Structured substrates for optical surface profiling

Abstract

This disclosure provides methods and devices for the label-free detection of target molecules of interest. The principles of the disclosure are particularly applicable to the detection of biological molecules (e.g., DNA, RNA, and protein) using standard SiO.sub.2-based microarray technology.

Claims

1. A layered substrate for a direct reflectivity method for optically profiling the height of a substrate, the substrate comprising a base layer, at least one coating layer having a refractive index different from the refractive index of said base layer, wherein said base layer is Si and said one coating layer is SiO.sub.2, and wherein said coating layer has a thickness of between about 1 micron and about 20 microns, and a plurality of spatially distinct binding locations, wherein each of said binding locations comprises capture molecules bound to the topmost coating layer.

2. The layered substrate of claim 1, wherein said layered substrate is disposed within an optical detection apparatus that includes a tunable light source that provides an illumination beam tunable to varying wavelengths, the illumination beam being directed substantially perpendicular to an uppermost surface of the layered substrate and a photodetector array positioned to capture light reflected from the layered substrate.

3. The layered substrate of claim 1, wherein the refractive index of said at least one coating layer is between about 1.1 and about 1.7.

4. The layered substrate of claim 1, wherein the refractive index of said at least one coating layer is about 1.4.

5. The layered substrate of claim 1, wherein said substrate comprises at least two different coating layers.

6. The layered substrate of claim 1, wherein said substrate further comprises a plurality of reaction wells.

7. The layered substrate of claim 1, wherein each of said binding locations comprise a single type of capture molecule.

8. The layered substrate of claim 1, wherein said capture molecules are selected from the group consisting of DNA, RNA, and protein.

9. The layered substrate of claim 1, wherein said capture molecules are covalently bound to said topmost coating layer.

10. A layered substrate for a split beam interferometry method for optically profiling the height of a substrate, the substrate comprising: a base layer; at least one coating layer having a refractive index different from the refractive index of said base layer, wherein said base layer is Si and said one coating layer is SiO.sub.2, and wherein said coating layer has a thickness of about 270 nm; and a plurality of spatially distinct binding locations, wherein each of said binding locations comprises capture molecules bound to the topmost coating layer.

11. The layered substrate of claim 10, wherein a refractive index of said at least one coating layer is about 1.4.

12. The layered substrate of claim 10, wherein the coating layer comprises one selected from the group consisting of SiO.sub.2 and Si.sub.3N.sub.4.

13. The layered substrate of claim 10, wherein said substrate comprises at least two different coating layers.

14. The layered substrate of claim 10, wherein said substrate further comprises a plurality of reaction wells.

15. The layered substrate of claim 10, wherein each of said binding locations comprise a single type of capture molecule.

16. The layered substrate of claim 10, wherein said capture molecules are protein.

17. The layered substrate of claim 10, wherein said capture molecules are covalently bound to said topmost coating layer.

18. The layered substrate of claim 10, wherein said layered substrate is disposed within an optical detection apparatus that includes a light source positioned above the layered substrate to provide an illumination beam, a movable reference reflector having substantially the same refractive index as the coating layer, and a beam splitter system that splits the illumination beam into a sample beam directed to the coating layer and a reference beam directed onto a reference reflector, and combines reflections of the sample beam and the reference beam onto a photodetector array.

19. A layered substrate for imaging height changes of a coating layer thereon via an optical detection apparatus, wherein the layered substrate comprises: a silicon (Si) base layer; a silicon dioxide (SiO.sub.2) coating layer; and a plurality of spatially distinct binding locations, each comprising capture molecules bound to the top surface of the SiO.sub.2 coating layer, and wherein the layered substrate is disposed within the optical detection apparatus, the optical detection apparatus comprising: a light source positioned above the layered substrate to provide an illumination beam from above and onto the layered substrate, the illumination beam being directed substantially perpendicular to an uppermost surface of the layered substrate; and a photodetector array positioned to capture and image light reflected from the layered substrate.

20. The layered substrate of claim 19, wherein the light source positioned above the layered substrate is a tunable laser.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) The foregoing and other features and advantages of the present disclosure will be more fully understood from the following detailed description of the exemplary embodiments, taken in conjunction with the accompanying drawings in which:

(2) FIG. 1 is schematic of a microarray methodology using fluorescence detection;

(3) FIG. 2 is a schematic diagram for a device capable of performing phase shift interferometry (PSI) or white light interferometry (WLI);

(4) FIG. 3 is schematic diagram for a device capable of measuring spectral interference (SI); the inset is a hypothetical interference spectrum that could be obtained using SI;

(5) FIG. 4A is schematic diagram of the direct reflectivity methodology; the inset is a simplified schematic showing the light paths;

(6) FIG. 4B is a schematic diagram showing features the layered substrate (e.g., microarray) and parts of the direct reflectivity methodology;

(7) FIGS. 5A-B are examples of the data expected to be measured using a direct reflectivity methodology;

(8) FIG. 6 is a schematic diagram of the split beam interferometry methodology; the inset is a simplified schematic showing the light paths;

(9) FIGS. 7A-B are examples of data expected to be measured using a split beam interferometry methodology;

(10) FIGS. 8A-B are examples of data expected to be measured using a modified split beam interferometry methodology;

(11) FIG. 9 is a schematic diagram of the direct reflectivity methodology and layered substrate adapted for use in a flow cell and configured to obtain real-time binding data;

(12) FIG. 10 is a schematic of the optical component set-up used in a proof-of-concept experiment for the direct reflectivity methodology;

(13) FIGS. 11A-C show the data obtained from a proof-of-concept experiment for the direct reflectivity methodology; FIG. 11A is a graph showing the measured reflective intensity as a function of wavelength for pixels corresponding to physical locations having a height difference of 10 nm; FIG. 11B is a 3D mesh graph of the surface of a test substrate; FIG. 11C is a 2D image of pixel intensity showing the apparent pixel height corresponding to the surface of a test substrate;

(14) FIG. 12 is a schematic optical detection apparatus illustrating the use of a layered substrate containing reaction wells.

DETAILED DESCRIPTION

(15) The present invention provides devices and methods for optically profiling the height of a substrate. These techniques are applied to the detection of target molecules bound to the surface of microarrays. Significant advantages over prior art methods include, but are not limited to, the label-free detection of biological and environmental target molecules in a microarray-style assay (i.e., using capture molecules to immobilize the target molecules) that allows for high throughput screening. Further, the invention may be adapted to provide real-time binding information in order that binding kinetics of individual target-capture molecule interactions may be determined.

(16) Three interferometry methodologies consistent with the principles of this invention are described. In each case, the highly sensitive detection to small height changes of a low-index binding surface is enabled by one or more semitransparent layers below the binding surface. When adapted to microarray detection, the low-index binding material consists of the low-index substrate with immobilized capture molecules on the surface. Captured target molecules (i.e., the molecules of interest) causes an increase in the apparent height of the binding surface, where the height change is an indicator of the amount of target molecules bound to the surface.

A. Direct Reflectivity Method

(17) The direct reflectivity method is the primary substrate enhanced method for the label-free detection of microarray binding. As described in more detail below, the basic principle of the invention uses a top illumination source bright field microscope which is reflected from the surface into a photodetector array (e.g., a CCD camera). The image that is formed is essentially an image of the reflectivity of the sample at every point. It would be difficult to detect molecules binding to the microarray surface fabricated on standard glass and using a normal microscope and collimated illumination source because the reflectivity change resulting from target molecule binding would be too small to reliably quantify.

(18) Several modifications must be made to the standard microscope and microarray set-up in order to obtain significant and observable changes in reflectivity caused by target molecule binding. FIGS. 4A and 4B are schematic illustrations of one such set-up that illustrates the principles of the direct reflectivity method. The illumination source 110 is a tunable laser and an appropriate photodetector array 130 (camera) is selected based on the laser's wavelength range. The illumination beam 112 is directed from above onto a layered microarray 120, preferably perpendicular to the plane of the microarray 120. Optionally, the illumination beam 112 is directed onto the microarray 120 using a beam splitter 140. The imaged light 114 is reflected from the microarray 120 onto the photodetector 130 where an image is captured. Optionally, objectives 150 are used to focus the illumination beam 112 and/or the imaged light 119. Desirably, all optical components are coated with an anti-reflective coating appropriate for the wavelength range used. The microarray 120 is fabricated as a layered substrate consisting of a thick, reflective lower substrate (base layer 121) and a thin coating of a low index material (coating layer 122). For example, one particularly useful microarray substrate has 10 microns of SiO.sub.2 layered on a 300 micron thick Si wafer. FIG. 4B shows a simplified schematic diagram of the principles of this embodiment. The microarray 120 is formatted as a plurality of spatially distinct locations 129. The locations 129 may have the same or different target molecule 124 binding specificities compared to each other location 129 on the microarray 120. Each location 129 contains a plurality of substantially identical capture molecules 123 that specifically bind a single type of target molecule 123. To measure target molecule 124 binding to the surface of the microarray 120, the laser 110 wavelength is then swept through its tuning range and the reflectivity from each position on the microarray 120 is recorded as a function of position and wavelength, resulting in a reflectivity vs. wavelength curve. As target molecules 124 bind to the capture molecules 123 on the microarray 120 surface, the reflectivity vs. wavelength curve 132 for each point of the surface will change in an observable way compared to the unbound state.

(19) In one example of the direct reflectivity method, the tunable laser illumination source 110 has a range of 1500 nm to 1580 nm. The photodetector array 130 is an InGaAs array based camera appropriate for these wavelengths. The layered microarray 120 is fabricated as a 10 micron SiO.sub.2 coating layer 122 on 300 micron base layer 121 of Si. As the laser wavelength (illumination light 112) is tuned over the 80 nm range, the resulting reflectivity vs. wavelength curve 132 is characterized both a maximum and a minimum value (FIG. 5A). Small amounts of target molecule 24 binding to the microarray 120 will shift the wavelength of maximum and minimum reflectivity (FIG. 5A). The photodetector array 130 records these curves for each pixel as the wavelength is tuned, and a central processor (i.e., computer) compares how each pixel is shifted following a binding event. Since the refractive index of most biomaterial is close to that of glass (both low index around n=1.4), this binding can be modeled as a small increase in the glass layer thickness.

(20) FIG. 5B shows the change in intensity due to a 1 nm increase in SiO.sub.2 thickness as a percent of the peak intensity recorded. A 1 nm increase in SiO.sub.2 thickness corresponds, for instance, to about a 50 pg/mm.sup.2 layer streptavidin (50 kDa protein) binding to a microarray location 129. The percent change in intensity without using a layered substrate (relying only on increase absorption to affect the reflectivity) would be negligible and undetectable.

(21) The SiO.sub.2 on Si layered microarray 120 structure demonstrates the principle of (layered) substrate enhanced detection. More complicated layered structures may be used to further improve detection sensitivity. When choosing materials for the layered microarray 120 of this invention, it is important that the refractive index of the top layer be closely matched to the index of the target molecules 124 to be detected. SiO.sub.2 works well for many biomolecules including, for example, DNA, RNA, and protein. Also, the addition of target molecules 124 (e.g., biomolecules) to the coating layer 122 significantly shifts the wavelength-reflectivity characteristic of the microarray 120 as a whole.

(22) The direct reflectivity methodology combines the high throughput features of a microarray with high sensitivity of laser detection methods in a manner that can be configured to provide real-time binding information. Another advantage is that this can be accomplished using relatively inexpensive commercially available optical equipment including a gray scale camera and simple tunable laser. Alternative illumination sources 110 include, for example, a broad spectrum light source with a narrow tunable filter.

B. Split Beam Interferometry

(23) The component set-up for split beam interferometry method is similar to the direct reflectivity method described above in that the microarray 120 is illuminated from above by an illumination light 212. In the split beam method, however, differs from the direct reflectivity method as shown by the schematic device 200 in FIG. 6. The illumination source 210, in this case, is preferably a single wavelength laser, but a broad spectrum light with a narrow band-pass filter may also be used. The illumination beam 212 is split by a beam splitter 240 into a sample illumination beam 213 and a reference illumination beam 216 which are directed onto the microarray 120 and the reference reflector 260, respectively. The sample illumination beam is reflected by the microarray 120 as the sample image light 214 and the reference illumination beam 216 is reflected by the reference reflector 260 as the reference image light 218. The sample image light 214 and the reference image light 218 are combined by the beam splitter 240 into the reflected beam 219 which is directed onto the photodetector 230. The reference image light 218 interferes with the sample image light 214 in the combined reflected beam 219. As detailed further below, it is the interference pattern that provides information about the apparent height of the microarray 120.

(24) During operation, the position of the reference reflector 260 is swept, perpendicular to the reference illumination beam 216, by a distance “d”. Interference between the reference image light 218 and the sample image light 214 changes as a function of the position of the reference reflector 260. As shown in FIGS. 7A-B, the photodetector 230 and associated central processor create curves of reflective intensity vs. reference mirror position for each pixel. The curve shifts as the apparent height of the microarray changes. The calculation and analysis methodology is the same as for PSI {supra).

(25) The standard split beam interferometry setup is capable of detecting microarray 120 surface heights with 1 nm accuracy or better for single layer, highly reflective surfaces. For low-index material such as SiO.sub.2 and biomaterial, standard interferometry perform poorly as a result of the low surface reflectivity. One simple solution is to use an equally low reflectivity reference reflector 260 and turn up the source power to compensate for the loss. The results can be improved even further, however, by using a layered substrate as described for the microarrays useful in the standard illumination method. However, further modification of the layered substrate yields greater improvements. For split beam interferometry, a thinner coating layer 122 and a thicker base layer 121 are desirable. In one embodiment, the coating layer is 270 nm of SiO.sub.2 (n=1.4) on a thicker piece of Si for use with an illumination beam 112 having a wavelength (λ) of 1550 nm. Thus, the coating layer 122 of SiO.sub.2 has a thickness of λ/4 (i.e., “a quarter-wave layer”). At this thickness, reflectivity around 1550 nm is minimized. Sensitivity of the interference pattern in the combined reflected beam 219 to small changes in reference mirror position is, therefore, maximized. Table 1 shows the maximum change in intensity (as a percent of peak intensity) as a function of mirror position recorded during the data collection.

(26) Again, a quarter-wave layer of SiO.sub.2 on Si is only one example of a layered substrate useful with the split beam method. More complicated substrates may yield even greater sensitivities. The important feature of a desirable layered substrate is that the phase of the sample image light 214 change rapidly with the addition of biomaterial to top of the coating layer 122 of closely matched index.

(27) Another example a useful layered substrate for use in microarrays is SiO.sub.2 on gold. Gold is highly reflective and so a highly reflective gold reference mirror should be used as well. The reflectivity of the sample will remain high across different wavelengths, but the phase of the reflected light will change rapidly with the addition of a small amount of biomaterial when the apparent thickness of the SiO.sub.2 layer is approximately an odd integral number of wavelengths.

C. Modified Split Beam Interferometry

(28) The modified split beam interferometry set-up and methodology is very similar to the split beam method described above. The optical setup is the same as that shown in FIG. 6 for split beam interferometry. The difference is that the illumination source 210 is a white light source instead of a single wavelength laser. Again a reference reflector 260 is swept over a distance “d” with the difference being that interference using a white light source will only be observed when the reference reflector 260 is about the same distance from the photodetector 230 as the apparent surface of the microarray 120 (within the source coherence length). The intensity of the interference is recorded at each pixel and curves of intensity vs. reference reflector 260 position are again generated (FIGS. 8A-B). The reference reflector 260 position where interference is greatest indicates the apparent surface height at that location. This method is normally accurate down to the nanometer scale using a highly reflecting sample reference mirror. Similar accuracy is attainable using low reflectivity samples with a low reflectivity reference mirror and turning up the source power. Additional sensitivity enhancements are gained from the use of a layered substrate in the microarray. Table 1 shows the maximum change in intensity (as a percent of peak intensity) as a function of mirror position recorded during the data collection using the same 270 nm SiO.sub.2 on Si substrate. The increased sensitivity is because the layered substrate causes a phase shift in the reflected light greater in some wavelength regions depending on the thicknesses of the layers chosen.

(29) TABLE-US-00001 TABLE 1 Sensitivity Comparison of Layered Substrates Using Various Optical Detection Methodologies Sensitivity 100* (Change Reference in intensity) Detection Base Coating Material Reflector (Peak Intensity Method* Layer Layer Sensed Material Recorded) DRM Thick None 1 nm — 0.00 SiO.sub.2 SiO.sub.2 DRM Thick  10 μm 1 nm — 0.47 Si SiO.sub.2 SiO.sub.2 SBI Thick None 1 nm SiO.sub.2 0.41 SiO.sub.2 SiO.sub.2 SBI Thick 270 nm 1 nm SiO.sub.2 0.73 Si SiO.sub.2 SiO.sub.2 MSBI Thick None 1 nm SiO.sub.2 0.32 SiO.sub.2 SiO.sub.2 MSBI Thick 270 nm 1 nm SiO.sub.2 0.65 Si SiO.sub.2 SiO.sub.2 *DRM = direct reflectivity method; SBI = split beam interferometry; MSBI = modified split beam inferometry.

D. Microarray Detection

(30) Microarray technology, including methods for making microarrays, procedures for conducting microarray experiments, and applications are well known in the art [see, for example, Schena 2000]. The chemistry for the attachment of capture molecules to SiO.sub.2 substrates (i.e., the coating layer) are also well known in the art. A significant advantage of the present invention over current microarray detection methodologies is that the present techniques eliminate the need to detectably label the target molecules prior to performing the binding reaction on the microarray. A second advantage of the present techniques described herein is that a baseline height scan of the microarray may be performed prior to running the binding reaction with the target molecules so that the height of each detection location may be compared before and after target molecule binding. This eliminates the need for height and/or density uniformity of the capture molecules across the entire microarray. It also serves to reduce interexperimental variability (e.g., that result from manufacturing defects) where replicate microarrays are compared.

(31) An exemplary microarray useful in accordance with the principles of this disclosure may be created on the layered substrate by first cleaning the substrate surface with acetone, methanol, water, and N.sub.2 gas, then etching the surface with 10% NaOH for about 10 minutes. The surface is next silanized and functionalized with an amino-silane (for instance: 3-aminopropyl-triethoxysilane). Capture DNA is then be spotted at spatially distinct locations on the surface using a hollow pin (usually done robotically), using standard ink-jet printing technology [Hughes 2001], or using standard photolithography techniques [Singh-Gasson 1999]. The DNA is cross-linked (covalently bonded) to the surface by irradiation with UV light. The surface is finally rinsed before use. Alternative methods exist for making arrays including methods that use photolithography.

(32) The microarray is then scanned using any method in accordance with the principles of this invention to determine the initial height of each location. Next, target DNA is introduced to the surface via a solution, rinsed, and dried. The array is scanned again using the same method and the increase in height is recorded for each location. The change in height is an index of the amount of target DNA bound to that location.

E. Alternative Substrate Designs

(33) SiO.sub.2 layered on Si, as described above, is the simple case of a layered substrate that can be used in accordance with the principles of this disclosure. More complex layered substrates may also be used. The most desirable property for layered substrates is that the beam reflected from the target molecule surface undergoes a maximum phase change for a small change in the amount of material bound. A layered substrate consisting of many semitransparent layers of different optical indices can exhibit a very rapid change in both the intensity and phase of the reflected light for a small amount change in wavelength. Similarly, such a structure may exhibit a very rapid change in phase for a small amount of material modifying the thickness of the top layer. For example, a stack consisting of 270 nm of SiO.sub.2, 340 nm of Si, 270 nm of SiO.sub.2, 340 nm of Si, and 270 nm of SiO.sub.2 on an Si substrate has high reflectivity for wavelengths of 1550 nm. If the top SiO.sub.2 layer is slightly modified with binding molecules, the reflectivity will remain high, but the phase will change rapidly. This rapid phase change will give an enhanced signal in either of the split beam interferometry methods described above.

(34) The key is to create layered substrates that cause a rapid change in the phase of the reflecting light resulting from a small change in surface height. Materials may be used other than Si and SiO.sub.2. Alternative coating layers that are useful in layered substrates include dielectric substances such as Si.sub.3N.sub.4.

(35) In addition to the standard substrate configurations such as surface coating with capture molecules, either as a film or in spatially discrete locations as a microarray, alternative configurations may be useful depending upon the application. For example, in one alternative embodiment, an additional discontinuous layer is formed on top of the coating layer such that individual reaction wells are created. These reaction wells are desirably about 200 μm×200 μm×1 mm, but any convenient size may be used, depending upon the specific application and reaction conditions. These reaction wells may serve to contain the bonding reaction that fixes the capture molecules to the substrate surface, or the wells may be used to contain individual binding reactions in spatially and/or chemically distinct environments. FIG. 12 illustrates a layered substrate 500 having a base layer 121, a top coating layer 122a and an intermediate coating layer 122b built in accordance with the principles of this disclosure. The layered substrate 500 further comprises reactions wells 575 formed by well walls 570. Each reaction well 575 may contain the same or different reactants (e.g., target molecules, capture molecules, biological/environmental samples), in a liquid medium, as the other reaction wells 575 on the same layered substrate 500. The reaction wells 575 may be formed by layering a polymeric (e.g., PDMS) or other coating material (e.g., SiO.sub.2) on top of the top coating layer 122a. Alternatively, the reaction wells 575 may be formed by etching or soft lithography such that the wells are “cut” into the top coating layer 122a. For convenience, the layered substrate 500 is shown in conjunction with the direct reflectivity measurement apparatus, but these substrates are also useful with either the split beam interferometry or the modified split beam inferometry methodologies of this disclosure.

F. Real-time Instrument Design

(36) In order to perform real-time measurements so that binding kinetics between the target and capture molecules may be calculated, the substrate or microarray is desirably incorporated into a flow cell. The flow cell should be at least semi-transparent and allow the delivery of target molecules to the capture molecules in an fluid environment. Suitable fluids include liquids (e.g., an aqueous solution) and gases (e.g., air or an inert gas). FIG. 10 is a schematic illustrating the manner in which a substrate 420 comprising capture molecules 123 (not shown) may be incorporated into a direct reflectivity device constructed in accordance with the principles of this disclosure. The flow cell 400 is easily adapted for the split beam methodologies. When used in a flow cell 400 configuration, the height measurements indicating binding are desirably be performed quickly and repeatedly to observe binding at various times during the pre-equilibrium state. This would enable the user to extract kinetics information about the rate of the binding reaction. If desired, the user may continue the measurements after binding equilibrium is reaching and change the fluid to one that lacks target molecules in order to measure off-rate kinetics. The user may also introduce heat, pH change, electric field, or other physical or chemical alterations to further investigate binding kinetics.

Example 1. Direct Reflectivity Method

(37) FIG. 10 is a schematic of the optical set-up used for the following experiments.

(38) The illumination source was a tunable wavelength laser (Anritsu MG9638A) that can step light between 1500 nm and 1580 nm in picometer increments, and was controlled using a GPIB card and central processor. The power was kept at about 0.1 mW. SMF-28 fiber optic carries the light from the laser to the optical setup. The light exiting the fiber was collimated by an objective and then beam expanded with two additional lenses. There was an aperture in the beam expander to spatial filter and pass the lowest order Gaussian mode exiting the fiber. The light then reached a beam splitter that directed part of the light onto the sample. The light path was as follows: the light from the laser was directed by a beam splitter onto the sample; the light reflected from the sample and passed through the beam splitter, reaching the camera mounted above.

(39) Imaging optics were included for imaging the sample surface onto the camera. An objective was placed above the sample and below the beam splitter. The light exiting the beam expander configuration was converging such that the objective lens re-collimated it when it passes through to the sample. Alternatively, the beam splitter may be placed close to the sample and the objective above it. In this case, the beam expander would produce a collimated beam. The illumination light that reaches the sample in either case is collimated and the reflected light is imaged. The lenses and beam splitter were AR coated for 1550 nm to avoid unwanted cavity effects that would produce a wavelength dependency.

(40) The camera used an InGaAs array (SU 128-1.7R; Sensors Unlimited). Lab View software was used to control the laser and capture images from the camera. An NI-1422 frame grabber card (National Instruments) was used to capture the images.

(41) A layered substrate “test sample” was prepared by oxidizing 5 microns of SiO.sub.2 on a 500 micron thick Si wafer piece. To mimic biomaterial binding to the surface, 10 nm×100 micron strips of SiO.sub.2 were patterned on the substrate surface. The index of SiO.sub.2 is about n=1.4 which is very similar to the index of DNA and many proteins.

(42) The illumination light wavelength was stepped from 1500 nm to 1580 nm in 0.2 nm increments and an image was recorded at each step. First, a dark frame is captured with the lens cap on the camera. This dark frame was subtracted from all future measurements taken by the camera. A reference sample was used to characterize any wavelength dependence of the system. Then, the reference sample was replaced with the “test sample” and the measurement procedure was repeated.

(43) The intensity vs. wavelength curve for each pixel was obtained and divided by the characteristic determined by the reference scan. The resulting curves were fit in a least squares sense to a model similar to the Matlab code entitled Method A included in the software package (Mathworks, Inc., Ver. 7.0.1). This curve-fitting model is based on the scattering matrix method for determining the reflectivity of thin films as described in chapter 5 of “Optical Waves in Layers Media” [Yeh 1988]. Alternatively, the curves may be fit to a simple sine wave as an approximation of the true reflectivity vs. wavelength curve. Another alternative is to take the Fourier transform of a collected curve and observe a phase increase which indicates a shift in the curve which indicates a change in surface height. However, results using the scattering matrix model are most accurate because the model accounts for multiple reflections within the semitransparent layer. The scattering matrix method works equally well for calculating the multiple reflections in more complicated structures with more layers.

(44) FIGS. 11A-C provide the results of this experiment. The relative layer thickness across the sample surface gives the change in height across the surface may be plotted as a 3D mesh or as a 2D image where the intensity of each pixel indicates its height. FIG. 11A is a graph of wavelength vs. intensity for two different pixels. The actual data and the fitted curve are shown. The lower curve represents a pixel corresponding to a location that has a greater height than the location corresponding to the upper curve. FIG. 11B is a 3D mesh graph showing the height measured at each pixel. FIG. 11C is a 2D image showing the intensity at each pixel in the image which represents the calculated height at the corresponding location.

(45) This experiment has been successfully repeated with a visible CCD camera (Rolera from QImaging) and a tunable laser (New Focus Velocity) with a center wavelength of about 770 nm. Measurements of the 10 nm high strips were repeated with better than 1 nm repeatability.

REFERENCES

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Other Embodiments

(47) Although the foregoing invention has been described in some detail by way of illustration and example for purposes of clarity of understanding, it will be readily apparent to those of ordinary skill in the art in light of the teachings of this invention that certain changes and modifications may be made thereto without departing from the spirit or scope of the appended claims.