Metrological sensitivity improvement of through-focus scanning optical microscopy by controlling illumination coherence

We investigate the influence of the degree of illumination coherence on throughfocus scanning optical microscopy (TSOM) in terms of metrological sensitivity. The investigation reveals that the local periodicity of the target object is a key structural parameter to consider when determining the optimal degree of illumination coherence for improved metrological sensitivity. The optimal coherence conditions for the TSOM inspection of several target objects are analyzed through numerical simulation. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Conventional high-numerical aperture (NA) optical microscopy is limited in resolution and depth-of-focus (DOF) when measuring high-aspect-ratio and nano-scale structures. Recently, through-focus scanning optical microscopy (TSOM) was proposed as a solution to this issue of optical microscopy [1,2]. The prominent feature of the TSOM which is contrast to the conventional optical microscopy is its computation-assisted indirect metrology scheme, which requires TSOM to computationally interpret a measured TSOM image by comparing it to an a priori prepared TSOM reference image database. In practice, differential TSOM images are analyzed in terms of mathematically designed measures to explicitly extract the structural features that they implicitly reflect. TSOM image databases are numerically constructed using finely modeled optical scattering simulators to create reference targets based on a range of structural parameters. TSOM image computation engines can also be constructed based on the finite difference time domain (FDTD) method, finite element method (FEM) or Fourier modal method (FMM).
To quantify the TSOM analysis, several quantitative measurement factors such as optical intensity range (OIR), different TSOM image (DTI), and mean square difference (MSD) are commonly used [1][2][3][4][5][6]. In practice, TSOM metrology uses MSD and OIR curves. In addition, the combined use of MSD and OIR can be used to determine the metrological information of the target sample. The difference of MSD becomes zero at the minimum point where the specification of the target sample is matched to a reference target in the TSOM image database. However, as the structural parameters deviate from the determination point, the MSD or OIR values move away from the minimum point where the structure is selected.
In order to sensitivity of nano-structure OIR in respo measurement other variable device (CCD) showed that T and collection use of incoher taken as a fixe illumination c However, it w when fitting t and that the Examining th structural var The optimal performance i In this pap the possibility This work is and partially illumination c of illuminatio periodicity of of sensitivity

TSOM im
The TSOM im method (FMM parameters su are depicted in Fig The TSOM in ref [7], wi semiconducto width (800 n respectively. A be seen that t the total OIR particular, for expected to b TSOM image under the coh have local pe diffraction pa of the incoher an incoherent above expect regarding TSO Figure 3 p specifically th change of i illumination. quite differen ( Fig. 3 For the simulation experiment, TSOM image databases of the six targets were created for three levels of illumination coherence: incoherent, partially coherent, and coherent modes. For the respective ten steps of degrees of coherence, two hundred TSOM images like those presented in Fig. 5 were created for DTI calculations, corresponding to fin widths varying in 0.1 nm steps. The DTI values were obtained from each database (DB) according to the reference widths of each structure, and their OIR and MSD values are plotted in Fig. 6 to compare the changes in those values. The differences in OIR values between the reference image and the DB image are calculated and those of the six target samples are shown in Figs. 6(a)-6(f) (left panel in Fig. 6). In the case of the OIR of the DTI images, it is apparent that the OIR of the coherent lighting is more sensitive than that of the incoherent lighting. The OIR values corresponding to partial coherence are in between those of the incoherence and coherence graphs, as shown in the Fig. 6. Considering the difference between the OIR graphs of the six samples, the larger the local periodicity, the more the difference between the absolute value of OIR and the OIR slope depends on the coherence. In the plots in Figs. 6(g)-6(l) (the right panel on Fig. 6), the structure is determined at the minimum value of the MDS curve.
As shown in Fig. 6, the OIR graph increases or decreases sharply and linearly, and the MSD graph has a parabolic curve pattern with a dip. Thus, the variation around the dip (sample space with extremely small structural change) is round. Thus the MSD cannot easily pinpoint the optimal point. At this microscopic tuning stage of analyzing very similar shaped structures with small MSD differences, the OIR may be useful to find the dip of the MSD curve. That is why previous TSOM papers recommend the combinatorial use of the MSD and OIR. In actual TSOM for metrology, the parabolic curve of the MSD value around the true value of the MSD is calculated, so the curvature value of the curve must be large. For example, considering cases 1 and 2 (40nm and 100nm single fin structures), we can see that the MSD sensitivity under incoherent illumination is better than that of coherent illumination with respect to the true reference value. In other words, the incoherent TSOM is more sensitive for structural changes in the single fin structures, so in such cases the use of incoherent illumination is preferable to coherent illumination. This is an important feature for increasing measurement accuracy and reinforcing robustness to noise in real TSOM systems. This tendency continues to the multi-fin structures in cases 3 and 4. Figures 6(i)-6(j) indicate that the MSD curves of the coherent cases tend to be lower than the curves of the incoherent cases. That is, the incoherent TSOM increases sharply with distance from the reference value. On the other hand, a notable switch is apparent in cases 5 and 6, in that the MSD curves of the coherent cases tend to be higher than the curves of the incoherent cases and the coherent TSOM increases more sharply with distance from the reference value.
In terms of MSD sensitivity, we can classify the six sample cases into two major categories, namely cases 1-4 and cases 5-6. The MSD of the first group showed higher sensitivity to incoherent illumination while the MSD of the second group exhibits higher sensitivity to coherent illumination. The physical origin of this noticeable difference can be qualitatively explained using the concept of local periodicity. Actually, for optical fields at 546nm, cases 3 and 4 of the first group can be seen as effective media [19]. Accordingly, cases 3 and 4 can be equivalently to a single fin structure with an effective permittivity. They are considered homogeneous structures without local periodicity or more generally, local corrugation. From hundreds of numerical simulations, we could infer that the MSD sensitivity of target structures with deep subwavelength structures that can be considered effective media is higher with incoherent illumination than coherent illumination. On the other hand, the structures of cases 5 and 6, feature a local periodicity, which results in a diffraction pattern due to the homogenization of the effective medium. In such cases, the MSD of DTI by coherent illumination is more sensitive. In the structure of case 3, the 100nm fin pitch is deepsubwavelength length and then appears to be an effective medium of 440nm total width rather than a periodic structure. In addition, the structures of cases 5  , it is noteworthy that the MSD value rises to its maximum value in a region of partial coherent lighting. In addition, for the noneffective medium samples in cases 5 and 6, in Fig. 7(d), the MSD curves are almost flat as the illumination changes from incoherent to partial coherent, but in the remaining cases 1-4 almost flat as it transitions from partially coherent to perfectly coherent. Moreover, comparing the data corresponding to the INA of 0.1 and 0.3, we can see that the sensitivity of the MSD is higher for coherent lighting when decreasing the INA. This phenomenon implies that the smaller INA with coherent lighting produces larger MSD values and higher sensitivity with non-effective medium samples of local periodicity. In other words, when the diffraction pattern due to the periodicity of the target structure appears in the TSOM image, the sensitivity for resolving structural discrepancies is high when coherent lighting is used. However, for the case of aperiodic deep-subwavelength effective medium structures, it is incoherent lighting that results in more sensitivity. Thus incoherent lighting is expected to be more advantageous for measurement of aperiodic structures.

Conclusion
In conclusion, we have shown the possibility of TSOM metrology sensitivity improvements through controlling the degree of the coherence of illumination. It is revealed that for the effective medium structures, including single fin and deep-subwavelength multi-fin structures, using incoherent illumination with high INA allows TSOM metrology to be more robust than using a high degree of coherent illumination. On the other hand, non-effective medium structures with local periodicity producing relatively strong interference in the scattering field are more sensitive to higher coherent illumination in terms of MSD.
Elucidating an accurate interpretation of the relationship between the effective medium theory and the local periodicity of target structures in terms of quantitative criteria requires further theoretical research. In actual usage of the TSOM system, it is preferable to construct an appropriate adaptive illumination system capable of controlling the INA and of switching from partially coherent mode to incoherent mode according to the type of target sample. It is hoped that coherence-controlled TSOM will develop to become a high-performance in-line optical microscope inspection and metrology technique for state of the art semiconductor devices, such as the recent three-dimensional (3D) nanoscale semiconductor structures including silicon via (TSV) and fin field-effect transistors (Fin-FETs).