Thin film interference filter and bootstrap method for interference filter thin film deposition process control
A thin film interference filter system includes a plurality of stacked films having a determined reflectance; a modeled monitor curve; and a topmost layer configured to exhibit a wavelength corresponding to one of the determined reflectance or the modeled monitor curve. The topmost layer is placed on the plurality of stacked films and can be a low-index film such as silica or a high index film such as niobia.
1. A method for forming a thin film interference filter comprising:
measuring a reflectance of a stack of a plurality of films;
modeling a monitor curve at a modeled monitor wavelength for a topmost layer to be deposited on the stack of the plurality of films;
depositing the topmost layer on the stack of the plurality of films; and
recording a plurality of monitor curves during the deposition, each monitor curve being recorded for a different monitor wavelength of the topmost layer; wherein
the topmost layer is a high index of refraction layer that exhibits a wavelength that is determined according to the characteristics of either the modeled monitor curve or one of the recorded monitor curves; and
determining an anticipated standard deviation in φκ for each different monitor wavelength in the high-index of refraction layer and discarding any monitor wavelengths with σ greater than 0.9 degrees.
2. The method as in claim 1 , further comprising the step of computing expected error in δ for the monitor wavelengths with σ less than 0.9 degrees at a target thickness of the high index of refraction layer.
3. The method according to claim 1 , the method further comprising
determining phase angle φκ at the modeled monitor wavelength from |r k ′| and R k using a first equation expressed as:
cos
(
±
ϕ
k
)
=
r
k
′
2
(
1
+
R
k
r
2
2
)
-
r
2
2
-
R
k
2
r
2
R
k
(
1
-
r
k
′
2
)
;
and
estimating r k ′ using a second equation and
r
k
′
=
r
k
-
r
2
1
-
r
2
r
k
.
4. The method according to claim 1 , wherein the step of measuring the reflectance of the stack of the plurality of films comprises measuring the intensity reflectance of the stack, the method further comprising
determining from the measurement of intensity reflectance at the topmost interface a phase angle φ at an interface k according to an equation expressed as:
cos
(
ϕ
k
)
=
(
A
(
1
+
r
2
2
)
sin
(
δ
)
±
B
cos
(
δ
)
C
)
A
=
R
f
+
r
2
4
(
R
f
-
R
k
)
-
R
k
+
2
r
2
2
(
(
1
-
R
f
)
(
1
+
R
k
)
cos
(
2
δ
)
-
(
1
-
R
f
R
k
)
)
B
=
D
(
1
+
r
2
12
)
+
F
(
r
2
2
+
r
2
10
)
+
G
(
r
2
4
+
r
2
8
)
+
H
r
2
6
C
=
sin
(
δ
)
(
4
r
2
(
1
-
R
f
)
R
k
1
/
2
(
2
r
2
2
cos
(
2
δ
)
-
1
-
r
2
4
)
)
D
=
-
(
R
f
-
R
k
)
2
F
=
2
(
R
k
(
2
+
R
k
)
+
R
f
2
(
1
+
2
R
k
)
+
2
R
f
(
1
-
5
R
k
+
R
k
2
)
-
2
(
1
-
R
f
)
(
1
-
R
k
)
(
R
f
+
R
k
)
cos
(
2
δ
)
)
G
=
-
6
-
4
R
f
-
5
R
f
2
-
4
R
k
+
38
R
f
R
k
-
4
R
f
2
R
k
-
5
R
k
2
-
4
R
f
R
k
2
-
6
R
f
2
R
k
2
+
8
(
1
-
R
f
2
)
(
1
-
R
k
2
)
cos
(
2
δ
)
-
2
(
1
-
R
f
)
2
(
1
-
R
k
)
2
cos
(
4
δ
)
H
=
4
(
3
+
2
R
f
2
-
10
R
f
R
k
+
2
R
k
2
+
3
R
f
2
R
k
2
-
2
(
1
-
R
f
)
(
1
-
R
k
)
(
2
+
R
f
+
R
k
+
2
R
f
R
k
)
cos
(
2
δ
)
+
(
1
-
R
f
)
2
(
1
-
R
k
)
2
cos
(
4
δ
)
)
.
5. The method as in claim 4 , further comprising the step of validating two resultant solutions according to the expression:
R
f
=
2
r
2
2
+
R
k
(
1
+
r
2
4
)
+
2
r
2
Q
1
+
r
2
4
+
2
r
2
2
R
k
+
2
r
2
Q
Q
=
r
2
2
R
k
1
/
2
cos
(
2
δ
+
ϕ
k
)
+
R
k
1
/
2
cos
(
2
δ
-
ϕ
k
)
-
r
2
(
1
+
R
k
)
cos
(
2
δ
)
-
(
1
+
r
2
2
)
R
k
1
/
2
cos
(
ϕ
k
)
.
6. The method as in claim 4 , further comprising the step of averaging calculated and modeled reflectance and phase values to obtain a new value to be used in all future modeling at a given wavelength.
7. The method of claim 1 , wherein measuring a reflectance includes measuring the transmittance of a stack of a plurality of films and determining the reflectance from the transmittance.
8. The method of claim 1 , wherein the high index of refraction material layer is a niobia layer.
9. A method for forming a thin film interference filter comprising:
measuring a reflectance of a stack of a plurality of films;
modeling a monitor curve at a modeled monitor wavelength for a topmost layer to be deposited on the stack of the plurality of films;
depositing the topmost layer on the stack of the plurality of films;
recording a plurality of monitor curves during the deposition, each monitor curve being recorded for a different monitor wavelength of the topmost layer, wherein the topmost layer exhibits a wavelength that is determined according to the characteristics of either the modeled monitor curve or one of the recorded monitor curves; and
computing two possible values of phase angle for each monitor wavelength other than the modeled monitor wavelength.
10. The method of claim 9 , wherein measuring a reflectance includes measuring the transmittance of a stack of a plurality of films and determining the reflectance from the transmittance.
11. A method for forming a thin film interference filter comprising:
measuring a reflectance of a stack of a plurality of films;
modeling a monitor curve at a modeled monitor wavelength for a topmost layer to be deposited on the stack of the plurality of films;
depositing the topmost layer on the stack of the plurality of films;
recording a plurality of monitor curves during the deposition, each monitor curve being recorded for a different monitor wavelength of the topmost layer, wherein the topmost layer exhibits a wavelength that is determined according to the characteristics of either the modeled monitor curve or one of the recorded monitor curves; and
using information extracted from the model for r k at each monitor wavelength and the computed best value of δ, and computing an estimated standard deviation of phase at all monitor wavelengths except the modeled monitor wavelength.
12. The method as in claim 11 , further comprising the steps of using the computed phase closest to the model phase for r k at each monitor wavelength, measured R f and R k values and the computed best value of δ, and computing the estimated standard deviation of phase at all monitor wavelengths for which the magnitude of r k was estimated other than the modeled monitor.
13. The method as in claim 11 , further comprising the steps of determining if a phase error estimate is less than about 1.3 degrees and averaging calculated and modeled reflectance and phase values to obtain a new value for use in subsequent modeling at that wavelength.
14. The method of claim 11 , wherein measuring a reflectance includes measuring the transmittance of a stack of a plurality of films and determining the reflectance from the transmittance.
15. A method for forming a thin film interference filter comprising:
measuring a reflectance of a stack of a plurality of films;
modeling a monitor curve at a modeled monitor wavelength for a topmost layer to be deposited on the stack of the plurality of films;
depositing the topmost layer on the stack of the plurality of films; and
recording a plurality of monitor curves during the deposition, each monitor curve being recorded for a different monitor wavelength of the topmost layer, wherein the topmost layer exhibits a wavelength that is determined according to the characteristics of either the modeled monitor curve or one of the recorded monitor curves, the top layer having an intensity of reflectance of greater than 9%; and
replacing the magnitude of the amplitude reflectance at each monitor wavelength with √{square root over (R k )}.
16. The method of claim 15 , wherein measuring a reflectance includes measuring the transmittance of a stack of a plurality of films and determining the reflectance from the transmittance.
17. The method as in claim 15 , further comprising the step of averaging calculated and modeled reflectance and phase values to obtain a new value for use in subsequent modeling at that wavelength.
18. The method of claim 15 , wherein the topmost layer is a silica layer.
19. A method for forming a thin film interference filter comprising:
measuring a reflectance of a stack of a plurality of films;
modeling a monitor curve at a modeled monitor wavelength for a topmost layer to be deposited on the stack of the plurality of films;
depositing the topmost layer on the stack of the plurality of films; and
recording a plurality of monitor curves during the deposition, each monitor curve being recorded for a different monitor wavelength of the topmost layer;
wherein the topmost layer exhibits a reflectance maximum for at least one of the monitor curves being recorded; and
obtaining a phase for the reflectance using the measured reflectance and the reflectance maximum,
wherein a standard deviation for the phase is found for each of the monitor curves having a reflectance maximum and a reflectance, and a monitor curve is selected such that the standard deviation for the phase is less than a pre-selected value.
20. The method of claim 19 wherein depositing the topmost layer on the stack proceeds according to a pure model deposition if no monitor curve is found having a standard deviation for the phase less than the pre-selected value.
21. The method of claim 20 wherein the topmost layer is a niobia layer and the pre-selected value is 0.9 degrees.
22. The method of claim 20 wherein the topmost layer is a silica layer and the pre-selected value is 2.4 degrees.
23. The method of claim 19 wherein a standard deviation for the reflectance is found for each of the monitor curves having a reflectance maximum; and the monitor curve having the lowest standard deviation for the reflectance is selected to proceed with the thin film layer deposition.
24. The method of claim 23 wherein the thin film deposition proceeds according to a pure model deposition if the standard deviation for the reflectance is larger than or equal to the reflectance of an infinite slab of the material being deposited.
25. The method of claim 24 wherein the material being deposited is silica.
26. The method of claim 24 wherein the material being deposited is niobia.
27. The method of claim 19 , wherein measuring a reflectance includes measuring the transmittance of a stack of a plurality of films and determining the reflectance from the transmittance.