DMA Size-Selection and Electrostatic Deposition of Particle Size Standards Down to 10nm

Transcription

1 DMA Size-Selection and Electrostatic Deposition of Particle Size Standards Down to 10nm Ben Hunt, William Dick, Zeeshan Syedain MSP Corporation 1 AAAR IM.4

2 Presentation Outline Particle Deposition System Overview DMA Size Selection Particle Deposition Theory DMA Inversion Prediction of Deposited Size Distribution Recipe-Deposit Correlation Results Peak Prediction Test NanoSilica TM and PSL Deposits Wafer Surface Scanning Characterization Conclusions 2 AAAR IM.4

3 Particle Deposition System (PDS) Applications Produce Calibration Standards for Scanning Surface Inspection System (SSIS) Tools (KLA-Tencor and Hitachi) Bare Si Wafers Film Wafers (e.g., Poly, Oxide, Nitride) Produce Challenge Wafers for Cleaning Tools (Particle Removal Efficiency Studies) 3 AAAR IM.4

4 Principle of Operation 4 AAAR IM.4

5 DMA Inversion Goal: predict size distribution entering deposition chamber Requires knowledge of size distribution before DMA Transfer Function, Ω nd For Q c = Q m, Q a = Q s Ω nd = 1 Z p = Z p < 1 Z p Z p Transfer function is broadened by diffusion 1 Increases with decreasing particle size 5 AAAR IM.4 1 (Stolzenburg and McMurry, 2008)

6 DMA Inversion (cont d) Concentration Measured by CPC 1 R i = 0 G(i, x) N(x)dx, i = 1,2,... n G(i, x) = Ω d (i, ν, x) η trans. η CPC φ ν dx ν=1 Response Matrix (n x 1) R = GN Kernel function (n x m) Size distribution (m x 1) DMA Transfer Functions overlap Channel-particle size correspondence is not 1:1 1 (Hagen and Alofs 1983) 6 AAAR IM.4

7 Twomey-Markowski Inversion Procedure Outline 1. Calculate Initial Guess Distribution Assuming constant size distribution across width of kernel 2. Twomey Algorithm 1 Compare measured responses (R i ) to calculated responses (y i ) and calculate weighting factor Apply weighting factor to size distribution guess Continue until: SIGMA = 1 n 3. Smoothing n i=1 R i y i k E i 2 < 1 Smooth solution using Markowski algorithm 2 Calculate solution roughness 4. Repeat Steps 2-3 until change in roughness is less than 2.5% or SIGMA < 1 1 (Twomey, 1975), 2 (Markowski, 1987) 7 AAAR IM.4

8 Simulated Data Tests 8 AAAR IM.4

9 Comparison to MSP WPS Commander TM Software Electrosprayed 39nm SiO 2 Electrosprayed 33nm SiO 2 9 AAAR IM.4

10 Peak Diameter Shifts Range of particle sizes can be selected from a suspension D rec : DMA-selected diameter (in Deposition Recipe) D dep : Peak diameter of deposited distribution Off-peak DMA classification can result in deposited peak diameter shift 10 AAAR IM.4

11 Prediction of Deposited Distributions Distribution entering deposition chamber: N dep d p = N d p φ ν η trans. Ω d ν=1 D rec = D peak Magnitude of D rec -D dep is a function of atomized size distribution width 24nm SiO 2 atomized with 3480 TSI Electrospray 11 AAAR IM.4

12 Recipe-Deposit Correlation Relationship between Recipe diameter and peak diameter of deposited size distribution 9 diameters are chosen d rec = d peak d peak ± 1.5 FWHM d peak ± FWHM d peak ± (2 3) FWHM d peak ± (1 3) FWHM 3 rd order polynomial fit 3 2 D dep = ad rec + bd rec + cd rec + d 12 AAAR IM.4

13 Peak Prediction Test Deposit 4 wafers 4 Particle Suspensions NIST SRM 1964 (60.4nm) MSP NanoSilica TM NS-0060A (61.1nm) MSP NanoSilica TM NS-0100A (100.0nm) NIST SRM 1963a (101.8nm) 12 spots, 2K particles per spot 4 spots D rec = D peak, 4 spots D rec < D peak, 4 spots D rec > D peak Inspect wafers with Surface Scanner (KLA-Tencor SP2) Compare predicted peak sizes to SP2-measured sizes 13 AAAR IM.4

14 SP2 Non-Linearity Characterize SP2 by depositing range of PSL Sizes (49-105nm) SP2 response is often non-linear with particle size Correction must be applied to SP2 size measurements 14 AAAR IM.4

15 SP2 Non-Linearity (cont d) Assume linear response from 49nm 65nm and nm 5 measurement Avg. NS size PSL size 0.90 Necessary to correct NanoSilica TM SP2 sizes 15 AAAR IM.4

16 Predictions NIST SRM 1964 (60.4nm PSL) Dep. No. D rec D dep Recipe (D peak D rec ) Deposited (D peak D dep ) RFWHM ~ 19% Negligible shifts for broad size distributions 16 AAAR IM.4

17 NIST SRM 1964 Inspection Results 17 AAAR IM.4

18 Results NIST SRM 1964 (cont d) Dep. No. D rec SP2 Measured Size SP2 Corrected Size Recipe D peak D rec Predicted D peak D dep SP2 corrected D peak D dep Difference nm nm Large error for spots 9-12 most likely due to SP2 non-linearity PSL Correction (linear fit for 49-65nm) may be inadequate 18 AAAR IM.4

19 Dep. No. D rec Predictions NS-0060A (60nm SiO 2 ) D dep Recipe D peak D rec Deposited D peak D dep RFWHM ~ 4% NS-0060A is narrower than NIST SRM1964 More dramatic shift for off-peak selections 19 AAAR IM.4

20 NS-0060A Inspection Results 20 AAAR IM.4

21 Results NS-0060A (cont d) Dep. No. D rec Avg SP2 Measured Size SP2 Corrected Size Recipe D peak D rec Predicted D peak D dep SP2 corrected D peak D dep Difference nm nm Measured shifts (D peak D dep ) are in predicted direction Symmetric predicted/measured difference 21 AAAR IM.4

22 Predictions NIST SRM 1963a Dep. No. D rec D dep Recipe D peak D rec Deposited D peak D dep RFWHM ~ 6% Fitted distribution (normal) used for predictions Secondary peak is most likely doubly-charged particles Inverted distribution results in artificially low D rec -D dep shift 22 AAAR IM.4

23 NIST SRM 1963a Inspection Results 23 AAAR IM.4

24 Dep. No. D rec Results NIST 1963a (cont d) Avg SP2 Measured Size SP2 Corrected Size Recipe D peak D rec Predicted D peak D dep SP2 corrected D peak D dep Difference nm nm Shifts are in predicted direction More data needed to account for SP2 non-linearity 24 AAAR IM.4

25 Predictions NS-0100A (100nm SiO 2 ) Dep. No. D rec D dep Recipe D peak D rec Deposited D peak D dep RFWHM ~ 3% Large shift due to narrow size distribution 25 AAAR IM.4

26 NS-0100A Inspection Results 26 AAAR IM.4

27 Dep. No. D rec Results NS-0100A Avg SP2 Measured Size SP2 Corrected Size Recipe D peak D rec Predicted D peak D dep SP2 corrected D peak D dep Difference nm nm SP2 instability most likely cause of offset 13-Sep-2013: NPT Size = 100.6nm, SP2 Size = 90.6nm 19-Sep-2013: NPT Size = 100.0nm, SP2 size = 91.7nm 2300NPT peak size repeatability using NanoSilica TM ~ 0.2nm 27 AAAR IM.4

28 Conclusions Magnitude of D rec -D dep shift is a function of size distribution width Prediction of deposited peak shift is within 1.5nm of measured peak shift for all cases Accuracy can be improved by repeated wide-range measurements to characterize SP2 NanoSilica TM and PSL 28 AAAR IM.4

29 Acknowledgements and References Thanks to: Chris Libby (MSP Corporation) NanoSilica TM poster: 8NM.5 Thursday Oct. 3 12:15PM Sources: Alofs, D. J., and P. Balakumar. "Inversion to Obtain Size Distributions with Measurements with a Differential Mobility Analyzer." Journal of Aerosol Science 13, no. 6 (1982): Baron, Paul A., and Klaus Wilileke. Aerosol Measurement: Principles, Techniques, and Applications. New York: Wiley, Bowen, B. D., S. Levine, and N. Epstein. "Fine Particle Deposition in Laminar Flow Through Parallel-plate and Cylindrical Channels." Journal of Colloid and Interface Science 54, no. 3 (1976): Gormley, P. G., and M. Kennedy. "Diffusion from a Stream Flowing Through a Cylindrical Tube." Proceedings of the Royal Irish Academy 52A (1949): Hagen, D. E., and A. Alofs. "Linear Inversion Method to Obtain Aerosol Size Distributions from Measurements with a Differential Mobility Analyzer." Aerosol Science and Technology 2, no. 4 (1983): Igushi, T., and H. Yoshida. "Investigation of Low Angle Laser Light Scattering Patterns Using the Modified Twomey Iterative Method for Particle Sizing." Review of Scientific Instruments 82 (2011): Kandlikar, M., and G. Ramachandran. "Inverse Methods for Analyzing Aerosol Spectrometer Measurements: A Critical Review." Journal of Aerosol Science 30, no. 4 (1999): Knutson, E. O., and K. T. Whitby. "Aerosol Classification by Electric Mobility: Apparatus, Theory, and Applications." Journal of Aerosol Science 6, no. 6 (1975): Markowski, Gregory R. "Improving Twomey's Algorithm for Inversion of Aerosol Measurement Data." Aerosol Science and Technology 7, no. 2 (1987): Stolzenburg, M., and P. McMurry. "Equations Governing Single and Tandem DMA Configurations and a New Lognormal Approximation to the Transfer Function." Aerosol Science and Technology 42, no. 6 (2008): Stolzenburg, Mark. An ultrafine aerosol size distribution measuring system. PhD Thesis, Minneapolis, MN: University of Minnesota, Twomey, S. "Comparision of Constrained Linear Inversion and an Iterative Nonlinear Algorithm Applied to the Indirect Estimation of Particle Size Distributions." Journal of Computational Physics 18, no. 2 (1975): Voutilainen, A. Statistical Inversion Methods for the Reconstruction of Aerosol Size Distributions. PhD Thesis, Finland: University of Kuopio, Wang, S. C., and R. C. Flagan. "Scanning Electrical Mobility Spectrometer." Aerosol Science and Technology 13, no. 2 (1990): Wang, X. Optical Particle Counter (OPC) Measurements and Pulse Height Analysis (PHA) Data Inversion. PhD Thesis, Minneapolis, MN: University of Minnesota, Wiedensohler, A. "An Approximation of the Bipolar Charge Distribution for Particles in the Sub-Micron Size Range." Journal of Aerosol Science 19, no. 3 (1988): AAAR IM.4