Method for controlling a process in a multi-zonal apparatus

A method for controlling planarization of a work piece in a processing apparatus comprising a plurality of zones and with which removal rate of material from the work piece surface is a function of pressure applied to the work piece and a localized pressure profile P(x) applied to the work piece surface is a function of pressure P(Zi) in each of the plurality of zones i, the method comprising the steps of:

• a) determining an analytical model for the processing apparatus correlating P(x) to P(Zi);
• b) setting a first pressure P1(Zi) in each of the zones and determining the resultant localized pressure profile P1(x) applied to the surface of a work piece;
• c) planarizing a test work piece using the pressures profile P1(x) and determining a test removal rate profile RR1(x) as a function of position (x) on the test work piece for the pressures profile P1(x);
• d) determining a target removal rate profile RRt(x) for a work piece to be planarized;
• e) calculating a difference D1 between RR1(x) and RRt(x);
• f) calculating a revised removal rate profile RR2(x) resulting from a change in pressure to P2(Zi) as a result of changing the pressure P1(Z1) in zone one in one direction to a pressure P2(Z1) where RR2(X)=RR1(x)*P2(X)/P1(x) and P2(X) is the localized pressure profile applied to the work piece surface as a result of the pressure P2(Zi);
• g) calculating a difference D2 between RR2(X) and RRt(x);
• h) maintaining the pressure P2(Z1) if D2 is less than D1;.
• i) if D2 is greater than D1, calculating a revised removal rate profile RR3(x) resulting from a change in pressure to P3(Zi) as a result of changing the pressure P1(Z1) in a direction opposite to the one direction in zone one to a pressure P3(Zl) where RR3(x)=RR1(x)*P3(x)/P1(x) and P3(x) is the localized pressure profile applied to the work piece surface as a result of the pressure P3(Zi);
• j) calculating a difference D3 between RR3(x) and RRt(x);
• k) maintaining the pressure P3(Z1) if D3 is less than Dl and maintaining the pressure P1(Z1) if D3 is greater than D1;
• l) repeating steps f) through k) for each of the plurality of zones in the processing apparatus where for each iteration RRn(x) is calculated in accordance with RRn(x)=RRn−1(x)*Pn(x)/Pn−1(x) and Dn is the difference between RRn(x) and RRt(x) where(n) denotes the iteration being calculated and (n−1) denotes the previous iteration having the least difference between the removal rate for that iteration and the target removal rate;
• and
• m) planarizing a work piece using the pressure values determined in steps f) through l) that result in a minimum value for Dn.

A method for controlling a process on a work piece in a processing apparatus, the processing apparatus comprising a plurality of zones Zi within each of which a processing parameter J(Zi) can be controlled to establish a processing parameter profile J(x) as a function of position x on the work piece, the processing apparatus producing a process result Q(x) as a function of the application of J(x) to the work piece, the method comprising the steps of:

• processing a test work piece using initial settings Jl(Zi) of a processing parameter J in each of the plurality of zones i to establish an initial process parameter profile J1(x) and to achieve an initial process result Q1(x) as a function of position x on the test work piece;
• calculating a revised processing result Qf(x) as a function of position (x) on a work piece as a result of modifying the processing parameter in at least one of the plurality of zones to establish a processing parameter profile Jf(x) as a function of position (x) on the work piece in accordance with the relationship Qf(x)=Q1(x)*Jf(x)/J1(x);
• and
• processing a work piece using the processing apparatus with the process parameter in the plurality of zones set to achieve the process parameter profile Jf(x).