Design method and temperature control device

Abstract

A temperature control device (1) comprises: a heat diffusion plate (10) that is a member provided with a first surface (S1) facing a controlled object (CO) and a second surface (S2) parallel to the first surface (S1) and facing the opposite direction therefrom, and in which heat is diffused in the surface direction of the first surface (S1); and a heat source (11) that is thermally bonded with the heat diffusion plate (10) at the second surface (S2) and heats or absorbs heat from the heat diffusion plate (10). In this design method, the sizes of the heat diffusion plate (10) and the heat source (11) and the thermal conductivity and overall heat transfer coefficient of the heat diffusion plate (10) are determined on the basis of a computation formula indicating the relationship between the ambient temperature around the controlled object (CO), a target temperature for the controlled object (CO), the amount of heat input to the heat diffusion plate (10) from the heat source (11), the sizes of the heat diffusion plate (10) and the heat source (11), the thermal conductivity and the overall heat transfer coefficient of the heat diffusion plate (10), and variation in temperature on the first surface (S1) so that the difference between the maximum temperature and the minimum temperature of a part of the first surface (S1) in contact with the controlled object (CO) when the ambient temperature, the target temperature, and the input amount of heat serve as given design conditions falls within a permissible value range for in-plane temperature variation in the controlled object (CO).

Description

[Technical Field]

[0001] This invention relates to a method for designing a temperature control device and a temperature control device. [Background technology]

[0002] The physical properties of objects and the reactions between objects are temperature-dependent. Therefore, in a processing step that performs some kind of treatment on the entire surface of an object that extends in the planar direction, it is necessary to reduce the temperature variation within the surface of the object in order to reduce the variation in the physical properties of the object being treated or the reaction rate of the reaction field that occurs during the treatment. For example, an assembly has been disclosed that incorporates a thermal phase diffuser into a pedestal that supports a wafer in a semiconductor manufacturing process to reduce the temperature variation within the wafer surface (see Patent Document 1). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Special Publication No. 2020-526012 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] In the semiconductor manufacturing process described above, there are tolerance limits for variations in the reaction rate of the reaction field within the wafer surface, and also tolerance limits for variations in temperature within the wafer surface. The assembly described above can reduce the temperature variation of the wafer. However, Patent Document 1 does not disclose how to keep the temperature variation within the wafer surface within the tolerance limits. In order to keep the temperature variation within the tolerance limits, the control capability of the temperature control device that controls the temperature within the wafer surface must be designed to meet the tolerance limits.

[0005] The present invention was made under the circumstances described above, and aims to provide a method for designing a temperature control device and a temperature control device that can suppress temperature variations within the plane of a controlled object having a plane extension to within an acceptable range. [Means for solving the problem]

[0006] To achieve the above objective, the design method for a temperature control device according to the first aspect of the present invention is: A method for designing a temperature control device, The temperature control device is A member having a first surface facing the object to be controlled and a second surface parallel to and opposite to the first surface, wherein the first surface includes a heat diffusion plate that diffuses heat in the planar direction, The device comprises a heat source that is thermally bonded to the heat diffusion plate on the second surface and heats or absorbs heat from the heat diffusion plate, Based on a calculation formula showing the relationship between the ambient temperature around the controlled object, the target temperature of the controlled object, the amount of heat input from the heat source to the heat diffuser plate, the size of the heat diffuser plate and the heat source, the thermal conductivity and overall heat transfer coefficient of the heat diffuser plate, and the temperature variation on the first surface, the size of the heat diffuser plate and the heat source, the thermal conductivity and overall heat transfer coefficient of the heat diffuser plate are determined such that the difference between the highest and lowest temperatures of the portion of the first surface in contact with the controlled object, given the ambient temperature, target temperature, and amount of heat input as design conditions, falls within the allowable range for the temperature variation within the surface of the controlled object.

[0007] In this case, the heat diffusion plate is A housing having a sealed internal space, composed of one of the following: ceramics, ceramic composites, or inorganic materials excluding metals. A working fluid located in the internal space circulates along the surface direction of the first surface, repeatedly vaporizing due to heat absorption and condensing due to heat dissipation, and diffuses heat in the surface direction of the first surface. Equipped with, It would be acceptable to do so.

[0008] The thermal expansion coefficient of the material of the housing is 8.0 × 10-6 [1 / K] or less, It would be acceptable to do so.

[0009] Based on the temperature characteristics of the physical properties of the controlled object or, if the controlled object is a reaction field, the characteristics of the reaction rate within that plane, an allowable value for the in-plane temperature variation of the controlled object is set. It would be acceptable to do so.

[0010] The heat source is one of a heater, a Peltier element, and a cold plate. It would be acceptable to do so.

[0011] The heat source and the heat diffusion plate are integrated on the second surface. It would be acceptable to do so.

[0012] The heat source is incorporated into the heat diffusion plate. It would be acceptable to do so.

[0013] The heat source and the heat diffusion plate each have a disc-shaped outer form and are arranged concentrically with each other. The radius of the heat source is smaller than the radius of the heat diffuser plate. It would be acceptable to do so.

[0014] A temperature control device according to a second aspect of the present invention is: It is designed using the design method for temperature control devices relating to the first aspect. [Effects of the Invention]

[0015] According to the present invention, the size of the heat source and the heat diffuser plate, as well as the thermal conductivity and overall heat transfer coefficient of the heat diffuser plate, can be determined so that the difference between the highest and lowest temperatures on the first surface in contact with the controlled object is less than the allowable value for in-plane temperature variation of the controlled object. Therefore, the in-plane temperature variation of the controlled object can be kept within an allowable value. [Brief explanation of the drawing]

[0016] [Figure 1]These are a side view and a bottom view of a temperature control device according to an embodiment of the present invention. [Figure 2] This is a schematic diagram showing the internal structure of a heat diffusion plate. [Figure 3A] This graph shows the temperature characteristics of the reaction rate. [Figure 3B] This graph shows the temperature characteristics of the physical properties. [Figure 4] This is a schematic diagram illustrating how thermal energy is transferred in the planar direction within a thermal diffusion plate. [Figure 5] This graph shows the dimensionless temperature distribution in the radial direction of a heat diffusion plate. [Figure 6A] This is a block diagram showing the hardware configuration of an information processing device. [Figure 6B] This is a flowchart of the design process performed by an information processing device. [Figure 7] This graph shows the temperature characteristics of the thermal conductivity of a heat diffusion plate. [Figure 8A] This is a schematic diagram showing a first modified example of the configuration of a temperature control device. [Figure 8B] This is a schematic diagram showing a second modified configuration of a temperature control device. [Figure 9] This is a side view showing the configuration of a substrate holding device incorporating a temperature control device. [Figure 10] This is a perspective view showing a cylindrical temperature control device. [Modes for carrying out the invention]

[0017] Embodiments of the present invention will be described in detail below with reference to the drawings. In each drawing, the same or equivalent parts are denoted by the same reference numerals.

[0018] [Basic configuration of a temperature control device] First, the basic configuration of the temperature control device that is the target of the design method according to this embodiment will be described. As shown in Figure 1, the temperature control device 1 controls the temperature of the target CO. The target CO represents, for example, a disc-shaped object or a reaction field. The temperature control device 1 comprises a heat diffusion plate 10 with a disc-shaped outer shape and a heat source 11 with a disc-shaped outer shape.

[0019] In the heat diffusion plate 10, the circular surface with the z-axis direction as the normal direction is defined as the surface facing the +z direction, i.e., the surface facing the controlled object CO, which is the first surface S1. The surface with the z-axis direction as the normal direction and facing the -z direction is defined as the second surface S2. The first surface S1 and the second surface S2 are the main front and back surfaces of the heat diffusion plate 10, which are parallel to each other and facing opposite directions, and the distance between the first surface S1 and the second surface S2 is the thickness of the heat diffusion plate 10.

[0020] The heat diffusion plate 10 and the heat source 11 are arranged concentrically with the controlled CO around the z-axis. In this embodiment, the radius of the heat diffusion plate 10 is the same as the radius of the controlled CO, and the radius of the heat source 11 is smaller than the radius of the heat diffusion plate 10.

[0021] The heat diffuser plate 10 is positioned on the +z side of the heat source 11 so as to be in surface contact with the heat source 11 on the second surface S2 and thermally joined to it. The controlled object CO is positioned on the +z side of the heat diffuser plate 10 so as to be in surface contact with the heat diffuser plate 10 on, for example, the first surface S1. The heat source 11 is in surface contact with the heat diffuser plate 10 in a circular region 11a (a region with the same radius as the heat source 11) on the second surface S2.

[0022] The heat source 11 heats or absorbs heat from the heat diffusion plate 10. The heat diffusion plate 10 diffuses heat in the planar direction of the first surface S1. The heat diffusion plate 10, whose temperature has been made uniform in the planar direction of the first surface S1 by the heating or absorption of heat from the heat source 11, heats or absorbs heat from the controlled CO.

[0023] When the heat source 11 heats the heat diffusion plate 10, heat from the heat source 11 is applied to the heat diffusion plate 10 through the circular region 11a of the second surface S2. The heat diffusion plate 10 diffuses this heat in the radial direction centered on the surface direction of the first surface S1, i.e., the z-axis direction. The heat diffused in the radial direction is transferred to the controlled material CO. The temperature of the controlled material CO is controlled to the target temperature by the transferred heat.

[0024] When the heat source 11 cools the heat diffuser plate 10, the heat absorbed by the heat source 11 lowers the temperature of the heat diffuser plate 10 via the circular region 11a of the second surface S2. Due to the temperature decrease in this region 11a, the coolant moves radially on the heat diffuser plate 10, uniformly lowering the temperature of the first surface S1. As a result, the heat diffuser plate 10 uniformly cools the controlled CO across the entire first surface S1.

[0025] As shown in Figure 2, the heat diffusion plate 10 comprises a housing 20 having a sealed internal space IS, and a working fluid 21 as a coolant sealed in the internal space IS. In the internal space IS, liquefied working fluid 21 and vaporized working fluid 21 coexist in equilibrium. Liquefied working fluid 21 is present directly above the heat source 11. Due to the heat transferred from the heat source 11, the working fluid 21 vaporizes and moves within the internal space IS in the planar direction of the first surface S1, transferring (dissipating) heat to the housing 20, and gradually condenses. The condensed working fluid 21 is configured to return to the heat source 11 by the capillary force of capillary channels (not shown) formed in the internal space IS. In this way, the working fluid 21 undergoes vaporization due to heat absorption and Heat dissipation The fluid circulates through the internal space IS while repeatedly condensing, diffusing heat in the planar direction of the first surface S1. The working fluid 21 can be, for example, pure water, but it may also be an organic substance or a mixture of an organic substance and water.

[0026] The housing 20 is made of a low thermal expansion material. Such materials include, for example, ceramics. Examples of ceramics that can be used include, but are not limited to, alumina, SN (silicon nitride), AIN (aluminum nitride), Y2O3, zirconia, cordierite, and single-crystal materials such as diamond and sapphire. Other examples of such materials include ceramic composites. Examples of ceramic composites that can be used include, but are not limited to, SiSiC and CMC. Other materials that can be used include, but are not limited to, glass, carbon, graphite, and silicon. In other words, the housing 20 is made of either ceramics, ceramic composites, or inorganic materials other than metals.

[0027] The thermal expansion coefficients of each substance are shown in the table below. [Table 1] The material used for the housing 20 is selected to have a lower coefficient of thermal expansion than metals such as copper. By using a material with a low coefficient of thermal expansion for the housing 20, when the controlled CO or heat source 11 generates heat, the deformation of the heat diffusion plate 10 can be reduced, and the change in the overall heat transfer coefficient h can be reduced, making it easier to determine the overall heat transfer coefficient h. In this embodiment, the coefficient of thermal expansion is 8.0 × 10 -6 It is desirable to select a material with a temperature of [1 / K] or lower as the material for the enclosure 20.

[0028] When heating the CO to be controlled, the heat source 11 can be a heater. Furthermore, the heat source 11 may include elements, devices, etc. that generate heat when operating, or it may be a heat source 11 in which a gas, liquid, etc. that generates heat circulates internally. In addition, a high-frequency induction heating device, a plasma heating device, or a laser heating device may be used as the heat source 11. In the temperature control device 1 according to this embodiment, the type of heat source 11 is not limited, and various heat sources 11 can be used.

[0029] Furthermore, when cooling the CO to be controlled, the heat source 11 can be a Peltier element or a cold plate. In addition, the heat source 11 can be a water-cooled type or one using a heat exchanger. In the temperature control device 1 according to this embodiment, the type of heat source 11 is not limited, and various heat sources 11 can be used.

[0030] [Effects of the configuration of the temperature control device 1] When the heat source 11 is a solid, the heat source 11 and the controlled CO are indirectly connected via the heat diffusion plate 10. This is because if the heat source 11 and the controlled CO were directly connected, there would be a difference in heat transfer rate between the parts in contact with the heat source 11 and the parts that are not, resulting in non-uniformity in the temperature distribution of the controlled CO.

[0031] It is also conceivable to directly connect a heat source 11 having the same radius as the controlled CO to the controlled CO. However, in this case, if the heat source 11 is, for example, a heater, the electrical resistance will change locally due to temperature unevenness inside the heater, making it difficult to achieve sufficient temperature smoothness. Also, if the heat source 11 is, for example, a Peltier module, multiple elements with heat transfer surfaces smaller than the entire module are arranged on the surface, and each element performs heat transfer or heat absorption. However, there are gaps between the elements, and to mitigate the effects of these gaps, small heat diffusers are placed on the heat transfer surfaces. These heat diffusers are much smaller than the heat diffuser 10. Since these heat diffusers are made of copper, their heat diffusion performance is insufficient. Therefore, it is not possible to sufficiently mitigate the non-uniformity of the heat flux between areas with and without elements, and as a result, it becomes difficult to achieve sufficient temperature smoothness relative to the allowable temperature unevenness. Thus, when the heat source 11 and the controlled CO are directly connected, it becomes difficult to equalize the heat transfer rate across the entire surface of the controlled CO in order to achieve a sufficiently smooth temperature distribution relative to the allowable temperature unevenness. To mitigate this non-uniformity of heat transfer rate, the temperature control device 1 has a configuration that connects the heat source 11 via a heat diffusion plate 10.

[0032] In addition, when the heat source 11 cools the control target CO, fins (not shown) may be provided on the heat source 11.

[0033] [Design method of temperature control device] A design method of the temperature control device 1 according to this embodiment will be described. In this design method, the temperature control device 1 is designed so that the variation in the in-plane temperature of the first surface S1 of the heat dissipation plate 10 in contact with the control target CO is within the allowable value.

[0034] [Determination of allowable value] In this design method, first, an allowable value ΔT C of the variation in the temperature between the control target CO and the first surface S1 of the heat dissipation plate 10 needs to be determined. The allowable value ΔT C is determined based on the temperature characteristics of the control target CO.

[0035] [Allowable value ΔT C obtained from reaction variation] Assume that the control target CO is a reaction field where substances react with each other. In a reaction field having a planar spread, it is necessary to make the reaction rate uniform in the plane, that is, to suppress the variation in the reaction rate in the plane to less than the allowable value. Let the reaction rate of the control target CO in the plane be v, and assume that the allowable value of the variation in the reaction rate v is Δv c . From Arrhenius' law, the dependence of the reaction rate constant v r on the temperature T of the control target CO is given by the following formula (1). In FIG. 3A, a curve showing formula (1) is shown. [Number] Here, A r is the frequency factor, Ea [J·mol -1 is the activation energy, R [J·K -1 ·mol -1 is the gas constant, and T [K] is the temperature of the control target CO.

[0036] The frequency factor A rThe unit of the reaction changes depending on the order of the reaction. For example, if the reaction being considered here is a first-order reaction, then the frequency factor A r The unit is [S -1 ]. At this time, the concentration of the reactants is C A [mol·m -3 If ] then the reaction rate v is expressed by the following formula.

number

number

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[0037] Let Δη be the allowable variation in the reaction rate in the reaction field. In this case, the variation Δv in the reaction rate v must satisfy the conditions shown in the following equation.

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[0038] Here, the minimum temperature in the plane of the heat diffusion plate 10 is T. min Let [K] be the maximum value, and T be the maximum value. max If we let [K] be the case, then as shown in Figure 3A, ΔT = T max -T min And from equation (1)

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[0039] Furthermore, as shown in Figure 3B, the physical property value Φ of the substance contained in the controlled CO pc.i Let the temperature dependence of (pc.i=1,2,3,···,n:n is any integer) be given by the following equation (9).

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[0040] Note that the temperature T[K] shown in equations (1) to (10) above is the temperature of the controlled CO. When the thickness of the controlled CO is negligibly thin, the temperature of the controlled CO and the temperature of the first surface S1 of the heat diffusion plate 10 are approximately the same. When the thickness of the controlled CO is not negligible, the heat transfer coefficient on the surface of the controlled CO opposite to the heat diffusion plate 10 is U top Let T be the temperature of the heat diffusion plate 10, and T be the temperature of the controlled CO on the opposite side of the heat diffusion plate 10. top Let the thermal conductivity of the controlled CO in the thickness direction be k. t , the thickness of the CO to be controlled is δ t When the heat conduction field within the heat diffusion plate 10 is coupled with the heat transfer field to the controlled object CO, the following relationship holds.

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[0041] [Design parameters for temperature control devices] The allowable variation ΔT of the in-plane temperature T of the first surface S1. C The size of the temperature control device 1 and the design parameters related to heat transfer that satisfy the above conditions can be determined, for example, as follows:

[0042] As shown in Figure 4, we consider a small interval between a radial position r with respect to the center point of the heat diffusion plate 10 and position r+Δr. This small interval forms a double-cylindrical shell. Let the thickness of the heat diffusion plate 10 be d. In the radial direction r, heat is conducted from position r by heat quantity q in this shell. r As it enters, heat q is obtained from position r+Δr. r Let q be the amount of heat that goes out. Also, let q be the amount of heat input from the heat source 11. in Let q be the amount of heat transferred from the heat diffusion plate 10 to the controlled CO. out Let's assume that, in the shell, heat is transferred in the thickness direction from the section in contact with the heat source 11, and heat is released from the section in contact with the controlled CO. In this case, the governing equations for the conservation of thermal energy in the shell in a steady state can be defined as follows.

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[0043] h[W·m -2 ·K -1 ] is the overall heat transfer coefficient based on the first surface S1 of the heat diffusion plate 10. Also, T ∞ This is the reference temperature that serves as the basis for thermal diffusion. If there is a controlled CO, the reference temperature T ∞ The ambient temperature around the controlled CO can be set. Thermal conductivity k r [W·m -1 ·K -1 ] and the overall heat transfer coefficient h[W·m -2 ·K -1 Assuming that ] and are constant within the heat diffusion plate 10, the above equation (12) becomes as follows.

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[0044] Here, the surface temperature at radius r[m] on the first surface S1 of the controlled object CO is T. * Let (r)[K] be the surface temperature T. * (r)[K] is defined as follows:

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[0045] Ambient temperature T surrounding the controlled CO ∞ [K] and q r [W·m -2Assuming that ] is constant, the following equation can be obtained from equation (15).

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[0046] Using equations (18A) and (18B), we obtain the following equation from equation (16).

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[0047] Here, R[m] is the radius of the heat source 11. d[m] is the thickness of the heat diffuser plate 10, as previously mentioned. Furthermore, α is the ratio of the radius r of the heat diffuser plate 10 to the radius R of the heat source 11.

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[0048] Differentiating the above formula (22) gives the following formula. [Mathematics] Here, \(I_1\) is the modified Bessel function of the first kind of order 1. \(K_1\) is the modified Bessel function of the second kind of order 1.

[0049] As shown in FIG. 4, the first surface \(S_1\) can be divided into the following two regions. Region (Zone) I (0 ≤ r ≤ R): Central region where heat is transmitted from the bottom surface Region (Zone) II (R ≤ r): Peripheral region where heat is not transmitted from the bottom surface In region I, as r * approaches +0, the second term of formula (22) diverges to +∞. Since \(\Theta\) I (r) is a bounded function, \(C_2\) must be 0. Then, the second term of formula (22) in region I becomes 0. Also, since \(\Theta\) I (r II ) becomes 1 when r * = 1, it becomes the following formula. [Mathematics]

[0050] Furthermore, from the boundary conditions of the end (r * = α) of the heat diffusion plate 10 according to Newton's law, and various boundary conditions such as \(\Theta\) * = 1 when r II = 1, \(\Theta\) II (r * ) is derived as follows. [Mathematics] As shown in Fig. 5, in the heat diffusion plate 10, the highest temperature point in the plane is the central part in contact with the center of the heat source 11, and is given by Θ I (0). Also, the lowest temperature point is at the end (r = αR) of the heat diffusion plate 10, and is given by Θ II (α). Therefore, the value of the dimensionless temperature non-uniformity ΔΘ in the plane is given by the following equation.

Equation

[0051] Θ I (0), Θ II (α) being determined, from equation (18A), the surface temperatures T * = 0, r * = α at the first surface S1 at each point are as follows. * (r * ) [K] are as follows respectively.

Equation

Equation

Equation

[0052] Therefore, in this design method, T(R), T ∞ , q in If we take the value of as a given design condition, and further determine the values ​​of the design parameters d, R, and α related to the size of the heat diffusion plate 10 and the heat source 11, then, as shown in Figure 5, from equation (29), ΔT = ΔT c The number of Bios that satisfies Bi r Upper limit of Bi r.MAX The value can be determined.

[0053] Bio number Bi r Upper limit of Bi r.MAX Once the value of is determined, the thermal conductivity k in the planar direction of the heat diffusion plate 10 is determined to satisfy the following equation (30). r By determining the overall heat transfer coefficient h, the design conditions for the temperature control device 1 can be determined.

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[0054] [Design process for temperature control device 1] As shown in Figure 6A, the design of the temperature control device 1 is performed by the information processing device 100. The information processing device 100 is a computer hardware having a CPU 60, memory 61, external storage device 62, operation unit 63, display unit 64, and internal bus 65. It is realized when the CPU 60 executes a software program read from the external storage device 62 into the memory 61 according to an operation via the operation unit 63. The result of the design process of the temperature control device 1 by the CPU 60 is displayed, for example, on the display unit 64. The information processing device 100, whose function is realized by the computer executing this program, performs the design process (design method) of the temperature control device 1 shown in Figure 6B.

[0055] As shown in Figure 6B, first, the information processing device 100 determines the ambient temperature T surrounding the controlled CO. ∞ , heat input q from heat source 11 in、 The system inputs the given design conditions, such as the target temperature T(R) of the controlled CO, and the values ​​of design parameters d, R, and α related to the size of the heat diffusion plate 10 and the heat source 11 (Step S1).

[0056] Next, the information processing device 100 calculates the variation Δr of the reaction value based on the relationships shown in equations (1) to (8). c The corresponding tolerance value for temperature unevenness ΔT r Determine f pc.i (T) to Δφ pc,i ΔT that satisfies pc,i Find ΔT r、 ΔT pc.i From among them, the smallest is the allowable temperature variation ΔT. c This is determined (Step S2). That is, the information processing device 100 sets an allowable value for the in-plane variation of the temperature of the controlled CO based on the temperature characteristics of the physical properties of the controlled CO or the in-plane reaction rate characteristics when the controlled CO is a reaction field.

[0057] Next, the information processing device 100 uses the above equation (29) to calculate ΔT = ΔT c The maximum number of Biot Bi is such that r.MAX Explore (step S3). Maximum number of Biot Bir.MAX ΔT = ΔT c This is the Biot number Bi at that time. The maximum Biot number Bi r.MAX For example, a bipartite method can be used to search for it.

[0058] In the bipartite method, the evaluation function is defined as F = ΔT - ΔTc. In this case, F is a monotonically increasing function with respect to Bi. The bipartite method is performed using the following procedure.

[0059] Step 1) Biot number Bi r As initial values ​​for both ends of the solution interval, a sufficiently small appropriate Biot number Bir1 (for example, 10) -6 ) and a sufficiently large appropriate Bio number Bi r2 (For example, 10 6 ) gives the number Bi r1 Substituting this into equation (29) yields the value of F, i.e., F(Bi r1 If ) does not have a negative value, then F(Bi r1 Until Bi becomes a negative value, r1 The value of is repeatedly divided by 2. Also, F(Bi r2 If the value is negative, then F(Bi r2 Until the value of ) becomes positive, Bi r2 The value is repeatedly doubled.

[0060] Step 2) Bi r1 and Bi r2 The median value Bi rm =( Bi r1 +Bi r2 The value of F at ) / 2, i.e., F(Bi rm ) is calculated using equation (29). F(Bi rm The solution interval is updated according to the following rule based on the sign of the value of ). ·φ(Bi rm When ) < 0, Bi rm New Bi r1 Let's assume ·φ(Bi rm When )≧0, Bi rm New Bi r2 Let's assume Step 3) The newly determined Bi r1 ,Bi r2 More Birm We seek.

[0061] Step 4) Bi r2 -Bi r1 The threshold (for example, 10) ―6 Repeat steps 2 and 3 until the value falls below [value]. Step 5) Final Bi rm The value of the maximum number of Biot Bi r.MAX The result of searching for the convergence value is the maximum Bio number Bi. r.MAX End the search.

[0062] Next, the information processing device adds the maximum number of Biots Bi to equation (30). r.MAX Enter the value of k and satisfy equation (30) for thermal conductivity k r And the overall heat transfer coefficient h is determined (step S4). Note that the thermal conductivity k r For example, using the temperature characteristics shown in Figure 7, the thermal conductivity k corresponding to the target temperature T(R) of the controlled CO is used. r It can be done this way.

[0063] In this embodiment, the Biot number Bi r The target of the search was the thermal conductivity k corresponding to the target temperature T(R) of the controlled CO, based on the temperature characteristics shown in Figure 7. r First, determine the overall heat transfer coefficient h and search for the maximum Bio number Bi as described above. r.MAX Alternatively, one could try to find the Biot number Bi. r Furthermore, the search may also target any of the following: the radius R of the heat source 11, the thickness d of the heat diffusion plate 10, or the ratio α of the radius of the heat diffusion plate 10 to the heat source 11.

[0064] (Design example) For example, suppose the design conditions are defined as follows: • Heat source 11 diameter 2R: 55mm • Diameter (2αR) of the heat diffusion plate 10 and the controlled CO: 30 mm • Allowable value ΔT for in-plane temperature unevenness C :0.1K • Target temperature T(R) of the controlled CO: 350K • Ambient temperature (the temperature of the surrounding environment) T∞ :298K When this condition is entered into equation (29), the maximum number of Biots Bi r.MAX The value is 2.321 × 10 -32 This is the result. Furthermore, this maximum number of Biots Bi r.MAX Thermal conductivity k that satisfies the following conditions r The minimum value is 1.185 × 10⁻⁶. 3 [W·m -1 ·K -1 The thermal conductivity k of the ceramic heat diffusion plate 10 is as follows. r The temperature dependence is given in Figure 7. In Figure 7, kr.exp is the experimental value, and kr.fitted is the fitting curve that shows the characteristic. Here, the temperature of the heat transfer element T corresponding to the given design conditions is btm Thermal conductivity k at 350[K] r The value is 5.987 × 10 3 [W·m -1 ·K -1 This value is k r The minimum value that must be satisfied (maximum number of Biot Bi) r.MAX The value is greater than the corresponding value and satisfies the necessary conditions. Furthermore, since the value of the in-plane temperature uniformity in the controlled CO at this time is 0.0201 [K], it is clear that the heat diffusion plate 10 can achieve a temperature uniformity of the controlled CO below the allowable value.

[0065] As described in detail above, according to this embodiment, the maximum temperature T on the first surface S1 in contact with the controlled CO is * (0) and the lowest temperature T * The difference from (α) is within the allowable value ΔTc, and the radius R at which the heat source 11 and the heat diffuser plate 10 are in contact, the radius ratio α between the heat diffuser plate 10 and the circular region 11a, the thickness d of the heat diffuser plate 10, and the thermal conductivity k of the heat diffuser plate 10 are determined accordingly. r Since the overall heat transfer coefficient h can be determined, the temperature variation of the controlled CO can be kept within an acceptable range.

[0066] [Variations in the structure] Note that the configuration of the temperature control device 1 is not limited to that shown in Figure 1. For example, as shown in Figure 8A, the heat source 11 and the heat diffusion plate 10 may be integrated on the second surface S2. Specifically, the heat source 1 1 Alternatively, the heat source 11 can be formed from the same material as the housing 20 of the heat diffusion plate 10, and the heat source 11 and the housing 20 of the heat diffusion plate 10 can be directly joined at the second surface S2 to form an integral structure. Alternatively, the heat source 11 can be formed by screen printing a heater circuit onto a ceramic substrate, and the heat diffusion plate 10 and the heat source 11 can be formed integrally by simultaneous sintering.

[0067] Alternatively, the heat source 11 may be incorporated into the heat diffusion plate 10. In this case, as shown in Figure 8B, a heater layer that serves as the heat source 11 is incorporated into the housing 20 of the heat diffusion plate 10.

[0068] [Substrate holding device] Furthermore, the configuration of the temperature control device 1 according to this embodiment can be applied to electrostatic adsorption type and vacuum adsorption type substrate holding devices. As shown in Figure 9, the substrate holding device 50 is equipped with the temperature control device 1. The temperature control device 1 is provided with the function of controlling the temperature of the wafer W and adsorbing the wafer W by electrostatic adsorption or vacuum adsorption. In this way, the in-plane temperature T of the wafer W can be kept within an acceptable range during exposure processing, development processing, etching processing, etc. of the wafer W. It is also possible to incorporate the temperature control device 1 into substrate holding devices that hold liquid crystal substrates other than wafer W or other substrates.

[0069] Furthermore, although the temperature control device 1 according to this embodiment was disc-shaped, it is not limited to this, and may be, for example, polygonal flat plate-shaped. Also, the temperature control device 1 is not limited to a planar shape. For example, as shown in Figure 10, the temperature control device 1 may be cylindrical. In this case, the heat source 11 is cylindrical, and a cylindrical heat diffusion plate 10 is formed so as to be in contact with the side surface of the heat source 11. The side surface of the heat diffusion plate 10 is in contact with the controlled CO, and controls the temperature of the controlled CO. When the temperature control device 1 is polygonal flat plate-shaped, we consider a plane that passes through the center of the heat source 11 and includes the Z-axis. When this plane is rotated around the Z-axis, the length of the line segment crossing the heat source 11 changes with rotation. In such a temperature control device 1, the heat flux flowing into the heat diffusion plate 10 is maximum in the plane where the length of the line segment crossing the heat source 11 is shortest. Therefore, the above formula should be applied in the plane where this heat flux is maximum to perform thermal design and evaluate safety.

[0070] This invention allows for various embodiments and modifications without departing from the broad spirit and scope of the invention. Furthermore, the embodiments described above are for illustrative purposes only and do not limit the scope of the invention. In other words, the scope of this invention is indicated not by the embodiments, but by the claims. Various modifications made within the scope of the claims and the equivalent scope of the meaning of the invention are considered to be within the scope of this invention.

[0071] This application claims priority based on Japanese Patent Application No. 2022-189258, filed on November 28, 2022, and incorporates the entire specification, claims, and drawings of Japanese Patent Application No. 2022-189258 by reference within this specification. [Industrial applicability]

[0072] This invention can be applied to homogenizing the temperature of a substance or reaction field that has a planar spread. [Explanation of Symbols]

[0073] 1 Temperature control device, 10 Heat diffusion plate, 11 Heat source, 11a Area, 20 Housing, 21 Working fluid, 50 Substrate holder, 60 CPU, 61 Memory, 62 External storage device, 63 Operation unit, 64 Display unit, 65 Internal bus, 100 Information processing device, CO Controlled object, IS Internal space, S1 First surface, S2 Second surface, HW Computer, W Wafer

Claims

1. A method for designing a temperature control device, The temperature control device is A member having a first surface facing the object to be controlled and a second surface parallel to and opposite to the first surface, wherein the first surface includes a heat diffusion plate that diffuses heat in the planar direction, The device comprises a heat source that is thermally joined to the heat diffusion plate on the second surface and heats or absorbs heat from the heat diffusion plate, Based on a calculation formula showing the relationship between the ambient temperature around the controlled object, the target temperature of the controlled object, the amount of heat input from the heat source to the heat diffuser plate, the size of the heat diffuser plate and the heat source, the thermal conductivity and overall heat transfer coefficient of the heat diffuser plate, and the temperature variation on the first surface, the size of the heat diffuser plate and the heat source, the thermal conductivity and overall heat transfer coefficient of the heat diffuser plate are determined such that the difference between the highest and lowest temperatures of the portion of the first surface in contact with the controlled object, given the ambient temperature, target temperature, and amount of heat input as design conditions, falls within the allowable range for the temperature variation within the surface of the controlled object. Design method for temperature control devices.

2. The aforementioned heat diffusion plate is A housing having a sealed internal space, composed of one of the following: ceramics, ceramic composites, or inorganic materials excluding metals. A working fluid located in the internal space circulates along the surface direction of the first surface while repeatedly vaporizing due to heat absorption and condensing due to heat dissipation, and diffuses heat in the surface direction of the first surface. Equipped with, A method for designing a temperature control device according to claim 1.

3. The thermal expansion coefficient of the material of the housing is 8.0 × 10 －６ [1 / K] or less, A method for designing a temperature control device according to claim 2.

4. Based on the temperature characteristics of the physical properties of the controlled object or, if the controlled object is a reaction field, the characteristics of the reaction rate within that plane, an allowable value for the in-plane temperature variation of the controlled object is set. A method for designing a temperature control device according to claim 1.

5. The heat source is one of a heater, a Peltier element, and a cold plate. A method for designing a temperature control device according to claim 1.

6. The heat source and the heat diffusion plate are integrated on the second surface. A method for designing a temperature control device according to claim 1.

7. The heat source is incorporated into the heat diffusion plate. A method for designing a temperature control device according to claim 1.

8. The heat source and the heat diffusion plate each have a disc-shaped outer form and are arranged concentrically with each other. The radius of the heat source is smaller than the radius of the heat diffuser plate. A method for designing a temperature control device according to claim 1.

9. A temperature control device designed using the temperature control device design method described in any one of claims 1 to 8.

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