Jin Jwang Wu

DEPOSITION OF SUBMICRON AEROSOL PARTICLES DURING INTEGRATED CIRCUIT MANUFACTURING: THEORY

ABSTRACT Submicron (≤1μm) particle contamination can produce unacceptably low yields in the manufacture of integrated circuits. Calculations were made to predict deposition velocities of 0·01-lOμm particles, incorporating gravitational, dlffusional, and electrostatic effects. The results were summarized in equations that correlate non-dimensional deposition (Sherwood number) with convective-diffusion (Peclet number) and with electrostatics (Boltzmann and Fuchs charge distributions). These equations were used In conjunction with particle size distributions to predict particle deposition. In a companion paper |25| the predictions were shown to compare well with limited experimental data. To reduce deposition product surfaces should not be electrically charged and, where possible, these surfaces should be at higher temperatures than the ambient gas. For quality control purposes, the deposition flux predictions could serve to link the specifications of gas cleanliness with the specifications of surface cleanl...

The inversion matrix and error estimation in data inversion: application to diffusion battery measurements

Judicious selection of the measurement conditions and analysis methods to be used can make it less difficult to produce accurate data inversions in the presence of experimental error. The response (data) vector (b) of a multi-channel instrument, such as an optical particle counter or multi-stage impactor or diffusion battery, to an input distribution vector (x) can be modelled as a set of linear equations given by the vector-matrix equation b = Ax. For low resolution instruments, one of several methods of data inversion is usefully employed: simple inversion, least-squares inversion, various smoothing inversions and various non-linear approaches. One non-linear approach [Twomey, S. (1975) J. Comput. Phys.18, 188–200.] we found to be sensitive to starting conditions and to show cycling during iteration, similar to equations leading to ‘chaos’ [Wu, J. J. et al. (1989) J. Aerosol Sci.20, 477–482.]. Simple inversion, least-squares inversion and smoothing are alike in that they produce their solutions from x = Zb, where Z(i, j) are the elements of what one could call the ‘inversion matrix’, Z, a kind of transfer function. Z gives the sensitivity of the inferred values to changes (or errors) in the data values. A criterion for the best measurement instrument or measurement conditions could be the minimum largest absolute Z(i, j) or the mean absolute value or some other weighting. Propagation of error analysis indicates that another measure of Z(i, j) that would be useful would be its root mean square. The ‘condition number’ is another measure that has also been suggested [Cooper, D. W (1974) Ph.D. dissertation. Division of Engineering and Applied Science, Harvard University, Cambridge, MA, (1975) 68th Annual Meeting of the Air Pollution Control Assoc., Boston, MA; Yu, P.-Y. (1983) Ph.D. dissertation. Department of Chemical and Nuclear Engineering, College Park, MD; Farzanah, F. F. et al. (1984) Environ. Sci. Technol.19, 121–126; Hirleman, E. D. (1987) 1st Intl. Conf. on Particle Sizing, Rouen, France.]. Some comparisons of these measures are made. The inversion matrix gives the clearest indication of the relationship between the data and the results of inversion. We recommend that proposed experimental conditions should be adjusted based on inversion matrix studies in order to lessen ill-conditioning and the reliance on various data analysis methods to cope with ill-conditioned systems.

Receptor Modeling for Contaminant Particle Source Apportionment in Clean Rooms

Receptor modeling is used to apportion the contaminant particle concentrations among their sources in clean rooms through particle number concentration balances at various size intervals. The technique is demonstrated with optical particle counter data from an IBM clean room and a clean room at the University of Cincinnati. Quantitative contributions of two particulate sources to the aerosol concentration near wafer fabricating units were determined in both clean rooms. Good agreement was obtained between measured and predicted size distributions of the aerosol at the receptor sites.

Optimizing Sensitivity: True Counts Versus Background Counts for Low Concentration Measurements

Optical particle counters usually offer the option to measure smaller particles at the cost of increased background (electronic noise) counts. This can be done by adjusting the threshold d* of the counter, or a set of thresholds, or the sensitivity. We explore the trade-off between more true counts, T(d*), at a lower particle size threshold vs. more false counts, F(d*), at the lower threshold. Amplification or thresholds may be adjusted or, more simply, some channels of a multichannel instrument used while others are ignored. If no correction for mean false count rate is to be made and if the false count increases monotonically as the threshold decreases (dF/dd* < 0) and increases more rapidly than the true count (dF/dd* < dT/dd* < 0) and if we wish to limit F to a fraction of T, F ≤ kT, then measurement of lower T concentrations, in the size range near the threshold, requires raising, not lowering, the threshold. Data on false counts (measuring clean air) from an optical particle counter are presented an...