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Optical Metrology

Metrology of Periodic Structures

- The metrology of gratings is currently the subject of intense applied research, driven by the need of fast high throughput process control methods in microelectronic industry. 
- Optical methods generically termed scatterometry, are indirect: the experimental data are fitted by multiparameter models describing the features to be “reconstructed”. 
- These features are essentially the profile of the grating lines and the lateral shift between superimposed gratings, or overlay.
- Scatterometry usually involves spectrally resolved polarized reflectometry or classical ellipsometry with the grating lines perpendicular to the incidence plane.
- In contrast, we evaluated full Mueller polarimetry in the most general conical diffraction configurations in the two ANR projects outlined below. Throughout both studies, the polarimetric responses of the grating structures were calculated by means of RCWA codes (both in 1D and 2D) developed by Tatiana Novikova and Martin Foldyna.

The “ScatteroMueller” Project

This project, (2007-2009), was aimed at line profile reconstruction based on spectral measurements carried out with LC based polarimeters. 
This project was coordinated by Horiba Jobin Yvon, in partnership with CEA/LETI which was in charge of the production of well characterized samples and LPICM for theoretical studies and first measurements.
After the first “proof-of principle” study, carried out at LPICM the final study was realized at LETI with the new instrument developed at Horiba (the AutoSE, subsequently commercialized).
This study involved a set of gratings with CDs down to 50 nm nominal.
The fitted parameters (Middle critical dimension (CD), depth and sidewall angle (SWA)) exhibited very small variations with azimuth (in spite of very large variations of the raw spectra) and their values agreed very satisfactorily with the state of the art 3D AFM, taken as “gold standard”, as shown in figure below.
Similar results have been obtained for all gratings.
Variation of the dimensional parameters (middle CD, depth (or height) and sidewall angle (SWA)) of a trapezoidal model for the line shape of the gratings studied at LETI with 50 nm nominal CDs. The pink dashed line is the AFM value. The error bars show
the variances (repeatability) of each measurement).

Contact : Nous contacter">Tatiana Novikova

The “MuellerFourier” Project

The purpose of this three year project (2009-2011), coordinated by T. Novikova at LPICM, was to validate Mueller polarimetry in conoscopic mode for the determination of overlay. 
The consortium was basically the same as that of “ScatteroMueller”, with similar tasks for each partner. 
The work realized at LPICM was the core of Clément Fallet’s thesis, defended in 2011.
Two types of structures with superimposed gratings were studied, with several CDs and overlays varying between -150 nm and 150 nm.
Starting from the sample conoscopic Mueller matrix M we calculate a scalar estimator 
whose value at each point of the Fourier image is proportional to the overlay.
A typical measurement corresponding to a 50 nm overlay  is shown in the figure (left pannel).
The linearity of the signal with overlay allows a simple calibration if two samples with known overlays are available, thus eliminating the need of multiparameter fits (right pannel).
Left: typical conoscopic estimator matrix E (sample with 50 nm nominal overlay). The white circle at the top right identifies the zone actually used for the evaluation of overlay. Right: Correlation between the overlay determined by conoscopic Mueller polarimetry and the AIM gold standard. [C. Fallet et al, J. Micro/Nanolithography, MEMS MOEMS 10, 033017 (2011)]


  • Conoscopic Mueller polarimetry is particularly well suited to measurements in very small (a few μm wide) targets, and for overlay metrology.
  • Conoscopic Mueller polarimetry needs only one target when other techniques, such as SCOL, require four to six 50 μm wide targets with controlled overlay offsets.
  • The “ideal” machine would be one with the full conoscopic Mueller capability to generate and to detect arbitrary polarization states, for repeated measurements.
  • Such a machine would accurately determine both the line profile and the overlay, which are currently measured by different systems.