Resonance enhancement of x rays in layered materials: Application to surface enrichment in polymer blends B. N. Dev* and Amal K. Das Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India S. Dev † European Molecular Biology Laboratory Hamburg Outstation, c/o Deutsches Elektronen-Synchrotron, Notkestrasse 85, 22603 Hamburg, Germany D. W. Schubert GKSS Forschungszentrum, Max-Plank-Strasse, 21502 Geesthacht, Germany M. Stamm Institut fu ¨r Polymerforschung Dresden e.V., Hohe ` Strasse 6, 01069 Dresden, Germany G. Materlik Hamburgersynchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron, Notkestrasse 85, 22603 Hamburg, Germany Received 21 October 1999 Resonance enhancement of x rays of both odd and even orders has been observed in a thin polymer blend film of polystyrene PS and polybromostyrene (PBr x S) spin cast on a smooth Au layer on a silicon substrate. The x-ray intensity enhancement has been measured by detecting fluorescence from the Br atoms in the PBr x S component of the compatible polymer blend. Analysis of the Br K fluorescence has yielded the PBr x S distribution in the polymer blend layer in agreement with a PS surface enrichment model. PS is largely enriched at the free surface of the polymer layer and partially enriched at the underlying interface. I. INTRODUCTION A variety of physical phenomena occurs when x rays are incident at glancing angles on flat surfaces of materials. These phenomena include total external reflection, 1 interfer- ence fringes in reflection from layers on a substrate, 2 and the formation of evanescent 3,4 and standing waves. 5 All these phenomena have been utilized for the characterizations of surfaces, interfaces, and thin films. For thin-film preparation, among other techniques, spin coating is widely used in the semiconductor industry. 6,7 Spin-coated polymer layers on solid substrates have been extensively studied by x-ray reflectometry. 8,9 Here we demonstrate the resonance en- hancement of x-ray intensity in such layers and describe its usefulness for the study of polymer layers and other layered materials in general. Resonance enhancement effects have been observed un- der glancing incidence conditions in thin films on a substrate. These are of two different varieties—one below the critical angle of the top layer in a thin-film waveguide structure 10 and the other above the critical angle. 11,12 Wang et al. 11 ob- served the resonance enhancement effect in a lipid multilayer film, prepared by the Langmuir-Blodgett LB technique, in- corporating a heavy atom layer approximately at the middle of the LB layer during preparation. They observed only odd order enhancement peaks. Here we report on our observa- tions of both odd and even order resonance enhancement in a polymer-blend layer, prepared by the usual spin coating on a gold-coated silicon substrate. The polymer-blend layer con- sists of polystyrene PS and polybromostyrene (PBr x S). We use the notation PBr x S for a statistical copolymer of poly ( p -bromostyrene-stat-styrene, which consists of statistically alternating monomers of para-bromostyrene at molar con- centration x and of styrene at molar concentration (1 -x ). The experiment involves x-ray reflectivity measurement with the simultaneous detection of Br K  fluorescent x rays. Both odd- and even-order enhancements are manifested as peaks in the Br K  fluorescence yield. Analysis of the fluorescence yield has been utilized to extract the depth distribution of PBr 0.06 S, which shows a surface and interface enrichment of the PS component of the polymer blend. This distribution could not be determined from standard x-ray reflectivity measurements because of the negligible electron density dif- ference between the two components in the polymer blend. II. THEORY We give a brief theoretical background for the resonance enhancement process. We mainly follow the formalisms given by Parratt 13 and de Boer 12 for the reflectivity and then give the expression for the field intensity. A. Reflection from a multilayer system If all interfaces are parallel in a multilayer system Fig. 1, a plane electromagnetic wave of frequency  in a medium j at a position r can be written as E j  r =E j  0  exp i   t -k j • r , 1 where E j (0) is the field amplitude at the top of the j th layer. PHYSICAL REVIEW B 15 MARCH 2000-II VOLUME 61, NUMBER 12 PRB 61 0163-1829/2000/6112/84627/$15.00 8462 ©2000 The American Physical Society