Substrate processing apparatus with vuv intensity control

Abstract

To provide a method for monitoring a light intensity of a vacuum ultraviolet light within a process chamber.SOLUTION: A substrate processing apparatus may be presented. The apparatus includes: a lamp unit configured to emit UV (ultraviolet) light; a lamp section configured to include one or more lamp units; a processing chamber having a susceptor configured to support a substrate for processing and configured to process the substrate; a separation window disposed between the lamp section and the processing chamber and configured to be transparent for light from the UV lamp to reach the substrate; a measurement unit disposed within a wall of the processing chamber and configured to measure a light intensity within the processing chamber; and a power controller electrically connected to the measurement unit and configured to adjust a power supply to the lamp compartment according to the light intensity measured by the measurement unit.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to an apparatus for processing substrates, and in particular to an apparatus capable of adjusting and controlling the intensity of vacuum UV (ultraviolet) light that can be applied to process film UV irradiation. [Background technology]

[0002] UV irradiation can be applied in a variety of processes to treat different types of films. Compared to thermal treatments, UV treatments can be more efficient and operate at lower temperatures.

[0003] However, the vacuum ultraviolet (VUV) light intensity within the process chamber may be significantly affected by the transmission efficiency of the quartz window and may not be controlled by the light intensity sensor within the VUV illumination assembly.

[0004] Furthermore, VUV light has a high energy level that can create defects inside the window, thereby increasing the light absorption rate of the quartz window, whose transmission typically decreases over time.

[0005] Therefore, the present disclosure presents a method for monitoring the light intensity of vacuum ultraviolet light inside a process chamber.

[0006] This summary is provided to introduce some concepts in a simplified form that are described in more detail below in the detailed description of exemplary embodiments of this disclosure. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. Summary of the Invention [Means for solving the problem]

[0007] According to one embodiment, a substrate processing apparatus may be provided, comprising: a lamp unit configured to emit UV light; a lamp section configured to include one or more lamp units; a processing chamber configured to process a substrate having a susceptor configured to support a wafer for processing; an isolation window disposed between the lamp section and the processing chamber and configured to be transparent to allow light from the UV lamp to reach the substrate; a measurement unit disposed in a wall of the processing chamber and configured to measure the light intensity in the processing chamber; and a power controller electrically connected to the measurement unit and configured to adjust the power supply to the lamp section according to the light intensity measured by the measurement unit.

[0008] In one embodiment, the lamp unit includes a UV lamp for emitting UV light, an intensity sensor configured to sense and measure the light intensity of the UV light, and a power regulator electrically connected to the intensity sensor and configured to control power supplied to the UV lamp according to the light intensity measured by the intensity sensor.

[0009] In one aspect, the measurement unit comprises a tube disposed through a sidewall of the processing chamber, a phosphor disposed at one end of the tube and configured to convert UV light into visible light, an optical fiber disposed at the other end of the tube and configured to guide the visible light, and a light sensor connected to the optical fiber and configured to sense and measure the intensity of the visible light received from the optical fiber.

[0010] In one aspect, the measurement unit further comprises a fixture configured to seal the tube and mount on a wall of the processing chamber.

[0011] In one embodiment, the phosphor is tilted at a first angle from the vertical.

[0012] In one embodiment, the first angle is in the range of 0° to 45°.

[0013] In one embodiment, the tube is inclined at a second angle relative to the horizontal.

[0014] In one embodiment, the phosphor is YAG [YAlO 12 :Ce 3+ 〕, LSN[La3Si6N 11 :Ce 3+ , LYSN[(La,Y)3Si6N 11 :Ce 3+ ], CASN[CaAlSiN3:Eu 2+ ], SCASN[(Sr,Ca)AlSiN3:Eu 2+ ], CSO[CaSc2O4:Ce 3+ ], β-SiAlON[(Si,Al)3(O,N)4:Eu 2+ ], GYAG[Y3(Al,Ga)5O 12 :Ce 3+ ], LuAG[LuAlO 12 :Ce 3+ , SBCA[(Sr,Ba) 10 (PO4)6Cl2:Eu 2+ ] or any mixture thereof.

[0015] In one embodiment, the isolation window is made of one of quartz, glass, crystal, or a mixture of at least one of these.

[0016] In one embodiment, the inside of the tube is coated with a material that reflects visible light.

[0017] In one embodiment, the cross-sectional shape of the tube is one of a circle, a rectangle, a pentagon, a hexagon, or a polygon with more than 6 sides.

[0018] According to another embodiment, there may be provided a substrate processing apparatus including: a lamp unit configured to emit UV light, the lamp unit including a UV lamp for emitting UV light, an intensity sensor configured to sense and measure the light intensity of the UV light, and a power regulator electrically connected to the intensity sensor and configured to control power supplied to the UV lamp according to the light intensity measured by the intensity sensor; a lamp section configured to include one or more lamp units; a process chamber configured to process a substrate, the process chamber having a susceptor configured to support and / or heat the substrate for processing; a gas inlet disposed on one side of the process chamber and configured to provide a gas for processing the substrate; an exhaust duct disposed opposite the gas inlet and configured to exhaust the gas from the process chamber; a separating window disposed between the lamp section and the process chamber and configured to be transparent to allow light from the UV lamp to reach the substrate; a measurement unit disposed in a wall of the process chamber and configured to measure the light intensity in the process chamber; and a power controller electrically connected to the measurement unit and configured to adjust power supply to the lamp section according to the light intensity measured by the measurement unit.

[0019] In one aspect, the measurement unit comprises a tube disposed through a sidewall of the processing chamber, a phosphor disposed at one end of the tube and configured to convert UV light into visible light, an optical fiber disposed at the other end of the tube and configured to guide the visible light, and a light sensor connected to the optical fiber and configured to sense and measure the intensity of the visible light received from the optical fiber.

[0020] In one aspect, the measurement unit further comprises a fixture configured to seal the tube and mount on a wall of the processing chamber.

[0021] In one embodiment, the phosphor is tilted at a first angle from the vertical.

[0022] In one embodiment, the first angle is in the range of 0° to 45°.

[0023] In one aspect, the tube is inclined at an angle relative to the horizontal.

[0024] In one embodiment, the phosphor is YAG [YAlO 12 :Ce 3+ 〕, LSN[La3Si6N 11 :Ce 3+ , LYSN[(La,Y)3Si6N 11 :Ce 3+ ], CASN[CaAlSiN3:Eu 2+ ], SCASN[(Sr,Ca)AlSiN3:Eu 2+ ], CSO[CaSc2O4:Ce 3+ ], β-SiAlON[(Si,Al)3(O,N)4:Eu 2+ ], GYAG[Y3(Al,Ga)5O 12 :Ce 3+ ], LuAG[LuAlO 12 :Ce 3+ , SBCA[(Sr,Ba) 10 (PO4)6Cl2:Eu 2+ ] or any mixture thereof.

[0025] In one embodiment, the isolation window is made of one of quartz, glass, crystal, or a mixture of at least one of these.

[0026] In one embodiment, the inside of the tube is coated with a material that reflects visible light.

[0027] In one embodiment, the cross-sectional shape of the tube is one of a circle, a rectangle, a pentagon, a hexagon, or a polygon with more than 6 sides.

[0028] It will be understood that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of the illustrated embodiments of the present disclosure. [Brief explanation of the drawings]

[0029] [Figure 1] 1 is a perspective view of a substrate processing apparatus according to an embodiment of the present disclosure; [Figure 2] (a) shows an overview of the measurement unit in a mode according to one embodiment of the present disclosure; (b) shows an overview of the measurement unit in another mode according to another embodiment of the present disclosure; and (c) shows how UV light emitted from a UV lamp travels and hits the phosphor. [Figure 3] FIG. 1A shows a circular cross-section of a tube used in the present disclosure according to one embodiment of the present disclosure; FIG. 1B shows a rectangular cross-section of a tube used in the present disclosure according to another embodiment of the present disclosure; FIG. 1C shows a pentagonal cross-section of a tube used in the present disclosure according to another embodiment of the present disclosure; and FIG. 1D shows a hexagonal cross-section of a tube used in the present disclosure according to another embodiment of the present disclosure. [Figure 4] 1 is a perspective view of a substrate processing apparatus according to an embodiment of the present disclosure; DETAILED DESCRIPTION OF THE INVENTION

[0030] While certain specific embodiments and examples are disclosed below, it will be understood by those skilled in the art that the scope of the invention extends beyond the specifically disclosed embodiments and / or uses of the invention, and obvious variations and equivalents thereof. It is therefore not intended that the scope of the disclosed invention should be limited by the specific disclosed embodiments described below.

[0031] As used in this disclosure, the term "substrate" may refer to any underlying material or materials, including any underlying material or materials that may be modified or upon which a device, circuit, or film may be formed. A "substrate" may be continuous or discontinuous, rigid or flexible, solid or porous, and combinations thereof. A substrate may be in any form, such as a powder, plate, or workpiece. Substrates in plate form include wafers of various shapes and sizes. Substrates may be made from semiconductor materials, including, for example, silicon, silicon germanium, silica, gallium arsenide, gallium nitride, and silicon carbide.

[0032] As an example, the substrate in powder form may have applications in pharmaceutical manufacturing. The porous substrate may include a polymer. Examples of workpieces may include medical devices (e.g., stents and syringes), jewelry, tooling devices, components for battery manufacturing (e.g., anodes, cathodes, or separators), or solar cell components.

[0033] The continuous substrate may extend beyond the boundaries of the process chamber in which the deposition process occurs. In some processes, the continuous substrate may move through the process chamber so that the process continues until the edge of the substrate is reached. The continuous substrate may be supplied from a continuous substrate supply system to enable the production and output of continuous substrates in any suitable form.

[0034] Non-limiting examples of continuous substrates may include sheets, nonwoven films, rolls, foils, webs, flexible materials, bundles of continuous filaments or fibers (e.g., ceramic fibers or polymer fibers). Continuous substrates may also include carriers, or sheets, onto which discontinuous substrates are placed.

[0035] The examples presented in this disclosure are not intended to be actual manifestations of any particular materials, structures, or devices, but merely conceptual representations used to describe embodiments of the present disclosure.

[0036] The specific implementations shown and described are illustrative of the present invention and its best mode and are in no way intended to limit the scope of aspects and implementations. Also, for the sake of brevity, conventional manufacturing, association, preparation, and other functional aspects of the systems may not be described in detail. Furthermore, connecting lines shown in the various figures are intended to represent example functional relationships and / or physical couplings between the various elements. Many alternative or additional functional relationships or physical connections may be present in an actual system and / or may not be present in some embodiments.

[0037] It will be understood that the configurations and / or approaches described in this disclosure are exemplary in nature, and that these specific embodiments or examples are not to be construed in a limiting sense, as numerous variations are possible. The specific routines or methods described in this disclosure may represent one or more of any number of process strategies. As such, the various illustrated operations may be performed in the order illustrated, in other orders, or may be omitted in some cases.

[0038] The subject matter of this disclosure includes all novel and non-obvious combinations and subcombinations of the various processes, systems, and configurations, and other features, functions, operations and / or properties disclosed in this disclosure, as well as all equivalents thereof.

[0039] In this disclosure, UV lamps and VUV lamps have the same or similar meaning in context.

[0040] FIG. 1 shows a schematic diagram of a substrate processing apparatus according to one embodiment of the present disclosure.

[0041] A substrate processing apparatus according to one embodiment of the present disclosure may include a lamp section 120, a processing chamber 170, a substrate susceptor 171, an isolation window 160, one or more lamp units (121, 122), a measurement unit 180, and a power controller 110.

[0042] The lamp units (121, 122) may be configured to include UV lamps (131, 132), intensity sensors (141, 142), and power regulators (151, 152).

[0043] The UV lamps (131, 132) may be configured to emit UV light. The intensity sensors (141, 142) may be configured to sense the intensity of the UV light emitted from the UV lamps (131, 132). Based on the results of sensing by the intensity sensors (141, 142), the power regulators (151, 152) adjust the power supplied to the UV lamps (131, 132). The power regulators (151, 152) may be configured to receive power supplied from the power controller 110 and may also adjust the distribution of power to the UV lamps (131, 132).

[0044] 1, two lamp units (121, 122) are shown as an example in the lamp section 120. However, there may be one or more lamp units in the lamp section 120.

[0045] A processing chamber 170 may be disposed below the lamp section 120. In the processing chamber 170, a substrate susceptor 171 may be positioned to support and / or heat a substrate 172 to be UV light processed. An isolation window 160 may be positioned between the lamp section 120 and the processing chamber 170. The isolation window 160 may be configured to be sufficiently transparent to allow UV light from each of the lamp units (121, 122) to pass through and into the processing chamber 170. Therefore, the level of UV transparency of the window 160 is important to substrate quality.

[0046] Each intensity sensor (141, 142) may primarily sense the light intensity within the lamp unit in which the sensor is installed. However, it is the intensity of the UV light within the processing chamber 170 that may be more important than the intensity of the lamp units (121, 122), as the UV light intensity within the processing chamber 170 may be an actual factor in substrate processing. To sense and measure the UV light intensity within the processing chamber 170, a measurement unit 180 may be located on a wall of the processing chamber 170.

[0047] The measurement unit 180 may be installed through the wall of the processing chamber as shown in Figure 1. The measurement unit 180 may be installed at the same or similar height of the substrate susceptor 171 so that it can measure the actual UV light intensity of the substrate processing.

[0048] 2(a) illustrates one mode of the measurement unit, which may include a tube 282a, a phosphor 281a disposed at the inner end of the tube 282a, an optical fiber 283a connected to the other end of the tube 282a, and an optical sensor 284a.

[0049] The phosphor 281a may be configured to convert UV light into visible light. In FIG. 2(c), UV light 288 emitted from a UV lamp travels and hits the phosphor 281. The phosphor 281 may be a very thin film-like film that has been chemically treated with a fluorescent material. It is well known that fluorescent materials emit visible light when hit by UV light. This chemical reaction turns the UV light 288 into visible light 289, which travels along the light guide 287 formed by the tube 282. The fluorescent material is Y3Al5O 12 :Ce 3+ (YAG), La3Si6N 11 :Ce 3+ (LSN), (La,Y)3Si6N 11 :Ce 3+ (LYSN), CaAlSiN3:Eu 2+ (CASN), (Sr,Ca)AlSiN3:Eu 2+ (SCASN), CaSc2O4:Ce 3+ (CSO), (Si,Al)3(O,N)4:Eu2+ (β-SiAlON), Y3(Al,Ga)5O 12 :Ce 3+ (GYAG), Lu3Al5O 12 :Ce 3+ (LuAG), (Sr,Ba) 10 (PO4)6Cl2:Eu 2+ (SBCA), or any mixture thereof.

[0050] If the phosphor 281a is installed vertically, UV light emitted from above may not hit the phosphor. Therefore, the phosphor 281a may be configured to be tilted to a certain degree relative to the vertical direction to obtain a sufficient and accurate amount of UV light (i.e., subsequent visible light) for sensing UV intensity. This tilt angle (shown as 'a' in Figure 2(a) may be in the range of 0° to 45°.

[0051] In FIG. 2(b), the measurement unit may be installed at a different angle relative to the horizontal. The tube 282b may be tilted so that the phosphor 281b can be exposed to UV light from above. The degree of tilt of the tube 282b (shown as 'b') may be in the range of 0° to 45°. In this case, tilting of the phosphor 281b may not be required, but may be provided if necessary.

[0052] The tubes 282a, 282b may be installed through the walls 273a, 273b of the processing chamber. Therefore, a fastening unit capable of sealing and fixing the walls 273a, 273b and the tubes 282a, 282b may be required, and the fastening fixtures 285a, 285b may be used. The fastening fixtures 285a, 285b may be sealing O-rings or any other device capable of sealing and fixing.

[0053] The light sensors (284a, 284b) may be set at a predetermined level of light intensity, which may be varied to meet system requirements.

[0054] Optical fibers (283a, 283b) may link the tubes (282a, 282b) and the light sensors (284a, 284b). Visible light 289 emitted from the phosphors (281, 281a, 281b) may travel along the light guide 287 until it reaches end B (the other end of the tube). When the visible light 289 reaches end B, it enters the optical fibers (283a, 283b) and reaches the light sensors (284a, 284b). For this purpose, the light guide 287 (inside the tubes 282, 282a, 282b) may be covered with a material that can reflect (visible) light in order to transmit the visible light 289 intact to the light sensors (284a, 284b).

[0055] The cross-sectional shapes of the measurement unit 180 may be those illustrated in Figures 3(a)-(d). As shown in Figure 3(a), a tube having a round cross-sectional shape may be used, but may be rotated around the tube's circular axis. Therefore, other cross-sectional shapes for the tube may be used. Figures 3(b), 3(c), and 3(d) may each show a rectangular, pentagonal, or hexagonal cross-sectional shape for the tube. Although the shapes may not be illustrated, polygons with more than 6 sides, such as heptagons or octagons, may also be used for the tubes (282, 282a, 282b) in the measurement unit 180.

[0056] The power controller 110 of FIG. 1 receives feedback signals from the light sensors (284a, 284b) from the measurement unit 180 and controls the power supplied to the UV lamps of the lamp section 120.

[0057] VUV lamps may generally decay over time, so the UV light condition (i.e., intensity) needs to be checked periodically to ensure good and efficient substrate processing quality, and the present disclosure provides a good method for measuring and sensing the actual UV light intensity inside a processing chamber.

[0058] FIG. 4 illustrates a substrate processing apparatus equipped with VUV lamps according to another embodiment of the present disclosure.

[0059] For simplicity, the lamp units (along with the UV lamps, intensity sensors, and power regulators within each of them) and power controllers within lamp section 420 are not shown.

[0060] The lamp section 420 may be configured to emit UV light into the processing chamber 470 through the isolation window 460. A gas inlet 482 may be disposed on one side of the processing chamber 470 to supply gas into the processing chamber 470 and process the substrate 472. In the processing chamber 470, a susceptor 471 may be disposed to support and / or heat the substrate 472. An exhaust duct 481 may be disposed on the processing chamber 470 opposite the gas inlet 482 to exhaust gas from the processing chamber 470. A measurement unit 480 may be disposed on a wall of the processing chamber 470. The gas inlet 482 may have two or more holes on the wall of the processing chamber 470.

[0061] The above-described arrangements of the devices are merely illustrative of the application of the principles of the present invention, and numerous other embodiments and modifications are possible without departing from the spirit and scope of the invention as defined in the appended claims. The scope of the invention should, therefore, be determined not with reference to the above description, but should instead be determined with reference to the appended claims along with their full scope of equivalents.

Claims

1. A substrate processing apparatus, 1. A lamp unit configured to emit UV light, comprising: a UV lamp for emitting said UV light; an intensity sensor configured to sense and measure the light intensity of the UV light; a power regulator electrically connected to the intensity sensor and configured to control power supplied to the UV lamp according to the light intensity measured by the intensity sensor; and a lamp section configured to include one or more lamp units; a processing chamber configured to process a substrate, the processing chamber comprising a susceptor, the susceptor configured to support and / or heat the substrate for processing; an isolation window disposed between the lamp compartment and the processing chamber, the isolation window configured to be transparent to allow light from the UV lamp to reach the substrate; a measurement unit disposed within a wall of the processing chamber, the measurement unit configured to measure light intensity within the processing chamber; a power controller electrically connected to the measurement unit and configured to adjust power supply to the lamp section according to the light intensity measured by the measurement unit; A substrate processing apparatus comprising:

2. The measuring unit a tube disposed through a sidewall of the processing chamber; a phosphor disposed at one end of the tube and configured to convert UV light into visible light; an optical fiber disposed at the other end of the tube and configured to guide the visible light; a light sensor connected to the optical fiber and configured to sense and measure the intensity of visible light received from the optical fiber; The substrate processing apparatus of claim 1 , comprising:

3. The measuring unit The substrate processing apparatus of claim 2 , further comprising a fixture configured to seal the tube and mount on a wall of the processing chamber.

4. The substrate processing apparatus of claim 2 , wherein the phosphor is tilted at a first angle from the vertical direction.

5. The substrate processing apparatus of claim 4, wherein the first angle is in the range of 0° to 45°.

6. The substrate processing apparatus according to claim 2 , wherein the pipe is inclined at a predetermined angle with respect to the horizontal direction.

7. The phosphor is YAG[Y ３ Al ５ O １２ : Ce ３＋ ], LSN [La ３ Si ６ N １１ : Ce ３＋ ], LYSN[(La,Y) ３ Si ６ N １１ : Ce ３＋ ], CASN[CaAlSiN ３ :Eu ２＋ ], SCASN[(Sr,Ca)AlSiN ３ :Eu ２＋ ], CSO[CaSc ２ O ４ : Ce ３＋ ], β-SiAlON [(Si,Al) ３ (O, N) ４ :Eu ２＋ ], gyag [Y ３ (Al, Ga) ５ O １２ : Ce ３＋ ], LuAG [Lu ３ Al ５ O １２ : Ce ３＋ ], SBCA [(Sr,Ba) １０ (PO4) ６ Cl ２ :Eu ２＋ 3. The substrate processing apparatus of claim 2, further comprising one of the following:

8. The substrate processing apparatus according to claim 1 , wherein the separation window is made of one of quartz, glass, and crystal, or a mixture of at least one of these.

9. The substrate processing apparatus according to claim 2 , wherein the inside of the tube is covered with a material that reflects the visible light.

10. The substrate processing apparatus according to claim 2 , wherein the cross-sectional shape of the tube is one of a circle, a rectangle, a pentagon, a hexagon, and a polygon having more than six sides.

11. A substrate processing apparatus, 1. A lamp unit configured to emit UV light, comprising: a UV lamp for emitting said UV light; an intensity sensor configured to sense and measure the light intensity of the UV light; a power regulator electrically connected to the intensity sensor and configured to control power supplied to the UV lamp according to the light intensity measured by the intensity sensor; and a lamp section configured to include one or more lamp units; a processing chamber configured to process a substrate, the processing chamber having a susceptor configured to support and / or heat the substrate for processing; a gas inlet disposed on one side of the processing chamber and configured to provide gas for processing the substrate; an exhaust duct disposed opposite the gas inlet and configured to exhaust the gas from the processing chamber; an isolation window disposed between the lamp compartment and the processing chamber, the isolation window configured to be transparent to allow light from the UV lamp to reach the substrate; a measurement unit disposed within a wall of the processing chamber and configured to measure light intensity within the processing chamber; a power controller electrically connected to the measurement unit and configured to adjust power supply to the lamp section according to the light intensity measured by the measurement unit; A substrate processing apparatus comprising:

12. The measuring unit a tube disposed through a sidewall of the processing chamber; a phosphor disposed at one end of the tube and configured to convert UV light into visible light; an optical fiber disposed at the other end of the tube and configured to guide the visible light; a light sensor connected to the optical fiber and configured to sense and measure the intensity of visible light received from the optical fiber; The substrate processing apparatus of claim 11 , comprising:

13. The measuring unit The substrate processing apparatus of claim 12 , further comprising a fixture configured to seal the tube and mount on a wall of the processing chamber.

14. The substrate processing apparatus of claim 12 , wherein the phosphor is tilted at a first angle from the vertical direction.

15. The substrate processing apparatus of claim 14, wherein the first angle is in the range of 0° to 45°.

16. The substrate processing apparatus according to claim 12 , wherein the tube is inclined at a predetermined angle relative to the horizontal.

17. The phosphor is YAG[Y ３ Al ５ O １２ : Ce ３＋ ], LSN [La ３ Si ６ N １１ : Ce ３＋ ], LYSN[(La,Y) ３ Si ６ N １１ : Ce ３＋ ], CASN[CaAlSiN ３ :Eu ２＋ ], SCASN[(Sr,Ca)AlSiN ３ :Eu ２＋ ], CSO[CaSc ２ O ４ : Ce ３＋ ], β-SiAlON [(Si,Al) ３ (O, N) ４ :Eu ２＋ ], gyag [Y ３ (Al, Ga) ５ O １２ : Ce ３＋ ], LuAG [Lu ３ Al ５ O １２ : Ce ３＋ ], SBCA [(Sr,Ba) １０ (PO4) ６ Cl ２ :Eu ２＋ 13. The substrate processing apparatus of claim 12, comprising one of the following:

18. The substrate processing apparatus of claim 11 , wherein the isolation window is made of one of quartz, glass, crystal, or a mixture of at least one of these.

19. The substrate processing apparatus of claim 12 , wherein the inside of the tube is covered with a material that reflects the visible light.

20. The substrate processing apparatus of claim 12 , wherein the cross-sectional shape of the tube is one of a circle, a rectangle, a pentagon, a hexagon, or a polygon with more sides than a hexagon.

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