Laser diffraction is considered to be a well-known particle size analysis method for many reasons, however there is no single technique that is ideal for any application or sample. This article shows how the single particle optical sizing (SPOS) method may serve as a complementary or superior approach for customers who are only familiar with laser diffraction.
SPOS is a standard method used to determine the concentration and size of particles in liquid suspension. In this method, particles suspended in liquid pass via a photozone where they interact through scattering, extinction or a combination of both with a laser light source, as shown in Figure 1.
Figure 1. The LE400 SPOS sensor
The scattering/extinction by the particle is associated with the size and concentration of particles through the application of a calibration curve and a pulse height analyzer. The result that is produced is the size distribution and concentration of particles in suspension. When a single particle flows via the sensing zone or photozone, light is refracted or absorbed because of the physical existence of the particle, or alternatively, it can be scattered or dispersed at a certain oblique angle.
The extent of this pulse is based on the particle’s cross-sectional area and the physical principle of detection such as light blocking or light scattering (LS). Light blockage is usually known as light extinction (LE) or light obscuration, which enables high resolution particle sizing and counting down to 1 µm. The required mode of detection is less than 1 µm light scattering, where the light is detected after being scattered by smaller submicron particles, and then the particle size is acquired.
Applied in the AccuSizer line of instruments, the SPOS method uses a patented LE+LS dual detection system, which facilitates sizing and counting of single particles down to 0.5 µm (Figure 1). The sensor is integrated with the illumination and detection system, which is made to render a monotonic increase in pulse height with increasing diameter of the particles.
A particle size distribution is created when each consecutive particle flows via the sensor. This is done by evaluating the pulse heights that were detected against a standard calibration curve, acquired from a series of homogeneous particles of known diameters. It is guarenteed that only adequately diluted particle suspension is used so that the particles can travel one by one via the illuminated region and prevent any coincidences. This is achieved using an automated dilution process or manual predilution. As such, a range of AccuSizer systems are available to determine samples without any need for dilution (AccuSizer SIS), with two-stage dilution (AccuSizer APS), or with single stage exponential dilution (AccuSizer AD).
The SPOS technique is completely different from the laser diffraction method, which simultaneously determines all of the particles (Figure 2). Instruments that are capable of executing particle size analysis through ensemble methods like laser diffraction are rather restricted in resolution and accuracy, because the detected raw signal is mathematically inverted to measure the particle size distribution.
Figure 2. Laser diffraction optics
1 = obscuration/optical concentration detector
2 = scattered beam
3 = direct beam
4 = Fourier lens
5 = scattered light not collected by lens 4
6 = ensemble of dispersed particles
7 = light source (e.g. laser)
8 = beam processing unit
9 = working distance of lens 4
10 = multi-element detector
11 = focal distance of lens 4
Factors Affecting Laser Diffraction Results
An algorithm is applied to change the scattered light to particle size after the light scattering is collected on the multiple detectors integrated into a laser diffraction system. The following interconnected factors influence the estimated result:
- Algorithm; Mie or Fraunhofer
- Optical design
- Refractive index of the dispersing medium/sample
A publication that explained the effect of algorithm and optics provided results from a laser diffraction analyzer, keeping the PIDs detectors switched on and off and using Mie versus Fraunhofer theory (Figure 3). Subsequently, the same publication provided six entirely different quantified results from the same measurement in order to describe the effect of refractive index (RI) on results (Figure 4).
Figure 3. Effect of Optics/Algorithm
Figure 4. Effect of RI on calculated results
However, considering the broad difference in results based on the option of RI, it was easy to see why certain users have concern even with the best method when choosing RI for optimum results.
A popular laser diffraction analyzer was used in an experimental study, where all measurements were performed by an expert - a user with over 20 years experience. The initial sample was a silica-based CMP slurry that is often used in the microelectronics sector.
The sample was studied once and then results were determined using Mie (green) and Fraunhofer theory (red) (Figure 5).
Figure 5. Fraunhofer vs. Mie results
A ghost peak at 1 µm is produced by the Fraunhofer which does not actually exist. In this specific application a customers’ focus is centered on the existence of particles that measure more than 1 µm, but this would pose serious difficulties if this result is misconstrued.
Manufacturers of laser diffraction analyzers always propose the use of Mie theory for better results, but the question at this juncture is which RI value has to be used. The sample RI can be ideally determined or identified via references. This approach usually works well and produces satisfactory results. However, in the case of samples where it is not possible to measure the best RI choice, users should refer to an error calculation called the Residual, which offers a suitable way for choosing the optimum RI value. The RI option that minimizes should be able to produce the optimum result.
An Al-based CMP slurry spiked with 1 µm PSL particles was used to test this method of basing the RI selection on the lowest Residual value. A 1 µm spike peak will be present in the result using this sample. Figure 6 shows the results obtained from the laser diffraction analyzer. The red result and the green result used RI values 1.59,0 and 1.78, 0.1, respectively. Figure 7 shows the quantified results obtained from this measurement.
Figure 6. Al CMP slurry spiked with 1 µm PSL
Figure 7. Calculated results for spiked Al CMP slurry
While the RI choice (1.78, 0.1) was able to detect the 1 µm spike peak, it possessed a higher Residual value (8.423%) as opposed to the choice (1.59, 0) which overlooked the 1 µm spike peak (5.023%). This paradigm shows the complexity of using the laser diffraction method. Both of the RI choice and algorithm are important and significantly impact the end result. However, the Residual calculation is not always a simple method when selecting the RI value and confirming the choice.
Sensitivity to Tails of Distributions
Any method that is capable of determining the particles one by one, such as the SPOS technique, has a higher resolution when compared to an ensemble light scattering method like laser diffraction. At a hypothetical level, if a single particle is present in a swimming pool and the whole volume is allowed to flow via an SPOS sensor, the system will be able to locate and determine the single particle. In contrast, laser diffraction would not be able to detect this particle.
The subsequent set of experiments was then carried out to draw a comparison between the two methods with regard to sensitivity to a known set of particles, which are larger than the primary peak.
In order to validate the SPOS method, 3.4 µL of 1 µm PSL particles were mixed to 250 mL of silica based CMP slurry. The AccuSizer Mini FX system was used to determine this sample, and the outcome is depicted in Figure 8. The peak and the increased concentration, which almost correlated with the predicted value, were detected.
Figure 8. AccuSizer SPOS result of spiked silica CMP slurry
Laser Diffraction Result
Once again, the silica-based CMP slurry was mixed with the 1 µm PSL particles to determine the level of concentration needed for the laser diffraction analyzer to report the existence of the tail distribution. It was observed that when 177 µL of the PSL particles was added to 250 mL of the CMP slurry, no tail distribution appeared as yet (Figure 9).
Figure 9. Laser diffraction result, 177 µL PSL into 250 mL silica CMP slurry.
The base CMP volume was reduced considerably to approximately 4 mL once it became clear that a large amount of PSL particles will be needed to detect the spike peak. At last, the PSL peak was reported after 360 µL was mixed with 4.3 mL of the base silica CMP slurry. Figure 10 shows this result.
Figure 10. Laser diffraction result; 360 µL into 4.3 mL silica CMP slurry
Comparison between the two methods shows that this experiment indicates that the AccuSizer SPOS system is more than 600 times more responsive to the presence of a tail distribution as opposed to the laser diffraction method:
- 0.36/4.3 = 0.0837
- 0.0034/250 = .0000136
- 0.0837/.000136 = 615.44
Effect of RI (Again)
In order to determine the best RI values, the result (Figures 10) was again estimated to retest the approach and apply the lowest Residual value as a suitable approach. Figure 11 shows the results obtained from three calculations.
Figure 11. Calculated results for spiked silica CMP slurry
It was observed that the link between accuracy and residual of the result is opposite of the predicted trend. The worst result was obtained from the highest residual.
Spreading of Distribution
Technique resolution can be defined by another method. This can be done be determining the extent at which the measured result is wider than the predicted value. If the result spreads broader, the technique will have lower resolution. To study this aspect of both methods, a sample flowing via a 45 µm sieve was examined on the AccuSizer system and a laser diffraction analyzer. Figure 12 shows these results.
Figure 12. SPOS vs. laser diffraction results for a sieved sample
The green result obtained from the AccuSizer system apparently reveals the truncated distribution, whereas the red result acquired from laser diffraction broadens the distribution to comprise greater than 100 µm particles that do not exist.
Integrated into all PSS AccuSizer systems, the SPOS is a high accuracy, high-resolution method that is capable of providing particle size as well as concentration results. The sensitivity and resolution to distribution tails is much better when compared to laser diffraction.
This information has been sourced, reviewed and adapted from materials provided by Particle Sizing Systems, An Entegris Company .
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