Nondestructive optical technique for simultaneously measuring optical constants and thickness of thin films

1. A system for simultaneously measuring optical constants (n, k) and thickness of a thin film formed on a substrate, comprising:

a first light source that emits light that is directed at an oblique angle toward the thin film;

a polarizer that disposed at the oblique angle between the first light source and the thin film;

a first detector disposed to detect light derived from the first light source that is reflected from the thin film that is disposed at an oblique angle that is complementary to the oblique angle that the light is incident upon the thin film;

an analyzer disposed at the complementary oblique angle between the first detector and the thin film;

a second light source that emits light that is incident at a normal angle upon the thin film;

a second detector disposed to detect light derived from the second light source that is reflected from the thin film; and

a computer coupled to outputs of the first and second detectors that implements an algorithm that simultaneously measures the optical constants (n, k) and the thickness of the thin film using multi-angle differential polarimetry by computing ratios of the change in ellipsometric parameters and reflectance of the thin film relative to the substrate.

2. The system recited in claim 1 wherein the thin film comprises a multilayer thin film.

3. The system recited in claim 1 wherein the computer further determines surface roughness of the thin film.

4. The system recited in claim 1 wherein the computer further determines the composition of the thin film.

5. The system recited in claim 1 wherein the computer further determines the energy band gap of the thin film.

6. The system recited in claim 1 wherein the algorithm implemented in the computer:

measures normal incident reflection spectra (R) of the thin film as a function of frequency;

measures ellipsometric parameters of the thin film at an oblique angle ρ as a function of frequency;

determines theoretical values of R and ρ (R s and ρ s ) for the substrate;

determines new normalized parameters, given by:

ξ

0

≡

R

-

R

s

R

s

,

ξ

1

≡

ρ

-

ρ

s

ρ

s

,

and

⁢

⁢

R

⁢

⁢

ξ

≡

ξ

0

ξ

1

;

models the unknown optical constants using a general dispersion formula that describes the dispersion in the optical constants (n, k) in the measured wavelength range; and

determines the thickness of the thin film and coefficients of the dispersion formula, comprising the optical constants of the unknown layers of the thin film.

7. The system recited in claim 1 further comprising a compensator that is disposed at the oblique angle between the first light source and the thin film.

8. The system recited in claim 7 wherein the compensator comprises a rotating compensator.

9. The system recited in claim 7 wherein the polarizer comprises a fixed polarizer and the analyzer comprises a rotating analyzer.

10. The system recited in claim 7 wherein the polarizer comprises a rotating polarizer and the analyzer comprises a fixed analyzer.

11. The system recited in claim 7 further comprising a controller coupled to the first and second light sources and the first and second detectors.

12. The system recited in claim 7 wherein the polarizer comprises a fixed polarizer, the analyzer comprises a fixed analyzer, and wherein the system further comprises a rotating compensator disposed at the oblique angle between the first light source and the thin film.

13. The system recited in claim 7 wherein the polarizer comprises a fixed polarizer, the analyzer comprises a fixed analyzer, and wherein the system further comprises an electrically controlled non-rotating compensator disposed at the oblique angle between the first light source and the thin film.

14. A method for simultaneously measuring optical constants (n, k) and thickness of a thin film disposed on a substrate, comprising the steps of:

measuring normal incident reflection spectra (R) of the thin film as a function of frequency;

measuring ellipsometric parameters of the thin film at an oblique angle ρ as a function of frequency;

determining theoretical values of R and ρ (R s and p s ) for the substrate;

determining new normalized parameters, given by:

ξ

0

≡

R

-

R

s

R

s

,

ξ

1

≡

ρ

-

ρ

s

ρ

s

,

and

⁢

⁢

R

⁢

⁢

ξ

≡

ξ

0

ξ

1

;

modeling the unknown optical constants using a general dispersion formula that describes the dispersion in the optical constants (n, k) in the measured wavelength range;

determining the thickness of the thin film and coefficients of the dispersion formula, comprising the optical constants of the unknown layers of the thin film; and

outputting the optical constants to a user, displaying the optical constants to a user, or storing the optical constants for later use by a user.

15. The method recited in claim 14 which further comprises a nonlinear global optimization algorithm that minimizes a merit function of measured and theoretical data.

16. The method recited in claim 15 wherein the merit function is defined by the equation:

Merit

⁢

⁢

Function

=

[

∑

j

=

1

n

⁢

[



Y

exp

j

-

Y

calculated

j



β

×

weight

j

]

]

1

β

,

where Y exp j and Y calculated j represent the measured and calculated (simulated) data of parameter j, and β=1, 2 for absolute deviation and least squares, respectively.

17. The method recited in claim 15 wherein each fitted parameter has its own merit function that is minimized that is defined by the equation:

(

Merit

⁢

⁢

Function

)

j

=

[



Y

target

j

-

Y

calculated

j



β

×

weight

j

]

1

β

.

where Y target j and Y calculated j represent the measured data and calculated (simulated) data of parameter j, and β=1, 2 for absolute deviation and least squares, respectively.