ELSEVIER Microelectronic Engineering 46 (1999) 365-368 Analytical Model of the "Shot Noise" Effect in Photoresist* Gregg M. Gallatin and J. Alexander Liddle Bell Labs, Lucent Technologies, 600 Mountain Ave, Murray Hill, NJ 07974 Decreasing feature size implies increased sensitivity to statistical fluctuations in various process parameters such as dose and the number of relevant bonds broken during post exposure bake. Here we develop a generic analytical model which accounts for essentially all these effects. The lowest order contribution to surface roughness from the bond statistics alone are shown to be very similar to recent experimental data. The lowest order contribution to a scaling law for predicting edge roughness is also derived. 1. INTRODUCTION The push toward smaller critical dimension (CD) implies increased sensitivity to small effects. The desire to maintain throughput, leads to the requirement of minimum possible dose per fea- ture. Also, physical interactions in the exposure tools themselves which degrade image quality, such as absorption induced aberrations in photon tools and space charge effects in electron tools, generally scale with dose. Since dose corresponds to the number of actinic "particles" per unit area, the relevant statistics are Poisson, i.e., shot noise, and the relative rms dose fluctuation then scales as 1/dv/-do~. Therefore, decreasing dose increases its statistical impact on CD variation. This effect has been studied in recent years by a number of authors [1-7]. With the exception of the original work by Smith [1], most of this work has been essentially either numerical or experimental. The purpose of the present work is to develop an analytical representation of this problem by tracking the flow of the statistics through the process steps involved in exposing and develop- ing a chemically amplified resist (CAR). As might be expected, a full accounting of the details of all the relevant processes leads to a very complex and highly non-linear set of equations. Here, in order to extract information from these equations, we examine their behavior to lowest order. We will consistently indicate where we have taken just the lowest order terms from a general expression by using the standard '%--." notation. *This work was supported in part by DARPA contract MDA978-98-C-007. 0167-9317/99/$- see front matter © 1999 Elsevier Science PII: S0167-9317(99)00105-7 The overall approach used here to model dose statistics is close in spirit to the work by Smith [1], but we also include the statistics of bond break- ing which has a nontrivial impact on the variation of surface roughness with dose and post exposure bake (PEB). In fact we find that just allowing for the statistics of bond breaking and ignoring shot noise predicts behavior similar to that seen recently experimentally by He and Cerrina [7]. The statistics of bond breaking are implicitly in- cluded in the work by Scheckler, et.al. [3] and by Nakamura, et. al., [5], but th.ey seem not to have realized the full impact that these statistics by themselves have on surface roughness. 2. PROCESS FLOW The process steps considered are the generic ones for a CAR. First, exposure produces a latent image in the form of a density distribution of re- leased "acid" molecules. This is followed by the PEB in which the "acid" molecules perform a ran- dom walk, "deprotecting" crosslinks, i.e. break- ing bonds in a positive resist or by "protecting", i.e., making bonds or crosslinks in a negative re- sist. For concreteness we consider just the pos- itive resist case here. The final step is develop- ment wherein the dissolution rate is a function of the local density of broken or "deprotected" crosslinks. The exposure statistics can be derived by tak- ing the probability for one actinic "particle" to cross a fundamental area element A in time dt to be given by dt/T where 7 is a scale factor with units of time. The probability of having n "par- B.V. All fights reserved.