JP2021005648A - Substrate processing apparatus and substrate processing method - Google Patents

Abstract

To provide a substrate processing apparatus and a substrate processing method capable of easily improving the in-plane uniformity of processing.SOLUTION: A substrate processing apparatus includes a substrate rotating portion that holds and rotates a substrate, a processing liquid discharge portion that discharges processing liquid toward the rotating substrate, and a cooling gas discharge portion that discharges cooling gas to N points (N is an integer of 2 or more) in the radial direction of the rotating substrate.SELECTED DRAWING: Figure 2

Description

The present disclosure relates to a substrate processing apparatus and a substrate processing method.

Conventionally, in the manufacturing process of semiconductor parts, flat displays, electronic parts, etc., the substrate is used in order to remove the oxide film, resist film, etc. formed on the surface of the substrate such as a semiconductor wafer, a liquid crystal substrate, or a disk-shaped storage medium. A substrate processing device for cleaning is used. For cleaning the substrate, for example, a hydrogen peroxide solution (SPM) in which sulfuric acid and hydrogen peroxide solution are mixed is used as a cleaning solution.

In order to improve the uniformity of treatment while reducing the consumption of the treatment liquid, the flow path of the hydrogen peroxide solution is branched into a plurality of flow paths, and the main discharge port and the sub discharge port are provided in the plurality of flow paths. Further, a substrate processing apparatus in which a heater is provided in the middle of the flow path has been proposed (Patent Document 1).

Japanese Unexamined Patent Publication No. 2016-157851

The present disclosure provides a substrate processing apparatus and a substrate processing method capable of easily improving the in-plane uniformity of processing.

The substrate processing apparatus according to one aspect of the present disclosure includes a substrate rotating portion that holds and rotates the substrate, a processing liquid discharging portion that discharges the processing liquid toward the rotating substrate, and the rotating substrate. It has a cooling gas discharge unit that discharges cooling gas at N points in the radial direction (N is an integer of 2 or more).

According to the present disclosure, the in-plane uniformity of the treatment can be easily improved.

It is a figure which shows the substrate processing apparatus which concerns on 1st Embodiment. It is a figure which shows the gas-liquid supply part included in the substrate processing apparatus which concerns on 1st Embodiment. It is a figure which shows the supply path of the cooling gas in the substrate processing apparatus which concerns on 1st Embodiment. It is a flowchart which shows the substrate processing method by the substrate processing apparatus which concerns on 1st Embodiment. It is a figure which shows the temperature distribution of a wafer. It is a schematic diagram which shows the distribution of the flow rate of a cooling gas. It is a flowchart which shows the substrate processing method by the substrate processing apparatus which concerns on 2nd Embodiment. It is a figure which shows the modification of the supply path of a cooling gas.

Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. In each drawing, the same or corresponding configurations may be referred to with the same or corresponding reference numerals and description thereof may be omitted. In the present specification, the term "lower" means vertically downward, and the term "upper" means vertically upward.

(First Embodiment)
First, the first embodiment will be described. FIG. 1 is a diagram showing a substrate processing apparatus according to the first embodiment. FIG. 2 is a diagram showing a gas-liquid supply unit included in the substrate processing apparatus according to the first embodiment. FIG. 3 is a diagram showing a cooling gas supply path in the substrate processing apparatus according to the first embodiment.

As shown in FIG. 1, the substrate processing apparatus according to the first embodiment includes a chamber 2, an outer cup 3, an inner cup 4, a rotary motor 5, and a spin chuck 8. The outer cup has a three-cylindrical shape and is arranged inside the chamber 2. The inner cup 4 is vertically attached to the inside of the outer cup 3. The rotary motor 5 is mounted on the inner center of the inner cup 4. The spin chuck 8 is attached to the tip of the drive shaft 6 of the rotary motor 5 and rotates horizontally while holding the wafer W. An elevating mechanism 9 is connected to the inner cup 4. Wafer W is an example of a substrate. The rotary motor 5, the drive shaft 6, and the spin chuck 8 are included in the substrate rotating portion.

The substrate processing device 1 has a gas-liquid supply unit 10. The gas-liquid supply unit 10 includes a drive unit 11, a cleaning liquid nozzle 20, and a cooling gas nozzle 30. As shown in FIGS. 1 and 2, the cleaning liquid nozzle 20 and the cooling gas nozzle 30 extend in parallel with each other and are fixed to the drive unit 11. The drive unit 11 moves the cleaning liquid nozzle 20 and the cooling gas nozzle 30 above the wafer W in the radial direction of the wafer W. The cleaning liquid nozzle 20 has a cleaning liquid discharge port 21 at the tip thereof. A cleaning liquid supply source 22 is connected to the cleaning liquid nozzle 20 via a flow rate adjusting unit 23. The cooling gas nozzle 30 has N (N is an integer of 2 or more) cooling gas discharge holes 31-1 to 1-31-N above the wafer W. A cooling gas supply source 32 is connected to the cooling gas nozzle 30 via a flow rate adjusting unit 33. As shown in FIG. 3, the cooling gas supply path is branched into N pieces between the cooling gas supply source 32 and the cooling gas discharge holes 31-1 to 31-N, and the flow rate adjusting unit 33 is branched. A flow rate adjusting valve 33-1 to 33-N is provided for each of the N supply paths. That is, the cooling gas discharge holes 31 to 1-31-N are connected to the flow rate adjusting valves 33 to 1-33-N independently of each other. For example, the cleaning liquid is hydrogen peroxide solution (SPM), and the cooling gas is nitrogen (N ₂ ) gas. The cleaning liquid is an example of a treatment liquid. Sulfuric acid hydrogen peroxide solution can be produced by mixing sulfuric acid and hydrogen peroxide solution, but at the time of mixing, sulfuric acid and hydrogen peroxide solution react to generate heat. The degree of heat generation depends on the mixing ratio of sulfuric acid and hydrogen peroxide solution. For example, the temperature of the cleaning liquid in the cleaning liquid supply source 22 is about 100 ° C. to 120 ° C., and the temperature of the cooling gas in the cooling gas supply source 32 is about 20 ° C. to 30 ° C.

The cooling gas discharge hole 31-1 is located directly above the center of rotation of the wafer W when cleaning the wafer W. The cooling gas discharge holes 31 to 1-31-N are arranged toward the drive unit 11 in the order of the cooling gas discharge holes 31-1, the cooling gas discharge holes 31-2, ..., And the cooling gas discharge holes 31-N. ing. The cooling gas discharge holes 31-1 to 1-31-N are arranged at regular intervals, for example. For example, when the diameter of the wafer W is 300 mm, the cooling gas discharge holes 31-1 to 31-N are arranged at regular intervals of 10 mm to 30 mm.

The cleaning liquid nozzle 20 extends in parallel with the cooling gas nozzle 30 as described above. For example, the distance between the cleaning liquid nozzle 20 and the cooling gas nozzle 30 is about 20 mm to 40 mm. Therefore, the cleaning liquid discharge port 21 is separated from the center of rotation of the wafer W by about 20 mm to 40 mm when cleaning the wafer W.

The spin chuck 8 is provided with M temperature sensors 12-1 to 12-M arranged in the radial direction (M is an integer of 2 or more). The temperature sensor 12-1 is located directly below the center of rotation of the wafer W. The temperature sensors 12-1 to 12-M are arranged in the order of the temperature sensor 12-1, the temperature sensor 12-2, ..., The temperature sensor 12-M toward the outer peripheral portion. The temperature sensors 12-1 to 12-M are arranged at regular intervals, for example. For example, when the diameter of the wafer W is 300 mm, the temperature sensors 12-1 to 12-M are arranged at regular intervals of 10 mm to 20 mm. The temperature sensors 12-1 to 12-M each detect the temperature of the portion directly above the wafer W. The number N of the cooling gas discharge holes 31-1 to 31-N and the number M of the temperature sensors 12-1 to 12-M may be equal to or different from each other. The temperature sensors 12-1 to 12-M are, for example, infrared (IR) sensors.

The substrate processing device 1 includes a rotary motor 5, an elevating mechanism 9, a drive unit 11, a flow rate adjusting unit 23, and a control unit 37 that controls the flow rate adjusting unit 33. The temperature detection result by the temperature sensors 12-1 to 12-M is input to the control unit 37. The control unit 37 has, for example, a controller 38 including a CPU (central processing unit) and a storage medium 39 connected to the controller 38. The storage medium 39 stores various setting data and programs, and is composed of a known memory such as a ROM or RAM, or a disk-shaped storage medium such as a hard disk, a CD-ROM, a DVD-ROM, or a flexible disk. Will be done.

Next, the substrate processing method in the first embodiment will be described. The substrate processing apparatus 1 cleans the wafer W according to the substrate processing program recorded on the storage medium 39, as described below. FIG. 4 is a flowchart showing a substrate processing method by the substrate processing apparatus 1 according to the first embodiment.

First, the drive unit 11 drives the cleaning liquid nozzle 20 and the cooling gas nozzle 30 to position the cooling gas discharge hole 31-1 directly above the rotation center of the wafer W (step S11).

Next, the wafer W is rotated, the temperature at the M location of the wafer W is measured by the temperature sensors 12-1 to 12-M, and the temperature distribution of the wafer W is acquired (step S12).

After that, the initial flow rate of the cooling gas discharged from each of the cooling gas discharge holes 31-1 to 1-31-N is set (step S13). The initial flow rate may be equal between the cooling gas discharge holes 31-13 to 31-N, and every cooling gas discharge hole 31 to 1-31-N based on the temperature distribution in the processing of other wafers so far. It may be different from. For example, the flow rate calculated from the first data and the second data in the second embodiment described later may be used.

Subsequently, the flow rate adjusting unit 23 is adjusted to discharge the cleaning liquid from the cleaning liquid discharge port 21, and the flow rate adjusting valves 33 to 1-33-N are adjusted to cool the cooling gas from the cooling gas discharge holes 31 to 1-31-N. Is discharged (step S14).

After that, the temperature of the M portion of the wafer W is measured by the temperature sensors 12-1 to 12-M, and the temperature distribution of the wafer W is acquired (step S15).

Subsequently, the flow rate of the cooling gas discharged from the cooling gas discharge holes 31-1 to 31-N is adjusted so that the temperature detected by the temperature sensors 12-1 to 12-M becomes uniform (step S16). .. For example, among the temperature sensors 12-1 to 12-M, the temperature detected by the temperature sensor 12-M located closest to the edge of the wafer W tends to be the lowest. In this case, the flow rate adjusting valve 33-1 to 33-N is set so that each temperature detected by the temperature sensor 12-1 to 12- (M-1) becomes equal to the temperature detected by the temperature sensor 12-M. adjust.

Then, the processes of steps S15 to S16 are repeated until a predetermined cleaning time elapses (step S17).

When the predetermined cleaning time elapses, the discharge of the cleaning liquid and the discharge of the cooling gas are stopped (step S18), the driving unit 11 drives the cleaning liquid nozzle 20 and the cooling gas nozzle 30, and the cooling gas discharge holes 31-1 are formed in the wafer W. It is retracted from above (step S19).

In this way, the wafer W is cleaned.

Here, the temperature distribution of the wafer W will be described. FIG. 5 is a diagram showing the temperature distribution of the wafer W. FIG. 5A shows the temperature distribution when the cooling gas is not discharged, and FIG. 5B shows the temperature distribution when the cooling gas is discharged. FIG. 5 shows, as an example, the temperature distribution of a wafer W having a diameter of 300 mm. FIG. 6 is a schematic diagram showing the distribution of the flow rate of the cooling gas.

When the cooling gas is not discharged, the wafer W rotates, and the cleaning liquid is discharged at a position separated from the center of rotation of the wafer W by about 20 mm to 40 mm. Further, as the wafer W rotates, the cleaning liquid flows from the vicinity of the center of the wafer W toward the edge due to centrifugal force, and the temperature of the cleaning liquid drops while flowing on the wafer W. Therefore, as shown in FIG. 5A, the temperature of the wafer W is the highest at the temperature T _{2 at} the position where the cleaning liquid is discharged, and the temperature of the wafer W is the lowest at the temperature T ₁ at the edge.

The temperature distribution shown in FIG. 5A can be detected by the temperature sensors 12-1 to 12-M. In the present embodiment, the control unit 37 acquires the detection result by the temperature sensors 12-1 to 12-M, and in order to make the temperature distribution in the plane of the wafer W uniform, as shown in FIG. 6, the cooling gas discharge hole. The flow rate of the cooling gas 40 discharged from each of 31-1 to 1-31-N is controlled through the flow rate adjusting valve 33-1 to 33-N. That is, the flow rate of the cooling gas is maximized near the position where the cleaning liquid is discharged, and the flow rate of the cooling gas is minimized near the edge of the wafer W. As a result, as shown in FIG. 5B, the difference between the temperature of the wafer W at the position where the cleaning liquid is discharged and the temperature at the edge becomes small, and the in-plane uniformity of the temperature of the wafer W is improved. By improving the in-plane uniformity of the temperature of the wafer W, the in-plane uniformity of the etching rate can be improved. As shown in FIG. 6, the cleaning liquid 50 is discharged from the cleaning liquid discharge port 21 at a position separated from the rotation center of the wafer W.

As described above, according to the first embodiment, the in-plane uniformity of the temperature of the cleaning liquid can be easily improved. Therefore, the in-plane uniformity of the cleaning treatment using the cleaning liquid can be easily improved.

It is possible to adjust the in-plane uniformity of the temperature of the cleaning liquid by swinging the cleaning liquid nozzle 20 without using the cooling gas, but in this case, the cleaning liquid nozzle 20 is moved to which place at what timing. Creating a recipe that indicates this becomes complicated.

(Second Embodiment)
Next, the second embodiment will be described. The second embodiment is different from the first embodiment in that the tendency of the temperature change of the cleaning liquid is acquired in advance and the flow rate of the cooling gas is adjusted based on the tendency of the temperature change.

In the second embodiment, data regarding the tendency of the temperature change of the cleaning liquid is stored in the storage medium 39. Specifically, the storage medium 39 stores, as the first data, data showing the temperature distribution of the cleaning liquid that wets and spreads on the wafer W when the cleaning liquid is discharged toward the rotating wafer W. For example, "The temperature at the center of rotation of the wafer W is -1.0 ° C., and the temperature at a position 75 mm away from the center of rotation of the wafer W is -2, based on the temperature of the cleaning liquid directly under the cleaning liquid discharge port 21. Data such as "The temperature at a position 150 mm away from the rotation center of the wafer W at 5 ° C. is -5.0 ° C." is stored. As the second data, the storage medium 39 stores data showing the relationship between the flow rate of the cooling gas when the cooling gas is discharged into the cleaning liquid and the amount of decrease in the temperature of the cleaning liquid. For example, "The temperature of the cleaning liquid drops by 1.0 ° C when the cooling gas is discharged at a flow rate of 0.7 l / m, and by 5.0 ° C when the cooling gas is discharged at a flow rate of 2.0 l / m. Store data such as "to do". The first data and the second data may be stored as a function or may be stored as a table.

The first data and the second data can be easily obtained by, for example, performing a test using a dummy wafer in advance.

Here, the substrate processing method in the second embodiment will be described. The substrate processing apparatus 1 cleans the wafer W according to the substrate processing program recorded on the storage medium 39, as described below. FIG. 7 is a flowchart showing a substrate processing method by the substrate processing apparatus 1 according to the second embodiment.

First, the drive unit 11 drives the cleaning liquid nozzle 20 and the cooling gas nozzle 30 to position the cooling gas discharge hole 31-1 directly above the rotation center of the wafer W (step S21).

Next, the wafer W is rotated, the flow rate of the cooling gas suitable for suppressing the temperature non-uniformity shown in the first data is calculated using the second data, and the calculation result is the cooling gas discharge hole. It is set as the flow rate of the cooling gas discharged from 31 to 1-31-N (step S22).

After that, the flow rate adjusting unit 23 is adjusted to discharge the cleaning liquid from the cleaning liquid discharge port 21, and the flow rate adjusting valves 33 to 1-33-N are adjusted to discharge the cooling gas from the cooling gas discharge holes 31 to 1-31-N. Discharge (step S23).

Then, in the second embodiment, the discharge of the cooling gas at the flow rate set in step S22 is continued until a predetermined cleaning time elapses (step S24).

When the predetermined cleaning time elapses, the discharge of the cleaning liquid and the discharge of the cooling gas are stopped (step S25), the drive unit 11 drives the cleaning liquid nozzle 20 and the cooling gas nozzle 30, and the cooling gas discharge holes 31-1 are formed in the wafer W. It is retracted from above (step S26).

In this way, the wafer W is cleaned.

Also according to the second embodiment, the in-plane uniformity of the temperature of the cleaning liquid can be easily improved, and the in-plane uniformity of the cleaning treatment using the cleaning liquid can be easily improved.

As the first data, different data may be used for each temperature of the cleaning liquid when it is discharged from the cleaning liquid discharge port 21 and reaches the wafer W. For example, the following data may be used.

(1) If the temperature of the cleaning liquid when it reaches the wafer W is 120 ° C., the temperature at the center of rotation of the wafer W is −1.0 ° C., based on the temperature of the cleaning liquid directly under the cleaning liquid discharge port 21. The temperature at a position 75 mm away from the center of rotation of the wafer W is -2.5 ° C, and the temperature at a position 150 mm away from the center of rotation of the wafer W is -5.0 ° C.
(2) If the temperature of the cleaning liquid when it reaches the wafer W is 115 ° C., the temperature at the center of rotation of the wafer W is −0.8 ° C., based on the temperature of the cleaning liquid directly under the cleaning liquid discharge port 21. The temperature at a position 75 mm away from the center of rotation of the wafer W is -2.3 ° C, and the temperature at a position 150 mm away from the center of rotation of the wafer W is -4.5 ° C.

In this case, it is preferable that any of the temperature sensors 12-1 to 12-M is arranged at a position overlapping the cleaning liquid discharge port 21 in a plan view or in the immediate vicinity thereof. This is because the temperature of the cleaning liquid when it reaches the wafer W can be estimated based on the detection result of the temperature sensor arranged at or near the position overlapping the cleaning liquid discharge port 21 in a plan view.

Further, as the first data, different data may be used for each temperature of the cleaning liquid at the edge of the wafer W. For example, the following data may be used.

(1) If the temperature of the cleaning liquid at the edge of the wafer W is 90 ° C, the temperature at the center of rotation of the wafer W is + 4.0 ° C and the cleaning liquid discharge port 21 is based on the temperature of the cleaning liquid at the edge of the wafer W. The temperature directly below is + 5.0 ° C, and the temperature at a position 75 mm away from the center of rotation of the wafer W is + 2.5 ° C.
(2) If the temperature of the cleaning liquid at the edge of the wafer W is 95 ° C, the temperature at the center of rotation of the wafer W is + 3.7 ° C and the cleaning liquid discharge port 21 is based on the temperature of the cleaning liquid at the edge of the wafer W. The temperature directly below is + 4.5 ° C, and the temperature at a position 75 mm away from the center of rotation of the wafer W is + 2.2 ° C.

In this case, it is preferable that the temperature sensor 12-M is arranged at a position overlapping the edge of the wafer W in a plan view or in the immediate vicinity thereof. This is because the temperature of the cleaning liquid at the edge of the wafer W can be estimated based on the detection result of the temperature sensor 12-M.

Further, after starting the discharge of the cleaning liquid and the cooling gas, the detection result of the temperature sensors 12-1 to 12-M may be acquired as appropriate to adjust the flow rate of the cooling gas discharged from the cooling gas discharge hole.

The larger the difference between the temperature of the cleaning liquid and the temperature of the cooling gas, the more difficult it is to finely adjust the temperature of the cleaning liquid by discharging the cooling gas. Therefore, as shown in FIG. 8, a temperature adjusting unit 34 for adjusting the temperature of the cooling gas may be provided between the cooling gas supply source 32 and the flow rate adjusting unit 33. For example, when the cooling gas at room temperature is supplied from the cooling gas supply source 32, the cooling gas may be heated to a temperature of about 50 ° C. to 60 ° C. by the temperature adjusting unit 34. Further, a temperature adjusting unit may be provided for each branched supply path on the cooling gas discharge hole 31-1 to 1-31-N side of the branch point of the cooling gas supply path.

The opening diameters of the cooling gas discharge holes 31-1 to 1-31-N may be equal to or different from each other. For example, the opening diameter of the cooling gas discharge hole closest to the distance from the rotation center of the wafer W to the rotation center of the wafer W of the cleaning liquid discharge port 21 is the largest, and the opening diameter becomes smaller as the distance from the cooling gas discharge hole becomes larger. You may.

Depending on the temperature distribution of the wafer W, it is not necessary to discharge the cooling gas from all of the cooling gas discharge holes 31 to 1-31-N, and the discharge of the cooling gas from some of the cooling gas discharge holes may be stopped. .. Further, the cooling gas may be discharged continuously or intermittently.

The positions of the cleaning liquid nozzle 20 and the cooling gas nozzle 30 need not be fixed during the cleaning process. For example, the time zone in which the cooling gas discharge hole 31-1 is located directly above the rotation center of the wafer W and the cleaning liquid discharge port 21 The time zones may be provided alternately so as to be located directly above the rotation center of the wafer W. Further, a drive unit for driving the cooling gas nozzle 30 and a drive unit for driving the cleaning liquid nozzle 20 are separately provided, and the cooling gas nozzle 30 moves independently of the cleaning liquid nozzle 20 above the wafer W during the cleaning process. You may.

A radiation thermometer or an infrared camera may be used instead of the temperature sensors 12-1 to 12-M. The installation positions of the temperature sensors 12-1 to 12-M, the radiation thermometer, and the infrared camera are not limited as long as the temperature of the wafer W can be detected.

The cooling gas does not have to be discharged to the center of rotation of the wafer W. For example, in a plan view, the center of rotation of the wafer W may be located between the cooling gas discharge hole 31-1 and the cleaning liquid discharge port 21.

Further, the cooling gas may be discharged to the back surface of the wafer W.

Although the preferred embodiments and the like have been described in detail above, the embodiments are not limited to the above-described embodiments and the like, and various embodiments and the like described above are used without departing from the scope of the claims. Modifications and substitutions can be added.

1 Substrate processing device 10 Air / liquid supply unit 11 Drive unit 12-1 to 12-M Temperature sensor 20 Cleaning liquid nozzle 21 Cleaning liquid discharge port 30 Cooling gas nozzle 31-1 to 31-N Cooling gas discharge hole 32 Cooling gas supply source 33 Flow rate adjustment Unit 33-1 to 33-N Flow rate adjustment valve 34 Temperature adjustment unit 37 Control unit 38 Controller 39 Storage medium 40 Cooling gas 50 Cleaning liquid

Claims (10)

The board rotating part that holds and rotates the board,
A processing liquid discharge unit that discharges the processing liquid toward the rotating substrate,
A cooling gas discharge unit that discharges cooling gas to N points (N is an integer of 2 or more) in the radial direction of the rotating substrate, and
A substrate processing apparatus characterized by having. The substrate processing apparatus according to claim 1, further comprising a temperature sensor that detects the temperature of the rotating substrate at M locations (M is an integer of 2 or more) in the radial direction. The substrate processing apparatus according to claim 1 or 2, wherein the cooling gas discharge unit has a nozzle in which N discharge holes are formed. The substrate processing apparatus according to claim 3, wherein the discharge holes are independently connected to a flow rate adjusting valve. The substrate processing apparatus according to any one of claims 1 to 4, wherein the cooling gas discharging unit discharges the cooling gas to at least the rotation center of the substrate. The treatment liquid is hydrogen peroxide solution with sulfuric acid.
The substrate processing apparatus according to any one of claims 1 to 5, wherein the cooling gas is nitrogen gas. The process of holding and rotating the board,
The process of discharging the processing liquid toward the rotating substrate and
A step of discharging a cooling gas having a temperature lower than that of the processing liquid to N points (N is an integer of 2 or more) in the radial direction of the rotating substrate.
A substrate processing method characterized by having. The substrate according to claim 7, wherein the cooling gas is discharged so that the temperature difference of the processing liquid in the radial direction of the processing liquid becomes smaller after the discharge of the cooling gas than before the discharge of the cooling gas. Processing method. A step of detecting the temperature of M points (M is an integer of 2 or more) in the radial direction of the rotating substrate, and
A step of adjusting the flow rate of the cooling gas at each of the N locations based on the detected temperature, and a step of adjusting the flow rate of the cooling gas.
The substrate processing method according to claim 8, wherein the substrate is processed. The first data showing the temperature distribution of the treatment liquid that wets and spreads on the substrate when the treatment liquid is discharged toward the rotating substrate, and the said when the cooling gas is discharged to the treatment liquid. Second data showing the relationship between the flow rate of the cooling gas and the amount of temperature drop of the treatment liquid is acquired in advance.
The substrate processing method according to claim 8, further comprising a step of setting the flow rate of the cooling gas at each of the N locations based on the first data and the second data.

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