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Figure 20. Measurements on reference sphere in closed-loop mode under different scan velocities.
Figure
18. Spatial Fourier transform of measured line gratings on SiMetrics RS-M.
Figure 19. Measured profile of the p nom = 4lm line grating.
chromatic differential confocal signals. For the special case of an approximately rectangular linear grating, the smallest pitch offering a plateau for height measurements was p nom = 20lm.
The shown resolution tests and demonstration on an rectangular grating proof, that the developed exposure and measurement tool can deal with non-continuous substrate surfaces in certain limits. If the non-continuous edge is interpreted as a very steep slope, the question arises, what is the maximum slope the tool can follow in closed loop mode. This especially regards continuous free-form substrates. For this purpose, a reference sphere shall be examined. Closed loop profile measurements radially across the apex of a D 0 = 8 mm steel sphere are shown in Figure 20. Different lateral scan velocities v x { 5 lm s �1, 10 lm s �1, 20lm s �1 } were tested. It can be seen that the slowest scan velocity leads to the earliest surface loss. For v x = 5lm s �1 the maximum surface angle can be calculated via equation( 21) as # max
5
¼ 6:62, while for v x = 20lm s �1 a # max
20
¼ 8:33 can be reached.
This effect can be explained with the dynamics of the control structure. The outer control loop incorporating the signal is too slow to follow the fast height changes that suddenly appear during the faster lateral movement. The employed sphere is not perfect and contains local trenches and humps. As these appear for all tested velocities, it is deduced, that these are real objects. Here the filter behavior of the outer control loop can be observed as smaller local peaks for higher velocities in Figure 20. As the NPMM- 5D follows these local peaks and slopes further for the slow v x = 5lm s �1, this local slope causes it to lose the surface for lower angles. This local slope then exceed the maximum angle only for a short lateral distance. The higher velocities there can jump over this local slope, until they lose the signal as well.
It however can be assumed, that an angle of # max = 8 ° can be achieved for the scan of free-form surfaces. As seen in Figure 20 for larger positive distances for v x = 20lm s �1, significant systematic deviations from a fitted reference circle may appear for the measurement signal on higher surface tilts. These stem from the dynamically changing aberration the reflected beam inherits after reflection towards the common fiber. This effect had been studied elsewhere [ 65, 66 ] and will lead to a defocus of the exposure tool on free-form substrates with steep slopes.
4.3 Angular measurements
The identified limits of the chromatic differential confocal measurement regarding the surface slope are now even more motivating for the ability of the tool to align its axis perpendicular to the local surface slope. The proposed angular measurement beam-path can provide the two necessary feedback signals u and #.
In order to characterize the angular measurement, the reflected spot image of the reference steel sphere was evaluated for a rectangular grid of lateral positions. The sphere apex was determined before by confocal measurements and is in center of the probed grid. For each lateral position, an axial stack of 15 images in steps of Dz = 20lm was taken. For each image the spot center is determined by the aforementioned centroid algorithm. An average center position is determined from all 15 respective centers. The procedure ensures, that angles can constructed from defocus positions, too. This is relevant for the previous situation when the confocal signal leads to a defocus position due to the surface curvature or signal loss.