# Multiple-Angle Incidence Ellipsometry Measures Very Thick Films

Ellipsometry is widely considered to be the best technique for measuring very thin films (a few hundred angstroms or less). It is less-well known that multiple-angle ellipsometry is also well suited to measuring very thick transparent films (up to 50 µm). The technique is analogous to the method used by spectral reflectometers to measure thick films. Ellipsometers from Rudolph Technologies Inc. (Flanders, NJ; 973-691-1300) are among the instruments successfully used in thick-film applications.

Just as the spectral reflectance (reflectance vs. wavelength) from a thick film exhibits distinct oscillations, thick films also cause oscillations in the ellipsometric parameters, delta and psi, as a function of angle of incidence (Fig. 1). The thickness of the film determines the period of these oscillations; the thicker the film the shorter the period of the oscillations. Hence, by measuring the oscillation period, one can quickly and accurately measure film thickness. Fig. 1: The oscillations in delta shown above were recorded by a SpectraLaser simultaneous angle of incidence ellipsometer while measuring the thickness of a thick (approx. 15 µm) photoresist on a silicon substrate.

The following is the formula for determining film thickness:

D = l/2[ (n2 - sin (q2)2)1/2 - (n<> - sin (q1)2)1/2]-1

In this formula, l is the measurement wavelength, n is the refractive index of the film, and q1 and q2 are the angles of incidence corresponding to delta passing through 180° (delta crossings). The refractive index of the film at the measurement wavelength must be known to measure accurate thicknesses with this technique. It can be accurately determined by using the ellipsometer.

The film model in Figure 2 shows the thickness measurement (1T) of a thick-resist film on silicon. The fit error is zero, as expected, because no fitting analysis is necessary. Note that the input thickness into the model was only 5 µm, yet the algorithm correctly determined the film thickness to be 14.756 µm. The model does not require any input thickness in order to determine the thickness of the film, giving it an advantage over methods that require a seed value and those which can exhibit order skipping. Fig. 2: A SpectraLaser system was used to map the thickness of a thick resist film on silicon.

Figure 3 shows a 49-point map of a 15-µm (nominal) resist film. The data analysis of the map shows a range of 7904 Å and a standard deviation of 2460 Å, which equals a film uniformity of 1.69%. Fig. 3: A 49-point map of a 15-µm (nominal) resist film.

The SpectraLaser ellipsometer from Rudolph Technologies Inc. provides a quick, easy, and reliable method to measure the thickness of thick (5–50 µm) films. These measurement and modeling capabilities are made possible by the multiple angles of incidence ellipsometry.