Patent Publication Number: US-11029668-B2

Title: Systems and methods for calibrating scalar field contribution values for a limited number of sensors including a temperature value of an electrostatic chuck and estimating temperature distribution profiles  based on calibrated values

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present disclosure is a continuation of U.S. patent application Ser. No. 14/860,009 filed on Sep. 21, 2015, which claims the benefit of U.S. Provisional Application No. 62/182,877, filed on Jun. 22, 2015. The entire disclosures of the applications referenced above are incorporated herein by reference. 
    
    
     FIELD 
     The present disclosure relates to substrate processing systems, and more particularly to systems and methods for controlling temperatures of an electrostatic chuck in a substrate processing system. 
     BACKGROUND 
     The background description provided here is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure. 
     Substrate processing systems may be used to perform etching, deposition, and/or other treatment of substrates such as semiconductor wafers. Example processes that may be performed on a substrate include, but are not limited to, a plasma enhanced chemical vapor deposition (PECVD) process, a chemically enhanced plasma vapor deposition (CEPVD) process, a sputtering physical vapor deposition (PVD) process, an ion implantation process, and/or other etch, deposition, and cleaning processes. A substrate may be arranged on a pedestal, an electrostatic chuck (ESC), etc. in a processing chamber of the substrate processing system. For example, during etching in a PECVD process, a gas mixture including one or more precursors is introduced into the processing chamber and plasma is struck to etch the substrate. 
     During processing of a substrate, temperatures of the substrate and components of the substrate processing system may vary. These temperature variations may have undesirable effects on the resulting substrates (e.g., non-uniform critical dimensions). Accordingly, the substrate processing systems may implement systems and methods for controlling temperatures of the substrate and the components of the substrate processing system. 
     SUMMARY 
     A system is provided and includes a controller, an interface, and a calibration controller. The controller is configured to (i) select a set of fields, and (ii) based on the set of fields, supply control effort to first actuators in zones of a chamber. The interface is configured to receive feedback signals from sensors. The feedback signals are indicative of fields respectively of the zones. The controller is configured to adjust an amount of control effort supplied to the actuators based on the fields. The calibration controller is configured to, based on the fields, generate calibration values for each of the sensors. The calibration values for each of the sensors are indicative of field contributions corresponding respectively to the actuators. 
     In other features, a system is provided and includes: a chamber, a first controller, a second controller and an interface. The chamber includes sensor elements. The first controller is configured to select a predetermined set of fields. The second controller is configured to adjust parameters of actuators based on the predetermined set of fields. The interface is configured to receive feedback signals from the sensor elements. The feedback signals are indicative of respectively fields of the heating plate. The first controller is configured to estimate a first field of a substrate based on the fields and a set of calibration values. The set of calibration values are indicative of an effect of the actuators respectively from the actuators. 
     In other features, a method is provided and includes: selecting a set of fields; based on the set of fields, supplying control effort to actuators in zones in the chamber; receiving, via an interface, feedback signals from sensors, where the feedback signals are indicative of fields respectively of the zones; adjusting an amount of control effort supplied to the actuators based on the fields; and based on the fields, generate calibration values for each of the sensors, where the calibration values for each of the sensors are indicative of an effect of actuation corresponding respectively to the actuators. 
     In other features, a method for processing a substrate in a chamber is provided. The chamber includes an actuation system. The actuation system includes sensor elements. The method includes: selecting a predetermined set of fields; adjusting parameters of actuators based on the predetermined set of fields; and receiving, via an interface, feedback signals from the sensor elements, where the feedback signals are indicative of respectively fields of the chamber. The method further includes estimating a first field of a substrate based on the fields and a set of calibration values. The first set of calibration values are indicative of an effect of actuation corresponding respectively from the actuators. 
     In other features, a system is provided and includes a first controller, first interface, and a calibration controller. The first controller is configured to (i) select a first set of temperatures, and (ii) based on the first set of temperatures, supply current to first thermal control elements in first zones of a heating plate of an electrostatic chuck. The first interface is configured to receive feedback signals from first sensors. The feedback signals are indicative of first temperatures respectively of the first zones. The first controller is configured to adjust an amount of current supplied to the first thermal control elements based on the first temperatures. The calibration controller is configured to, based on the first temperatures, generate calibration values for each of the first sensors. The calibration values for each of the first sensors are indicative of thermal energy contributions corresponding respectively to the first thermal control elements. 
     In other features, the system further includes a sensor array interface configured to receive second feedback signals from second sensors in a sensor array. The second feedback signals are indicative of second temperatures in second zones of the heating plate. The sensor array is on the electrostatic chuck. The calibration controller is configured to, based on the second temperatures, generate the calibration values for each of the first sensors. 
     In other features, the calibration controller is configured to determine azimuthally averaged temperatures. Each of the azimuthally averaged temperatures is based on corresponding group of the second temperatures. In other features, each of the groups of the second temperatures is indicated by ones of the second sensors that is at a same radius of the sensor array. 
     In other features, the radii corresponding to the azimuthally averaged temperatures match radii of the first sensors relative to a center of the electrostatic chuck. In other features, some of the radii corresponding to the azimuthally averaged temperatures do not match radii of the first sensors relative to the electrostatic chuck. 
     In other features, the calibration controller is configured to select the some of the radii corresponding to the azimuthally averaged temperatures that do not match radii of the first sensors relative to the electrostatic chuck. 
     In other features, the calibration controller is configured to (i) select points on the sensor array or top surface of the electrostatic chuck, (ii) estimate temperatures at the selected points based on the second temperatures, and (iii) determine the calibration values based on the estimated temperatures at the selected points. 
     In other features, the calibration controller is configured to (i) select points on the sensor array or top surface of the electrostatic chuck, and (ii) estimate temperatures at the selected points based on the second temperatures. The first controller is configured to adjust the amount of current supplied to the first thermal control elements based on the estimated temperatures and a predetermined criterion. 
     In other features, the first zones are concentric zones. The system further includes a second controller and a sensor array interface. The second controller configured to, based on the first set of temperatures or a second set of temperatures, supply current to a second plurality of thermal control elements in a second zones of the heating plate of the electrostatic chuck. The sensor array interface is configured to receive second feedback signals from second sensors of a sensor array. The second feedback signals are indicative of second temperatures of the second zones in the heating plate. The second controller is configured to adjust an amount of current supplied to the second thermal control elements based on the second temperatures. The calibration controller is configured to, based on the second temperatures, generate the calibration values for each of the first sensors. 
     In other features, the first zones include the second zones. In other features, the system further includes the electrostatic chuck, and the sensor array. 
     In other features, a system is provided and includes an electrostatic chuck, a first controller, a second controller, and a first interface. The electrostatic chuck includes a heating plate, where the heating plate includes a plurality of sensor elements. The first controller is configured to select a first predetermined set of temperatures. The second controller configured to adjust parameters of first thermal control elements based on the first predetermined set of temperatures. The first interface is configured to receive first feedback signals from the sensor elements. The first feedback signals are indicative of respectively first temperatures of the heating plate. The first controller is configured to estimate a first temperature of a substrate based on the first temperatures and a first set of calibration values. The first set of calibration values are indicative of thermal energy contributions respectively from the first thermal control elements. 
     In other features, the first controller is configured to estimate temperatures of the substrate based on the first temperatures and sets of calibration values. The temperatures of the substrate include the first temperature. The sets of calibration values include the first set of calibration values. The calibration values for each of the sensor elements are indicative of thermal energy contributions corresponding respectively to the first thermal control elements. 
     In other features, the first controller is configured to (i) select a point at a radius, where the radius is different than radii corresponding to locations of the sensor elements in the heating plate, (ii) estimate an azimuthally averaged temperature of the selected point based on the estimates of the temperatures, and (iii) estimate the first temperature of the substrate based on the azimuthally averaged temperature. 
     In other features, the system further includes a third controller configured to adjust parameters of a second thermal control elements based on a second predetermined set of temperatures. The heating plate includes the second thermal control elements. The first controller is configured to select the second predetermined set of temperatures. 
     In other features, the second controller is configured to coarsely adjust the first temperature of the substrate by adjusting the parameters of the first thermal control elements. The third controller is configured to finely adjust the first temperature of the substrate by adjusting the parameters of the second thermal control elements. A temperature range over which the coarse adjustment occurs is greater than a temperature range over which the fine adjustment occurs. 
     In other features, the first controller is configured to estimate a temperatures of the substrate based on the first temperatures and sets of calibration values. The temperatures of the substrate include the first temperature. The sets of calibration values include the first set of calibration values. The calibration values for each of the sensor elements are indicative of thermal energy contributions corresponding respectively to the first thermal control elements and the second thermal control elements. 
     In other features, a method is provided and includes: selecting a first set of temperatures; based on the first set of temperatures, supplying current to first thermal control elements in first zones of a heating plate of an electrostatic chuck; receiving, via a first interface, feedback signals from first sensors, where feedback signals are indicative of first temperatures respectively of the first zones; adjusting an amount of current supplied to the first thermal control elements based on the first temperatures; and based on the first temperatures, generate calibration values for each of the first sensors, where calibration values for each of the first sensors are indicative of thermal energy contributions corresponding respectively to the first thermal control elements. 
     In other features, the method further includes: receiving second feedback signals from second sensors in a sensor array, where the second feedback signals are indicative of second temperatures in second zones of the heating plate, and where the sensor array is on the electrostatic chuck; and based on the second temperatures, generating the calibration values for each of the first sensors. 
     In other features, the method further includes determining azimuthally averaged temperatures. Each of the azimuthally averaged temperatures are based on corresponding group of the second temperatures. 
     In other features, each of the groups of the second temperatures is indicated by ones of the second sensors that is at a same radius of the sensor array. In other features, the radii corresponding to the azimuthally averaged temperatures match radii of the first sensors relative to a center of the electrostatic chuck. In other features, some of the radii corresponding to the azimuthally averaged temperatures do not match radii of the first sensors relative to the electrostatic chuck. 
     In other features, the method further includes selecting the some of the radii corresponding to the azimuthally averaged temperatures that do not match radii of the first sensors relative to the electrostatic chuck. 
     In other features, the method further includes: selecting points on the sensor array or top surface of the electrostatic chuck; estimating temperatures at the selected points based on the second temperatures; and determining the calibration values based on the estimated temperatures at the selected points. 
     In other features, the method further includes: selecting points on the sensor array or top surface of the electrostatic chuck; estimating temperatures at the selected points based on the second temperatures; and adjusting the amount of current supplied to the first thermal control elements based on the estimated temperatures and a predetermined criteria. 
     In other features, the first zones are concentric zones. In other features, the method further includes: based on the first set of temperatures or a second set of temperatures, supplying current to second thermal control elements in second zones of the heating plate of the electrostatic chuck; receiving second feedback signals from second sensors of a sensor array, where the second feedback signals are indicative of second temperatures of the second zones in the heating plate; adjusting an amount of current supplied to the second thermal control elements based on the second temperatures; and based on the second temperatures, generating the calibration values for each of the first sensors. In other features, the first zones include the second zones. 
     In other features, a method for processing a substrate on an electrostatic chuck is provided. The electrostatic chuck includes a heating plate. The heating plate includes sensor elements. The method includes: selecting a first predetermined set of temperatures; adjusting parameters of first thermal control elements based on the first predetermined set of temperatures; receiving, via a first interface, first feedback signals from the sensor elements, where the first feedback signals are indicative of respectively first temperatures of the heating plate; and estimating a first temperature of a substrate based on the first temperatures and a first set of calibration values, where the first set of calibration values are indicative of thermal energy contributions respectively from the first thermal control elements. 
     In other features, the method further includes estimating temperatures of the substrate based on the first temperatures and sets of calibration values. The temperatures of the substrate include the first temperature. The sets of calibration values include the first set of calibration values. The calibration values for each of the sensor elements are indicative of thermal energy contributions corresponding respectively to the first thermal control elements. 
     In other features, the method further includes: selecting a point at a radius, where the radius is different than radii corresponding to locations of the sensor elements in the heating plate; estimating an azimuthally averaged temperature of the selected point based on the estimates of the temperatures; and estimating the first temperature of the substrate based on the azimuthally averaged temperature. 
     In other features, the method further includes: adjusting parameters of second thermal control elements based on a second predetermined set of temperatures, where the heating plate includes the second thermal control elements; and selecting the second predetermined set of temperatures. 
     In other features, the method further includes: coarsely adjusting the first temperature of the substrate by adjusting the parameters of the first thermal control elements; and finely adjusting the first temperature of the substrate by adjusting the parameters of the second thermal control elements, where a temperature range over which the coarse adjustment occurs is greater than a temperature range over which the fine adjustment occurs. 
     In other features, the method further includes estimating temperatures of the substrate based on the first temperatures and sets of calibration values. The temperatures of the substrate include the first temperature. The sets of calibration values include the first set of calibration values. The calibration values for each of the sensor elements are indicative of thermal energy contributions corresponding respectively to the first thermal control elements and the second thermal control elements. 
     Further areas of applicability of the present disclosure will become apparent from the detailed description, the claims and the drawings. The detailed description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure will become more fully understood from the detailed description and the accompanying drawings, wherein: 
         FIG. 1  is a functional block diagram of a substrate processing system incorporating a temperature controller in accordance with an embodiment of the present disclosure; 
         FIG. 2A  is a side view of an electrostatic chuck (ESC) and the temperature controller in accordance with an embodiment of the present disclosure; 
         FIG. 2B  is a top view of first layer of a heating plate of the ESC including macro thermal control elements (TCEs); 
         FIG. 2C  is a top view of a second layer of the heating plate of the ESC including micro TCEs; 
         FIG. 3  is a top view of a sensor array in accordance with the present disclosure; 
         FIG. 4  is a functional block diagram of a temperature controller in accordance with the present disclosure; 
         FIG. 5  illustrates a calibration method in accordance with the present disclosure; and 
         FIG. 6  illustrates a processing method in accordance with the present disclosure. 
     
    
    
     In the drawings, reference numbers may be reused to identify similar and/or identical elements. 
     DETAILED DESCRIPTION 
     Variations in the manufacturing of heating plates can cause corresponding variations (i.e., non-uniformities) in operating characteristics of the heating plates. The variations in operating characteristics of the heating plates results in performance variations of a substrate processing system in controlling temperatures of zones of the heating plates. Characteristic variations in heating plates may include, but are not limited to, differences in thicknesses of silicone bond layers, differences in the flatness of machined surfaces, and/or differences in characteristics of TCEs within the heating plates. These non-uniformities may result in local differences in heat transfer (i.e., local temperature non-uniformity), and therefore non-uniformities in substrate temperatures. Differences can also exist between ESCs and between processing chambers. Thus, there can be a substantial amount of variability between processing a substrate in a first processing chamber with a first ESC and processing the same substrate in a second processing chamber with a second ESC. 
     In a substrate processing system, temperatures of an electrostatic chuck (ESC) may be controlled during substrate processing to control temperatures of the substrate. Different substrate processes may have respective temperature requirements for one or more areas of corresponding substrates. Contact surface temperatures of the ESC may be controlled to maintain the one or more areas of the substrates at selected temperatures to satisfy the temperature requirements. As an example, an ESC may include a heating plate. The heating plate may include multiple TCEs. Current to the TCEs may be controlled to control temperatures of one or more zones, which in turn controls temperatures of one or more areas of a substrate. 
     As another example, a substrate processing system may include a heating plate having four concentric zones with four respective TCEs. The substrate processing system may implement a temperature control method to control temperatures of the concentric zones. Four temperature probes (or sensors) may be used to monitor respective temperatures of the concentric zones. Each of the temperature probes may be used to detect a temperature of the heating plate in an area where the temperature probe is located. One or more controllers may be used to monitor the temperatures detected by the temperature probes and adjust current to the TCEs to regulate and/or adjust temperatures of the concentric zones. This example temperature control method has limited accuracy and control over temperatures across each of the concentric zones for multiple reasons. The temperature control method does not account for thermal energy transfer contributions of each of the TCEs in each of the four zones. The temperature control method also has limited control as to temperatures across each of the zones, since a limited number of temperature probes and TCEs are provided and/or controlled. 
     Continuing with the same example, a sensor array may be used to calculate calibration values for use in estimating substrate temperatures corresponding to detected temperatures of the temperature probes. The sensor array may include an array of sensors (e.g., 65 sensors) distributed across an ESC. During calibration the sensor array may be placed on the ESC in a similar manner as placing a substrate on the ESC. The substrate processing system may control TCEs of the ESC to provide a predetermined set of temperatures at the temperature probes. The sensor array may then be used to detect temperatures across the ESC. The detected temperatures provide estimates of temperatures of a substrate, for example, if the sensor array were replaced with a substrate. These temperatures collectively are referred to as a temperature distribution profile and correspond to a respective set of temperatures of the temperature probes. Multiple sets of temperatures of the temperature probes may be implemented as part of respective cycles to provide a temperature distribution profile of the sensor array or substrate per cycle. 
     Calibration values may be determined based on the probe temperatures and the temperature distribution profiles. The calibration values may be determined using one or more of the following equations 1-2, where: PV i,p  refers to a temperature detected by a temperature probe for an i th  cycle; p identifies a number of a temperature probe; BP i  is a base plate temperature; APV i,p  is an azimuthally averaged temperature from the sensor array for a radius associated with a tip of a corresponding temperature probe relative to a center of the heating plate and/or ESC; SPAN x,y,p  refers to a calibration value for the p th  temperature probe that is indicative of an amount of thermal energy and/or temperature contributed by the y th  TCE at the p th  temperature probe; y may also be indicative of the column of a corresponding calibration matrix; x may refer to the x th  row of the corresponding calibration matrix and may be the same as p; OFFSET p  is a calibration offset value that corresponds to the p th  temperature probe; and SPAN 2,p  refers to a calibration value that corresponds to the p th  temperature probe and is indicative of a thermal energy and/or temperature loss due to the base plate. 
                       [         1         PV     1   ,   p             BP   i             1         PV     2   ,   p             BP   i             1         PV     3   ,   p             BP   i           ]     *     [           OFFSET   p               SPAN       1   :   p     ,   p                 SPAN     2   :   p             ]       =         [           APV     1   ,   p                 APV     2   ,   p                 APV     3   ,   p             ]     →       X   p     *     β   p         =     Y   p               (   1   )                 β   p     =         (       X   p   T     *     X   p       )       -   1       *     X   p   T     *     Y   p               (   2   )               
An azimuthally average temperature refers to an average of temperatures detected by sensors of the sensor array, which are on, closest to and/or proximate the radius of the corresponding temperature probe. In equation 2, T refers to the transpose function.
 
     The calibration values may be used to estimate temperatures T i,p  of a substrate being processed using equation 3, where T i,p  is the temperature of a substrate in an area above a p th  temperature probe. 
                                 [           ⁢           T     1   ,   i                 T     2   ,   i                 T     3   ,   i                 T     4   ,   i             ]     =       [           ⁢           SPAN       1   :   1     ,   1           0       0       0           0         SPAN       1   :   2     ,   2           0       0           0       0         SPAN       1   :   3     ,   3           0           0       0       0         SPAN       1   :   4     ,   4             ]     *             ⁢             [           ⁢           PV     1   ,   i                 PV     2   ,   i                 PV     3   ,   i                 PV     4   ,   i             ]     +                   [           ⁢           SPAN     2   :   1                 SPAN     2   :   2                 SPAN     2   :   3                 SPAN     2   :   4             ]     *     BP   i       +     [           OFFSET   1               OFFSET   2               OFFSET   3               OFFSET   4           ]             (   3   )               
During calibration, the calibration values are set, such that for each i th  cycle and for each temperature probe a difference between T i,p  and APV i,p  is minimized. Equations 1 and 3 are the same equations, but written in a different format. Equation 1 includes a calibration matrix β p , which includes calibration values OFFSET p , SPAN x,y,p , SPAN 2,p  that are represented in respective calibration matrices of equation 3. Equation 3 is shown for an example implementation that includes four temperature probes. Since there are three unknowns (SPAN x,y,p , SPAN 2,p , and OFFSET p ) for each row of equation 3, three cycles are performed to provide three sets of values. This is why equation 1 is shown as having matrices with three rows; one row for each cycle.
 
     The zero (‘0’) entries of the first calibration matrix of equation 3 indicate that contributions by TCEs other than the TCE that is in the zone of a corresponding temperature probe are not accounted for by equation 3. In other words, equation 3 is based on the assumption that the temperature detected at a temperature probe is due only to the thermal energy generated by a corresponding TCE in the area of the temperature probe and not due to thermal energy generated by other TCEs. Thus, this described calibration technique does not account for cross talk of TCEs (or thermal energy transfer from each TCE across a heating plate) as detected by a temperature probe. For this reason, this calibration technique does not account for spatial information of TCEs in an ESC. Also, this calibration technique is restricted to four points or radii (or the number of temperature probes). 
     Thus, the above-described calibration process does not provide arbitrary temperature measurement locations, but rather is limited to the number of points and/or radii associated with the number of temperature probes. The calibration process does not account for spatial structure of a heating plate of an ESC (i.e. TCE layout of the ESC and corresponding distributed thermal energy contributions) and thus can be inaccurate. The model provided by equations 1-3 is based on an assumption that a temperature of a point on a plane of a wafer, other than a plane in which a tip of a temperature probe is located, is a function of a temperature measurement of only a single point at which the tip of the temperature probe is located. This is a limited model, as the model does not account for temperature distributions on multiple planes as a result of heat transfer. Due to construction of an ESC having finite and non-negligible thermal resistance to heat flow in all directions, the temperature distributions in a heating plate arising from TCEs can result in temperature distributions with different temperatures on each plane of the heating plate. Some of the temperatures may not match temperatures measured by temperature probes. In actuality, a temperature on a point of the heating plate (or on a wafer set on the heating plate) is based on thermal energy provided by all of the TCEs supplying heat to the heating plate and thus is also a function of all of the measurements of all of the temperature probes in the heating plate. 
     Since ESCs have characteristic heating profiles that vary from ESC to ESC, temperature differences exist between ESCs for a given TCE and/or cooling assembly parameter set. Although radial temperatures measured via probes of a first ESC may match radial temperatures measured via probes of a second ESC, the heating profiles of the ESCs are typically different. This can be true due to for example manufacturing differences regardless of whether the ESCs are of the same type. 
     The calibration process also does not allow for arbitrary objective criteria (e.g., minimizing temperature errors in one or more selected zones of a heating plate) per ESC and thus is not suitable for ESC matching. ESC matching refers to being able to calibrate a substrate processing system for different ESCs to provide the same temperature distribution across heating plates of each of the ESCs. The calibration process also does not account for unknown differences between processing chambers. 
     Substrate processing systems and methods are disclosed below, which overcome the above-stated disadvantages of the described calibration process. Calibration methods are disclosed below that account for distributed thermal energy contributions of TCEs with respect to each temperature detected by a temperature probe. The disclosed calibration methods allow for arbitrary objective functions to be used to satisfy different temperature distribution criteria of heating plates. The disclosed calibration methods allow for ESC matching and account for unknown differences between processing chambers. 
     Referring now to  FIG. 1 , an example substrate processing system  100  for performing etching using RF plasma is shown. The substrate processing system  100  includes a processing chamber  102 . The processing chamber  102  encloses other components of the processing chamber  102  and contains the RF plasma. The processing chamber  102  includes an upper electrode  104  and an ESC  106 . During operation, a substrate  108  is arranged on the ESC  106 . 
     For example only, the upper electrode  104  may include a showerhead  109  that introduces and distributes gases. The showerhead  109  may include a stem portion  111  including one end connected to a top surface of the processing chamber  102 . The showerhead  109  is generally cylindrical and extends radially outwardly from an opposite end of the stem portion  111  at a location that is spaced from the top surface of the processing chamber  102 . A substrate-facing surface of the showerhead  109  includes a plurality of holes through which process or purge gas flows. Alternately, the upper electrode  104  may include a conducting plate and the gases may be introduced in another manner. 
     The ESC  106  includes a conductive baseplate  110  that acts as a lower electrode. The baseplate  110  supports a heating plate  112 , which may be formed at least partially of a ceramic material. A thermal resistance layer  114  may be arranged between the heating plate  112  and the baseplate  110 . The baseplate  110  may include one or more coolant channels  116  for flowing coolant through the baseplate  110 . 
     An RF generating system  120  generates and outputs an RF voltage to one of the upper electrode  104  and the lower electrode (e.g., the baseplate  110  of the ESC  106 ). The other one of the upper electrode  104  and the baseplate  110  may be DC grounded, AC grounded or at a floating potential. For example only, the RF generating system  120  may include an RF voltage generator  122  that generates the RF voltage, which is fed by a matching and distribution network  124  to the upper electrode  104  or the baseplate  110 . In other examples, the plasma may be generated inductively or remotely. 
     A gas delivery system  130  includes one or more gas sources  132 - 1 ,  132 - 2 , . . . , and  132 -N (collectively gas sources  132 ), where N is an integer greater than zero. The gas sources  132  supply one or more precursors and mixtures thereof. The gas sources  132  may also supply purge gas. Vaporized precursor may also be used. The gas sources  132  are connected by valves  134 - 1 , . . . , and  134 -N (collectively valves  134 ) and mass flow controllers  136 - 1 ,  136 - 2 , . . . , and  136 -N (collectively mass flow controllers  136 ) to a manifold  140 . An output of the manifold  140  is fed to the processing chamber  102 . For example only, the output of the manifold  140  is fed to the showerhead  109 . 
     A temperature controller  142  may be connected to TCEs  144  (sometimes referred to as actuators) arranged in the heating plate  112 . Although shown separately from a system controller  160 , the temperature controller may be implemented as part of the system controller  160 . As an example, the TCEs  144  may include, but are not limited to, respective macro TCEs (or first array of TCEs) corresponding to each macro zone of the heating plate  112  and/or micro TCEs (or second array of TCEs) corresponding to each micro zone of the heating plate  112 . Examples of the arrays of TCEs are shown in  FIGS. 2A and 2B . The macro TCEs may be used for coarse tuning temperatures and/or other fields of macro zones of the heating plate  112 . The micro TCEs may be used for fine tuning temperatures and/or other fields of micro zones of the heating plates. The macro zones may include the micro zones. One or more micro zones may overlap two or more of the macro zones. The macro zones and the micro zones may have predetermined, matching, different, or any arbitrary shape. 
     The heating plate  112  includes multiple temperature controlled zones. Each of the temperature controlled zones has corresponding macro and/or micro TCEs. The macro TCEs are controlled to roughly achieve selected temperatures in each of the respective temperature controlled zones. The micro TCEs may be individually controlled to finely adjust temperatures within the respective temperature controlled zones and/or to compensate for temperature non-uniformities in each temperature controlled zone. For example, for each setpoint temperature of a macro TCE, a temperature distribution response across a top surface of the heating plate  112  may be known and mapped (i.e., stored in memory). Similarly, a temperature distribution response of each of the micro TCEs across the surface of the heating plate  112  may be known and mapped. Although the systems and methods disclosed herein are described with respect to multi-zone heating plates and/or ESCs, the principles of the present disclosure may be applied to other temperature-controlled components of a substrate processing system. 
     The temperature controller  142  may control operation and thus temperatures of the TCEs  144  to control temperatures of the ESC  106  and a substrate (e.g., the substrate  108 ) on the ESC  106 . The temperature controller  142  may communicate with a coolant assembly  146  to control coolant flow through the channels  116 . For example, the coolant assembly  146  may include a coolant pump and reservoir. The temperature controller  142  operates the coolant assembly  146  to selectively flow the coolant through the channels  116  to cool the ESC  106  and the heating plate  112 . The temperature controller  142  may control the rate at which the coolant flows and a temperature of the coolant. 
     A valve  150  and pump  152  may be used to evacuate reactants from the processing chamber  102 . The system controller  160  may control components of the substrate processing system  100 . A robot  170  may be used to deliver substrates onto, and remove substrates from, the ESC  106 . For example, the robot  170  may transfer substrates between the ESC  106  and a load lock  172 . The robot  170  may be controlled by the system controller  160 . The system controller  160  may control operation of the load lock  172 . 
     Referring now to  FIGS. 2A, 2B, and 2C , an example ESC  200  having a heating plate  202  is shown. The ESC  200  may be an example of the ESC  106  of  FIG. 1  and/or may replace the ESC  106  of  FIG. 1 . A temperature controller  204  may communicate with and/or supply electrical current and/or other control effort to TCEs of the heating plate  202  via one or more conductive elements  208  (e.g., electrical connections, wires, cables, etc.). The term “control effort” may refer to an amount of current, voltage, power, frequency, duty cycle and/or other controlled parameter of the TCEs (or actuators). The TCEs may include macro TCEs  212 - 1 ,  212 - 2 ,  212 - 3 , and  212 - 4  (collectively macro TCEs  212 ) and micro TCEs  216 . The macro TCEs  212  may be on a different layer than the micro TCEs  216 . The temperature controller  204  may also be connected to and receive temperature feedback signals from detectors  218 , which are connected to temperature probes  220  (also referred to as sensor elements). The temperature probes  220  are in respective macro zones  224 - 1 ,  224 - 2 ,  224 - 3 , . . . ,  224 -N (collectively macro zones  224 ), where N is an integer. Although in  FIG. 2B  four macro zones are shown, the heating plate  202  may include any number of macro zones. Although, in  FIG. 2B  probes  220  are shown as one per detector  218 , there may be multiple detectors per zone for redundancy and/or for averaging to reduce variability due to sensor construction, calibration, and/or spatial variation in macro zones  224 . 
     As shown, the heating plate  202  includes macro zones  224 - 1 ,  224 - 2 ,  224 - 3 , and  224 - 4 . The temperature probes  220  are located respectively in the macro zones  224 . Also, each of the macro TCEs  212  is located respectively in the macro zones  224 . 
     The ESC  200  may include: a baseplate  228  having coolant channels  232 ; a thermal resistance layer  236  formed on the baseplate  228 ; and the heating plate  202  formed on the thermal resistance layer  236 . The heating plate  202  may include multiple bonded layers, including a first layer  244  as shown in  FIG. 2A  and a second layer  248  as shown in  FIG. 2B . The first layer  244  includes the macro TCEs  212  and the second layer  248  includes the micro TCEs  216 . As shown, the macro TCEs  212  and the first layer  244  are shown arranged above the micro TCEs  216  and the second layer  248 . As an alternative the second layer  248  may be arranged on the first layer  244 . 
     The temperature controller  204  controls the macro TCEs  212  according to predetermined setpoint temperatures. For example only, the temperature controller  204  may control the macro TCEs  212  to provide a same setpoint temperature for one or more of the macro zones  224  and/or different respective setpoint temperatures for each of the macro zones  224 . The setpoint temperatures for each of the macro zones  224  may vary across different processes and different steps of each process. The temperature controller  204  controls the macro TCEs  212  for each of the zones  224  based on the respective setpoint temperatures and temperature feedback signals provided by the detectors  218 . For example, the temperature controller  204  individually adjusts power (e.g., current) provided to each of the macro TCEs  212  to achieve the setpoint temperatures. The macro TCEs  212  may each include a single resistive coil or other structure schematically represented by the dashed lines of  FIG. 2B . Accordingly, adjusting one of the macro TCEs  212  affects the temperature of the entire respective macro zone and other macro zones. The temperature probes  220  may provide temperature feedback for only a local portion of each of the macro zones  224 . For example only, the temperature probes  220  may be positioned in a portion of each macro zone  224  previously determined to have a closest correlation to an average temperature of the macro zone  224 . 
     The temperature controller  204  may also individually control each of the micro TCEs  216  to locally adjust temperatures of the macro zones  224 . For example, although each micro TCE  216  may be located entirely within one of the zones  224 , adjusting a thermal output of any one of the micro TCEs  216  may have a thermal impact across multiple macro zones  224  and localities of the heating plate  202 . Accordingly, one or more of the micro TCEs  216  may be selectively activated and/or deactivated to further adjust temperatures of the macro zones  224 . 
     The temperature controller  204  may adjust current, voltage, and/or power provided to the TCEs  212 ,  216  when controlling temperatures of (i) the macro zones  224 , and/or (ii) portions of the macro zones  224 . The temperature controller  204  may activate adjust current to one or more of the micro TCEs  216  during process steps to compensate for non-uniformities in the macro zones  224  of the heating plate  202 . Although  FIG. 2B  shows a particular number of micro TCEs  216 , the heating plate  202  may include any number of micro TCEs  216 . As an example, the heating plate  202  may include 100-150 micro TCEs. 
       FIG. 3  shows an example sensor array  250 . The sensor array  250  may be set on an ESC (e.g., the ESC  106  or ESC  200  of  FIGS. 1 and 2 ) during calibration of the ESC. The sensor array  250  includes a substrate  252  having sensors  254  that are distributed across the sensor array  250 . The substrate  252  may be formed of similar materials as one or more substrates to be processed on the ESC. Although the sensor array  250  is shown as having a same number of sensors as there are micro TCEs  216  in the second layer  248  of  FIG. 2C , the sensor array  250  may have a different number of sensors. The sensor array  250  may include any number of sensors. As an example, the sensor array  250  may include 65 sensors. The sensor array  250  may be configured to have macro zones  256 , which are similar in size and shape as the macro zones  224  of  FIG. 2 . The sensor array  250  may include any number of macro zones. The sensors  254  may be connected to the temperature controller  204  via conductive elements  260  and connectors  262 ,  264 . The sensor array  250  is shown as including discrete sensors but may alternatively or in addition include a temperature sensitive material. Temperatures of the temperature sensitive material may be monitored. The temperature sensitive material may include a thermoplastic. The sensor array  250  may include an infrared (IR) image sensor and/or detect film loss from a temperature sensitive process. 
       FIG. 4  shows the temperature controller  204 . The temperature controller  204  may include a macro TCE controller  300 , a micro TCE controller  302 , a base plate temperature controller  304 , a probe interface  306 , a sensor array interface  308 , a calibration controller  309 , and a memory  310 . The controllers  204 ,  300 ,  302  may be, for example, proportional integral derivative (PID) controllers. The PID controllers may convert requested temperatures to various parameters (current, voltage, power, flow rates, etc.) to provide the requested temperatures. The macro TCE controller  300  may be used to control temperatures of macro TCEs including selecting current levels, voltages, and/or power supplied to the macro TCEs. The micro TCE controller  302  may be used to control temperatures of micro TCEs including selecting current levels, voltages, and/or power supplied to the micro TCEs. The base plate temperature controller  304  may control flow rates of coolant and temperatures of the coolant supplied to channels of a base plate of an ESC. The stated control provided by the controllers  300 ,  302 ,  304  may be provided during calibration of an ESC and/or during substrate processing. 
     The probe interface  306  may be connected to detectors (e.g., the detectors  218  of  FIG. 2A ) and/or other sensors connected to and/or disposed in a heating plate of an ESC. The probe interface  306  may receive feedback signals from the detectors and/or other sensors. The probe interface  306  may filter and/or signal process the feedback signals. The sensor array interface  308  may receive signals from sensors in a sensor array (e.g., the sensor array  250  of  FIG. 3 ). The sensor array interface  308  may filter and/or signal process the received signals from the sensors in the sensor array. The calibration controller  309  may determine calibration values, as further described below. 
     The memory  310  may store: temperatures detected during calibration and/or substrate processing; parameters used during calibration and/or substrate processing; and/or other information. For example, the memory  310  may store: sets of predetermined probe temperatures  320 ; reference profiles  322  of temperatures detected by sensors of a sensor array; sets of calibration values  324 ; predetermined criteria functions  326 ; and reference sets  328 . The predetermined criteria functions  326  and reference sets  328  are described below with respect to the method of  FIG. 5 . 
     The systems disclosed herein may be operated using numerous methods, example methods are illustrated in  FIGS. 5-6 . In  FIG. 5 , a calibration method is shown. Although the following tasks are primarily described with respect to the implementations of  FIGS. 1-4 , the tasks may be easily modified to apply to other implementations of the present disclosure. The tasks may be iteratively performed. 
     The method may begin at  350 . At  352 , a processing chamber may be initialized for calibration of an ESC (e.g., one of the ESCs  106  or  200 ). This may include setting up the ESC within a processing chamber and preparing conditions within the processing chamber to be similar to conditions associated with processing a substrate. At  354 , a sensor array, such as the sensor array  250 , is set on the ESC. 
     At  356 , the temperature controller (e.g., the temperature controller  204 ) or other controller (e.g., the system controller  160 ) selects a set of predetermined probe (or macro zone) temperatures and/or micro zone temperatures. In one embodiment, only macro zone temperatures are selected, not micro zone temperatures. The set of macro and/or micro temperatures are temperatures that the temperature controller is to attempt to match during tasks  358 - 362  by controlling macro TCEs, micro TCEs, and/or base plate characteristics. 
     At  358 , a macro controller and/or the micro controller (e.g., one of the controllers  300 ,  302 ) sets and/or adjusts the parameters of the macro TCEs, the micro TCEs and/or the base plate. This may include adjusting: current, voltage and/or power levels of the macro TCEs; current, voltage and/or power levels of the micro TCEs; and/or flow rates and coolant temperatures of the base plate. The adjustments may be based on differences between (i) the set of predetermined probe (or macro zone) temperatures and micro zone temperatures and (ii) temperatures of the heating plate as detected by temperature probes and/or sensors of a sensor array (e.g., the sensor array  250  of  FIG. 3 ). As an example, a predetermined criterion may include adjusting the parameters to minimize these differences. The parameters may also be adjusted to satisfy other predetermined criteria. As another example, an average of the stated differences may be calculated, and the parameters may be adjusted to minimize the average difference. As yet another example, each of the differences may be squared and summed. The result of the summation may be divided by the number of differences calculated to provide a “sum square error”. The parameters may be adjusted to minimize the sum square error. The differences, the average of the differences, and/or the sum square error may be provided for: only the macro zones; only the micro zones; some or all of the macro zones; some or all of the micro zones; and/or a portion of the macro zones and the micro zones. The criteria may include minimizing errors in one or more macro and/or micro zones of the heating plate. 
     At  360 , temperatures of the heating plate at the temperature probes are detected. At  362 , temperatures of the sensor array are detected via the sensors of the sensor array. At  364 , the temperatures of the heating plate and the sensor array determined at  360 ,  362  are recorded as a reference profile in the memory  310 . Tasks  360 ,  362 ,  364  may be performed by the temperature controller. 
     At  366 , azimuthally averaged temperatures may be determined. This may include, for each of the temperature probes, averaging temperatures indicated by sensors on and/or adjacent to a radius of the corresponding temperature probe. For example, for the temperature probe in the macro zone  224 - 1 , the temperatures indicated by the sensors of the sensor array in the macro zone  256 - 1  may be averaged to provide an azimuthally average temperature APV. 
     At  368 , the temperature control controller may store as a reference set in a memory (e.g., the memory  310 ): the set of predetermined probe temperatures; the reference profiles; the azimuthally average temperatures; the parameters of the macro TCEs, the micro TCEs, and/or the base plate; and/or the first predetermined criteria. 
     At  370 , the temperature controller determines whether: the temperatures as detected via the temperature probes match and/or are within predetermined ranges of the set of predetermined probe (or macro zone) temperatures selected at  356 ; the temperatures as detected via the sensors of the sensor array match and/or are within predetermined ranges of the micro zone temperatures selected at  356 ; and/or the temperatures as detected via the temperature probes and the sensors of the sensor array satisfy other criteria. The other criteria may include providing an average, an error value, and/or a sum square error that is within a predetermined range. The other criteria may include determining and minimizing a distribution of errors (e.g., e i,p =APV i,p −T i,p ) across the heating plate. If the detected temperatures match, are within the predetermined ranges and/or satisfy the first predetermined criteria, then task  372  is performed, otherwise task  358  is performed. In one embodiment, the temperature controller determines whether the temperatures as detected via the temperature probes match and/or are within predetermined ranges of the set of predetermined probe (or macro zone) temperatures and does not determine whether the temperatures as detected via the sensors of the sensor array match and/or are within predetermined ranges of the micro zone temperatures. 
     At  372 , the temperature controller may determine whether another cycle or set of predetermined probe temperatures are to be selected. A cycle may refer to performance of tasks  356 - 370 . The number of cycles performed may be equal to a number of unknowns to be determined per row of matrices used at  374  (e.g., matrices of below equations 6, 8). If another set is to be selected, task  356  may be performed; otherwise task  374  may be performed. 
     At  374 , a calibration controller (e.g., the calibration controller  309 ) determines calibration values for the ESC and processing chamber based on any and/or all of the information included in the reference sets determined during cycles of tasks  356 - 372 . The determination of the calibration values may be based on and determined using equations 4-6 and/or 5, 7, 8. Although the matrices are shown as having a certain number of entries, the number of entries may be different if a different number of probes, macro zones, micro zones, azimuthally averaged points, and/or arbitrarily selected points are monitored. The variables PV, OFFSET, SPAN, APV, T are defined above with respect to equations 1-3. Each of equations 4 and 7 includes a probe temperature and base plate matrix X, a contribution (or unknown) matrix β, and an azimuthally averaged temperature (or arbitrary point) matrix Y. The values of the contribution matrix β refer to contributions of thermal energy from each of the macro zones for a temperature detected by one of the probes. The arbitrary points refer to points on a top surface of an ESC and are designated by the variable AP M,N , where M and N are integers. The number of unknowns per row of the matrices of equations 6, 8 is six. As a result, 6 cycles may have been performed. The unknown values are the SPAN and OFFSET values. This includes determining terms of diagonals of the contribution/SPAN matrices of equations 6, 8 and off diagonal terms of the contribution/SPAN matrices of equations 6, 8. 
     
       
         
           
             
               
                 
                   
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               
                                 PV 
                                 
                                   1 
                                   , 
                                   1 
                                 
                               
                             
                             
                               
                                 PV 
                                 
                                   1 
                                   , 
                                   2 
                                 
                               
                             
                             
                               
                                 PV 
                                 
                                   1 
                                   , 
                                   3 
                                 
                               
                             
                             
                               
                                 PV 
                                 
                                   1 
                                   , 
                                   4 
                                 
                               
                             
                             
                               
                                 BP 
                                 1 
                               
                             
                           
                           
                             
                               
                                   
                               
                             
                             
                               
                                   
                               
                             
                             
                               ⋮ 
                             
                             
                               
                                   
                               
                             
                             
                               
                                   
                               
                             
                             
                               
                                   
                               
                             
                           
                           
                             
                               1 
                             
                             
                               
                                 PV 
                                 
                                   M 
                                   , 
                                   1 
                                 
                               
                             
                             
                               
                                 PV 
                                 
                                   M 
                                   , 
                                   2 
                                 
                               
                             
                             
                               
                                 PV 
                                 
                                   M 
                                   , 
                                   3 
                                 
                               
                             
                             
                               
                                 PV 
                                 
                                   M 
                                   , 
                                   4 
                                 
                               
                             
                             
                               
                                 BP 
                                 M 
                               
                             
                           
                         
                         ] 
                       
                       * 
                       
                           
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     OFFSET 
                                     1 
                                   
                                 
                                 
                                   
                                     OFFSET 
                                     2 
                                   
                                 
                                 
                                   
                                     OFFSET 
                                     3 
                                   
                                 
                                 
                                   
                                     OFFSET 
                                     4 
                                   
                                 
                               
                               
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         1 
                                       
                                       , 
                                       1 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         2 
                                       
                                       , 
                                       1 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         3 
                                       
                                       , 
                                       1 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         4 
                                       
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         1 
                                       
                                       , 
                                       2 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         2 
                                       
                                       , 
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                                     SPAN 
                                     
                                       
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                                         : 
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                                       , 
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                                     SPAN 
                                     
                                       
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                                         : 
                                         4 
                                       
                                       , 
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                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         1 
                                       
                                       , 
                                       3 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         2 
                                       
                                       , 
                                       3 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         3 
                                       
                                       , 
                                       3 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         4 
                                       
                                       , 
                                       3 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         1 
                                       
                                       , 
                                       4 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         2 
                                       
                                       , 
                                       4 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         3 
                                       
                                       , 
                                       4 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       
                                         1 
                                         : 
                                         4 
                                       
                                       , 
                                       4 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     SPAN 
                                     
                                       2 
                                       : 
                                       1 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       2 
                                       : 
                                       2 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       2 
                                       : 
                                       3 
                                     
                                   
                                 
                                 
                                   
                                     SPAN 
                                     
                                       2 
                                       : 
                                       4 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                           = 
                         
                           
                       
                       ⁢ 
                       
                         
                             
                             
                         
                         [ 
                         
                             
                         
                         ⁢ 
                         
                           
                             
                               
                                 APV 
                                 
                                   1 
                                   , 
                                   1 
                                 
                               
                             
                             
                               
                                 APV 
                                 
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                                   , 
                                   2 
                                 
                               
                             
                             
                               
                                 APV 
                                 
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                               ⋮ 
                             
                             
                               
                                   
                               
                             
                             
                               
                                   
                               
                             
                           
                           
                             
                               
                                 APV 
                                 
                                   M 
                                   , 
                                   1 
                                 
                               
                             
                             
                               
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                                   , 
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                                   M 
                                   , 
                                   3 
                                 
                               
                             
                             
                               
                                 APV 
                                 
                                   M 
                                   , 
                                   4 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                     → 
                     
                       X 
                       * 
                       β 
                     
                   
                   = 
                   Y 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     β 
                     p 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             X 
                             p 
                             T 
                           
                           * 
                           
                             X 
                             p 
                           
                         
                         ) 
                       
                       
                         - 
                         1 
                       
                     
                     * 
                     
                       X 
                       p 
                       T 
                     
                     * 
                     
                       Y 
                       p 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     [ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       
                                         
                                           
                                             T 
                                             
                                               1 
                                               , 
                                               i 
                                             
                                           
                                         
                                       
                                       
                                         
                                           
                                             T 
                                             
                                               2 
                                               , 
                                               i 
                                             
                                           
                                         
                                       
                                       
                                         
                                           
                                             T 
                                             
                                               3 
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                                             T 
                                             
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                                               , 
                                               i 
                                             
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   = 
                                   
                                     
                                       [ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   1 
                                                 
                                                 , 
                                                 1 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   1 
                                                 
                                                 , 
                                                 2 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   1 
                                                 
                                                 , 
                                                 3 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   1 
                                                 
                                                 , 
                                                 4 
                                               
                                             
                                           
                                         
                                         
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   2 
                                                 
                                                 , 
                                                 1 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   2 
                                                 
                                                 , 
                                                 2 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   2 
                                                 
                                                 , 
                                                 3 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   2 
                                                 
                                                 , 
                                                 4 
                                               
                                             
                                           
                                         
                                         
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   3 
                                                 
                                                 , 
                                                 1 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   3 
                                                 
                                                 , 
                                                 2 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   3 
                                                 
                                                 , 
                                                 3 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   3 
                                                 
                                                 , 
                                                 4 
                                               
                                             
                                           
                                         
                                         
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   4 
                                                 
                                                 , 
                                                 1 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   4 
                                                 
                                                 , 
                                                 2 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   4 
                                                 
                                                 , 
                                                 3 
                                               
                                             
                                           
                                           
                                             
                                               SPAN 
                                               
                                                 
                                                   1 
                                                   : 
                                                   4 
                                                 
                                                 , 
                                                 4 
                                               
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                     * 
                                   
                                 
                                   
                               
                               ⁢ 
                               
                                 
                                     
                                     
                                 
                                 [ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       
                                         PV 
                                         
                                           1 
                                           , 
                                           i 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         PV 
                                         
                                           2 
                                           , 
                                           i 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         PV 
                                         
                                           3 
                                           , 
                                           i 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         PV 
                                         
                                           4 
                                           , 
                                           i 
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                             + 
                           
                             
                         
                           
                       
                       [ 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             
                               SPAN 
                               
                                 2 
                                 : 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               SPAN 
                               
                                 2 
                                 : 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               SPAN 
                               
                                 2 
                                 : 
                                 3 
                               
                             
                           
                         
                         
                           
                             
                               SPAN 
                               
                                 2 
                                 : 
                                 4 
                               
                             
                           
                         
                       
                       ] 
                     
                     * 
                     
                       BP 
                       i 
                     
                   
                   + 
                   
                     [ 
                     
                       
                         
                           
                             OFFSET 
                             1 
                           
                         
                       
                       
                         
                           
                             OFFSET 
                             2 
                           
                         
                       
                       
                         
                           
                             OFFSET 
                             3 
                           
                         
                       
                       
                         
                           
                             OFFSET 
                             4 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Equations 6, 8 are linear equations without the offset matrices. Equations 6, 8 are affine equations with the offset matrices. Although task  374  is primarily described using equations 4-8, task  374  may be performed using some other functional relationship between probe temperatures PV and substrate temperatures T. The arbitrary temperature matrix Y of equation 7 may include (i) any number of arbitrarily selected points, and/or (ii) azimuthally averaged temperatures. The arbitrarily selected points may refer to tips of the probes, locations of the sensors in the sense array, and/or other points within and/or across the top surface of the ESC. The azimuthally averaged temperatures may be for any number of radii measured from a longitudinal center axis. The number of azimuthally averaged temperatures may be greater than the number of probes. The longitudinal center axis may extend vertically through a center of the ESC and the sensor array. 
                         [         1         PV     1   ,   1             PV     1   ,   2             PV     1   ,   3             PV     1   ,   4             BP   1                                     ⋮                                               1         PV     M   ,   1             PV     M   ,   2             PV     M   ,   3             PV     M   ,   4             BP   M           ]     *             [           OFFSET   1                       OFFSET   N               SPAN       1   :   1     ,   1                         SPAN       1   :   N     ,   1                 SPAN       1   :   1     ,   2                         SPAN       1   :   N     ,   2                 SPAN       1   :   1     ,   3           ⋯         SPAN       1   :   N     ,   3                 SPAN       1   :   1     ,   4                         SPAN       1   :   N     ,   4                 SPAN     2   :   1                         SPAN     2   :   N             ]     =           ⁢                 [           ⁢           APV     1   ,   1           ⋯         APV     1   ,   N                           ⋮                         APV     M   ,   1           ⋯         APV     M   ,   N             ]       →     X   *   β       =   Y           (   7   )                               [           ⁢           T     1   ,   i               ⋮             T     4   ,   i             ]     =       [           ⁢           SPAN       1   :   1     ,   1             SPAN       1   :   1     ,   2             SPAN       1   :   1     ,   3             SPAN       1   :   1     ,   4                           ⋮                                     SPAN       1   :   N     ,   1             SPAN       1   :   N     ,   2             SPAN       1   :   N     ,   3             SPAN       1   :   N     ,   4             ]     *             [           ⁢           PV     1   ,   i                 PV     2   ,   i                 PV     3   ,   i                 PV     4   ,   i             ]     +           [           ⁢           SPAN     2   :   1               ⋮             SPAN     2   :   N             ]     *     BP   i       +     [           OFFSET   1             ⋮             OFFSET   N           ]             (   8   )               
Tasks  352 - 374  and/or by tasks  352 - 386  may be performed to attempt to match the detected temperatures T to the APV temperatures and/or the AP temperatures.
 
     At  376 , the calibration values including the determined SPAN and OFFSET values are stored. The calibration values may be used at a later time for estimating temperatures of a substrate during substrate processing, such as during the method of  FIG. 6 . The following tasks  377 - 386  may be performed, for example, to fine tune the calibration performed during tasks  356 - 376 . This is especially true if temperatures of the micro zones were not monitored and/or accounted for during tasks  356 - 376 . 
     At  377 , the temperature controller may select a predetermined set of probe (or macro zone) temperatures and micro zone temperatures. During cycles of tasks  377 - 386 , these temperatures may be the same, similar to, or different than the temperatures selected during the cycles of tasks  356 - 374 . 
     At  378 , parameters of the micro TCEs are adjusted. These adjustments may be performed in a similar manner as the adjustments performed at  358 . The adjustments may also be based on differences between detected and predetermined temperatures, squares of the differences, a sum square error, and/or other criteria. 
     At  380 , the micro TCE controller determines temperatures of the micro zones via the sensors of the sensor array. At  382 , if the temperatures of the micro zones match and/or are within predetermined ranges of the micro zone temperatures selected at  377  and/or other criteria is satisfied, task  384  is performed, otherwise task  378  is performed. The other criteria may include determining an average of differences, an average of squared differences, and/or other calculations. The other criteria may include providing an average, an error value, and/or a sum square error that is within a predetermined range. The criteria used at task  382  may be different than the criteria used at  366 . 
     At  384 , the parameters used to control the micro TCEs to satisfy the criteria of task  382  are stored. These parameters may be used in addition to the parameters stored at  374  when processing a substrate to provide a selected temperature distribution profile across the substrate. The parameters stored at  374  and  384  may be used to provide a basis for estimating temperatures of a substrate during substrate processing. 
     At  386 , the temperature controller determines whether another cycle is to be performed and/or another set of predetermined macro and micro zone temperatures is to be selected. If another cycle is to be performed task  377  is performed, otherwise the method may end at  388 . The method may end at  388 . 
       FIG. 6  shows a substrate processing method. Although the following tasks are primarily described with respect to the implementations of  FIGS. 1-5 , the tasks may be easily modified to apply to other implementations of the present disclosure. The tasks may be iteratively performed. 
     The method may begin at  400 . At  402 , a processing chamber is initialized for processing a substrate (or wafer). At  404 , the substrate is placed on an ESC in the processing chamber. At  406 , a temperature controller (e.g., the temperature controller  204  of  FIG. 2A ) may access calibration values and/or parameters determined and/or stored during the method of  FIG. 5 . The calibration values and parameters correspond to the ESC and the processing chamber in which the ESC is located. 
     At  408 , the substrate is processed. At  408 A, a system controller (e.g., the system controller  160 ) selects a processing task (e.g., deposition, etching, etc.) to be performed. At  408 B, based on the processing task to be performed, the temperature controller selects a predetermined set of macro and/or micro zone temperatures. At  408 C, based on the set of macro and/or micro zone temperatures, the temperature controller selects and/or adjusts parameters of macro TCEs, micro TCEs, and/or a coolant assembly. 
     At  408 D, temperatures of a heating plate of the ESC are detected via probes (e.g., the probes  220  of  FIG. 2A ). At  408 E, a micro TCE controller (the micro TCE controller  302 ) and/or the temperature controller estimates: temperatures of the micro zones; azimuthally averaged temperatures; and/or arbitrary temperatures (e.g., temperatures anywhere in the heating plate and/or in the substrate); and/or temperatures of the substrate. The micro TCE controller may determine a temperature distribution of the substrate by estimated temperatures across the substrate based on the temperatures of the micro zones; azimuthally averaged temperatures; and/or the arbitrary temperatures. This temperature estimation may be based on predetermined characteristics (materials, layout, makeup, etc.) of the substrate. The temperature estimations may be determined using any of above equations 4-8 based on the calibration values. This may be done in a linear or approximately linear fashion, as the models provided by equations 4, 5 or 6, 7 are approximately linear and/or may be used without the OFFSET values and matrices. 
     At  408 F, the temperature controller determines whether: the temperatures as detected via the temperature probes match and/or are within predetermined ranges of the set of predetermined probe (or macro zone) temperatures selected at  408 C; the estimated temperatures of the micro zones match and/or are within predetermined ranges of the micro zone temperatures selected at  408 C; and/or the macro and micro temperatures satisfy a predetermined criteria. The criteria may include providing an average, an error value, and/or a sum square error that is within a predetermined range. This may include the temperature controller selecting points in the heating plate and determining azimuthally averaged temperatures based on the temperatures of the probes and/or the estimated macro and/or micro zone temperatures. If the detected temperatures match, are within the predetermined ranges and/or satisfy the predetermined criteria, then task  408 G is performed, otherwise task  408 C is performed. 
     At  408 G, the processing task selected at  408 A is performed. Task  408 G may be performed while tasks  408 B- 408 F are performed. At  408 H, if another processing task is to be performed, task  408 A is performed, otherwise task  410  is performed. 
     At  410 , the processed substrate is removed from the processing chamber. Subsequent to task  410 , the method may end at  412 . 
     The above-described tasks of  FIGS. 5-6  are meant to be illustrative examples; the tasks may be performed sequentially, synchronously, simultaneously, continuously, during overlapping time periods or in a different order depending upon the application. Also, any of the tasks may not be performed or skipped depending on the implementation and/or sequence of events. 
     By allowing for calibration and control of an arbitrary number of points and/or radii and by accounting for temperature distributions associated with macro and micro TCEs and temperature losses associated with a base plate, the above described examples allow ESCs to be calibrated. The ESCs may be calibrated such that each of the ESCs and/or corresponding heating plates provides the same temperature control performance. For example, a first ESC may have a first set of calibration values and a second ESC may have a second set of calibration values, which are different than the first set of calibration values. Parameters of TCEs and of a coolant assembly may be adjusted differently, due to the differences in the calibration values of the TCEs to provide a same temperature distribution profile across heating plates of the ESCs and thus across corresponding substrates. 
     The above disclosed examples provide spatial information of heating plates by allowing contributions of any number of TCEs of a heating plate to be accounted for when determining temperatures of any number of points of a heating plate. The examples allow for temperatures of many selected points to be estimated. More points may be monitored than probes used to measure temperature. This is referred to as an under actuated state. 
     The above described examples allow for an arbitrary number of points at predetermined or arbitrary locations to be accounted for in an estimation of temperature at a single point. The single point may be a predetermined or arbitrarily selected point in a macro zone, a micro zone and/or other zone in a chamber. Thus, the estimation accounts for differences in processing chambers by accounting for differences in heating profiles of heating plates due to the differences in processing chambers. 
     The foregoing description is merely illustrative in nature and is in no way intended to limit the disclosure, its application, or uses. The broad teachings of the disclosure can be implemented in a variety of forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be so limited since other modifications will become apparent upon a study of the drawings, the specification, and the following claims. For example, the macro zones in this example are concentric rings and the averaging of sensor readings is thus azimuthal, but any other shapes or relationships to each other could also be used where the averaging was over the approximate lines of equal temperature value. For example, pie shaped macro zones could be averaged over curves paralleling the edges of the macro zones. It should be understood that one or more steps within a method may be executed in different order (or concurrently) without altering the principles of the present disclosure. In addition, the examples herein may pertain directly to the thermal field T(x,y) in a plane above the ESC, but may also be extended to calibrate any volume a sensor array measures such as a volume including a plane (i) within the ESC, or (ii) obliquely above a surface (e.g., a top surface) of the ESC. Also, the temperature fields (or temperature field values) are only examples, the embodiments disclosed herein may be applied to and as a result used to set, monitor, measure, and/or adjust other scalar fields (or field values) such as deposited power values applied beneath the macro zones of an RF antenna or polymer thicknesses on a deposition surface in a reactor controlled by macro zones of a calibrated vapor delivery nozzle. 
     Chemical vapor deposition CVD(x,y) on a wafer or Silicon Nitride (SiNx, SiN) etch rate (ER) may be used as a function of position on the wafer SiN ER(x,y) as a field of interest. From other methodology, the SiN ER(x,y) position may be used to provide a good thermal sensitivity S, where S(x,y,T)=ΔSiN ER (x,y,T)/ΔTemp(x,y,T), where x and y are position coordinates, and T is temperature. Hence the SiN ER divided by the sensitivity S at (x,y,T) is directly related to a temperature of a field of a wafer, which may be used as a calibration value since the result of this division has a higher spatial resolution and homogeneous point-to-point self-consistent-calibration than that provided by wafer-encapsulated-thermal-sensors. 
     In the above-described implementations various actuators are disclosed for affecting various fields. The actuators associated with first zones and first fields when adjusted can affect other zones and fields corresponding to the other zones. Control of first actuators for first fields and first zones (e.g., macro zones, micro zones or other zones) can affect control of second actuators for second fields and second zones (e.g., macro zones, micro zones, or other zones). The control of the first actuators and the second actuators may be feedback control or feedforward control. The control of the first actuators may be feedback control and the control of the second actuators may be feedforward control or vice versa. The control of the first actuators may be feedforward control and the control of the second actuators may be feedforward control. Thus, the control effort provided for the first actuators and the control effort provided for the second actuators is feedback and feedforward independent. 
     Further, various embodiments are disclosed herein. Although each of the embodiments are described as having certain features, any one or more of the features described with respect to any one embodiment of the disclosure can be implemented in and/or combined with features of any of the other embodiments, even if that combination is not explicitly described. In other words, the described embodiments are not mutually exclusive, and permutations of one or more embodiments with one another remain within the scope of this disclosure. 
     Spatial and functional relationships between elements (for example, between modules, circuit elements, semiconductor layers, etc.) are described using various terms, including “connected,” “engaged,” “coupled,” “adjacent,” “next to,” “on top of,” “above,” “below,” and “disposed.” Unless explicitly described as being “direct,” when a relationship between first and second elements is described in the above disclosure, that relationship can be a direct relationship where no other intervening elements are present between the first and second elements, but can also be an indirect relationship where one or more intervening elements are present (either spatially or functionally) between the first and second elements. When a first element is adjacent to a second element, the first element may be in contact with the second element or the first element may be spaced away from the second element without any intervening element between the first element and the second element. When a first element is between a second element and a third element, the first element may be directly connected to the second element and the third element (referred to as “directly between”) or intervening elements may be connected (i) between the first element and the second element, and/or (ii) between the first element and the third element. As used herein, the phrase at least one of A, B, and C should be construed to mean a logical (A OR B OR C), using a non-exclusive logical OR, and should not be construed to mean “at least one of A, at least one of B, and at least one of C.” 
     In some implementations, a controller is part of a system, which may be part of the above-described examples. Such systems can include semiconductor processing equipment, including a processing tool or tools, chamber or chambers, a platform or platforms for processing, and/or specific processing components (a wafer pedestal, a gas flow system, etc.). These systems may be integrated with electronics for controlling their operation before, during, and after processing of a semiconductor wafer or substrate. The electronics may be referred to as the “controller,” which may control various components or subparts of the system or systems. The controller, depending on the processing requirements and/or the type of system, may be programmed to control any of the processes disclosed herein, including the delivery of processing gases, temperature settings (e.g., heating and/or cooling), pressure settings, vacuum settings, power settings, radio frequency (RF) generator settings, RF matching circuit settings, frequency settings, flow rate settings, fluid delivery settings, positional and operation settings, wafer transfers into and out of a tool and other transfer tools and/or load locks connected to or interfaced with a specific system. 
     Broadly speaking, the controller may be defined as electronics having various integrated circuits, logic, memory, and/or software that receive instructions, issue instructions, control operation, enable cleaning operations, enable endpoint measurements, and the like. The integrated circuits may include chips in the form of firmware that store program instructions, digital signal processors (DSPs), chips defined as application specific integrated circuits (ASICs), and/or one or more microprocessors, or microcontrollers that execute program instructions (e.g., software). Program instructions may be instructions communicated to the controller in the form of various individual settings (or program files), defining operational parameters for carrying out a particular process on or for a semiconductor wafer or to a system. The operational parameters may, in some embodiments, be part of a recipe defined by process engineers to accomplish one or more processing steps during the fabrication of one or more layers, materials, metals, oxides, silicon, silicon dioxide, surfaces, circuits, and/or dies of a wafer. 
     The controller, in some implementations, may be a part of or coupled to a computer that is integrated with the system, coupled to the system, otherwise networked to the system, or a combination thereof. For example, the controller may be in the “cloud” or all or a part of a fab host computer system, which can allow for remote access of the wafer processing. The computer may enable remote access to the system to monitor current progress of fabrication operations, examine a history of past fabrication operations, examine trends or performance metrics from a plurality of fabrication operations, to change parameters of current processing, to set processing steps to follow a current processing, or to start a new process. In some examples, a remote computer (e.g. a server) can provide process recipes to a system over a network, which may include a local network or the Internet. The remote computer may include a user interface that enables entry or programming of parameters and/or settings, which are then communicated to the system from the remote computer. In some examples, the controller receives instructions in the form of data, which specify parameters for each of the processing steps to be performed during one or more operations. It should be understood that the parameters may be specific to the type of process to be performed and the type of tool that the controller is configured to interface with or control. Thus as described above, the controller may be distributed, such as by including one or more discrete controllers that are networked together and working towards a common purpose, such as the processes and controls described herein. An example of a distributed controller for such purposes would be one or more integrated circuits on a chamber in communication with one or more integrated circuits located remotely (such as at the platform level or as part of a remote computer) that combine to control a process on the chamber. 
     Without limitation, example systems may include a plasma etch chamber or module, a deposition chamber or module, a spin-rinse chamber or module, a metal plating chamber or module, a clean chamber or module, a bevel edge etch chamber or module, a physical vapor deposition (PVD) chamber or module, a chemical vapor deposition (CVD) chamber or module, an atomic layer deposition (ALD) chamber or module, an atomic layer etch (ALE) chamber or module, an ion implantation chamber or module, a track chamber or module, and any other semiconductor processing systems that may be associated or used in the fabrication and/or manufacturing of semiconductor wafers. 
     As noted above, depending on the process step or steps to be performed by the tool, the controller might communicate with one or more of other tool circuits or modules, other tool components, cluster tools, other tool interfaces, adjacent tools, neighboring tools, tools located throughout a factory, a main computer, another controller, or tools used in material transport that bring containers of wafers to and from tool locations and/or load ports in a semiconductor manufacturing factory. 
     None of the elements recited in the claims are intended to be a means-plus-function element within the meaning of 35 U.S.C. § 112(f) unless an element is expressly recited using the phrase “means for,” or in the case of a method claim using the phrases “operation for” or “step for.”