Apparatus and methods with resolution enhancement feature for improving accuracy of conversion of required chemical mechanical polishing pressure to force to be applied by polishing head to wafer

Apparatus for reducing quantization error in a computation of a chemical mechanical polishing parameter, the apparatus comprising:

• first and second digital data processors each provided with data storage for storing synchronization data for synchronization operations of the first and second digital processors, the synchronization data defining a computational resolution, a set of values of the parameter to be used in computations, a set of values of output parameter data for communications between the first and second digital processors, a scale data conversion function that defines a relationship between the parameter and each one of a plurality of scales into which the set of values of the parameter is divided;
• a set point data conversion function that defines a relationship between a range of values of the parameter in a particular one of the scales and a set point that defines a required value of the parameter in the particular scale;
• the first processor being programmed to use the synchronization data to first convert a required value of the parameter to first output pressure digital data representing a particular one of the scales;
• the first processor being further programmed to use the synchronization data to second convert the required value of the parameter to second output pressure digital data representing the set point that defines the parameter in the particular scale;
• the second processor being further programmed to use the synchronization data to third convert the first output parameter digital data to scale data representing the particular one of the scales;
• and
• the second processor being further programmed to use the synchronization data to fourth convert the second output pressure digital data to digital data representing the required value of the parameter.

Apparatus for reducing quantization error in specifying chemical mechanical polishing pressure in which a computational resolution is to be used in processing a required value of the pressure to obtain a computed value of the pressure, the apparatus comprising:

• a chemical mechanical polishing system configured with a polishing pad for applying pressure to a wafer, the pressure being within a set of pressure values that includes the required value of the pressure;
• a first digital processor programmed with a computational resolution having a relatively average value, the first processor being further programmed to divide the highest value of pressure of the set by the value of the computational resolution to obtain a series of pressure scales of the set, the pressure scales representing uniformly increasing possible values of the pressure, the scales having equal ranges of pressure each of which ranges has a value in excess of the value of the required pressure;
• the first digital processor being further programmed to provide a different first identifier for each of the scales of the pressure, the number of different first identifiers being equal to the value of the computational resolution;
• and
• the first digital processor being further programmed to specify the required value of the pressure by providing a different second identifier to indicate a set point value within any specific one of the scales, the set point corresponding to any particular pressure value, the number of different second identifiers being equal to the value of the computational resolution.

Apparatus for processing a desired value among an entire range of pressure values to be applied to a wafer in chemical mechanical polishing, the processing providing improved accuracy in representing the desired value, the apparatus comprising:

• a processor programmed to computationally divide the pressure range by the value of a component resolution to define scale portions of the pressure range;
• the processor being programmed to generate a first output signal to identify one of the computationally defined scale portions that includes the desired value;
• and
• the processor being programmed to computationally generate a second output signal to identify a set point that defines the requested value in the identified scale portion.

Apparatus for reducing quantization error in a computation of a value of desired pressure as a chemical mechanical polishing parameter, the apparatus comprising:

• first and second digital data processors each provided with data storage for storing synchronization data for synchronization operations of the first and second digital processors, the synchronization data defining a particular relatively average computational resolution, a range of values of the pressure parameter to be used in computations, a set of values of output parameter data for communications between the first and second digital processors, a scale data conversion function that defines a relationship between the pressure parameter and each one of a plurality of scales into which the set of values of the pressure parameter is divided;
• a set point data conversion function that defines a relationship between a range of values of the pressure parameter in a particular one of the scales and a set point that defines a required value of the pressure parameter in the particular scale;
• the first processor being programmed to use the synchronization data to first convert a required value of the parameter to first output pressure digital data representing a particular one of the scales;
• the first processor being further programmed to use the synchronization data to second convert the required value of the parameter to second output pressure digital data representing the set point that defines the parameter in the particular one of the scales;
• the second processor being further programmed to use the synchronization data to third convert the first output parameter digital data to scale data representing the particular one of the scales;
• and
• the second processor being further programmed to use the synchronization data to fourth convert the second output pressure digital data to digital data representing the exact value of the pressure parameter in the particular scale.