White light interferometry is often deployed by industries and researchers for surface measurements. While this technique is fast and accurate, it suffers from a limitation in lateral resolution.
The principle underlying interferometric methods is simple. A beam of light is split into two. One part is reflected off a reference surface and the other from a test surface. The two parts are then recombined and the phase or contrast of the resulting combined light is measured. As the test surface moves through the interferometer’s focus, a series of optical fringes are obtained. These correspond to the test surface’s topography, quite similar to a topographic map generated for a geographic area.
Advantages and Limitations
The advantages of the white light interferometry method include negligible setup time and extremely low measurement times. However, a drawback of interferometry methods faced in some situations is that only a limited lateral resolution can be achieved when compared to optical systems based on the scanning electron microscope (SEM) or the atomic force microscope (AFM).
Figure 1. Illustration of pixel-limited resolution. The red bars represent the overall light collected in each pixel. The two adjacent features will not be distinguished because of inadequate camera pixel spacing.
One limitation to lateral resolution is related to pixel-limited resolution, which is observed at low magnifications. This pixel-limited resolution causes two adjacent features to be digitally imaged on to a single pixel. This prevents distinguishing between the two features in the final image. An increase in the pixel number in the camera used for imaging will increase resolution.
Another limitation is the diffraction-limited resolution that is observed at high magnifications. Here two camera pixels are available for each feature. Still, multiple features cannot be easily distinguished from one another, producing diffraction-limited images.
Figure 2. Illustration of diffraction-limited resolution. Features are wider than the camera pixel spacing but are blurred due to the optics of the system and in this case are barely separated.
Sparrow Criterion Formula
The Sparrow criterion formula defines the diffraction-limited resolution ä as
λ being the wavelength of light and NA the numerical aperture of the optical imaging system used.
High magnification objectives may be used to increase the resolution, but they are expensive. Besides, only objects of limited sizes can be imaged within a field of view.
If the diffraction limit is overcome, smaller features can be readily distinguished for a given microscope magnification, resulting in a larger field of view and minimizing the need to combine multiple images for complete characterization of a surface. Typical applications include detection of defects on substrates, sub-cellular structure imaging and quality control of nanoscale materials.
Overcoming the Diffraction Limit
Several techniques have been proposed to improve the diffraction-limited resolution of optical systems. However, not many systems that can solve this problem and provide real-time improvements in the measurement of lateral resolution of surfaces are commercially available. The major reason for this is the inability of optical systems to selectively enhance the signal while suppressing noise.
Bruker has developed an innovative interferometric measurement mode called AcuityXR, which can enhance the lateral resolution. AcuityXR uses a combination of hardware and software techniques to overcome the optical diffraction limit and measure the features of any smooth surface. Enhanced resolution microscopy is made possible by advanced system modeling and the use of multiple scans. As shown in Figures 3–5, fine features can be observed in greater detail, in the form of more separated lines or sharper defects using AcuityXR.
Figure 3. 350nm linewidth measurements taken with Standard PSI (top) with little feature separation and AcuityXR PSI (bottom), showing high levels of feature differentiation.
Figure 4. All the images have the same vertical scale of 2nm (red) to -8nm (blue). Standard PSI Measurements (left) and AcuityXR PSI Measurements (right) of 200, 150, and 130nm linewidth features. The two 130nm lines are indistinguishable in standard PSI measurements, but AcuityXR PSI is able to separate the two features.
Figure 5. Images taken with Standard PSI (left) and AcuityXR PSI (right) shows vast improvement in AcuityXR PSI in the ability to make images less pixilated while showing the proper structure on the sample.
Advantages and Limitations
The AcuityXR technology provides significant benefits in quantitative measurements of key surface features. For instance, enhanced lateral resolution offered by AcuityXR results in more accurate measurement of narrow linewidths, better feature separation capability and improved feature clarity.
The use of the AcuityXR mode is limited to surfaces that have local roughness less than 20 nm. In the case of rougher surfaces, the additional noise caused limits the ability to model the system's behavior accurately. When using AcuityXR, slight ringing may be observed for surfaces with great amounts of missing data, as the algorithms consider contiguous surfaces.
White light interferometry is commonly used in surface measurements. Bruker’s white light optical profilers make use of the AcuityXR technology, which can significantly enhance lateral resolution in these measurements. Using system modeling, multiple surface scans and low-noise measurements, the technology makes it possible to reduce the blur that optical elements in a system cause and observe smooth surfaces in greater detail.
This information has been sourced, reviewed and adapted from materials provided by Bruker Nano Surfaces.
For more information on this source, please visit Bruker Nano Surfaces.