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УДК 517.9
Two-layer Model of Reflective Ferromagnetic Films in Terms of Magneto-optical Ellipsometry Studies
Olga A. Maximova* Sergey G. Ovchinnikov^
Kirensky Institute of Physics Federal Research Center KSC SB RAS Akademgorodok, 50/38, Krasnoyarsk, 660036
Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041
Russia
Nikolay N. Kosyrev*
Kirensky Institute of Physics Federal Research Center KSC SB RAS Akademgorodok, 50/38, Krasnoyarsk, 660036
Russia
Sergey A. Lyaschenko§
Kirensky Institute of Physics Federal Research Center KSC SB RAS Akademgorodok, 50/38, Krasnoyarsk, 660036
Reshetnev Siberian State Aerospace University Krasnoyarsky Rabochy, 31, Krasnoyarsk, 660037
Russia
Received 17.11.2016, received in revised form 16.01.2017, accepted 02.02.2017 An approach to analysis of magneto-optical ellipsometry measurements is presented. A two-layer model of ferromagnetic reflective films is in focus. The obtained algorithm can be used to control optical and magneto-optical properties during films growth inside vacuum chambers.
Keywords: Magneto-optical ellipsometry, Kerr effect, two-layer model, ferromagnetic metal, reflection, growth control.
DOI: 10.17516/1997-1397-2017-10-2-223-232.
Recently it has become necessary to synthesize new materials that would be applied in spin-tronics devices. This field of study has significantly developed and it dictates the properties that materials should have in order to be used for its purposes. It is well-known that the simplest method of generating a spin-polarised current in a metal is to pass the current through a ferromagnetic material. That is why, one of the perspective materials for spintronics is a ferromagnetic/semiconductor two-layered structure [1].
§ [email protected] © Siberian Federal University. All rights reserved
In order to synthesize them and control their properties we have to use the methods that are non-destructive, precise, easy to use, applicable for in situ investigations in the high-vacuum chambers of molecular beam epitaxy. We suggest that magneto-optical ellipsometry is a technique that reflects these requirements. Magneto-optical ellipsometry usually combines the features of conventional ellipsometry and of magneto-optical Kerr effect measurements [2-6]. Applied to the sample magnetic field changes the ellipsometric parameters, this difference can be examined and used to investigate magneto-optic properties of the sample.
In this work we give detailed explanation how to analyse magneto-ellipsometric data and obtain information on magneto-optical and optical properties of the material.
1. General approach to magneto-ellipsometric data processing
Our approach is based on the analysis of a well-known equation that relates the experimental ellipsometric parameters ^ and A with complex reflection coefficients corresponding to in-plane (Rp) and out-of-plane (Rs) light polarizations [7-8]. Ellipsometric parameters ^ and A can be presented as a sum of conventional parameters and Ao measured without external magnetic field and additional ellipsometric parameters 5^ and SA that are the result of magnetic field application. We suggest to consider real and imaginary parts of these coefficients, so we mark them by ' and " respectively:
tan(^o + 5^) exp(i(Ao + 5A)) = RpR-1 = (Rp — iRp)(R'S — iR'S(1)
We are interested in magneto-optical properties of the sample. That is why it seems to be reasonable to present reflection coefficients as a sum of magnetic (subscript 1) and non-magnetic (subscript 0) summands [9-11]:
Rp = Rpp + Rps = RPo + RPi — i(RP'o + RP'i) (2)
Rs = Rss + Rsp = Rso = RSo — iR'So- (3)
This paper focuses on the case of transverse magneto-optic Kerr effect when the magnetization is perpendicular to the plane of incidence and parallel to the surface of the sample. That is why there are no magnetic summands for s-plane polarization.
From (1-3) four equations can be obtained. Two of them correspond to non-magnetic condition: _
, , / (RpoRSo + RSoRp'o)2 + (RSoRpo — Rp'oRSo)2 tan V>o = ]l -R2 + R2---> (4)
T) 2 I D"
Rso + Rso
Ac = arctan RR ~ , (5)
and two equations demonstrate the influence of an external magnetic field:
6A = A - Ac = arctan R^(Rp0 + Rpi) - R'so(R'p0 + Ki) - aQj (6)
RS0(Rp0 + Rp1) + RS0(Rp0 + Rp1)
= ^ — ^0 = arctan (F tan(^0)) — ^0, (7)
where F is a multiplier in
tan ('o + 5') = F tan 'o =
41
= tan 'M 11 + + R'p2 + 2(RoRpi + RpoRpi))(R2o + R2) (8)
(Rp0RS0 + RS0R'p0)2 + (RS0Rp0 — R'p0R's0)2
These equations do not depend on the number of layers in a sample, so can be used for every type of reflective nanostrustures models. Below, a two-layer model is presented.
2. Data processing for the case of a two-layer model
As it was mentioned above, ferromagnetic/semiconductor two-layer structures are a subject of interest nowadays. So in this chapter let us discuss a model consisting of an upper ferromagnetic layer 1 (the refraction index Ni = ni — iki), a middle non-magnetic layer 2 (the refraction index N2 = n2 — ik2) and a substrate 3 (the refraction index N3 = n3 — ik3). The light electromagnetic wave is incident from non-magnetic dielectric medium 0 (e.g. vacuum, characterized by the refraction index N0 = n0 — ik0) onto the upper layer. In the setup, a Cartesian coordinate system is defined with the x axis normal to the interfaces and pointing into the substrate from the sample surface. The y and x axis lie in the plane of incidence. We consider T-configuration (transverse) in which magnetization is z-axis directed, i.e perpendicular to the plane of incidence and parallel to the surface. So YX plane is a plane of incidence, YZ plane is a boundary plane.
For a two-layer model it is necessary to consider each interface (0-1, 1-2, 2-3) as each of them impacts the values of ellipsometric angles. The purpose of the data processing is to characterize a ferromagnetic layer.
The first step is carrying out ellipsometric and magneto-ellipsometric measurements. Here we do not focus on ellipsometric data analysis as there is a lot of research in this field [7,8,12]. So from ellipsometric measurements we can find complex refractive indices N0, Ni, N2, N3, thicknesses of both layers, while magneto-ellipsometric parameters spectra are necessary for magneto-optical properties study of a ferromagnetic layer.
Fresnel coefficients that reflect magneto-optical properties can be derived from the scattering matrix:
S = I01L1I12L2123, (9)
where Iab is an interface matrix and Lc is a layer matrix [7].
Rs = ^, (10)
(Sii)s
Rp =(Sr¥, (11)
(Sii)p
Rs = rois + ri2 S e-i2/31 + rois ri2 s r23 se^2?2 + r23 s
1 + roisri2se-i2/31 + ri2sr23se-i2?2 + roisr23se-i2(?l+?2)'
r = roip + ri2pToip e-i231 — roipr2ipr23pe-i232 + r23pToipTi2pe-i2(3l+32) (13) p 1 — riopri2pe-i231 — r2ipr23pe-i232 — riopr23pTi2pe-i2(3l+32) '
where
Toip = tioptoip — roipriop, (14)
т 12p — t21ptl2p — r12pr21p-
(15)
So, in order to process magneto-ellipsometric data the following expressions are necessary:
roip
N1 cos ф0 — N0 cos ф1 . 2QN§ sin ф0 cos ф0
- - i-
N1 cos ф0 + N0 cos ф1 (N1 cos ф0 + N0 cos ф1)2 '
r12p —
2QN2
1 sin ф1 cos ф1
N2 cos ф1 — N1 cos ф2
- - i
N2 cos ф1 + N1 cos ф2 (N2 cos ф1 + N1 cos ф2)2 '
N3 cos ф2 — N2 cos ф3
r10p
r23p лт
N3 cos Ф2 N0 cos ф1 — N1 cos ф0
+ i
r21p —
N0 cos ф1 + N1 cos ф0
N1 cos w2 — N2 cos w1
- + i
N1 cos ф2 + N2 cos ф1 (N1 cos ф2 + N2 cos ф1)2 '
N0 cos ф0 — N1 cos ф1
N2 cos фз '
2QN1 sin ф1 cos ф1 (N0 cos ф1 + N1 cos ф0)2 '
2QN| sin ф2 cos ф2
l01p
t10p —
r01S
Г12Б —
r23S
2N0 cos ф0
N0 cos ф0 + N1 cos ф1 '
N1 cos ф1 — N2 cos ф2 N1 cos ф1 + N2 cos ф2 '
N2 cos ф2 — N3 cos ф3 N2 cos ф2 + N3 cos фз '
2QN3 sin ф0 cos ф0
t12p
t21p
N1 cos ф0 + N0 cos ф1
2N1 cos ф1 N1 cos ф0 + N0 cos
2N1 cos ф1 N2 cos ф1 + N1 cos ф2
2N2 cos ф2
+ i
+ i
N1 (N1 cos ф0 + N0 cos ф1)2 '
2QN3 sin ф1 cos ф1 N0(N1 cos ф0 + N0 cos ф1)2 '
2QN3 sin ф1 cos N2(N2 cos ф1 + N1 cos ф2)2 '
2QN2 sin ф2 cos ф2
N2 cos ф1 + N1 cos ф2 N1 (N2 cos ф1 + N1 cos ф2)2 ' 2n
в1 — "T" N1 cos ф1d1, л
2n
в2 — -Г"N2 cos ф23,2, л
(16)
(17)
(18)
(19)
(20) (21) (22)
(23)
(24)
(25)
(26)
(27)
(28) (29)
where f31 and (32 are phase thicknesses of layer 1 and layer 2, respectively, d1 and d2 are thicknesses of layers 1 and 2. Subscripts 01, 12, 23 correspond to the wave propagation from medium 0 to medium 1, from 1 to 2 and from 2 to 3 respectively, while subscripts 10 and 21 correspond to the backward wave propagation. Indices r are refractive indices for the mentioned above interfaces, indices t are transmission coefficients. Angles 1 and 2 are related with (the angle of incidence) by Snell's law. Q is a magneto-optical coupling parameter that is responsible for non-diagonal elements of dielectric tensor. It means that if we know this parameter we can fully describe the dielectric permitivity, not only diagonal elements. Hereinafter we present the
i
formulae necessary for identifying Q from magneto-ellipsometric measurements. Let us rewrite (12-18) in the same manner as (2, 3):
rois = (RSo)oi — i(RSo)oi, (30)
ri2S = (RSo)i2 — i(RSo)i2, (31)
r2ís = (RSo)23 — i(RSo)23, (32)
r23p = (Rpo)23 : — i(Rpo)23 = rr'23 — i rÍ23, (33)
ro1P = (R'po)oi + (R'pi)oi — i((Rpo)oi + (Rpi)oi) = rroi — i rioi, (34)
r12P = (Rpo) i2 + (R'pi)i2 — i((Rpo)i2 + (Rpi)i2) = rri2 — i rii2, (35)
r2íP = (Rpo)23 + (Rpi)23 — i((Rpo)23 + (Rpi)23) = rf'23 — i ri23, (36)
r1oP = (Rpo)io — (Rpi)io — i((R^o)io — (Rpi)io) = rrio — i riio, (37)
r21P = (Rpo)2i — (Rpi)2i — i((Rpo)2i — (R^i)n) = rr2i — i ri2i, (38)
toip = = (Tpo)oi + (Tpi)oi — i((Tp'o)oi + (Tpi)oi) = troi — i tioi, (39)
tl2p = = (Tpo)i2 + (Tpi) i2 — i((Tpo ) 12 + (Tpi ) 12) = tr 12 — i ti 12, (40)
tiop - = (Tpo)io — (Tpi)io — i((Tp'o) i o — (Tpi) i o) = tr i o — i ti i o, (41)
t2ip - = (Tpo)2i — (Tpi)2i — i((Tp'o)2i — (Tpi)2i)= tr2i — i tin, (42)
(RSo)oi, (RSo)oi , (Rpo)oi, (Rpo)oi, Rpi)oi, (Rpi)oi correspond to R'so,R'So, Rpo, í?" í?' Rpo, Rpi,
Rpi in the model of a homogeneous semi-infinite medium, respectively [11]. Subscript 01 denotes the electromagnetic wave incidence from ambient medium 0 onto layer 1. Indices (R'so)i2, (R'so)i2, (R'po)i2, (Rpo)i2, (R'pi)i2, (R'Pi)i2 are also calculated by formulae for the model of a homogeneous semi-infinite medium, the only difference is that subscript 12 denotes the electromagnetic wave incidence from layer 1 onto layer 2 that leads to the following changes in the formulae for the model of a homogeneous semi-infinite medium: cos po ^ cos pi, cos pi ^ cosp2, sinpo ^ siny>i, ni ^ n2, no ^ ni, ki ^ k2, ko ^ ki. Likewise, indices (Rpo)io, (R'po)io, (R'pi)io, (Rpi)io describe the electromagnetic wave propagation from layer 1 to medium 0: cospo ^ cospi, sinpo ^ sinpi, no ^ ni, ko ^ ki. Indices (R'po)2i, (R'po)2i, (R'pi)2i, (R'Pi)2i correspond to the electromagnetic wave propagation from layer 2 to layer 1: cos po ^ cos p2, sin po ^ sin p2, no ^ n2, ko ^ k2. Finally, indices (R'so)23, (RSo)23, (Rpo)23, (Rpo)23, (Rpi)23, (Rpi)23 describe the electromagnetic wave incidence from layer 2 on substrate 3: cospo ^ cosp2, cospi ^ cosp3, sinpo ^ sinp2, ni ^ n3, no ^ n2, ki ^ k3, ko ^ k2.
Transmission coefficients necessary for data processing are the following:
(TP0)oi (TP'0)oi
2
2
(noni + koki )(a2 + c2) + (n20 + kl )(ab + cd)
Aí+B2 :
(n0 + k0)(ad — bc) + (niko — n0 ki)(a2 + c2)
AíTB2 :
Qi(pq + rs) — Q2(pr — sq)
(TPi)oi =2 (TP'i)oi = 2
(ni + k2)(A2 + B2)2 :
Ql(pr — sq) + Q2 (pq + rs)
(n
k2)(A2 + B2)2
(43)
(44)
(45)
2
1
where
A3 = n\a + k\c + nob + kod, (47)
B3 = kia — n\c + kob — nod, (48)
p = N (3n2ko — k3) + P (n0 — 3nokl), (49)
q = ni(Al — B32) — 2A3B3ki, (50)
r = ki (B32 — A3) — 2A3B3ni, (51)
s = N (n3 — 3nok2) — P (3n22ko — k3), (52)
a = Re(cos po), (53)
b = Re (cos p1), (54)
c = Im(cos ^0), (55)
d = Im(cos ^1), (56)
N = Re(sin p0 )a — Im(sin p0)c, (57)
P = — Re(sin p0)c — Im(sin p0)a. (58)
Transmission coefficients with subscripts 10, 12, 21 correspond to the electromagnetic wave propagation from layer 1 to medium 0, from layer 1 to layer 2, from layer 2 to layer 1, respectively. The changes in the formulae are the same as proposed for refractive indices.
Let us take into account N0 = n0 — ik0, N1 = n1 — ik1, N2 = n2 — ik2, Q = Q1 — iQ2 and compare expressions (12, 13) with (2, 3). Thus we obtain expressions for R'p0, R'po, Rp1,Rpi, R's0 and RSo in terms of numerators and denominators:
r = numeratorRso _ Re(n(Rso)) — i Im(n(Rso)) (59) denominatorRso Re(d(Rso)) — i Im(d(Rso)) '
R = Re(n(Rpo)) — i Im(n(Rpo)) (60)
po Re(d(Rpo)) — i Im(d(Rpo)) ' 1 J
R = Re(n(Rp)) — i Im(n(Rp)) (61)
p Re(d(Rp)) — i Im(d(Rp)), (6)
where n stands for numerator and d - for denominator. As a result, we have
r = Re(n(Rpo)) Re(d(Rpo)) + Im(n(Rpo)) Im(d(Rpo)) (62)
po (Re(d(Rpo)))2 + (Im(d(Rpo)))2 , ( )
= Im(n(Rpo)) Re(d(Rpo)) — Im(d(Rpo)) Re(n(Rpo)) (63)
po = (Re(d(Rpo)))2 + (Im(d(Rpo)))2 , (63)
R = Re(n(Rp)) Re(d(Rp)) + Im(n(Rp)) Im(d(Rp)) R (64)
p1 (Re(d(Rp)))2 + (Im(d(Rp)))2 po' J
'p)) Re(d(Rp)) — Im(d(Rp)) Rei (Re(d(Rp)))2 + (Im(d(Rp)))2
= Im(n(Rp)) Re(d(Rp)) — Im(d(Rp)) Re(n(Rp)) (65)
Rp1 (Re(d(R )))2 + (Im(d(R )))2 RP0, (65)
R = Re(n(Rso)) Re(d(Rso)) + Im(n(Rso)) Im(d(Rso)) (66)
so (Re(d(Rso)))2 + (Im(d(Rso)))2 , ( )
= Im(n(Rso)) Re(d(Rso)) - Im(d(Rso)) Re(n(Rso)) ( )
so (Re(d(Rso)))2 + (Im(d(Rso)))2 ' ( )
where the following notations are used:
Re(n(Rpo)) = (RPo)oi + CiRPo)i2 - ni(RPo)i2 + Lom&R'pohs - mR'Pohs)--Moi12(UKo)23 + n2(RPo)23) + (RPo)23(CiC2 - ni- Ro^fem + CmO
Im(n(Rpo)) = (Rp'o)oi + ni(RPo)i2 + CiR'o )i2 + LomfeRo^ + %(RPo)23) + + Moii2(C2(RPo)23 - n2(RP'o)23) + RoMC^ - n^) + RPo)23foni + Ci^),
Re(d(RPo)) = 1 + LomCi - Momm + C2L223 - mMi223+ + (CiC2 - ViV2)Loi23 - fam + Cin2)Moi23,
Im(d(RPo)) = Loii2ni + MomCi + C2Mi223 + n2^i223+ + (CiC2 - nin2)Moi23 + (C2ni + Cim)Loi23,
Re(n(RP)) = rroi + (Ci^ri2 - nirii2)(«i)oi - (Ci^«i2 + nirri2)(«2)oi--(rroirr2i - r«oiri2i)(C2rr23 - mri23) + (r«oirr2i + rroiri2i)(C2ri23 + n2rr23)+ + (rr23(CiC2 - nin2) - ri23(C2ni + Cin2))((«i)oi(«i)i2 - (K2)oi(K2)i2)--(r«23(CiC2 - nin2) + rT23(£im + niC2))((Ki)oi(K2)i2 + («i)i2 («2)oi),
Im(n(RP)) = rioi + (Cirii2 + nirri2)(«i)oi + (Cirri2 - nirii2)(«2)oi--(r«oirr2i + rroiri2i)(C2rr23 - n2ri23) - (rroirr2i - rioiri2i)(C2ri23 + n2rr23) + + (ri23(CiC2 - nins) + rr23(C2ni + Cin2))((«i)oi(«i)i2 - («2)oi(«2)i2) + + (rr23 (Ci C2 - ni m) - ri23 (Cin2 + niC2))((«i)oi(«2)i2 + («i) i2 («2 )oi),
Re(d(R)) = 1 - Ci(rriorri2 - riiorii2) + ni(riiorri2 + rriorii2)--C2(rr2irr23 - ri2iri23) + n2(ri2irr23 + ri23rr2i)-((«i )i2(rriorr23 - riio ri23) - («2 )i2(riiorr23 + ri23rrio))(CiC2 - nin2) + + ((«i)i2)(riiorr23 + ri23rrio) + («2)i2(rriorr23 - riiori23))(C2ni + Cin2),
Im(d(RP)) = -Ci(riiorri2 + rrwrii2) - ni(rrwrri2 - riwrii2)--C2(ri2irr23 + rr2iri23) - m(rr2irr23 - ri23«2i)-((«i)i2(riiorr23 + rriori23) + («2)i2(rriorr23 - ri23riio))(CiC2 - nim)--((«i)i2)(rriorr23 - ri23riio) - («2)i2(riiorr23 + rriori23))(C2ni + Cim),
Re(n(Rso)) = (R'so)oi + Ci(Rso)i2 - ni(Rso)i2 + Hoii2^2^)23 - m^o)23)--Joii2(C2(Rso)23 + m(R'so)23) + (Rso)23(CiC2 - m^) - (R'so)23(C2ni + C№),
(68)
(69)
(70)
(71)
(72)
(73)
(74)
(75)
Im(n(Rso)) = (R'so)oi + m(R'so )i2 + UR'Sohi + HoiniUR'Sohz + m&'sohs )+ +Jon2(&(R'soh3 - m(R'Sohs) + (R'Sohs^i& - mm) + (R'sohs&m + tim), Re(d(Rso)) = 1 + Hoii2ti - Joii2m + t2H1223 - V2J1223+ +(tit2 - mm)Hoi23 - (&m + tim)Joi23, lm(d(Rso)) = Hoii2 ni + Joii2ti + £,2-Ji223 + mHi223 + +(tit2 - mm)Joi23 + (&m + tim)Hoi23,
(77)
(78)
(79)
ti = Re(e-i231 ), (80)
ni = - Im(e-i231 ), (81)
t2 = Re(e-i232 ), (82)
n2 = - Im(e-i232 ), (83)
Loii2 = (Rpo)i2 (RPo)oi - (R'Po)i2(R'Po)oi, (84)
Moii2 = (Rpo)oi (Rpo)i2 + (R'Po)oi(R'po)i2, (85)
Li223 = (Rpo)23 (Rpo)i2 - (Rpo)23(Rpo)i2i (86)
Mi223 = (Rpo)i2 (Rpo)23 + (Rpo) i2 (Rpo)237 (87)
Loi23 = (Rpo)23 (Rpo)oi - (Rpo)23(Rpo)oi: (88)
Moi23 = (Rpo)oi (Rpo)23 + (Rpo)oi (Rpo)23: (89)
Hoii2 = (R'so)i2(R'so)oi - (R'so)i2(R'so)oi, (90)
Joii2 = (RSo)oi (RSo) i2 + (R'so)oi(R'so)i2, (91)
Hi223 = (R'so)23(R'so)i2 - (R'so)23(R'so)i2, (92)
Ji223 = (R'so)i2(R'so)23 + (R'so)i2(R'so)23, (93)
Hoi23 = (R'so)23(R'so)oi - (Rso)23(Rso)oi, (94)
Joi23 = (R'so)oi(R'so)23 + (R'so)oi(R'so)23, (95)
(ki)oi = triotroi - tiiotioi - rroirrio + rioiriio, (96)
(«2)oi = tiiotroi + triotioi - rroiriio - rioirrio, (97)
(Ki)i2 = tr2itri2 - ti2itii2 - rr2irri2 + ri2irii2, (98)
(K2)i2 = tii2tr2i + tri2ti2i - rruri2i - riurr2i. (99)
So all necessary expressions that relate measured ellipsometric and magneto-ellipsometric parameters with refraction indices, coefficients of extinction, magneto-optical coupling parameter in case of a two-layer model are obtained. The final step is giving the best fit to the experimental data by the use of the wavelength-to-wavelength Nelder-Mead minimization [13] of the
ellipsometric angles. It yields real and imaginary parts of magneto-optical parameter Q, thus information about all elements of the dielectric permittivity tensor can be obtained from the experiment.
Conclusion
To conclude, we have proposed an approach to studying two-layer nanomaterials by means of magneto-ellipsometry. The algorithm of experimental data analysis (^o, So, ^o + S^, Ao + SA) is presented. As a result, optical and magneto-optical properties can be easily and reliably characterized during films growth through the presented formulae that are to be used in the software for magneto-optical ellipsometry set-ups.
The reported study was funded by Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Region Science and Technology Support Fund to the research project 16-42-243058. The work was supported partly by the Russian Foundation for Basic Research, Grant No. 16-32-00209 mola, Grant No. 14-02-01211; the Complex program of SB RAS No. II.2P, project 0358-2015-0004; the Ministry of Education and Science of the RF (State task No. 16.663.2014); grant Scientific School 7559.2016.2.
References
[1] N.V.Volkov et al., Magnetic-field- and bias-sensitive conductivity of a hybrid Fe/SiO2/p-Si structure in planar geometry, J. Appl. Phys., 109(2011), 123924.
[2] K.Mok et al., Thickness independent magneto-optical coupling constant of nickel films in the visible spectral range, Rev. Sci. Instrum., 82(2011), 033112.
[3] K.Mok et al., Vector-magneto-optical generalized ellipsometry, J. Appl. Phys., 110(2011), 123110.
[4] K.Mok et al., Magneto-optical coupling in ferromagnetic thin films investigated by vector-magneto-optical generalized ellipsometry, Phys. Rev. B, 84(2011), 094413.
[5] G.Neuber et al., Temperature-dependent spectral generalized magneto-optical ellipsometry for ferromagnetic compounds, Rev. Sci. Instrum., 76(2005), 023910.
[6] S.Visnovsky, Magneto-optical ellipsometry, Czech. J. Phys. B 36 (1986), 625-650.
[7] R.M.A.Azzam, N.M. Bashara, Elipsometry and polirilized light, North Holland Publishing Company, New York, 1977.
[8] H.Fujiwara, Spectroscopic Ellipsometry Principles and Applications, Chichester, John Wiley & Sons, 2007.
[9] O.A.Maximova et al., Magnetic contribution to Fresnel coefficients at magneto-ellipsometric investigation, Vestnik SibGAU , 49(2013), no. 3, 212-217.
[10] O.A.Maximova et al., Features of the ellipsometric investigation of magnetic nanostructures, Journal of Structural Chemistry, 55(1964), no. 6, 1134-1141.
[11] O.A.Maximova et al., In situ magneto-optical ellipsometry data analysis for films growth control, JMMM, Available online 20 December 2016 (http://dx.doi.org/10.1016/j.jmmm. 2016.12.050).
[12] I.A.Tarasov et al., Quick ellipsometric technique for determining the thicknesses and optical constant profiles of Fe/Si02/Si(100) nanostructures during growth, Tech. Phys., 57(2012), no. 6, 1225-1229 .
[13] J.A.Nelder, A.D.Mead, A Simplex Method for Function Minimization, Computer Journal, 7(1965), 308-313.
Двухслойная модель отражающих ферромагнитных пленок для исследования тонких пленок методом магнитоэллипсометрии
Ольга А. Максимова Сергей Г. Овчинников
Институт физики им. Л. В. Киренского, КНЦ СО РАН Академгородок, 50/38, Красноярск, 660036
Сибирский федеральный университет Свободный, 79, Красноярск, 660041
Россия
Николай Н. Косырев
Институт физики им. Л. В. Киренского, КНЦ СО РАН Академгородок, 50/38, Красноярск, 660036
Россия
Сергей А. Лященко
Институт физики им. Л. В. Киренского, КНЦ СО РАН Академгородок, 50/38, Красноярск, 660036
СибГАУ им. академика М. Ф. Решетнева Красноярский рабочий, 31, Красноярск, 660037
Россия
Представлен метод анализа магнито-эллипсометрических измерений. Детально 'рассматривается двуслойная модель ферромагнитных отражающих пленок. Полученный алгоритм может использоваться для контроля оптических и магнито-оптических свойств пленок в процессе их роста в вакуумных камерах.
Ключевые слова: магнито-оптическая эллипсометрия, эффект Керра, двухслойная модель, ферромагнетик, отражение, контроль роста.
