Real-Time Monitoring and Growth Control of Si-Gradient-Index Structures by Multiwavelength Ellipsometry
Applied Optics, Vol. 37, Issue 1, pp. 113-124 (1998)
http://dx.doi.org/10.1364/AO.37.000113
Acrobat PDF (255 KB)
Abstract
Real-time monitoring and control of the growth of plasma-deposited gradient-index structures by multiwavelength phase-modulated ellipsometry are presented. An efficient method for estimating the optical parameters based on a least-squares fitting on the most recent recorded measurements is described. This method is used for real-time monitoring of the outerlayer refractive index and rate of deposition during deposition of inhomogeneous transparent films. An accurate integral expansion of the reflection coefficient, giving a continuous optical model describing inhomogeneous films, is used in the real-time modeling of the deposited structure. A variety of increasing complexities of the optical model is studied within inversion algorithms. Furthermore several ways of defining the optical parameters to be estimated are discussed. Inversion of simulated growth trajectories by using the described algorithms show what kind of information is available from the various approximations and in what conditions they are useful. Since real-time measurements during growth involves statistical noise and systematic errors, it becomes necessary to stabilize the fit. Various stabilizing functionals are discussed and implemented to solve this problem. Several plasma-deposited silicon oxynitride gradient-index structures where both rate of deposition and the refractive index are varied continuously are inverted in real time. As an example of application, a successful real-time control of the growth of a linear gradient index is demonstrated by using inversion algorithms. Inversion algorithms are extremely fast, with calculation times from less than a second (for the lowest-order approximation) to ~3 s.
© 1998 Optical Society of America
OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.5700) Instrumentation, measurement, and metrology : Reflection
(310.0310) Thin films : Thin films
Citation
M. Kildemo, "Real-Time Monitoring and Growth Control of Si-Gradient-Index Structures by Multiwavelength Ellipsometry," Appl. Opt. 37, 113-124 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-1-113
Sort: Year | Journal | Reset
References
- H. Fabricius, “Gradient-index filters: designing filters with steep skirts, high reflection, and quintic matching layers,” Appl. Opt. 31, 5191–5196 (1992).
- W. H. Southwell, “Gradient-index antireflection coatings,” Opt. Lett. 8, 584–586 (1983).
- A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed., 2nd ed. (McGraw-Hill, New York, 1994).
- V. Nguyen Van, A. Brunet-Bruneau, S. Fisson, J. M. Frigerio, G. Vuye, Y. Wang, F. Abelés, M. Berger, and P. Chaton, “Determination of refractive-index profiles by a combination of visible and infrared ellipsometry measurements,” Appl. Opt. 35, 5540–5544 (1996).
- A. V. Tikhonravov and M. K. Trubetskov, “Program package for the ellipsometry of inhomogeneous layers,” in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J. A. Dobrowolski and P. G. Verly, eds., Proc. SPIE 2046, 167–178 (1993).
- A. V. Tikhonravov, M. K. Trubetskov, J. Hrdina, and J. Sobota, “Characterization of quasirugate filters using ellipsometric measurements,” Thin Solid Films 277, 83–89 (1996).
- P. G. Snyder, Y. Xiong, A. Woollam, G. A. Al-Jumaily, and F. J. Gagliardi, “Graded refractive index silicon oxynitride thin film characterized by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 10, 1462–1466 (1992).
- C. K. Carniglia, “Ellipsometric calculation for nonabsorbing thin films with linear refractive-index gradients,” J. Opt. Soc. Am. A 7, 848–855 (1990).
- M. Kildemo and B. Drévillon, “Real time monitoring of the growth of transparent thin films by spectroscopic ellipsometry,” Rev. Sci. Instrum. 67, 1956–1960 (1996).
- M. Kildemo, S. Deniau, P. Bulkin, and B. Drevillon, “Real time control of the growth of silicon alloy multilayers by multiwavelength ellipsometry,” Thin Solid Films 290–291, 46–50 (1996).
- I. F. Wu, J. B. Dottelis, and M. Dagenais, “Real-time in situ ellipsometric control of antireflection coatings for semiconductor laser amplifiers using SiO_{x},” J. Vac. Sci. Technol. A 11, 2398–2405 (1993).
- W. M. Duncan, S. A. Henck, J. W. Kuehne, L. M. Loewenstein, and S. Maung, “High-speed spectral ellipsometry for in situ diagnostics and process control,” J. Vac. Sci. Technol. B 12, 2779–2784 (1994).
- M. Kildemo, P. Bulkin, S. Deniau, and B. Drévillon, “Real time control of plasma deposited multilayers by multiwavelength ellipsometry,” Appl. Phys. Lett. 68, 3395–3397 (1996).
- M. Kildemo, P. Bulkin, B. Drévillon, and O. Hunderi, “Real time control by multiwavelength ellipsometry of plasma deposited multilayers on glass using incoherent reflection model,” Appl. Opt. 36, 6352–6359 (1997).
- M. Kildemo, O. Hunderi, and B. Drévillon, “Approximation of the reflection coefficient for rapid real time calculation of inhomogenous films,” J. Opt. Soc. Am. A 14, 931–939 (1997).
- G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust. Speech. Signal. Process. 37, 2024–2036 (1989).
- M. Bertero, C. de Mol, and G. A. Viano, “The stability of inverse problems,” in Inverse Scattering Problems in Optics, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1980), pp. 161–212.
- A. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems (Winston-Wiley, New York, 1977).
- J. H. Kaiser, “Regularization in ellipsometry,” Appl. Phys. B 45, 1–5 (1988).
- P. V. Bulkin, P. L. Swart, and B. M. Lacquet, “Fourier-transform design and electron cyclotron resonance-PECVD of lossy graded-index optical coatings,” Appl. Opt. 35, 4413–4419 (1996).
- B. Drévillon, “Phase modulated ellipsometry from the ultraviolet to the infrared: In situ applications to the growth of semiconductors,” Prog. Cryst. Growth Charact. Mat. 27, 1–87 (1993).
- W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).
- D. E. Aspnes, “Minimal-data approaches for determining outer-layer dielectric responses of films from kinetic reflectometric and ellipsometric measurements,” J. Opt. Soc. Am. A 10, 974–983 (1993).
- S. Kim and R. W. Collins, “Optical characterization of continuous compositional gradients in thin films by real time spectroscopic ellipsometry,” Appl. Phys. Lett. 67, 3010–3012 (1995).
- F. K. Urban, III and M. F. Tabet, “Development of artificial neural networks for in situ ellipsometry of films growing on unknown substrates,” J. Vac. Sci. Technol. A 12, 1952–1956 (1994).
- D. A. G. Bruggeman, “Berechnung verschiedener physikalisher konstanten von heterogenen substanzen,” Ann. Phys. (Leipzig) 24, 636–679 (1935).
- J. C. Maxwell Garnett, “Colors in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
- F. Abeles, “Optical properties of inhomogeneous films,” Natl. Bur. Stand. (U.S.) Misc. Publ. 256, 41–58 (1964).
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
« Previous Article | Next Article »
OSA is a member of CrossRef.