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

A system includes sensors, an interface and a controller. The interface receives feedback signals from the sensors. At least some of the sensors are disposed in an electrostatic chuck. The feedback signals are indicative respectively of fields of a heating plate of the electrostatic chuck. The controller, based on the fields and sets of calibration values, estimates values of a first field respectively for multiple points on a substrate. Each of the sets of calibration values corresponds respectively to one of multiple actuators. The calibration values, in each of the sets of calibration values, define amounts of contribution provided by a respective one of the actuators to the first field for the points. The controller changes physical states of the actuators based on the estimated values of the first field of the points to provide a predetermined temperature distribution profile across the electrostatic chuck.