Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
  • G01B11/00—Measuring arrangements characterised by the use of optical techniques
  • G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
  • G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
  • G01B11/0616—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating
  • G01B11/0683—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating measurement during deposition or removal of the layer
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
  • G01B11/00—Measuring arrangements characterised by the use of optical techniques
  • G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
  • G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
  • G01B11/0616—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating
  • G01B11/0625—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating with measurement of absorption or reflection

Definitions

• the present invention relates to thin film optical devices. More particularly, the invention relates to complex interference filters.
• optical interference filters can be manufactured using thin film deposition processes. These optical interference filters are used for multivariate optical computing, multiple-band-pass, and the like and can.' exhibit complex optical spectra defined over a range of wavelengths. These filters are typically constructed by depositing alternating layers of transparent materials where one layer possesses a much larger refractive index relative to the other layer. Theoretically, the proper choice of composition, thickness and quantity of layers could result in a device with any desired transmission spectrum. [0005] Among the simplest devices is the single cavity bandpass filter; i.e., the thin- film form of an etalon. This device consists of three sets of layers.
• the first stack is a dielectric mirror
• a next thicker layer forms a spacer
• a second stack forms another dielectric mirror.
• the mirror stacks are typically fabricated by depositing alternating transparent materials that have an optical thickness that is one quarter of the optical wavelength of light.
• each layer must possess a precise and specific physical thickness and refractive index. Any nonuniformity in the deposition of the layers can affect the spectral placement and transmission or reflection characteristics of the device.
• a design that requires very tight manufacturing tolerances over large substrate areas could result in the costly rejection of many devices.
• Another electrically actuated thin film optical filter uses a series of crossed polarizers and liquid crystalline layers that allow electrical controls to vary the amount of polarization rotation in the liquid by applying an electric field in such a way that some wavelengths are selectively transmitted.
• these electrically actuated thin film optical filters have the characteristic that the light must be polarized and that the frequencies of light not passed are absorbed, not reflected.
• Another electrically actuated thin film optical device is the tunable liquid crystal etalon optical filter.
• the tunable liquid crystal etalon optical filter uses a liquid crystal between two dielectric mirrors.
• the common cavity filter such as the etalon optical filter
• the common cavity filter is an optical filter with one or more spacer layers that are deposited in the stack and define the wavelength of the rejection and pass bands.
• the optical thickness of the film defines the placement of the passband.
• U.S. Pat. No. 5,710,655, issued January 20, 1998 to Rumbaugh et al discloses a cavity thickness compensated etalon filter.
• an electric field is applied to the liquid crystal that changes the optical length between the two mirrors so as to change the passband of the etalon.
• Still another tunable optical filter device tunes the passband by using piezoelectric elements to mechanically change the physical spacing between mirrors of an etalon filter.
• Bulk dielectrics are made by subtractive methods like polishing from a larger piece; whereas thin film layer are made by additive methods like vapor or liquid phase deposition.
• a bulk optical dielectric, e.g., greater than ten microns, disposed between metal or dielectric mirrors suffers from excessive manufacturing tolerances and costs.
• the bulk material provides unpredictable, imprecise, irregular, or otherwise undesirable passbands.
• These electrical and mechanical optical filters disadvantageously do not provide precise rejection bands and passbands that are . repeatably manufactured.
• modeling of interference filters can be conducted during on-line fabrication with in-situ optical spectroscopy of the filter during deposition.
• the current state of the art for on-line correction of the deposition involves fitting the observed spectra to a multilayer model composed of "ideal" films based on a model for each film.
• the resulting model spectra are approximations of the actual spectra.
• reflectance As an example: the measured reflectance of a stack of films can be approximately matched to a theoretical reflectance spectrum by modeling. Layers remaining to be deposited can then be adjusted to compensate for errors in the film stack already deposited, provided the film stack has been accurately modeled.
• films vary in ways that cannot be readily modelled using any fixed or simple physical model. Heterogeneities in the films that cannot be predicted or compensated by this method cause the observed spectra to deviate more and more from the model. This makes continued automatic deposition very difficult; complex film stacks are therefore very operator-intensive and have a high failure rate. To improve efficiency in fabrication, laboratories that fabricate these stacks strive to make their films as perfectly as possible so the models are as accurate as possible.
• the present invention is directed to a layered, thin film interference filter and related bootstrap methods.
• a bootstrap method permits a user to focus on a single layer of a film stack as the layer is deposited to obtain an estimate of the properties of the stack.
• the single layer model is a guideline and not a basis for compensating errors, only the most-recently-deposited layer - and not the already-deposited film stack - need be modeled according to an aspect of the present invention. Thus, the user can neglect deviations of the stack from ideality for all other layers.
• the single-layer model can then be fit exactly to the observed spectra of the film stack at each stage of deposition to allow accurate updating of the remaining film stack for continued deposition.
• a method using experimental measurements to determine reflectance phase and complex reflectance for arbitrary thin film stacks includes the steps of determining reflectance of a stack of a plurality of films before depositing a topmost layer; considering a modeled monitor curve for a wavelength of a high-index layer; and discarding a plurality of monitor curves without maxima in their reflectance during the topmost layer deposition.
• the topmost layer can be a niobia layer.
• the exemplary method can also include the steps of determining an
• aspect is computing expected error in ⁇ for wavelengths with ⁇ less than 0.9 degrees
• a further step according to this method is to proceed with a full model deposition of the niobia layer.
• another step according to the exemplary method is to use only the modeled monitor curve during the topmost layer deposition.
• the method according to this aspect of the invention can further include the step of computing two possible values of phase angle for each wavelength other than the monitor wavelength. [0020] Additional steps according to the exemplary method include using
• the method may further include the steps of using the computed phase
• Further steps according to the exemplary method include 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.
• the topmost layer can be a silica film. Accordingly, the method can include the step of replacing the
• the method can also include the step of determining if a phase error estimate is less than about 1.3 degrees when the magnitude of the amplitude reflectance at each
• wavelength has been replaced with . ⁇ R ⁇ and averaging calculated and modeled reflectance and phase values to obtain a new value for use in subsequent modeling at that wavelength.
• a method for correcting thin film stack calculations for accurate deposition of complex optical filters can include the steps of
• Still another aspect of the invention includes a method for automated
• deposition of complex optical interference filters including the steps of determining
• A R f +r 2 4 (R f -R k )-R k +2r 2 2 ((l- R f ⁇ i + R k )cos(2 ⁇ ) - (l-R f R k )) B ⁇ D(l + ri 2 ) + F(r 2 2 + ri 0 >G(r 2 4 + rI> Hr
• a process control for a deposition system is bootstrapped by detaching the deposition system from all but the topmost
• the method can further include the step of validating two resultant solutions according to the expression:
• the method can also include 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.
• 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 being disposed on the plurality of stacked films.
• the topmost layer according to this aspect can be a low-index film such as silica or a high index film such as niobia.
• FIGURE 1 is a schematic, cross sectional view of a stack of films
• FIGURE 2 is a schematic, cross sectional view of a stack of films similar
• FIGURE 1 showing an internal interface in the stack of films according to another
• FIGURE 3 is a schematic, cross sectional view of a stack of films
• FIGURE 4 is a representation of regions of permissible values of Rk and
• Rmax particularly showing lowest values of ⁇ k for silica according to an aspect of the invention
• FIGURE 5 is similar to FIGURE 4 but for niobia according to another
• FIGURE 6 is a histogram for silica as in FIGURE 4;
• FIGURE 7 is a histogram for niobia as in FIGURE 5;
• FIGURE 8 is a perspective plot showing an error logarithm versus Rmax
• FIGURE 9 is a histogram of FIGURE 8 data.
• FIGURE 1 shows a thin film interference filter 10, which broadly includes a substrate 12 upon which a stack of films 14A-X is deposited (where x represents a theoretically infinite number of film layers). As shown, the last (alternatively, final, top or topmost) deposited film is designated by the alphanumeral 14A while previously deposited or lower level films are designated 14B-X. An incoming ray 18 is shown in FIGURE 1 being reflected at an interface 16 (also referred to herein as top or top surface and when mathematically referenced as k). The reflected ray is designated by the number 20.
• reflectance of the top surface 16 is obtained using a matrix calculation that is in turn built from the characteristic matrices of each of the preceding films 14A-X. As shown in FIGURE 1, a computed value of an electric
• the complex reflectance of a stack of films is computed using the admittances of the incident medium (often air), and the first interface of the stack. For s and p polarization, this reflectance is:
• ⁇ is a complex
• the problematic part of the calculation is how to express the admittance of the initial interface.
• the matrix calculation proceeds by relating the admittance of the initial interface to that of the second interface, the admittance of the second to the third, etcetera, through a series of 2X2 matrices, until the calculation is related to the final interface.
• the admittance ratio of magnetic to electric fields
• the admittance of the exit medium which is simple to compute because there is only a single ray (the transmitted ray), rather than rays propagating in two different directions.
• the superscript (3) indicates the exit medium.
• the admittance of the exit medium for s-polarized light is given by
• ⁇ film is the phase thickness of the film, given by
• dfiim is the physical thickness of the film and ⁇ o is the free-space wavelength
• the matrices describing the film are used as "transfer" matrices. This permits propagation of the calculation of the admittance of the initial interface down through a stack of films. The downward propagation is stopped at the substrate because, once there are no longer rays propagating in both directions, a simple form (the admittance of the exit medium) can be written.
• the matrices allow an impossible calculation to be related to a simplified calculation via a 2X2 matrix.
• Equation 6 ⁇ ⁇ in Equation 6 is the admittance of the final interface.
• the final interface is always chosen because a
• a Bootstrap Method according to an aspect of the invention depends on finding experimental values for the complex reflectance at a given interface in a film stack. Thus, an initial matter of using the amplitude reflectance of a film surface alone to complete the matrix calculation for the films above the film surface in question will be described.
• Equation 13 If the amplitude reflectivity for an interface k (which can be any interface, including the final interface) is known, an equivalent expression to Equation 13 can be obtained in terms of the admittance of that interface in lieu of carrying the
• Step 1 Determine the reflectance of an existing film stack prior to the deposition of a new layer.
• the reflectance of a film stack provides some information regarding the complex amplitude reflectance that can be used to refine the model of the reflectance, and that is totally independent of any modeling. If one does not measure reflectance directly, it can be obtained by noting that transmission plus reflectance for an absorption-free thin film stack is unity.
• the relationship between the amplitude and intensity reflectance is that the intensity reflectance is the absolute square of the amplitude reflectance. Considering the amplitude reflectance for a moment, it will be clear that it can be expressed in standard Cartesian coordinates on a complex plane, or in complex polar coordinates:
• ⁇ k tan- ⁇ [0071] If the amplitude reflectance is expressed in polar coordinates, it is the magnitude of the amplitude reflectance that is provided by a measure of intensity
• Equation 3 The standard deviation of the magnitude of the amplitude reflectance is given by Equation 3 :
• Rk is a minimum (the amplitude reflection is on the real
• Step 2 Replace the magnitude of the amplitude reflectance at each wavelength with - ⁇ R ⁇ whenever measuring a freshly completed silica film with an intensity reflectance greater than 9% or a low-index film with an intensity reflectance greater than the limiting value of the high-index material. [0075] While the intensity measurement provides useful information (most of the
• present description relates to how to obtain these phase angles in at least some
• the magnitude of r ⁇ at the base of a niobia layer can be
• phase of the amplitude reflectance is more difficult to ascertain, but there are two general approaches. The first is to consider what values of phase are consistent with the final value of reflectance after the next layer is added. To use this information, the optical thickness of the next layer must be known. This is sometimes a redundant calculation since the estimation of optical thickness is usually based on an understanding of the initial reflectance. This is, in fact, a weakness of the usual matrix modeling approach - the calculation is somewhat redundant. [0077] Without additional information, redundant calculation would normally be the only option. However, monitor curves are usually recorded during deposition, and those curves contain all the information necessary to compute the phase, ⁇ , without
• Step 3 Consider the modeled monitor curve for each wavelength of a niobia (high-index) layer. Discard any monitor curves without maxima in their reflectance during the niobia layer deposition. If none meet this criterion, deposit the layer using a pure model approach. [0078] Based on Equation 14 above, the maxima and minima of a monitor curve can
• Equation 21 The maximum and minimum reflectance during the monitor curve are given by Equation 21 :
• R ma ⁇ or R m in can be used in the monitor curve to convey the
• This magnitude can be related to the reflectance as follows.
• the R max expression also has two solutions in principle but can be discarded because it provides nonphysical results.
• the second problem with the equation from R n U n is
• a maximum reflectance i.e., a minimum in the transmission monitor curve
• phase angle ⁇ k at the monitor wavelength can be determined from
• r£ can be computed using Equation 20 and a monitor curve can be
• phase at the monitor wavelength should have been obtained that is as correct as possible. It depends, of course, on accurately
• a full-spectrum monitor (acquiring
• Equation 25 depends, ultimately, on only two measurements: the measurement of the initial reflectance and the measurement of the maximum reflectance. For those wavelengths that exhibit a maximum reflectance during deposition, these can be evaluated quantitatively as possible monitor wavelengths. [0083] It can be shown that the anticipated standard deviation of the phase calculation can be written as:
• FIGURE 4 shows a representation of the regions of permissible values of
• Rmax represents possible values of Rmax
• Rk the left axis
• FIGRURES 4 and 5 illustrate, be less than the
• FIGURE 5 in dark yellow). Possible values of Rk can be evaluated for each value
• Equation 27 This is accomplished by dividing the phase thickness of the top
• Equation 24 that is less than 2.4 degrees. No values less than about 1.5 degrees
• the calculated phase error of possible monitor wavelengths will tend to be considerably better for niobia films than for silica. If a limit of 0.9 degrees phase error is placed on the monitors before this calculation is performed, only niobia will give possible monitor wavelengths, and 30% of all wavelengths (overall) will meet this criterion. On some layers, it is possible that no wavelengths will meet this criterion, while on others many may do so.
• Step 4 For the remaining possible monitor wavelengths in a niobia layer deposition, determine the anticipated standard deviation in ⁇ [ ⁇ . Discard any with ⁇ greater than 0.9 degrees (0.016 radians). If none remain, proceed with a pure model deposition. [0090] For low-index layers, bootstrapping is not recommended. For layers with
• curve wavelength can be used to determine what value of ⁇ is most accurate for the
• FIGURE 8 can also be rendered as a histogram as shown in
• FIGURE 9 The histogram in FIGURE 9 implies that the error in phase thickness is
• Step 5 Compute the expected error in ⁇ for the remaining
• wavelengths at the target thickness of the niobia layer If no wavelengths have an error less than 0.9 degrees, proceed with a full model deposition of the layer. If some do meet this criterion, select the lowest error in this category.
• This physical thickness and the modeled refractive index of the film can be used to calculate the thickness of the film.
• Step 6 Compute the value of ⁇ for all wavelengths based on the value calculated for the monitor wavelength.
• Equation 29 the exponential has been replaced with a trigonometric
• Equation 31 The resulting expression can be simplified as Equation 31 :
• G - 6 - 4R f - 5R 2 - - 4R k + 38R f R k - 4R ⁇ R k - 5R ⁇ - 4R f R ⁇ - 6R 2 ⁇ R 2 - +8(l -R f )(J - R k );os(2 ⁇ )- 2(1 - R f ) 2 (1 - R k ) 2 cos(4 ⁇ )
• Equation 32 can be used to solve for the phase angle. By doing so, the deposition system process control is effectively "bootstrapped” by detaching the system completely from everything that came before the last layer. Equation 32 provides four (4) solutions for the phase angle; two come from the +/- portion of the calculation; two more from the fact that cosine is an even function, so positive and negative angles both work equally well. However, only two of these solutions are
• Equation 31 for validity. Only two solutions should be left after this process is complete.
• Step 7 Compute the two possible values of phase angle for each wavelength other than the monitor wavelength.
• phase angle is dependent on three reflectivity measurements (R ma ⁇ > Rf
• Equation 32 While this works well for a hypothetical system with no noise, a real spectrometer exhibits errors in measurement of the intensity transmittance.
• Equation 32 Based on work already done, the analysis of Equation 32 is fairly straightforward for extending phase information to other wavelengths.
• the following expression can be constructed from it:
• Step 8 Using information extracted from the model for r ⁇ at each wavelength and the computed best value of ⁇ , compute the estimated standard deviation of phase at all wavelengths except the monitor.
• Step 9 Using the computed phase closest to the model phase for r ⁇ at
• Step 10 If the phase error estimate is less than 1.3 degrees AND the criterion of Step 2 is met, average the calculated and modeled reflectance and phase values to obtain a new value that will be used in all future modeling at that wavelength.

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