Virtual sensor for spatially resolved wafer temperature control

Abstract

The present disclosure relates to methods and apparatus for temperature sensing and control during substrate processing. Substrate temperatures that are difficult to measure directly during processing can be determined by examining deposited film properties or by measuring changes in the power output of a substrate heating device over time. The temperatures of many substrates are determined during processing, showing how the substrate temperatures change over time, and then the temperature changes are used to build a model through machine learning techniques. The model is used to adjust the heating device set points for future processing operations.

Description

Background Art Technical Field

[0001] Embodiments of the present disclosure relate to methods and apparatus for temperature sensing and control during substrate processing.

[0002] Description of Related Technology

[0003] In the processing of substrates, the substrate is typically placed on a substrate support in a process chamber while maintaining suitable process conditions in the process chamber to deposit, etch, form a layer on, or otherwise process the surface of the substrate. For example, a high temperature plasma processing environment may be used to process the substrate. It is often desirable to control various process conditions that affect substrate properties during processing, such as substrate temperature.

[0004] As feature sizes of substrates decrease and process complexity increases with advanced nodes, the problem of maintaining the temperature of a substrate being processed at a target substrate temperature is of increasing concern. The processing of substrates in such advanced processes is highly sensitive to temperature fluctuations during processing, and controlling the temperature of the substrate is utilized to achieve a process that exhibits substantially no temperature drift during processing. Additionally, as process chamber components age and are eventually replaced, the thermal properties of the process chamber components change over time, increasing the difficulty of maintaining precise temperature control. Furthermore, it is difficult to directly measure substrate temperature (particularly for plasma-based processes).

[0005] Therefore, there is a need in the art for methods and apparatus for controlling substrate temperature during processing. Summary of the invention

[0006] In one embodiment, a method is provided. The method includes performing a plurality of substrate processing operations on a plurality of substrates in a process chamber, wherein one of the plurality of substrates is processed during each of the plurality of substrate processing operations. The method also includes determining a substrate temperature variation of each of the plurality of substrates during the plurality of substrate processing operations and inputting the measured process variables into a substrate temperature variation model based on the substrate temperature of each of the plurality of substrates, the substrate temperature variation model including:

[0007]

[0008] Where W1 is the first substrate count, W2 is the second substrate count, ΔT i and ΔT o are the total changes in temperature from W1 to W2 in the inner and outer regions, respectively, and and are the rates of change of the inner zone temperature and the outer zone temperature, respectively. The method further comprises controlling one or more of a temperature or a power set point of a heater device in a substrate support of the process chamber in response to an output of the substrate temperature variation model.

[0009] In another embodiment, a method is provided. The method includes: performing a plurality of substrate processing operations on a plurality of substrates in a process chamber, wherein one of the plurality of substrates is processed during each of the plurality of substrate processing operations; determining a temperature of an interior region of each of the plurality of substrates during the plurality of substrate processing operations; and determining a temperature of an exterior region of each of the plurality of substrates during the plurality of substrate processing operations. The method also includes: determining an interior region temperature model based on the temperature of the interior region of each of the plurality of substrates; determining an exterior region temperature model based on the temperature of the exterior region of each of the plurality of substrates; controlling an interior region set point of a heater device in a substrate support of the process chamber based on the interior region temperature model; and controlling an exterior region set point of the heater device in the substrate support of the process chamber based on the exterior region temperature model.

[0010] In another embodiment, a non-transitory machine-readable storage medium is provided. The medium has a computer program stored thereon. The computer program is configured to: determine a substrate temperature variation model based on a substrate temperature of each of a plurality of substrates during each of a plurality of substrate processing operations in a process chamber; and control a set point of a heater device in a substrate support of the process chamber based on the substrate temperature model, the substrate temperature variation model comprising:

[0011]

[0012] Where W1 is the first substrate count, W2 is the second substrate count, ΔT i and ΔT o are the total changes in temperature from W1 to W2 in the inner and outer regions, respectively, and and are the rates of change of the temperature in the inner and outer regions, respectively. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Thus, in a manner that the above-described features of the present disclosure may be understood in detail, a more particular description of the present disclosure briefly summarized above may be obtained by reference to the aspects of the present disclosure, some of which are illustrated in the accompanying drawings. It should be noted, however, that the drawings illustrate only typical aspects of the present disclosure and are therefore not to be considered limiting of its scope, as the disclosure may admit to other equally effective aspects.

[0014] Figure 1 A schematic cross-sectional view of a process chamber according to one embodiment is shown.

[0015] Figure 2 A flow chart of a method according to one embodiment is shown.

[0016] Figure 3 A flow chart of a method according to one embodiment is shown.

[0017] Figure 4A is data plotting substrate counts since a maintenance event versus the optical absorption coefficient of a film deposited on the substrate according to one embodiment.

[0018] Figure 4B is data plotting substrate counts since a maintenance event versus the optical absorption coefficient of a film deposited on the substrate according to one embodiment.

[0019] Figure 5 A schematic cross-sectional view of a substrate support with a heater apparatus according to one embodiment is shown.

[0020] Figure 6 The data is a graph of substrate counts since the maintenance event versus the change in temperature for each successive substrate.

[0021] To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. Additionally, elements in one example may be advantageously adapted for use in other examples described herein. DETAILED DESCRIPTION

[0022] The present disclosure relates to methods and apparatus for substrate temperature sensing and control during substrate processing. The substrate temperature, which is usually difficult to measure directly during processing (particularly in high temperature (e.g., above about 600°C) vacuum plasma processing operations), can be determined by examining the deposited film properties or by measuring the change in power output of the substrate heating device over time. The temperature of many substrates is determined during processing, showing how the substrate temperature changes over time, and then the temperature changes are used to build a model through machine learning techniques. The model is used to adjust the heating device set points for future processing operations.

[0023] It should be noted that the heater temperature may be different from the substrate temperature. When an additional plasma energy source is exposed to the substrate, measuring the substrate temperature with or without the plasma may produce potentially misleading substrate temperature data. In addition, as the process chamber ages over time, maintaining a given heater set point does not guarantee that the substrate temperature will be maintained as desired due to changes in heat transfer between the substrate and the chamber. Therefore, embodiments described herein provide improved substrate temperature control.

[0024] Figure 1 1 is a schematic cross-sectional view of a process chamber 100 according to one embodiment. The process chamber 100 may be a plasma enhanced chemical vapor deposition (PECVD) chamber suitable for depositing chemical vapor deposition (CVD) films on a substrate, such as substrate 154. An example of a process chamber that may be suitable to benefit as described herein is available from Applied Materials, Inc. located in Santa Clara, California. CVD process equipment and PRECISION TM Process Equipment. Other suitably configured process chambers, including process chambers from other manufacturers or for other applications, such as PECVD of substrates such as glass substrates, may also be used in accordance with the embodiments described herein.

[0025] The process chamber 100 can be used for various plasma processes (including deposition processes and removal processes). In one aspect, the process chamber 100 is used to perform CVD using one or more precursor gases with or without a radio frequency (RF) power source. In another embodiment, the process chamber 100 is used for a plasma enhanced chemical vapor deposition (PECVD) process.

[0026] The process chamber 100 includes a chamber body 102, a lid assembly 106, and a substrate support assembly 104. The lid assembly 106 is positioned at an upper end of the chamber body 102. The substrate support assembly 104 is disposed within the interior of the chamber body 102, and the lid assembly 106 is coupled to the chamber body 102 and encloses the substrate support assembly 104 within a process volume 120. The chamber body 102 includes a slit valve opening 126 formed in a sidewall thereof. The slit valve opening 126 is selectively opened and closed to allow substrate transfer in and out of the process volume 120 by a substrate handling robot (not shown). An exhaust port 152 in fluid communication with the process volume 120 is shown extending through the chamber body 102.

[0027] The top electrode 108 is disposed adjacent to the chamber body 102 and separates the chamber body 102 from the other components of the lid assembly 106. The top electrode 108 may be part of the lid assembly 106, or may be a separate sidewall electrode.

[0028] An isolator 110 (which may be a dielectric material such as a ceramic or metal oxide, for example, aluminum oxide and / or aluminum nitride) contacts the top electrode 108 and electrically and thermally separates the top electrode 108 from a gas distributor 112 and the chamber body 102. The gas distributor 112 has an opening 118 for allowing a process gas to enter the process volume 120. The process gas is supplied to the process chamber 100 via a conduit 114, and the process gas enters a gas mixing region 116 before flowing through the opening 118. The gas distributor 112 is coupled to a source of a power supply 142, such as an RF generator. In one embodiment, pulsed RF power is utilized to form a plasma in the process volume 120. In other embodiments, DC power or pulsed DC power is utilized to form a plasma in the process volume 120.

[0029] The substrate support assembly 104 includes a substrate support surface 180 disposed at an upper end thereof. The substrate support assembly 104 is formed of a metal or ceramic material, such as a metal oxide or nitride or oxide / nitride mixture, such as aluminum, aluminum oxide, aluminum nitride, or an aluminum oxide / nitride mixture. The substrate support surface 180 is configured to support the substrate 154 during processing. The substrate support surface 180 is coupled to a lift mechanism via a shaft 144 that extends through a bottom surface of the chamber body 102. The lift mechanism is flexibly sealed to the chamber body 102 via a bellows that prevents vacuum from leaking around the shaft 144. The lift mechanism enables the substrate support surface 180 to be vertically moved within the chamber body 102 between a lower transfer position and one or more elevated process positions.

[0030] An electrostatic chuck (ESC) 160 is disposed in the substrate support assembly 104. The electrostatic chuck 160 includes one or more electrodes 162 and a dielectric material 164. In some embodiments, the dielectric material 164 of the electrostatic chuck 160 forms a substrate support surface 180. Figure 1 The dashed lines in FIG. 1 depict four electrodes 162, however, it is contemplated that a greater or lesser number of electrodes 162 may be utilized in accordance with the embodiments described herein. The dielectric material 164 is a dielectric material suitable for use in an electrostatic chuck. In embodiments of the electrostatic chuck 160, the dielectric material 164 includes an oxide and / or nitride material, such as aluminum oxide, aluminum nitride, or an aluminum oxide / aluminum nitride mixture.

[0031] In one embodiment, the electrodes 162 are embedded in the dielectric material 164. In another embodiment, the electrodes 162 are embedded in the substrate support assembly 104 or coupled to the surface of the substrate support assembly 104. The one or more electrodes 162 can be a plate, a perforated plate, a mesh, a wire mesh, or any other distributed arrangement. The one or more electrodes 162 are coupled to an electrode power supply 166 via an electrode control line 168 to provide power to the electrodes 162 and to help clamp the substrate 154 during processing of the substrate 154.

[0032] Powering the electrode 162 with the electrode power supply 166 generates an electric field to attract the substrate 154 toward the electrode 162 and the substrate support surface 180, thereby securing the substrate 154 to the substrate support surface 180 of the substrate support assembly 104. The electrode power supply 166 may apply a DC voltage to the electrode 162. A leakage current sensor 178 is coupled to the electrode 162 via the electrode power supply 166 to measure a leakage current flowing between the substrate 154 and the electrode 162. In some embodiments, the leakage current sensor 178 is directly coupled to the electrode control line 168.

[0033] In some embodiments, the substrate support assembly 104 includes an additional electrode 162 for use in conjunction with the top electrode 108 to generate plasma during processing of the substrate 154. The use of the top electrode 108 and the additional electrode 162 disposed in or near the substrate support assembly 104 to generate plasma may have a variety of embodiments. Additionally, one or more electrodes 162 may be used in conjunction with the top electrode 108 to generate plasma during processing of the substrate 154.

[0034] In some embodiments, the electrode power supply 166 provides up to about 1000 W (but not limited to about 1000 W) of RF energy at a frequency of, for example, about 13.56 MHz, although other frequencies and powers may be provided depending on the application. The electrode power supply 166 can produce either or both of continuous power or pulsed power. In some aspects, the bias source can be a DC or pulsed DC source. In some aspects, the bias source can provide multiple frequencies, such as 13.56 MHz and 2 MHz.

[0035] The substrate support assembly 104 further includes a heater device 170 disposed therein. The heater device 170 is used to heat the substrate 154 and may incidentally heat the process volume 120 of the process chamber 100 during processing of the substrate 154. The heater device 170 is coupled to a heater power supply 172 via a heater control line 174. The heater device 170 includes a heater element 176 that outputs heat. In one embodiment, the heater element 172 is a resistive heater. A conduit (not shown) in the substrate support assembly 104 provides a passage between the heater device 170 and the substrate support surface 180 and the process volume 120 to facilitate application of heat to the substrate 154. In some embodiments, the heater device 170 is disposed outside the substrate support assembly 104 and proximate to the process volume 120 to heat the substrate 154 during processing operations of processing the substrate 154. In this embodiment, the heater device 170 is disposed in the lid assembly 106.

[0036] A heater temperature sensor 182 is used to determine the temperature of the heater device 170. The heater temperature sensor 182 uses a thermocouple to determine the temperature of the heater device 170. The heater temperature sensor 182 can be other forms of sensors for measuring the temperature of the heater device 170 (including thermistors and lattice vibration sensors). The heater temperature sensor 182 is coupled to a system controller 186 via a sensor control line 184. The system controller 186 is coupled to the heater power supply 172 to control the temperature of the heater device 170. The system controller 186 adjusts the parameters of the heater device 170 to adjust and control the temperature of the heater device 170.

[0037] In one example, the system controller 186 is a general purpose computer that includes memory for storing software. In another example, the system controller 186 is a special purpose computer that is configured to facilitate software to implement control for one or more substrate processing operations. The software includes instructions for controlling the process chamber 100, including the temperature of the heater device 170 to control the temperature of the substrate 154 during processing.

[0038] Over time, as more substrates 154 are processed in the process chamber 100, the substrate temperature may vary during the process, even though the set point of the heater device 170 remains fixed. Such variations in substrate temperature may be due to various heat inputs and outputs to the substrate 154. For example, the radiation boundary conditions of the process chamber 100 may change due to coatings on surfaces of components or aging of components in the process chamber 100, including components surrounding the process volume 120.

[0039] Surfaces of chamber components in the process chamber 100 may be coated by the deposition during processing. The coating may be incrementally increased for each additional process run in a process cycle. Incrementally increasing the coating in the process chamber 100 during each process run may result in changes in the operation of the process chamber 100. For example, a given heater set point may result in a different substrate temperature as the coating becomes thicker.

[0040] The substrate temperature may be affected by various factors. Plasma power may add a heat source to provide thermal energy to the substrate 154 during processing operations. Additionally, certain components in the processing chamber 100 may operate at different temperatures for various reasons, including plasma coupling and variations in the emissivity of various chamber components. Different conditions often result in variations in the heat input to the substrate 154 and the substrate temperature at a selected heater temperature set point during processing operations.

[0041] Figure 2 A flow chart of a method 200 for predicting substrate temperature variation and adjusting a heater device set point according to one embodiment is shown. At operation 201, the method 200 includes performing a plurality of substrate processing operations on a plurality of substrates in a process chamber, wherein one of the plurality of substrates is processed during each of the plurality of substrate processing operations. At operation 202, a substrate temperature of each of the plurality of substrates is determined during the associated substrate processing operation. At operation 203, the determined substrate temperature is used to generate a substrate temperature variation model. At operation 204, the substrate temperature variation model is used to control a set point of a heater device for future substrate processing operations. Thus, the method 200 is capable of adaptive temperature control of a substrate in response to variable process chamber characteristics.

[0042] Figure 3 A flow chart of a method 300 for predicting temperature changes in the inner and outer regions of a substrate and adjusting heater device set points for both the inner and outer regions according to one embodiment is shown. As used herein, the inner region refers to a region including the center of the substrate, and the outer region refers to a region surrounding the inner region and extending to the edge of the substrate. For example, for a circular substrate with a diameter of 300 mm, the inner region may be a circular region with a diameter of 100 mm, and the outer region may be an annular region extending from the edge of the inner region to the edge of the substrate.

[0043] At operation 301, method 300 includes: performing a plurality of substrate processing operations on a plurality of substrates in a process chamber, wherein one of the plurality of substrates is processed during each of the plurality of substrate processing operations. At operation 302, an inner region temperature of each substrate is determined during the associated substrate processing operation. At operation 303, an outer region temperature of each substrate is determined during the associated substrate processing operation of the substrate. At operation 304, an inner region temperature model is established using the determined inner region temperature. At operation 305, an outer region temperature model is established using the determined outer region temperature. At operation 306, the inner region temperature model is used to control an inner region set point of a heater device. And at operation 307, the outer region temperature model is used to control an outer region set point of the heater device.

[0044] At operation 202 of method 200 and at operations 302 and 303 of method 300, the temperature may be determined in a variety of ways. In some embodiments, the substrate processing operation includes depositing a film on substrate 154. For example, the film may be a carbon hard mask. A temperature-dependent property of the film may be measured and the temperature may be determined based on the temperature-dependent property. For example, the temperature-dependent property may be an optical absorption coefficient (optical k) of the film. Figure 4A and Figure 4B 2 is a data graph illustrating this relationship, which shows how the substrate temperature (and therefore the optical k of the deposited film) drifts during subsequent substrate processing operations.

[0045] Figure 4A is a graph of substrate counts since a maintenance event versus the optical absorption coefficient of a film deposited on a substrate according to one embodiment. Data 401 and data 402 are for variables measured in an experimental setup in which the process chamber used was equipped with "new" components (i.e., components that have seen no or little substrate processing operations). Data 401 shows the relationship between the number of substrates in the inner region of the substrate and the relationship between the number of substrates in the outer region of the substrate. Since the optical k of the deposited film depends on the substrate temperature during processing, data 401 and data 402 not only show that the substrate temperature drifts in continuous substrate processing operations, but also show that the inner region temperature drifts faster than the outer region temperature.

[0046] Figure 4Bis a graph of substrate counts since a maintenance event versus the optical absorption coefficient of a film deposited on a substrate, according to one embodiment. Data 403 and data 404 are for variables measured in an experimental setup in which the process chamber used was equipped with "old" parts (i.e., parts that have seen a large number of substrate processing operations). Data 403 shows the relationship of substrate counts for an inner region of the substrate versus optical k, and data 404 shows the relationship of substrate counts for an outer region of the substrate versus optical k. Since the optical k of the deposited film depends on the substrate temperature during processing, data 403 and data 404 not only show that the substrate temperature drifts in consecutive substrate processing operations, but also show that the inner region temperature drifts faster than the outer region temperature.

[0047] In other embodiments, the temperature of operation 202 of method 200 and operations 302 and 303 of method 300 is determined by measuring the power output of the heater device during time intervals during substrate processing operations. Figure 5 and Figure 6 To discuss this method.

[0048] Figure 5 Shows that there is Figure 1 Schematic diagram of a cross-section of a substrate support 104 with a heater device 170. The substrate support 104 supports a substrate 154, and the heater device 170 is disposed in the substrate support 104. The substrate support 104 is divided into an inner region 501 and an outer region 502. The heater device 170 (shown as a resistive heater) includes a separate heater for each region: an inner heater 510 for the inner region 501 and an outer heater 520 for the outer region 502. The inner heater 510 includes a power meter 511, a power supply 512, and a resistive heating element 513. Similarly, the external heater 520 includes a power meter 521, a power supply 522, and a resistive heating element 523. The power supplies 512 and 522 may be Figure 1 The internal heater 510 and the external heater 520 are also coupled to heater temperature sensors (not shown) that are coupled to the heater power supply 172 as shown. Figure 1 Controller 186 shown in .

[0049] During operation, the heater device 170 responds to changes in temperature of the inner region 501 or the outer region 502 by changing the power output of the power supply 512 or the power supply 522. It is contemplated that the change in power output is proportional to the change in temperature. However, due to the frequency of the power supplies 512 and 513 (e.g., 50 Hz), attempting to instantaneously measure the power output results in a noisy data set from which it is difficult to extract the temperature.

[0050] Instead, power meters 511 and 521 record the total power output over a relatively long period of time compared to the cycle period of power supplies 512 and 513. For example, for a 50 Hz power supply, power meters 511 and 521 measure the total power output over a period of time from about 1 second to about 10 minutes, such as about 2 minutes. Therefore, rather than attempting to extract temperature from instantaneous power measurements, temperature changes can be extracted from power output changes across consecutive time intervals. In one embodiment, power meters 511 and 521 measure peak-to-peak power fluctuations, and software communicatively coupled to power meters 511 and 521 calculates average power output to enable lower frequency data acquisition.

[0051] Figure 6 is a graph of the substrate counts since the maintenance event versus the change in temperature for each successive substrate. Regardless of the method used to determine the temperature, the temperature change can then be plotted as a function of the substrate counts since the last maintenance event. Figure 6 , the y-axis is the temperature change of each substrate (multiplied by 100 to normalize the scale) in degrees Celsius. The x-axis is the substrate count since the last maintenance event. Data 601, 602, and 603 are suitable for Figure 4A and Figure 4B The data 601 represents the inner region, the data 603 represents the outer region, and the data 602 represents the average across the substrate 154. Figure 4A and Figure 4B , data 601 and data 603 show that the substrate temperature changes faster in the inner region than in the outer region.

[0052] Once the temperature is determined, either for the entire substrate of method 200 or for the inner and outer regions of method 300, the temperature change over time is used to build a temperature model in operation 203 of method 200 and operations 304 and 305 of method 300. One way to build these models is through machine learning techniques. For example, based on the temperature change data, the following equations can be used to predict the temperature change of the inner and outer regions of the substrates from the first substrate W1 and the second substrate W2:

[0053]

[0054] Where ΔT i and ΔT o are the total changes in temperature from W1 to W2 for the inner and outer regions, respectively. and are the rate of change of the inner zone temperature and the outer zone temperature, respectively, for each wafer count W since the last maintenance event. Note that W is tracked by software and reset at maintenance events. In one embodiment, W1 is the first substrate count and W2 is the second substrate count. Once these models are established, the models can be used to adjust the heater device set points for future substrate processing operations, such as operation 204 of method 200 and operations 306 and 307 of method 300.

[0055] The methods described herein enable numerous improvements to substrate processing operations. The present disclosure provides various methods for indirectly determining substrate temperature. By determining the temperature and building models to predict how the substrate temperature will change over the life of the chamber and components, the heater set points can be adjusted to help keep the substrate temperature within the desired process parameters. Doing so can both reduce maintenance downtime and improve device quality (especially when the process parameters specify a temperature range of only a few degrees Celsius).

[0056] While the foregoing is directed to examples of the present disclosure, other and further examples of the disclosure may be devised without departing from the basic scope thereof; and the scope of the disclosure is determined by the claims that follow.

Claims

1. A method for controlling substrate temperature, comprising: performing substrate processing operations on a plurality of substrates sequentially in a process chamber, wherein one of the plurality of substrates is processed during each substrate processing operation; determining a substrate temperature of each substrate of the plurality of substrates during the substrate processing operation; A substrate temperature variation model is established based on the substrate temperature of each substrate in the plurality of substrates, the substrate temperature variation model comprising: Where W1 is the first substrate count, W2 is the second substrate count, ΔT i and ΔT o are the total changes in temperature from W1 to W2 in the inner and outer regions, respectively, and and are the rates of change of the temperature in the inner and outer regions, respectively; as well as One or more of a temperature or a power set point of a heater device in a substrate support of the process chamber is controlled in response to an output of the substrate temperature variation model.

2. The method of claim 1, wherein the heater device is a resistive heater.

3. The method of claim 1 , wherein the determining a substrate temperature of each substrate of the plurality of substrates further comprises: measuring a temperature-dependent film property of a film deposited on each of the plurality of substrates during the substrate processing operation; as well as The substrate temperature of each substrate of the plurality of substrates is determined based on the temperature-dependent film property. The method of claim 3 , wherein the temperature-dependent film property is the optical absorption coefficient. The method of claim 3 , wherein the film is a carbon hard mask.

6. The method of claim 1 , wherein said determining a substrate temperature of each substrate of said plurality of substrates further comprises: measuring a power output of the heater device during each of a plurality of time intervals during each substrate processing operation; as well as During each time interval of the plurality of time intervals, the substrate temperature of each substrate of the plurality of substrates is determined based on the power output. The method of claim 6 , wherein the power output is measured using a power meter.

8. A method for controlling substrate temperature, comprising: performing substrate processing operations on a plurality of substrates sequentially in a process chamber, wherein one of the plurality of substrates is processed during each substrate processing operation; determining a temperature of an interior region of each of the plurality of substrates during the substrate processing operation; determining a temperature of an outer region of each of the plurality of substrates during the substrate processing operation; determining an interior region temperature model based on the temperature of the interior region of each of the plurality of substrates; determining an outer region temperature model based on the temperature of the outer region of each substrate of the plurality of substrates; controlling an interior zone setpoint of a heater device in a substrate support of the process chamber based on the interior zone temperature model; as well as controlling an outer zone set point of the heater device in the substrate support of the process chamber based on the outer zone temperature model, The internal area temperature model includes: The external area temperature model includes: Where W1 is the first substrate count, W2 is the second substrate count, ΔT i and ΔT o are the total changes in temperature from W1 to W2 in the inner and outer regions, respectively, and and are the rates of change of the temperature in the inner and outer regions, respectively.

9. The method of claim 8, wherein the heater device is a resistive heater.

10. The method of claim 8, wherein determining the temperature of the interior region of each of the plurality of substrates further comprises: measuring a temperature-dependent film property in the interior region of the substrate of a film deposited on each of the plurality of substrates during the substrate processing operation; as well as The interior region temperature of each substrate of the plurality of substrates is determined based on the temperature-dependent film property.

11. The method of claim 8, wherein said determining an outer region temperature of each of said plurality of substrates further comprises: measuring a temperature-dependent film property in the outer region of the substrate of a film deposited on each of the plurality of substrates during the substrate processing operation; as well as The outer region temperature of each substrate of the plurality of substrates is determined based on the temperature-dependent film property.

12. The method of claim 10, wherein the temperature-dependent film property is an optical absorption coefficient.

13. The method of claim 12, wherein the film is a carbon hard mask.

14. The method of claim 11, wherein the temperature-dependent film property is optical absorption coefficient.

15. The method of claim 14, wherein the film is a carbon hard mask.

16. The method of claim 8, wherein determining the temperature of an interior region of each of the plurality of substrates further comprises: measuring a power output of the heater device corresponding to the interior region of the substrate during each of a plurality of time intervals during each substrate processing operation; as well as The interior region temperature of each substrate in the plurality of substrates is determined based on the power output during each time interval in the plurality of time intervals.

17. The method of claim 8, wherein said determining an outer region temperature of each of said plurality of substrates further comprises: measuring a power output of the heater device corresponding to the outer region of the substrate during each of a plurality of time intervals during each substrate processing operation; as well as The outer region temperature of each substrate in the plurality of substrates is determined based on the power output during each time interval in the plurality of time intervals.

18. The method of claim 16, wherein the power output is measured using a power meter.

19. The method of claim 17, wherein the power output is measured using a power meter.

20. A non-transitory machine-readable storage medium having a computer program stored thereon, the computer program being configured to: sequentially performing a plurality of substrate processing operations in the process chamber and determining a substrate temperature variation model based on a substrate temperature of each substrate during each substrate processing operation; controlling a set point of a heater device in a substrate support of the process chamber based on a substrate temperature variation model, the substrate temperature variation model comprising: Where W1 is the first substrate count, W2 is the second substrate count, ΔT i and ΔT o are the total changes in temperature from W1 to W2 in the inner and outer regions, respectively, and and are the rates of change of the temperature in the inner and outer regions, respectively.

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