Temperature adjusting device

A temperature adjusting device includes a first member and a flow path. The first member has thereon a first surface as a temperature control target. The flow path is formed within the first member along the first surface. A first end of the flow path serves as an inlet opening through which a heat transfer medium is introduced and a second end of the flow path serves as an outlet opening through which the heat transfer medium is discharged. The flow path is formed such that a thermal resistance between the first surface and the flow path increases as the flow path goes from the outlet opening toward the inlet opening.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of Japanese Patent Application No. 2019-136176 filed on Jul. 24, 2019, the entire disclosures of which are incorporated herein by reference.

TECHNICAL FIELD

The various aspects and embodiments described herein pertain generally to a temperature adjusting device.

BACKGROUND

Patent Document 1 describes a plasma processing apparatus configured to cool a substrate by allowing a coolant to flow in a flow path within a placing table to adjust a temperature of the substrate placed on the placing table.

SUMMARY

In one exemplary embodiment, a temperature adjusting device includes a first member and a flow path. The first member has thereon a first surface as a temperature control target. The flow path is formed within the first member along the first surface. A first end of the flow path serves as an inlet opening through which a heat transfer medium is introduced and a second end of the flow path serves as an outlet opening through which the heat transfer medium is discharged. The flow path is formed such that a thermal resistance between the first surface and the flow path increases as the flow path goes from the outlet opening toward the inlet opening.

DETAILED DESCRIPTION

Hereinafter, an exemplary embodiment of a temperature adjusting device will be explained in detail with reference to the accompanying drawings. Further, the present disclosure is not limited by the present exemplary embodiment.

Conventionally, a plasma processing apparatus is configured to cool a substrate by allowing a coolant to flow in a flow path provided within a placing table. In the plasma processing apparatus, however, heat from plasma is transferred to the coolant through the substrate and the placing table, and a temperature of the coolant is varied within the flow path by this heat from the plasma. As a result, there is generated a difference between a temperature of the coolant at an inlet of the flow path within the placing table and a temperature of the coolant at an outlet thereof, so that a temperature difference is generated within a placing surface, which causes a temperature difference within the substrate placed on the placing table. In this regard, it is required to reduce the temperature difference within the surface.

EXEMPLARY EMBODIMENT

[Configuration of Plasma Processing Apparatus]

FIG.1is a schematic cross sectional view illustrating an example configuration of a plasma processing apparatus100according to an exemplary embodiment. The plasma processing apparatus100is hermetically configured and includes a processing vessel1which is electrically grounded. The processing vessel1has a cylindrical shape and is made of, by way of example, aluminum or the like. The processing vessel1has therein a processing space in which plasma is formed. A placing table2configured to horizontally support a semiconductor wafer (hereinafter, simply referred to as “wafer”)8as a substrate is provided within the processing vessel1. In the present exemplary embodiment, the placing table2corresponds to a temperature adjusting device.

The placing table2includes a base2aand an electrostatic chuck (ESC)6. The base2ais made of a conductive metal, for example, aluminum and has a function as a lower electrode. The electrostatic chuck6has a function of attracting the wafer8electrostatically. The placing table2is supported by a support4. The support4is supported by a supporting member3which is made of, by way of non-limiting example, quartz or the like. Further, a focus ring5formed of, by way of non-limiting example, single crystalline silicon is disposed on an upper peripheral portion of the placing table2. Further, a cylindrical inner wall member3amade of, by way of example, but not limitation, quartz is disposed within the processing vessel1, surrounding the placing table2and the support4.

A first RF power supply10ais connected to the base2avia a first matching device11a. Further, a second RF power supply10bis also connected to the base2avia a second matching device11b. The first RF power supply10ais used for plasma formation and is configured to supply a high frequency power of a preset frequency to the base2aof the placing table2. Further, the second RF power supply10bis used for ion attraction (bias) and is configured to supply a high frequency power having a predetermined frequency lower than that of the first RF power supply10ato the base2aof the placing table2. In this way, the placing table2is configured such that the high frequency powers having the different frequencies are applied thereto from the first RF power supply10aand the second RF power supply10b. Meanwhile, a shower head16serving as an upper electrode is disposed above the placing table2, facing the placing table2in parallel. The shower head16and the placing table2serve as a pair of electrodes (upper electrode and lower electrode).

The electrostatic chuck6has a disk shape with a flat top surface, and this top surface is configured as a placing surface6eon which the wafer8is placed. The electrostatic chuck6includes an insulator6band an electrode6aembedded in the insulator6b, and the electrode6ais connected with a DC power supply12. The electrostatic chuck6is configured to attract the wafer8by a coulomb force generated by a DC voltage applied to the electrode6afrom the DC power supply12.

A flow path20is formed within the base2a. One end of the flow path20is connected with a coolant inlet line21a, and the other end of the flow path20is connected with a coolant outlet line21b. The coolant inlet line21aand the coolant outlet line21bare connected to a non-illustrated chiller unit. The flow path20is located under the wafer8and serves to absorb heat of the wafer8. The plasma processing apparatus100is configured to control the placing table2to a preset temperature by circulating a coolant, for example, cooling water or an organic solvent such as GALDEN from the chiller unit in the flow path20via the coolant inlet line21aand the coolant outlet line21b.

Further, the plasma processing apparatus100may be configured to supply a heat transfer gas to a rear surface of the wafer8to control a temperature of the wafer8independently. By way of example, a gas supply line for supplying the heat transfer gas (backside gas) such as a helium gas to the rear surface of the wafer8may be formed through the placing table2. The gas supply line is connected to a non-illustrated gas source. With this configuration, the wafer8attracted to and held on the top surface of the placing table2by the electrostatic chuck6is regulated to a preset temperature.

The shower head16is provided at a ceiling portion of the processing vessel1. The shower head16includes a main body16aand a ceiling plate16bserving as an electrode plate. The shower head16is supported at an upper portion of the processing vessel1with an insulating member95therebetween. The main body16ais made of a conductive material, for example, aluminum having an anodically oxidized surface, and configured to support the ceiling plate16bthereunder in a detachable manner.

A gas diffusion space16cis provided within the main body16a. Further, the main body16ais provided with a multiple number of gas through holes16dlocated under the gas diffusion space16c. The ceiling plate16bis provided with gas discharge holes16ewhich are formed through the ceiling plate16bin a thickness direction thereof to be overlapped with the gas through holes16d, respectively. With this configuration, a processing gas supplied into the gas diffusion space16cis supplied into the processing vessel1through the gas through holes16dand the gas discharge holes16ewhile being distributed in a shower shape.

The main body16ais provided with a gas inlet opening16gthrough which the processing gas is introduced into the gas diffusion space16c. One end of a gas supply line15ais connected to the gas inlet opening16g, and the other end of this gas supply line15ais connected to a processing gas source (gas supply)15configured to supply the processing gas. The gas supply line15ais provided with a mass flow controller (MFC)15band an opening/closing valve V2in sequence from the upstream side. The processing gas for plasma etching is supplied from the processing gas source15into the gas diffusion space16cthrough the gas supply line15a. The processing gas is supplied from this gas diffusion space16cinto the processing vessel1through the gas through holes16dand the gas discharge holes16ewhile being distributed in the shower shape.

The shower head16is electrically connected with a variable DC power supply72via a low pass filter (LPF)71. This variable DC power supply72is configured to turn on/off a power feed by an on/off switch73. A current/voltage of the variable DC power supply72and an on/off operation of the on/off switch73are controlled by a controller90to be described later. Further, when plasma is formed in the processing space as the high frequency powers from the first RF power supply10aand the second RF power supply10bare applied to the placing table2, the on/off switch73is turned on by the controller90when necessary, and a preset DC voltage is applied to the shower head16.

A cylindrical grounding conductor1aextends upwards from a sidewall of the processing vessel1to be higher than a height position of the shower head16. This cylindrical grounding conductor1ahas a ceiling wall at a top portion thereof.

An exhaust port81is formed at a bottom of the processing vessel1. The exhaust port81is connected with an exhaust device83via an exhaust line82. The exhaust device83has a vacuum pump. The exhaust device83is configured to decompress the inside of the processing vessel1to a preset vacuum level by operating the vacuum pump. Meanwhile, a carry-in/out opening84for the wafer8is formed at the sidewall of the processing vessel1. A gate valve85configured to open or close the carry-in/out opening84is provided at the carry-in/out opening84.

Inside the processing vessel1, a deposition shield86is provided along an inner wall surface of the sidewall of the processing vessel1. The deposition shield86suppresses an etching byproduct (deposit) from adhering to the processing vessel1. A conductive member (GND block)89, which is provided such that a potential thereof with respect to the ground is controllable, is disposed at the deposition shield86substantially on a level with the wafer8. With this configuration, an abnormal discharge is suppressed. Further, a deposition shield87extending along the inner wall member3ais provided at a lower end portion of the deposition shield86. The deposition shields86and87are detachably provided.

An overall operation of the plasma processing apparatus100having the above-described configuration is controlled by the controller90. The controller90includes a process controller91provided with a CPU and configured to control the individual components of the plasma processing apparatus100; a user interface92; and a storage93.

The user interface92includes a keyboard through which a process manager inputs commands to manage the plasma processing apparatus100; a display configured to visually display an operational status of the plasma processing apparatus100; and so forth.

The storage93stores therein control programs (software) for implementing various processings performed in the plasma processing apparatus100under the control of the process controller91; and recipes in which processing condition data or the like are stored. When necessary, a required recipe is retrieved from the storage93in response to an instruction from the user interface92and executed by the process controller91, so that a required processing is performed in the plasma processing apparatus100under the control of the process controller91.

Now, referring toFIG.2, a configuration of major components of the placing table2will be elaborated.FIG.2is a schematic cross sectional view illustrating a configuration example of the major components of the placing table2according to the exemplary embodiment.

The placing table2includes the base2aand the electrostatic chuck6. The electrostatic chuck6has a circular plate shape. Further, the electrostatic chuck6is fixed to the base2aby an adhesive layer7such that the electrostatic chuck6is arranged coaxially with the base2a. The top surface of the electrostatic chuck6is configured as the placing surface6eon which the wafer8is placed. Protrusions6fare formed at the placing surface6e. The wafer8is placed on the placing surface6e. Due to the presence of the protrusions6f, a space9is formed between the placing surface6eand the wafer8. The heat transfer gas such as the helium gas is supplied into the space9. When a plasma processing is performed in the plasma processing apparatus100, heat from the plasma is inputted to the placing table2through the wafer8and the space9.

Within the base2a, the flow path20is provided along the placing surface6e. The plasma processing apparatus100is configured to control a temperature of the placing table2by allowing the coolant to flow in the flow path20.

[Configuration of Flow Path]

Now, a configuration of the flow path20of the placing table2will be explained.FIG.3is a plan view illustrating an example configuration of the placing table2according to the exemplary embodiment, seen from the top. InFIG.3, the placing surface6eof the placing table2is illustrated to have a circular plate shape. The flow path20is formed in a spiral shape in a region within the base2acorresponding to the placing surface6e, as illustrated inFIG.3, for example. The flow path20has, at one end thereof, an inlet opening20athrough which the coolant is introduced, and, at the other end, an outlet opening20bthrough which the coolant is discharged. The inlet opening20ais connected with the coolant inlet line21a. The outlet opening20bis connected with the coolant outlet line21b. The coolant introduced into the inlet opening20afrom the coolant inlet line21apasses through the inside of the flow path20, and the coolant having passed through the inside of the flow path20is then discharged into the coolant outlet line21bfrom the outlet opening20b. Accordingly, in the plasma processing apparatus100, the temperature of the wafer8is controlled on the entire placing surface6eof the placing table2.

FIG.4AandFIG.4Bare schematic cross sectional views illustrating a configuration example of the flow path20of the placing table2according to the exemplary embodiment.FIG.4Aschematically illustrates a cross section of the base2ataken along the flow path20.FIG.4Bschematically illustrates a cross section of the base2aon a plane perpendicular to a flow of the coolant. InFIG.4A, a horizontal coordinate axis x is shown along the flow path20. In the following, a position of the flow path20will be explained by using a position on the coordinate axis x. A position of the inlet opening20aof the flow path20is referred to as a position xi. A position of the outlet opening20bof the flow path20is referred to as a position xe. A boundary between a thermal entrance region and a thermally fully developed region to be described later is referred to as a position x0. A thickness between an inner wall at a top portion of the flow path20and a top surface2bat a position x of the flow path20is referred to as a thickness tw(x). A temperature of the coolant at the position x is referred to as a temperature Tm(x). A temperature of the top surface2bat the position x is referred to as a temperature Tw(x). A heat flux inputted from the plasma at the position x is referred to as q″(x). Further, when it is assumed that the plasma has a uniform distribution, the heat flux q″(x) of the plasma may be regarded as a constant value q″.

The top surface2bof the base2ais formed as a flat surface. The flow path20is formed along the top surface2bwithin the base2a. One end of the flow path20serves as the inlet opening20athrough which the coolant is introduced, and the other end thereof serves as the outlet opening20bthrough which the coolant is discharged. The flow path20is formed to have a rectangular cross sectional shape, as illustrated inFIG.4B, and has the same cross sectional shape from the inlet opening20ato the outlet opening20b.

The flow path20is formed such that a thermal resistance between the flow path20and the top surface2bis increased as it goes from the outlet opening20btoward the inlet opening20a. In the present exemplary embodiment, by changing the thickness tw(x) between the inner wall at the top portion of the flow path20and the top surface2b, the thermal resistance between the flow path20and the placing surface6eis changed. In the present exemplary embodiment, the flow path20is formed such that the thickness tw(x) is increased as it goes from the outlet opening20btoward the inlet opening20a.

Here, a configuration of a flow path120according to a comparative example will be described.FIG.5AandFIG.5Bare schematic cross sectional views illustrating the configuration of the flow path120of the placing table2according to the comparative example.FIG.5Aschematically illustrates a cross section of the base2ataken along the flow path120.FIG.5Bschematically illustrates a cross section of the base2aon a plane perpendicular to a flow of the coolant. In the comparative example, the flow path120is formed in the base2asuch that the thickness twfrom the top surface2bis uniform.

In the plasma processing apparatus100, the heat from the plasma is transferred to the coolant in the flow path120through the wafer8and the placing table2, and a temperature of the coolant increases along the flow path120. Accordingly, a temperature of the top surface2bof the base2aincreases along the flow path120. As a result, a temperature difference is generated within the placing surface6eof the placing table2, which results in a temperature difference within a surface of the wafer8placed on the placing table2.

Further, when the coolant is flown into the flow path120, a thermal entrance region and a thermally fully developed region are formed in the coolant in a range where there is a heat input. The thermal entrance region is a section where a thermal boundary layer is not developed and is formed at an upstream side. The thermally fully developed region is a section where the thermal boundary layer is developed and is formed after the thermal entrance region.FIG.6is a diagram for describing the thermal entrance region and the thermally fully developed region when the coolant is flown into the flow path.FIG.6illustrates a case where the coolant is flown into a pipe200, which is a model of the flow paths20and120, from an inlet opening200aas one end thereof. When there is a heat input to the pipe200from the vicinity thereof, the coolant flowing in the pipe200becomes to have a thermal boundary layer201formed along an inner wall of the pipe200. The thermal boundary layer201is gradually developed toward a center of the pipe200as it goes down the pipe200from the inlet opening200aand is merged at the center of the pipe200. A section LTfrom the inlet opening200ato a position where the thermal boundary layer201is merged is the thermal entrance region. The thermally fully developed region in which the flow of the coolant is developed is formed after the thermal entrance region. A heat transfer coefficient of the coolant in the thermal entrance region is higher than that in the thermally fully developed region.

Reference is made back toFIG.5AandFIG.5B. When the coolant is flown into the flow path120, the thermal entrance region is formed near the inlet opening120a, and the thermally fully developed region is formed after the thermal entrance region in the coolant. A boundary between the thermal entrance region and the thermally fully developed region is referred to as a position x0. The temperature Tm(x) of the coolant increases along the flow path120, and the temperature Tw(x) of the top surface2bof the base2aalso increases along the flow path120.

FIG.7is a diagram illustrating an example of a temperature variation along the flow path120of the placing table2according to the comparative example. A horizontal axis ofFIG.7indicates a position x along the flow path120, and a vertical axis represents a temperature T. A section from the position xito the position x0is the thermal entrance region. A section from the position x0to the position xeis the thermally fully developed region. The temperature Tm(x) of the coolant increases as it goes from the position xito the position xe, and the temperature Tw(x) of the top surface2bof the base2aalso increases. The heat transfer coefficient in this thermal entrance region is higher than that in the thermally fully developed region. Accordingly, the temperature Tw(x) of the top surface2bof the base2abecomes lower near the inlet opening120aof the flow path120.

If the coolant is flown into the flow path20(120), the thermal entrance region is formed in the coolant as a physical phenomenon. For the reason, it is difficult to form a flow path having a uniform heat transfer coefficient. Thus, if the flow path120is formed in the base2ato have a uniform thickness twfrom the top surface2b, as shown inFIG.5AandFIG.5B, the temperature of the wafer8increases along the positions xito the position xeof the flow path120in which the coolant flows. Further, since the thermal entrance region having the high heat transfer coefficient is formed near the inlet opening120aof the flow path120, a cold spot is generated.

In view of the foregoing, in the plasma processing apparatus100according to the present exemplary embodiment, the flow path20is formed such that the thickness tw(x) from the top surface2bis increased toward the inlet opening20afrom the outlet opening20b, as depicted inFIG.4A.

Now, an example design method for the flow path20according to the exemplary embodiment will be explained. A temperature rise ΔTmof the coolant when the coolant passes through the flow path20is represented by the following expression 1-1. Further, in the temperature rise ΔTmof the coolant, a relationship represented by the following expression 1-2 is established between a mass flow rate m of the coolant and a specific heat Cp of the coolant.

Here, Tm(xi) denotes a temperature [° C.] or [K] of the coolant at the position xi; Tm(xe), a temperature [° C.] or [K] of the coolant at the position xe; m, the mass flow rate [kg/s] of the coolant; Cp, the specific heat [J/kg·K] of the coolant; and q, a heat amount [W] inputted from the plasma.

From the expressions 1-1 and 1-2, the mass flow rate m of the coolant can be represented by the following expression 2. Thus, by using the expression 2, the mass flow rate m of the coolant can be calculated from the heat amount q inputted from the plasma and the temperature rise ΔTmof the coolant.

In case of designing the thickness tw(x) from the top surface2bat the position x of the flow path20, a thickness from the top surface2bat a position of an end of the flow path20is first decided. Then, a thickness from the top surface2bis decided from the end of the flow path20by using a thickness at the position of the end of the flow path20as a reference. In the present exemplary embodiment, a thickness tw(xe) from the top surface2bat the outlet opening20bof the flow path20is first decided. By way of example, the thickness tw(xe) can be calculated from the following expression 3. Further, in the expression 3, a heat flux of the plasma is set as a constant value q″.

Here, tW(xe) denotes the thickness from the top surface2bat the position xeof the flow path20; TW(xe), a temperature [° C.] or [K] of the top surface2bat the position xeof the flow path20; Tm(xe), the temperature [° C.] or [K] of the coolant at the position xe; q″, the heat flux [W/m2] inputted from the plasma; h(x), a heat transfer coefficient [W/m2·K] of the flow path20at the position x; h(xe), the heat transfer coefficient [W/m2·K] of the flow path20at the position xe; kW(x), the thermal conductivity [W/m·K] of the base2aat the position x; and kW(xe), the thermal conductivity [W/m·K] of the base2aat the position xe.

By way of example, the thickness tw(xe) is calculated from the temperature Tw(xe) of the top surface2b, the temperature Tm(xe) of the coolant, the heat transfer coefficient h(xe) and the thermal conductivity kw(xe) of the base2aand the heat flux q″ at the position xeof the outlet opening20bby using the expression 3.

Then, the thermal entrance region (ranging from the positions x0to xi) and the thermally fully developed region (ranging from the positions x0to xe) of the flow path20are calculated from a flowing state of the coolant. The coolant flows as a laminar flow or a turbulent flow within the flow path20depending on the Reynold's number Re thereof. The Reynold's number Re is calculated from the following expression 4.

Here, ρ denotes a density [kg/m3] of the coolant; um, an average flow velocity [m/s] of the coolant; μ, a viscosity [Pa·s] of the coolant; A, a cross sectional area [m2] of the flow path20; DH, a hydraulic diameter of the flow path20(DH=4A/Pwet); and Pwet, a wetted perimeter [m] of the flow path20(for example, a length of a wall surface in contact with the coolant on a cross section of the flow path20along a plane perpendicular to the flow of the coolant).

Theoretically, a length Δx0iof the thermal entrance region of the flow path20is represented by the following expressions 5-1 and 5-2 according to the Reynold's number Re of the coolant.

Here, Pr denotes a Prandtl number of the coolant; and Δx0i, the length [m] of the thermal entrance region of the flow path20.

Actually, in case that the coolant flows as the turbulent flow, the length Δx0iof the thermal entrance region is in a range from twice the hydraulic diameter DHof the flow path20to 10 times the hydraulic pressure DH. In case that the flow of the coolant is the turbulent flow, the thermal entrance region is set to be a range from the position xiof the inlet opening20ato the position x0where the length of the thermal entrance region falls within the range from the twice the hydraulic diameter DHof the flow path20to 10 times the hydraulic pressure DH. Further, in case that the flow of the coolant is the laminar flow, the thermal entrance region is decided to be a range from the position xiof the inlet opening20ato the position x0where the length of the thermal entrance region becomes the length of the expression 5-1. The thermally fully developed region is decided to be a range from the position x0after the thermal entrance region of the flow path20to the position xe.

Thereafter, for the thermal entrance region (ranging from the positions x0to xi) and the thermally fully developed region (ranging from the positions x0to xe) of the flow path20, a thickness from the top surface2bat each position of the flow path20is decided such that the thickness from the top surface2bincreases toward the inlet opening20afrom the outlet opening20b.

For the thermally fully developed region, the thickness tw(x) from the top surface2bat the position x of the flow path20can be calculated from the following expression 6 by using the thickness tw(xe) at the position xeas a reference.

By way of example, the thickness tw(x0) at the position x0as the boundary between the thermal entrance region and the thermally fully developed region is calculated from the following expression 7 based on the expression 6.

For example, for the thermally fully developed region (ranging from the positions x0to xe), the thickness tw(x) at the position x of the flow path20is decided to be linearly increased from the thickness tw(xe) at the position xeshown in the expression 6 to the thickness tw(x0) at the position x0shown in the expression 7.

For the thermal entrance region, the thickness tw(x) at the position x of the flow path20can be calculated from the following expression 8 by using the thickness tw(xe) at the position xeas a reference.

In the thermally fully developed region, the heat transfer coefficient h(x) becomes a constant value h. The heat transfer coefficient h of the thermally fully developed region can be calculated from the following expression 9, for example.

Here, Pr denotes the Prandtl number of the coolant; DH, the hydraulic diameter of the flow path20; and k, a thermal conductivity [W/m·K] of the coolant.

The heat transfer coefficient h(x) of the thermal entrance region (ranging from the positions x0to xi) varies from h(xi) to h. Theoretically, though the heat transfer coefficient h(xi) is infinite (h(xi))=∞), it needs to be appropriately estimated as the thickness near the inlet opening20ais large and thermal diffusion in a transversal direction is not negligible. In a region where the flow of the coolant becomes the turbulent flow, the thickness tw(x) of the flow path can be calculated from the expression 8, assuming that h(xi) is in a range from 1.1 h to 2.0 h.

In the region where the flow of the coolant becomes the turbulent flow, the thermal entrance region is very short. Thus, in the region where the flow of the coolant is the turbulent flow, the thickness tw(x) at the position x in the thermal entrance region is decided to be linearly increased from the thickness tw(xi) at the position Xito the thickness tw(x0) at the position x0.

In the above-described design method according to the present exemplary embodiment, if the flow path20is designed by assuming a maximum heat input from the plasma, higher temperature uniformity can be obtained with respect to a heat input smaller than the maximum heat input.

In case that the base2ais made of a material such as titanium or stainless steel having a low thermal conductivity, the thickness tw(xi) at the inlet opening20ais not greatly increased as compared to the thickness tw(xe) at the outlet opening20b. Meanwhile, if the base2ais made of a material such as alumina having a high thermal conductivity, the thickness tw(xi) at the inlet opening20ais largely increased as compared to the thickness tw(xe) at the outlet opening20b. In such a case, a material such as stainless steel, titanium or alumina ceramic having a low thermal conductivity or a thermally sprayed film may be provided at a ceiling of the flow path20.

Besides the electrostatic chuck6, in case that a top surface and a bottom surface of the flow path20or four surfaces thereof receive heat, a temperature of an outer wall of the flow path20can be uniformed along the flow path20when the thickness of the outer wall around the flow path20is designed according to the design method of the present exemplary embodiment. Furthermore, in case that the flow path20has a circular or another cross sectional shape, when a thickness of a wall of a heat receiving surface is designed according to the design method of the present exemplary embodiment, the temperature of the outer wall of the flow path ranging from the inlet opening20ato the outlet opening20bcan be uniformed along the flow path20.

Now, a specific configuration example of the flow path20will be explained. In the flow path20shown inFIG.4AandFIG.4B, a width and a height of the flow path20are set to be 12 mm; a length (ranging from the positions xito xe) of the flow path20is set to be 4.5 m; and a width W of a heated surface which receives the heat inputted to the flow path20from the plasma is set to be 22 mm. Further, the heat amount inputted from the plasma is set to be 4950 [W], and the heat flux from the plasma is set to be 50000 [W/m2]. The temperature rise ΔTmof the coolant is set to be 5.84° C. Novec 7200 produced by 3M is used as the coolant, and the mass flow rate m of the coolant is set to be 0.821 [kg/s]. The base2ais made of titanium. The thickness tw(xe) of the outlet opening20bis set to be 1 mm. The length of the thermal entrance region (ranging from the positions x0to xi) is set to be 3·DH=36 mm. The position xiof the inlet opening20ais set to be a position of x=0 mm, and the position xeof the outlet opening20bis set to be a position of x=4500 mm. The position x0which is the boundary between the thermal entrance region and the thermally fully developed region is set to be a position of x=36 mm, which is located at an upstream of the position xeof the outlet opening20bby 4464 mm (4500 mm−36 mm).

If the above-stated design method according to the present exemplary embodiment is used, the thickness tw(x0) at the position x0is calculated to be 3.50 mm. Further, the thickness tw(xi) at the position xiis calculated to be 6.04 mm.

In the placing table2according to the present exemplary embodiment, the flow path20is formed such that the thickness tw(x) from the top surface2bincreases toward the inlet opening20afrom the outlet opening20b. By way of example, the flow path20is formed such that the thickness tw(x) is linearly increased from 1 mm to 3.50 mm in the range from the position xeto the position x0(x=4500 mm to 36 mm). Further, the flow path20is formed such that the thickness tw(x) is linearly increased from 3.50 mm to 6.04 mm in the range from the position x0to the position xi(x=36 mm to 0 mm).

A ceramic plate is attached to the placing table2in which this flow path20is formed, and a simulation of cooling the wafer8by using the helium gas is performed. The heat amount inputted from the plasma is set to be 4950 [W], and the heat flux from the plasma is set to be 50000 [W/m2]. Further, as a comparative example, the same simulation is conducted for a case where the thickness twfrom the top surface2bis set to be uniform, as illustrated inFIG.5AandFIG.5B.

FIG.8is a diagram illustrating an example simulation result according to the exemplary embodiment. A horizontal axis ofFIG.8represents the position x from the inlet opening20a, and a vertical axis indicates the temperature of the top surface of the placing table2. In the flow path120according to the comparative example, the temperature of the top surface of the placing table2increases in the range from the positions xito xe. Accordingly, there is generated the temperature difference within the placing surface6eof the placing table2, which results in the temperature difference within the surface of the wafer8placed thereon.

Meanwhile, in the flow path20according to the present exemplary embodiment, the temperature of the top surface of the placing table2can be uniformed approximately. Accordingly, the temperature of the wafer8placed on the placing table2can be uniformed approximately, so that the temperature difference within the surface of the wafer8can be reduced.

Further, by setting the heat amount inputted from the plasma to be 2475 [W], that is, a half of 4950 [W], the same simulation is conducted for the placing table2in which the flow path20according to the present exemplary embodiment is formed and for the placing table2in which the flow path120according to the comparative example is formed.

FIG.9is a diagram illustrating another example simulation result according to the exemplary embodiment. A horizontal axis ofFIG.9represents the position x from the inlet opening20a, and a vertical axis indicates the temperature of the top surface of the placing table2. Even in case that the heat amount inputted from the plasma is set to be the half of the heat amount in the previous simulation, the temperature of the top surface of the placing table2can be uniformed approximately in the flow path20according to the present exemplary embodiment. Meanwhile, in the flow path120according to the comparative example, the temperature of the top surface of the placing table2is found to increase along the flow path120.

As stated above, in the placing table2in which the flow path20according to the present exemplary embodiment is formed, the temperature difference within the surface of the wafer8placed thereon can be reduced.

Here, in the above-described configuration of the placing table2, by changing the thickness between the inner wall at the top portion of the flow path20and the top surface2b, the thermal resistance between the flow path20and the placing surface6eis changed. However, the thermal resistance between the flow path20and the placing surface6emay be changed by varying a thickness or a material of a member between the flow path20and the placing surface6e.

The thermal resistance of the placing table2will be explained.FIG.10is a diagram for describing the thermal resistance of the placing table2according to the exemplary embodiment.FIG.10shows a cross section of the placing table2taken along a plane perpendicular to the flow of the coolant at the position x.

The placing table2is composed of a multiple number of members such as the base2a, the adhesive layer7and the electrostatic chuck6stacked on top of each other. The wafer8is placed on the electrostatic chuck6. InFIG.10, a thermal resistance between the flow path20and the top surface2bof the base2aat the position x is indicted as a thermal resistance R1(x). Further, a thermal resistance of the adhesive layer7at the position x is indicated as a thermal resistance R2(x). Further, a thermal resistance of the electrostatic chuck6at the position x is indicated as a thermal resistance R3(x). A thermal resistance between the electrostatic chuck6and the wafer8at the position x is indicated as a thermal resistance R4(x). Further, a thermal resistance of the wafer8at the position x is indicated as a thermal resistance R5(x). Further, inFIG.10, the heat flux q″(x) from the plasma at the position x and the temperature Tw(x) of the wafer8at the position x are shown. Furthermore, the temperature Tm(x) of the coolant at the position x is shown, and a heat flux q″inner(x) inputted to the coolant at the position x is also shown.

In a thermal equilibrium state where the temperature of the wafer8and the placing table2are maintained constant by the heat input from the plasma and the cooling by the coolant, the heat amount inputted from the plasma and the heat amount radiated by the coolant becomes substantially equal. That is, a condition of q″(x)≈q″inner(x) is satisfied. Further, when the temperature of the wafer8is uniform, the temperature Tw(x) of the wafer8at the position x is equal to the temperature at the position xe, so that a condition of TW(x)=TW(xe)=TWis obtained.

The thermal resistance between the wafer8and the flow path20at the position x is a sum of thermal resistances Rnof the individual members between the wafer8and the flow path20, and is indicated by the following expression 10. By way of example, inFIG.10, the thermal resistance between the wafer8and the flow path20at the position x is a sum of the thermal resistances R1to R5(n=5).

The temperature Tm(x) of the coolant at the position x may be represented by the following expression 11.

Here, Tm(xi) denotes a temperature [° C. or K] of the coolant at the position xi; and W, a width [m] of the heated surface which receives the heat inputted to the flow path20from the plasma. By way of example, when the flow path20is formed to have a spiral shape at a regular distance, W is set to be a width between middle points of two adjacent portions of the flow path20.

The thermal resistance between the wafer8and the flow path20at the position xeof the outlet opening20bmay be represented by the following expression 12.

Here, Twdenotes a temperature [° C. or K] of the wafer8; Tm(xe), a temperature [° C. or K] of the coolant at the position xe; q″(xe), a heat flux [W/m2] from the plasma at the position xe; and h(xe), a heat transfer coefficient [W/m2·K] of the flow path at the position xe.

In the thermally fully developed region, the heat transfer coefficient h(x) becomes a constant value h∞. Accordingly, in the thermally fully developed region, the thermal resistance between the wafer8and the flow path20at the position x needs to satisfy the following expression 13.

Meanwhile, in the thermal entrance region of the flow path20or in a region thereof where the heat transfer coefficient h(x) varies, the thermal resistance between the wafer8and the flow path20at the position x needs to satisfy the following expression 14.

When the heat flux q″(x) from the plasma has a distribution, the aforementioned expressions 11 to 14 are used. Meanwhile, when the heat flux q″(x) from the plasma is a constant value q″, the thermal resistance between the wafer8and the flow path20at the position xeof the outlet opening20b, which is represented by the expression 12, becomes the following expression 15.

Further, when the heat flux q″(x) from the plasma becomes the constant value q″, the thermal resistance between the wafer8and the flow path20at the position x, which is represented by the expression 13, becomes the following expression 16.

The second item on the right-hand side of the expression 16 is the left-hand side of the expression 15. Accordingly, in the thermally fully developed region, the thermal resistance between the wafer8and the flow path20at the position x increases according to a distance (|xe−x|) from the position xeof the outlet opening20bof the flow path20.

Further, when the heat flux q″(x) from the plasma becomes the constant value q″, the thermal resistance between the wafer8and the flow path20at the position x, which is represented by the expression 14, becomes the following expression 17 in the thermal entrance region of the flow path20or in the region thereof where the heat transfer coefficient h(x) varies.

The first item and the third item on the right-hand side of the expression 17 is the right-hand side of the expression 16. Accordingly, in the thermal entrance region of the flow path20or in the region thereof where the heat transfer coefficient h(x) varies, the thermal resistance between the wafer8and the flow path20at the position x is increased larger than that in the thermally fully developed region.

The heat transfer coefficient h(x) becomes a very large value at the inlet opening20a, rapidly decreases as the position is distanced away from the inlet opening20a, and does not change if the position exceeds the thermal entrance region.FIG.11is a diagram illustrating an example variation of the heat transfer coefficient according to the exemplary embodiment. A horizontal axis ofFIG.11indicates the position x along the flow path20, and a vertical axis thereof represents the heat transfer coefficient. The heat transfer coefficient h(x) becomes the very large value at the position xiof the inlet opening20aand becomes h∞when the position exceeds the thermal entrance region. The length Δx0iof the thermal entrance region becomes as indicated by the expressions 5-1 and 5-2 according to the Reynold's number Re of the coolant.

If the flow of the coolant is the laminar flow, the heat transfer coefficient h∞of the thermally fully developed region depends on the cross sectional shape. By way of example, if the cross sectional shape is a circular shape, the heat transfer coefficient h∞is calculated from the following expression 18.
[Expression 18]
h∞=4.36(k/DH)  (18)

Here, k denotes the thermal conductivity [W/m·K] of the coolant, and DHrepresents the hydraulic diameter of the flow path20.

If the cross sectional shape is a shape other than the circular shape, the heat transfer coefficient h∞of the thermally fully developed region can be calculated from a handbook in which a calculation method for the heat transfer coefficient is described, an experiment result or a heat flow simulation. Furthermore, in case that the flow of the coolant is the turbulent flow, the heat transfer coefficient h∞of the thermally fully developed region can be calculated from the above-described expression 9.

If the flow of the coolant is the laminar flow, the heat transfer coefficient h(x) of the thermal entrance region depends on the cross sectional shape, and can be calculated from a handbook in which a calculation method for the heat transfer coefficient is described, an experiment result or a heat flow simulation. Likewise, in case that the flow of the coolant is the turbulent flow, the heat transfer coefficient h(x) of the thermal entrance region can be calculated from a handbook in which a calculation method for the heat transfer coefficient is described, an experiment result or a heat flow simulation.

By calculating the heat transfer coefficient h(x) of the thermal entrance region and the transfer coefficient h∞of the thermally fully developed region and putting the calculated values in the expressions 11 to 17, conditions of the thermal resistances of the individual members between the wafer8and the flow path20to allow the temperature of the top surface of the placing table2to be uniformed approximately can be obtained. By way of example, if thermal resistances R2(x) to R5(x) are set inFIG.10, the thermal resistance R1(x) between the flow path20and the top surface2bof the base2ais changed to satisfy the condition. By way of example, by changing the thickness between the inner wall at the top portion of the flow path20and the top surface2bor the material of the base2apartially, the sum of the thermal resistances R1(x) to R5(x) is changed to satisfy the condition. As a result, the flow path20is capable of allowing the temperature of the top surface of the placing table2to be uniformed approximately. As a consequence, the temperature of the wafer8placed on the placing table2can be uniformed approximately, so that the temperature difference within the surface of the wafer8can be reduced.

As stated above, the placing table2according to the present exemplary embodiment includes the base2aand the flow path20. Within the base2a, the flow path20is formed along the top surface2b. One end of the flow path20serves as the inlet opening20athrough which the coolant is introduced, and the other end thereof serves as the outlet opening20bthrough which the coolant is discharged. The flow path20is formed such that the thermal resistance with respect to the top surface2bis increased as it goes toward the inlet opening20afrom the outlet opening20b. Accordingly, in the placing table2, the temperature difference within the top surface2bcan be reduced. As a result, the temperature of the wafer8placed on the placing table2can be made approximately uniform, so that the temperature difference within the surface of the wafer8can be reduced.

Further, in the base2aaccording to the present exemplary embodiment, the heat from the plasma is inputted to the top surface2b. The flow path20is formed such that the thermal resistance with respect to the top surface2bis increased as it goes toward the inlet opening20afrom the outlet opening20baccording to a temperature gradient of the coolant which flows from the inlet opening20atoward the outlet opening20b. Accordingly, in the placing table2, the temperature difference within the top surface2bcan be reduced.

Furthermore, the flow path20according to the present exemplary embodiment is formed such that an increment degree of the thermal resistance in the thermal entrance region in which the temperature boundary layer is not developed yet by the coolant introduced from the inlet opening20ais larger than an increment degree of the thermal resistance in the thermally fully developed region in which the temperature boundary layer is developed. Accordingly, it is possible to suppress the generation of the cold spot in the region of the top surface2bof the placing table2corresponding to the thermal entrance region.

Moreover, the flow path20according to the present exemplary embodiment is formed such that the aforementioned expression 13 is satisfied in the thermally fully developed region. Accordingly, the temperature difference in the region of the top surface2bof the placing table2corresponding to the thermally fully developed region can be reduced.

In addition, the flow path20according to the present exemplary embodiment is formed such that the aforementioned expression 14 is satisfied in the thermal entrance region. Accordingly, in the placing table2, the temperature difference in the region of the top surface2bof the placing table2corresponding to the thermal entrance region can be reduced.

Besides, the flow path20according to the present exemplary embodiment is formed such that the thickness tw(x) is increased from the outlet opening20btoward the inlet opening20a. By changing the thickness tw(x), the thermal resistance between the top surface2band the flow path20can be changed in the placing table2, so that the temperature difference within the top surface2bcan be reduced.

So far, the exemplary embodiment has been described. It will be appreciated that the exemplary embodiment of the present disclosure is illustrative only and is not intended to be limiting. Various modifications may be made therefrom. Further, the above-described exemplary embodiment may be omitted, substituted or changed in various ways without departing from the scope and spirit of the following claims.

By way of example, the above exemplary embodiment has been described for the example where the placing table2is used as the temperature adjusting device and the temperature difference within the surface of the wafer8and the placing surface6eand the temperature difference within the top surface2bof the base2aare reduced. However, the exemplary embodiment is not limited thereto and may be applied to another component of the plasma processing apparatus100. By way of example, in order to cool the upper electrode, the plasma processing apparatus100may perform a temperature control by circulating a coolant in a flow path provided in the upper electrode. Further, in order to cool the processing vessel1uniformly, the plasma processing apparatus100may perform a temperature control by circulating a coolant in a flow path provided in the sidewall of the processing vessel1. The design method of the exemplary embodiment may be applied to these flow paths for use in the temperature control.FIG.12is a schematic cross sectional view illustrating another example configuration of the plasma processing apparatus100according to the exemplary embodiment. The plasma processing apparatus100has the shower head16serving as the upper electrode. InFIG.12, the shower head16corresponds to the temperature adjusting device. The shower head16is equipped with the main body16aand the ceiling plate16b. The main body16ahas a flat bottom surface, and a flow path220is formed along the bottom surface. The flow path220has, at one end thereof, an inlet opening220aconnected to a coolant inlet line221, and has, at the other end thereof, an outlet opening220bconnected to a coolant outlet line221b. The shower head16reaches a high temperature by receiving heat input from the plasma. The plasma processing apparatus100is configured to control a temperature of the shower head16by allowing a coolant to flow in the flow path220. The design method of the present exemplary embodiment may be applied to this flow path220, and the flow path220may be formed such that a thickness between this flow path220and the bottom surface of the main body16aincreases as it goes from the outlet opening220btoward the inlet opening220a. With this configuration, the flow path220is capable of making the temperature of the bottom surface of the main body16aapproximately uniform, so that the temperature difference within the surface of the shower head16can be reduced.

Further, the above exemplary embodiment has been described for the example where the plasma is the heat source from which the heat is inputted to the placing table2and the heat from the plasma is radiated in the flow path20. However, the exemplary embodiment is not limited thereto. The heat source may not be the plasma. In the placing table2, a heater as the heat source may be provided in the entire placing surface6eto control the temperature of the wafer8. In such a case, by designing the flow path20in consideration of the heat input from the heater as well, the temperature difference within the surface of the wafer8and the placing surface6eand the temperature difference within the top surface2bof the base2acan be reduced even if the heater is provided.

Moreover, the above exemplary embodiment has been described for the example where the placing table2is cooled by circulating the heat transfer medium such as the coolant having a temperature lower than that of the placing table2in the flow path20. However, the exemplary embodiment is not limited thereto. A temperature control of heating the placing table2may be performed by circulating a heat transfer medium having a temperature higher than that of the placing table2in the flow path20. In this case, by altering a sign of the heat flux q″ (q″(x)) or the like appropriately, the temperature difference within the wafer8and the placing surface6eand the temperature difference within the top surface2bof the base2acan be reduced even if the temperature control of heating the placing table2is performed.

Further, the above exemplary embodiment has been described for the example where the number of the flow path20formed in the placing table2is one. However, the exemplary embodiment is not limited thereto. The flow path20may include multiple flow paths provided in a central portion, a middle portion and an outer portion arranged concentrically around the placing table2within the base2a. In such a case, by circulating coolants having different temperatures in the multiple flow paths, the temperature distribution in which the temperature gradient is formed from the center of the placing table2in a diametrical direction and the temperature difference is reduced in the circumferential direction can be achieved.

Moreover, though the above-described plasma processing apparatus100is the capacitively coupled plasma processing apparatus, the exemplary embodiment is applicable to any of various types of plasma processing apparatuses. By way of example, the plasma processing apparatus100may be any of various types such as an inductively coupled plasma processing apparatus, a plasma processing apparatus configured to excite a gas by a surface wave such as a microwave, and so forth.

In addition, though the above-exemplary embodiment has been described for the example where the first RF power supply10aand the second RF power supply10bare connected to the base2a, a configuration of the plasma source may not be limited thereto. For example, the first RF power supply10afor plasma formation may be connected to the shower head16which serves as the upper electrode. Further, the second RF power supply10bfor ion attraction (bias) may not be connected to the base2a.

Further, though the above-described exemplary embodiment is the plasma processing apparatus configured to perform the etching as the plasma processing, the exemplary embodiment may be applicable to a plasma processing apparatus configured to perform any of various types of plasma processings. By way of non-limiting example, the plasma processing apparatus100may be a single-wafer deposition apparatus configured to perform a chemical vapor deposition (CVD), an atomic layer deposition (ALD), a physical vapor deposition (PVD), or the like, or a plasma processing apparatus configured to perform plasma annealing, plasma implantation, or the like.

Furthermore, though the above exemplary embodiment has been described for the example where the semiconductor wafer is used as the substrate, the exemplary embodiment is not limited thereto. By way of example, the substrate may be any of various types, such as a glass substrate.

According to the exemplary embodiment, it is possible to reduce a temperature difference within the first surface.