Analytical calculation on the determination of steep side wall angles from far field measurements

Cisotto, Luca; Pereira, Silvania F.; Urbach, H. P.

doi:10.1088/2040-8986/aabb59

Cited by 4 publications

(4 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has been demonstrated in previous work [23,25,26] that an object can be described as a phase step if its slope is sufficiently steep. The phase step will introduce an offset to the scattered light due to the path difference on either side of the step, as shown in figure 1(c).…”

Section: Methodsmentioning

confidence: 99%

“…Numerical calculations using the FDTD method are carried out to verify the detection capabilities of the scheme. The rigorous electromagnetic interaction between a cliff-like structure and the focused laser beam generated by a cylindrical lens is modeled to distinguish different steep SWAs, which is closer to the experimental situation and more accurate than the scalar analysis [23]. We conduct lateral and longitudinal scanning of the structure for both TE and TM polarization, and monitor the scattered light by a split detector to analyze the polarization effect in the far field.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Determination of steep sidewall angle using polarization-sensitive asymmetric scattering

Dou

Pereira

Min

et al. 2021

Meas. Sci. Technol.

Self Cite

View full text Add to dashboard Cite

The sidewall angle (SWA) of a nanostructure exerts influence on the performance of the nanostructure and plays an important role in processing nano-structural chips. It is still a great challenge to determine steep SWAs from far field measurements especially when the SWAs are close to 90 • . Here, we propose a far-field detection system to determine steep SWA of a cliff-shape step structure on a silicon substrate by combining a split detector with a scanning method. The far-field radiation field is asymmetric due to the scattering of the step structure, and further numerical analysis demonstrates the reliability of this far-field measurement method. In the simulations, two key variables, i.e. the polarization state and the focus position of the incident laser beam, are considered to explore their impacts. By scanning over the structure laterally and longitudinally with both TE and TM polarizations, polarization effects on the far-field occur. These effects show higher sensitivity to steep SWA variation for TM polarization as compared to TE. Furthermore, with a comprehensive longitudinal scanning analysis for the TM polarization case, a feasible focus interval can be optimized to retrieve the steep SWA. As the proposed method is fast, highly sensitive and easy to implement, it provides a powerful approach to investigate the scattering behavior of nanostructures.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Determination of steep sidewall angle using polarization-sensitive asymmetric scattering

Dou

Pereira

Min

et al. 2021

Meas. Sci. Technol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The nanostructure described above can be assumed to act as a pure phase object i.e. a phase step if the slope of the cliff is steep enough [9]. When the phase step interacts with an illuminating focused beam, as shown in figure 1(b), the beam will encounter different path differences across the cliff, and the resulting scattered beam will experience different offsets depending on the reflection function of the nanostructure.…”

Section: Theorymentioning

confidence: 99%

“…While there have been extensive numerical studies focused on accurately measuring both height and steep swa, a method that achieves precise measurements in both aspects remains elusive. Prior endeavors predominantly leaned on simulations and theoretical models, which offered valuable insights [7][8][9][10]. However, the practical measurements of these structural parameters remain a formidable task.…”

Section: Introductionmentioning

confidence: 99%

Investigation of coherent Fourier scatterometry as a calibration tool for determination of steep side wall angle and height of a nanostructure

Paul,

Rafighdoost,

Dou

et al. 2024

Meas. Sci. Technol.

Self Cite

View full text Add to dashboard Cite

Nanostructures with steep side wall angles (swa) play a pivotal role in various technological applications. Accurate characterization of these nanostructures is crucial for optimizing their performance. In this study, we propose a far-field detection method based on coherent Fourier scatterometry (CFS) for accurate quantification of steep swa and heights in cliff-like nanostructures. Our approach introduces a parameter termed “visibility”, derived from the unique far-field signatures of cliff-like nanostructures. This parameter serves as a quantitative metric for the calibration of swa and heights. The heightened sensitivity of our method is demonstrated, particularly when the incident polarization is perpendicular to the invariant direction of the nanostructure for swa calibration, while both polarization states exhibit sensitivity to height calibration. Furthermore, a comprehensive sensitivity analysis reveals the stable nature of our method, showcasing that even with fluctuations of ±10 nm in the position of the nanostructure, the resulting swa remains stable within a range of ±0.5°. The exponential variation of the visibility parameter with edge roundness is observed, with fluctuations in edge roundness within 10 nm resulting in swa variations within 1.7° for both polarization states. In experimental validations, our results demonstrate reasonable agreement between CFS-derived and AFM measurements. The AFM data for swa (77.99° ± 1.37°) and height (148.35 nm ±2.11 nm) are corroborated with CFS-derived value of swa (77.75° ± 3.61°, 78.36° ± 3.89°) and height (149.42 nm ±1.66 nm, 150.05 nm ±1.04 nm) obtained from calibration curves for TM and TE incident beams, respectively. Overall, our findings underscore CFS as a potential and reliable tool for nanostructure characterization, offering precise measurements that are pivotal for advancing nanotechnology.

show abstract

Optimal parameter estimation of shaped phase objects

Villegas,

Passos,

Pereira

et al. 2024

Phys. Rev. A

View full text Add to dashboard Cite

We show a general method to estimate with optimum precision, i.e., the best precision determined by the light-matter interaction process, a set of parameters that characterize a phase object. The method is derived from ideas presented by Pezze []. Our goal is to illuminate the main characteristics of this method as well as its applications to the physics community probably not familiar with the quantum language usually employed in works related to quantum estimation theory. First, we derive precision bounds for the estimation of the set of parameters characterizing the phase object. We compute the Crámer-Rao lower bound for two experimentally relevant types of illumination: a multimode coherent state with mean photon number N and N copies of a multimode single-photon quantum state. We show under which conditions these two models are equivalent. Second, we show that the optimum precision can be achieved by projecting the light reflected or transmitted from the object onto a set of modes with engineered spatial shape. We describe how to construct these modes and demonstrate explicitly that the precision of the estimation using these measurements is optimum. As an example, we apply these results to the estimation of the height and sidewall angle of a cliff-like nanostructure, an object relevant in the semiconductor industry for the evaluation of nanofabrication techniques. Published by the American Physical Society 2024

show abstract

Analytical calculation on the determination of steep side wall angles from far field measurements

Cited by 4 publications

References 22 publications

Determination of steep sidewall angle using polarization-sensitive asymmetric scattering

Determination of steep sidewall angle using polarization-sensitive asymmetric scattering

Investigation of coherent Fourier scatterometry as a calibration tool for determination of steep side wall angle and height of a nanostructure

Optimal parameter estimation of shaped phase objects

Contact Info

Product

Resources

About