Abstract

The dependence of the azimuth angle settings on the change in off-null intensity of a polarizer-compensator-sample-analyzer ellipsometer owing to changes in sample properties is studied. First, a closed-form expression for the relationship between azimuth angles that fulfill the null condition is presented. An approximation for the off-null light intensity near null that is valid for small changes of the p- and s-reflection coefficients of an isotropic sample is then derived. This approximation shows that the intensity change near the null can be described by changes in the ellipsometric parameters tan ψ and Δ only. Expressions for finding the azimuth angle that gives the maximum possible intensity change for a given change in the sample parameters are also derived. The importance of optimization of azimuth angle settings for different samples is investigated and found to depend on tan ψ. Numerical and experimental results chosen from the investigation of gas sensors based on porous silicon are included to verify the approximations as well as the optimization.

© 2003 Optical Society of America

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References

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  1. K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
    [CrossRef]
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).
  3. D. L. Confer, R. M. A. Azzam, N. M. Bashara, “Ellipsometer nulling: convergence and speed,” Appl. Opt. 15, 2568–2575 (1976).
    [CrossRef] [PubMed]
  4. P. A. Cuypers, W. T. Hermens, H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84, 56–57 (1978).
    [CrossRef] [PubMed]
  5. H. Arwin, S. Welin-Klintström, R. Jansson, “Off-null ellipsometry revisited: basic considerations for measuring surface concentrations at solid/liquid interfaces,” J. Colloid Interface Sci. 156, 377–382 (1993).
    [CrossRef]
  6. H. Arwin, “Is ellipsometry suitable for sensor applications?” Sens. Actuators A 92, 43–51 (2001).
    [CrossRef]
  7. S. Guo, R. Rochotzki, I. Lundström, H. Arwin, “Ellipsometric sensitivity to halothane vapors of hexamethydisiloxane plasma polymer layers,” Sens. Actuators B 44, 243–247 (1997).
    [CrossRef]
  8. S. Zangooie, “Fabrication, characterization and application of porous silicon thin films and multilayered systems,” Ph. D. dissertation 581 (Linköping University, Linköping, Sweden, 1999).

2001

H. Arwin, “Is ellipsometry suitable for sensor applications?” Sens. Actuators A 92, 43–51 (2001).
[CrossRef]

1998

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
[CrossRef]

1997

S. Guo, R. Rochotzki, I. Lundström, H. Arwin, “Ellipsometric sensitivity to halothane vapors of hexamethydisiloxane plasma polymer layers,” Sens. Actuators B 44, 243–247 (1997).
[CrossRef]

1993

H. Arwin, S. Welin-Klintström, R. Jansson, “Off-null ellipsometry revisited: basic considerations for measuring surface concentrations at solid/liquid interfaces,” J. Colloid Interface Sci. 156, 377–382 (1993).
[CrossRef]

1978

P. A. Cuypers, W. T. Hermens, H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84, 56–57 (1978).
[CrossRef] [PubMed]

1976

Arwin, H.

H. Arwin, “Is ellipsometry suitable for sensor applications?” Sens. Actuators A 92, 43–51 (2001).
[CrossRef]

S. Guo, R. Rochotzki, I. Lundström, H. Arwin, “Ellipsometric sensitivity to halothane vapors of hexamethydisiloxane plasma polymer layers,” Sens. Actuators B 44, 243–247 (1997).
[CrossRef]

H. Arwin, S. Welin-Klintström, R. Jansson, “Off-null ellipsometry revisited: basic considerations for measuring surface concentrations at solid/liquid interfaces,” J. Colloid Interface Sci. 156, 377–382 (1993).
[CrossRef]

Azzam, R. M. A.

Bashara, N. M.

Confer, D. L.

Cuypers, P. A.

P. A. Cuypers, W. T. Hermens, H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84, 56–57 (1978).
[CrossRef] [PubMed]

Guo, S.

S. Guo, R. Rochotzki, I. Lundström, H. Arwin, “Ellipsometric sensitivity to halothane vapors of hexamethydisiloxane plasma polymer layers,” Sens. Actuators B 44, 243–247 (1997).
[CrossRef]

Hemker, H. C.

P. A. Cuypers, W. T. Hermens, H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84, 56–57 (1978).
[CrossRef] [PubMed]

Hermens, W. T.

P. A. Cuypers, W. T. Hermens, H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84, 56–57 (1978).
[CrossRef] [PubMed]

Jansson, R.

H. Arwin, S. Welin-Klintström, R. Jansson, “Off-null ellipsometry revisited: basic considerations for measuring surface concentrations at solid/liquid interfaces,” J. Colloid Interface Sci. 156, 377–382 (1993).
[CrossRef]

Lundström, I.

S. Guo, R. Rochotzki, I. Lundström, H. Arwin, “Ellipsometric sensitivity to halothane vapors of hexamethydisiloxane plasma polymer layers,” Sens. Actuators B 44, 243–247 (1997).
[CrossRef]

Rochotzki, R.

S. Guo, R. Rochotzki, I. Lundström, H. Arwin, “Ellipsometric sensitivity to halothane vapors of hexamethydisiloxane plasma polymer layers,” Sens. Actuators B 44, 243–247 (1997).
[CrossRef]

Vedam, K.

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
[CrossRef]

Welin-Klintström, S.

H. Arwin, S. Welin-Klintström, R. Jansson, “Off-null ellipsometry revisited: basic considerations for measuring surface concentrations at solid/liquid interfaces,” J. Colloid Interface Sci. 156, 377–382 (1993).
[CrossRef]

Zangooie, S.

S. Zangooie, “Fabrication, characterization and application of porous silicon thin films and multilayered systems,” Ph. D. dissertation 581 (Linköping University, Linköping, Sweden, 1999).

Anal. Biochem.

P. A. Cuypers, W. T. Hermens, H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84, 56–57 (1978).
[CrossRef] [PubMed]

Appl. Opt.

J. Colloid Interface Sci.

H. Arwin, S. Welin-Klintström, R. Jansson, “Off-null ellipsometry revisited: basic considerations for measuring surface concentrations at solid/liquid interfaces,” J. Colloid Interface Sci. 156, 377–382 (1993).
[CrossRef]

Sens. Actuators A

H. Arwin, “Is ellipsometry suitable for sensor applications?” Sens. Actuators A 92, 43–51 (2001).
[CrossRef]

Sens. Actuators B

S. Guo, R. Rochotzki, I. Lundström, H. Arwin, “Ellipsometric sensitivity to halothane vapors of hexamethydisiloxane plasma polymer layers,” Sens. Actuators B 44, 243–247 (1997).
[CrossRef]

Thin Solid Films

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313–314, 1–9 (1998).
[CrossRef]

Other

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).

S. Zangooie, “Fabrication, characterization and application of porous silicon thin films and multilayered systems,” Ph. D. dissertation 581 (Linköping University, Linköping, Sweden, 1999).

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Figures (6)

Fig. 1
Fig. 1

Configuration of a PCSA ellipsometer.

Fig. 2
Fig. 2

χ̃ i for P = 20° with C as the ordinate (solid curve) and for C = 40° with P as the ordinate (dotted curve). The straight solid line with the slope of tan Δ shows the loci of -ρ̃ cot A with A as the ordinate.

Fig. 3
Fig. 3

Intensity changes for a porous silicon sample that has p = 0.189, s = 0.428, and Δ = 63.5° when δ p is varied from -0.02 to 0.02 (corresponding to a ±10% change in p ) for some specific values of δ s and δΔ (corresponding to 1% and 5% changes, respectively, in these parameters). Solid curves, exact calculations from Eq. (9); dotted curves, approximate calculations from relation (14).

Fig. 4
Fig. 4

Intensity changes versus analyzer azimuth for a porous silicon sample that has p = 0.189, s = 0.428, and Δ = 63.5° for several values of χ̂in and some specific values of δ p , δ s , and δΔ that correspond to (a) a 1% change and (b) a simultaneous 5% change in these parameters. Solid curves, calculations by from Eq. (9); dotted curves, approximate calculations by from relation (14).

Fig. 5
Fig. 5

Intensity changes of a porous silicon sample exposed to concentrations of 205 to 1231 parts in 106 of 2-propanol vapor pulses in a nitrogen carrier gas for three settings, which correspond to the conventional null where C = -45°, to a null where P = 30°, and to the optimal null. The azimuth angle settings and the magnitude of the intensity changes (normalized with respect to the intensity change that occurs for the conventional settings) are given in Table 1.

Fig. 6
Fig. 6

Off-null intensity change [given by relation (14)] divided by the maximum possible off-null intensity change [given by Eq. (19)] versus χ̂in for three values of ρ̂ = tan ψ.

Tables (1)

Tables Icon

Table 1 Azimuth Angle Settings and Magnitude of Intensity Changes of Several Nulls for a Sample with ψ = 19.42° and Δ = 65.35°a

Equations (23)

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ρ˜=ρˆ expiΔ=tan ψ expiΔ=R˜p/R˜s,
χ˜=χˆ expiφ=E˜y/E˜x,
χ˜i=tan C-i tanP-C1+i tan C tanP-C,
χ˜i=ρ˜χ˜o.
Io=|T˜12χ˜i+T˜11|2+|T˜22χ˜i+T˜21|21+χˆi2,
T˜SA=R-ATARAT˜s= cos A-sin Asin Acos A 1000 cos Asin A-sin Acos A×R˜p00R˜s,
T˜11T˜12T˜21T˜22= R˜p cos2 AR˜s sin A cos AR˜p sin A cos AR˜s sin2 A.
Io= |R˜p cos A+χ˜iR˜s sin A|21+χˆi2.
Io=11+χˆi2Rˆp2 cos2 A+χˆi2Rˆs2 sin2 A+2χˆiRˆpRˆs sin A cos A cosΔ-φi,
χ˜on=tanAn+π2=-cot An,
χ˜in=-ρ˜ cot An.
tanCn=±κ1γ cos Δ, Δ± π2, γ±1,
tanPn-Cn= κ2γ sin Δ,
κ1= 1-γ222+γ2 cos2 Δ±1-γ2×1-γ224+γ2 cos2 Δ1/2,
κ2= 1+γ222-γ2 sin2 Δ±1+γ2×1+γ224-γ2 sin2 Δ1/2,
γ=ρˆ cot An.
δIoRˆs2χˆin2ρˆ21+χˆin2 χˆin2+ρˆ2δρˆρˆ2+δΔ2.
cos δΔ1-δΔ2/2,
δRˆpRˆp-δRˆsRˆsδρˆρˆ,
dδIodχˆin=0,
χˆin2=ρˆ.
cot An=±1ρˆ.
δI0,max=Rˆs2ρˆ1+ρˆ2δρˆρˆ2+δΔ2.

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