US 12,175,173 B2 · Scattering measurement analysis method, scattering measurement analysis device, and non-transitory computer-readable storage medium storing scattering measurement analysis program

Abstract

Provided is a scattering measurement analysis method including obtaining a theoretical scattering intensity from a structural model that contains a lot of scatterers, wherein the obtaining of a theoretical scattering intensity includes obtaining a contribution to the theoretical scattering intensity of a pair of a scatterer “m” and a scatterer “n” existing at a distance “r” from the scatterer “m” among a plurality of scatterers by at least one of calculations in accordance with the distance “r”, the calculations including a first calculation of calculating contributions of the scatterer “m” and the scatterer “n” from respective scattering factors fm(q) and fn*(q) and a center-to-center distance rmn between the scatterer “m” and the scatterer “n”, and a second calculation of substituting the scattering factor fn*(q) of the scatterer “n” by a first representative value and substituting a probability density function of the number of scatterers existing at the distance “r” by a constant value.

A scattering measurement analysis method comprising:

measuring, by a scattering measurement unit of an X-ray scattering measurement device, a scattering intensity of scattered X-ray generated from a sample;
obtaining, by the X-ray scattering measurement device, the measured scattering intensity data through an input unit or storage unit;
obtaining, by the X-ray scattering measurement device, a theoretical scattering intensity from a structure model that consists a plurality of scatterers, the obtaining of a theoretical scattering intensity including:
obtaining, by the X-ray scattering measurement device, a contribution to the theoretical scattering intensity of a pair of a scatterer “m” and a scatterer “n” existing at a distance “r” from the scatterer “m” among the plurality of scatterers by at least one of calculations in accordance with the distance “r”, the calculations including:
obtaining, by the X-ray scattering measurement device, scattering factor fm(q) of the scatterer “m” and fn*(q) of the scatterer “n” which is representative of complex conjugate for fn(q);
obtaining, by the X-ray scattering measurement device, a probability density function ρm(r) of a number of scatterers existing at the distance “r”;
a first calculation, by the X-ray scattering measurement device, of calculating contributions of the scatterer “m” and the scatterer “n” from the respective scattering factors fm(q) and fn*(q) and a center-to-center distance rmn between the scatterer “m” and the scatterer “n”, and
a second calculation, by the X-ray scattering measurement device, of substituting the scattering factor fn*(q) of the scatterer “n” by a first representative value and substituting the probability density function ρm(r) by a constant value;
fitting, by the X-ray scattering measurement device, the theoretical scattering intensity to the measured scattering intensity data;
evaluating, by the X-ray scattering measurement device, a fitting result;
and
finishing, by the X-ray scattering measurement device, the evaluating the fitting result when the fitting result is determined that the theoretical scattering intensity fits the measured scattering intensity data,
wherein the first representative value substituting the scattering factor of the scatterer “n” is an average value of scattering factors of the plurality of scatter, and
wherein the first calculation is expressed by a following expression:
∑
m
∑
n
f
m
(
q
)
⁢
f
n
*
(
q
)
⁢
sin
⁢
qr
mn
qr
mn
,
wherein the second calculation is expressed by following Expression:
4
⁢
π
⁢
N
⁢
ρ
a
⁢
f
ave
(
q
)
⁢
f
ave
*
(
q
)
⁢
∫
r
2
⁢
sin
⁢
qr
qr
⁢
dr
,
and
wherein the theoretical scattering intensity is obtained based on the results of the first and second calculations,
where:
I (q) denotes the theoretical scattering intensity,
fm (q) denotes the scattering factor of scatterer m,
fn*(q) denotes scattering factor of scatterer n,
q denotes a magnitude of difference of wavenumber vectors of incident and outgoing waves, respectively,
rmn denotes a distance between centers of scatterers m and n,
N denotes the number of scatterers,
fave (q) denotes an average value of scattering factor fm (q),
fave*(q) denotes an average value of scattering factor fn*(q), and
ρa denotes an average number of particles per unit volume of structure model.

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Scattering measurement analysis method, scattering measurement analysis device, and non-transitory computer-readable storage medium storing scattering measurement analysis program

Life of this patent

Scattering measurement analysis method, scattering measurement analysis device, and non-transitory computer-readable storage medium storing scattering measurement analysis program

Life of this patent

Abstract

Claims4