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

A method of reducing quantization error in a computation of chemical mechanical polishing parameter, comprising the operations of:

• defining synchronization data for synchronization operations of 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;
• performing a first conversion operation in the first processor and based on the synchronization data, the first conversion operation being performed on a required value of the parameter, the first conversion operation converting the required value of the parameter to first output parameter digital data representing a particular one of the scales;
• performing a second conversion operation in the first digital processor and based on the synchronization data, the second conversion operation being performed on the required value of the parameter to convert the required value to second output parameter digital data representing the set point that defines the required value of the parameter in the particular scale;
• performing a third conversion operation in the second processor and based on the synchronization data, the third conversion operation being performed on the first output parameter digital data to convert the first output parameter digital data to scale data representing the particular one of the scales;
• and
• performing a fourth conversion operation in the second processor and based on the synchronization data, the fourth conversion operation being performed on the second output parameter digital data to convert the second output parameter digital data to digital data representing the required value of the parameter.

A method of reducing quantization error in specifying a chemical mechanical polishing parameter in which a computational resolution is to be used in processing a required value of the parameter to obtain a computed value of the parameter, comprising the operations of:

• defining a relatively average value of the computational resolution;
• defining a set of values of the parameter, the set containing possible values of the parameter, the set of possible parameter values including the required value of the parameter;
• dividing the highest value of the parameter of the set by the relatively average value of the computational resolution to obtain a series of parameter scales of the set, the parameter scales representing uniformly increasing possible values of the parameter, the scales having equal ranges of value of the parameter each of which ranges has a value in excess of the value of the required parameter;
• providing a different first identifier for each of the scales of the parameter, the number of different first identifiers being equal to the value of the computational resolution;
• and
• specifying the required value of the parameter 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 parameter value, the number of different second identifiers being equal to the value of the computational resolution.

A method of reducing quantization error in an analog computation for converting an input representing force in terms of units of force to an analog force output representing force in terms of a force actuator signal, comprising the operations of:

• converting the input to two analog force signals and a plurality of digital logic signals, the analog force signals representing the boundaries of a range of force actuator signals to be input to a force actuator, the range including a force actuator signal having a value corresponding to the value of the force in force units;
• the digital logic signals having a resolution less than or equal to 12 bits, the digital logic signals representing the force actuator signals in the range having the value corresponding to the value of the force in force units;
• based on the resolution of the digital logic signals, converting a difference between the two analog force signals to an analog force increment signal;
• based on logic defined by the digital logic signals, converting the analog force increment signal to an analog force set point signal;
• and
• adding one of the analog force signals to the analog force set point signal to determine the value of the force actuator signal.