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PII: S0040-6090(97)01020-1
Copyright © 1998 Elsevier Science S.A. All rights reserved


        Letter


    Analysis of X-ray reflectivity curves of non-Gaussian surfaces

G. Vignauda <#orfa>, * <#cor*>, A. Gibauda <#orfa>, F. Parisb <#orfb>,
D. Ausserréb <#orfb> and G. Grübelc <#orfc>

a Université du Maine, URA 807 CNRS, Faculté des Sciences Le Mans Cedex
72017, France
b Université du Maine, URA 509 CNRS, Faculté des Sciences, Le Mans Cedex
72017, France
c ESRF, Experimental division, Avenue des Martyrs, BP 220, Grenoble
Cedex F 38043, France

Received 30 September 1997; accepted 30 October 1997. Available online
28 July 1998.


    Abstract

Surfaces of symmetric diblock copolymers thin films exhibiting
non-Gaussian distribution of height are studied by X-ray reflectivity
and atomic force microscopy (AFM). When deposited on a silicon
substrate, the surface is essentially flat and its roughness may be
described by a Gaussian distribution of height. Upon annealing, films
operate a two-dimensional phase transformation and form islands at the
free surface having height and size that evolve as a function of
annealing time. The height probability function cannot be represented by
a Gaussian distribution anymore, and the question that arises is how to
take into account the morphology of such surfaces in the reflectivity
calculations. In a first approach, we show that the height distribution
function derived from AFM measurements is directly transferable to
analyze X-ray reflectivity curves according to a formalism that we
present. In a second part, we determine the height distribution function
from a fit to the observed reflectivity.

Author Keywords: X-ray reflectometry; Thin film structure and
morphology; Polymers; Elastomers and plastics

Index Terms: Plastic films; Block copolymers; Atomic force microscopy;
Annealing; Probability density function; Phase transitions; Morphology;
Elastomers; Thin films; Surface roughness; X ray reflectivity


    Article Outline

1. Introduction
2. Conclusion

References



Enlarge Image
</science?_ob=MiamiCaptionURL&_method=retrieve&_udi=B6TW0-3T87PJ2-1&_image=figFig.1&_ba=1&_user=875668&_coverDate=06%2F22%2F1998&_rdoc=1&_fmt=summary&_orig=browse&_srch=%23toc%235548%231998%23996769998%2315826!&_cdi=5548&_acct=C000046981&_version=1&_urlVersion=0&_userid=875668&md5=297b9264d50c863015a8bd18bfcf468e>
(72K)
Fig. 1. AFM image of relief domains at the free surface of PS/PBMA
diblock copolymer films annealed for 6 min (a) and 4 h (b) at 150°C.

Enlarge Image
</science?_ob=MiamiCaptionURL&_method=retrieve&_udi=B6TW0-3T87PJ2-1&_image=figFig.2&_ba=2&_user=875668&_coverDate=06%2F22%2F1998&_rdoc=1&_fmt=summary&_orig=browse&_srch=%23toc%235548%231998%23996769998%2315826!&_cdi=5548&_acct=C000046981&_version=1&_urlVersion=0&_userid=875668&md5=0891847a77a5797a3bfca35b4804999a>
(14K)
Fig. 2. Height probability function extracted from the AFM measurements
on PS/PBMA copolymer films annealed for 6 min (a) and for 4 h (b) at
150°C. Note the appearance of the peak at 600 Å after 4 h of annealing.

Enlarge Image
</science?_ob=MiamiCaptionURL&_method=retrieve&_udi=B6TW0-3T87PJ2-1&_image=figFig.3&_ba=3&_user=875668&_coverDate=06%2F22%2F1998&_rdoc=1&_fmt=summary&_orig=browse&_srch=%23toc%235548%231998%23996769998%2315826!&_cdi=5548&_acct=C000046981&_version=1&_urlVersion=0&_userid=875668&md5=b0d89a42c93bb55f615de68392740b17>
(7K)
Fig. 3. Calculated (solid line) and observed reflectivities (dotted
line) of PS/PBMA copolymer film annealed for 6 min (a) and for 4 h (b)
at 150°C. The calculated curves begin at Qz=0.05 Å-1 because of the
limitation fixed by the Born approximation. The calculations have been
done by entering the height probability extract from the AFM
measurements shown in Fig. 2 <#figFig.2>.

Enlarge Image
</science?_ob=MiamiCaptionURL&_method=retrieve&_udi=B6TW0-3T87PJ2-1&_image=figFig.4&_ba=4&_user=875668&_coverDate=06%2F22%2F1998&_rdoc=1&_fmt=summary&_orig=browse&_srch=%23toc%235548%231998%23996769998%2315826!&_cdi=5548&_acct=C000046981&_version=1&_urlVersion=0&_userid=875668&md5=5538e1203055a308fc771b0fd74149af>
(8K)
Fig. 4. (a) Height probabilities extracted from the AFM measurement
compared to the functional form (solid line) used in the calculation.
(b) Calculated (solid line) and observed reflectivities (dotted line) of
a PS/PBMA copolymer film annealed for 4 h at 150°C (compare Fig. 4
<#figFig.4>b and Fig. 3 <#figFig.3>b).


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* <#bcor*>Corresponding author.

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