as direct displacement. At trial, Chai testified for Steag that the Marangoni dryer does not use direct displacement, but instead uses the Marangoni effect to dry. He also testified that the rinsing fluid is not displaced by drying vapor in the Steag process, because it is the wafer that moves and not the rinsing fluid/drying vapor interface. CFMT responds by quoting from claim 1, which calls for direct displacement of the rinsing fluid “from said surfaces.” It argues that the direct displacement step must be understood from the perspective of the wafer surface, and that therefore it does not matter whether the wafer remains in one place and the rinsing fluid/drying vapor interface moves (as it does in the Full Flow process when the rinsing fluid drains from below) or the wafer moves and the interface remains in one place (as it does in the Marangoni dryer). CFMT also refutes the argument that the existence of a layer of IPA liquid at the rinsing fluid/drying vapor interface means that there is no infringement. In fact, CFMT points out, the specification for the ’761 patent expressly mentions the possibility that this liquid layer might form. Furthermore, McConnell testified for CFMT that the liquid IPA layer makes the drying process more “robust.” The court can dispense with the first dispute quickly. During claim construction, Steag argued that the term “suspended in a rinsing fluid” in claim 1 required that the wafers be held in a fixed position. The court disagreed, and pointed out that claim 19 specifically limited claim 1 by claiming a “method according to claim 1 which does not require movement or handling of said surfaces between rinsing and drying steps.” Steag now attempts to argue that the direct displacement requirement in claim 1 also means that the wafers must be held in a fixed position. The court again disagrees. In fact, the court specifically instructed the jury that “[t]he term ‘directly displacing’ as used in Claim 1 of the ’761 patent means: Replacing with no intervening substance and is not limited to a descending level of rinsing fluid.” As for the second dispute, both sides agree that a layer of IPA liquid forms on the surface of the rinsing fluid in Steag’s process. The parties appear to dispute whether this IPA liquid is an “intervening substance.” If it is an intervening substance, then drying vapor does not directly displace rinsing fluid. Steag raised this same argument during claim construction. The court found that Steag did not seek further definition of any of the terms in the patent, but rather wanted a ruling that the presence of a liquid layer in its process means it does not infringe. The court declined to address the issue at that time, as it was not a claim construction issue. As mentioned above, CFMT disclosed in its patent specification that the ’761 process often, includes a layer of IPA liquid. CFMT’s own machine uses a process that includes such a layer. McConnell testified that the warmer drying vapor condenses as it strikes the cooler wafer chamber and cooler rinsing fluid. He testified that this condensation was the natural result of the difference in temperature. It appears that the liquid layer might even improve the drying process. From the evidence presented, the jury could reasonably conclude that the IPA vapor displaces rinsing fluid, and that part of this process involves the formation of a liquid layer in the interface. While this IPA liquid might be in a different phase than the IPA vapor, the jury could reasonably find that it is not an intervening substance. In other words, the jury could reasonably conclude that the forming of an IPA liquid layer is simply one step in the displacement of rinsing fluid with drying vapor. After the close of briefing on the post-trial motions, Steag submitted to the court several documents that CFMT had filed in its prosecution of the Japanese counterpart to the ’761 patent. In the Japanese proceeding, CFMT amended claim 1 so that it claims an extra step of forming a liquid layer of drying fluid on top of the rinsing fluid, and then having the drying “fluid” directly displace the rinsing fluid. Steag claims that this is an admission by CFMT that a process that allows the presence of a liquid layer is different than the process disclosed in the ’761 patent. However, CFMT’s choice to further describe its process in the claims of its Japanese patent is irrelevant to the matters litigated in this court. Here, the jury found that Steag’s process infringes despite the presence of an IPA liquid layer. The court finds that this conclusion is reasonable. Finally, Steag argues that its system dries using the Marangoni effect, and not using direct displacement. Steag appears to rely upon a passage in the ’761 specification that states that “it is believed that the method of the invention involves a physical pushing by the vapor or pulling by the liquid surface, resulting in direct displacement by vapor for liquid.” However, both Helms and Raghavan testified for CFMT that Steag’s dryer uses direct displacement, regardless of the force that drives the drying process. The court’s construction of the term did not include an element of pushing or pulling, but instead defined it to mean “replacing.” The jury could reasonably have found that this replacing does occur, and that the use or nonuse of the Marangoni effect in the Steag process is irrele