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Production sequence of Si-spheres and interferometrical determination of the sphere volume

AFM Linewidth Metrology

Working Group 5.23

Developments of high resolution CD/3D AFMs


The traceable calibration of 3D geometry of complex nanostructures still remains as a challenging task today. In this working group, new traceable route is developed by applying two complementary methods, referred to as the bottom-up and top-down approaches, respectively.
The concept of the bottom-up approach is to apply the silicon crystal lattice as an internal rule, as shown in Fig 1(a). After the structure is measured by e.g. a high-resolution transmission electron microscopy (HR-TEM), its geometry can be calculated directly by counting the number of the crystal planes (N) inside the structure, together with the known silicon crystal constant d111 determined traceably as 313.560 11(17) pm by combined x-ray and optical interferometry from bulk silicon material. This method is highly accurate, however, is limited in the range of single-crystal material. 
For metrology of structures with noncrystal material, an alternative top-down method has been developed, as shown in Fig. 1(b). Using this method, the pitch L of line features was accurately and traceably calibrated in advance, for instance, by a metrological AFM. After the line features were imaged in a HR-TEM, the pitch (M) and width (N) of the feature pair could be determined in pixel units. Thus, the scaling factor of the HRTEM image could be calculated as K = L/M nm/pixel and the width of the structure could be evaluated as W = N×L/M. An important idea underlying the proposed method is that unlike the CD metrology the pitch calibration using AFMs is independent of its tip geometry.
The traceability chains of two approaches mentioned above are quite different. In the first method, the traceability chain is ensured via the lattice constant in the Si single-crystal TEM lamella, x-ray interferometry in Si bulk material, optical interferometry and then to the optical wavelength and the metre definition of the International System of Units (SI); while in the second method, the traceability chain is ensured via the AFM sample stage position measured by laser interferometer, and then to the optical wavelength and the SI metre definition. Consistency of these two methods has been verified in our previous study.

Figure 1. Two strategies applied in traceable calibration of the geometry of the reference nano structure based on its transmission microscopic images, (a) via silicon crystal lattice constant and (b) via metrological AFM

For more details of this research task, please refer to some selected publications listed below:

[1] Gaoliang Dai et al.  Gaoliang Dai, Ludger Koenders, Jens Fluegge, Harald Bosse, “Two approaches for realizing traceability in nanoscale dimensional metrology,” Opt. Eng. 55(9), 091407 (2016), doi: 10.1117/1.OE.55.9.091407.
[2] Gaoliang Dai et al. Reference nano-dimensional metrology by scanning transmission electron microscopy, Meas. Sci. Technol. 24 (2013) 085001
[3] Gaoliang Dai et al. Development and characterisation of a new line width reference material, Meas. Sci. Technol. 26 (2015) 115006
[4] Gaoliang Dai et al. Comparison of line width calibration using critical dimension atomic force microscopes between PTB and NIST, Meas. Sci. Technol. 28 (2017) 065010