A method to deposit a known number of polystyrene latex particles on a flat surface

Figures & data

Figure 1. Illustration of (a) GTC, (b) droplet detection and deposition system, and (c) the trajectories of streamlines and condensation-grown droplets.

Figure 2. Schematic diagram of the particle deposition system.

Table 1. Experimental procedure for a PNS wafer.

	(i) Evaluation of particle number conversion factor	(ii) Making a particle number standard wafer
Contents of evaluation	Evaluation of particle number conversion factor ${\gamma }_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}$	Comparison of the count value and the predicted value $N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}$
Equations	${\gamma }_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}=N_{\mathrm{SEM}}/N_{\mathrm{DC}}$ (Equation (3)(3) $$N_{\mathrm{w}}={\gamma }_{\mathrm{w}|\mathrm{DC}}·N_{\mathrm{DC}}$$(3) )	$N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}={\overline{\gamma }}_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}·N_{\mathrm{DC}}$ (Equation (7)(7) $$N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}={\overline{\gamma }}_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}·N_{\mathrm{DC}}$$(7) )
Particle number evaluation instruments	SEM (JEOL, JSM-6060) (=$N_{\mathrm{SEM}}$) Laser Scanning Microscope (Carl Zeiss, LSM700)	Optical microscope (Carl Zeiss, Axio Imager2) (=$N_{\mathrm{OM}}$) Fluorescence light source (Illuminator HXP 120 V, Carl Zeiss)
Particles	0.814 µm PSL particles (JSR Stadex SC-081-S)	0.814 µm: PSL particles (JSR Stadex SC-081-S) 0.18 µm: Fluoresbrite plain microspheres (Polysciences) 0.046 and 0.102 µm: Fluoresbrite carboxylate microspheres (Polysciences)
Deposited particle number	>1000	10–10,000
Wafers	Half-inch wafer (Ø12.5 mm)
Deposition area	One spot	Entire surface (Ø10.5 mm) or 3 mm x 0.3 mm

Figure 3. PSD measured by the LS-DC. Solid, long dash, and short dash lines are the PSD of PSL particles whose diameters are 0.81, 2.0, and 3.2 µm, respectively. Solid gray lines are condensation-grown droplets whose seed particles are 0.81 µm PSL particles. Particle diameter is defined as PSL-equivalent optical diameter.

Figure 4. SEM images of the deposited particles on a wafer at rest. Gray arrows in the inset image indicate PSL particles whose average diameter is 0.814 µm.

Figure 5. Particle number conversion factor, ${\gamma }_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}.$ Five wafer samples were made on a day, and the same experiments were carried out for five days. The dotted line is the average value.

Table 2. Uncertainty analysis on the experimentally evaluated PNCC, ${\overline{\gamma }}_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}.$

Uncertainty component	Symbol or expression	Standard uncertainty
Repeatability	$s_{\mathrm{e}}/\sqrt{n_{\mathrm{R}}{n}_{\mathrm{e}}}$	0.0017
Day-to-day variability	$s_{\mathrm{R}}/\sqrt{n_{\mathrm{R}}}$	Negligibly small
Systematic error	$u_{\mathrm{sys}}\left({\overline{\gamma }}_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}\right)$	0.0053
Combined	$u\left({\overline{\gamma }}_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}\right)$	0.0056
Average	${\overline{\gamma }}_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}$	0.9914

Figure 6. (a) Example of a programed deposition trajectory and (b) a map of particulate matter observed on a fabricated PNS wafer (right). A WSS (Minimal WSS, YGK, Japan) was used to detect particulate matters on the wafer.

Table 3. Uncertainty analysis on the predicted number of particles on a newly fabricated PNS wafer, $N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}.$

Uncertainty component	Symbol or expression	Relative standard uncertainty
Average PNCC, ${\overline{\gamma }}_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}$	$u\left({\overline{\gamma }}_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}\right)/{\overline{\gamma }}_{\mathrm{w}|\mathrm{DC}}^{\mathrm{SEM}}$	0.0056
True PNCC, ${\gamma }_{\mathrm{w}|\mathrm{DC}}$	$u\left({\gamma }_{\mathrm{w}|\mathrm{DC}}\right)/{\gamma }_{\mathrm{w}|\mathrm{DC}}$	0.0086
Predicted particle number, $N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}$	$u(N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.})/N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}$	0.0103

Figure 7. Optical micrograph of a PNS wafer whose particle number is about 11,000. PSL particles with a 0.814 µm particle diameter were used to fabricate the PNS wafer. A laser optical microscope set to 10× magnification was used to obtain the image. Inset image is the close-up of the boxed area under 100× magnification.

Figure 8. The ratio of particle number on a fabricated PNS wafer measured by optical microscope, $N_{\mathrm{OM}}$ to the predicted particle number. “In series with GTC” means the predicted number $N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}$ is measured by the LS-DC at the exit of GTC. “In parallel with GTC” means that the predicted number $N_{\mathrm{w}|\mathrm{OPC}}^{\mathrm{pr}.}$ is calculated from the number concentration measured by an OPC upstream of the GTC and the sampling flowrate of the GTC. Dashed lines are 95% confidence intervals calculated from the uncertainty analysis. Gray lines are 95% confidence intervals of a scenario in which Poisson sampling process is the only source of uncertainty.

Table 4. Summary of fabricated PNS wafer with 0.814 µm PSL particles.

Component	Symbol	Unit	Wafer No.
			1	2	3	4	5	6	7
In series with GTC
Particle counts of LS-DC	$N_{\mathrm{DC}}$	particles	11	40	123	343	1004	2905	10,985
Predicted particle number	$N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}$	particles	10.91	39.66	121.94	340.06	995.39	2880.08	10890.78
Particle number measured by the optical microscope	$N_{\mathrm{OM}}$	particles	11	40	123	336	984	2849	10,825
Ratio of ${\mathit{N}}_{\mathbf{OM}}$ to ${\mathit{N}}_{\mathbf{w}|\mathbf{DC}}^{\mathbf{pr}.}$	$N_{\mathrm{OM}}/N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}$	–	1.009	1.009	1.009	0.988	0.989	0.989	0.994
In parallel with GTC
Aerosol flowrate of GTC	$Q$	cm^3/s	6.40	6.39	6.39	6.39	6.26	6.47	6.47
Particle number concentration measured by OPC	$C_{\mathrm{OPC}}$	particles /cm^3	0.0949	0.2343	0.2343	0.2343	0.7591	1.9160	1.9160
Collection time	$t$	s	20	20	70	219	206	240	935
Predicted particle number	$N_{\mathrm{w}|\mathrm{OPC}}^{\mathrm{pr}.}$	particles	11.20	27.82	96.14	302.38	901.55	2741.56	10685.69
Ratio of ${\mathit{N}}_{\mathbf{OM}}$ to ${\mathit{N}}_{\mathbf{w}|\mathbf{OPC}}^{\mathbf{pr}.}$	$N_{\mathrm{OM}}/N_{\mathrm{w}|\mathrm{OPC}}^{\mathrm{pr}.}$	–	0.982	1.438	1.279	1.111	1.091	1.039	1.013

Figure 9. Optical microscope image of fluorescent particles on a PNS wafer. Particle diameter is 0.046 µm. The image was taken under fluorescence mode with an Axio Imager 2 (Carl Zeiss Germany).

Table 5. Summary of particle size dependence of $N_{\mathrm{OM}}/N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}.$

Component	Symbol	Unit	Diameter of PSL particles
			0.814 µm [0.028]^a	0.18 µm [0.04]	0.102 µm [0.05]	0.046 µm [0.1]
Deposition area		mm^2	$\frac{\pi }{4}\times {10.5}^2$	$\frac{\pi }{4}\times {10.5}^2$	$3\times 0.3$	$3\times 0.3$
Imaging mode of optical microscope (OM)			DF^b	DF and FL^c	FL	FL
Magnification of OM			10×	20×	50×	50×
LS-DC count number	$N_{\mathrm{DC}}$	particles	1004	1218	683	625
Predicted particle number	$N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}$	particles	995	1207	677	619
Particle number measured by OM	$N_{\mathrm{OM}}$	particles	984	1194	665	608
Ratio of ${\mathit{N}}_{\mathbf{OM}}$ to ${\mathit{N}}_{\mathbf{w}|\mathbf{DC}}^{\mathbf{pr}.}$	$N_{\mathrm{OM}}/N_{\mathrm{w}|\mathrm{DC}}^{\mathrm{pr}.}$	–	0.989	0.989	0.982	0.982

^a Coefficient of variation.

^b DF: dark-field.

^c FL: fluorescence.

Figure 10. Optical microscope images of fluorescent particles deposited on a PNS wafer. Particle diameter is 0.18 µm. (a) Images were taken under dark-field mode and (b) images under fluorescence mode.