Pressure sensor

Abstract

To provide a pressure sensor capable of preventing deterioration of measurement accuracy due to a deposition film with a structure to be easily manufactured.SOLUTION: A pressure sensor includes: a diaphragm 28 for partitioning between a fluid chamber to which measured fluid is introduced and an inner space; a sensor element 22 for detecting pressure based on a displacement of the diaphragm 28; and a tabular structure 21 opposing to the diaphragm 28 at a predetermined interval. The structure 21 includes a plurality of above-structures 23 aligned with penetration areas 33 in a surface direction orthogonal to a thickness direction. The above-structure 23 has a surface which is not vertical to the diaphragm 28 at a distance equal to or less than a mean free path from a pressure reception surface 34 of the diaphragm 28.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a pressure sensor having a diaphragm that comes into contact with a fluid to be measured. [Background technology]

[0002] Vacuum gauges are devices used to detect pressure when controlling the operation of semiconductor manufacturing equipment. Among the various processes performed in semiconductor manufacturing equipment, this type of vacuum gauge is also used in the film deposition process and the process of etching wafers such as silicon. Film deposition methods used in the film deposition process include sputtering, CVD (chemical vapor deposition), and ALD (atomic layer deposition).

[0003] During the film deposition and etching processes used in semiconductor manufacturing equipment, it is known that the film being deposited and by-products generated during the process accumulate inside the chamber, piping, pumps, etc. As a result, film deposition materials and by-products also accumulate on the pressure-receiving part of the pressure sensor installed in the vacuum gauge. The pressure-receiving part of this pressure sensor is formed by a diaphragm. If the above-mentioned substances accumulate on the pressure-receiving surface of this diaphragm, the zero point of the pressure sensor will shift and the pressure sensitivity will change. If the deposition of film deposition materials and by-products progresses on the diaphragm and a deposited film is formed, the measurement accuracy of the pressure sensor may deteriorate beyond its specified value.

[0004] Techniques for preventing deposition films from forming on the diaphragm of a pressure sensor are described in Patent Documents 1 and 2. The diaphragms shown in Patent Documents 1 and 2 are provided with a structure for dividing the deposition films. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Special Publication No. 2009-524024 [Patent Document 2] Japanese Patent Application Laid-Open No. 2008-107214 Summary of the Invention [Problem to be solved by the invention]

[0006] The diaphragm of the pressure sensor mounted in a vacuum gauge is a component that directly affects the sensitivity and accuracy of the pressure sensor. For this reason, when realizing the structures described in Patent Documents 1 and 2 on the diaphragm of the pressure sensor, high uniformity is required, which is difficult and causes a decrease in manufacturing efficiency.

[0007] An object of the present invention is to provide a pressure sensor that has a structure that is easy to manufacture and that can prevent a decrease in measurement accuracy due to a deposited film. [Means for solving the problem]

[0008] In order to achieve this object, the pressure sensor of the present invention has a diaphragm that separates a fluid chamber into which a fluid to be measured is introduced and an internal space, and is equipped with a sensor element that detects pressure based on the displacement of the diaphragm, and a plate-like structure that is arranged inside the fluid chamber and facing the diaphragm at a predetermined distance, and the structure has a plurality of direct structures that are arranged in a planar direction perpendicular to the thickness direction, separated by a through region that is a space extending in the thickness direction with a predetermined width, and the direct structures have a surface that does not face the diaphragm and is not perpendicular to the diaphragm, at a distance of less than the mean free path from the pressure-receiving surface of the diaphragm that comes into contact with the fluid to be measured.

[0009] In the pressure sensor of the present invention, the directly above structure may have a portion that is farther away from the diaphragm than the mean free path, near the center of the cross section as viewed from the surface direction.

[0010] In the pressure sensor of the present invention, when the distance from the diaphragm of a surface that does not face the diaphragm and is not perpendicular to the diaphragm is defined as the height, the average height may be less than the mean free path.

[0011] In the pressure sensor of the present invention, the structure may be connected to a portion of the sensor element other than the diaphragm.

[0012] In the pressure sensor of the present invention, the distance D equal to or less than the mean free path may be calculated by the following formula.

[0013]

number

[0014] According to the present invention, it is possible to provide a pressure sensor that has a structure that is easy to manufacture and that can prevent a decrease in measurement accuracy due to a deposited film. [Brief explanation of the drawings]

[0015] [Figure 1] FIG. 1 is a cross-sectional view of a capacitance diaphragm vacuum gauge equipped with a pressure sensor according to the present invention. [Figure 2] FIG. 2 is an enlarged cross-sectional view showing a part of the pressure sensor, the support diaphragm, and the base member. [Figure 3] FIG. 3 is a cross-sectional view of a main part of the pressure sensor. [Figure 4] FIG. 4 is a plan view of the structure. [Figure 5] FIG. 5 is a cross-sectional view of a main part of a pressure sensor showing a state in which a deposit has formed. [Figure 6] FIG. 6 is a cross-sectional view showing a modified example of the direct-above structure. [Figure 7] FIG. 7 is a schematic diagram for explaining the average height. [Figure 8] FIG. 8 is a cross-sectional view of a main part of a pressure sensor showing a state in which a deposit has formed. [Figure 9]FIG. 9 is a cross-sectional view showing a modified example of the direct-above structure. [Figure 10] FIG. 10 is a schematic diagram for explaining the average height. [Figure 11] FIG. 11 is a cross-sectional view of a main part of a pressure sensor showing a state in which a deposit has formed. DETAILED DESCRIPTION OF THE INVENTION

[0016] (Principle of the Invention) In the cases of Patent Documents 1 and 2, in which a structure is provided on the diaphragm itself to separate the deposited film, the diaphragm is a component directly related to sensitivity and precision, so its processing requires extremely high uniformity, making it difficult and reducing manufacturing efficiency. The inventors therefore conducted extensive research into the behavior of particles that cause deposition and discovered that the deposited film can be separated not necessarily by the structure of the diaphragm itself, but also by a structure directly above the diaphragm (directly above structure). More specifically, they found that providing a directly above structure at a distance equal to or less than the mean free path significantly reduces the intrusion of particles, which inhibits the separation of the deposited film. This directly above structure reduces the difficulty compared to processing the diaphragm itself, improving manufacturing efficiency and enabling a stable supply.

[0017] (First embodiment) An embodiment of a pressure sensor according to the present invention will be described in detail below with reference to Figures 1 to 5. Here, an example will be described in which the pressure sensor according to the present invention is applied to a capacitance diaphragm vacuum gauge. The capacitance diaphragm vacuum gauge 1 shown in FIG. 1 is configured by assembling various functional parts in a housing 2 depicted on the outermost side in FIG. 1, a cylindrical upper housing 3, a cylindrical lower housing 5 welded to the upper housing 3 with a support diaphragm 4 sandwiched between the upper housing 3 and the lower housing 5, and a cover 6 that closes the opening of the lower housing 5. An electrode terminal 7 for transmitting signals penetrates the cover 6. The electrode terminal 7 is connected to a pressure sensor 9 (described later) via a conductive contact spring 8.

[0018] The end of the upper housing 3 opposite to the lower housing 5 is an inlet 11 into which the fluid to be measured is introduced. The support diaphragm 4 is for supporting the pressure sensor 9 within the housing 2 , and is formed in a ring shape having one pressure-conducting opening 12 , and its outer edge is fixed to the housing 2 . As shown in Fig. 2, the opening 12 of the support diaphragm 4 is closed by a pressure sensor 13 bonded to one surface 4a of the support diaphragm 4. By bonding the pressure sensor 13 to the support diaphragm 4 in this manner, the interior of the housing 2 is divided into two chambers. As shown in Fig. 1, these two chambers are a fluid chamber 14 that communicates with the introduction portion 11 and into which the fluid to be measured is introduced, and a vacuum chamber 15 that serves as the internal space of the pressure sensor 13. The interior of the vacuum chamber 15 is maintained in a vacuum state with a predetermined vacuum level.

[0019] A base member 16 is bonded to the surface of the support diaphragm 4 opposite to the pressure sensor 13. The pressure sensor 13 and base member 16 are bonded to the support diaphragm 4 so as to surround the central opening 12 of the support diaphragm 4. In this embodiment, the base member 16 is provided with a plurality of through holes 17 through which the fluid to be measured passes.

[0020] As shown in Fig. 2, the pressure sensor 13 is composed of a structure 21 bonded to the support diaphragm 4 and a sensor element 22 bonded to the structure 21. The structure 21 shown in Fig. 2 is drawn larger than it actually is to make the structure easier to understand. The structure 21 is formed in a plate shape having a plurality of direct-above structures 23. A detailed description of the structure 21 will be given later. The sensor element 22 detects the pressure in the introduction portion 11 based on capacitance, and has a diaphragm support portion 24 joined to the structure 21, and a sensor base 25 joined to the diaphragm support portion 24. The diaphragm support portion 24 and the sensor base 25 can be made of, for example, sapphire.

[0021] The diaphragm support portion 24 is formed in a plate shape and has a first recess 26 that opens on the surface facing the sensor base 25, a second recess 27 that opens on the surface facing the structure 21, and a diaphragm 28 formed between the first recess 26 and the second recess 27. The opening shapes of the first recess 26 and the second recess 27 are circular. Therefore, the diaphragm 28 is formed in a disk shape. The space formed by the first recess 26 and the sensor base 25 is in communication with the vacuum chamber 15 via a communication hole (not shown). The diaphragm 28 separates the fluid chamber 14 on the second recess 27 side from the vacuum chamber 15 on the first recess 26 side.

[0022] A pair of pressure-sensitive electrodes 29, 30 are provided at the center of the bottom surface (the surface of the diaphragm facing the vacuum chamber) of the first recess 26 and at the center of the end surface of the sensor pedestal 25 facing this bottom surface. In addition, a pair of reference electrodes 31, 32 are provided on the outer periphery of the bottom surface of the first recess 26 and on the outer periphery of the end surface of the sensor pedestal 25 facing this bottom surface. Such a sensor element 22 can be fabricated by so-called semiconductor manufacturing techniques including photolithography, dry etching, film formation, etc.

[0023] The diaphragm 28 is displaced by the pressure difference between the fluid chamber 14 and the vacuum chamber 15. This displacement changes the capacitance of the pressure-sensitive capacitor consisting of the pressure-sensitive electrodes 29 and 30 and the capacitance of the reference capacitor consisting of the reference electrodes 31 and 32. The sensor element 22 detects the pressure applied to the diaphragm 28 based on the capacitance of the pressure-sensitive capacitor and the capacitance of the reference capacitor.

[0024] The structure 21 is bonded to the support diaphragm 4 and the diaphragm support part 24 of the sensor element 22 in a state where it is sandwiched between these members. In other words, the structure 21 is connected to a part of the sensor element 22 other than the diaphragm 28, and is disposed inside the fluid chamber 14 at a position facing the diaphragm 28 at a predetermined distance.

[0025] The structure 21 according to this embodiment has a plurality of direct-above structures 23 formed to have a rectangular cross-sectional shape. Hereinafter, when indicating directions in describing the configuration of the structure 21, for convenience, the direction from the diaphragm 28 toward the structure 21 will be referred to as "upper." In addition, below, when describing the distance between the diaphragm 28 and the upper surface of the direct-above structure 23, it will be referred to as "height of the upper surface."

[0026] As shown in FIG. 3, the multiple direct structures 23 are arranged in a plane direction (left-right direction in FIG. 3) perpendicular to the thickness direction (up-down direction in FIG. 3) of the structure 21, with through-holes 33 between them. The through-holes 33 are spaces extending in the thickness direction of the structure 21 with a predetermined width. The fluid to be measured is introduced into the through-holes 33 from the fluid chamber through the through-holes 17 in the base member 16 and the openings 12 in the support diaphragm 4. Therefore, the diaphragm 28 of the sensor element 22 comes into contact with the fluid to be measured at a portion that forms the bottom of the second recess 27. The portion of the diaphragm 28 that forms the bottom of the second recess 27 will be referred to as a pressure-receiving surface 34 of the diaphragm 28 hereinafter.

[0027] The shape of the structure 21 as viewed from the thickness direction is circular, as shown in Fig. 4. Furthermore, the penetration region 33 according to this embodiment is formed by a circular hole when the structure 21 is viewed from the thickness direction, as shown in Fig. 4. The direct-on structure 23 according to this embodiment can be fabricated by, for example, photolithography and dry etching. Note that the penetration region 33 shown in Fig. 4 is drawn larger than it actually is to make the configuration easier to understand.

[0028] 3, the lower surface 23a facing the diaphragm 28 and the upper surface 23b located on the opposite side from the diaphragm 28 are both formed parallel to the pressure-receiving surface 34 of the diaphragm 28. In other words, the lower surface 23a and the upper surface 23b are surfaces that are not perpendicular to the diaphragm 28. The lower surface 23a is the surface facing the diaphragm 28, and the upper surface 23b is the surface not facing the diaphragm 28. The upper surface 23b of the direct-over structure 23 is formed at a distance D that is equal to or less than the mean free path from the pressure-receiving surface 34 of the diaphragm 28. The distance D that is equal to or less than the mean free path can be calculated using the following formula.

[0029]

number

[0030] In the above formula (2), T is the temperature in K, d is the particle diameter in m, and p is the pressure in Pa. The right-hand side of the above equation (2), i.e., the equation for calculating the mean free path, is described in "The 60th Vacuum Summer University Text, sponsored by the Japan Society of Vacuum and Surface Science, Public Interest Incorporated Association, page A-22."

[0031] Substituting specific values ​​into the above formula (2), for example, nitrogen molecules (d=0.374 nm), a temperature T of 20°C, and a pressure p of 10 Pa, results in D≦651 μm. A direct-above structure 23 having such a configuration can be realized, for example, by microfabrication technology. The thickness of the direct-above structure 23 may be any thickness as long as the following conditions are satisfied: the upper surface 23b is formed at a distance D from the pressure-receiving surface 34 of the diaphragm 28 that is equal to or less than the mean free path, and the lower surface 23a is spaced apart from the pressure-receiving surface 34 of the diaphragm 28. The position of the diaphragm 28 changes depending on the pressure p, but it can be designed based on the pressure p at which the deposition film is expected to form. That is, the pressure p at which the particles that cause deposition are mixed in is limited, so it is possible to design the diaphragm 28 so that the deposition film can be separated.

[0032] 3, molecules 35 of the film-forming component contained in the fluid to be measured are depicted at a position that is the mean free path λ away from the pressure-receiving surface 34 of the diaphragm 28. When these molecules 35 fly toward the diaphragm 28 as indicated by the two-dot chain arrow, some of the molecules 35 are blocked by the directly above structure 23, and the remaining molecules 35 pass only through the penetration region 33 and reach the pressure-receiving surface 34. Most of the molecules 35 that collide with the upper surface 23b of the direct-above structure 23, change their flight direction, and fly into the penetration region 33, and the molecules 35 that collide with other molecules 35 near the upper surface 23b and fly into the penetration region 33, reach the pressure-receiving surface 34 of the diaphragm 28 within the penetration region 33 without colliding with other molecules 35 within the penetration region 33.

[0033] It is conceivable that some of the molecules 35 of the film-forming component that have entered the penetration region 33 will collide with other molecules 35 within the penetration region 33, changing their flight direction and entering the back side of the direct-above structure 23. However, by making the distance D between the upper surface 23b of the direct-above structure 23 and the pressure-receiving surface 34 equal to or less than the mean free path λ, the frequency of the phenomenon in which the molecules 35 fly into the back side of the direct-above structure 23 can be reduced. In other words, it is possible to minimize the number of molecules 35 flying into the area below the direct-above structure 23 from the penetration region 33. 3 is used, deposits made of film-forming components are generated on the direct-above structure 23 and the pressure-receiving surface 34, as indicated by reference numeral 36 in FIG. 5. The deposits 36 that accumulate on the direct-above structure 23 are generated on the upper end portions of the top surface 23b and the side surface 23c. The deposits 36 that accumulate on the pressure-receiving surface 34 are generated at positions corresponding to the penetration region 33.

[0034] According to this embodiment, as shown in Fig. 5, deposits 36 are scattered on the pressure-receiving surface 34 of the diaphragm 28. That is, the pressure-receiving surface 34 of the diaphragm 28 is no longer covered with a deposition film formed by the deposition of the film-forming components, and the deposition film is deposited on the pressure-receiving surface 34 in a form that resembles a plurality of divided deposition films. The number of divided films depends on the widths of the direct-over structure 23 and the penetrating region 33 (the width in the plane direction of the structure 21, i.e., the width in the left-right direction in Fig. 5).

[0035] The width of the direct-above structure 23 and the through-hole region 33 is such that the pressure-receiving surface 34 of the diaphragm 28 is divided into approximately 300 parts in the radial direction. The term "approximately 300 divisions" here is based on the disclosure of JP 2021-131300, a patent application filed by the inventor of the present application. JP 2021-131300 discloses that, compared to when a membrane is formed across the entire diaphragm 28 (when the membrane is not divided), in order to limit the deformation of the central portion of the diaphragm 28 due to the influence of the membrane to approximately 5%. For example, if the diameter of the diaphragm 28 is 8 mm, the width of the direct-above structure 23 plus the width of the through-hole region 33 is 8 mm / 300, or 26.7 μm.

[0036] Therefore, according to this embodiment, the deposited film can be divided by a structure in which multiple direct-over structures 23 are simply lined up along the diaphragm 28, so a pressure sensor can be provided that has a structure that is easier to manufacture than processing the diaphragm itself, which requires high uniformity, and that can prevent a decrease in measurement accuracy due to the deposited film. Moreover, since the directly above structure 23 is formed at a distance D that is equal to or less than the mean free path, there is no need to make the area near the diaphragm particularly large, compared to when the diaphragm itself is directly machined.

[0037] (Second embodiment) The direct-above structure 23 can be formed as shown in Figures 6 to 11. In these figures, the same or equivalent members as those described with reference to Figures 1 to 5 are given the same reference numerals, and detailed description thereof will be omitted as appropriate. The direct structures 41, 42 shown in Figures 6 to 11 have a portion near the center of the cross section viewed from the surface direction of the structure 21 that is higher than the portion where the distance from the diaphragm 28 is the mean free path λ, i.e., a portion that is away from the diaphragm 28.

[0038] The direct-top structure 41 shown in FIG. 6 has a convex cross-section formed by a base 43 adjacent to the diaphragm 28 and an apex 44 protruding upward from the base 43. The base 43 is formed to have a rectangular cross-section, as in the first embodiment. The apex 44 protrudes upward from the center of the base 43 in the width direction (the surface direction of the structure 21, which is the left-right direction in FIG. 6). The cross-section of the apex 44 is also rectangular. The upper surface 44a of the apex 44 is located above the position where the distance from the pressure-receiving surface 34 of the diaphragm 28 is the mean free path λ. The upper surface 43a of the base 43 and the upper surface 44a of the apex 44 are parallel to the pressure-receiving surface 34 of the diaphragm 28, but are not opposed to or perpendicular to the diaphragm 28. The lower surface 43b of the base 43 is also parallel to the pressure-receiving surface 34 of the diaphragm 28.

[0039] In the direct structure 41 formed in a convex cross section as shown in FIG. 6, the top 44 essentially functions as a reinforcing material, so that the strength of the structure 21 can be improved compared to when the first embodiment is adopted. The direct-over structure 23 is configured such that the average height Dave is equal to or less than the mean free path λ when the height is the distance between the upper surface 43a of the base 43 and the upper surface 44a of the top 44 and the diaphragm 28. That is, since the upper surface 43a in FIG. 6 is equal to or less than the mean free path λ, the deposited film can be divided in the same way as in the first embodiment.

[0040] 7, the average height Dave here refers to the average value of the height D1 of multiple measurement points P1 set on the upper surface 43a of the base 43 and the height D2 of multiple measurement points P2 set on the upper surface 44a of the apex 44. Measurement points P1 and P2 can be set at positions where the line forming the upper surface 43a of the base 43 or the upper surface 44a of the apex 44 in the cross section is divided at a predetermined interval. In this way, by making the average height Dave of the directly above structure 41 equal to or less than the mean free path λ, it is possible to improve the rigidity of the structure 21 and simultaneously separate the film deposited on the pressure-receiving surface 34 .

[0041] When the direct-over structure 41 shown in FIG. 6 is used, the deposition of the film-forming material results in the formation of a deposit 36 ​​as shown in FIG. 8. The deposit 36 ​​is generated on the upper end of the top surface 43a and the side surface 43c of the base 43, and on the upper end of the top surface 44a and the side surface 44b of the top 44. The deposit 36 ​​is also formed on the pressure-receiving surface 34 corresponding to the penetration region 33. Even in this case, as in the case of employing the first embodiment, it is possible to prevent a deposited film made of the film-forming material from being formed on the pressure-receiving surface 34 of the diaphragm 28. Furthermore, because the central portion in the width direction of the direct-over structure 41 is formed sufficiently thick, the strength of the structure 21 can be ensured.

[0042] 9 is formed in a triangular cross section having a bottom surface 42a parallel to the diaphragm 28. This direct-above structure 42 also has a top portion 42b near the center of the cross section as viewed from the surface direction of the structure 21, which is higher than the portion where the distance from the diaphragm 28 is the mean free path λ. The upper surface 42c of the direct-over structure 42 is formed by two inclined surfaces. These inclined surfaces are surfaces that do not face the diaphragm 28 and are not perpendicular to the diaphragm 28.

[0043] In this direct-above structure 42, the average height Dave of the upper surface 42c is also set to be equal to or less than the mean free path λ. The average height Dave of the upper surface 42c in this embodiment is calculated by setting a plurality of measurement points P3, for example, at regular intervals along the upper surface 42c of the direct-above structure 42, and averaging the heights of the measurement points P3, as shown in FIG. Even in the direct-above structure 42 having a triangular cross section, the average height Dave is equal to or less than the mean free path λ, thereby achieving both improved rigidity of the structure 21 and separation of the deposited film on the pressure-receiving surface 34.

[0044] When the direct-over structure 42 shown in Fig. 9 is used, the deposition of the film-forming material causes the formation of deposits 36 as shown in Fig. 11. The deposits 36 are formed on the inclined upper surface 42c of the direct-over structure 42 and in the portion of the pressure-receiving surface 34 of the diaphragm 28 that corresponds to the through region 33. Even in this case, as in the case of employing the first embodiment, it is possible to prevent the formation of a deposited film made of the film-forming material on the pressure-receiving surface 34 of the diaphragm 28. Furthermore, because the central portion of the direct-over structure 42 in the width direction is formed sufficiently thick, the strength of the structure 21 can also be ensured.

[0045] In the first and second embodiments described above, the structure 21 having the direct-above structures 23, 41, 42 is connected to a location other than the diaphragm 28 of the sensor element 22. Therefore, the structure 21 can be provided without affecting the sensitivity and accuracy of the pressure sensor 13, making it easy to realize. [Explanation of symbols]

[0046] 1...capacitive diaphragm vacuum gauge, 13...pressure sensor, 14...fluid chamber, 15...vacuum chamber (internal space), 21...structure, 22...sensor element, 23, 41, 42...directly above structure, 23b, 43a, 44a, 42c...top surface (surface not perpendicular to the diaphragm), 24...diaphragm support part (part that is not a diaphragm), 28...diaphragm, 33...penetration area, 34...pressure-receiving surface, 44, 42b...top (part farther from the diaphragm than the mean free path), D...(distance less than the mean free path), Dave...average height, λ...mean free path.

Claims

1. a sensor element having a diaphragm separating an internal space from a fluid chamber into which a fluid to be measured is introduced, the sensor element detecting pressure based on the displacement of the diaphragm; a plate-like structure disposed inside the fluid chamber and facing the diaphragm at a predetermined distance; The structure has a plurality of direct-over structures arranged in a plane direction perpendicular to the thickness direction, with a through region being a space extending in the thickness direction with a predetermined width, A pressure sensor characterized in that the direct-above structure has a surface that does not face the diaphragm and is not perpendicular to the diaphragm, at a distance less than the mean free path from the pressure-receiving surface of the diaphragm that comes into contact with the fluid to be measured.

2. 2. The pressure sensor according to claim 1, The pressure sensor is characterized in that the directly above structure has a portion near the center of the cross section viewed from the surface direction that is farther away from the diaphragm than the mean free path.

3. 3. The pressure sensor according to claim 2, A pressure sensor characterized in that, when the distance from the diaphragm of a surface that does not face the diaphragm and is not perpendicular to the diaphragm is defined as the height, the average height is equal to or less than the mean free path.

4. 2. The pressure sensor according to claim 1, A pressure sensor characterized in that the structure is connected to a portion of the sensor element other than the diaphragm.

5. The pressure sensor according to any one of claims 1 to 4, A pressure sensor characterized in that a distance D equal to or less than the mean free path is calculated by the following formula. [Equation 1] In the above formula, T is the temperature in K, d is the particle diameter in m, and p is the pressure in Pa.

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