Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 31
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When measuringsurface texture, one must consider the ability to measure the spacing ofpoints in an image along with the ability to accurately determine the heightsof features. We need an optical equivalent of equation (6.1) for stylusinstruments. This is not a simple task and, at the time of writing, the exactdefinitions have not been decided on. Also, there may not be a commonexpression that can be used for all optical instruments. One such definition isthe lateral (50 %) resolution or the wavelength at 50 % depth modulation.This is defined as one half the spatial period of a sinusoidal profile for whichthe instrument response (measured feature height compared to actual featureheight) falls to 50 %.
The instrument response can be found by directmeasurement of the instrument transfer function (see [42] and annex C in[43]). Note that this definition is not without its faults – the value of thelateral (50 %) resolution will vary with the height of the features beingmeasured (as with equation (6.1) for a stylus instrument).Another important factor for optical instruments that magnify thesurface being measured is the optical spot size.
For scanning type instruments the spot size will determine the area of the surface measured as theinstrument scans. To a first approximation, the spot size mimics the actionof the tip radius on a stylus instrument, i.e. it acts as a low-pass filter [44].The optical spot size is given byfld0 ¼(6.4)w0where f is the focal length of the objective lens and w0 is the beam waist (theradius of the 1/e2 irradiance contour at the plane where the wavefront isflat [41]).129130C H A P T ER 6 : Surface topography measurement instrumentationIn a non-scanning areal instrument it will be the field of view thatdetermines the lateral area that is measured.
In the example given inTable 6.1 the areas measured are 0.3 mm 0.3 mm and 1.2 mm 1.2 mmfor the 50 and 10 objectives respectively.Many optical instruments, especially those utilizing interference, can beaffected by the surface having areas that are made from different materials[45,46]. For a dielectric surface there is a p phase change on reflection (atnormal incidence), i.e. a p phase difference between the incident andreflected beams. For materials with free electrons at their surfaces (i.e. metalsand semiconductors) there will be a (p d) phase change on reflection, whered is given by2n1 k2d ¼(6.5)1 n22 k22where n and k are the refractive and absorption indexes of the surrounding air(medium 1) and the surface being measured (medium 2) respectively. For theexample of a chrome step on a glass substrate, the difference in phase changeon reflection gives rise to an error in the measured height of approximately 20nm (at a wavelength of approximately 633 nm) when measured using anoptical interferometer.
A stylus instrument would not make this error inheight. In the example of a simple step, it may be possible to correct for thephase change on reflection (if one has prior knowledge of the opticalconstants of the two materials) but, when measuring a multi-materialengineered surface, this may not be so easy to achieve.Most optical instruments can experience problems when measuringfeatures with very high slope angles or discontinuities. Examples includesteep-sided vee-grooves and steps. The NA of the delivery optics will dictatethe slope angle that is detectable and in the case of a microscope objective itwill be the acceptance angle. For variable focus and confocal instruments (seesections 6.7.2.2 and 6.7.3.1) sharp, overshooting spikes are seen at the top ofsteps and often the opposite at the bottom of the step.
These are usuallycaused by the instrument not measuring the topography correctly, sometimes due to only a single pixel spanning the discontinuity. For lowcoherence interferometers (see section 6.7.3.4) there can be problems thatare caused by diffraction and interference from the top and bottom surfacewhen a step height is less than the coherence length of the source [47,48].These effects give rise to patterns known as batwings (see Figure 6.9). Ingeneral, care should be taken when measuring steep slopes with opticalinstruments.
Note that some optical instruments can extend the slopelimitation of the objective by making use of diffusely scattered light. This canonly be achieved when the surface of the slope is sufficiently rough to obtainOptical instrumentsFIGURE 6.9 Example of the batwing effect when measuring a step using a coherencescanning interferometer.enough diffuse scatter. It is also possible to extend the slope limitation withsome surfaces using controlled tilting of the sample and specialist imageprocessing [49].Many optical instruments for measuring surface topography utilizea source that has an extended bandwidth (for example, coherence scanninginterferometers and confocal chromatic microscopy).
Such instruments canbe affected by dispersion in the delivery optics or due to thin films at thesample surface. For example, due to dispersion, coherence scanning interferometers can miscalculate the fringe order, giving rise to what are referredto as 2p discontinuities or ghost steps [50]. Dispersion effects can also befield or surface gradient dependent [51]. Also, all optical instruments will beaffected by aberrations caused by imperfections in the optical componentsand these will affect the measurement accuracy and optical resolution (suchsystems will not be diffraction limited).Finally it is important to note that surface roughness plays a significantrole in measurement quality when using optical instrumentation. Manyresearchers have found that estimates of surface roughness derived fromoptical measurements differ significantly from other measurement techniques [52–55].
The surface roughness is generally over-estimated by opticalinstrumentation (this is not necessarily true when considering areaintegrating instruments) and this can be attributed to multiple scattering.Although it may be argued that the local gradients of rough surfaces exceedthe limit dictated by the NA of the objective and, therefore, would be classified as beyond the capability of optical instrumentation, measured valueswith high signal-to-noise ratio are often returned in practice.
If, for example,a silicon vee-groove (with an internal angle of approximately 70 ) is131132C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.10 Over-estimation of surface roughness due to multiple scattering in veegrooves.measured using coherence scanning interferometry, a clear peak is observedat the bottom of the profile due to multiple reflections (scattering) [56].Although this example is specific to a highly polished vee-groove fabricated insilicon it is believed to be the cause for over-estimation of surface roughnesssince a roughened surface can be considered to be made up of lots ofrandomly oriented grooves with random angles (see Figure 6.10).
Note thatrecent work has shown that, whilst multiple scattering may cause problemsin most cases for optical instruments, it is possible to extend the dynamicrange of the instrument by using the multiple scatter information andeffectively solving an inverse problem. For example, [57] have recently discussed the measurement of vertical sidewalls and even undercut featuresusing this method.6.7.2 Scanning optical techniquesScanning optical techniques measure surface topography by physicallyscanning a light spot across the surface, akin to the operation of a stylusinstrument. For this reason scanning optical instruments suffer from thesame measurement-time limitations discussed for stylus instruments(although in many cases the optical instruments can have higher scanningspeeds due to their non-contact nature). The measurement will also beaffected by the dynamic characteristics of the scanning instrumentation andby the need to combine, or stitch, the optical images together.
Stitching canbe a significant source of error in optical measurements [58,59] and it isimportant that the process is well characterized for a given application.6.7.2.1 Triangulation instrumentsLaser triangulation instruments measure the relative distance to an object orsurface. Light from a laser source is projected usually using fibre optics on tothe surface, on which the light scatters. The detector/camera is fitted withoptics that focus the scattered light to a spot on to a CCD line array orposition-sensitive detector. As the topography of the surface changes thisOptical instrumentscauses the spot to be displaced from one side of the array to the other (seeFigure 6.11).
The line array is electronically scanned by a digital signalprocessor device to determine which of the pixels the laser spot illuminatesand to determine where the centre of the electromagnetic energy is located onthe array. This process results in what is known as sub-pixel resolution andmodern sensors claim to have between five and ten times higher resolutionthan that of the line array.Triangulation sensors came to the market at the beginning of the 1980sbut initially had many problems.
For example, they gave very differentmeasurement results for surfaces with different coefficients of reflectance.So, historically laser triangulation sensors were used in applications wherea contact method was not practical or perhaps possible, for example, hot, softor highly polished surfaces. Many of these early problems have now beenFIGURE 6.11 Principle of a laser triangulation sensor.133134C H A P T ER 6 : Surface topography measurement instrumentationminimized and modern triangulation sensors are used to measure a largearray of different surfaces, often on a production line.Triangulation instruments usually use an xy scanning stage with linearmotor drives giving a flatness of travel over the typically 150 mm by 100 mmrange of a few micrometres. Over 25 mm the flatness specification is usuallybetter than 0.5 mm.
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