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Abstract
This paper describes how to quantify the scattering that appears in thin films deposited on a flat substrate. The defects appear during the deposition process and are hard to identify from classical optical microscopy pictures due to their small surface and contrast. A new way to probe the microroughness of optical components is described for heterogeneous or large samples (cm2) that requires a statistical analysis of each image over a full mapping of the sample. Due to possible optical misalignment or surface waviness, an automatic adjustment of the optical focus plane was implemented for each image during the surface mapping. In this way, we could measure the scattering using a microscope set-up. The results are linked to diffuse reflection and transmission losses (extinction coefficient k) and several different contributions from the total scattering are identified.
© 2017 Optical Society of America
1. Introduction
Analysis of optical microscopy images is a fast growing field of research in life [1] and material [2] science, with the appearance of in situ applications nowadays [3–5]. Using digital cameras, the users generally calibrate the spatial response of the camera [6] with a standard target, only few users adjust other parameters such as gain, shutter time, gamma and sharpness corrections. This paper addresses the way to detect defects having weak contrasts and generally hidden in the native image. The defects can be revealed by proper tuning of the illumination and camera parameters and some image analysis. The approach shown can also be used to measure the microroughness of optical components (coated or not) avoiding the use of atomic force microscopy, scanning electron microscopy, or bench measuring the bidirectional reflectance distribution function scattering (BRDF), total scattering (TS), total integrated scattering (TIS) or white light interferometer on the whole surface [7,8].
The samples are often either heterogeneous or large surfaces, so one image is not necessarily representative. The analysis was carried out by means of mapping of the whole surface using a motorized scanning stage and an adjustment of the microscope focus plane for each spot. A fully automatic optical microscope for on-line analysis was employed. Here the mapping was used to improve sol-gel layers manufactured at CEA (French Alternative Energies and Atomic Energy Commission) [9–11].
For the Megajoule Laser (LMJ) project [12], where most of the optical components working in transmission are coated with an antireflective sol-gel layer developed by CEA [9], we had to build an in-house set-up for the characterization of layers. The colloidal silica is used for lenses made of silica since its refractive index is close to 1.22 [10]. Therefore, we can build antireflective layers at 1 ω, the fundamental frequency of LMJ (i.e. 1053 nm) if their thickness is 216 nm and after frequency tripling at 3 ω (i.e. 351 nm) if their thickness is 72 nm. These films are deposited by dip coating [13] and are quite mechanically fragile. The coated components are then immersed into vapor of ammonia and water [11] to harden them and to increase their mechanical resistance against wiping, cleaning, handling or procedures for maintenance. This processing causes a small layer shrinkage in thickness which is sometimes accompanied by crazing for thicker layers and longer exposition times. We need to study this crazing effect in order to avoid it by optimizing the parameters of deposition and treatment. As a fast way to evaluate the crazing process of the total wafer surface (~20 cm2), we used video optical microscopy using a Leica DMR microscope, a camera DFW-V500 used in the past [14,15] and an x*y motorized scanning stage at the sample position.
A typical crazing of a sol-gel layer is shown in Fig. 1 as observed in interferential contrast (IC) conditions. A clear mosaicity appears in such conditions but it needs to be further characterized in terms of dimensions and shapes using image processing.
2. Samples preparation
The investigated samples are wafers of silicon (polished on both faces) covered by a thin layer of colloidal silica deposited by sol-gel process. The sol-gel solution used for the treatment is a colloidal suspension synthesized from a Stöber approach [16]. The synthesis corresponds to a hydrolyzation-condensation of tetraethyl orthosilicate (TEOS) in an alcoholic solution (see Fig. 2).
The wafers were dip-coated with these solutions and the films consist in a collection of nanoparticles having an average diameter of 10 nm. The film micro-porosity is about 55% so that the refractive index can be as low as 1.22 while the refractive index of silica at 1.053 µm is 1.45. The thicknesses of the layer depend on the speed of withdrawing, on the concentration and viscosity of the solution as studied previously [17].
The cohesion between particles and the adherence on the substrate are relatively weak just after drying, thus the coating is mechanically fragile. To increase the number of particles covalently connected and thus the thin film robustness, a chemical modification of the accessible nanoparticles surface was achieved by means of a post-processing treatment in ammonia vapor, called “ammonia curing process” [11]. This process induces a modification of the nanoparticles contacts from Van der Walls to hydrogen and then covalent bonding, increasing the mechanical properties of the films [18,19]. The samples were then placed in a desiccator under an ammonia and water atmosphere (saturated steam at stable 20° C ambient temperature). The ammonia vapors are generated by an aqueous ammonia solution with a concentration of 28%. One of our aims is to follow the crazing process, without curing and after such ammonia curing process over 17 hours, for layers of different thicknesses (coatings ranging from 80 nm to 280 nm and all produced in a single dip).
3. Settings of the digital microscopy camera
3.1. Measured camera global characteristics
The employed digital camera was a DFW-V500 manufactured by Sony Company [20] with a CCD sensor of 640x480 pixels. The pixel size is 7.4 X 7.4 µm2. The camera interface is an IEEE 1394 [21]. The nominal parameter values used and their maximum and minimum attributes are given in Table 1.
Table 1. Possible values of settings according to the camera attribute.
The lighting power and the objective (X5) of our microscope were fixed. Some images were recorded with different camera parameters in order to process them after. For each picture, we determined the maximum (Max), the minimum (Min), the average (Ave) and the volume (V), which is defined by the Eq. (1). The maximum was set below the saturation of the camera intensity (Max < 255).
where Li,j is the level value of the (i, j) pixel.Each parameter (Brightness, Auto Exposure, Sharpness...) was gradually changed while fixing all other parameters. We only show here the parameters varied for next measurements: the gain [Fig. 3] and the shutter [Fig. 4]. The maximum gain found is 13 dB and it was slightly lower than the indicated value (−18 dB giving an approximate inconsistency of 3 dB with the manufacturer data). We can reduce or increase by 16-fold the value here. Cameras with a gain going to 24 dB (for example the XCD-V60 [22]) allow us to have a higher increase or lower reduction.
The shutter value represents τ, the integration time of the sensor to reach its higher dynamical range (theoretically almost 104). Equation (2) links the shutter parameter value S and integration time [17]:
For higher values than S = 2048, a difference between the expected value and the experimental curve was observed. That was due to the illumination, which was too weak at lower integration times.
3.2. Setup for sample lighting
The microscope source is a tungsten filament lamp and a Köhler illumination setup. The microscope illumination was checked by a standard sample calibration to have a reproducible metrology in the time. Before all experiments, the intensity level was set to obtain an image volume equal to 60x106 [Eq. (1)] to within ± 2% for a polished silica substrate with a X5 bright field objective, a camera gain set to 0 and a shutter value equal to 2,048 (the other parameters set at their nominal value). In such a way, we could compare quantitatively the results obtained between different samples.
4. Improvement of the image dynamical range
Thin films often come with local defects [23, 24] that strongly scatter light and saturate the camera, so that the roughness of the thin layer cannot be estimated using the dark field configuration. On the opposite, the roughness of the layer could be observed at weak intensity levels. To differentiate the roughness and local defects scattering, the gain and the shutter of the camera were adjusted. One value of shutter SNon Sat and gain gNon Sat was chosen so that the local defects gave an intensity level between 150 and 255 and another value SSat and gSat to have scattered intensity from the roughness between 100 and 255. Two images were recorded for each spot, one with the parameters SNon Sat and gNon Sat (the so-called not saturated image see Fig. 5) and another one with the parameters SSat and gSat (the so-called saturated image, see Fig. 6).
After recording, both images were recombined to create a new image see Fig. 7, formed by the Li,j pixels corresponding to Eq. (3):
where:
Ii,jNon Sat or Sat is a pixel level I,j for Non Saturated (Non Sat) or Saturated Image (Sat),
τNon Sat or Sat is the integrating time corresponding to SNot Sat or Sat,
SNon Sat or Sat is the shutter set for Non Saturated (Non Sat) or Saturated image (Sat),
gNon Sat or Sat is the real gain set for Non Saturated (Non Sat) or Saturated image (Sat).
In this case, the dynamic range was increased 38-fold.
A possible application of this method is the determination of the fluence of the laser beam in particular during experiments of laser damage knowing its energy without forgetting the energy located in the beam’s edge, which is not commonly measured because the dynamics of the camera is limited. Therefore, it is possible to suppress the device compound by a λ/2 plate and a polarizer in order to reduce the laser flux in the laser damage bench [25] and to accurately determine the fluence in the laser spot by adjusting the camera gain. Moreover, this removes the astigmatism produced by a polarizer plate set in incidence in the convergent laser beam [26].
5. Automated focusing on the sample surface
Coated samples were made with either silica or silicon polished substrates. Silica substrates were sufficiently flat and their roughness was good (flatness << λ/4 and roughness Rq << 0.5 nm [27]). Silicon substrates were not as flat [Fig. 8] as measured using a Dektak profilometer on several silicon wafers in two perpendicular directions. Measurements revealed height differences of few microns [28] that have to be taken into account for microscopy sample mappings.
Indeed, the depth of focus is weaker than the silicon wafer distortion for microscope objective used (X50, X100 or X150). The depth of focus for a microscope objective is given by the Eq. (4) [29]:
where:n is the refractive index of the medium (here n = 1),
NA is the objective numerical aperture,
M is the objective magnification,
e is the smallest distance that can be resolved by the detector, e is equal to 3 pixels (e = 22.2 µm),
λ is the wavelength: λ = 0.55 µm.
The experimental and theoretical depths of focus are plotted in Fig. 9 as a function of objective numerical aperture or magnification. This curve highlights that the check of focus before a mapping is needed for magnifications higher than X50.
To realize the automatic focusing around a position, a displacement was carried out using several motor steps as a function of the objective magnification. Pictures at each position were recorded (see Table 2) with a dynamic range of 8 bits determined from: D = Lmax -Lmin, where Lmax is the maximal intensity of the histograms (Lmin ≤ Lmax ≤ 255) and Lmin is the minimal one (0 ≤ Lmin ≤ Lmax).
Table 2. Range of displacements according to the microscope magnification.
When the image is at the focus of the objective, the dynamic range is higher, the contrast is the highest. Figure 10 illustrates the principle of the automatic focusing used with five images over 5 µm range.
Fig. 10 Principle of automatic focusing. The image 3 is the sharpest image while the others are blurred. Image 3 corresponds to the searched focusing position.
Our focalization method has been compared to Brenner’s gradient focusing that is a reference autofocus method [30–32] in two cases with similar results:
Investigations must be done to conclude about our method with several situations (different ranges, steps, magnifications, lights, dark field, differential interference contrast…).
6. Results and discussion
Six silica samples covered by a sol-gel silica film of 80, 125, 170, 210, 240 and 285 nm without and with ammonia curing are considered in the following. A matrix of 7x7 images was recorded by microscopy with a X100 objective with a step of 0.25 mm along x and along y axes (so a total surface of 0.2 mm2). The dark field configuration is used because this is very sensitive inspection technique but it has relied upon experienced inspector [33] that nowadays can be easily employed in laboratories and industries.
6.1. Measurement of the density of local defects
Figure 15 shows the surface percentage of local defects measured for the 240 nm layer. The dispersion over 49 images is about 1%.
Figure 15 exhibits the interest mappings to analyze a material to be more representative, the percentage of surface covered by defects varies according to the image from 0.5% up to 5%.
Then Fig. 16 was constructed for the average defect surface in percentage of the whole surfaces as a function of the layer thickness.
We observed that the defects surface density increased slightly with the layer thickness. The points give the values at ± 1σ (σ: root mean square). Local defects appear with the increasing thicknesses.
6.2. Optical microscopy observations
The scattering volume attributed to the crazing for each image and measured for the 210 nm film was plotted in Fig. 17. The relative dispersion (σ) of the scattering volume on these 36 images was about 11% due to the image n°29, which exhibits many scattering spots.
Fig. 17 Scattering volume calculated for each recorded image surface with local images showing the scattering defects.
The images n°10 and n°29 in Fig. 17 confirm us the link between the volume of scattering and the total intensity in the image.
The scattering due to the crazing was also compared as a function of the film thickness for layers without curing and layers with curing during 17 hours [Fig. 18]. Here, the scattering level was normalized to 1 at its maximum value.
Fig. 18 Normalized scattering according to the layer thickness for layer cured or not cured. A fit to the data was added to the figure.
The scattering linked to the crazing increases exponentially with the layer thickness. Untreated layers presented clearly less scattering than the cured layers.
We adjusted our data with 3 terms:
- • a constant term for the substrate surface: A surface
- • an exponential term for the sol-gel layer:
- • an exponential term for crazing:
In this case and with such decomposition, we obtained:
- • A surface not cured = 0.328 A surface cured = 0.239
- • ALayer cured or not cured = 3 10−6 αLayer cured or not cured = 0.029
- • ACuring = 639 10−6 αCuring = 0.024 if layer is cured
- • ANo curing = 0 αNo curing = 0 if layer is not cured
The optical scattering of the sol-gel layer that was cured with ammonia treatment comes thus from the substrate scattering, the sol gel layer scattering and the ammoniac curing. In this additive decomposition model the scattering of the sol-gel layer and the curing varied exponentially with the thickness. An extinction coefficient of scattering could be assumed: kScattering = kLayer + kCuring. Note that for thicknesses above 200 nm, the scattering becomes large and the crazing quite visible. By means of the method, we could identify the origin of the scattering.
6.3. Comparison of microscopy and spectrophotometer measurements
The nanoparticles thin films, deposited on silicon wafers have been further investigated using a Cary 5000 spectrophotometer. The measurements were conducted with an integrating sphere over the [250-750 nm] spectral range see Fig. 19.
The spectral diffuse reflection signal increased quickly above 200 nm thickness. The edge displacements of spectral curves towards the larger wavelengths come from the thicknesses that increase.
Some films were dip coated on silica substrates (one was not cured and another cured during 14 hours), in order to measure the extinction coefficient from a transmission measurement with a spectrophotometer (see Fig. 20). Both sides of the silica substrate were coated from the dip-coating technique.
Fig. 20 Spectral transmission for two silica substrates coated with a silica sol-gel layer on both sides: one was not cured and the other was cured during 14 hours. The spectrum of bare silica is also shown.
From these spectral curves and the envelope approach [34], we could calculate:
- • t: the layer thickness,
- • n (λ): the refractive index function,
- • k (λ): the extinction coefficient function.
Where n(λ) and k(λ) follow Cauchy's laws.
The spectral curves (red curves) with their fits (green curve) are plotted in Fig. 21 (not cured) and Fig. 22 (cured).
The best fit parameters for both spectra are summarized in Table 3 and the spectral extinction coefficient is plotted in Fig. 23.
The extinction coefficient of cured layers is clearly higher than untreated ones, which confirms us the trend observed from the analysis of the optical microscopy and diffuse reflection measurements.
7. Size and shape of crazing by microscopy
7.1. Average intensity levels
We could assimilate this crazing as local defects [23] or microroughness. We used a matrix of image Nx x Ny (with a size: lx X ly mm2), to obtain a bigger observation area using a microscope objective X100 that only represents 4,256 µm2 (a rectangle of 56 X 76 µm2) in order to see crazing over larger scales. Nevertheless most of the intensity came from localized defects and crazing appeared with smaller intensity levels. An increasing of the intensity dynamics was thus necessary to study crazing patterns. The camera parameters (gain and shutter) were varied for that purpose and a gain and shutter optimum were found to avoid saturation [Fig. 5] for a given lighting. For each point of our matrix two images were recorded, one with the parameters gain and shutter optimal [Fig. 5] and another with a different shutter corresponding to an integration time 8 time longer [Fig. 6]. The combination of both images [Fig. 7] gave a sufficient dynamical range to quantify the crazing (low levels) as well as the local defects (high level).
The level of the threshold chosen for the crazing intensities was determined from the histogram at twice of its average level. The volume V of the scattering observed in dark field was divided into two parts VScattering = VLocal Defects + VCrazing (see Eq. (5) where Nx ( = 680) and Ny ( = 480) are the number of pixel along x and y axes of the CCD).
The local defects surface S Local Defects was determined by the pixels having a level superior than a chosen threshold.
Thus, the average level of crazing was calculated LAv Crazing (see Eq. (6)):
This average level of crazing will be used to quantify our layer homogeneity and the effects of the ammonia curing.
7.2. Clusters average size
Figure 1 shows an assembly of clusters that has to be quantified by a number density and an average diameter. The average size of the clusters was obtained by processing the image with LabView [Figs. 24(a)-24(g)] in 7 steps:
An analysis of particles with connectivity equal to 8 (i.e. only the pixels that had 8 neighbors were counted) gave values is plotted in Fig. 25.
A histogram (Fig. 26) was obtained. This histogram gave the number of cluster according to their surface (number of pixels time the pixel surface) therefore, the distribution in size of the cluster. Its shape comes from the large number of small particles.
The surface or diameter average and the number of particles were given by the treatment of such curves. The pixel sizes according to the microscope magnification were calibrated before with a standard target sample over the two dimensions. 752 clusters have been found in this image and a mean surface was 1.6 µm2 with a root mean square of 2.7 µm2.
The microscopy observations were compared to atomic force microscopy (AFM) topological images on a similar sample. They clearly show the crazing process and some clusters appeared with a size of 4 µm2 [Fig. 27]. The measurements were conducted in the tapping mode without contact using AFM-tips from Nano-World Innovative Technologies (Pointprobe® NCHR types in silicon with resonance frequency fo~320 kHz, force constant C~42 N/m and radius below 10nm).
This size was accounted for our image if the small clusters were removed setting a threshold at the average value of the distribution (Fig. 28). Larger particles were counted and the average surface reached 4.5 µm2 with a root mean square of 4.3 µm2.
Fig. 28 Distribution in size of treated image using a threshold at the mean value of the distribution [Fig. 26].
8. Conclusions
So, camera dynamics improvements done in this paper can give access to new applications as: the roughness measurement which needs a higher dynamic, the detection of objects having a small contrast, and a better knowledge of the laser beam intensity in particular for a laser damage metrology experiment.
The metrology of heterogeneous materials imposes to carry out mapping of large surfaces and statistical analysis. We developed an automatic focusing with a contrast increase. Large image matrices over the whole surface were carried out using this automatic focus and a motorized sample stage (along x and y axes). From these mappings, a statistical analysis of the localized defects giving a number and size of particles over a whole sample surface was made.
We applied these points to characterize the crazing of sol-gel layers due to ammonia curing in order to measure and quantify local defects giving rise to scattering from series of optical microscopy images taken over the whole areas of a film. The dark field images are often used to detect such kinds of defects. Using our measurements, we can conclude that the crazing (and the defects) increases exponentially with the layer thickness inducing. This increase of scattering that can be divided in three components: a substrate contribution, a layer contribution and a post-treatment contribution. This scattering is also observed with diffuse reflection and specular transmission measurements using a spectrophotometer. An analysis of spectral curves to determine the extinction coefficient by reverse engineering program has been made and also correlated to our scattering measurement obtained with optical microscopy.
A morphological analysis of images made on sol-gel layers made for optical components with large surface (a few cm2) gives clusters sizes similar to AFM images.
Detected defects might come in industrial applications from a broad variety of causes such as: manufacturing processes (polishing or deposit), post-treatments such as the “superpolishing”, the advanced mitigation process [35] or the cleaning of substrates for example to detect the dust or adhesive trace before deposition, the ageing as for example the ageing of silver layers under humid atmosphere or temperature [14]. Our analysis system is cheaper than other devices used to measure the scattering.
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