Practical Implementation of Order Parameter Calculation for Directed Assembly of Block Copolymer Thin Films CHI-CHUN LIU, 1 GORDON S. W. CRAIG, 1 HUIMAN KANG, 1 RICARDO RUIZ, 3 PAUL F. NEALEY, 1 NICOLA J. FERRIER 2 1 Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706 2 Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706 3 Hitachi Global Storage Technologies, San Jose Research Center, 3403 Yerba Buena Road, San Jose, California 95135 Received 31 May 2010; revised 8 July 2010; accepted 9 July 2010 DOI: 10.1002/polb.22114 Published online 2 September 2010 in Wiley Online Library (wileyonlinelibrary.com). ABSTRACT: A computationalprocedure is presented to quantify the order achieved in assembled block copolymer films when no disruptive defects are present (i.e., dislocations or disclina- tions). Both simulated and real systems were used to show that sub-nm variation in the domain position, as well as the corresponding reciprocallattice vectors,can reduce the accu- racy in the quantification of the order of the system. The com- putationalprocedure in this work was based on fitting to the measured spatialocation of the domain centroids, and incorpo- rated a tolerance factor to account for domain position variation. The procedure was used to analyze the translational and orienta- tional order parameters of block copolymer films assembled on a chemicalpattern as well as their corresponding autocorrelation functions.The procedure was applied to a patterned substrate during three stages of a template forming process: an e-beamed patterned photoresist, the domains of a block copolymer directed to assemble on this pattern,and the underlying structure after lift-off.Use of the procedure demonstrated that the order of the block copolymer film could be retained in subsequent processing of the underlying template. V C 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2589–2603, 2010 KEYWORDS: block copolymers; diblock copolymers; self- assembly INTRODUCTION Thin films of block copolymers are gaining interestfor potentialapplications in advanced lithography and template fabrication. 1–8 A variety ofmethods have been developed to guide the assembly of the block copolymer morphology, such as thermal 9 and solventannealing, 10,11 electricfield alignment, 12,13 the use of chemically neutral surfaces,and topographically or chemically patterned sub- strates. 7,14–19 Recent work has shown that directed assembly of block copolymers may provide increased uniformity, pat- tern rectification, and resolution enhancement, which are especially attractive properties for patterned media or elec- tronic memory devices. 5,19–21 For such applications, retaining a high degree oforder over a large area is essentialfor accessing each individual storage cell. Hence,the ability to quantitatively analyze the extent of order of block copolymer domains assembled with different methods and materials is crucial. 9 Previousstudieshave used translational and orientational order parameters to quantify the order of thin films ofself- assembled block copolymer systems. 22–26 An order parame- ter is a normalized measure of the deviation from perfect order,with perfectorder equaling 1. The localtranslational and orientational order parameters provide a measure of the location or orientation of a crystalline domain with respect to the lattice. Autocorrelationfunctions (ACFs) can be applied to these order parameters to give more information on the large-scale order of the system. An ACF applied to the translational order parameter yields a pair-wise correlation based on the distance between points (domains, in our case) in an array, whereasan ACF applied to the orientational order parameter represents the pair-wise correlation based on the angularrotation betweenhexagonalunit cells. 25 Segalman et al. 25,26 used the translational and orientational order parameters to characterize the melting processes in a two-dimensional (2-D) layer of sphericaldomains.In the case of Harrison et al., 23,24 the orientational order parameter and corresponding correlation length were used to analyze the ordering dynamics in 2-D layers of sphericaland cylin- dricaldomains.As shown in the work ofSegalman et al. 25 and Park etal., 22 the translational order parameter proved to be a more stringent measure oforder,in some cases resulting in correlation lengths that were orders ofmagni- tude lower than the corresponding correlation lengths deter- mined from the orientational order parameter for the same system. In some of these examples, the observed lattice was highly ordered and the measured orientational order agreed, however, they measured a relatively short correlation length and decay in translational order,which caused difficulty in Correspondence to: N. J. Ferrier (E-mail: ferrier@engr.wisc.edu) Journal of Polymer Science: Part B: Polymer Physics, Vol. 48, 2589–2603 (2010) V C 2010 Wiley Periodicals, Inc. BLOCK COPOLYMER ORDER PARAMETER, LIU ET AL. 2589