Abstract

Real-time monitoring by multiwavelength phase-modulated ellipsometry of the growth of plasma-deposited microcrystalline silicon (μc-Si) is presented. We discuss the construction of a growth model for process monitoring, and, in particular, we treat the inhomogeneity in the μc-Si layer by using an approximation of the reflection coefficient known as the WKBJ method. By also using the Bruggeman effective medium theory to describe the optical properties of μc-Si, we demonstrate monitoring the crystallinity in the upper and the lower part of the layer together with the thickness. The inversion algorithms thus remain very fast, with calculation times within 5 s on a standard Pentium computer. This makes possible precise control of the thickness and the crystallization of both the top and the bottom interface of the layer during the elaboration of devices such as solar cells and thin-film transistors.

© 1998 Optical Society of America

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References

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  1. P. Roca i Cabarrocas, N. Layadi, T. Heitz, B. Drévillon, I. Solomon, “Substrate selectivity in the formation of microcrystalline silicon: Mechanisms and technological consequences,” Appl. Phys. Lett. 66, 3609–3611 (1995).
    [CrossRef]
  2. M. Fang, B. Drévillon, “In situ spectroellipsometry study of the nucleation and growth of microcrystalline silicon,” J. Appl. Phys. 70, 4894–4898 (1991).
    [CrossRef]
  3. 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).
    [CrossRef]
  4. S. Kim, R. W. Collins, “Optical characterization of continuous compositional gradients in thin films by real-time spectroscopic ellipsometry,” Appl. Phys. Lett. 67, 3010–3012 (1995).
    [CrossRef]
  5. M. Kildemo, “Real-time monitoring and growth control of Si-gradient index structures by multiwavelength ellipsometry,” Appl. Opt. 37, 1–12 (1998).
    [CrossRef]
  6. M. Kildemo, O. Hunderi, B. Drévillon, “Approximation of the reflection coefficient for rapid real time calculation of inhomogenous films,” J. Opt. Soc. Am. A 14, 931–939 (1997).
    [CrossRef]
  7. 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]
  8. D. A. G. Bruggeman, “Berechnung verschiedener physikalisher konstanten von heterogenen substanzen,” Ann. Phys. (Leipzig) 24, 636–679 (1935).
  9. D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
    [CrossRef]
  10. G. E. Jellison, M. F. Chisholm, S. M. Gorbatkin, “Optical functions of chemical vapor deposited thin film silicon determined by spectroscopic ellipsometry,” Appl. Phys. Lett. 62, 3348–3350 (1993).
    [CrossRef]
  11. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).

1998

M. Kildemo, “Real-time monitoring and growth control of Si-gradient index structures by multiwavelength ellipsometry,” Appl. Opt. 37, 1–12 (1998).
[CrossRef]

1997

1995

S. Kim, R. W. Collins, “Optical characterization of continuous compositional gradients in thin films by real-time spectroscopic ellipsometry,” Appl. Phys. Lett. 67, 3010–3012 (1995).
[CrossRef]

P. Roca i Cabarrocas, N. Layadi, T. Heitz, B. Drévillon, I. Solomon, “Substrate selectivity in the formation of microcrystalline silicon: Mechanisms and technological consequences,” Appl. Phys. Lett. 66, 3609–3611 (1995).
[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]

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).
[CrossRef]

G. E. Jellison, M. F. Chisholm, S. M. Gorbatkin, “Optical functions of chemical vapor deposited thin film silicon determined by spectroscopic ellipsometry,” Appl. Phys. Lett. 62, 3348–3350 (1993).
[CrossRef]

1991

M. Fang, B. Drévillon, “In situ spectroellipsometry study of the nucleation and growth of microcrystalline silicon,” J. Appl. Phys. 70, 4894–4898 (1991).
[CrossRef]

1979

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

1935

D. A. G. Bruggeman, “Berechnung verschiedener physikalisher konstanten von heterogenen substanzen,” Ann. Phys. (Leipzig) 24, 636–679 (1935).

Aspnes, D. E.

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).
[CrossRef]

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung verschiedener physikalisher konstanten von heterogenen substanzen,” Ann. Phys. (Leipzig) 24, 636–679 (1935).

Chisholm, M. F.

G. E. Jellison, M. F. Chisholm, S. M. Gorbatkin, “Optical functions of chemical vapor deposited thin film silicon determined by spectroscopic ellipsometry,” Appl. Phys. Lett. 62, 3348–3350 (1993).
[CrossRef]

Collins, R. W.

S. Kim, R. W. Collins, “Optical characterization of continuous compositional gradients in thin films by real-time spectroscopic ellipsometry,” Appl. Phys. Lett. 67, 3010–3012 (1995).
[CrossRef]

Drévillon, B.

M. Kildemo, O. Hunderi, B. Drévillon, “Approximation of the reflection coefficient for rapid real time calculation of inhomogenous films,” J. Opt. Soc. Am. A 14, 931–939 (1997).
[CrossRef]

P. Roca i Cabarrocas, N. Layadi, T. Heitz, B. Drévillon, I. Solomon, “Substrate selectivity in the formation of microcrystalline silicon: Mechanisms and technological consequences,” Appl. Phys. Lett. 66, 3609–3611 (1995).
[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]

M. Fang, B. Drévillon, “In situ spectroellipsometry study of the nucleation and growth of microcrystalline silicon,” J. Appl. Phys. 70, 4894–4898 (1991).
[CrossRef]

Fang, M.

M. Fang, B. Drévillon, “In situ spectroellipsometry study of the nucleation and growth of microcrystalline silicon,” J. Appl. Phys. 70, 4894–4898 (1991).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).

Gorbatkin, S. M.

G. E. Jellison, M. F. Chisholm, S. M. Gorbatkin, “Optical functions of chemical vapor deposited thin film silicon determined by spectroscopic ellipsometry,” Appl. Phys. Lett. 62, 3348–3350 (1993).
[CrossRef]

Heitz, T.

P. Roca i Cabarrocas, N. Layadi, T. Heitz, B. Drévillon, I. Solomon, “Substrate selectivity in the formation of microcrystalline silicon: Mechanisms and technological consequences,” Appl. Phys. Lett. 66, 3609–3611 (1995).
[CrossRef]

Hottier, F.

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Hunderi, O.

Jellison, G. E.

G. E. Jellison, M. F. Chisholm, S. M. Gorbatkin, “Optical functions of chemical vapor deposited thin film silicon determined by spectroscopic ellipsometry,” Appl. Phys. Lett. 62, 3348–3350 (1993).
[CrossRef]

Kildemo, M.

M. Kildemo, “Real-time monitoring and growth control of Si-gradient index structures by multiwavelength ellipsometry,” Appl. Opt. 37, 1–12 (1998).
[CrossRef]

M. Kildemo, O. Hunderi, B. Drévillon, “Approximation of the reflection coefficient for rapid real time calculation of inhomogenous films,” J. Opt. Soc. Am. A 14, 931–939 (1997).
[CrossRef]

Kim, S.

S. Kim, R. W. Collins, “Optical characterization of continuous compositional gradients in thin films by real-time spectroscopic ellipsometry,” Appl. Phys. Lett. 67, 3010–3012 (1995).
[CrossRef]

Layadi, N.

P. Roca i Cabarrocas, N. Layadi, T. Heitz, B. Drévillon, I. Solomon, “Substrate selectivity in the formation of microcrystalline silicon: Mechanisms and technological consequences,” Appl. Phys. Lett. 66, 3609–3611 (1995).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).

Roca i Cabarrocas, P.

P. Roca i Cabarrocas, N. Layadi, T. Heitz, B. Drévillon, I. Solomon, “Substrate selectivity in the formation of microcrystalline silicon: Mechanisms and technological consequences,” Appl. Phys. Lett. 66, 3609–3611 (1995).
[CrossRef]

Solomon, I.

P. Roca i Cabarrocas, N. Layadi, T. Heitz, B. Drévillon, I. Solomon, “Substrate selectivity in the formation of microcrystalline silicon: Mechanisms and technological consequences,” Appl. Phys. Lett. 66, 3609–3611 (1995).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).

Ann. Phys. (Leipzig)

D. A. G. Bruggeman, “Berechnung verschiedener physikalisher konstanten von heterogenen substanzen,” Ann. Phys. (Leipzig) 24, 636–679 (1935).

Appl. Opt.

M. Kildemo, “Real-time monitoring and growth control of Si-gradient index structures by multiwavelength ellipsometry,” Appl. Opt. 37, 1–12 (1998).
[CrossRef]

Appl. Phys. Lett.

P. Roca i Cabarrocas, N. Layadi, T. Heitz, B. Drévillon, I. Solomon, “Substrate selectivity in the formation of microcrystalline silicon: Mechanisms and technological consequences,” Appl. Phys. Lett. 66, 3609–3611 (1995).
[CrossRef]

G. E. Jellison, M. F. Chisholm, S. M. Gorbatkin, “Optical functions of chemical vapor deposited thin film silicon determined by spectroscopic ellipsometry,” Appl. Phys. Lett. 62, 3348–3350 (1993).
[CrossRef]

S. Kim, R. W. Collins, “Optical characterization of continuous compositional gradients in thin films by real-time spectroscopic ellipsometry,” Appl. Phys. Lett. 67, 3010–3012 (1995).
[CrossRef]

J. Appl. Phys.

M. Fang, B. Drévillon, “In situ spectroellipsometry study of the nucleation and growth of microcrystalline silicon,” J. Appl. Phys. 70, 4894–4898 (1991).
[CrossRef]

J. Opt. Soc. Am. A

Phys. Rev. B

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[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]

Other

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1986).

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Figures (4)

Fig. 1
Fig. 1

χ2(t) in Eq. (6) computed during the fitting of each spectrum during the growth: Open squares, χ2(t) using growth model 1 (homogeneous film) entirely through the growth and fitting directly upon the thickness; dotted curve, χ2(t) obtained using growth model 1 for the first 600 s and then using model 2 (gradient index) and fitting directly for the thickness; solid curve, χ2(t) obtained using model 1 and then model 2 after 1500 s while fitting the rate of deposition and calculating the thickness from Eq. (7). In the latter case three kinetic spectra were combined.

Fig. 2
Fig. 2

Thickness of the bulk layer on the right axis (solid curve) and thickness of the surface roughness on the left axis (dotted curve). The solid and dotted curves correspond to the results obtained with model 2 (gradient index) and fitting the rate of deposition and thickness, respectively. The crossed curves represent the results of model 1.

Fig. 3
Fig. 3

Upper three curves show the crystalline fraction fitted during deposition of the μc-Si layer. Solid curve, average composition fitted by using model 1 throughout the growth; upper curve (black triangles), crystalline fraction near the surface; curve of open diamonds, fraction near the substrate. The latter two are obtained by using model 2 (gradient index). The lower three curves show the fitted amorphous fraction. Similarly, the solid curve is the amorphous volume fraction fitted by using model 1; the solid triangles represent the fraction near the surface, and the open diamonds show the fraction near the substrate.

Fig. 4
Fig. 4

Measured ellipsometric intensities (a) I s and (b) I c recorded after deposition of the μc-Si layer (scatter graphs). The dotted curves show the values of I s and I c calculated from the fitted values obtained by using the real-time inversion algorithm with model 2 (gradient index) and by fitting the rate of deposition. The solid curves correspond to the spectroscopic fit using the same model but with an inhomogeneous surface roughness.

Equations (10)

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ρ = r p / r s = tan Ψ exp i Δ
I s = sin 2 Ψ sin Δ = 2   Im r s r p * r s r s * + r p r p * , I c = sin 2 Ψ cos Δ = 2   Re r s r p * r s r s * + r p r p * .
ν = 1 3   f ν ε ν - ε eff ε ν + 2 ε eff = 0 ,
M H film = cos   β - i η   sin   β - i η - 1 sin   β cos   β ,
β = 2 π λ   d ε - ε a sin 2   φ 0 1 / 2 ,
η = n   cos   φ = ε - ε a sin 2   φ 0 1 / 2 s   polarization n cos   φ = ε ε - ε a sin 2   φ 0 1 / 2   p   polarization .
M WKBJ = η ( d ) η ( 0 ) ½ cos   β ( d ) - i η ( 0 ) η ( d ) ½ sin   β ( d ) - i 1 η ( 0 ) η ( d ) ½ sin   β ( d ) η ( 0 ) η ( d ) ½ cos   β ( d ) .
β d = 2 π λ 0 d ε ζ - ε a sin 2   φ 0 1 / 2 d ζ .
χ 2 = 1 2 * j - i * N k = 1 N r = i + 1 j × | I s θ ¯ i + 1 ,   t r ,   λ k - I smeas t r ,   λ k | 2 δ k , r 2 + | I c θ ¯ i + 1 ,   t r ,   λ k - I cmeas t r ,   λ k | 2 δ k , r 2 ,
d t = 0 t   r d τ d τ .

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