29 June 2012 Errata: Stochastic modeling in lithography: autocorrelation behavior of catalytic reaction-diffusion systems
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J. of Micro/Nanolithography, MEMS, and MOEMS, 11(2), 029801 (2012). doi:10.1117/1.JMM.11.2.029801
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Mack: Errata: Stochastic modeling in lithography: autocorrelation behavior of catalytic reaction–diffusion systems

This article [J. Micro/Nanolith. MEMS MOEMS 8, 029701 (2009)] was originally published online 18 June 2009 with two errors. Equation (6) for the two-dimensional reaction-diffusion point spread function is missing a 2 in the denominator. The correct equation is

2-D:RPSF(r)=-12πσD2Ei(-r22σD2),r=(x2+y2)1/2.
Also, Fig. 1 shows the numerical evaluation of the reaction-diffusion autocorrelation function for the 1-D, 2-D, and 3-D cases. Unfortunately, an error in the algorithm used to perform the 2-D and 3-D numerical convolutions needed to generate the 2-D and 3-D autocorrelation functions was in error. When performed correctly, the calculations for the 2-D and 3-D cases produce the exact same results as for the 1-D case. Thus, the 1-D curve shown in Fig. 1 is correct, and the 2-D and 3-D curves should fall exactly on top of the 1-D curve.

Likewise, Table 1 shows the results of fitting these three curves to a function. The fitting parameters obtained for the 1-D case are correct, and the 2-D and 3-D cases should be identical to the 1-D case.

Chris A. Mack, "Errata: Stochastic modeling in lithography: autocorrelation behavior of catalytic reaction-diffusion systems," Journal of Micro/Nanolithography, MEMS, and MOEMS 11(2), 029801 (29 June 2012). http://dx.doi.org/10.1117/1.JMM.11.2.029801
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KEYWORDS
Lithography

Systems modeling

Stochastic processes

3D modeling

Point spread functions

Diffusion

Convolution

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