Abstract

An algorithm is described whereby the thickness of polycrystalline silicon (polysilicon) films on oxidized silicon substrates may be determined from the magnitude and wavelength positions of extrema in the visible reflectance spectra. The underlying layer structure, which can consist of two or more layers, is combined mathematically with the silicon into an effective homogeneous substrate to facilitate analysis. Polysilicon layers from about 20 nm to about 1 μm in thickness are measurable for underlying layers in approximately the same range. Proper account is taken of absorption in the polysilicon layer, and interference effects in the underlying layers when they are sufficiently thick. Reflectance lowering caused by scattered light is corrected with the aid of the measured reflectance at 400-nm wavelength, where the polysilicon is opaque. The algorithm is practically insensitive to overlying oxide layers up to 55 nm in thickness, so that buried polysilicon layers are also measurable. When implemented on an automated spectrophotometer, the algorithm provides thickness values in essentially real time, with a precision of about 0.1 nm.

© 1979 Optical Society of America

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References

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  1. K. L. Konnerth and F. H. Dill, “In-situ Measurement of Dielectric Thickness During Etching or Development Process,” IEEE Trans. Electron Devices ED-22, 452–456 (1975).
    [Crossref]
  2. F. H. Dill, W. P. Hornberger, P. S. Hauge, and J. M. Shaw, “Characterization of Positive Photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
    [Crossref]
  3. K. L. Konnerth and F. H. Dill, “IOTA, A Computer Controlled Thin Film Thickness Measurement Tool,” Solid State Electronics 15, 371–380 (1972).
    [Crossref]
  4. P. S. Hauge and F. H. Dill, “Design and Operation of ETA, an Automated Ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973);E. A. Irene and Y. J. van der Meulen, “Silicon Oxidation Studies: Analysis of SiO2 Film Growth Data,” J. Electrochem. Soc. 123, 1380–1384 (1976).
    [Crossref]
  5. C. J. Dell’Oca, “Nondestructive Thickness Determination of Polycrystalline Silicon Deposited on Oxidized Silicon,” J. Electrochem. Soc. 119, 108–111 (1972).
    [Crossref]
  6. F. Schwidefsky and F. Holtz, “Optical Interference Phenomena in Silicon Films on Oxidized Silicon and Similar Two-Film systems,” Thin Solid Films 17, 93–103 (1973).
    [Crossref]
  7. M. H. Brodsky, R. S. Title, K. Weiser, and G. D. Pettit, “Structural, Optical, and Electrical Properties of Amorphous Silicon Films,” Phys. Rev. B 1, 2632–2641 (1970).
    [Crossref]
  8. F. Schwidefsky, “Increase of the Refractive Index of Silicon Films by Dangling Bonds,” Thin Solid Films 18, 45–52 (1973).
    [Crossref]
  9. H. R. Philipp and E. A. Taft, “Optical Constants of Silicon in the Region 1 to 10 eV,” Phys. Rev. 120, 37–38 (1960).
    [Crossref]
  10. P. H. Berning, “Theory and Calculation of Optical Thin Films,” in Physics of Thin Films, edited by Georg Haas, Vol. 1, pp 69–121 (Academic, New York, 1963).
  11. F. Reizman and W. VanGelder, “Optical Thickness Measurement of SiO2-Si3N4 Films on Silicon,” Solid State Electronics 10, 625–632 (1967).
    [Crossref]
  12. Standard deviation is calculated as if the thickness values were normally distributed, while in fact they are not. Spread in these values is more indicative of systematic error than of random error. The quantity is typically less than 1% of the film thickness for measurements of films thicker than about 200 nm.
  13. A wavelength cutoff point is used to eliminate from consideration extrema below a certain wavelength, typically 500 nm, as they are more likely to be inaccurate or extraneous (e.g., produced by noise.)
  14. S. Tolansky, Surface Microphotography, (Interscience, New York, 1960).

1975 (2)

K. L. Konnerth and F. H. Dill, “In-situ Measurement of Dielectric Thickness During Etching or Development Process,” IEEE Trans. Electron Devices ED-22, 452–456 (1975).
[Crossref]

F. H. Dill, W. P. Hornberger, P. S. Hauge, and J. M. Shaw, “Characterization of Positive Photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[Crossref]

1973 (3)

P. S. Hauge and F. H. Dill, “Design and Operation of ETA, an Automated Ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973);E. A. Irene and Y. J. van der Meulen, “Silicon Oxidation Studies: Analysis of SiO2 Film Growth Data,” J. Electrochem. Soc. 123, 1380–1384 (1976).
[Crossref]

F. Schwidefsky and F. Holtz, “Optical Interference Phenomena in Silicon Films on Oxidized Silicon and Similar Two-Film systems,” Thin Solid Films 17, 93–103 (1973).
[Crossref]

F. Schwidefsky, “Increase of the Refractive Index of Silicon Films by Dangling Bonds,” Thin Solid Films 18, 45–52 (1973).
[Crossref]

1972 (2)

C. J. Dell’Oca, “Nondestructive Thickness Determination of Polycrystalline Silicon Deposited on Oxidized Silicon,” J. Electrochem. Soc. 119, 108–111 (1972).
[Crossref]

K. L. Konnerth and F. H. Dill, “IOTA, A Computer Controlled Thin Film Thickness Measurement Tool,” Solid State Electronics 15, 371–380 (1972).
[Crossref]

1970 (1)

M. H. Brodsky, R. S. Title, K. Weiser, and G. D. Pettit, “Structural, Optical, and Electrical Properties of Amorphous Silicon Films,” Phys. Rev. B 1, 2632–2641 (1970).
[Crossref]

1967 (1)

F. Reizman and W. VanGelder, “Optical Thickness Measurement of SiO2-Si3N4 Films on Silicon,” Solid State Electronics 10, 625–632 (1967).
[Crossref]

1960 (1)

H. R. Philipp and E. A. Taft, “Optical Constants of Silicon in the Region 1 to 10 eV,” Phys. Rev. 120, 37–38 (1960).
[Crossref]

Berning, P. H.

P. H. Berning, “Theory and Calculation of Optical Thin Films,” in Physics of Thin Films, edited by Georg Haas, Vol. 1, pp 69–121 (Academic, New York, 1963).

Brodsky, M. H.

M. H. Brodsky, R. S. Title, K. Weiser, and G. D. Pettit, “Structural, Optical, and Electrical Properties of Amorphous Silicon Films,” Phys. Rev. B 1, 2632–2641 (1970).
[Crossref]

Dell’Oca, C. J.

C. J. Dell’Oca, “Nondestructive Thickness Determination of Polycrystalline Silicon Deposited on Oxidized Silicon,” J. Electrochem. Soc. 119, 108–111 (1972).
[Crossref]

Dill, F. H.

K. L. Konnerth and F. H. Dill, “In-situ Measurement of Dielectric Thickness During Etching or Development Process,” IEEE Trans. Electron Devices ED-22, 452–456 (1975).
[Crossref]

F. H. Dill, W. P. Hornberger, P. S. Hauge, and J. M. Shaw, “Characterization of Positive Photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[Crossref]

P. S. Hauge and F. H. Dill, “Design and Operation of ETA, an Automated Ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973);E. A. Irene and Y. J. van der Meulen, “Silicon Oxidation Studies: Analysis of SiO2 Film Growth Data,” J. Electrochem. Soc. 123, 1380–1384 (1976).
[Crossref]

K. L. Konnerth and F. H. Dill, “IOTA, A Computer Controlled Thin Film Thickness Measurement Tool,” Solid State Electronics 15, 371–380 (1972).
[Crossref]

Hauge, P. S.

F. H. Dill, W. P. Hornberger, P. S. Hauge, and J. M. Shaw, “Characterization of Positive Photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[Crossref]

P. S. Hauge and F. H. Dill, “Design and Operation of ETA, an Automated Ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973);E. A. Irene and Y. J. van der Meulen, “Silicon Oxidation Studies: Analysis of SiO2 Film Growth Data,” J. Electrochem. Soc. 123, 1380–1384 (1976).
[Crossref]

Holtz, F.

F. Schwidefsky and F. Holtz, “Optical Interference Phenomena in Silicon Films on Oxidized Silicon and Similar Two-Film systems,” Thin Solid Films 17, 93–103 (1973).
[Crossref]

Hornberger, W. P.

F. H. Dill, W. P. Hornberger, P. S. Hauge, and J. M. Shaw, “Characterization of Positive Photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[Crossref]

Konnerth, K. L.

K. L. Konnerth and F. H. Dill, “In-situ Measurement of Dielectric Thickness During Etching or Development Process,” IEEE Trans. Electron Devices ED-22, 452–456 (1975).
[Crossref]

K. L. Konnerth and F. H. Dill, “IOTA, A Computer Controlled Thin Film Thickness Measurement Tool,” Solid State Electronics 15, 371–380 (1972).
[Crossref]

Pettit, G. D.

M. H. Brodsky, R. S. Title, K. Weiser, and G. D. Pettit, “Structural, Optical, and Electrical Properties of Amorphous Silicon Films,” Phys. Rev. B 1, 2632–2641 (1970).
[Crossref]

Philipp, H. R.

H. R. Philipp and E. A. Taft, “Optical Constants of Silicon in the Region 1 to 10 eV,” Phys. Rev. 120, 37–38 (1960).
[Crossref]

Reizman, F.

F. Reizman and W. VanGelder, “Optical Thickness Measurement of SiO2-Si3N4 Films on Silicon,” Solid State Electronics 10, 625–632 (1967).
[Crossref]

Schwidefsky, F.

F. Schwidefsky, “Increase of the Refractive Index of Silicon Films by Dangling Bonds,” Thin Solid Films 18, 45–52 (1973).
[Crossref]

F. Schwidefsky and F. Holtz, “Optical Interference Phenomena in Silicon Films on Oxidized Silicon and Similar Two-Film systems,” Thin Solid Films 17, 93–103 (1973).
[Crossref]

Shaw, J. M.

F. H. Dill, W. P. Hornberger, P. S. Hauge, and J. M. Shaw, “Characterization of Positive Photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[Crossref]

Taft, E. A.

H. R. Philipp and E. A. Taft, “Optical Constants of Silicon in the Region 1 to 10 eV,” Phys. Rev. 120, 37–38 (1960).
[Crossref]

Title, R. S.

M. H. Brodsky, R. S. Title, K. Weiser, and G. D. Pettit, “Structural, Optical, and Electrical Properties of Amorphous Silicon Films,” Phys. Rev. B 1, 2632–2641 (1970).
[Crossref]

Tolansky, S.

S. Tolansky, Surface Microphotography, (Interscience, New York, 1960).

VanGelder, W.

F. Reizman and W. VanGelder, “Optical Thickness Measurement of SiO2-Si3N4 Films on Silicon,” Solid State Electronics 10, 625–632 (1967).
[Crossref]

Weiser, K.

M. H. Brodsky, R. S. Title, K. Weiser, and G. D. Pettit, “Structural, Optical, and Electrical Properties of Amorphous Silicon Films,” Phys. Rev. B 1, 2632–2641 (1970).
[Crossref]

IBM J. Res. Dev. (1)

P. S. Hauge and F. H. Dill, “Design and Operation of ETA, an Automated Ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973);E. A. Irene and Y. J. van der Meulen, “Silicon Oxidation Studies: Analysis of SiO2 Film Growth Data,” J. Electrochem. Soc. 123, 1380–1384 (1976).
[Crossref]

IEEE Trans. Electron Devices (2)

K. L. Konnerth and F. H. Dill, “In-situ Measurement of Dielectric Thickness During Etching or Development Process,” IEEE Trans. Electron Devices ED-22, 452–456 (1975).
[Crossref]

F. H. Dill, W. P. Hornberger, P. S. Hauge, and J. M. Shaw, “Characterization of Positive Photoresist,” IEEE Trans. Electron Devices ED-22, 445–452 (1975).
[Crossref]

J. Electrochem. Soc. (1)

C. J. Dell’Oca, “Nondestructive Thickness Determination of Polycrystalline Silicon Deposited on Oxidized Silicon,” J. Electrochem. Soc. 119, 108–111 (1972).
[Crossref]

Phys. Rev. (1)

H. R. Philipp and E. A. Taft, “Optical Constants of Silicon in the Region 1 to 10 eV,” Phys. Rev. 120, 37–38 (1960).
[Crossref]

Phys. Rev. B (1)

M. H. Brodsky, R. S. Title, K. Weiser, and G. D. Pettit, “Structural, Optical, and Electrical Properties of Amorphous Silicon Films,” Phys. Rev. B 1, 2632–2641 (1970).
[Crossref]

Solid State Electronics (2)

K. L. Konnerth and F. H. Dill, “IOTA, A Computer Controlled Thin Film Thickness Measurement Tool,” Solid State Electronics 15, 371–380 (1972).
[Crossref]

F. Reizman and W. VanGelder, “Optical Thickness Measurement of SiO2-Si3N4 Films on Silicon,” Solid State Electronics 10, 625–632 (1967).
[Crossref]

Thin Solid Films (2)

F. Schwidefsky and F. Holtz, “Optical Interference Phenomena in Silicon Films on Oxidized Silicon and Similar Two-Film systems,” Thin Solid Films 17, 93–103 (1973).
[Crossref]

F. Schwidefsky, “Increase of the Refractive Index of Silicon Films by Dangling Bonds,” Thin Solid Films 18, 45–52 (1973).
[Crossref]

Other (4)

P. H. Berning, “Theory and Calculation of Optical Thin Films,” in Physics of Thin Films, edited by Georg Haas, Vol. 1, pp 69–121 (Academic, New York, 1963).

Standard deviation is calculated as if the thickness values were normally distributed, while in fact they are not. Spread in these values is more indicative of systematic error than of random error. The quantity is typically less than 1% of the film thickness for measurements of films thicker than about 200 nm.

A wavelength cutoff point is used to eliminate from consideration extrema below a certain wavelength, typically 500 nm, as they are more likely to be inaccurate or extraneous (e.g., produced by noise.)

S. Tolansky, Surface Microphotography, (Interscience, New York, 1960).

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Figures (11)

FIG. 1
FIG. 1

Polysilicon FET film structures. Silicon substrate, SiO2 and possible Si3N4 gate dielectric, and polysilicon electrode, (a) before and (b) after oxidation. (Layer thicknesses are not shown to scale.)

FIG. 2
FIG. 2

Single-layer, absorbing film on absorbing substrate in transparent ambient. Optical constants, film thickness d2, Fresnel coefficients r12 and r23, and reflection coefficient r1 are shown. Near-normal incidence is indicated only for clarity. The analysis assumes normal incidence.

FIG. 3
FIG. 3

General multilayer film and mathematically equivalent single-layer film. Equivalent film has the same top layer on an effective substrate that replaces the actual substrate and underlying layers. Equating the substrate reflection coefficients rS leads to values for n3eff, and k3eff. For simplicity, internal reflections are not indicated.

FIG. 4
FIG. 4

Measured (open circles) and haze-corrected (closed circles) reflectance curves for a polysilicon film deposited on a 100-nm thick gate oxide on Si. Dehaze factor at 400-nm wavelength is γ = 1.39. Using (N, K) = (1.05, 3), the analysis algorithm gave a polysilicon thickness of 516.5 nm with a standard deviation (for seven extrema) of 1.2 nm. Extrema below 500-nm wavelength (dashed line) were not used. Full curve is calculated reflectance for the measured polysilicon thickness. Analysis of the uncorrected data gave 516.6 nm and 1.1 nm for thickness and standard deviation respectively, showing the insensitivity of the algorithm to scattering. The agreement of corrected data with calculated reflectance is the main advantage gained from the dehaze correction.

FIG. 5
FIG. 5

Wavelength positions of reflectance extrema for film in Fig. 1(a) with varying gate oxide thickness. Solid curves are for maxima, dashed curves for minima. Layer thicknesses: polysilicon, 600 nm; gate oxide, 20–600 nm. (N, K) multipliers: (1.05,3).

FIG. 6
FIG. 6

Reflectance (heavy) and envelope (dashed) curves for film of Fig. 1(a) showing the effects of substrate order changes. Reflectance extrema are shown as closed circles. Layer thicknesses: polysilicon, 600 nm; gate oxide, 600 nm. (N, K) multipliers: (1.05, 3). Solid envelope curves were calculated assuming a transparent top layer. At the order changes, (λ = 440, 583 nm), the gate oxide is a multiple half-wave thick, and is effectively absent. Because of the optical similarity of polysilicon and the Si substrate, reflectance is almost independent of the polysilicon thickness at these points. The substrate reflectance (thin solid curve) is seen to be tangent to the lower envelope curve, and to have maxima at the substrate order changes.

FIG. 7
FIG. 7

Thicknesses associated with reflectance extrema for the curve of Fig. (6). Each set of values assumes the indicated order number for the right-most extremum and increments the order by 0.5 for each extremum to the left. No account is taken for substrate order changes, or for the poor approximation of extrema to points of tangency within 15 nm of substrate order changes (shown by dashed lines).

FIG. 8
FIG. 8

Thicknesses associated with reflectance extrema for the curve of Fig. (6). Each set of values assumes the indicated order number for the right-most extremum and increments the order by 0.5 for each extremum to the left, but decrements the order by unity as each substrate order change is passed. Because of the poor approximation of extrema to points of tangency within 15 nm of substrate order changes, extrema in these regions have been excluded. The average of the middle set of values is 599.7 nm and the standard deviation is 2.1 nm.

FIG. 9
FIG. 9

Effect on reflectance of adding an overlying oxide layer in Fig. 1(b). Dashed curve without, solid curve with top oxide layer. Layer thicknesses: top oxide, 300 nm; polysilicon, 500 nm; gate oxide, 100 nm. (N, K) multipliers: (1.05, 3). The reflectance extrema are lowered by the top oxide layer, but their wavelengths λext are only slightly changed (less than 6 nm in each case). Analyzed polysilicon thickness and standard deviations: Dashed curve, 499.8 and 0.3 nm; solid curve, 498.8 and 3.7 nm.

FIG. 10
FIG. 10

Measured polysilicon thickness at 2.5-mm spacings across six wafers partially overlaid with oxide. Polysilicon thickness variation is noted across the wafers, but the measurements are continuous at the oxide edges (dashed lines). The right portion of each set of data has the top oxide layer. Layer thicknesses: polysilicon, as indicated; wafers 1,3,5: gate oxide, 70 nm; top oxide, 220 nm. Wafers 2, 4, 6: gate oxide, 98 nm; top oxide, 620 nm. (N, K) multipliers: (1.05, 3).

FIG. 11
FIG. 11

Calculated reflectance (solid) and envelope (dashed) curves for film of Fig. 1(b). Layer thicknesses: top oxide, 300 nm; polysilicon, 500 nm; gate oxide, 100 nm. (N, K) multipliers: (1.05,3). Note the extreme variation in all curves, and the consecutive points of tangency to the bottom envelope curve at wavelengths of 570, 591, and 609 nm.

Equations (40)

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n P N ( T ) n S i , k P K ( T ) k S i ,
1.02 N ( T ) 1.10 ,
3 K ( T ) 10 ,
900 ° C T 650 ° C .
n j = n j i k j , j = 1 , 2 , 3 ; k 1 0 .
r i j = n j n j n i + n j = r i j exp ( i δ i j ) , r i j 0 .
tan δ i j = 2 ( n i k j n j k i ) ( n i 2 + k i 2 ) ( n j 2 + k j 2 )
r 1 = r 12 + r 23 exp i d 2 1 + r 12 r 23 exp i d 2
= exp ( i δ 12 ) r 12 + r 23 exp i ( x + δ 12 ) 1 + r 12 r 23 exp i ( x + δ 12 )
x = 4 π n 2 d 2 / λ δ 23 ,
r 23 = r 23 exp ( 4 π k 2 d 2 / λ ) ,
d 2 = 4 π n 2 d 2 / λ .
R = r 1 r 1 * = r 12 2 + r 23 2 + 2 r 12 r 23 cos ( x + δ 12 ) 1 + r 12 2 r 23 2 + 2 r 12 r 23 cos ( x δ 12 ) ,
R T = r 12 2 + r 23 2 2 r 12 r 23 cos x 1 + r 12 2 + r 23 2 2 r 12 r 23 cos x ,
cos x = ( r 12 2 + r 23 2 ) R T ( 1 + r 12 2 r 23 2 ) ( 2 r 12 r 23 ) ( 1 R T ) ,
d 2 = λ 4 π n 2 { δ 23 + 2 p π ± cos 1 ( r 12 2 + r 23 2 R T ( 1 + r 12 2 r 23 2 ) ( 2 r 12 r 23 ) ( 1 R T ) ) } .
d R / d x = 0
d R / d λ = 0 .
d 2 = ( λ ext / 4 π n 2 ) ( δ 23 + 2 p π + q π ) ,
A cos x + B sin x = 1 ,
d R / d x = 0
tan x = ( tan δ 12 ) ( R + 1 ) / ( R 1 ) .
d R / d λ = 0 .
d 2 = λ ext 4 π n 2 [ δ 23 + 2 p π + tan 1 ( ( tan δ 12 ) R ext + 1 R ext 1 ) ] ,
r j 1 = r j 1 , j + r j exp i d j 1 + r j 1 , j r j exp i d j ,
d j = 4 π n j d j / λ .
r q = r q , q + 1 ,
R = r 1 r 1 * .
n 3 eff = n 3 eff i k 3 eff .
r S ( λ ) n 1 n 3 eff ( λ ) n 1 + n 3 eff ( λ ) .
n 3 eff ( λ ) = n 1 1 r S ( λ ) 1 + r S ( λ ) .
| r S | 1 .
n 3 eff 0 .
R bulk ( 400 ) 0.52 .
γ = R bulk ( 400 ) / R meas ( 400 )
R corr ( λ ) = R meas ( λ ) [ 1 + ( γ 1 ) ( 400 / λ n m ) ] .
δ d 2 0.1 δ d gate .
δ d 2 / d 2 = δ N / N .
d oxide 2.2 δ d poly .
20 d gate 150 nm , 200 d poly 700 nm , 0 d oxide 500 nm ,