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# Algorithm for Computing Thin Film Thicknesses

IP.com Disclosure Number: IPCOM000085445D
Original Publication Date: 1976-Apr-01
Included in the Prior Art Database: 2005-Mar-02
Document File: 2 page(s) / 13K

IBM

## Related People

Ananthakrishnan, RB: AUTHOR [+1]

## Abstract

In the measurement of film thicknesses, particularly films utilized in integrated circuits, the major computation burden is the solution of the equation: R ( Lambda ) = A + B cos Z over C + B cos Z for Z where; R = measured reflectivity. A, B, C = Functions of Frenel coefficients and are functions of Lambda. Z = 4 Pi nd over Lambda where; n = Refractive index. d = Thickness to be measured. Lambda = Wavelength.

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Algorithm for Computing Thin Film Thicknesses

In the measurement of film thicknesses, particularly films utilized in integrated circuits, the major computation burden is the solution of the equation: R ( Lambda ) = A + B cos Z over C + B cos

Z for Z where; R = measured reflectivity. A, B, C = Functions of Frenel coefficients and are

functions of Lambda.

Z = 4 Pi nd over Lambda

where; n = Refractive index.

d = Thickness to be measured.

Lambda = Wavelength.

The solution of the reflectivity equation for Z has to deal with the uncertainty of the order number. Several techniques have been devised to deal with this problem. One such technique is to make an estimate of the order number, and to compute the thickness based on this order number for various Lambda's. This process is repeated for various different order numbers. The correct order number is the one that yields the minimum scatter on the thickness estimate.

Another technique involves the extrema of the "now alized" reflectivity curve which are used to estimate the thickness in the following way:

Use is made of the fact that the order numbers at the extrema are integers, odd or even depending on whether the extremum is a minimum or a maximum. Since successive order numbers differ by 1, the extreme Lambda taken two at a time will yield several estimates of the thickness, the average of which is used to further refine the estimate by a Fourier power spectrum analysis and a subsequent cosine fit.

The algorithm pre...