J. Eur. Opt. Society-Rapid Publ. 21, 7( 2025) 59
Figure
1.( a) Vertical scanning of a microscope. One image is taken at each vertical position.( b) 3D image stack for CM and TFCM. would be required. However, a thin layer with an alternative, preferable inorganic and stable markers e. g. on top or within the substrate could be acceptable as well, as long as the intended device manufacturing and function is not affected.
3. Ease of use: The metrology methods should not be too complex and time-consuming both on the measurement and on the data analysis side in order to enable in-line measurements in particular.
4. Potential for quantitative measurement and traceability: The difference between imaging and imaging metrology is the reliable and traceable quantification. This requires a stable deterministic measurement process with a good reproducibility and a good understanding and control of the whole measurement process. Since today nearly any sophisticated metrology requires a reliable and efficient modelling of the whole measurement process, it is required to have a good understanding and efficient means to model particularly the light-structure interaction, e. g. with the help of Maxwell solvers. Traceability of the measurement means that any measurement parameter( such as the microscope magnification or sample movement) must be traced back to the corresponding SI units. This can be supported or achieved e. g. by access to suitable calibrated reference standards [ 28 ].
Figure 2. Height of grating profile obtained from z-stack image profile( multi colours), grating profile( black stars) from z-stack image directly and grating profile after( blue line) deconvolution of the z-image stack. The nominal height is 138 nm, and the pitch is 300 nm. The intensity of the z-image stack is shown by the colour scale in the background.
3 Label-free super-resolution microscopy for dimensional metrology
As indicated in Section 1, the main goal of our research is to investigate and develop universal methods of imaging optical nanometrology based on label-free SRM techniques. The intended applications in( dimensional) nanometrology define some specific requirements:
1. Universality: the method should allows to cover a broad range of applications, both in terms of materials( particularly including inorganic) and structures to be characterised to enable dimensional nanometrology for important applications such as semiconductor, nanophotonics or other nanotechnologies.
2. Label-free or“ acceptable labelling”: A conditioning with organic molecules as fluorescence markers is typically not acceptable e. g. for wafer manufacturers, so that in the best case a label-free metrology method
Requirement 4 is the reason why in our research we did not consider stochastic functional opto-numerical SRM methods such as STORM, since besides the difficulties in finding stochastic labels alternative to fluorescence markers the stochastic nature of the imaging process would make it, at least, a big challenge to provide traceability.
In the following, we will shortly discuss a number of different label-free SRM methods and consider their potential for dimensional metrology. Many of them have already been extensively described and summarised in [ 13 ], and some have been developed or improved within our research.
Regarding the classification given in Section 1, most approaches to achieve label-free SRM are either based on non-uniform illumination / collection( SIM and related methods), or deterministic functional pump / probe techniques following the basic principles of STED or, more generally, RESOLFT [ 29 ]( reversible saturable optical linear( fluorescence) transition) microscopy methods.
3.1 Methods based on non-uniform( structured) illumination
If we consider an optical imaging system with an imaging numerical aperture NA Img, thenk 0 = 2NA Img / k em( k em being the wavelength of the light used for imaging) is the modulus of the wavevector corresponding to the cut-off frequency x 0 = c k 0 the spatial frequency which can be transmitted by the optical imaging system. SIM is a non-uniform illumination / collection method that extends resolution through the extraction of higher spatial frequency information beyond this cut-off wavevector k 0, and transferring it into an observable region of conventional microscopy in the form of Moiré fringes [ 15 ]. It can be considered as a