Abstract

A direct numerical inversion method is applied to the monitoring of thin-film growth. Several improvements of the method, including a correction for weakly absorbing materials, are presented. The method has been successfully applied to the inversion of the growth of constant-refractive-index layers and used for the process calibration of plasma-enhanced chemical vapor deposition of silicon oxynitrides. The validity of this calibration has been successfully tested on a linear index gradient and quintic matching layer between a polycarbonate substrate and a scratch-resistant coating.

© 2002 Optical Society of America

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References

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  1. D. Kouznetsov, A. Hofrichter, B. Drévillon, “Direct numerical inversion method for kinetic ellipsometric data. I. Presentation of the method and numerical evaluation,” Appl. Opt. 41, 4510–4518 (2002).
    [CrossRef] [PubMed]
  2. P. Bulkin, N. Bertrand, B. Drévillon, “Deposition of SiO2 in integrated distributed electron cyclotron resonance microwave reactor,” Thin Solid Films 296, 66–68 (1997).
    [CrossRef]
  3. B. Drévillon, “Phase modulated ellipsometry from the ultraviolet to the infrared: in situ applications to the growth of semiconductors,” Prog. Cryst. Growth Charact. Mater. 27, 1–87 (1993).
    [CrossRef]
  4. T. Heitz, A. Hofrichter, P. Bulkin, B. Drévillon, “Real time control of plasma deposited optical filters by multiwavelength ellipsometry,” J. Vac. Sci. Technol. A 18, 1303–1307 (2000).
    [CrossRef]
  5. W. H. Southwell, R. L. Hall, “Rugate filter sidelobe suppression using quintic and rugated quintic matching layers,” Appl. Opt. 28, 2949–2951 (1989).
    [CrossRef] [PubMed]

2002

2000

T. Heitz, A. Hofrichter, P. Bulkin, B. Drévillon, “Real time control of plasma deposited optical filters by multiwavelength ellipsometry,” J. Vac. Sci. Technol. A 18, 1303–1307 (2000).
[CrossRef]

1997

P. Bulkin, N. Bertrand, B. Drévillon, “Deposition of SiO2 in integrated distributed electron cyclotron resonance microwave reactor,” Thin Solid Films 296, 66–68 (1997).
[CrossRef]

1993

B. Drévillon, “Phase modulated ellipsometry from the ultraviolet to the infrared: in situ applications to the growth of semiconductors,” Prog. Cryst. Growth Charact. Mater. 27, 1–87 (1993).
[CrossRef]

1989

Bertrand, N.

P. Bulkin, N. Bertrand, B. Drévillon, “Deposition of SiO2 in integrated distributed electron cyclotron resonance microwave reactor,” Thin Solid Films 296, 66–68 (1997).
[CrossRef]

Bulkin, P.

T. Heitz, A. Hofrichter, P. Bulkin, B. Drévillon, “Real time control of plasma deposited optical filters by multiwavelength ellipsometry,” J. Vac. Sci. Technol. A 18, 1303–1307 (2000).
[CrossRef]

P. Bulkin, N. Bertrand, B. Drévillon, “Deposition of SiO2 in integrated distributed electron cyclotron resonance microwave reactor,” Thin Solid Films 296, 66–68 (1997).
[CrossRef]

Drévillon, B.

D. Kouznetsov, A. Hofrichter, B. Drévillon, “Direct numerical inversion method for kinetic ellipsometric data. I. Presentation of the method and numerical evaluation,” Appl. Opt. 41, 4510–4518 (2002).
[CrossRef] [PubMed]

T. Heitz, A. Hofrichter, P. Bulkin, B. Drévillon, “Real time control of plasma deposited optical filters by multiwavelength ellipsometry,” J. Vac. Sci. Technol. A 18, 1303–1307 (2000).
[CrossRef]

P. Bulkin, N. Bertrand, B. Drévillon, “Deposition of SiO2 in integrated distributed electron cyclotron resonance microwave reactor,” Thin Solid Films 296, 66–68 (1997).
[CrossRef]

B. Drévillon, “Phase modulated ellipsometry from the ultraviolet to the infrared: in situ applications to the growth of semiconductors,” Prog. Cryst. Growth Charact. Mater. 27, 1–87 (1993).
[CrossRef]

Hall, R. L.

Heitz, T.

T. Heitz, A. Hofrichter, P. Bulkin, B. Drévillon, “Real time control of plasma deposited optical filters by multiwavelength ellipsometry,” J. Vac. Sci. Technol. A 18, 1303–1307 (2000).
[CrossRef]

Hofrichter, A.

D. Kouznetsov, A. Hofrichter, B. Drévillon, “Direct numerical inversion method for kinetic ellipsometric data. I. Presentation of the method and numerical evaluation,” Appl. Opt. 41, 4510–4518 (2002).
[CrossRef] [PubMed]

T. Heitz, A. Hofrichter, P. Bulkin, B. Drévillon, “Real time control of plasma deposited optical filters by multiwavelength ellipsometry,” J. Vac. Sci. Technol. A 18, 1303–1307 (2000).
[CrossRef]

Kouznetsov, D.

Southwell, W. H.

Appl. Opt.

J. Vac. Sci. Technol. A

T. Heitz, A. Hofrichter, P. Bulkin, B. Drévillon, “Real time control of plasma deposited optical filters by multiwavelength ellipsometry,” J. Vac. Sci. Technol. A 18, 1303–1307 (2000).
[CrossRef]

Prog. Cryst. Growth Charact. Mater.

B. Drévillon, “Phase modulated ellipsometry from the ultraviolet to the infrared: in situ applications to the growth of semiconductors,” Prog. Cryst. Growth Charact. Mater. 27, 1–87 (1993).
[CrossRef]

Thin Solid Films

P. Bulkin, N. Bertrand, B. Drévillon, “Deposition of SiO2 in integrated distributed electron cyclotron resonance microwave reactor,” Thin Solid Films 296, 66–68 (1997).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Experimental and reconstructed trajectory Is(Ic) at a 58° angle of incidence 58° for (a) 1.8 eV and (b) 3.8 eV of two PECVD silicon oxynitrides deposited at a processing power of 500 W and a N2 flow of 15 sccm and variable oxygen flow.

Fig. 2
Fig. 2

Reconstructed refractive index versus thickness at 1.8 and 3.8 eV of two PECVD silicon oxynitrides at a processing power of 500 W and a N2 flow of 15 sccm and variable oxygen flow. The straight lines represent the refractive-index evolution found by spectroscopic modeling of the film after deposition.

Fig. 3
Fig. 3

Oxygen flow and reconstructed refractive index at 1.8 and 3.8 eV as a function of deposition time.

Fig. 4
Fig. 4

Refractive index at 1.8 (squares) and 3.8 (circles) as a function of the oxygen flow.

Fig. 5
Fig. 5

Refractive index versus thickness for a linear index profile at 1.8 (circles) and 3.8 eV (triangles) determined by the reconstruction algorithm (symbols) and by spectroscopic fitting (curve).

Fig. 6
Fig. 6

Comparison of the ellipsometric intensities Is and Ic between the spectroscopic fit (solid curve) and the experimental points (symbols).

Fig. 7
Fig. 7

Comparison of transmission data of a PC sample coated with a 5-µm-thick scratch-protection coating with (solid curve) and without (dashed curve) index-matching layer.

Equations (14)

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IS=sin 2Ψ sin Δ=2 Imrs*rprsrs*+rprp*, IC=sin 2Ψ cos Δ=2 Rers*rprsrs*+rprp*.
dIc=Ac±2dx2+Bc±1dx,
dIs=As±2dx2+Bs±1dx,
B±1=C1B+C0B+C-1B/,
A±2=C2A2+C1A+C0A+C-1A/+C-2A/2,
dIc,st=Ac,st dt2+Bc,stdt.
dIc,st=Ac,stν2 dx2+Bc,stν dx.
Ac,s±2=Ac,stν2, Bc,s±1=Bc,stν.
P±2=Ac,stBc,s±12-Ac,s±2Bc,st2=0.
dI>γ MaxΔIe, ΔIt,
dI=I1 Re  d Re +I1 Im  d Im +I1x dx.
dIc=ReI1 Re d Re +ReI1 Im d Im , dIs=ImI1 Re d Re +ImI1 Im d Im .
n=n1+n2-n11+Φ/Φ0p,
nx=nL+nH-nL10x/dq3-15x/dq4+6x/dq5.

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