Single-layer model of reflective nanostructures for magneto- ellipsometry data analysis

Transcription

1 IOP Confeence Seies: Mateials Science and Engineeing PAPER OPEN ACCESS Single-laye model of eflective nanostuctues fo magneto- ellipsomety data analysis To cite this aticle: O A Maximova et al 6 IOP Conf. Se.: Mate. Sci. Eng View the aticle online fo updates and enhancements. Related content - New tavel-time appoximations fo a tansvesely isotopic medium Alexey Stovas and Bjon Usin - Selective Cu filling of nanopoes using supecitical cabon dioxide Eiichi Kondoh, Yukihio Tamegai, Mitsuhio Watanabe et al. - Monitoing of Si Molecula-Beam Epitaxial Gowth by an Ellipsometic Method Yoshifumi Yoshioka, Tetsuya Ikuta, Toshiya Taji et al. This content was downloaded fom IP addess on 4//8 at 9:53

2 TIAA6 IOP Conf. Seies: Mateials Science and Engineeing 55 (6 3 doi:.88/ x/55//3 Single-laye model of eflective nanostuctues fo magnetoellipsomety data analysis O A Maximova,, N N Kosyev 3, S N Vanakov,3, S A Lyashchenko,3 and S G Ovchinnikov,,3 Reshetnev Sibeian State Aeospace Univesity, Kasnoyask, 6637, Russia Sibeian Fedeal Univesity, Kasnoyask, 664, Russia 3 Kiensky Institute of Physics, Fedeal Reseach Cente KSC SB RAS, Kasnoyask, 6636, Russia maximo.a@mail.u Abstact. In this wok we pesent the method of magneto-ellipsomety data analysis. Magnetoellipsomety measuements ae conducted in situ duing nanostuctues synthesis. Magnetic field is applied in configuation of magneto-optical tansvese Ke effect. Single-laye model of eflective nanostuctues is in focus.. Intoduction Magneto-ellipsomety is consideed as one of poweful eliable nondestuctive methods fo nanostuctues synthesis contol that is highly impotant fo spintonics, electonics and nanotechnology. This technique combines ellipsomety and magneto-optical Ke effect measuements. Magneto-ellipsomety has to be developed and in this wok we epot on magnetoellipsomety measuements analysis fo the case of single-laye nanostuctues study. We have developed the appoach that can be applied to investigation of eflective feomagnetic/nonfeomagnetic nanostuctues that ae a subject of inteest due to obseved spin tanspot phenomena. We offe an algoithm that yields infomation about dielectic pemittivity tenso of feomagnetic laye [], whee diagonal tenso elements ae esponsible fo efactive index and extinction coefficient, off-diagonal tenso elements ae elated to magneto-optical effects: i i( i ( Q iq i( i ( Q iq i, ( 33 i whee ε is a complex pemittivity of a medium (ε =ε ε 33, ε =-ε, eal pats ae maked by ', imaginay by '', Q=Q -iq is a popotional to magnetization magneto-optical paamete. In the nonmagnetic condition (Q= the off-diagonal tenso elements vanish. In the following, we descibe the method of intepetation of the ellipsometic and magnetoellipsometic measuements data fom the in situ setup of a magneto-optical genealized ellipsomete, which is integated into an ulta-high vacuum chambe with the electomagnet fo magnetization evesal of the sample. The key idea of this appoach and the case of the model of a homogeneous semi-infinite medium have been epoted in [] and at the 8 th Joint Euopean Magnetic Symposia (JEMS-6 [3]. Hee we epeat some of ou basic ideas and pesent developed expessions fo expeimental data pocessing fo a single-laye model of eflective nanostuctues in ode to study thei optical and magneto-optical popeties. We conside the case of electomagnetic wave incidence fom non-magnetic dielectic medium (chaacteized by the efaction index N onto feomagnetic metal (the efaction index N on substate (the efaction index N. We set the magnetization vecto to be z-axis diected, so that YX plane is a plane of incidence, YZ plane is a bounday plane. The tansvese configuation is in focus because of the design featues of high-vacuum chambe and Content fom this wok may be used unde the tems of the Ceative Commons Attibution 3. licence. Any futhe distibution of this wok must maintain attibution to the autho(s and the title of the wok, jounal citation and DOI. Published unde licence by Ltd

3 TIAA6 IOP Conf. Seies: Mateials Science and Engineeing 55 (6 3 doi:.88/ x/55//3 electomagnet that ae commonly used fo magnetization evesal. In this pape, we conside the visible light ange, as a geat amount of moden ellipsometes wok in this ange.. Ellipsomety and magneto-ellipsomety measuements data Let us denote the ellipsometic paametes in the non-magnetic condition (Q= as ψ and Δ []. In the case of magneto-ellipsometic chaacteization of the sample (Q=Q -iq the suface tansvese magneto-optical Ke effect esults in the ellipsometic angles coections δψ and δδ. Thus, the ellipsometic paametes become ψ +δψ, Δ +δδ. It means that fou independent eal-valued quantities (ψ, δψ, Δ, δδ ae measued and, as a esult, fou eal-valued quantities (ε, ε, ε, ε can be deived. To stat analysis of magneto-ellipsomety expeimental data ( and we have to wite the eal and imaginay pats of complex eflection coefficients in the basic equation of ellipsomety [4, 5]: tg( exp( ( ( i RpR S Rp ir P ( R S ir S, ( whee is the complex ellipsometic paamete, R p and R s ae complex eflection coefficients coesponding to in-plane p-polaization and out-of-plane s-polaization espectively, eal pats again ae maked by ', imaginay by ''. Accoding to mode convesion fom the p to the s polaized channel we can wite that Rp Rpp Rps R p R p i( R p R p, (3 R S R SS R sp R S R S ir S, (4 whee we have distinguished the magnetic field contibution and maked it by subscipt, nonmagnetic summands by subscipt. One can see that tansvese Ke effect yields to R s =, R s =. By substituting equations (3-4 into ( we obtain fo non-magnetic condition: tg ( R R R R ( R R R R p S S p S p p S R S R S p S p S, (5 R S R p R pr S actg, (6 R R R R while the influence of an extenal magnetic field leads to ellipsometic paametes δψ and δδ: actg F tg(, (7 R S ( R p R p ( R p R p R S R S R p R pr S actg actg, (8 ( R R R ( R R R R R R R whee F is a helpful notation: p p S p p S p S p S tg F tg tg ( R S R p ( R pr S R pr p( R S R S ( R pr S ( Rp R S Rp Rp ( R S R S ( R R R R R R R R ( R R R R R R R R p S p S S p p S p S p S S p p S. (9

4 TIAA6 IOP Conf. Seies: Mateials Science and Engineeing 55 (6 3 doi:.88/ x/55//3 3. Data analysis In Figue one can see a diagam of single-laye model, whee ambient medium, feomagnetic metal (d thickness, substate, φ, φ and φ ae the angles of incidence and efaction and elated to each othe by Snell s law. Figue. Single-laye model of eflective nanostuctues Fo a single-laye model complex efactive indices of the mateial unde study (N =n -ik ae calculated fom ψ, Δ measuements by the Nelde-Mead method. The values of N =n -ik, N =n -ik, N =n -ik ae necessay fo the following ellipsometic angles calculation. Analytical expessions fo the Fesnel coefficients that take into account the magneto-optical paamete in the off-diagonal pemittivity tenso elements wee pesented in [, 4]. It was shown that the following expessions should be used fo a single-laye model: R R p tpt p p exp( i p, ( exp( i p p exp( i S S S, ( S S exp( i N cos N cos QN sin cos p i N cos N cos ( N cos N cos N cos N cos QN sin cos p i N cos N cos ( N cos N cos N cos N cos QN sin cos p i N cos N cos ( N cos N cos S S, (, (3, (4 N cos N cos, (5 N cos N cos N cos N N cos N cos, (6 cos N cos QN sin cos 3 p i N cos N cos N ( N cos N cos t N cos QN sin cos 3 p i N cos N cos N ( N cos N cos t, (7, (8 3

5 TIAA6 IOP Conf. Seies: Mateials Science and Engineeing 55 (6 3 doi:.88/ x/55//3 N cosd, (9 whee β is phase thickness of the film. Indices p, s and p, s in expessions (, 5 and (3, 6 ae the efactive indices fo intefaces - and -, espectively. Indices t p and t p in expessions (7, 8 ae tansmission coefficients. Indices p and t p coespond to the wave popagation fom medium to medium, while p and t p to the backwad popagation. Taking into account expessions (3, 4 let us wite p, p, s, s, p, t p, t p in the same manne as the efactive indices and tansmission coefficients fo the model of a homogeneous semi-infinite medium: S ( R S i( R S. ( S ( R S i( R S. ( ( R ( R i(( R ( R i i, ( p p p p p ( R ( R i(( R ( R i i, (3 p p p p p ( R ( R i(( R ( R i i, (4 p p p p p t ( T ( T i(( T ( T t i ti, (5 p p p p p t ( T ( T i(( T ( T t i ti, (6 p p p p p whee (R s, (R s, (R p, (R p, (R p, (R p ae R s, R s, R p, R p, R p, R p in the model of a homogeneous semi-infinite medium, espectively. Subscipt denotes the electomagnetic wave incidence fom ambient medium onto laye. Indices (R s, (R s, (R p, (R p, (R p, (R p ae also calculated by fomulae fo the model of a homogeneous semi-infinite medium, the only diffeence is that subscipt denotes the electomagnetic wave incidence fom laye onto substate that leads to the following changes: cos φ cos φ, cos φ cos φ, sin φ sin φ, n n, n n, k k, k k. Likewise, indices (R p, (R p, (R p, (R p descibe the electomagnetic wave popagation fom laye to medium : cos φ cos φ, sin φ sin φ, n n, k k. Tansmission coefficients wee not involved into algoithm of data pocessing fo the model of a homogeneous semi-infinite medium. Theefoe, we epot on (T p, (T p, (T p, (T p hee: whee ( n n k k ( a c ( n k ( ab cd ( T, (7 p A3 B3 ( n k ( ad bc ( n k n k ( a c ( T, (8 p A3 B3 Q( pq s Q( p sq ( T p, (9 ( n k ( A3 B3 Q ( p sq Q ( pq s ( T, (3 ( ( p n k A3 B3 A3 n a kc nb kd, (3 B k a n c k b n d, ( ( ( p N(3 n k k P( n 3 n k, (33 q n A B A B k, (34 k B A A B n, (35 4

6 TIAA6 IOP Conf. Seies: Mateials Science and Engineeing 55 (6 3 doi:.88/ x/55//3 3 3 s N( n 3 nk P(3 n k k, (36 a Re(cos, (37 b Re(cos, (38 c Im(cos, (39 d Im(cos, (4 N Re(sin a Im(sin c (4 P Re(sin c Im(sin a (4 Coefficients (T p, (T p, (T p, (T p coespond to the electomagnetic wave popagation fom laye to medium, that leads to the changes: cos φ cos φ, sin φ sin φ, n n, k k. Let us take into account N =n -ik, N =n -ik, N =n -ik, Q=Q -iq and compae expessions (, with (, 3. Thus we obtain expessions fo R p, R p, R p, R p, R s and R s. R ((( R ( R ( R ( L M p p p p (( R ( R ( R ( M L (( L M ( M L, (43 p p p R ((( R ( R ( R ( L M p p p p (( R ( R ( R ( M L (( L M ( M L, (44 p p p R p R p, (45 R p R p, (46 R ((( R ( R ( R ( H J S S S S (( R S ( R S ( R S ( J H (( H J ( J H, (47 R ((( R ( R ( R ( H J S S S S (( R S ( R S ( R S ( J H (( H J ( J H, (48 whee the following notations ae used: L ( R ( R ( R ( R, (49 p p p p M ( R ( R ( R ( R, (5 p p p p Re(exp( i, (5 Im(exp( i, (5 J ( R S ( R S ( R S ( R S, (53 H ( R ( R ( R ( R, (54 S S S S ( i i ( i i, (55 i ( i ( i i ( i ( i i, (56 ( i i ( i i, (57 ( i ( i i ( i ( i i, (58 t t ti ti, (59 ti t ti t. (6 Thus, we have all fomulae that ae necessay fo theoetical calculation of the ellipsometic angles (-9 in case of a single-laye model. Final step is giving the best fit to the expeimental data by the use of the wavelength-to-wavelength Nelde Mead minimization of the ellipsometic angles. It yields 5

7 TIAA6 IOP Conf. Seies: Mateials Science and Engineeing 55 (6 3 doi:.88/ x/55//3 the spectal dependences of eal (Q and imaginay pats (Q of magneto-optical paamete Q. So, we have infomation about all elements of the dielectic pemittivity tenso. 4. Conclusion To conclude, we have poposed an appoach to studying single-laye nanomateials by means of magneto-ellipsomety. The algoithm of expeimental data analysis (ψ, Δ, ψ +δψ, Δ +δδ is pesented. As a esult, optical and magneto-optical popeties can be easily and eliably chaacteized duing synthesis. 5. Acknowledgements The wok was suppoted by the Russian Foundation fo Basic Reseach, Gant No mol_a, Gant No , Gant No The wok was suppoted patly by The Complex pogam of SB RAS II.P, poject , the Ministy of Education and Science of the RF (State task No К, gant Scientific School Refeences [] Sokolov A V 96 Optical Popeties of Metals (Moscow: GIFML p.3 [] Maksimova O A et al. 4 Jounal Of Stuctual Chemisty 55. No. 6 pp 34 4 [3] Maximova O, Kosyev N, Vanakov S et al. Poc of JEMS-6 (Glasgow: IOP p 7-8 [4] Maximova O A, Ovchinnikov S G, Hatmann U et al. 3 J. SibSAU Vestnik (Kasnoyask 49. No. 3 pp 7 [5] Azzam R M A and Bashaa N M 977 Ellipsomety and Polaized Light (Amstedam: Noth- Holland chapte 4 6