Принципы нанометрологии (1027623), страница 36
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The detector measures theintensity of the light as the optical path is varied in the vertical direction(z axis) and finds the interference maximum. Each pixel of the camera149150C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.25 Schema of a coherence scanning interferometer.measures the intensity of the light and the fringe envelope obtained can beused to calculate the position of the surface.A low-coherence source is used rather than monochromatic light because ithas a shorter coherence length and, therefore, avoids ambiguity in determiningthe fringe order. Different instruments use different techniques to control thevariation of the optical path (by moving either the object being measured,the scanning head or the reference mirror) and some instruments havea displacement-measuring interferometer to measure its displacement [87].As the objective lens is moved a change of intensity due to interferencewill be observed for each camera pixel when the distance from the sample tothe beam-splitter is the same as the distance from the reference mirror to thebeam-splitter (within the coherence length of the source).
If the objective ismoved downwards the highest points on the surface will cause interferencefirst. This information can be used to build up a three-dimensional map ofthe surface. Figure 6.26 shows how the interference is built up at each pixel inthe camera array.There are a number of options for extracting the surface data from the CSIoptical phase data. Different fringe analysis methods give advantages withOptical instrumentsFIGURE 6.26 Schematic of how to build up an interferogram on a surface using CSI.different surface types, and many instruments offer more than one method.These are simply listed here but more information can be found in [85] and[86].
The fringe analysis methods include:-envelope detection;-centroiding;-envelope detection with phase estimation;-scan domain convolution;-frequency domain analysis.CSI instruments can have sub-nanometre resolution and repeatabilitybut it is very difficult to determine their accuracy, as this will be highlydependent on the surface being measured. Most of their limitations werediscussed in section 6.7.1 and are reviewed in [47]. The range of the opticalpath actuator, usually around 100 mm, will determine their axial range,although this can be increased to several millimetres using a long-rangeactuator and stitching software. The xy range will be determined by the fieldof view of the objective and the camera size. Camera pixel arrays range from256 by 256 to 1024 by 1024 or more, and the xy range can be extended toseveral tens of centimetres using scanning stages and stitching software.
CSIinstruments can be used with samples that have very low optical reflectancevalues (below 5 %), although, as with PSI, the signal-to-noise ratio is likely torise as the reflectance is decreased.To avoid the need to scan in the axial direction, some CSI instrumentsoperate in a dispersive mode. Dispersive CSI generates the spectral distributions of the interferograms directly by means of dispersive optics without151152C H A P T ER 6 : Surface topography measurement instrumentationthe need for depth scanning [88]. This method is well suited to in-lineapplications with high immunity to external vibration and high measurement speed. Researchers have recently developed a CSI technique that can beused to measure relatively large areas (several centimetres) without the needfor lateral scanning [89].
As such a full-field method does not use a microscope objective, the lateral resolution is necessarily limited.Some CSI instruments have been configured to measure the dynamicbehaviour of oscillating structures by using a stroboscopic source to essentially freeze the oscillating structure [90]. (Note that confocal instrumentshave also been used to measure the motion of vibrating structures [91].)CSI (and PSI) is often used for the measurement of the thickness ofoptical films by making use of the interference between reflections from thetop surface and the different film interfaces [92,93]. Recent advances can alsomeasure the individual thickness of a small number of films in a multilayerstack and the interfacial surface roughness [94].6.7.4 Scattering instrumentsThere are various theories to describe the scattering of light from a surface(see [95] for a thorough introduction and review).
The theories are based onboth scalar and vector scattering models and many were developed todescribe the scattering of radio waves from the ocean surface. Light scatteredfrom a surface can be both specular, i.e. the reflection as predicted bygeometrical optics, and diffuse, i.e. reflections where the angle of reflection isnot equal to the angle of incidence. Diffuse reflection is caused by surfaceirregularities, local variations in refractive index and any particulates presentat the surface (for this reason cleanliness is important). From the theoreticalmodels, the distribution of light scattered from smooth surfaces is found tobe proportional to a statistical parameter of the surface (often Rq or Sq),within a finite bandwidth of spatial wavelengths [96,97].
Hence, scatteringinstruments do not measure the actual peaks and valleys of the surfacetexture; rather they measure some aspect of the surface height distribution.There are various methods for measuring light scatter and there are manycommercially available instruments [98,99]. As scattering instrumentssample over an area (they are area-integrating methods) they can be very fastand relatively immune to environmental disturbance. For these reasons,scattering methods are used extensively in on-line or in-process situations,for example measuring the effects of tool wear during a cutting process ordamage to optics during polishing.
It can be difficult to associate an absolutevalue to a surface parameter measured using a scattering technique, soscattering is often used to investigate process change.Optical instrumentsThe function that describes the manner in which light is scattered froma surface is the bi-directional scatter distribution function (BSDF) [95]. Thereflective properties of a surface are governed by the Fresnel equations [41].Based upon the angle of incidence and material properties of a surface (opticalconstants), the Fresnel equations can be used to calculate the intensity andangular distribution of the reflected waves. The BSDF describes the angulardistribution of scatter.The total integrated scatter (TIS) is equal to the light power scattered intothe hemisphere above the surface divided by the power incident on thesurface. The TIS is equal to the integral of the BSDF over the scatteringhemisphere multiplied by a correction factor (known as the obliquity factor).Reference [100] derived a relationship between the TIS and Rq (or Sq)given byRqzl pffiffiffiffiffiffiffiffiTIS4p(6.6)where the TIS is often approximated by the quotient of the diffusely scatteredpower to the specularly reflected power.The instrumentation for measuring TIS [101] consists of a light source(usually a laser), various filters to control the beam size, a device for collectingthe scattered light, and detectors for measuring the scattered light andspecularly reflected light.
The scattered light is captured either using anintegrating sphere or a mirrored hemisphere (a Coblentz sphere). Oftenphase-sensitive detection techniques are used to reduce the noise whenmeasuring optical power.An integrating sphere is a sphere with a hole for the light to enter, anotherhole opposite where the sample is mounted and a third position inside thesphere where the detector is mounted (see Figure 6.27). The interior surfaceof the sphere is coated with a diffuse white material. Various corrections haveto be applied to integrating sphere measurements due to effects such as straylight and the imperfect diffuse coating of the sphere [102].With a Coblentz sphere the light enters through a hole in the hemisphereat an angle just off normal incidence, and the specularly reflected light exitsthrough the same hole.
The light scattered by the surface is collected by theinside of the hemisphere and focused onto a detector.A number of assumptions are made when using the TIS method. Theseinclude:-the surface is relatively smooth (l >> 4pRq);-most of the light is scattered around the specular direction;153154C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.27 Integrating sphere for measuring TIS.-scattering originates solely at the top surface, and is not attributable tomaterial inhomogeneity or multilayer coatings;-the surface is clean.TIS instruments are calibrated by using a diffusing standard usually madefrom white diffusing material (material with a Lambertian scattering distribution) [103].When comparing the Rq value from a TIS instrument to that measuredusing a stylus instrument, or one of the optical instruments described insections 6.7.2 and 6.7.3, it is important to understand the bandwidth limitations of the instruments.
The bandwidth limitations of the TIS instrumentwill be determined by the geometry of the collection and detection optics (andultimately by the wavelength of the source) [104]. TIS instruments canmeasure Rq values that range from a few nanometres to a few micrometres(depending on the source). Their lateral resolution is diffraction limited, butoften the above bandwidth limits will determine the lower spatial wavelengths that can be sampled.Another scattering method that is commercially available is angleresolved scatter (ARS) [97,105,106]. However, ARS methods tend to be morecomplicated than TIS and the theory relating the ARS to a surface roughnessCapacitive instrumentsparameter is not so clear.
Basically, the angular distribution of the scatteredlight is measured either using a goniophotometer-type instrument ora dedicated scatterometer (see [98] for examples). The angular distribution ofthe scattered light can be expressed as the product of an optical factor anda surface factor. The optical factor can be calculated from the illuminatingwavelength, the angles of incidence and scattering, the material properties ofthe surface, and the polarization of the incident and scattered beams.
Thesurface factor is called the power spectral density (PSD) function and isa function of the surface roughness. From the PSD quantitative values for theheight and spatial wavelength distributions can be obtained, although a gooda priori model of the surface is required for accurate measurements. It is alsopossible to extract the BRDF from ARS data. The range and resolution of ARSinstruments are very similar to those for TIS instruments. As with TISinstruments, ARS instruments do not measure the actual surface topography, but measure some aspect of the height and spatial wavelengthdistributions.
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