Wednesday, September 22, 2010

Estimating Drying Times

Estimating Drying Times, Break-through Times, Permeation Rates, and Post-Purge Outgassing For Microenvironments


Sung In Moon
L. Monson
Y. Liu
M. Fuller
C. W. Extrand

In the future, microenvironments will be required to maintain low oxygen and relative humidity levels to facilitate newer technology nodes.

Polycarbonate is an amorphous engineering thermoplastic. With excellent clarity, toughness, and a high softening temperature, it is used in a wide variety of semiconductor, medical, aerospace, and consumer applications. Within the semiconductor arena, Polycarbonate is used for containers or microenvironments that protect and transport critical materials, such as silicon and ceramics, as they are converted from raw wafers or disks into integrated circuits or rotating memory. In the past, moderate humidity and oxygen found in ambient air were usually benign. Today, some semiconductor manufacturing technologies have advanced to the point where even the water and oxygen in air can be detrimental, causing time-dependent haze or corrosion.1,2

Purging with an inert gas is one method for lowering water or oxygen levels inside microenvironments. However, once the purge gas stops flowing, oxygen and water levels quickly rise. For example, after purge the relative humidity inside a traditional Polycarbonate wafer microenvironment can reach 30% in several hours. The post-purge rise in oxygen and water may have multiple causes: permeation from the exterior, leakage, or de-sorption from the materials of construction. Understanding these different factors and ultimately engineering a solution requires knowledge of the mass transport coefficients of the microenvironment materials of construction.

In this article, we describe measurements of the mass transport coefficients of oxygen and water through Polycarbonate. Subsequently, these coefficients were used to estimate drying times to remove absorbed oxygen or water, break-through times for oxygen or water, initial permeation rates as well as post-purge humidity rise of a 300 mm front opening unified pod (FOUP) constructed from Polycarbonate.

ANALYSIS
Relative humidity (RH) was calculated as the ratio of water vapor pressure (p) to saturation water vapor pressure (psat) at a given temperature, (equation 1)

equation 1

Vapor permeates through homogeneous materials by first dissolving and then diffusing.3 The downstream pressure rise (pl) of the permeant can be converted to an equivalent volume of gas (q) at standard temperature and pressure (STP), (equation 2)

equation 2

where T is the measurement temperature, V is the volume of the downstream side of the permeation apparatus, T0 is standard temperature (0°C = 273 K) and p0 is standard pressure (1 atm = 76 cmHg). The volume (q) of gas that permeates through a film with time (t) under steady state conditions depends on the permeability coefficient (P), as well as film thickness (B), film area (A) and the applied upstream pressure (ph),3,4 (equation 3)

equation 3

The time required for a permeant to break though a film (tb) depends on the film thickness (B) and the diffusion coefficient (D) of the material, (equation 4)

equation 4

Solubility coefficients (S) were calculated from permeability and diffusion coefficients as, (equation 5)

equation 5

EXPERIMENTAL DETAILS
The Polycarbonate evaluated in this study was extruded film from GE (now Sabic) (8010-MC-112). Mass transport coefficients were measured according to standard manometric procedures5-8 as described below. The permeation apparatus consisted of a sample holder inside a temperature-controlled chamber, a series of valves, an upstream ballast tank, a pressure gauge for the upstream gas or vapor, and a downstream solid-state manometer (10 Torr MKS Baratron Type 628B). The apparatus was constructed from stainless steel. Connections were made by welding or with VCR flanges to minimize leaks. Data acquisition and control were performed remotely with a personal computer.

A circular specimen with a diameter of 4.6 cm and an effective area (A) of 13.7 cm2 was placed in a permeation apparatus. The apparatus was pumped down to approximately 3 x 10-3 cmHg and held overnight to remove volatile constituents from the apparatus as well as from the specimen. The next day, the apparatus was leak tested. If the leak rate was sufficiently low (typically ~ 2 x 10-8 cmHg/s), then the upstream side of the apparatus was charged with either oxygen gas or water vapor. After pressure and temperatures were allowed to equilibrate for a few minutes, the test was started. The downstream pressure rise (pl) was recorded with the passage of time. Temperature and upstream pressure (ph) also were monitored over the duration of the experiment to assure their constancy. Measurements were made with samples having a thickness of B = 0.25 and 0.51 mm at 25°C (77°F). Given the uncertainty of the temperature, the pressures, the downstream volume, and the dimensions of the polymer specimen, the uncertainty of our mass transport measurements was estimated to be 3-5%.

Mass transport properties
Figure 1 shows an example of raw data obtained from a 0.51 mm thick Polycarbonate specimen exposed to three different upstream pressures of oxygen gas, ph = 0.2, 0.5, and 1.0 atm (15, 38, and 76 cmHg). Initially, the downstream pressure remained constant. Once oxygen broke through the sample, the downstream pressure began to increase. Eventually steady state was established, where permeation rates were proportional to the applied upstream pressure. Note that the lag time from the three different pressures was the same.

These data can be rearranged to calculate permeation properties using equation 3. The results are shown in Figure 2. The points are experimental data and the solid line represents linear regression from longer times. The slope of the line in Figure 2 is equal to the oxygen permeability coefficient (P), which for this film, had a value of P = 1.2 x 10-10 cm3·cm/ cm2·s·cmHg. The break-through or lag times (tb) were estimated from the intersection of two lines—the first is defined by the permeability coefficient and the second is a zero slope dashed line passing through the initial pl at t = 0 s. For the data in Figure 2, tb = 11,000 s (about 3 hr), which corresponds to a diffusion coefficient of D = 3.8 x 10-8 cm2/s. From the quotient of P and D (equation 5), the solubility coefficient was estimated as S = 3.3 x 10-3 cm3/cm3·cmHg. If analyzed individually, data from each of the pressures gave nearly identical values of P, D, and S. The various thicknesses gave nearly identical results for oxygen. The permeation of water through Polycarbonate showed similar behavior.

Mass transport coefficients for both oxygen and water are summarized in Table 1. The diffusion coefficient describes how fast a molecule can move through a material and the solubility coefficient describes how many molecules are dissolved inside that material. As the size of the water and oxygen molecules is similar, their diffusion coefficients were comparable. In contrast, water is much more soluble in Polycarbonate than oxygen; thus, the solubility coefficient of water was greater than that of oxygen.

The permeability coefficient is an inherent material property that describes the normalized “flow” rate through a material. As the permeability coefficient is a product of D and S, the much greater solubility of water in Polycarbonate led to a P value that was nearly three orders of magnitude larger for water than for oxygen. The measured values generally agreed with previously reported ones.9-11

figure 1

figure 2

table 1

figure 3

Estimates of product performance
The mass transport coefficients listed in Table 1 can be used to estimate the performance of real products constructed from Polycarbonate. In the following examples, we use an Entegris A300, which is a 300 mm front opening unified pod (FOUP), shown in Figure 3. The wafer columns and rear wafer retainer were removed so that this FOUP contains only unfilled Polycarbonate. The A300 has an average wall thickness of B = 0.35 cm, an internal area of A = 5,200 cm2 and internal volume of VME = 25,700 cm3. The Polycarbonate shell and inner door weighed 2830 g. The concentration of gas or vapor inside of a microenvironment can be estimated from the quotient of gas or vapor that has diffused or permeated and the volume of the microenvironment, (equation 6)

equation 6

Semiconductor chip fabrication facilities or “fabs” are often maintained at one atmosphere of pressure (76 cmHg), 25ºC, and 40-45% RH. Since air contains 21% oxygen, the appropriate partial pressure of oxygen for our estimates is 16 cmHg (= 0.21 × 76 cmHg). On the other hand, at 25ºC, water has a saturation vapor pressure of psat = 2.38 cmHg. Therefore, according to equation 1 a RH of 45% equates to partial water vapor pressure of 1.07 cmHg.

Drying times. How long does it take to remove oxygen and water from an A300 FOUP? De-sorption or “outgassing” from materials of construction is a potential contributor to oxygen and water inside of microenvironmnets. Two methods to minimize oxygen and water inside a microenvironment would be to dry in a vacuum or to purge with an inert gas. We can use the mass transport coefficients to estimate how long this would take. The “drying” time (td) to reduce oxygen or water in the PC to a fraction (f) of its original concentration depends on the part thickness (B) and the diffusivity (D) of PC, (equation 7)

equation 7

(Here we assume the FOUP door was open during drying.) From the solubility coefficients, we can estimate the amount of oxygen and water absorbed in Polycarbonate under standard fab conditions. If in equilibrium with the fab surroundings, the Polycarbonate in an A300 FOUP will contain approximately 130 cm3 (180 mg) of absorbed oxygen gas and 5040 cm3 (3.7 g) of water vapor. To reduce these oxygen levels to one-tenth of the original values would require eight days of pumping under a full vacuum. To reach the same level for water would require more than five days. To reduce the oxygen and water levels in the Polycarbonate to one-hundredth, the drying times for oxygen and water would be more than 16 and 11 days respectively. Increasing the temperature during the drying cycle could dramatically decrease these times by boosting the diffusivity.12

Break-through times. After oxygen or water has been removed, how much time would pass before oxygen or water would begin to reappear on the inside of a closed 300 mm A300 PC FOUP? Equation 4 can be used along with the average wall thickness and diffusion coefficients to estimate break-through times, tb. Assuming we have a perfect seal and the closed, dry FOUP is exposed to ambient fab air, oxygen and water levels inside the FOUP would begin to climb within a week, tb = six days for oxygen and four days for water. Thus, if oxygen or moisture levels inside of this FOUP climb significantly in minutes or hours, we can conclude that this post-purge rise is not due to permeation from the external environment, but is likely due to seal leakage or de-sorption from the materials of construction.

Initial permeation rates. Once oxygen or water break through to the interior of a pre-dried A300 FOUP, how quickly would their concentrations rise? The initial rate of concentration rise (C • ) inside the “empty space” of a fully purged ME due to permeation from the external environment depends upon the permeation rate and the volume of the microenvironment. Combining equations 3 and 6 gives us our working equation, (equation 8)

equation 8

By inputting the appropriate partial pressure, the permeability coefficient (P), area, and volume into (equation 8), we can estimate initial concentration rise inside the freshly degassed A300 FOUP with a perfect seal. The anticipated rate for oxygen is C • = 4.4 x 10-6 cm3/cm3·hr and for water, C • = 2.6 x 10-4 cm3/cm3·hr (or in terms of RH, approximately 1% per hr). The rate for water is much higher, due primarily to the much greater solubility of water in Polycarbonate as compared to oxygen. Note that as time passes and the concentration inside the microenvironment rises, the driving force, i.e., the partial pressure differential between the inside and outside of the FOUP, will diminish. Accordingly, the permeation rate will decrease over time. With enough time, the concentration of oxygen and water inside the FOUP will reach the level of the outside, fab environment.

Post purge rise of moisture. Extensive drying of ME materials of construction with inert gases or vacuum may not be a practical method of protecting critical materials from oxygen or water. A more practical alternative is purge, where the internal volume of a ME is flushed with an inert gas for a short period to reduce oxygen and water levels. If the A300 FOUP has not been pre-dried, how quickly would levels climb after purging? An answer to this question is shown in Figure 4. An A300 FOUP was conditioned in air under typical fab conditions (T = 25ºC and RH = 45%) for several weeks with the door open. The door was closed and the FOUP was purged with nitrogen gas for 130 s at a rate of 35 standard liters per minute to reduce RH to 1%. Once the flow of purge gas was stopped, RH rose rapidly, climbing to almost 7% in ten minutes. As more time passed, RH increased more slowly, reaching 20% within two hours. Given enough time, the RH inside the FOUP would have eventually equaled that of the ambient environment, 45%.

As stated earlier, this rapid post-purge rise in RH is not due to permeation from the external environment. More likely, it is seal leakage or de-sorption. The mass transport data generated here can be used to gauge de-sorption from ME materials of construction. The post-purge rise of concentration (CME) inside a ME of volume VME due to outgassing or de-sorption alone can be approximated as,4 (equation 9)

equation 9

Here, ph is the partial pressure in the ambient or fab environment and pl is the partial pressure inside the ME. CME values were calculated from equation 9 using measured P, D, and S values found in Table 1, the appropriate partial pressures and the dimensions of the A300 FOUP. Computations were made in Excel with time increments of 10-1000 s, adjusting for rising pl values at each step.13 CME values were converted from STP to ambient conditions and finally converted to RH values. The calculated RH values are plotted as a solid curve in Figure 4.

figure 4

Agreement between the measured and predicted values was quite good. Therefore, we conclude that the post-purge rise in RH was dominated by desorption of water from its Polycarbonate structure. For this FOUP, while the seal may not have been perfect, it was more than adequate to impede the entry of water from the ambient environment over the course of the experiment.14 The purge for the example shown in Figure 4 was quite short. Longer or more aggressive purging significantly depletes the amount of dissolved oxygen and water in a conditioned FOUP. Consequently, the post purge rise is slower. As equation 9 assumes, the concentration of oxygen and water dissolved in the Polycarbonate remains constant during purge, estimates for long purge times overestimated post-purge rise.

All examples given here were based on a single part geometry and material. We have successfully used this approach to de-convolute the pieces of the permeation puzzle for other part geometries and materials.

CONCLUSION
Permeability, diffusion, and solubility coefficients of oxygen gas and water vapor were measured for Polycarbonate at 25ºC. With similar molecular size, oxygen and water had similar diffusivity. However, water has a much greater affinity for Polycarbonate than oxygen does. Consequently, water exhibited a faster permeation rate than oxygen. These inherent material properties were used to estimate the performance of a microenvironment constructed from Polycarbonate. Calculations gave realistic estimates of drying times in vacuum, break-through times, permeation rates, and post-purge RH rise due to desorption from the ME materials of construction.

Acknowledgements
We thank Entegris management for supporting this work and allowing publication. Also, thanks to A. Anderson, B. Arriola, E. Adkins, S. Cantor, J. Goodman, T. King, S. Moroney, J. Pillion, P. Rosenfeld, S. Sirignano, S. Tison, B. Waldridge, and H. Wang for their suggestions on the technical content and text.

References

  1. Shrive, L. W.; Blank, R. E.; Lamb, K. H., Investigating the Formation of Time-Dependent Haze on Stored Wafers, Micro, 2001, 19, 59.
  2. Extrand, C., The Permeation Resistance of Polymers, Semiconductor Fabtech, 2008, 3, 43.
  3. Osswald, T.A.; Menges, G., Materials Science of Polymers for Engineers; Hanser: New York, 1995.
  4. Crank, J. The Mathematics of Diffusion; Oxford University Press: London, 1970.
  5. Schult, K.A.; Paul, D.R., Techniques for Measurement of Water Vapor Sorption and Permeation in Polymer Films, J. of Appl. Polym. Sci., 1996, 61, 1865..
  6. Standard Test Method for Determining Gas Permeability Characteristics of Plastic Film and Sheeting; American Society for the Testing of Materials: West Conshohocken, PA, 1998; ASTM D1434-82. Test Method for Gas Transmission Rate through Plastic Film and Sheeting; Japanese Industrial Standard: Tokyo, Japan, 1987, JIS K7126.
  7. Daynes, H. A., The Process of Diffusion through a Rubber Membrane, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1920, 97, 286.
  8. Monson, L.; Moon, S. I.; Extrand, C. W., Gas Permeation Resistance of Various Grades of Perfluoroalkoxy-polytetrafluoroethylene Copolymers, J. of Appl. Polym. Sci., 2009, 111, 141.
  9. Norton, F. J., Gas Permeation through Lexan Polycarbonate Resin, J. Appl. Polym. Sci., 1963, 7, 1649.
  10. Kim, C. K.; Aguilar-Vega, M.; Paul, D. R., Dynamic Mechanical and Gas Transport Properties of Blends and Random Copolymers of Bisphenol-A Polycarbonate and Tetramethyl Bisphenol-A Polycarbonate, J. Polym. Sci., Part B: Polym. Phys., 1992, 30, 1131.
  11. Permeability Properties of Plastics and Elastomers, 2nd ed., Massey, L. K., Ed., Plastics Design Library: Norwich, NY, 2003.
  12. Pauly, S.; In Polymer Handbook, 4th ed., Brandrup, J., Immergut, E.H., Grulke, E.A., Eds.; Wiley: New York, 1999.
  13. Equation 9 assumes that both ph and pl are constant; it was not derived to accommodate a time dependent concentration on either side. In our case, the external pressure, pl, outside the FOUP remains constant. The pressure inside the FOUP does not; after purging an un-dried FOUP, pl rises rapidly to a RH value much greater than zero. Nevertheless, using small time steps early on and adjusting the pl after each step produced reasonable estimates.
  14. Additional tests were performed to verify that the post-purge RH rise in our A300 FOUP was due solely to de-sorption. For example, purge tests were run after seals were fortified with vacuum-grade epoxy, sealants, and/or metallized tape. The RH rise rate was unaffected. We also used rise of oxygen as a gauge of leakage.

Sung In Moon is a scientist in the Surface Science Research and Development Group at Entegris. His research area includes surface engineering, surface analysis, and the permeation resistance of polymers.

Loxie Monson is a test technician at Entegris. She has been part of Entegris since 1993. In her time with the company, she has worked in both laboratory and manufacturing positions.

Yingkai Liu, Ph.D. came to Entegris in 2006 where he is employed as a test engineer in the Technology Characterization Lab (TCL lab). His primary responsibilities are to test existing and new products and to characterize new technologies.

Matt Fuller is a mechanical design engineer for Entegris. He has a B.S. in mechanical engineering from the University of Colorado, Boulder, and an MBA from the University of Colorado, Colorado Springs.

Chuck Extrand is a principal scientist and manager of Surface Science R&D at Entegris. His responsibilities include materials research, new product concepts, new processing technologies, and design of new test methods. Recent research activities have focused on surface engineering and measuring the permeation resistance of polymers.

www.entegris.co

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