We present a model independent approach for the analysis of X-ray fluorescence yield modulated by an X-ray standing wave (XSW), that allow a fast reconstruction of the atomic distribution function inside a sample without fitting procedure. The approach is based on the direct regularized solution of the system of linear equations that characterizes the fluorescence yield. The suggested technique was optimized for, but not limited to, the analysis of periodic layered structures where the XSW is formed under Bragg conditions. The developed approach was applied to the reconstruction of the atomic distribution function for LaN/BN multilayers with 50 periods of 43 Å thick layers. The object is especially difficult to analyze with traditional methods, as the estimated thickness of the interface region between the constituent materials is comparable to the individual layer thicknesses. However, using the suggested technique, it was possible to reconstruct width of the La atomic distribution showing that the La atoms stay localized within the LaN layers and interfaces and do not diffuse into the BN layer. The analysis of the reconstructed profiles showed that the positions of the center of the atomic distribution function can be estimated with an accuracy of 1 Å.

1.
A. M.
Afanasev
and
V. G.
Kohn
,
Zh. Eksp. Teor. Fiz.
74
,
300
(
1978
).
2.
M. V.
Kovalchuk
and
V. G.
Kohn
,
Usp. Fiz. Nauk
149
,
69
(
1986
).
3.
J.
Zegenhagen
and
A.
Kazimirov
,
The X-ray Standing Wave Technique: Principles and Applications: World Scientific Publishing Company Incorporated
(
World Scientific Publishing Co., Pte., Ltd
,
2013
).
4.
S. I.
Zheludeva
 et al.,
Rev. Sci. Instrum.
63
(
1
),
1519
(
1992
).
5.
M. K.
Tiwari
,
K. J. S.
Sawhney
, and
G. S.
Lodha
,
Surf. Interface Anal.
42
(
2
),
110
(
2010
).
6.
S. K.
Ghose
and
B. N.
Dev
,
Phys. Rev. B
63
,
245409
(
2001
).
7.
S. I.
Zheludeva
 et al.,
Thin Solid Films
259
,
131
(
1995
).
8.
M. J.
Bedzyk
 et al.,
Science
241
(
4874
),
1788
(
1988
).
9.
A.
Gupta
 et al.,
Phys. Rev. B
72
(
7
),
075436
(
2005
).
10.
V. V.
Roddatis
 et al.,
J. Mater. Res.
28
(
11
),
1432
(
2013
).
11.
L.
Cheng
 et al.,
Phys. Rev. Lett.
90
(
25
),
255503
(
2003
).
12.
V.
Kohli
,
M. J.
Bedzyk
, and
P.
Fenter
,
Phys. Rev. B
81
(
5
),
054112
(
2010
).
13.
A. N.
Tikhonov
and
V. Y.
Arsenin
,
Solutions of Ill-Posed Problems
(
Winston
,
1977
).
14.
S. N.
Yakunin
,
E. M.
Pashaev
,
A. A.
Zaitsev
,
A. G.
Sutyrin
and
V. G.
Mokerov
,
Proc. SPIE
5401
,
573
(
2004
).
15.
I. A.
Makhotkin
 et al.,
J. Micro/Nanolithogr., MEMS, MOEMS
11
(
4
),
040501
(
2012
).
16.
Yu.
Platonov
 et al.,
Proc. SPIE
8076
, EUV and X-Ray Optics: Synergy between Laboratory and Space II,
80760N
(4 May
2011
).
17.
T.
Tsarfati
 et al.,
Thin Solid Films
518
,
7249
(
2010
).
18.
A. M.
Afanas'ev
and
M. A.
Chuev
,
J. Theor. Exp. Phys.
80
(
3
),
560
(
1995
).
19.
T.
Hohage
,
K.
Giewekemeyer
and
T.
Salditt
,
Phys. Rev. E
77
(
5
),
051604
(
2008
).
21.
M.
Born
and
E.
Wolf
,
Principles of Optics
(
Cambridge University Press
,
1999
).
22.
E.
Louis
 et al.,
Prog. Surf. Sci.
86
(
11
),
255
(
2011
).
You do not currently have access to this content.