Mobility-Based Particle Size Classification and Detection down to 2nm Theory to Practice

Transcription

1 Mobility-Based Particle Size Classification and Detection down to 2nm Theory to Practice Robert C. Anderson Presented at SEMATECH November 12, 2012 Current and Future Defectively Issues from Components in the Semiconductor Industry 11/13/2012

2 What is Electrical Mobility Analysis? Technology to size-classify aerosols with D p <1µm Online results Reference technology Could also be called band-pass filter 3-Step process Charge Neutralization resp. bipolar charging Fractionation classification by mobility using an Differential Mobility Analyzer (DMA) Detection ISO standards describing the technology in draft Class of instruments

3 Electrical Mobility Theory Z p electrical mobility; ability of a charged particle to traverse an electric field Two forces affect particle trajectories: Electrical Field strength, viscous drag: Z p = Particle Velocity = Electric Field Strength V = E nec 3µD p Inversely proportional to D p Low Mobility n p = number of charges/particle e = elementary unit of charge = gas viscosity D p = particle diameter C = Cunningham slip correction High Mobility

4 DMA Theory Z p = Particle Velocity = Electric Field Strength V = E nec 3µD p n p e D p C = number of charges/particle = elementary unit of charge = gas viscosity = particle diameter = Cunningham slip correction DMA uses Electrical Mobility (Z p ) to select a particle size Band-pass Filter for Particle Size Low Mobility Differential Mobility Analyzer DMA High Mobility

5 Electrical Mobility Analysis Z p electrical mobility; ability of a charged particle to traverse an electric field

6 Electrical Mobility Analysis Z p electrical mobility; ability of a charged particle to traverse an electric field F electric n ee p Where: n p = number of charges per particle e = elementary unit of charge E = electric field strength

7 Electrical Mobility Analysis Z p electrical mobility; ability of a charged particle to traverse an electric field F electric F viscous drag n ee p Dpv 3 C Where: n p = number of charges per particle e = elementary unit of charge E = electric field strength = viscosity of gas D p = particle diameter C = Cunningham slip correction v = Velocity

8 Electrical Mobility Analysis Z p electrical mobility; ability of a charged particle to traverse an electric field F F F electric viscous drag electric n ee p Dpv 3 C Fviscous drag Where: n p = number of charges per particle e = elementary unit of charge E = electric field strength = viscosity of gas D p = particle diameter C = Cunningham slip correction v = Velocity Z p v E npec 3 D p

9 Electrical Mobility Analysis Z p electrical mobility; ability of a charged particle to traverse an electric field F F F electric viscous drag electric n ee p Dpv 3 C Fviscous drag Where: n p = number of charges per particle e = elementary unit of charge E = electric field strength = viscosity of gas D p = particle diameter C = Cunningham slip correction v = Velocity Z p v E npec 3 D p Electrical mobility: inversely proportional to particle size

10 Electrical Mobility Analysis Z p electrical mobility; ability of a charged particle to traverse an electric field F F F electric viscous drag electric n ee p Dpv 3 C Fviscous drag Where: n p = number of charges per particle e = elementary unit of charge E = electric field strength = viscosity of gas D p = particle diameter C = Cunningham slip correction v = Velocity Z p v E npec 3 D p Electrical mobility: inversely proportional to particle size Differential Mobility Analysis Uses Electrical Mobility (Z p ) to select a particle size Band-pass Filter for Particle Size

11 Mobility Particle Sizing Aerosol Conditioner Produces a known charge distribution

12 Mobility Particle Sizing Z p v E npec 3 D p Aerosol Conditioner Differential Mobility Analyzer Classifier Produces a known charge distribution Selects particles according to electrical mobility particle size

13 Mobility Particle Sizing Z p v E npec 3 D p Aerosol Conditioner Differential Mobility Analyzer Classifier Particle Counter Produces a known charge distribution Selects particles according to electrical mobility particle size Counts size selected particles to build distribution

14 Mobility Particle Sizing Aerosol Conditioner Differential Mobility Analyzer Classifier Particle Counter Produces a known charge distribution Selects particles according to electrical mobility particle size Counts size selected particles to build distribution Control hardware & software

15 Sizing using Electrical Mobility Electrical Aerosol Analyzer = EAA + Step up current on rod + Measure current that gets to electrometer + Current for each size channel is difference between successive steps 15 Model 3000 Whitby Aerosol Analyzer

16 Cylindrical DMA Voltage & Flowrates Sheath Air In Z p v E npec 3 D p Polydisperse Air In Z p [ q t 1/ 2( q p q 2VL m r )]ln( r 2 1 ) High Voltage Rod Excess Air Out Where: q t = total flowrate (sheath + poly) q m = monodisperse flowrate q p = polydisperse flowrate r 2 r 1 V L = outer electrode radius = inner electrode radius = voltage on center electrode = length between sample exit and aerosol inlet Monodisperse Air Out

17 Scanning Mobility Particle Sizer SMPS Combination of a DMA and a CPC (Condensation Particle Counter) by a fast scanning mode of the DMA voltage makes it a Scanning Mobility Particle Sizer. Typical operating parameters: Particle Size Range: 2.5 nm 1 µm Size Resolution: channels Measurement Time: s Polydisperse Aerosol Concentration Size Distribution DMA Selects Single Size Counter Monodisperse Aerosol Voltage/Diameter

18 Mobility Particle Sizing?? Aerosol Conditioner Differential Mobility Analyzer Classifier Particle Counter Produces a known charge distribution Selects particles according to electrical mobility particle size Counts size selected particles to build distribution Control hardware & software

19 Bipolar Charge Distribution Must know number of charges per particle Z p = Particle Velocity Electric Field Strength = V E = nec 3µD p Equilibrium Charge Distribution 90% of 10nm particles are neutral Aerosol In Aerosol Out Kr-85 gas sealed stainless-steel tube Beta-Emitter + Kr-85 inert gas sealed in air-tight stainless steel, 10.4 year half-life + Ni-63, 100 year half-life Alpha-Emitter + Po-210, Am-241 Soft X-ray Unipolar charger and Particle Charge Particle Diameter (m) Note: Poor charging leads predominately to concentration inaccuracies. However, since charging is size dependent it leads to sizing inaccuracies as well.

20 Multiple Charges Fuch s Equilibrium Charge Distribution Percent of particles carrying n p elementary charge units D p (nm) A. Wiedensohler: An Approximation of the Bipolar Charge Distribution for Particles in the Submicron Size Range, Journal of Aerosol Science, Vol. 19, No. 3, pp , 1988.

21 Poor Charging affects Size Distribution Measurement: Generated aerosol is very highly charged High aerosol concentration and 1 neutralizer TSI model 3077: SMPS measurement shows that charge equilibrium was not reached Diluted s aerosol and neutralizers TSI models 3077 and 3012 in series: Charge equilibrium was reached If the aerosol is highly charged & poorly neutralized (left hand side) large errors in size distribution and concentration.

22 Mobility Particle Sizing? Aerosol Conditioner Differential Mobility Analyzer Classifier Particle Counter Produces a known charge distribution Selects particles according to electrical mobility particle size Counts size selected particles to build distribution Control hardware & software

23 Condensation Particle Counters Measurement: Single Particle Counting Particle Size Range: 2.5 nm to ~ 3 µm To Vacuum Pump To Pump Three Basic Components 1) Saturator 2) Condenser 3) Detector (Optics) Optics & Photodetector Condenser Sample Flow Saturator Lower Temp The smallest non-evaporating drop (D kelvin ) is determined by: 1) Particle surface Higher Temp 2) Supersaturation Ratio (S) Limited by Homogenous Nucleation: working vapor forms particles due to thermodynamic state Likely to occur when S > 4

24 Counting Efficiency % Efficiency Curve of CPC 50% cut point ~ 2.5 nm Particle Diameter (nm) CPC Efficiency curves affected by: 1) Instrument to instrument variation 2) Working fluid 3) Carrier gas (Niida et al 1988) Sizing Accuracy: 1) Most applications, small CPC efficiency curve differences have very little effect on accuracy. 2) Nanoparticle applications can be sensitive to efficiency curves: large numbers of particles close to the lower detection limit. 3) Can generate custom efficiency curve to use in data inversion (Liu et al 2006).

25 3776 Ultrafine Butanol CPC 3776 Specs D 50 : 2.5 nm Max Conc: 3x10 5 pt/cm 3 Aerosol Flow: 0.05 Lpm 95% Response Time High Flow: <0.8 sec Low Flow: 5 sec 25

26 Transport Losses + Mechanisms Brownian Diffusion Electrostatic Deposition Thermophoretic Effects + Recommendations Keep sample tube as short as possible all mechanisms Use grounded metallic tubes electrostatic effects Avoid temperature gradients and changes in the thermodynamic state of the aerosol (thermophoretic effects) 26

27 Diffusion Losses Example: 1 m of tubing with inner diameter of 6 mm at T = 400 K Diffusion Loss 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1 nm 5 nm Particle Size 10 nm 50 nm 100 nm 1 l/min 10 l/min 20 l/min laminar 20 l/min turbulent Flow Rate 1 nm 5 nm 10 nm 50 nm 100 nm 1 l/min 98% 26% 12% 2,50% 0,70% 10 l/min 43% 7% 3% 0,30% 0,15% 20 l/min laminar 29% 4% 2% 0,20% 0,10% 20 l/min turbulent 75% 12% 5% 0,60% 0,30%

28 Penetration Diffusion Losses 1.0 Circular Tube Penetration Efficiency Diffusion losses are size dependent Gormley and Kennedy (1949) derived an equation for circular tube penetration efficiency D = Diffusion coefficient; D = ƒ(t, Gas type, d p) ) L = Length of tube Q = Volumetric flow rate DL Q Diffusion is a stronger than gravitational forces for particle <100nm

29 Diffusion Losses SMPS Diffusion loss: 1) Sampling scheme 2) System losses through Controller platform DMA CPC Connection tubing 3) Diffusion broadening Diffusion losses increase with: 1) Increasing tubing length 2) Decreasing particle diameter 3) Increasing temperature

30 Diffusion Loss Algorithm Example Ambient Air Without correction With correction

31 Calibration Combination of bipolar diffusion charger + DMA + electrometer is a primary standard itself! Traceable parameters: DMA dimensions DMA voltage Flows Electrometer resistor Bipolar charger requirements

32 Calibration Method used by NIST to size 60 and 100nm SRM (Mulholland et al 2006 & Mulhollan et al 1991) Noted to have improved resolution over surface measurement techniques. (surface techniques designed to image nanoparticles - not designed for sizing accuracy). Vasilou from Duke Scientific (2005) studied the scanning technique using DMA for sizing PSL in the size range of 20 to 100 nm using electrosprayed PSL. Concluded: In all cases, the SMPS mean diameter fell within the uncertainty of the reference standard [TEM].

33 ISO ISO TC24 / SC 4 / WG 12 developed a new standard Published 15th May 2009 Determination of particle size distribution Differential electrical mobility analysis for aerosol particles Includes slip correction and equilibrium charge distribution What else does ISO/TC 24/SC 4 do? WG12 actually works on a standard for the calibration of CPCs against aerosol electrometers and against traceably calibrated reference CPCs (Watch out for ISO 27891!) TSI s SMPS is fully compatible with standard

34 Calibration Particle concentration standard was developed + Monodisperse 28nm colloidal silica + Known particle number concentration + Enables calculation of original number concentration in sample + Stable over >12 months + Stability testing is ongoing 28nm Concentration Standard

35 LNS Size Resolution Tri-modal silica polishing slurry TSI Model 3985 LNS Dynamic Light Scattering Laser Diffraction Volume Weighted 1.00 Dynamic Light Scattering - Volume Weighted Lognomal 20 Laser Diffraction - Volume Weighted Relative concentration Fraction of distribution (%) Particle diameter (nm) Particle diameter (nm)

36 PSL Size Resolution and Analysis Volume weighted size distribution Coefficient of Variation (CV%) as claimed by Duke Scientific and as measured by LNS Differential volume weighted concentration PSL CV (%) Claimed Measured Particle diameter (nm) Simultaneous measurement of 20, 50, and 83 nm PSL Instrument resolves each PSL size Particle diameter (nm) Measured and claimed CV of individual sizes are similar indicating no variation due to instrument

37 Sizing of Gold Nanoparticles Independent measurement of gold nanoparticles showing correlation to TEM data 40 Sizing of gold particles Particle diameter (nm) nm 20.3 nm 30.3 nm Fraction of particles exceeding size (%) Gold nanoparticles Nominal Size (nm) Claimed size Measured size Mean (nm) CV (%) Mean (nm) CV (%) < < <

38 Distinguishing particulates from dissolved residue 8e+14 Measurement of 0.1% 28nm silica particles and 1% sucrose Differential number concentration d (#/ml) / d log (D P ) 7e+14 6e+14 5e+14 4e+14 3e+14 2e+14 1e+14 2,000:1 6,700:1 20,000:1 67,000:1 200,000: Particle diameter (nm)

39 Slurry Characterization Differentiation of two batches of silica slurry with different polishing characteristics Number weighted Hydrosol size Distributions: distribution Fujimi PL4224 Good Volume vs. Suspect weighted size distribution 3.0e e+20 Differential Number Concentration d (#/cm 3 ) / dlog (D p ) 2.5e e e e e+13 Good Suspect Differential Volume Concentration d (nm 3 /cm 3 ) / dlog (D p ) 1.0e e e e e Particle Diameter (nm) Particle Diameter (nm) 2012 TSI Incorporated

40 Slurry Characterization Particle size distribution shift during circulation of a slurry containing colloidal silica Differential volume concentration d (nm 3 /ml) / d log (D P ) 1.2e e e e e e+16 Initial 10T 20T 50T 100T 197T 508T 1013T 3217T Number of Turnovers Particle diameter (nm)

41 Sizing of Macromolecules 2.0e+19 Sizing of dextran molecules Differential volume concentration d (nm 3 /cm 3 ) / d log (D P ) 1.5e e e+18 10K 21K 44K 150K 670K Particle diameter (nm)

42 Literature Baron, Willeke (2001), Wiley-Interscience, Second Edition, Aerosol Measurement Principles, Techniques, and Applications. Hinds (1998), Wiley Interscience, Aerosol Technology, 2nd Edition. Fissan et al. (1996), Aerosol Science and Technology,24:1,1 13, Experimental Comparison of Four Differential Mobility Analyzers for Nanometer Aerosol Measurements. Fuchs (1963), Geophys. Pura. Appl.,56, S. 185ff, On Stationary Charge Distribution on Aerosol Particles in a Bipolar Ionic Atmosphere. Myojo et al (2002), DMA as a Gas Converter from Aerosol to "Argonsol" for Real-Time Chemical Analysis Using ICP-MS, Aerosol Science and Technology, 36:1, Reischl et al. (1997), Aerosol Science and Technology 27, , Performance of the Vienna type differential mobility analyser at nm. Wang and Flagan (1990), Aerosol Science and Technology, 13, , Scanning Electrical Mobility Spectrometer. Knutson, Whitby (1975), Journal of Aerosol Science, 6 (6), , Aerosol classification by electric mobility: apparatus, theory, and applications.

43 Conclusions With understanding of key factors important to the accuracy of DMA sizing methods, it is possible to achieve the highest quality measurement possible. DMA voltage CPC & DMA flow Charge distribution Efficiency curve of the CPC Multiple Charge Correction DMA transfer function Scan time Working gas Diffusion loss

44 Thank You For Your Attention Acknowledgements Dr. Hans-Georg Horn Oliver Bischof Gilmore Sem Any Questions?