J. Eur. Opt. Society-Rapid Publ. 21, 27( 2025) 289
resolution of the chromatic differential confocal probe. A flat mirror had been moved by 3 nm steps with a hold time of 10 s for each step. As there is only a single reflective interface involved, this is determining the single-surface resolution. As illustrated in Figure 16, the steps of 3 nm can be distinguished. Additional filtering with an ideal low-pass f C = 20 Hz emphasizes the attained axial single-surface resolution of the probe as shown by the dark-turquoise line.
However, the additional filtering also reveals aperiodic waveforms in the dark-turquoise line, that do not correlate with the stage movement as shown by the interferometer values below. These indicate the underlying instability of the fiber-coupled laserdiodes. Although the used laserdiodes are temperature- and current-controlled, chaotic de-stabilization from back reflection into the source appears. Note that these power uncertainties are below one percent. This unfortunately takes place in an unfavorable frequency space from approximately 0 – 1000 Hz. Thereby it overlaps with the measurement signal and cannot be removed with the lock-in filter.
4.2 Demonstration on reference targets
The shown axial single-digit nanometer resolution promises a very good performance for the accurate exposure focus control on pre-structured substrates. To test this ability, a lateral resolution reference target was measured. The SiMetrics RS-M was employed for this purpose. Its a bare silicon chip with various etched line gratings with pitches. from 4 lm to 800 lm and a nominal depth of h RSM 3 lm. Measurements were performed orthogonal to the lines of the grating. Thereby, a closed loop measurement towards the surface was performed. This means that the signal of the chromatic differential confocal probe was directly used to move the axial stage back into the working point. Nevertheless, the axial stage still has an inner control loop where the interferometers provide feedback([ 60 ], p. 135). The differential confocal signal had been used as slower outer feedback. As it is slower, it may not always be possible to move back into the working point of the differential probe during lateral scans. To compensate for this lag, the characterized non-ambiguous range was used to calculate correct depth values during movements:
z M ðx M; y M Þ¼z IM þ z DCM ð24Þ
Figure 17 shows the result on the grating with the nominal pitch of p nom = 80lm in comparison to a measurement of a large range prototype for atomic force microscopy( AFM) [ 61, 62 ]. Both measurements are area scans that were performed approximately in the same region on the line grating. These area scans then were corrected for their respective slant and rotation. In the end, the area scan was flushed into its projection on the xz-plane by taking the average along the y-direction.
Visibly, the chromatic differential confocal measurement in Figure 17 exhibits large signal peaks at the edges of the structure. These are caused by the diffraction of the coherent focused measurement leasers. Typically, these so called bat-wings are symmetrical towards the grating [ 63, 64 ]. However, the here found asymmetry suggests, that
Figure 17. Measured profile of the p nom = 80lm line grating in comparison to a long range AFM measurement.
the specimen is slightly tilted, because one side of the trench can be measured well. On the other side of the trenches, the about 7 lm deep diffraction minima are amplified by the shadow of the structure.
Comparing the result to the AFM-measurement, both confirm each other well. Of special importance is the height measurement in order to demonstrate a correct height reconstruction. The wide plateaus of the p nom = 80lm will be evaluated to prevent the diffraction to affect this height measurement. Relevant height data is identified through the diagrams histograms. The chromatic differential confocal measurement reconstructs an average h CDCM = 2.769 ± 0.212 lm, k = 1 while the AFM provides h AFM = 2.687 ± 0.129lm, k = 1. As the uncertainty region of one measurement includes the average value of the respective other measurement, this comparison implies an accurate height reconstruction for flat specimen regions. The major contributor to this uncertainty is the specimen itself. The chromatic differential confocal probe exhibits higher uncertainty due to the power fluctuation from the two laserdiodes.
The pitches of the two measurements p CDCM = 79.714 ± 0.695 lm, k = 1 and p AFM = 79.956 ± 0.406 lm, k = 1 align well. The inset in Figure 17 shows a single period and the critical dimension. The latter is warped by the diffraction effect and cannot be clearly derived. Overall, the p nom = 80lm line grating is clearly resolved by the chromatic differential confocal probe. With expected Airy disks for the measurement focus of r C 1.64 lm, the p nom = 4lm grating should be resolved. Indeed, the spatial Fourier transforms of the respective line grating measurement shown in Figure 18 reveal significant peaks at the nominal pitches of the SiMetrics RS-M.
The peak at f x = 250 LP / mm in Figure 18 confirms sufficient imaging contrast for the smallest grating. The actual profile measurement is shown in Figure 19. Visibly, the pitch of the grating can be derived, but the height is not accurate anymore. The depth of the grating is considerably too large. AFM measurements disprove this. This is caused by the merging diffraction effects of the grating onto