Dynamic calibration of a control system that controls a heater

Abstract

A method for dynamically calibrating a heater having multiple zones defined by one or more resistive heating elements includes controlling power to the heater having multiple zones based on a dynamic resistance-temperature (RT) model to control the temperature of the heater to a temperature setpoint. For each of the multiple zones, the method further includes measuring the temperature of the respective zone based on the resistance value of the resistive heating element in the respective zone and the dynamic RT model, measuring a reference temperature for each zone, and incrementally adjusting the resistance value associated with the temperature setpoint provided in the dynamic RT model for each zone to a calibrated resistance value. The method further includes providing the dynamic RT model correlating the calibrated resistance values ​​of the multiple zones to the temperature setpoint as a calibrated RT model.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and the benefit of U.S. Provisional Application No. 62 / 980,738, filed February 24, 2020, the disclosure of which is incorporated herein by reference. [Technical Field]

[0002] The present disclosure relates to calibrating a control system that controls a heater having multiple zones. [Background technology]

[0003] The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.

[0004] A heater typically includes a resistive heating element that defines one or more heating zones. In some applications, the resistive heating element functions both as a heater to generate heat and as a sensor to measure temperature. In one aspect, such a resistive heating element may be defined by a material having a nonlinear temperature coefficient of resistance (TCR), and the temperature of the resistive heating element may be determined based on the resistance of the heating element.

[0005] To control the heater, the control system measures the temperature of the resistive heating element(s) based on their resistance. Specifically, the control system measures the voltage and / or current of the resistive heating element to determine its resistance, and uses data correlating resistance and temperature to determine the temperature of the zone(s). While predefined resistance-temperature (RT) data can be used, even if the resistive heating elements are made of the same material, heaters may operate differently from one another. Variations in RT data can arise, for example, from manufacturing variations, material batch variations, heater aging, number of cycles, and / or other factors, which can introduce errors into the calculated temperature. Other issues related to the use of resistive heaters, such as operating as sensors in multi-zone applications, are addressed by the present disclosure. Summary of the Invention

[0006] This section provides a general summary of the disclosure and is not an exhaustive disclosure of its entire scope or all of its features.

[0007] In one aspect, the present disclosure is directed to a method for dynamically calibrating a heater having multiple zones defined by one or more resistive heating elements. The method includes controlling power to the heater having multiple zones to control the temperature of the heater to a temperature setpoint based on a dynamic resistance-temperature (RT) model. For each of the multiple zones, the method further includes measuring a temperature of the respective zone based on the resistance values ​​of one or more resistive heating elements in the respective zone and the dynamic RT model, measuring a reference temperature for each zone, and incrementally adjusting a resistance value associated with a temperature setpoint provided in the dynamic RT model for each zone to a calibrated resistance value. The method further includes providing the dynamic RT model correlating the calibrated resistance values ​​of the multiple zones with the temperature setpoint as a calibrated RT model.

[0008] In one variation, controlling the power to the heater further includes measuring the resistance of the resistive heating element, determining a temperature of each of the plurality of zones based on the measured resistance and the dynamic RT model for each zone, and adjusting the power to each zone in response to the temperature of each zone differing from the temperature set point until the temperature of each zone is equal to the temperature set point.

[0009] In another variation, when the temperature of each of the plurality of zones is equal to the temperature setpoint, the method further includes applying a voltage pulse to the plurality of zones and measuring a thermal response of the plurality of zones.

[0010] In yet another variation, when the temperature of each of the plurality of zones is equal to the temperature setpoint, the method further includes adjusting an external system variable and measuring a thermal response of the plurality of zones, wherein the external system variable includes a chamber pressure, a backside gas pressure, a gas flow rate, a chamber emissivity, a pedestal emissivity, or a combination thereof.

[0011] In one variation, incrementally adjusting the resistance value further includes determining, for each zone, a resistance adjustment rate based on a predefined gain factor and a difference between a reference temperature associated with each zone and the temperature of each zone.

[0012] In another variation, incrementally adjusting the resistance value further includes decreasing the resistance value associated with each zone when the reference temperature of the respective zone is higher than the temperature of the respective zone, and increasing the resistance value associated with each zone when the reference temperature of the respective zone is lower than the temperature of the respective zone.

[0013] In yet another variation, the reference temperatures of the multiple zones are measured by one or more sensors.

[0014] In one variation, the method further includes applying a nominal measurement voltage to each of the plurality of zones and measuring a cold start resistance for each of the plurality of zones before controlling the temperature of the heater to the temperature setpoint.

[0015] In another variation, the temperature setpoint is selected from among a plurality of temperature setpoints, and a calibrated resistance value for each of the zones is determined for each of the plurality of temperature setpoints, and the dynamic RT model provides a calibrated resistance value for each of the plurality of zones for each of the plurality of temperature setpoints.

[0016] In yet another variation, the method further includes thermally equalizing the reference temperatures of the plurality of zones such that the reference temperature of a first zone is substantially the same as the reference temperature of a second zone associated with the first zone.

[0017] In one variation, the method further includes, for each of the zones, determining whether the temperature of the respective zone is equal to a reference temperature for the respective zone, and in response to the temperature not being equal to the reference temperature, incrementally adjusting the resistance value, and in response to the temperature of the respective zone being equal to the reference temperature, storing the resistance value as a calibrated resistance value for the respective zone.

[0018] In one aspect, the present disclosure is directed to a method for dynamically calibrating a heater having multiple zones defined by one or more resistive heating elements. The method includes controlling power to the heater based on a dynamic resistance-temperature (RT) model to control the temperature of the heater to a temperature setpoint. For each of the multiple zones, the method includes measuring a reference temperature for the respective zone, measuring a zone temperature for each zone based on the resistance values ​​of one or more resistive heating elements in the respective zone and the dynamic RT model, and determining, for each zone, whether the zone temperature is equal to the reference temperature. In response to the zone temperature not equaling the reference temperature, for each zone, incrementally adjusting a resistance value associated with the temperature setpoint of the dynamic RT model, and in response to the zone temperature equaling the reference temperature, providing the resistance value of the dynamic RT model as a calibrated resistance value for the temperature setpoint. The method further includes storing the dynamic RT model as a calibrated RT model in response to providing the calibrated resistance value for each of the multiple zones.

[0019] In one variation, the method further includes thermally equalizing the reference temperatures of the plurality of zones such that the reference temperature of a first zone is substantially the same as the reference temperature of a second zone associated with the first zone.

[0020] In another variation, the resistance value is stored in the dynamic RT model as a calibrated resistance value for the temperature setpoint in response to the zone temperature being equal to the reference temperature and the plurality of reference temperatures being thermally equalized.

[0021] In yet another variation, the temperature setpoint is selected from among a plurality of temperature setpoints, a calibrated resistance value is determined for each of the plurality of temperature setpoints, and the dynamic RT model provides a calibrated resistance value for each of the plurality of zones for each of the plurality of temperature setpoints.

[0022] In one variation, incrementally adjusting the resistance value further includes determining a resistance adjustment rate based on a predefined gain factor and a difference between the reference temperature and the zone temperature of the respective zone.

[0023] In another variation, incrementally adjusting the resistance value of each zone further includes decreasing the resistance value associated with each zone when the reference temperature of the respective zone is higher than the temperature of the respective zone, and increasing the resistance value associated with each zone when the reference temperature of the respective zone is lower than the temperature of the respective zone.

[0024] In one aspect, the present disclosure is directed to a control system for controlling power to a heater having multiple zones, each of the multiple zones defined by one or more resistive heating elements. The control system includes a controller configured to control power to the heater and to determine a temperature of each of the multiple zones based on a calibrated resistance-temperature (RT) model. The controller is configured to perform a dynamic calibration process to define the calibrated RT model. The dynamic calibration process includes performing closed-loop temperature control to maintain a temperature of the heater at a temperature setpoint using the dynamic RT model. For each of the multiple zones, the dynamic calibration process further includes obtaining a reference temperature for the respective zone; thermally equalizing the reference temperature of the respective zone with one or more other reference temperatures by adjusting a resistance value associated with the respective zone in response to the temperature of the heater not equaling the temperature setpoint; and measuring the zone temperature for each zone based on the resistance values ​​of the one or more resistive heating elements in the respective zone and the dynamic RT model for the respective zone. For each zone, determining whether the zone temperature is equal to a reference temperature; incrementally adjusting a resistance value associated with a temperature setpoint provided in the dynamic RT model of the respective zone in response to the zone temperature not being equal to the reference temperature; and providing the resistance value of the dynamic RT model as a calibrated resistance value for the temperature setpoint of the respective zone in response to the zone temperature being equal to the reference temperature and the reference temperature being thermally leveled, wherein the dynamic calibration process further includes storing the dynamic RT model correlating the calibrated resistance values ​​with the temperature setpoints of the plurality of zones as a calibrated RT model.

[0025] In one variation, incrementally adjusting the resistance value further includes determining a resistance adjustment rate based on a predefined gain factor and a difference between the reference temperature and the zone temperature of the respective zone.

[0026] In another variation, incrementally adjusting the resistance value of each zone further includes decreasing the resistance value associated with each zone when the reference temperature of the respective zone is higher than the temperature of the respective zone, and increasing the resistance value associated with each zone when the reference temperature of the respective zone is lower than the temperature of the respective zone.

[0027] Further areas of applicability will become apparent from the description provided herein. It should be understood that the description and specific examples are for purposes of illustration only and are not intended to limit the scope of the present disclosure. [Brief explanation of the drawings]

[0028] In order that the present disclosure may be better understood, various forms thereof will now be described, given by way of example, with reference to the accompanying drawings, in which:

[0029] [Figure 1A] FIG. 1A is a block diagram of a thermal system according to the present disclosure.

[0030] [Figure 1B] FIG. 1B is a block diagram of a control system for the thermal system of FIG. 1A.

[0031] [Figure 1C] Figure 1C shows different variations of the multi-zone heater. [Figure 1D] Figure 1D shows different variations of the multi-zone heater.

[0032] [Figure 2] FIG. 2 is a block diagram of a calibration system according to the present disclosure.

[0033] [Figure 3] FIG. 3 is a functional block diagram of the dynamic calibration control of FIG.

[0034] [Figure 4]FIG. 4 is an example of a resistance-temperature (RT) model for dynamic calibration according to the present disclosure.

[0035] [Figure 5A] FIG. 5A is a flow chart of a dynamic calibration control routine according to the present disclosure. [Figure 5B] FIG. 5B is a flow chart of a dynamic calibration control routine according to the present disclosure.

[0036] [Figure 6] 6 is a flow chart of the closed-loop temperature setpoint control routine of FIG. 5A.

[0037] [Figure 7] 7 illustrates the dynamic adjustment of resistance values ​​provided in the dynamically calibrated RT model of FIG. 4.

[0038] [Figure 8] FIG. 8 is an example of a dynamic calibration graph according to the present disclosure.

[0039] [Figure 9] FIG. 9 is an example of a semiconductor processing lab according to the present disclosure.

[0040] The drawings described herein are for illustrative purposes only and are not intended to limit the scope of the present disclosure in any way. DETAILED DESCRIPTION OF THE INVENTION

[0041] The following description is merely exemplary in nature and is not intended to limit the present disclosure, its application, or uses. It should be understood that throughout the drawings, corresponding reference numerals indicate like or corresponding parts and features.

[0042] The present disclosure is directed to a dynamic calibration control that automatically calibrates a control system that operates a heater while controlling the temperature of a resistive heating element (i.e., filament temperature). Specifically, the dynamic calibration control dynamically changes the resistance of a resistance-temperature (RT) model while the heater is controlled to a temperature setpoint. The RT model relates the resistance of the resistive heating element to a temperature setpoint. The dynamic calibration control incrementally adjusts the resistance of the RT model over time to suppress disturbances and provide a smoother resistance and filament temperature response. Once calibrated, the RT model is used to determine the temperature of each zone of the heater during standard operation and control the thermal performance of the heater.

[0043] To better understand dynamic calibration control, we first provide an example configuration of a thermal system having a multi-zone heater and a control system. While dynamic calibration control is described in connection with a multi-zone heater, the heater may include one or more zones, and is not limited to two or more zones. Referring to FIGS. 1A and 1B, a thermal system 100 includes a multi-zone pedestal heater 102 and a control system 104 having a heater controller 106 and a power converter system 108. In one embodiment, the heater 102 includes a heating plate 110 and a support shaft 112 disposed on the bottom surface of the heating plate 110. The heating plate 110 includes a substrate 111 and multiple resistive heating elements (not shown) embedded in the substrate 111 or disposed along the surface of the substrate 111. In one embodiment, the substrate 111 may be made of ceramic or aluminum. The resistive heating elements are independently controlled by the control system 104 and define multiple heating zones 114, as shown by the dashed lines in FIG. 1A. It will be readily understood that the heating zones can be configured in a variety of suitable ways and can include more than one heating zone while remaining within the scope of this disclosure. For example, Figure 1C illustrates a multi-zone heater 103-A having three zones (Z1-Z3), and Figure 1D illustrates a multi-zone heater 103-B having nine zones (Z1-Z9).

[0044] In one form, the heater 102 is a "two-wire" heater in which the resistive heating element has only two leads operatively connected to it, rather than four, to function as both a heater and a temperature sensor. Such two-wire functionality is disclosed, for example, in U.S. Pat. No. 7,196,295, which is commonly assigned and incorporated herein by reference in its entirety. Typically, in a two-wire system, the resistive heating element is defined by a material that exhibits a resistance that changes with temperature, such that the average temperature of the resistive heating element is determined based on the change in resistance of the resistive heating element. In one embodiment, the resistance of the resistive heating element is calculated by first measuring the voltage across and current through the heating element, and then Ohm's Law is used to determine the resistance. The resistive heating element may be defined by a relatively high temperature coefficient of resistance (TCR) material, a negative TCR material, or in other words, a material with a nonlinear TCR.

[0045] The control system 104 is configured to control the operation of the heater 102, and more particularly, to independently control power to each of the zones 114. In one form, the control system 104 is electrically coupled to the zones 114 via a plurality of terminals 115, with each zone 114 being coupled to two terminals to provide power and sense temperature.

[0046] In one form, the control system 104 is communicatively coupled (e.g., wireless and / or wired communication) to a computing device 117 having one or more user interfaces, such as a display, keyboard, mouse, speakers, touch screen, etc. Using the computing device 117, a user can provide inputs or commands, such as temperature setpoints, power setpoints, commands to execute tests or processes stored by the control system 104, etc.

[0047] The control system 104 is electrically coupled to a power supply 118, which provides an input voltage (e.g., 240V, 208V) to the power converter system 108, via an interlock 120. The interlock 120 controls the power flowing between the power supply 118 and the power converter system 108 and is operable by the heater controller 106 as a safety mechanism to shut off power from the power supply 118. Although illustrated in FIG. 1A, the control system 104 need not include the interlock 120.

[0048] The power converter system 108 regulates the input voltage and outputs an output voltage (V OUT ) to the heater 102. In one embodiment, the power converter system 108 includes multiple power converters 122 (122-1 through 122-N in FIG. 1B ) operable to apply adjustable power to the resistive heating elements in a given zone 114 (114-1 through 114-N in the figures). An example of such a power converter system is described in co-pending application U.S. Serial No. 15 / 624,060, filed June 15, 2017, entitled "POWER CONVERTER FOR A THERMAL SYSTEM," which is commonly owned with the present application, the contents of which are incorporated herein by reference in their entirety. In this embodiment, each power converter includes a step-down converter operable by the heater controller to generate a desired output voltage for one or more heating elements in a given zone 114. Thus, the power converter system is operable to provide a customizable amount of power (i.e., desired power) to each zone 114 of the heater 102. It should be readily understood that other power converter systems may be employed to provide the desired power, and the present disclosure is not limited to the examples provided herein.

[0049] With the use of two-wire heaters, the control system 104 includes multiple sensor circuits 124 (i.e., 124-1 through 124-N in FIG. 1B ) for measuring the electrical properties (i.e., voltage and / or current) of the resistive heating elements, which are then used to determine performance characteristics of the zones 114, such as resistance, temperature, and other suitable information. In one embodiment, a given sensor circuit 124 includes an ammeter 126 and a voltmeter 128 for measuring the current through and the voltage applied to the heating element(s) in the given zone 114, respectively. Although not depicted, additional circuitry, such as shunts and voltage dividers, may be implemented as part of the sensor circuitry for the ammeter 126 and voltmeter 128. In one embodiment, the ammeter 126 and voltmeter 128 are provided as power measurement chips for simultaneously measuring current and voltage regardless of the power applied to the heating elements. In another embodiment, voltage and / or current measurements may be taken at zero crossings, as described in U.S. Pat. No. 7,196,295.

[0050] In one form, the heater controller 106 includes one or more microprocessors and memory for storing computer-readable instructions executed by the microprocessors. In one form, the heater controller 106 is configured to execute one or more control processes in which the controller 106 determines a desired power to be applied to the zone 114, such as 100% of the input voltage, 90% of the input voltage, etc. Exemplary control processes are described in the above-mentioned co-pending application U.S. Serial No. 15 / 624,060 and in co-pending application U.S. Serial No. 16 / 100,585, filed August 10, 2018, entitled "SYSTEM AND METHOD FOR CONTROLLING POWER TO A HEATER," which are commonly owned herewith and the contents of which are incorporated herein by reference in their entireties. In one form, the heater controller 106 executes closed-loop temperature control in which the temperature of the heater 102 is controlled to a temperature setpoint. For example, using the resistance of the resistive heating element and the calibrated RT model 150, the heater controller 106 determines the temperature of the zone 114 and then adjusts the power to the zone 114 to bring the temperature of the zone 114 closer to the temperature setpoint.

[0051] In one form, the calibrated RT model 150 correlates resistance values ​​for a given zone with one or more temperature setpoints. The calibrated RT model may be provided as one or more look-up tables that correlate calibrated resistance values ​​to temperature setpoints for each zone 114. The calibrated RT model 150 may also be provided as one or more algorithms that describe the nonlinear relationship between temperature and resistance.

[0052] In one form, the heater controller 106 is configured to include a dynamic calibration control 152 that dynamically calibrates the resistance values ​​of the resistive heating elements at one or more temperature setpoints to provide a calibrated RT model. As described further herein, the dynamic calibration control 152 controls the temperature setpoints of the heater 102 based on the dynamic RT model and incrementally adjusts the resistance values ​​associated with the temperature setpoints in the dynamic RT model to drive the temperature of each zone toward its respective reference temperature. The reference temperature is measured using at least one discrete sensor, such as a thermocouple (TC), a TC wafer having multiple TCs embedded in the wafer, an infrared camera, an array of temperature probes, and / or other suitable discrete sensor.

[0053] 2, calibration system 200 is configured to provide dynamic calibration control of a thermal system including a control system 206 and a two-zone pedestal heater 208, which is a two-wire heater. In one form, control system 206 is similar to control system 104 for controlling the two-wire heater and includes a heater controller 210, which is similar to heater controller 106. Heater controller 210 includes a calibration RT model 212 that correlates the resistance value of each zone with one or more temperature setpoints, and a dynamic calibration control 214 for calibrating two-zone heater 208 as described herein.

[0054] The heater 208 includes a plurality of resistive heating elements 220 that define a two-zone heater having an inner zone (IZ) generally identified by reference numeral 222 and an outer zone (OZ) generally identified by reference numeral 224. Hereinafter, the inner zone 222 and the outer zone 224 may be collectively referred to as zones 222, 224. Although two zones are illustrated, the heater 208 may include one or more zones, and a zone may be defined by one or more resistive heating elements.

[0055] As provided above, in a two-wire heater, the control system 206 is configured to determine the temperature of each zone 222, 224 based on the resistance of the resistive heating element 220 provided in each zone 222, 224 and a resistance-temperature (RT) model. Hereinafter, the temperatures of the inner zone 222 and the outer zone 224 may be collectively referred to as the zone temperature, and individually referred to as the inner temperature and the outer temperature.

[0056] The calibration system 200 further includes one or more discrete reference sensors for measuring a reference temperature for each of the zones 222, 224. Here, the reference sensors include a central TC 226 integrated with the heater 208 and a TC wafer 228 disposed along the surface of the heater 208. The central TC 226 and the TC wafer 228 are communicatively coupled to the heater controller 210 via an input / output interface (not shown). The central TC 226 measures the temperature at the center of the heater 208, which is the reference temperature associated with the inner zone 222.

[0057] The TC wafer 228 includes multiple TCs 229 distributed within the wafer 230 to obtain multiple temperature measurements along the surface of the heater 208. The TCs 229 located in specific areas of the wafer 230 are associated with respective zones 222, 224 of the heater 208. In one embodiment, for each of the zones 222, 224, the temperature measurements acquired by the TCs 229 in the respective zones 222, 224 are aggregated and averaged to provide a reference temperature for the respective zone. Thus, instead of measurements from the central TC 226, the reference temperature for the inner zones may be based on measurements from the TC wafer 228. It will be readily understood that other reference sensors may be employed. For example, in one variation, an infrared camera is positioned above the heater 208 to acquire a thermal image of the heater 208. Each zone of the heater 208 is associated with a respective portion of the thermal image to obtain a reference temperature for the zone.

[0058] In one form, a virtual TC temperature in the outer zone 224 may be determined as a reference temperature for the outer zone based on temperature measurements from the TC wafer 228 and the central TC 226. Specifically, the virtual TC temperature may be determined as T_VTC=(T_CTC-T_IW)+T_OW, where "T_VTC" is the virtual thermocouple temperature, "T_CTC" is the temperature detected by the central TC 226, "T_IW" is the temperature of the inner portion of the TC wafer and is based on the TC of the TC wafer 228 associated with the inner zone 224 of the heater 208, and "T_OW" is the temperature of the outer portion of the TC wafer 228 and is based on the TC of the TC wafer 228 associated with the outer zone 224 of the heater 208. Hereinafter, the reference temperatures associated with the inner and outer zones may be provided as inner reference temperature and outer reference temperature, respectively.

[0059] 3, in one form, the dynamic calibration control 214 provides an RT calibration 302, a closed-loop temperature setpoint control 304 that operates in a manner similar to the closed-loop temperature control described above, and a dynamic RT model 306. The dynamic RT model 306 may be the same as the current calibration RT model 212 used to control the heater 208 and is provided in temporary storage of the heater controller 210. FIG. 4 provides an exemplary dynamic RT model as a table 400 that associates multiple temperature setpoints with resistance values ​​of the resistive heating elements ("RHE" in FIG. 4) that define the inner and outer zones 222, 224.

[0060] The RT calibration 302 is configured to select a temperature setpoint to be calibrated and determine a calibration resistance value for the temperature setpoint for each zone 222, 224. Specifically, the closed-loop temperature setpoint control 304 operates the heater 208 to the selected temperature setpoint using the dynamic RT model 306. Once at the selected temperature setpoint, the RT calibration 302 determines a reference temperature for each zone 222, 224 based on data from a reference sensor.

[0061] In one form, as the closed-loop temperature setpoint control 304 ramps the temperature of the heater 208 to a selected temperature setpoint, the RT calibration 302 thermally equalizes the reference sensor. More specifically, the reference temperature of each zone is controlled (i.e., adjusted) to be substantially the same as the temperature of one or more selected adjacent zones. For example, with respect to the heater 208, the RT calibration 302 compares an inner reference temperature with an outer reference temperature. If the inner reference temperature is higher or lower than the outer reference temperature, the resistance of the resistive heating element of the outer zone is adjusted (i.e., decreased or increased) so that the outer reference temperature is substantially the same as the inner reference temperature. Thus, the thermal profile of the reference sensor, and therefore the heater 208, is substantially uniform. Thermally equalizing the reference sensor during ramping may reduce or prevent the possibility of physical damage, such as cracking, to the heater 208. In another example, for the three-zone heater 103-A of FIG. 1C, the reference temperature of Z2 is thermally equalized to the reference temperature of Z1, and the reference temperature of Z3 is thermally equalized to the reference temperature of Z2. In yet another example, for the nine-zone heater 103-B of FIG. 1D, the reference temperatures of Z2 through Z9 are thermally equalized to the reference temperature of Z1. Alternatively, the reference temperature of each outer zone (i.e., Z2 through Z9) is thermally equalized to the reference temperature of Z1 and selected adjacent outer zones. Thus, the reference temperature of a zone (e.g., zone 1) is thermally equalized to the reference temperature of its associated adjacent zone (e.g., zone 2).

[0062] With the zone temperatures at the selected temperature setpoints, the RT calibration 302 converges the zone temperatures to a reference temperature. Specifically, the resistive heating element 220 of each zone 222, 224 is driven toward a target temperature, which may be the reference temperature or a temperature within a convergence band based on the reference temperature (e.g., the reference temperature ±0.5°C; the reference temperature ±(0.5% * reference temperature)). For each zone 222, 224, the RT calibration 302 determines whether the target temperature for the given zone differs from the temperature of the resistive heating element 220 of the zone 222, 224 (i.e., the "zone temperature") and performs incremental resistance control to adjust the resistance value provided in the dynamic RT model. Specifically, if the target temperature of the respective zone is higher than the temperature of the resistive heating element 220 of the respective zone, the resistance value in the dynamic RT model 306 is gradually decreased. If the target temperature of the respective zone is lower than the temperature of the resistive heating element 220, the resistance value is incrementally increased. By incrementally adjusting the resistance values ​​associated with the temperature setpoints, the dynamic calibration control 214 can reduce or suppress temperature spikes that could induce faults. For example, the resistance values ​​provided in table 400 of FIG. 4 may be adjusted every second in defined increments provided by the following equation, where T_RHE is the temperature of the respective zone, Ref_Temp is the reference temperature associated with the respective zone, and GF is a gain factor that can be predefined based on various characteristics of the thermal system (e.g., 0.5 milliohms per second, among others): Defined Increment = I(T_RHE-Ref_Temp) / GF)I.

[0063] Once the resistive heating elements in the inner zone 222 and outer zone 224 reach the target temperature (e.g., the reference temperature or a temperature within the convergence zone), the resistance value of the temperature setpoint is considered calibrated, and RT calibration 302 continues to the next temperature setpoint of the dynamic RT model 306 to calibrate the resistance value. After each temperature setpoint is calibrated, the dynamic RT model 306 is stored as the calibrated RT model 212 for use during normal operation of the pedestal heater 208.

[0064] 5A, 5B, and 6, an exemplary dynamic calibration control routine 500 is provided that can be executed by the control system (104, 206) of the present disclosure to calibrate the multi-zone heater (102, 208). Prior to execution, reference sensor(s), such as the TC wafer 228 and / or the central TC 226, are placed on the heater 208. The dynamic calibration control routine 500 is merely one example of the dynamic calibration control of the present disclosure, and other suitable routines may be used to implement the dynamic calibration control of the present disclosure.

[0065] When the heater 102, 208 is in a cold state, the control system 104, 206 applies a nominal measurement voltage (e.g., 5 V) to the resistive heating element at 502. In one embodiment, the nominal measurement voltage provides enough power to measure the voltage and / or current but prevents the resistive heating element from generating heat. At 504, the control system uses data from the sensor circuit to measure the resistance of the resistive heating element in each zone of the heater 102, 208 and correlates the measured resistance with a cold-state temperature provided in the dynamic RT model. For example, in FIG. 4, the cold-state temperature is provided as 20.35°C, and the associated resistances of the inner and outer zones are recorded. At 504, the control system 104, 206 also measures a reference temperature associated with each of the zones. The cold-start measurement provides a homogeneity measurement of the resistive heating element and reference sensor and may serve as a first temperature setpoint measurement. While the reference temperature is not shown, this data may be stored as part of the dynamic RT model.

[0066] In 506, the control system sets the control temperature setpoint to the i-th calibration temperature setpoint or next calibration point based on the dynamic RT model. For example, in Figure 4, the dynamic RT model would be calibrated for four temperature setpoints with the next calibration setpoint being 250°C. In 508, the control system executes the closed-loop temperature setpoint control 600 provided in Figure 6.

[0067] 6, the control system 104, 206 applies power to each zone at 602 and 604 and measures the resistance of the resistive heating element in each zone as described above. At 606, the control system 104, 206 determines the zone temperature (i.e., the temperature of the resistive heating element for each zone) based on the measured resistance for each zone and the dynamic RT model. For each of the zones, the control system 104, 206 determines at 608 whether the zone temperature is equal to the control temperature setpoint. If not, at 610, the power to the particular zone is adjusted so that the zone temperature is equal to the control temperature setpoint. The control system then returns to 604 and continues to control the temperature of each zone to the control temperature setpoint.

[0068] Returning to FIG. 5A , when the control system 104, 206 executes the closed-loop temperature setpoint control 600, the system continues the dynamic calibration control routine 500 to determine whether the zone temperature is at the control temperature setpoint. Thus, at 510, the control system 104, 206 measures the resistance of the resistive heating element for the zone and, at 511, thermally equalizes the reference sensor as described above. At 512, the control system 104, 206 determines the zone temperature based on the zone's resistance and the dynamic RT model. At 514, the control system determines, for each of the zones, whether the zone temperature is equal to the control temperature setpoint. If not, the control system returns to 510 and waits until the zone reaches the control temperature setpoint.

[0069] In one embodiment, once a zone reaches its control temperature setpoint, the control system maintains the zone temperature for a set period of time (e.g., 2 minutes, 5 minutes, etc.) to allow the calibration system to equalize and stabilize before driving the zone temperature to the target temperature, more specifically, the reference temperature described herein. Referring to FIG. 5B , at 516, the control system 104, 206 measures the reference temperature of each zone using one or more reference sensors and determines at 518 whether each zone temperature is equal to its respective reference temperature. If not, for a given zone that is not equal to its respective reference temperature, the control system 104, 206 incrementally adjusts the resistance setpoint provided in the dynamic RT model at 520 to converge the zone temperature with the reference temperature. As provided above, in one embodiment, the control system 104, 206 determines the resistance adjustment rate based on a predefined gain factor and the difference between the reference temperature associated with the zone and the zone temperature. In one embodiment, if the reference temperature associated with the zone is higher than the zone temperature, the resistance value is incrementally decreased. Alternatively, the resistance value is increased incrementally when the reference temperature associated with the zone is lower than the zone temperature.

[0070] For example, referring to FIG. 4, if the temperature of the inner zone is not equal to the inner reference temperature, the control system incrementally changes the resistance by 61.20 Ω for a given temperature setpoint (250°C). That is, FIG. 7 illustrates a dynamic RT model 700 in which the resistance of the inner zone is adjusted to 61.15 Ω. Keeping in mind that the control systems 104, 206 are simultaneously performing closed-loop temperature setpoint control 600, the heaters 102, 208 use the adjusted resistance to control the temperature of the inner zone to the control temperature setpoint, thereby converging the reference temperature and the zone temperature. The resistance is incrementally adjusted at the rate determined above until the reference temperature and the zone temperature maintained at the temperature setpoint are the same. In steps 518 and 520, instead of comparing the zone temperature to the reference temperature and converging to the reference temperature, the control systems 104, 206 can compare the zone temperature to a temperature within a defined convergence zone based on the reference temperature and converge. In this manner, the zone temperature is more generally compared to and converged to a target temperature.

[0071] Referring back to FIG. 5B, once the zone temperatures are equal to or within their respective convergence bands, the control system 104, 206 saves the resistance value provided in the dynamic RT model for the control temperature setpoint as the calibrated resistance value at 522. At 524, the control system determines whether all calibration setpoints have been processed. For example, in FIG. 4, the control system determines that two of the four temperature setpoints have been calibrated and therefore can proceed to the next temperature setpoint (i.e., 450°C). Thus, at 526, the control system sets the control temperature setpoint to the ith calibration setpoint and returns to 510. Alternatively, if all calibration setpoints have been processed, the control system terminates closed-loop temperature setpoint control at 528 and saves the dynamic RT model as the calibrated RT model.

[0072] It should be readily understood that routines 500 and 600 can be configured in a variety of suitable ways and should not be limited to the steps described herein. For example, dynamic calibration control routine 500 may not include a thermal leveling step. Thus, at 520, the control system simply converges the zone temperatures to the reference temperature.

[0073] It should be readily understood that the temperature setpoints and resistance values ​​provided in FIGS. 4 and 7 are for illustrative purposes only, and that the calibrated RT model can define other temperature setpoints and any number of temperature setpoints.

[0074] Referring to FIG. 8, dynamic calibration graph 800 illustrates an example of the convergence of zone temperatures and reference temperatures as resistance values ​​are modified during dynamic calibration control. Here, line 802 illustrates the temperature of the resistive heating element in zone 1, and line 804 illustrates the reference temperature associated with zone 1. During a cold start (e.g., approximately 25°C), the initial resistance value of zone 1 would be recorded and stored in the dynamic RT model. The temperature of zone 1 would then be controlled to the next temperature setpoint (e.g., 100°C). When zone 1 reaches 100°C (near point A in FIG. 8), the control system would recognize that the zone temperature and the reference temperature are not the same and would begin adjusting the resistance value associated with zone 1's temperature setpoint in the dynamic RT model at a predetermined rate (e.g., 0.5 milliohms per second or other suitable rate). Once the reference and zone temperatures have converged (graph 800 At approximately point B), the control system will store the resistance value associated with the 100°C setpoint as the calibrated resistance value for the first zone and continue until the next temperature setpoint (e.g., 200°C).

[0075] In one aspect, the dynamic calibration control may be configured to measure the thermal response of the heater when the power to the heater is adjusted and / or when an external system variable is adjusted. For example, with the zone temperature at the temperature setpoint, the control system may apply a voltage or energy pulse to each of the zones and measure the thermal response of the zone.

[0076] Referring to FIG. 9 , in an exemplary application, the control system of the present disclosure is provided in a semiconductor process lab 900, which includes at least one chamber 902 having one or more heaters (not shown) disposed therein. The heaters may be configured in a manner similar to heaters 102 and 208. Although not shown, one or more control systems similar to control systems 104 and 206 are provided to control the heaters. The lab 900 includes other subsystems for processing semiconductor wafers, which may affect the thermal response of the heaters. For example, a fluid line system having delivery lines 904 and exhaust lines 906 transports process gases to and from the chamber 902. Gas flow rates and even pressures within the chamber are exemplary external system variables. With the zone temperatures at temperature setpoints, one or more external system variables may be adjusted by the respective subsystems, and the control system measures the thermal response of the heater zones. The external system variables may include, but are not limited to, chamber pressure, backside gas pressure, emissivity of the chamber 902, and / or emissivity of the pedestal. It should be readily understood that the lab 900 includes other subsystems that may affect the operation of the heater, and the present disclosure should not be limited to the examples provided herein.

[0077] The dynamic calibration control of the present disclosure performs live calibration of the RT model used by the control system to determine the heater temperature. Thus, the dynamic calibration control improves the accuracy of the RT model and temperature measurements. Furthermore, incremental adjustments made to the resistance value can reduce or suppress erroneous measurements (e.g., temperature spikes) and improve the accuracy of the calibrated resistance value.

[0078] While specific components are shown and described, it should be readily understood that the thermal system may include other components while remaining within the scope of the present disclosure. For example, in one aspect, the control system may include electronic components that isolate low voltage components from high voltage components and allow the components to exchange signals.

[0079] As used herein, the term "controller" can refer to, be a part of, or include an application specific integrated circuit (ASIC), digital, analog, or mixed analog / digital discrete circuitry, a digital, analog, or mixed analog / digital integrated circuit, a combinational logic circuit, a field programmable gate array (FPGA), a processor circuit (shared, dedicated, or group) that executes code, a memory circuit (shared, dedicated, or group) that stores code executed by the processor circuitry, other suitable hardware component that provides the described functionality, or a combination of some or all of the above, such as a system-on-chip.

[0080] The term memory is a subset of the term computer-readable medium. As used herein, the term computer-readable medium does not encompass transient electrical or electromagnetic signals propagating through a medium (such as on a carrier wave); therefore, the term computer-readable medium is considered to be tangible and non-transitory.

[0081] Unless expressly indicated otherwise herein, all numerical values ​​expressing mechanical / thermal properties, compositional proportions, dimensions and / or tolerances, or other properties are to be understood as being modified by the word "about" or "approximately" in describing the scope of this disclosure. This modification may be desirable for various reasons, including industrial practices; material, manufacturing, and assembly tolerances; and testing capabilities.

[0082] As used herein, the phrase at least one of A, B, and C should be construed to mean a logical non-exclusive OR (A OR B OR C), and not to mean "at least one of A, at least one of B, and at least one of C."

[0083] The description of the present disclosure is merely exemplary in nature and, thus, variations that do not depart from the substance of the disclosure are intended to be within the scope of the disclosure. Such variations are not to be regarded as departing from the spirit and scope of the disclosure. The inventions described in the original claims of this application are set forth below. [Appendix 1] A method for dynamically calibrating a heater having multiple zones defined by one or more resistive heating elements, comprising: controlling power to a multi-zone heater based on a dynamic resistance-temperature (RT) model to control the temperature of the heater to a temperature setpoint; For each of the plurality of zones, measuring a temperature of each zone based on the resistance of the one or more resistive heating elements in each zone and the dynamic RT model; measuring a baseline temperature for each of said zones; incrementally adjusting a resistance value associated with the temperature setpoint provided in the dynamic RT model of the respective zone to a calibrated resistance value; providing the dynamic RT model correlating the calibrated resistance values ​​of the plurality of zones with the temperature setpoints as a calibrated RT model; A method comprising: [Appendix 2] measuring the resistance of the resistive heating element; determining the temperature of each of the plurality of zones based on the measured resistance and the dynamic RT model for each zone; adjusting power to the respective zone in response to the temperature of the respective zone differing from the temperature setpoint until the temperature of the respective zone is equal to the temperature setpoint; 2. The method of claim 1, further comprising: [Appendix 3] When the temperature of each of the plurality of zones is equal to the temperature setpoint, the method includes applying a voltage pulse to the plurality of zones and measuring a thermal response of the plurality of zones; 3. The method of claim 2, further comprising: [Appendix 4] When the temperature of each of the plurality of zones is equal to the temperature setpoint, the method further includes adjusting an external system variable and measuring a thermal response of the plurality of zones, the external system variable comprising a chamber pressure, a backside gas pressure, a gas flow rate, a chamber emissivity, a pedestal emissivity, or a combination thereof. The method described in Appendix 2. [Appendix 5] Incrementally adjusting the resistance value includes determining, for each of the zones, a resistance adjustment rate based on a predefined gain factor and a difference between the reference temperature associated with the respective zone and the temperature of the respective zone; 2. The method of claim 1, further comprising: [Appendix 6] Incrementally adjusting the resistance value decreasing a resistance value associated with the respective zone when the reference temperature of the respective zone is greater than the temperature of the respective zone; increasing the resistance value associated with the respective zone when the reference temperature of the respective zone is lower than the temperature of the respective zone; 2. The method of claim 1, further comprising: [Appendix 7] 2. The method of claim 1, wherein the reference temperatures of the multiple zones are measured by one or more sensors. [Appendix 8] applying a nominal measurement voltage to each of the plurality of zones; measuring a cold start resistance for each of the plurality of zones before controlling the temperature of the heater to the temperature setpoint; 2. The method of claim 1, further comprising: [Appendix 9] the temperature setpoint is selected from among a plurality of temperature setpoints, and the calibrated resistance value for each of the zones is determined for each of the plurality of temperature setpoints; the dynamic RT model provides the calibrated resistance values ​​for each of the plurality of zones for each of the plurality of temperature setpoints. The method described in Appendix 1. [Appendix 10] thermally equalizing the reference temperatures of the plurality of zones such that the reference temperature of a first zone is substantially the same as a reference temperature of a second zone associated with the first zone. The method described in Appendix 1. [Appendix 11] For each of said zones: determining whether the temperature of the respective zone is equal to the reference temperature for the respective zone, and in response to the temperature not being equal to the reference temperature, the resistance value being incrementally adjusted; storing the resistance value as the calibrated resistance value for the respective zone in response to the temperature of the respective zone being equal to the reference temperature; 2. The method of claim 1, further comprising: [Appendix 12] 1. A method for dynamically calibrating a heater having multiple zones defined by one or more resistive heating elements, comprising: controlling power to the heater based on a dynamic resistance-temperature (RT) model to control the temperature of the heater to a temperature setpoint; For each of the multiple zones, measuring a baseline temperature for each zone; measuring a zone temperature for each of the zones based on the resistance of the one or more resistive heating elements in the respective zones and the dynamic RT model; for each said zone, determining whether said zone temperature is equal to said reference temperature; In response to the zone temperature not being equal to the reference temperature, incrementally adjusting a resistance value associated with the temperature setpoint of the dynamic RT model for the respective zone; providing the resistance value of the dynamic RT model as a calibrated resistance value for the temperature setpoint in response to the zone temperature being equal to the reference temperature; and storing the dynamic RT model as a calibrated RT model in response to the calibrated resistance value being provided for each of the plurality of zones. A method comprising: [Appendix 13] 13. The method of claim 12, further comprising thermally equalizing the plurality of reference temperatures of the plurality of zones such that the reference temperature of a first zone is substantially the same as a reference temperature of a second zone associated with the first zone. [Appendix 14] 14. The method of claim 13, wherein the resistance value is stored in the dynamic RT model as a calibrated resistance value for the temperature setpoint in response to the zone temperature being equal to the reference temperature and the plurality of reference temperatures being thermally equalized. [Appendix 15] the temperature setpoint is selected from among a plurality of temperature setpoints, and a calibrated resistance value is determined for each of the plurality of temperature setpoints; 13. The method of claim 12, wherein the dynamic RT model provides the calibrated resistance value for each of the plurality of zones for each of the plurality of temperature setpoints. [Appendix 16] 13. The method of claim 12, wherein incrementally adjusting the resistance value further comprises determining a resistance adjustment rate based on a predefined gain factor and a difference between the reference temperature and the zone temperature of the respective zone. [Appendix 17] Incrementally adjusting the resistance value of each of the zones comprises: decreasing a resistance value associated with the respective zone when the reference temperature of the respective zone is greater than the temperature of the respective zone; increasing the resistance value associated with the respective zone when the reference temperature of the respective zone is lower than the temperature of the respective zone; 13. The method of claim 12, further comprising: [Appendix 18] 1. A control system for controlling power to a heater having a plurality of zones, each of the plurality of zones being defined by one or more resistive heating elements, the control system comprising: a controller configured to control power to the heater and to determine a temperature of each of the plurality of zones based on a calibrated resistance-temperature (RT) model, the controller configured to perform a dynamic calibration process to define the calibrated RT model, the dynamic calibration process comprising: performing closed-loop temperature control to maintain the temperature of the heater at a temperature setpoint using a dynamic RT model; For each of the plurality of zones Obtaining the reference temperature for each zone; adjusting the resistance associated with the respective zone in response to the temperature of the heater not being equal to the temperature setpoint to thermally equalize the reference temperature of the respective zone with one or more other reference temperatures; measuring a zone temperature for each of the zones based on the resistance of the one or more resistive heating elements in the respective zones and the dynamic RT model for the respective zones; for each said zone, determining whether said zone temperature is equal to said reference temperature; incrementally adjusting the resistance value associated with the temperature setpoint provided in the dynamic RT model for the respective zone in response to the zone temperature not being equal to the reference temperature; providing the resistance value of the dynamic RT model as a calibrated resistance value for the temperature setpoint of the respective zone in response to the zone temperature being equal to the reference temperature and the reference temperature being thermally equalized; storing the dynamic RT model correlating the calibrated resistance values ​​with the temperature setpoints of the plurality of zones as the calibrated RT model; A control system comprising: [Appendix 19] 19. The control system of claim 18, wherein incrementally adjusting the resistance value further comprises determining a resistance adjustment rate based on a predefined gain factor and a difference between the reference temperature and the zone temperature of the respective zone. [Appendix 20] Incrementally adjusting the resistance value of each of the zones comprises: decreasing a resistance value associated with the respective zone when the reference temperature of the respective zone is greater than the temperature of the respective zone; increasing a resistance value associated with the respective zone when the reference temperature of the respective zone is lower than the temperature of the respective zone; 19. The control system of claim 18, further comprising:

Claims

1. 1. A method for dynamically calibrating a heater having multiple zones defined by one or more resistive heating elements, comprising: controlling power to a multi-zone heater based on a dynamic resistance-temperature (RT) model to control the temperature of the heater to a temperature setpoint; For each of the plurality of zones, measuring a temperature of each zone based on the resistance of the one or more resistive heating elements in each zone and the dynamic RT model; measuring a baseline temperature for each of said zones; incrementally adjusting a resistance value associated with the temperature setpoint provided in the dynamic RT model of the respective zone to a calibrated resistance value, wherein incrementally adjusting the resistance value comprises increasing or decreasing the resistance value in steps over a period of time; providing the dynamic RT model correlating the calibrated resistance values ​​of the plurality of zones with the temperature setpoints as a calibrated RT model; A method comprising:

2. measuring the resistance of the resistive heating element; determining the temperature of each of the plurality of zones based on the measured resistance and the dynamic RT model for each zone; adjusting power to the respective zone in response to the temperature of the respective zone differing from the temperature setpoint until the temperature of the respective zone is equal to the temperature setpoint; The method of claim 1 further comprising:

3. When the temperature of each of the plurality of zones is equal to the temperature setpoint, the method includes applying a voltage pulse to the plurality of zones and measuring a thermal response of the plurality of zones; The method of claim 2 further comprising:

4. When the temperature of each of the plurality of zones is equal to the temperature setpoint, the method further includes adjusting an external system variable and measuring a thermal response of the plurality of zones, the external system variable comprising a chamber pressure, a backside gas pressure, a gas flow rate, a chamber emissivity, a pedestal emissivity, or a combination thereof. The method of claim 2.

5. Incrementally adjusting the resistance value includes determining, for each of the zones, a resistance adjustment rate based on a predefined gain factor and a difference between the reference temperature associated with the respective zone and the temperature of the respective zone; 10. The method of claim 1, further comprising: wherein the resistance adjustment rate comprises an adjusted resistance value per unit time.

6. Incrementally adjusting the resistance value comprises: decreasing a resistance value associated with the respective zone when the reference temperature of the respective zone is greater than the temperature of the respective zone; increasing the resistance value associated with the respective zone when the reference temperature of the respective zone is lower than the temperature of the respective zone; The method of claim 1 further comprising:

7. The method of claim 1 , wherein the reference temperatures of the plurality of zones are measured by one or more sensors.

8. applying a nominal measurement voltage to each of the plurality of zones; measuring a cold start resistance for each of the plurality of zones before controlling the temperature of the heater to the temperature setpoint; The method of claim 1 further comprising:

9. the temperature setpoint is selected from among a plurality of temperature setpoints, and the calibrated resistance value for each of the zones is determined for each of the plurality of temperature setpoints; the dynamic RT model provides the calibrated resistance values ​​for each of the plurality of zones for each of the plurality of temperature setpoints. The method of claim 1.

10. thermally equalizing the reference temperatures of the plurality of zones such that the reference temperature of a first zone is substantially the same as a reference temperature of a second zone associated with the first zone. The method of claim 1.

11. For each of said zones: determining whether the temperature of the respective zone is equal to the reference temperature for the respective zone, and in response to the temperature not being equal to the reference temperature, the resistance value being incrementally adjusted; storing the resistance value as the calibrated resistance value for the respective zone in response to the temperature of the respective zone being equal to the reference temperature; 10. The method of claim 1, further comprising:

12. 1. A method for dynamically calibrating a heater having multiple zones defined by one or more resistive heating elements, comprising: controlling power to the heater based on a dynamic resistance-temperature (RT) model to control the temperature of the heater to a temperature setpoint; For each of the multiple zones, measuring a baseline temperature for each zone; measuring a zone temperature for each of the zones based on the resistance of the one or more resistive heating elements in the respective zones and the dynamic RT model; for each said zone, determining whether said zone temperature is equal to said reference temperature; incrementally adjusting, for each zone, a resistance value associated with the temperature setpoint of the dynamic RT model in response to the zone temperature not equaling the reference temperature, wherein incrementally adjusting the resistance value comprises increasing or decreasing the resistance value in steps over a period of time; providing the resistance value of the dynamic RT model as a calibrated resistance value for the temperature setpoint in response to the zone temperature being equal to the reference temperature; and storing the dynamic RT model as a calibrated RT model in response to the calibrated resistance value being provided for each of the plurality of zones. A method comprising:

13. 13. The method of claim 12, further comprising thermally equalizing the plurality of reference temperatures of the plurality of zones such that the reference temperature of a first zone is substantially the same as a reference temperature of a second zone associated with the first zone.

14. 14. The method of claim 13, wherein the resistance value is stored in the dynamic RT model as a calibrated resistance value for the temperature setpoint in response to the zone temperature being equal to the reference temperature and the plurality of reference temperatures being thermally equalized.

15. the temperature setpoint is selected from among a plurality of temperature setpoints, and a calibrated resistance value is determined for each of the plurality of temperature setpoints; The method of claim 12, wherein the dynamic RT model provides the calibrated resistance value for each of the plurality of zones for each of the plurality of temperature setpoints.

16. 13. The method of claim 12, wherein incrementally adjusting the resistance value further comprises determining a resistance adjustment rate based on a predefined gain factor and a difference between the reference temperature and the zone temperature of the respective zone, wherein the resistance adjustment rate comprises an adjusted resistance value per unit time.

17. Incrementally adjusting the resistance value of each of the zones comprises: decreasing the resistance value associated with the respective zone when the reference temperature of the respective zone is greater than the temperature of the respective zone; increasing the resistance value associated with the respective zone when the reference temperature of the respective zone is lower than the temperature of the respective zone; The method of claim 12 further comprising:

18. 1. A control system for controlling power to a heater having a plurality of zones, each of the plurality of zones being defined by one or more resistive heating elements, the control system comprising: a controller configured to control power to the heater and to determine a temperature of each of the plurality of zones based on a calibrated resistance-temperature (RT) model, the controller configured to perform a dynamic calibration process to define the calibrated RT model, the dynamic calibration process comprising: performing closed-loop temperature control to maintain the temperature of the heater at a temperature setpoint using a dynamic RT model; For each of the plurality of zones Obtaining the reference temperature for each zone; adjusting a resistance value associated with the respective zone in response to the temperature of the heater not being equal to the temperature setpoint to thermally equalize the reference temperature of the respective zone with one or more other reference temperatures; measuring a zone temperature for each zone based on the resistance of the one or more resistive heating elements in the respective zone and the dynamic RT model for the respective zone; for each said zone, determining whether said zone temperature is equal to said reference temperature; incrementally adjusting the resistance value associated with the temperature setpoint provided by the dynamic RT model for the respective zone in response to the zone temperature not equaling the reference temperature, wherein incrementally adjusting the resistance value comprises increasing or decreasing the resistance value in steps over a period of time; providing the resistance value of the dynamic RT model as a calibrated resistance value for the temperature setpoint of the respective zone in response to the zone temperature being equal to the reference temperature and the reference temperature being thermally equalized; storing the dynamic RT model correlating the calibrated resistance values ​​with the temperature setpoints of the plurality of zones as the calibrated RT model; A control system comprising:

19. 20. The control system of claim 18, wherein incrementally adjusting the resistance value further comprises determining a resistance adjustment rate based on a predefined gain factor and a difference between the reference temperature and the zone temperature of the respective zone, wherein the resistance adjustment rate comprises a value of adjusted resistance per unit time.

20. Incrementally adjusting the resistance value of each of the zones comprises: decreasing a resistance value associated with the respective zone when the reference temperature of the respective zone is greater than the temperature of the respective zone; increasing a resistance value associated with the respective zone when the reference temperature of the respective zone is lower than the temperature of the respective zone; 20. The control system of claim 18, further comprising:

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