This article was downloaded by:[Fyzikalni ustav AV CR]On: 31 July 2007Access Details: [subscription number 780637501]Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Integrated FerroelectricsAn International JournalPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t713618055

Far infrared and Raman spectroscopy of ferroelectricsoft mode in SrTiO3 thin films and ceramicsJan Petzelt a; Tetyana Ostapchuk a; Ivan Gregora a; Susanne Hoffmann bc;Johannes Lindner de; David Rafaja f; Stanislav Kamba a; Jan Pokorny a; ViktorBovtun a; Viktor Porokhonsky a; Maxim Savinov a; Přemysl Vaněk a; IvanRychetský a; Vratislav Peřina g; Rainer Waser bca Institute of Physics, Acad. Sci. Czech Rep., Praha 8, Czech Repb IFF,Research Center Julich, Julich, Germanyc Institut für Werkstoffe der Elektrotechnik,RWTH Aachen, Aachen, Germanyd LMPG-INPG-ENSPG-UMR CNRS PB46, St. Martin d'Hères, Francee AIXTRON AG Kackertstr, Aachen, Germanyf Faculty of Mathematics and Physics, Charles University Prague, Praha 2, Czech

Repg Nuclear Physics Institute, Acad. Sci. Czech Rep., Re u Prahy, Czech Rep

Online Publication Date: 01 January 2001To cite this Article: Petzelt, Jan, Ostapchuk, Tetyana, Gregora, Ivan, Hoffmann, Susanne, Lindner, Johannes, Rafaja,David, Kamba, Stanislav, Pokorny, Jan, Bovtun, Viktor, Porokhonsky, Viktor, Savinov, Maxim, Vaněk, Přemysl,Rychetský, Ivan, Peřina, Vratislav and Waser, Rainer (2001) 'Far infrared and Raman spectroscopy of ferroelectric softmode in SrTiO3 thin films and ceramics', Integrated Ferroelectrics, 32:1, 11 - 20To link to this article: DOI: 10.1080/10584580108215673URL: http://dx.doi.org/10.1080/10584580108215673

PLEASE SCROLL DOWN FOR ARTICLE

Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf

This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction,re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expresslyforbidden.

The publisher does not give any warranty express or implied or make any representation that the contents will becomplete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should beindependently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings,demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with orarising out of the use of this material.

© Taylor and Francis 2007

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

0 2001 OPA (Owseas Yublirhers Aiwcialion) N V Pubhched by Iscme under the

Cordon and Breuch Science Publishers imprint. Printed i n Mala!\ia

Far Infrared and Raman Spectroscopy of Ferroelectric Soft Mode in SrTi03 Thin Films

and Ceramics

JAN PETZELTa, TETYANA OSTAPCHUKa, IVAN G R E G O R A a ,

SUSANNE HOFFMANN~, JOHANNES LINDNER~*,

DAVID RAFAJA~, STANISLAV KAMBA~, JAN POKORN+,

MAXIM SAVINOV~, P ~ M Y S L V A N ~ K ~ , IVAN RYCHETSK?~. VIKTOR BOVTUNa, VIKTOR POROKHONSKYi,

VRATISLAV PEkINAe and RAINER WASERb

'Institute of Physics, Acad. Sci. Czech Rep., Nu Slovunce 2, 18221 Pruha 8, Czech Rep, bIFE Research Center Jiilich, 0-52425 Julich, Germany; Institut fiir

Werkstoffe der Elektroterhnik, RWTH Aachen, D-52056 Aachen, Germany, 'LMPG-INPG-ENSPG- UMR CNRS PB46,38402 St. Martin d'H2res. France,

dFaculty of Mathematics and Physics, Charles Universih, Prague, Ke Karlovu 5. 121 16 Pruha 2, Czech Rep and e_Nuclear Physics Institute, Acud. Sci. Czech

Rep., 25068 Redu Prahy, Czech Rep

(Received Murch 15. 2000)

The ferroelectric soft mode behaviour was studied in several SrTiO3 (ST) films on sapphire substrates using far infrared (FIR) transmission measurements and in the bulk ST ceramics using Raman and FIR reflectivity measurements down to 15 K. The recently established dra- matic differences in softening and soft mode width compared to single crystal behaviour were confirmed in all the cases. Clear evidence of polar cluster appearance in the pure hulk ceramics indicates that the main reason for the observed differences in thin films are inhomo- geneities due to the appearance of polar clusters or even a macroscopic ferroelectric transi- tion at about 130 K in the case of well oriented injection MOCVD film.

Keywordst ferroelectric soft mode; far infrared and Raman spectroscopy: SrTiO3 thin films and ceramics; microwave properties; polar clusters

* Present address: AIX'IRON AG Kackertstr. 15 - 17D - 52072 Aachen, Germany

1703 1/1 I

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

12/[704] JAN PETZELT et al.

INTRODUCTION

Recently, an enormous effort has been exerted to analyze and elucidate the dramatic differences observed among the dielectric properties of various thin ST and (Ba,Sr)Ti03 (BST) films and bulk materials [l-71 The always observed lower permittivity and higher losses in the case of films represents the main limitation of their use in DRAMS and microwave integrated circuits, The best investigated is the B% 7Sro ?Ti03 composition used for room-temperature applications, where the effects of non- stoichiometry, misfit strain from the substrate and interphase dead layer of lower permittivity were analyzed separately [6,7]. All these factors were shown to play an important role influencing dramatically the low- frequency permittivity. The last important issue, whose influence was not yet isolated from other effects, is the film granularity. It was studied only in the case of pure bulk BT ceramics with the grain size down to 40 nm where it was shown that a thin nonferroelectric, temperature independent low-permittivity layers can model well the grain boundaries for explaining the permittivity dependence on the grain size [8].

Much less is known about the separate influence of the above mentioned factors on the dielectric behaviour in pure ST films, but it is observed that particularly at low temperatures the differences among various films and bulk materials are tremendous [ 1-51, The complicating feature is the antiferrodistortive structural transition at 105 K and particularly the quantum paraelectricity in single crystals below about 37 K where the permittivity increase saturates at a very high value of more than 20 000 [9]. However, pure ST is a relatively convenient object to study the dynamic dielectric response because no dielectric dispersion appears in single crystals up to 10'' Hz and, unlike BT, the ferroelectric soft phonon mode is well underdamped in the whole temperature range [lo-121. Recently, some of us studied the FIR transmission of several ST films and have shown that the soft phonon softening is blocked in the low temperature range (particularly below the structural transition) at about 60 cm" and the soft mode response remains extremely broad in the whole temperature range [12-141. These features have been confirmed very recently also by FIR ellipsometry on a high-quality epitaxial film [ 151 Raman spectroscopy on the same film has revealed polar clusters activating the forbidden IR active modes [ 161. Several other recent papers report on low-temperature ferroelectricity in ST films revealed by permittivity maxima at low temperatures and sometimes even hysteresis loops [4,6,17]. A very recent detailed thermodynamic theory by Pertsev et al. [ 181 revealed that even weakly biaxially strained (due to misfit with the

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

SrTiO3 THIN FILMS AND CERAMICS r70s1113

substrate), single domain epitaxial ST film should undergo a ferroelectr~c transition at low temperature, irrespective of the strain sign (for both compressive and tensile stresses).

In this work we have continued our FIR transmission measurements to study the soft mode behaviour in ST films of different origins and thicknesses. To investigate separately the effect of grain boundaries on the dielectric response, we studied also a bulk dense ST ceramics using IR reflectivity, Raman spectroscopy and dielectric properties including 36 GHz waveguide line measurements. Even in this case we surprisingly revealed polar clusters dramatically growing on cooling and soft mode response dramatically different from that in single crystals To our knowledge, this is the first spectroscopic study of a bulk ST ceramics Some preliminary data have been already published [ 141.

EXPERIMENTAL

Four films were studied, three prepared by chemical solution deposition (CSD) [ 19-2 I ] and one by injection MOCVD technique [22]. The CSD films were grown on (1 T 02) sapphire substrates. The precursor solution consisted of Sr-propionate and Ti-tetra-butoxide stabilized with acetylacetone dissolved in a mixture of propionic acid and 1-butanol. The solution was diluted to a concentration of 0.1 molar to obtain a single layer thickness of approximately 9 nm. After the spin-on process each layer was crystallized at a temperature of 750°C for 5 min in oxygen. The final films were post-annealed at 8OOoC for 1 h in oxygen. We investigated two stoichiometric SrTiOJ thin films with thicknesses of 157 nm and 477 nm (sample No. 1 and 2, respectively) and one non-stoichiometric film of 180 nm thickness with a SriTi ratio of about 0.83 (sample No.3). The microstructure was columnar with the mean column diameter of about 60 nm. The thickness and stoichiometry was determined using Rutherford Back Scattering, the good stoichiometry of the sample No.1 was also confirmed from the stress free lattice parameter by the XRD analysis, which perfectly agreed with the ideal single crystal one. The films exhibit a polycrystalline perovskite structure with a preferred ( 1 10) orientation except for the sample No. 1, which was without preferred orientation. The XRD analysis using Bragg-Brentano symmetrical and parallel-beam asymmetrical geometry has detected a tensile stress of 1.5 GPa in the sample No. 1 and about 1 GPa in the sample No.3.

The MOCVD film (sample No.4) was deposited at 800°C in a vertical MOCVD reactor on a (0001) sapphire substrate. XRD on a triple

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

14/[7061 JAN PETZELT et (11.

crystal difiactometer with rotating anode generator (Rigaku) has detected a very good (1 11) orientation parallel to the (0001) axis of sapphire. Due to misfit of the lattices, the epitaxy is broken at long distances. The resulting microstructure consists of columnar blocks mutually rotated by 60". The mean disorientation within blocks is only about 8' Unlike the CSD films, the slightly smaller lattice parameter 0.3902 nrn indicates a small compressive stress.

The ST bulk ceramic samples were prepared by a conventional mixed-oxide route [23] starting from high-purity SrC03 (Selectipur, Merck, Darmstadt, FRG) and fine grained Ti02 powder (TM-I, Fuji, Koygo, Japan). The powders were mixed in a cyclohexanolic suspension for 1 h, ball milled for 3 h and subsequently calcined at 1050°C for I8 h. The formation of perovskite phase was checked by XRD. Cold-pressed cylinders of SrTiOB were sintered at 1380°C for 7h. The single-phase samples exhibit a density of about 5.05 g/cm3 what equals to 98.8% of the theoretical density. The stoichiometry of the samples was adjusted to S r l . ~ L , ~ T i 1 . ~ ~ 1 0 3 by mixing of the right amounts of the precursor powders. RBS analysis confirmed the good resulting stoichiometry. The mean grain size of the ceramics of around 1 - 2 pm was determined from SEM analysis of polished samples. The symmetrical and asymmetrical X R D experiments have confirmed negligible inhomogeneous strain, but revealed a small stress-free lattice parameter gradient at the surface (from the bulk value of 0.903 to surface value of 0,906 nm) which could be caused by a surface deficiency of oxygen. This effect was observed on both the optically polished as well as freshly chemically etched surface. The concentrations of impurities of the SrTi03 ceramic samples were determined by means of ICP-AES analysis. Concentrations of heterovalent impurities (e.g. Al, Fe, K, Na, Nb) are specified to be less than 0.015 mol%. Homovalent impurities of Ba (320 ppm) and Ca (550 ppm) originate from the SrC03 precursor powder. Additionally, a slight contamination with approx. 0.015 mol% Si, 0.01 1 mol% Y and 0.21 mol % Zr is caused by the milling process.

The IR and FIR measurements were performed with Bruker IFS 11 3v Fourier spectrometer and evaluated using the standard fitting procedure to obtain the dielectric response hnction [ 12,241. The temperature dependent Raman spectra of the polished ceramics were taken using Ar' laser Coherent INOVA 90 and Jobin Yvon T64000 spectrometer with CCD and photon counting detector in a pseudo back-scattering geometry and the full spectra will be published elsewhere [25]. Preliminary micro- Raman scans have shown that the Raman signal was homogeneous within the sample and did not depend on the depth within several pm from the

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

SrTiO? THIN FILMS AND CERAMICS (707 I/ I5

sample surface (the effective penetration depth in the conventional Raman set up was estimated to about 5 pm using the measured extinction coefficient of 120 cm”). All the spectral features to be discussed were also found on the chemically etched surface RF dielectric measurements were performed with HP4192-LF impedance analyzer. For the microwave measurements at 36 GHz the impedance method for the section of a shorted rectangular waveguide was used in the temperature range 300 --

I00 K. Plate-shaped samples filling the full cross-section of the waveguide were inserted into the end of the shorted waveguide. DSC measurements using a Perkin-Elmer DSC 7 calorimeter have not detected any specific heat anomaly connected with the structural phase transition, which, however, was detected on a ST single crystal

. , j 200 100 0

J 1

2ou 0 0 50 100 150 200 250 300

TEMPERATURE (K)

FIGURE I . Temperature dependences of the soft mode frequencies, strengths and dampings of ST films on sapphire (film numbers see text).

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

16/[708] JAN PETZELT et al.

RESULTS

In FIGURE 1 we show the temperature dependence of the fitted soft mode parameters for all the films. For the film No. 4 the data are only preliminary, because for technical reasons we have not measured the bare substrate at low temperatures yet. Therefore the data for the damping and dielectric strength are not given For the film No. 1 an additional weak mode around 30 cm-' was added to improve the fit at low temperatures, We show only its frequency, its dielectric strength being around 200 In agreement with previous data [ 12- 151 the soft-mode frequency remains above 50 cm-' and heavily damped in the whole temperature range. In the sample No. 4 a clear minimum of the frequency was found near 130 K indicating a possible ferroelectric transition

WAVENUMBER (cm I )

10000

1000

100

10

300 K 150 K

-

- - 1

0 1 0 100 200 300 400 500 600

WAVENUMBER (cm ') 0

FIGURE 2. Reduced Raman spectra and dielectric loss spectra evaluated from FIR reflectivity measurements at selected temperatures

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

SrTiO, THIN FILMS AND CERAMICS (7O9]/17

In FIGURE 2 we show the reduced (by the Bose-Einstein factor) Raman spectra and dielectric loss spectra evaluated from the fits to reflectivity measurements. For this fitting procedure, the low-frequency permittivity data were included showing a typical Curie-Weiss increase with deviations below about 100 K and saturation near 10000 below 15 K Our 36 GHz data show no dispersion (above 100 K) compared to 100 kHz ones, but tan6 of about 0 05 independent of temperature, which is much higher than in single crystals The Raman spectra consist of a complex mixture of the first and second order features (in the cubic phase

15o i -.......mi

-i : .

m : m i ..

TO 8

c 0 0

0 0 0 i CM (overdamped) 0 , 1 . 1 . ' , ' I ' I ' l 0 50 100 150 200 250 3(

TEMPERATURE (K)

FIGURE 3 . Temperature dependences of low-frequency modes in ST ceramics evaluated from Raman and FIR reflectivity measurements.

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

1 X/[7 101 JAN PETZELT et al.

the first order spectra are forbidden) and their full discussion will be presented elsewhere [25]. However, it is clear that all the main three 1R modes (soft mode, 171, 546 cm-') are well visible in the low temperature Raman spectra with their intensity decreasing to room temperature, evidencing the presence of polar phase in our ceramics.

Whereas the polar modes have traces seen up to room temperature, the hard R-point modes (at 145, 229, 448 cm") indicating the structural transition appear only below -132 K. The low temperature spectra are dominated by a strong mode near 40 cm which we assign to the structural soft-mode component of the E, symmetry strongly coupled with the ferroelectric soft mode component of E, symmetry, allowed only in a polar phase. The temperature dependences of the main mode frequencies below 300 cm" with the mode assignment are plotted in FIGURE 3. A good agreement between the first order Raman and IR modes is seen. The low-frequency IR data are somewhat influenced by the quality of the polished surface which was verified by room temperature measurements on the etched surface. It gave a better fit without the week mode at 71 cm-' which might be therefore a surface feature, in analogy to the well known and studied surface layers in ST single crystals [26].

1

DISCUSSION

Let us first discuss the ceramics. It is clear that the forbidden IR modes are seen from room temperature and their strengths increase exponentially on cooling. This should be distinguished from the new modes from the R- point of the Brillouin zone appearing below the structural transition which is here shifted up to 132 K. Their strengths follow the theoretically expected proportionality to the order parameter squared [25, 271. The full assignment of all the observed modes and discussion of the temperature behaviour will be published elsewhere [ 2 5 ] .

The ST ceramics is sufficiently stoichiometric, pure, dense and unstrained at room temperature to exclude these factors as a possible cause of the appearance of polar clusters. The additional micro-Raman measurements have proven that the observed spectra describe the bulk properties, even if minor spectra changes (both IR and Raman) can be caused by the surface treatment of the sample (quality of polishing, etching; best quality is shown by etched surfaces). Therefore the main reason for the different behaviour compared to single crystals in the cubic phase remains the presence of grain boundaries. Their pronounced influence was studied in BT ceramics by Frey et al. [8]. Unlike BT, to

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

SrTiOj THIN FILMS AND CERAMICS 17 1 11/19

explain the observed features one has to assume that a narrow region near grain boundary is polar in the case of ST and broadens progressively on cooling. This could be understood through the coupling with the paraelectric soft mode in the bulk of the grains [25]. The existence of polar grain boundaries can be caused by charged defects diffised into the grain boundaries, as very recently discussed by Vendik and Ter- Martirosyan [28]. According to these authors, however, the built-in electric fields from these defects should prevent the polarization reversal so that the ceramics is not supposed to be ferroelectric, even if permittivity vs. temperature maxima might be observed as well as hysteresis loops due to migration of defects at low frequencies

It seems clear that, in analogy to the bulk ceramics, the grain boundaries may play an important role in the dielectric behaviour of thin films. They may be the main reason of the soft mode broadening due to local inhomogeneities and the strange temperature dependences due to coupling with the structural soft mode In addition to it, the biaxial strains due to the misfit with the substrate may easily cause the ferroelectricity, as calculated by Pertsev et al. [18]. It should be taken into account that our IR wave probes the films with the electric field parallel to the plane of the film so that the measured soft mode is sensitive to the appearance of ferroelectricity with P, in the plane, and the effect of an interface dead layer on the measured dielectric response is negligible. Therefore a direct comparison with the measured low-frequency dielectric properties is impossible. Nevertheless, our soft mode frequency behaviour indicates that at least in the sample No.4 the in-plane ferroelectricity sets in at about 130 K. This agrees with the theoretical estimate [I81 which predicts an appearance of P, in the plane of the film at a comparable temperature in an ideal but compressively stressed film.

Acknowledgements The authors acknowledge the assistance of Ch. Ohly with the thin film processing. Furthermore, we want to thank A. Jouck for preparing the bulk samples and G. Wasse for metallography and microscopical studies. We appreciate the support of H. Lippert and M. Michulitz (ZCH, FZ Juelich) in performing the chemical analysis. This work was supported by the Grant Agency of the Czech Rep. (project No.202/98/1282) and Acad. Sci. Czech Rep. (project No. AlO10918).

References [ I ] H.-Ch. Li, W. SI, A.D. West and X.X Xi, Appl. Phw. k t t . 73,464 (1998). 121 M. Lippmaa, N. Nakagawa, M. Kawasaki, S. Ohashi, Y. Inagurna, M. Itoh, H. Koi-

numa. Appl. Phys. Left. 74,3543 (1999).

Dow

nloa

ded

By:

[Fyz

ikal

ni u

stav

AV

CR

] At:

08:1

8 31

Jul

y 20

07

2047 1 21 JAN PETZELT e l al.

L. Ryen, E. Olsson, L.D. Medsen, X. Wang, C.N.L. Edvardsson, S.N. Jacobsen, U. Helmersson, S. Rudner, L.-D. Wernlund, J. Appl. Phys. 83,4884 (1998).

I). Fuchs, C.W. Schneider, R. Schneider, H. Rietschel, J. Appl. PhyJ. 85,7362 (1999).

H. Ota, Sh. Migita, S.-B. Xiong, H. Fujino, Y. Kasai, Sh. Sakai, Jpn. J. Appl. Phys. 38, L1535 (1999).

T.M. Shaw, Z. Suo, M. Huang, E. Liniger, R.B. Laibowitz, J.D. Baniecki, Appl. Phys. Len. 75,2129 (1999).

S.K. Streiffer, C. Basceri, C.B. Parker, S.E. Lash, A.I. Kingon, J. Appl. Phys. 86,4565 (1999).

M.H. Frey, Z. Xu, P. Han, D.A. Payne, Ferroelectrics 206207,337, 1998.

K.A. Miiller, H. Burkard, Phys. Rev. B 19,3593 (1979).

A.S. Barker, Jr., andM. Tinkham, Phys. Rev. 125, 1527 (1962).

K. Kamaras, K.-L. Barth, F. Keilmann, R. Henn, M. Reedyk, C. Thomsen, M. Cardona, J. Kircher, P.L. Richards, J.-L. Stehle, J. Appl. Phys. 78, 1235 (1995).

I. Fedorov, V. Zelezn?, J. Petzelt, V. Trepakov, M. Jelinek, V. Trtik, M. EeGanski, V. Studnizka, Ferroelectrics 208-20!4 41 3 (1998).

V. klezni, J. Petzelt, K. Kgmmer, J. KO,: Phys. SOC. 32, S1615 (1998).

J. Petzelt, T. Ostapchuk, S. Karnba, I. Rychetsky, M. Savinov, A. Pronin, S. Hoffmann, R. Waser, J. Lindner, Proc. EMF-9, to appear in Ferroelectrics.

A.A. Sirenko, C. Bernhard, A. Golnik, A.M. Clark, J. Hao, W. Si, X.X. Xi, Nature, in press.

A.A Sirenko, LA. Akimov, J.R. Fox, A.M. Clark, H.-Ch. Li, W. Si, X.X. Xi, Phys. Rev. Lett. 82,4500 ( I 999).

B.M. Gol'tsman, V.V. Lemanov, A.I. Dedyk, L.T. Ter-Martirosyan, S.F. Karmanenko, Phys. Solid State 38, 1368 (1996).

N.A. Pertsev, A.K. Tagantsev, N. Setter, Phys. Rev. B 61, R825 (2000).

S. Hoffmaun, R. Waser, J. Europ. Ceram. SOC. 19,1339 (1999).

U. Hasenkox, S. Hoffmann, R. Waser, J. of Sol-Gel Science and Technology 12,61 (1 998).

S. Hoffmann, U. Hasenkox, R. Waser, C. L. Jia, K. Urban, Mar. Res. SOC. Symp. Pmc. 474,9 (1997).

F. Felteu, J.P. Senateur, F. Weiss, R. Madar, J . Phys. IY Coll. C5, Suppl. J. Phys. II, 5,

R. Waseir, T. Baiatu, K.-H. Hardtl, J. Am. Ceram. SOC. 73, 1645 (1990).

V. Zelezni, I. Fedorov, J. Petzelt, Czechoslovak J. Phys. 48,537 (1998).

J. Petzelt et al., to be published.

R. Wang, Y. Zhu, S.M. Shapiro, Phys. Rev. Lett. 80,2370 (1998).

J. Petzelt, V. Dvofik, J. Phys. C: SolidState Phys. 9, 1587 (1976).

O.G. Vendik, L.T. Ter-Martirosyan, J. Appl. Phys. 87, 1435 (2000).

C5-1079 (1995).