Method for modeling devices in a wafer
View Patent ↗A method for modeling devices in a wafer comprises the step of providing the wafer comprising a first plurality of devices having a track width and a first stripe height, a second plurality of devices having the track width and a second stripe height, and a third plurality of devices having the track width and a third stripe height. The method further comprises the steps of measuring resistance values for the first, second and third plurality of devices to obtain a data set correlating a stripe height and a resistance value for each of the first, second and third plurality of devices, and estimating a linear relationship between resistance and inverse stripe height for the first, second and third plurality of devices based on the data set.
1. A method for modeling devices in a wafer, comprising the steps of:
providing the wafer comprising a first plurality of devices having a track width TW and a first stripe height SH 1 , a second plurality of devices having the track width TW and a second stripe height SH 2 , and a third plurality of devices having the track width TW and a third stripe height SH 3 ;
measuring resistance values for the first, second and third plurality of devices to obtain a data set correlating a stripe height and a resistance value for each of the first, second and third plurality of devices; and
estimating a linear relationship between resistance and inverse stripe height for the first, second and third plurality of devices based on the data set,
wherein SH 1 differs from SH 2 by a first predetermined amount δH 1 , and wherein SH 2 differs from SH 3 by a second predetermined amount δH 2 , such that SH 1 +δH 1 =SH 2 and SH 2 +δH 2 =SH 3 .
2. The method according to claim 1 , wherein the first, second and third plurality of devices comprise magnetoresistive transducers.
3. The method according to claim 1 , wherein the first, second and third plurality of devices comprise electronic lapping guides.
4. The method according to claim 1 , wherein SH 1 ≠SH 2 ≠SH 3 .
5. The method according to claim 1 , wherein the first predetermined amount δH 1 is equal to the second predetermined amount δH 2 , such that δH=δH 1 =δH 2 .
6. The method according to claim 5 , further comprising the step of estimating SH 1 , SH 2 and SH 3 according to the formula SH 1 +δH=SH 3 −δH=SH 2 =2δH((R 3 −R 1 )/(R 3 +R 1 −2R 2 )), wherein R 1 is a measured resistance value for one of the first plurality of devices, R 2 is a measured resistance value for one of the second plurality of devices, and R 3 is a measured resistance value for one of the third plurality of devices.
7. The method according to claim 1 , wherein the wafer comprises m pluralities of devices, each plurality of devices having a different stripe height than other ones of the plurality of devices.
8. The method according to claim 7 , wherein m is greater than 3.
9. The method according to claim 1 , wherein the linear relationship between resistance R and inverse stripe height 1/SH is estimated according to the formula R=Intercept+Slope/SH, where
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and where n is a number of points in the data set, x is an inverse of a stripe height in the data set, and y is a resistance value in the data set.
10. The method according to claim 9 , wherein the Intercept represents a resistance value of leads connected to each of the first, second and third plurality of devices.
11. The method according to claim 9 , wherein the Slope represents a device resistance area (RA) divided by the track width TW.
12. The method according to claim 11 , wherein the first, second and third plurality of devices comprise magnetoresistive transducers.
13. The method according to claim 9 , wherein the first, second and third plurality of devices comprise electronic lapping guides, and wherein the Slope represents a sheet resistance times the track width TW.
14. The method according to claim 9 , further comprising the step of estimating a correlation coefficient r for the data set according to the formula
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15. The method according to claim 14 , wherein if r 2 is below a predetermined threshold, one or more correlated stripe height and resistance values are removed from the data set before estimating the linear relationship.
16. The method according to claim 15 , further comprising averaging stripe height and resistance values from one or more devices adjacent to the devices corresponding to the removed values to replace the values removed from the data set.
17. The method according to claim 14 , wherein if r 2 is below a predetermined threshold, residuals within the data set are calculated, the correlated stripe height and resistance value corresponding to the largest calculated residual is rejected, and the Intercept, Slope and r 2 are recalculated with the remaining data.
18. The method according to claim 1 , wherein the first, second and third plurality of devices are arranged in corresponding first, second and third rows.
19. The method according to claim 18 , further comprising the steps of:
cutting the wafer to separate the first, second and third rows to form a first, a second and a third bar of devices; and
lapping each of the first, second and third bar of devices until a remaining stripe height for each of the corresponding plurality of devices therein is reached, based upon a measured change in resistance value and the estimated linear relationship.
20. The method according to claim 19 , wherein the step of cutting the wafer occurs after the step of estimating the linear relationship.