Single side polishing using shape matching

1. A method of polishing a wafer, the method comprising:

measuring a first wafer to determine a starting wafer profile;

polishing the first wafer after determining the starting wafer profile;

measuring the first wafer after polishing to determine a polished wafer profile;

determining a removal profile by comparing the starting wafer profile and the polished profile to compute the amount and shape of material removed from the first wafer during polishing;

measuring a second wafer to determine an initial profile;

determining an initial predicted profile by comparing the initial profile of the second wafer to the removal profile of the first wafer; and

determining an initial predicted flatness parameter of an initial predicted polished surface from the initial predicted profile.

2. The method of claim 1 , further comprising the steps of:

determining a rotated predicted profile by rotating the initial profile with respect to the removal profile and comparing the initial profile in a rotated orientation to the removal profile of the first wafer; and

determining a rotated predicted flatness parameter of a rotated predicted polished surface from the rotated predicted profile.

3. The method of claim 2 , wherein the flatness parameter is selected from the group consisting of SBIR, GBIR, SFQR, and ESFQR.

4. The method of claim 2 , wherein the initial profile is rotated with respect to the removal profile at an angle of approximately 5 degrees.

5. The method of claim 2 , further comprising the step of:

determining a superior flatness parameter by comparing the initial predicted parameter and the rotated predicted flatness parameter.

6. The method of claim 5 , further comprising repeating the steps of determining a rotated predicted profile, determining a rotated predicted flatness parameter, and determining a superior flatness parameter for additional rotated orientations to determine an optimal flatness parameter.

7. The method of claim 6 , further comprising the step of placing the second wafer into a polisher in the rotational orientation corresponding to the optimal flatness parameter.

8. The method of claim 7 , further comprising the step of polishing the second wafer.

9. The method of claim 8 , further comprising the steps of:

measuring the second wafer after polishing to determine a second polished wafer profile; and

determining a second removal profile by comparing the initial profile of the second wafer to the second polished wafer profile to compute the amount and shape of material removed from the second wafer during the polishing process.

10. A method of processing a wafer with respect to an indexed polishing head in a polisher, the method comprising:

measuring a first wafer to determine a starting profile;

polishing the first wafer after the starting profile is determined;

measuring the first wafer after polishing to determine a polished wafer profile;

calculating the removal profile of the first wafer by superposing the starting profile with the polished wafer profile

measuring a second wafer to determine an initial profile;

superposing the removal profile of the first wafer on the initial profile of the second wafer to predict the shape of the second wafer after single side polishing to determine an initial predicted profile and; and

predicting a flatness parameter of the initial predicted profile.

11. The method of claim 10 , further comprising the step of obtaining the removal profile within 300 minutes of processing the second wafer.

12. The method of claim 10 , wherein the flatness parameter is selected from the group consisting of SBIR, GBIR, SFQR, and ESFQR.

13. The method of claim 10 , wherein the flatness parameter includes a combination of at least two flatness parameters selected from the group consisting of SBIR, GBIR, SFQR, and ESFQR.

14. The method of claim 10 , further comprising the step of calculating the optimal rotation of a wafer relative to the polishing head to optimize the flatness parameter.

15. The method of claim 10 , further comprising the step of indexing the rotational head according to the optimal rotational angle.

16. The method of claim 10 , further comprising the step of optimizing the predicted flatness parameters by determining the rotation angle of the indexed polishing head to provide optimal flatness parameters.

17. The method of claim 10 , further comprising the step of polishing the second wafer.

18. The method of claim 10 , further comprising the step of:

measuring the second wafer after polishing to determine a second polished wafer profile; and

determining a second removal profile by comparing the initial profile of the second wafer to the second polished wafer profile to compute the amount and shape of material removed from the second wafer during the polishing process.

19. A method of polishing a wafer, the method comprising:

measuring a first wafer to determine a starting wafer profile;

polishing the first wafer after determining the starting wafer profile;

measuring the first wafer after polishing to determine a polished wafer profile;

measuring a second wafer to determine an initial profile; and

placing the second wafer into a polisher in a rotational orientation corresponding to a provided optimal flatness parameter,

wherein the provided optimal flatness parameter and the corresponding rotational orientation are based on:

a removal profile determined by comparing the starting wafer profile and the polished profile to compute the amount and shape of material removed from the first wafer during polishing;

an initial predicted profile determined by comparing the initial profile of the second wafer in an initial relational orientation to the removal profile of the first wafer;

an initial predicted flatness parameter of an initial predicted polished surface determined from the initial predicted profile;

a rotated predicted profile determined by rotating the initial profile with respect to the removal profile and comparing the initial profile in a rotated orientation to the removal profile of the first wafer;

a rotated predicted flatness parameter of a rotated predicted polished surface determined from the rotated predicted profile;

a superior flatness parameter determined by comparing the initial predicted parameter and the rotated predicted flatness parameter; and

an iteration of determining a rotated predicted profile, determining a rotated predicted flatness parameter, and determining a superior flatness parameter for additional rotated orientations to determine the optimal flatness parameter.

20. The method of claim 19 , wherein the flatness parameter is selected from the group consisting of SBIR, GBIR, SFQR, and ESFQR.