Apparatus for and a method of determining a characteristic of a layer or layers

• US 7,755,768 B2
• Filed: 01/16/2007
• Issued: 07/13/2010
• Est. Priority Date: 07/14/2004
• Status: Expired due to Fees

• Current Assignee: Taylor Hobson Limited (Ametek Incorporated)
• Original Assignee: Taylor Hobson Limited (Ametek Incorporated)
• Inventors: Mansfield, Daniel
• Primary Examiner(s): Toatley, Jr.; Gregory J
• Assistant Examiner(s): Richey; Scott M
• Application Number:
  US11/653,700
• Publication Number:
  US 20070188768A1
• Time in Patent Office: 1,274 Days
• Field of Search: 356/485, 356/497, 356/511, 356/512, 356/503, 356/504, 356/630, 356/632, 702/109, 702155-159, 702/166, 702/167, 702/170
• US Class Current: 356/497
• CPC Class Codes: G01B 11/0675 using interferometry

Abstract

In respective measurement operations on a first sample surface area having a layer structure (81) and a characterized second sample surface area (82), light reflected by the region of the sample surface and the reference surface interfere and a sensing device (10) senses light intensity representing interference fringes at intervals during the relative movement along a measurement scan path to provide first intensity data in the form of a first series of intensity values resulting from a measurement operation on the first sample surface area and second intensity data in the form of a second series of intensity values resulting from a measurement operation on the second sample surface area. A layer structure determiner (100) determines a frequency transform ratio corresponding to a ratio between the first and second intensity data and fits a layer structure model having variable model parameters related to the layer thicknesses and refractive indices of the layers of a layer structure to the determined ratio by adjusting the model parameters, thereby obtaining for the model parameters values representing the layer thicknesses and refractive indices of the layers of the sample layer structure.

Claims

1. Apparatus for determining information relating to a sample layer structure, the apparatus comprising:

a beam splitter configured to direct light along a sample path towards a region of a surface of a sample and along a reference path towards a reference surface such that light reflected by the region of the sample surface and light reflected by the reference surface interfere;

a mover configured to effect movement of at least one of the sample and the reference surface so as to effect relative movement along a measurement scan path between the sample and the reference surface;

a sensing device configured to sense light representing the interference fringes produced by a sample surface region during relative movement along the measurement scan path;

a controller configured to carry out a measurement operation by causing the mover to effect relative movement while the sensing device senses light intensity at intervals to provide a series of intensity values representing interference fringes produced by a region of a sample surface during the relative movement; and

a data processor configured to receive and process first intensity data comprising a first series of intensity values resulting from a measurement operation on a first sample surface area having a layer structure and second intensity data comprising a second series of intensity values resulting from a measurement operation on a characterised second sample surface area, the data processor comprising;

a frequency transform ratio determiner configured to determine a ratio between frequency transformed first intensity data and frequency transformed second intensity data; and

a data fitter configured to fit a layer structure model having variable model parameters related to the layer thicknesses and refractive indices of the layers of a layer structure to the ratio determined by the ratio determiner by adjusting the model parameters, thereby obtaining for the model parameters values representing the layer thicknesses and refractive indices of the layers of the sample layer structure.

2. Apparatus according to claim 1, wherein the frequency transform ratio determiner comprises a frequency transformer configured to determine first frequency transformed data corresponding to the first intensity data and second frequency transformed data corresponding to the second intensity data and a ratio determiner configured to determine the frequency transform ratio by dividing one of the first and second frequency transformed data by the other of the first and second frequency transformed data.

3. Apparatus according to claim 1, wherein the frequency transform ratio determiner comprises a frequency transformer configured to determine first frequency transformed data corresponding to the first intensity data and second frequency transformed data corresponding to the second intensity data and a ratio determiner configured to determine the frequency transform ratio by dividing one of the first and second frequency transformed data by the other of the first and second frequency transformed data and multiplying that ratio by a field reflectance term.

4. Apparatus according to claim 1, wherein the frequency transform ratio determiner comprises a frequency transformer configured to determine first frequency transformed data corresponding to the first intensity data and second frequency transformed data corresponding to the second intensity data and a ratio determiner configured to determine the frequency transform ratio by dividing one of the first and second frequency transformed data by the other of the first and second frequency transformed data and by multiplying that ratio by a field reflectance term:

${\left(\frac{1-n_{\mathrm{base}}<br><br>\left(v\right)}{1+n_{\mathrm{base}}<br><br>\left(v\right)}\right)}^{\mathrm{†<br><br>}}$

where n_base (v) is the refractive index at frequency v of the second sample surface area and †

indicates either the ratio or its complex conjugate.

5. Apparatus according to claim 1, wherein the data processor is configured to receive and process second intensity data comprising the second series of intensity values resulting from the measurement operation on the characterised second sample surface area having a layer structure and being characterised by having a defined dispersive admittance.

6. Apparatus according to claim 1, wherein the ratio determiner is configured to determine

$\mathrm{HCF}$

( v ) = ( 1 - n base ⁡

( v ) 1 + n base ⁡

( v ) ) †

⁢

ℱ

thin ⁡

( I ⁡

( Z k ) ) SB ⁢

⁢

†

ℱ

base ⁡

( I ⁡

( Z k ) ) SB ⁢

⁢

†

where †

indicates either the ratio or its complex conjugate, where n_base(v) is the refractive index at frequency v of the second sample surface area, and where

$\frac{{F_{\mathrm{thin}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{{\mathrm{SB}}^{\mathrm{†<br><br>}}}}{{F_{\mathrm{base}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{{\mathrm{SB}}^{\mathrm{†<br><br>}}}}$

is the ratio between the frequency transformed first intensity data and the frequency transformed second intensity data.

7. Apparatus according to claim 1, wherein the ratio determiner is configured to determine:

$\begin{array}{c}\mathrm{HCF}<br><br>\left(v\right)\equiv <br><br><br><br>a_{\mathrm{HCF}}<br><br>\left(v\right)<br><br>{\mathrm{e<br><br>}}^{{\mathrm{i<br><br>\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v\right)}\\ =<br><br>\frac{1}{2}<br><br>{\int <br><br>}_0^{\mathrm{\pi <br><br>}/2}<br><br>\left(\begin{array}{c}\frac{1-{\mathrm{\eta <br><br>}}_{\mathrm{base}}^p<br><br>\left(v,\mathrm{\theta <br><br>}\right)<br><br><br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}{<br><br>1+{\mathrm{\eta <br><br>}}_{\mathrm{base}}^p<br><br>\left(v,\mathrm{\theta <br><br>}\right)<br><br><br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}+\\ \frac{1-{\mathrm{\eta <br><br>}}_{\mathrm{base}}^s<br><br>\left(v,\mathrm{\theta <br><br>}\right)/\cos <br><br><br><br>\mathrm{\theta <br><br>}}{<br><br>1+{\mathrm{\eta <br><br>}}_{\mathrm{base}}^s<br><br>\left(v,\mathrm{\theta <br><br>}\right)/\cos <br><br><br><br>\mathrm{\theta <br><br>}}\end{array}\right)<br><br>w<br><br>\left(\mathrm{\theta <br><br>}\right)<br><br>d<br><br>\mathrm{\theta <br><br>}<br><br>\frac{{{\mathrm{ℱ<br><br>}}_{\mathrm{thin}}<br><br>\left(I<br><br>\left(z_i\right)\right)}_{\mathrm{SB}<br><br><br><br>\mathrm{†<br><br>}}}{{{\mathrm{ℱ<br><br>}}_{\mathrm{base}}<br><br>\left(I<br><br>\left(z_i\right)\right)}_{\mathrm{SB}<br><br><br><br>\mathrm{†<br><br>}}}\\ \approx <br><br><br><br>\stackrel{\_}{r<br><br>\left(v\right)<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>\phi <br><br>}<br><br>\left(v\right)}}<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>4<br><br>\mathrm{\pi <br><br>}<br><br><br><br>v<br><br><br><br>\mathrm{\Delta <br><br>}<br><br><br><br>z_{\mathrm{HCF}}<br><br>\cos <br><br><br><br>{\mathrm{\theta <br><br>}}_o}\\ \equiv <br><br><br><br>E<br><br>\left(v\right)\end{array}$

where

${\mathrm{\eta <br><br>}}_{\mathrm{base}}^s={\mathrm{\eta <br><br>}}_{\mathrm{base}}<br><br>\left(v\right)<br><br>\sqrt{1-{\sin }^2<br><br>{\mathrm{\theta <br><br>}}_0/{\mathrm{\eta <br><br>}}_{\mathrm{base}}<br><br>\left(v\right)}$ ${\mathrm{\eta <br><br>}}_{\mathrm{base}}^p=\frac{{\mathrm{\eta <br><br>}}_{\mathrm{base}}<br><br>\left(v\right)}{\sqrt{1-{\sin }^2<br><br>{\mathrm{\theta <br><br>}}_0/{\mathrm{\eta <br><br>}}_{\mathrm{base}}<br><br>\left(v\right)}}$

and where †

indicates either the ratio or its complex conjugate, where n_base(v) is the refractive index at frequency v of the second sample surface area, and where

$\frac{{F_{\mathrm{thin}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{{\mathrm{SB}}^{\mathrm{†<br><br>}}}}{{F_{\mathrm{base}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{{\mathrm{SB}}^{\mathrm{†<br><br>}}}}$

is the ratio between the frequency transformed first intensity data and the frequency transformed second intensity data, where θ

is the angle of incidence accepted by the numerical aperture, where

$r<br><br>\left(v\right)<br><br>{\mathrm{e<br><br>}}^{\mathrm{i<br><br>\phi <br><br>}<br><br><br><br>\left(v\right)}$

is the resultant field reflectance at frequency v, where a_HCF(v) is the amplitude of the HCF function at frequency v, e<sup>iφ

HCF(v)</sup> is the phase component of the HCF function at frequency v, and where Δ

z_HCF=Δ

z−

Δ

z_base where Δ

z is the path difference for the first sample surface area and Δ

z_base is the path difference for the second sample surface area.

8. Apparatus according to claim 1, wherein the layer structure model is a thin film layer structure optical admittance model.

9. Apparatus according to claim 1, wherein the layer structure model is a thin film layer structure optical admittance model:

$E<br><br>\left(v\right)=r^{\mathrm{†<br><br>}}<br><br>\left(v\right)<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>}<br><br><br><br>4<br><br><br><br>\mathrm{\pi <br><br>}<br><br><br><br>v<br><br><br><br>\mathrm{\Delta <br><br>}<br><br><br><br>z_{\mathrm{HCF}}}=\left(\frac{1-Y^{+}<br><br>\left(v\right)}{1+Y^{+}<br><br>\left(v\right)}\right)<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>4\pi <br><br>}<br><br><br><br>v<br><br><br><br>\mathrm{\Delta <br><br>}<br><br><br><br>z_{\mathrm{HCF}}}$

where the r^†

and Y^†

indicate, respectively, the electric field reflectance and optical admittance, or their complex conjugates, E(v) is the electric field at frequency v, Δ

z_HCF=Δ

z−

Δ

z_base where Δ

z is the path length difference for the first sample surface area and Δ

z_base is the path length difference for the second sample surface area.

10. Apparatus according to claim 1, wherein the layer structure model is a thin film layer structure optical admittance model:

$\begin{array}{c}E<br><br>\left(v\right)\equiv <br><br><br><br>a_E<br><br>\left(v\right)<br><br>{\mathrm{e<br><br>}}^{{\mathrm{i<br><br>\phi <br><br>}}_E<br><br>\left(v\right)}\\ =<br><br>\frac{1}{2}<br><br>{\int <br><br>}_0^{\mathrm{\pi <br><br>}/2}<br><br>\left(\begin{array}{c}\frac{1-Y_p^{\mathrm{†<br><br>}}<br><br>\left(v,\mathrm{\theta <br><br>}\right)<br><br><br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}{<br><br>1+Y_p^{\mathrm{†<br><br>}}<br><br>\left(v,\mathrm{\theta <br><br>}\right)<br><br><br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}+\\ \frac{1-Y_s^{\mathrm{†<br><br>}}<br><br>\left(v,\mathrm{\theta <br><br>}\right)/\cos <br><br><br><br>\mathrm{\theta <br><br>}}{<br><br>1+Y_s^{\mathrm{†<br><br>}}<br><br>\left(v,\mathrm{\theta <br><br>}\right)/\cos <br><br><br><br>\mathrm{\theta <br><br>}}\end{array}\right)<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>4}<br><br><br><br>\mathrm{\pi <br><br>}<br><br><br><br>v<br><br><br><br>\mathrm{\Delta <br><br>}<br><br><br><br>z_{\mathrm{HCF}}<br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}<br><br>w<br><br>\left(\mathrm{\theta <br><br>}\right)<br><br>d<br><br>\mathrm{\theta <br><br>}\end{array}$

where †

indicates the quantity or its complex conjugates, where θ

is the angle of incidence accepted by the numerical aperture, where Y_p and Y_s, indicate, respectively, the p and s polarisations of optical admittance, a_E(v) is the amplitude of the electric field at frequency v, where e<sup>iφ

E(v)</sup> is the phase component of the electric field at frequency v, where E(v) is the electric field at frequency v, where Δ

z_HCF=Δ

z−

Δ

z_base where Δ

z is the path difference for the first sample surface area and Δ

z_base is the path difference for the second sample surface area.

11. Apparatus according to claim 1, wherein the data fitter is configured to use a conjugate gradient or simulated annealing fitting procedure to fit the model parameters to the ratio.

12. Apparatus according to claim 1, wherein the data fitter is configured to use the following merit function:

$\mathrm{\varepsilon <br><br>}=\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)<br><br>\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)<br><br>\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_E<br><br>\left(v_j\right)\right)}^2+{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)<br><br>\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)<br><br>\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_E<br><br>\left(v_j\right)\right)}^2$

or the merit function;

$\mathrm{\varepsilon <br><br>}=\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)<br><br>\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)<br><br>\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_E<br><br>\left(v_j\right)\right)}^2+\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)<br><br>\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)<br><br>\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_E<br><br>\left(v_j\right)\right)}^2+\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)\right)}^2$

where a_HCF (v_j) is the amplitude of the HCF function at frequency v_j, a_E(v_j) is the amplitude of the electric field at frequency v_j, e<sup>iφ

HCF(vj)</sup> is the phase component of the HCF function at frequency v_j, where e<sup>iφ

E(vj)</sup> is the phase component of the electric field at frequency v_j, and where e^iφ

=cos φ

+i sin φ

.

13. Apparatus according to claim 1, wherein the data fitter is configured to use the following merit function:

$\mathrm{\varepsilon <br><br>}=\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)\right)}^2$

where a_HCF (v_j) is the amplitude of the HCF function at frequency v_j and a_E(v_j) is the amplitude of the electric field at frequency v_j.

14. Apparatus according to claim 1, wherein the frequency transform ratio determiner is configured to determine the frequency ratio such that it is equivalent to a term having an amplitude component, a phase component and a helical phase component.

15. Apparatus according to claim 1, wherein the frequency transform ratio determiner is configured to use a Fourier transform to convert data into frequency space.

16. Apparatus according to claim 1, wherein the data processor is configured to average the first series of intensity values resulting from measurement operations on a number of adjacent regions of the first sample surface area to provide the first intensity data.

17. Apparatus according to claim 1, wherein the data processor is configured to average the second series of intensity values resulting from measurement operations on a number of regions of the second sample surface area to provide the second intensity data.

18. Apparatus according to claim 1, wherein the frequency transform ratio determiner is configured to adjust the first and second series of intensity vales to position a maximum or minimum intensity value at or close to zero before frequency transformation.

19. Apparatus according to claim 1, configured to carry out measurement operations on plural surface areas of a sample having a layer structure.

20. Apparatus according to claim 1, further comprising a broadband light source.

21. Data processing apparatus for processing series of intensity values provided by a coherence scanning interferometer, the data processing apparatus being configured to receive a first series of intensity values resulting from a measurement operation on a first sample surface area having a layer structure and a second series of intensity values resulting from a measurement operation on a characterised second sample surface area and the data processor comprising:

a frequency transform ratio determiner configured to determine a ratio between frequency transformed first intensity data and frequency transformed second intensity data; and

a data fitter configured to fit variable model parameters related to characteristics of a layer structure of a layer structure model to the determined ratio to obtain for the model parameters values representing the characteristics of the sample layer structure.

22. Data processing apparatus according to claim 21, wherein the frequency transform ratio determiner is configured to determine the ratio by dividing one of the transformed first and second intensity data by the other of the transformed first and second intensity data.

23. A method of determining information relating to a sample layer structure, the method comprising the steps of:

carrying out respective measurement operations on a first sample surface area having a layer structure and a characterised second sample surface area -by, in each measurement operation, directing light along a sample path towards a region of the sample surface and along a reference path towards a reference surface such that light reflected by the region of the sample surface and light reflected by the reference surface interfere and causing movement of at least one of the sample and the reference surface so as to cause relative movement therebetween along a measurement scan path between the sample and the reference surface while a sensing device senses light intensity representing interference fringes produced by the sample surface region at intervals during the relative movement to provide first intensity data comprising a first series of intensity values resulting from a measurement operation on the first sample surface area and second intensity data comprising a second series of intensity values resulting from a measurement operation on the second sample surface area;

frequency transforming the first intensity data to produce frequency transformed first intensity data, frequency transforming the second intensity data to produce frequency transformed second intensity data and determining a ratio between the frequency transformed first intensity data and the frequency transformed second intensity data to form a frequency transform ratio; and

fitting a layer structure model having variable model parameters related to the layer thicknesses and refractive indices of the layers of a layer structure to the determined ratio by adjusting the model parameters, thereby obtaining for the model parameters values representing the layer thicknesses and refractive indices of the layers of the sample layer structure.

24. A method according to claim 23, wherein the ratio determining step determines the frequency transform ratio by dividing one of the first and second frequency transformed data by the other of the first and second frequency transformed data.

25. A method according to claim 23, wherein the ratio determining step determines the frequency transform ratio by dividing one of the first and second frequency transformed data by the other of the first and second frequency transformed data and multiplying that ratio by a field reflectance term.

26. A method according to claim 23, wherein the ratio determining step determines the frequency transform ratio by dividing one of the first and second frequency transformed data by the other of the first and second frequency transformed data and by multiplying that ratio by a field reflectance term:

${\left(\frac{1-n_{\mathrm{base}}<br><br>\left(v\right)}{1+n_{\mathrm{base}}<br><br>\left(v\right)}\right)}^{\mathrm{†<br><br>}}$

where n_base (v) is the refractive index at frequency v of the second sample surface area and †

indicates either the ratio or its complex conjugate.

27. A method according to claim 23, wherein the ratio determining step determines:

$\mathrm{HCF}<br><br>\left(v\right)=\left(\frac{1-n_{\mathrm{base}}<br><br>\left(v\right)}{1+n_{\mathrm{base}}<br><br>\left(v\right)}\right)<br><br>\frac{{{\mathrm{ℱ<br><br>}}_{\mathrm{thin}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{\mathrm{SB}<br><br><br><br>\mathrm{†<br><br>}}}{{{\mathrm{ℱ<br><br>}}_{\mathrm{base}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{\mathrm{SB}<br><br><br><br>\mathrm{†<br><br>}}}$

where †

indicates either the ratio or its complex conjugated, where n_base(v) is the refractive index at frequency v of the second sample surface area, and where

$\frac{{F_{\mathrm{thin}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{{\mathrm{SB}}^{\mathrm{†<br><br>}}}}{{F_{\mathrm{base}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{{\mathrm{SB}}^{\mathrm{†<br><br>}}}}$

is the ratio between the frequency transformed first intensity data and the frequency transformed second intensity data.

28. A method according to claim 23, wherein the ratio determining step determines the frequency transfer ratio:

$\begin{array}{c}\mathrm{HCF}<br><br>\left(v\right)\equiv <br><br><br><br>a_{\mathrm{HCF}}<br><br>\left(v\right)<br><br>{\mathrm{e<br><br>}}^{{\mathrm{i<br><br>\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v\right)}\\ =<br><br>\frac{1}{2}<br><br>{\int <br><br>}_0^{\mathrm{\pi <br><br>}/2}<br><br>\left(\begin{array}{c}\frac{1<br><br>-<br><br>{\mathrm{\eta <br><br>}}_{<br><br>\mathrm{base}}^{<br><br>p}<br><br>\left(v,<br><br>\mathrm{\theta <br><br>}\right)<br><br><br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}{<br><br>1<br><br>+<br><br>{\mathrm{\eta <br><br>}}_{<br><br>\mathrm{base}}^{<br><br>p}<br><br>\left(v,<br><br>\mathrm{\theta <br><br>}\right)<br><br><br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}+\\ \frac{1<br><br>-<br><br>{\mathrm{\eta <br><br>}}_{<br><br>\mathrm{base}}^{<br><br>p}<br><br><br><br>\left(v,<br><br>\mathrm{\theta <br><br>}\right)<br><br><br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}{<br><br>1<br><br>+<br><br>{\mathrm{\eta <br><br>}}_{<br><br>\mathrm{base}}^{<br><br>p}<br><br><br><br>\left(v,<br><br>\mathrm{\theta <br><br>}\right)<br><br><br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}\end{array}\right)<br><br><br><br>w<br><br>\left(\mathrm{\theta <br><br>}\right)<br><br>d<br><br>\mathrm{\theta <br><br>}<br><br>\frac{{{\mathrm{ℱ<br><br>}}_{\mathrm{thin}}<br><br>\left(I<br><br>\left(z_i\right)\right)}_{\mathrm{SB}<br><br><br><br>\mathrm{†<br><br>}}}{{{\mathrm{ℱ<br><br>}}_{\mathrm{base}}<br><br>\left(I<br><br>\left(z_i\right)\right)}_{\mathrm{SB}<br><br><br><br>\mathrm{†<br><br>}}}\\ \approx <br><br><br><br>\stackrel{\_}{r<br><br>\left(v\right)<br><br>{\mathrm{e<br><br>}}^{-i<br><br><br><br>\mathrm{\phi <br><br>}<br><br>\left(v\right)}}<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>4\pi <br><br>}<br><br><br><br>v<br><br><br><br>\mathrm{\Delta <br><br>}<br><br><br><br>z_{\mathrm{HCF}}<br><br>\cos <br><br><br><br>{\mathrm{\theta <br><br>}}_o}\\ \equiv <br><br><br><br>E<br><br>\left(v\right)\end{array}$

where

${\mathrm{\eta <br><br>}}_{\mathrm{base}}^s={\mathrm{\eta <br><br>}}_{\mathrm{base}}<br><br>\left(v\right)<br><br>\sqrt{1-{\sin }^2<br><br>{\mathrm{\theta <br><br>}}_0/{\mathrm{\eta <br><br>}}_{\mathrm{base}}<br><br>\left(v\right)}$ ${\mathrm{\eta <br><br>}}_{\mathrm{base}}^p=\frac{{\mathrm{\eta <br><br>}}_{\mathrm{base}}<br><br>\left(v\right)}{\sqrt{1-{\sin }^2<br><br>{\mathrm{\theta <br><br>}}_0/{\mathrm{\eta <br><br>}}_{\mathrm{base}}<br><br>\left(v\right)}}$

and where †

indicates the quantity or its complex conjugate, where n_base(v) is the refractive index at frequency v of the second sample surface area, and where

$\frac{{F_{\mathrm{thin}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{{\mathrm{SB}}^{\mathrm{†<br><br>}}}}{{F_{\mathrm{base}}<br><br>\left(I<br><br>\left(Z_k\right)\right)}_{{\mathrm{SB}}^{\mathrm{†<br><br>}}}}$

is the ratio between the frequency transformed first intensity data and the frequency transformed second intensity data, where r(v)e<sup>iφ

(v)</sup> r(v)e<sup>iφ

(v)</sup> is the resultant field reflectance at frequency v, θ

is the angle of incidence accepted by the numerical aperture, where Δ

z_HCF=Δ

z−

Δ

z_base where Δ

z is the path difference for the first sample surface area and the Δ

z_base is the path difference for the second sample surface area, where a_HCF (v) is the amplitude of the HCF function at frequency v, and e<sup>iφ

HCF(v)</sup> is the phase component of the HCF function at frequency v.

29. A method according to claim 23, wherein the layer structure model is a thin film layer structure optical admittance model.

30. A method according to claim 23, wherein the layer structure model is a thin film layer structure optical admittance model:

$E<br><br>\left(v\right)=r^{\mathrm{†<br><br>}}<br><br>\left(v\right)<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>4\pi <br><br>}<br><br><br><br>v<br><br><br><br>\mathrm{\Delta <br><br>}<br><br><br><br>z_{\mathrm{HCF}}}=\left(\frac{1-Y^{\mathrm{†<br><br>}}<br><br>\left(v\right)}{1+Y^{\mathrm{†<br><br>}}<br><br>\left(v\right)}\right)<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>4\pi <br><br>}<br><br><br><br>v<br><br><br><br>\mathrm{\Delta <br><br>}<br><br><br><br>z_{\mathrm{HCF}}}$

where †

indicates the quantity or its complex conjugate, E(v) is the electric field at frequency v, Δ

z_HCF=Δ

z−

Δ

z_base where Δ

z is the path length difference for the first sample surface area and the Δ

z_base is the path length difference for the second sample surface area where Y is the optical admittance, and where r(v) indicates the electric field reflectance at frequency v.

31. A method according to claim 23, wherein the layer structure model is a thin film layer structure optical admittance model:

$E<br><br>\left(v\right)\equiv <br><br>a_E<br><br>\left(v\right)<br><br>{\mathrm{e<br><br>}}^{{\mathrm{i<br><br>\phi <br><br>}}_E<br><br>\left(v\right)}=\frac{1}{2}<br><br>{\int <br><br>}_0^{\mathrm{\pi <br><br>}/2}<br><br>\left(\frac{1-Y_p^{\mathrm{†<br><br>}}<br><br>\left(v,\mathrm{\theta <br><br>}\right)<br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}{1+Y_p^{\mathrm{†<br><br>}}<br><br>\left(v,\mathrm{\theta <br><br>}\right)<br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}+\frac{1-Y_s^{\mathrm{†<br><br>}}<br><br>\left(v,\mathrm{\theta <br><br>}\right)/\cos <br><br><br><br>\mathrm{\theta <br><br>}}{1+Y_s^{\mathrm{†<br><br>}}<br><br>\left(v,\mathrm{\theta <br><br>}\right)/\cos <br><br><br><br>\mathrm{\theta <br><br>}}\right)<br><br>{\mathrm{e<br><br>}}^{-\mathrm{i<br><br>4\pi <br><br>}<br><br><br><br>v<br><br><br><br>\mathrm{\Delta <br><br>}<br><br><br><br>z_{\mathrm{HCF}}<br><br>\cos <br><br><br><br>\mathrm{\theta <br><br>}}<br><br>w<br><br>\left(\mathrm{\theta <br><br>}\right)<br><br><br><br>d<br><br>\mathrm{\theta <br><br>}$

where †

indicates the quantity or its complex conjugate, where θ

is the angle of incidence accepted by the numerical aperture, where Y_p and Y_s indicate, respectively, the p and s polarisations of optical admittance, where E(v) is the electric field at frequency v, where Δ

z_HCF=Δ

z−

Δ

z_base where Δ

z is the path difference for the first sample surface area and the Δ

z_base is the path difference for the second sample surface area, where a_E(v_j) is the amplitude of the electric field at frequency v_j, and e<sup>iφ

E(v)</sup> is the phase component of the electric field at frequency v.

32. A method according to claim 23, wherein the data fitting step uses a conjugate gradient or simulated annealing fitting procedure to fit the model parameters to the ratio.

33. A method according to claim 23, wherein the data fitting step uses the following merit function:

$\mathrm{\varepsilon <br><br>}=\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)<br><br>\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)<br><br>\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_E<br><br>\left(v_j\right)\right)}^2+{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)<br><br>\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)<br><br>\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_E<br><br>\left(v_j\right)\right)}^2$

or the merit function;

$\mathrm{\varepsilon <br><br>}=\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)<br><br>\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)<br><br>\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_E<br><br>\left(v_j\right)\right)}^2+\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)<br><br>\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)<br><br>\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_E<br><br>\left(v_j\right)\right)}^2+\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)\right)}^2$

where a_HCF (v_j) is the amplitude of the HCF function at frequency v_j, a_E(v_j) is the amplitude of the electric field at frequency v_j, e<sup>iφ

HCF(vj)</sup> is the phase component of the HCF function at frequency v_j, where e<sup>iφ

E(vj)</sup> is the phase component of the electric field at frequency v_j, and where e^iφ

=cos φ

+i sin φ

.

34. A method according to claim 23, wherein the data fitting step uses the following merit function:

$\mathrm{\varepsilon <br><br>}=\underset{j=1}{\overset{J}{\sum <br><br>}}<br><br>{\left(a_{\mathrm{HCF}}<br><br>\left(v_j\right)-a_E<br><br>\left(v_j\right)\right)}^2$

where a_HCF (v_j) is the amplitude of the HCF function at frequency v_j and a_E(v_j) is the amplitude of the electric field at frequency v_j.

35. A method according to claim 23, wherein the frequency transform ratio determining step determines the frequency ratio such that it is equivalent to a term having an amplitude component, a phase component and a helical phase component.

36. A method according to claim 23, wherein the frequency transform ratio determining step uses a Fourier transform to convert data into frequency space.

37. A method according to claim 23, wherein the first series of intensity values resulting from measurement operations on a number of regions of the first sample surface area are averaged to provide the first intensity data.

38. A method according to claim 23, wherein the second series of intensity values resulting from measurement operations on a number of regions of the second sample surface area are averaged to provide the second intensity data.

39. A method according to claim 23, further comprising adjusting the first and second series of intensity values to position a maximum or minimum intensity value at or close to zero before frequency transformation.

40. A method according to claim 23, comprising carrying out measurement operations on plural surface areas of a sample having a layer structure.

41. A method according to claim 23, wherein the first and second sample areas are sample areas of the same sample.

42. A method according to claim 23, wherein the first and second sample areas are sample areas of different samples.

43. A method according to claim 23, wherein the light used is provided by a broadband light source.

47. A method according to claim 23, wherein the second sample area does not carry a layer structure and is characterised by having a defined dispersive refractive index.

48. A method according to claim 23, wherein the second sample area carries a layer structure and is characterised by having a defined dispersive admittance.

49. A method of manufacturing a thin film product, which method comprises the steps of:

providing a thin film design for the thin film product;

depositing material onto a substrate in accordance with the thin film design to form a thin film product comprising the substrate carrying a thin film structure; and

determining the thin film structure of the thin film product by carrying out a method in accordance with claim 23.

50. A method according to claim 49, further comprising controlling at least one of the providing a design step and the depositing steps in accordance with the thin film structure determined in the determining step to modify the thin film structure of the thin film product.

51. A storage medium carrying program instructions for programming processing means to carry out a method in accordance with claim 23.

53. A computer programmed to perform the steps of the method of claim 23.

44. A method of processing series of intensity values provided by a coherence scanning interferometer, the method comprising the steps of receiving first intensity data comprising a first series of intensity values resulting from a measurement operation on a first sample surface area having a layer structure and second intensity data comprising a second series of intensity values resulting from a measurement operation on a characterised second sample surface area and the data processing comprising:

frequency transforming the first intensity data to produce frequency transformed first intensity data;

frequency transforming the second intensity data to produce frequency transformed second intensity data;

determining a ratio between the frequency transformed first intensity data and the frequency transformed second intensity data; and

fitting variable model parameters related to characteristics of a layer structure of a layer structure model to the determined ratio to obtain for the model parameters values representing the characteristics of the sample layer structure.

45. A method according to claim 44, wherein the determining a ratio step comprises dividing one of the transformed first and second intensity data by the other of the transformed first and second intensity data.

52. A storage medium carrying program instructions for programming processing means to carry out a method in accordance with claim 44.

54. A computer programmed to perform the steps of the method of claim 44.

46. Apparatus for determining information relating to a sample layer structure, the apparatus comprising:

light directing means for directing light along a sample path towards a region of a surface of a sample and along a reference path towards a reference surface such that light reflected by the region of the sample surface and light reflected by the reference surface interfere;

moving means for effecting movement of at least one of the sample and the reference surface so as to effect relative movement therebetween along a measurement scan path between the sample and the reference surface;

sensing means for sensing light representing the interference fringes produced by a sample surface region during relative movement along the measurement scan path;

control means for carrying out a measurement operation by causing the moving means to effect relative movement while the sensing means senses light intensity at intervals to provide a series of intensity values representing interference fringes produced by a region of a sample surface during the relative movement; and

data processing means for receiving and processing first intensity data comprising a first series of intensity values resulting from a measurement operation on a first sample surface area having a layer structure and second intensity data comprising a second series of intensity values resulting from a measurement operation on a characterised second sample surface area, the data processing means comprising;

frequency transform ratio determining means for determining a ratio between frequency transformed first intensity data and frequency transformed second intensity data; and

data fitting means for fitting a layer structure model having variable model parameters related to the layer thicknesses and refractive indices of the layers of a layer structure to the ratio determined by the ratio determining means by adjusting the model parameters, thereby obtaining for the model parameters values representing the layer thicknesses and refractive indices of the layers of the sample layer structure.