Methods and apparatus for deriving thermal flux data for processing a workpiece

A method of maintaining a process chamber for performing a temperature sensitive process on a semiconductor wafer, the process chamber includes a support for supporting the bottom surface of the wafer and regulating the temperature of the wafer, the method comprising the steps of:

• A. providing target heat flux values, FT, for heat flux into and out of the wafer for predetermined conditions;
• B. making new measurements of temperatures experienced by the semiconductor wafer for the predetermined conditions;
• C. deriving new heat flux values, FN, using the temperatures from step B;
• D. comparing the target heat flux, FT, to the new heat flux, FN, to assign a status for the process chamber so that the process chamber status is operational if FT and FN are substantially equal or malfunctioning if FT and FN are not substantially equal.

A method of operating a manufacturing facility for processing wafers using temperature sensitive processes, the method comprising the steps of:

• A. providing at least one process chamber capable of processing the wafers, wherein the process chamber is part of the manufacturing facility;
• B. providing a sensor apparatus for measuring temperatures experienced by the wafer and capable of wirelessly collecting and transmitting or storing temperature data from within the process tool;
• C. providing target heat flux values, FT, for heat flux into and out of the wafer for predetermined conditions;
• D. making new measurements of temperatures experienced by the semiconductor wafer for the predetermined conditions;
• E. deriving new heat flux values, FN, using the temperatures from step D;
• F. comparing the target heat flux, FT, to the new heat flux, FN, to assign a status for the process chamber so that the process chamber status is
• i. operational if FT and FN are substantially equal or
• ii. malfunctioning if FT and FN are not substantially equal.

A computer readable medium encoded with computer executable steps for deriving heat flux values for managing a plasma process chamber, the chamber being capable of generating a plasma, the chamber having a chuck for supporting a workpiece in the plasma, at least one of the heat flux values being a plasma heat flux, at least one of the heat flux values being a chuck heat flux, the steps comprising:

• A. obtaining temperature meausurements, T(x,y,t), representing the temperature of the workpiece in the chamber in the presence of the plasma;
• B. using the temperature measurements, T(x,y,t), to compute the within workpiece thermal flux term ∇2T(x, y, t) using the equation
• ∇2T(x,y,t)=Average of T over a circle of small radius centered at (x,y)−T(x,y,t);
• C. estimating the chuck temperature, Tc, and the chuck conduction coefficients, α, for spatial co-ordinates (x,y) by determining a best fit of the temperature measurements to the equation
• 6 ⅆ T ⅆ t = k w ⁢ ∇ 2 ⁢ T - k c ⁢ α ⁡ ( T - T c ) ;
• and
• D. computing the plasma heat flux, Φp, and the chuck heat flux, Φc, using the equations
• Φc=α(T−Tc) and 7 k p ⁢ Φ p = ⅆ T ⅆ t - k w ⁢ ∇ 2 ⁢ T + k c ⁢ Φ c .