Frequency domain laser ultrasound microscopy for nanometric layer thickness imaging with GHz elastic plate resonances

Abstract

Nanometric layer thickness imaging is crucial for fundamental research and characterization of micro fabricated devices. Here, we assess the potential of a non-contact opto-acoustic frequency domain laser ultrasound (FreDomLUS) microscopy technique for imaging nanometric thickness variations via GHz zero-group velocity (ZGV) elastic plate resonances. The method exploits the ZGV's lateral energy confinement that leads to sharp resonance peaks which can be effectively probed with the FreDomLUS technique at GHz acoustic frequencies. For demonstration purposes we introduced sub-10 nm height variation patterns in the topmost layer of solidly mounted bulk-acoustic wave resonators with a design frequency of around 1.7 GHz. They are raster-scanned to retrieve ZGV-frequencies from local acoustic spectra as a contrast quantity for imaging. We show how to retrieve quantitative height information by numerically calibrating the factor which inversely relates ZGV frequency change with the layer thickness change. Height variations in stacks with nominal thickness changes of 8 nm, 4 nm, and 1 nm can be resolved and indicate sub-nanometer depth resolution capabilities. The lateral resolution is studied by measuring the method's step edge function and it is found to be in the micrometer range. Atomic force microscopy imaging is used to validate the results.

Figures (7)

• Figure 1: Samples and Setup. (a) Sketch of the cross section of the studied BAW-resonator samples. They consist of a piezoelectric Sc$_x$Al$_{1-x}$N-layer ($x\!=\!0.09$) sandwiched by two metallic electrodes placed on an acoustic Bragg mirror. The topmost 205nm thick SiN-passivation-layer is structured with pits of depth $\Delta{}d$ that are arranged in either a stepped (b, top) or checkered (b, bottom) geometry. Note that the lateral dimensions of the structures (150µm) are large compared to the total thickness of the layer-system (5.562µm). The red-solid lines are calculated mode-shapes at the ZGV-point (c) Sketch of the FreDomLUS-microscopy setup used for the measurement of acoustic response spectra. (d) Broadband GHz-acoustic response spectrum (left) from an unstructured region of a BAW-device sample and calculated plate-wave dispersion curves (right). The strongest peak in the spectrum is identified as zero-group velocity resonance (labeled as ZGV).
• Figure 2: FreDomLUS line scan on a 8 nm stepped resonator. (a) Narrowband acoustic spectra recorded along a line in $y$-direction. The dark region corresponds to the ZGV-resonance peak and clearly reflects the thickness step in the sample. (b) Example spectra taken from an unpatterned-region (blue), a patterned-region (with reduced thickness; red) and from the transition region (yellow). The locations of the spectra are indicated by horizontal lines in (a). The grey-dots are the original measured data-points, while the solid colored lines are smoothed by Savitzky-Golay filtering. The overlayed bars are histograms of extracted ZGV-frequencies taken from the unpatterned (blue) and patterened-region (red) which are marked by vertical thick lines in (a).
• Figure 3: Calibration of thickness model. (a) Calculated BAW-stack dispersion curves in the region of the first ZGV-resonance with varying top SiN-layer thickness. The ZGV-points are marked by a cross. (b) Relative change of ZGV-frequency vs. relative thickness change. The reference thickness $d\!=\!2167nm$ corresponds to the stack thickness without Bragg-mirror.
• Figure 4: Thickness variation from ZGV-measurements. ZGV-resonance center-frequency variation (grey data points) from FreDomLUS-measurements in stepped resonators with different nominal step-heights of 8nm (a), 4nm (b), and 1nm (c). The additional y-axis on the right side of the plots illustrate the frequency change $\Delta{}f_\mathrm{ZGV}$ with respect to the unpatterned regions of the resonators and the estimated thickness variation $\Delta{}d$ according to Eq. \ref{['eq:freqThick']}. The solid black lines are fits of a step-edge function which has been used to quantify the total step-height $\Delta{d}$ and the lateral resolution $\Delta{}y$ of the method. The grey areas are the distribution functions related to the chosen step-edge function.
• Figure 5: ZGV-resonance based nanometric height-imaging I. (a-c) Images of checkered resonators with different nominal step heights generated from measured ZGV-resonance center-frequencies. Lower regions appear brighter in the image. The additional $\Delta{}d$-axis on the right hand sides of the colorbars were calculated based on Eq. \ref{['eq:freqThick']} (d-f) Histograms of extracted ZGV-center frequencies extracted from five lowered squares (red bars; bright squares in (a-c)) and five squares with unchanged SiN-layer thickness (blue bars; dark squares in (a-c)) and according Gaussian-fits (black solid lines). The ZGV-frequency distribution of the entire image is indicated by the grey bars in the background (they are scaled with the specified factors to fit to the graph). (g-i) Example spectra from lowered regions in (red color), from regions with original SiN-height (blue color) and from transition regions (yellow color). The locations are marked in (a-c) with colored dots/circles.