- Email: [email protected]
Study of amorphous thin films of (Ti, Nb)O2 solid solutions by X-ray absorption at the Ti K edge
0022.3697189 53.00 + 0.00 0 1989 Pergamon Press plc
J. Phys. Chew. So/ids Vol. 50. No. 12. pp. 1211-1220. 1989 Printed in Great Britam.
STUDY OF AMORPHOUS THIN FILMS OF (Ti, Nb)O, SOLID SOLUTIONS BY X-RAY ABSORPTION AT THE TiK EDGE F. PICARD-LAGNPL,~
B.
PouMELLEct and R. CORTES$
jURA D-0446, Laboratoire des Composes non-stoechiometriques, Bat. 415, Universite Paris&d, 91405 Orsay Cedex, France fCNRS, Laboratoire Physique des Liquides et Electrochimie, ESPCI, 10, Rue Vauquelin, 75005 Paris, France (Received 29 March 1989; accepted 13 July 1989)
Abstract-As the (Ti, Nb)O, amorphous thin films cannot be prepared under a self-supported form, we have recorded the X-ray reflectivity. A new program which allows extraction of the X-ray absorption from the reflectivity is briefly described. The correction of the anomalous dispersion effect is effective, particularly near the edge within 200eV. Hence, it has allowed a comparison between the amorphous layers and the crystalline analogues for which the X-ray absorption has been recorded by transmission. In the amorphous state, the TiO, group is smaller than in the crystalline state because of the relaxation of the crystallographic constraints. The oxygen coordination octahedron is almost regular in the films. On the other hand, in both cases, an electron transfer takes place from Nb to Ti. Keywords: Amorphous
material, thin films, (Ti, Nb)O,, X-ray absorption, Ti K edge.
1. INTRODUCTION Amorphous Ti, _JNb,02 solid solutions (0 < x ,< 1) exhibit interesting electrical properties: the resistivity in the amorphous range is low and close to that of the high temperature crystalline phases [l]. This feature is rather scarce in amorphous oxides. It can be explained by the absence of antiferromagnetic coupling in the amorphous state which gives rise to a high conductivity. In order to interpret the electron transport properties in the amorphous phases, information about the electronic density of states or the local structure around the metallic atoms is useful and has led us to begin a study of the X-ray absorption fine structures. A previous X-ray absorption study carried out on related crystalline solid solutions [2] at the titanium K edge brought the following information: the chemical shift of the Ti K edge spectra indicates a partial electronic transfer between 3d Ti and 4d Nb. This implies that the levels of titanium and niobium are nearly at the same energy (the energy difference is of the order of 0.1 eV). Analysis of the prepeaks shows a decrease of the crystal field splitting when the niobium content increases. This is related to screening by the d electrons and the increase of the oxygen-metal bond length. Finally, the change of the shape of the Ti spectra with changing niobium content is due to a continuous modification around the titanium in going from TiOz to NbOz and can be interpreted in terms of disordered solid solutions. The aim of this paper is to show how the structural disorder related to the amorphous state modifies the
above conclusions. Hence, analysis of the XANES at the Ti K edge will bring information about changes in the electronic density of states and analysis of the EXAFS changes about the neighbourhood of the titanium atom, especially the metallic neighbourhood which governs the electron transport properties. 2. EXPERIMENTAL
The method of sample preparation is described in [3]. Films were obtained by RF sputtering of oxide targets in an argon atmosphere. The first idea was the preparation of 10-20 pm thick films in order to record the absorption spectra by transmission. However, mismatch of the thermal expansion coefficient between the layer and the substrates did not allow one to obtain self-supported samples. Consequently, we decided to use a few 1000 h; thick films deposited on silica or on float glass substates. Then, the absorption related spectra were recorded by reflection or electron detection. An extended description of the X-ray reflection spectrum technique (ReflEXAFS technics) can be found in [4]. The relevant parameter is the glancing angle which ranges from 2 to 10 m rad at the Ti K edge. Smoothness of the surface is also required. This question will be analysed in [S] where the program that computes the absorption from the reflectivity data is described. The electron detection method is described in [6]. The photon beam strikes the sample surface at a 45”
1211
5 (Kapton or NaCl).
1212
F. PICARD-LAGNEL et al.
angle. The extracted electrons ionize the helium atoms. A cathode, placed perpendicular to the beam and kept at a potential of 100 V, collects the ions. In this case, the quality of the sample surface is not important; moreover the recorded signal is proportional to the absorption. These experiments were useful in order to check whether the absorption extraction procedure from the reflectivity measurements was correct or not. Spectra were recorded at Lure, Orsay, at the Ti K edge (_ 4975 eV) with a Si (3 11) monochromator and glass mirrors for harmonic rejection. The slit entrance was 100pm wide in the ReflEXAFS configuration and 1 mm in the electron detection method. An initial investigation in the laboratory was made to record the reflectivity vs the glancing angle RE(0) at constant energy. This enables one to check the sample surface quality and the density of the layer (at 8028 eV for example [7]) or to compute the initial critical angle (i.e. 0, at 4900eV). Then, R,(E) spectra were recorded from 4900eV up to 5500eV for various values of 0/O,. ranging from 0.2 to 0.9.
beginning of the EXAFS one, up to 200 eV from the edge. Specifically, the greatest alteration occurs at the edge where the first maximum shows up. As a matter of fact, the spectrum recorded under the smallest glancing angle is the least distorted and approximates the true absorption; but, in that case, noise becomes important because the XAS modulation decreases with angle [7] whereas the absolute reflectivity increases. Therefore, it is necessary to correct the X-ray reflectivity spectra so that the comparison between different samples be valid. 3.1.2. The solution. The computation of the correction is obtained by the inversion of the Fresnel equation (1) giving the reflectivity R(B
’
E) _ (s!n 8 - u+)~+ a2 - (sm 8 + ~2~)~+ al
with ai = -!- ((sin2 Q - 0:)’ + 4p2)* + (4p2)“’ 4 + (sin’ 0 - Qf)li2
3. DATA
TREATMENT
3.1. Computation of the absorption from the reflectivity spectra 3.1.1. The problem. As a rough estimate, a reflectivity spectrum vs energy has the same shape as an absorption spectrum, except that the edge is reversed and values of the reflectivity range between 0 and 1. However, the shape of a reflectivity spectrum depends on the glancing angle. For the sake of clarity, in Fig. 1, normalized spectra are displayed (the EXAFS part from 5200 up to 5500 eV is the same for all the spectra). An increase of 6 gives rise to an enhancement of the whole XANES spectrum and of the
R(E)-R(4950) 3 R(5200LRI49501 :;-..._
Fig.
1. Dependence
of the normalized glancing angle.
reflectivity
on the
where 8 represents the glancing angle, 0, the critical angle, E the energy, h and c are the usual constants; the absorption b and the dispersion 6 are related to the refractive index n by n = 1 - 6 - @I. Hence, the reflectivity depends on the energy through /? and 6
R(Q,E) = Rut 836). The inversion on /I leads to b = fi(0,6, R). R and 0 are known but the whole determination of p requires the knowledge of 6 at each energy. Now 6, especially the anomalous dispersion, is often unknown. This difficulty is overcome by the fact that p and 6 are related by the Kramers-Kronig transformation. Therefore, it is possible to determine b by iterative computation, provided some constants such as the normal dispersion curve are imposed. The flow diagram of the program is given in the Appendix. Details of the procedures will be supplied in [5] but are available from [8]. The program is named JOGGING II. 3.1.3. The ejkiency. Figure 2 shows the efficiency of the method when the full dispersion curve is taken into account. As in all computational procedures containing integral transformations, the curve is noisy at the part where the correction is large. Nevertheless, it is clear that the absorption spectrum is well restored when it is compared with curve (b) which has been obtained on the same sample by the electron detection method.
Amorphous
thin films of (Ti, Nb)O,
1213
solid solutions Ti-0 L .::.
3r
..
:
?;i
’
b
a
4 Distance
4950
5000 Energy
(eV)
-
3.2. Treatment of the EXAFS
signal
3.2.1. Foreword. As a result of the superposition of the metal-oxygen and the metal-metal shells in the Fourier transform, it was impossible to extract experimental values for the phases and amplitudes of the EXAFS signal. On the other hand, the previous analysis of the crystalline TiO, EXAFS has shown that the theoretical values of Teo et al. [9] are not very applicable to these compounds. Therefore, in this paper, we discuss only the Fourier transforms and not the fits. We shall go further in the future by recording the polarized spectra. Indeed, this method allows one to cancel the Ti-Ti shell parallel to the c-axis. 3.2.2. Observations. The insertion of a smoothing procedure on the EXAFS signal before the Fourier transform improves its readability. Nevertheless, when the target atom is very diluted in the absorbing bulk, this procedure is going to be inoperative. This effect is shown in Figs 7 and 8, specifically for x = 0.8, when the Fourier transform of the ReflEXAFS spectrum is compared with one of the electron detection spectra: the first peak relative to the metal-oxygen shell is almost the same in both spectra whereas differences are appreciable for larger radii; because these spectra were recorded from the same sample, the differences arise from the noise which is greater in the ReflEXAFS method than in the electron detection one. Lastly, we have observed that no correction is required for the weak EXAFS modulations. On the other hand, concerning the metal-oxygen shell, the first oscillations are rather large and, in this case, the dispersion effect is active and implies a distortion of the first peak in the Fourier transform.
-
Fig. 3. Fourier transform of TiO, EXAFS signal: the full curve is relative to the film (~9= 0.9 0,) and the dotted one to the crystalline sample.
Fig. 2. Illustration of the efficiency of the dispersion correction method: curve (a) obtained from the reflectivity with only a normal dispersion correction; curve (a’) is for the full
dispersion correction; curve (b) is obtained on the same sample by the photoelectron detection method.
(A)
4. ABSORPTION
4.1.
SPECTRUM
ANALYSIS
XANES
4.1.1. TiO, . Despite the drastic preparation conditions used, the TiOz films were partially crystalline [3]. In fact, the edge (specifically for 0 = 0.8 0,) exhibits the feature of a crystalline sample, i.e. well structured prepeaks, bump in the middle of the edge and three peaks after the edge. The comparison of the Fourier transforms between crystalline TiO, and the film confirms this fact (Fig. 3). The second and third neighbours are similarly distant although the disorder leads to less separated bands. On the contrary, the first shell radius is shorter in film than in the crystal, i.e. by ~5 x lO-=A.
4950
5000 Energy
Fig. 4. TiO, film absorption spectra t7 = 0.28,. and 0.80, (smoothing
(eV) for two glancing angles: window = 2.3 eV).
F.
1214
PICARD-LAGNELet
Figure 4 shows the absorption spectra for two glancing angles: 0 = 0.20, and 0.88,. A shift of the main maximum (relative to the prepeak) is clearly seen and corresponds to a variation of the titaniumoxygen shell distance. Using Natoli’s relation [lo] and the coefficient published in [ll], a shortening of 6 x 10m2A from 0.8 to 0.28, is deduced. Besides, the smaller the glancing angle, the smaller the X-ray penetration depth. Therefore, this titanium-oxygen distance variation probably arises from a larger disordered layer at the film surface. 4.1.2. Ti, _xNb,02(x # 0). XANES spectra are displayed in Fig. 5 [Fig. 5(b) is from a previous study [2]]. The main differences between the two phases are clearly perceptible: -firstly, the magnitude of the prepeak transitions, i.e. the A, intensity, is independent of x for the amorphous films where the modulation disappears for the crystalline solid solutions; -secondly, the modulations after the edge are weaker for the amorphous phases and seem to be dependent on the niobium content. Particularly, the C, feature has almost disappeared and for x = 0.8, only one C peak seems to be present. Quantitative information is available from the analysis of the second derivative spectra in Fig. 6 and Table 1. The A, peak shifts from TiO, to x = 0.8 by about 0.6 eV. This value corresponds to the one previously observed in the crystalline analogues (0.7 eV) [2]. The A,-A, difference seems to be almost constant around 3.8 eV but the A, transition is rather weakly defined. The B, C and D features do not shift appreciably for x # 0 indicating that the Ti coordina-
al.
tion octahedron does not change much in size and shape, contrary to the crystalline phases. 4.2. EXAFS analysis In the absence of a good table of phases and amplitudes, changes in distance were measured by the shifts of the maxima of the imaginary part in the Fourier transform. Figures 7-9 show the Fourier transforms of the amorphous films recorded by reflection, by electron detection and of the crystalline solid solutions recorded by transmission. At a first glance, compared with the titaniumoxygen peak amplitude (i.e. we assume six oxygen neighbours in the first shell), we see a decrease of the second and third peak representative of the metallic neighbours, either in the films or in the crystalline samples. However, the decrease or the complexity of the 2-3 A part of the Fourier transform is larger in the amorphous films. 4.2.1. Titanium-oxygen distance. From Fig. 7 or Fig. 8, a sudden variation of the Ti-Q distance (3.3 x 10e2 A) is detected from x = 0 to x = 0.3 and then the change is small from x = 0.3 to x = 0.8 (i.e. < 1.7 x 10e2 A). From Fig. 9, a reverse behaviour is observed: the Ti-O distance increases by about 5 x 10e2A. On the other hand, a comparison of Figs 7-9 for x around 0.5 yields a reduction in the size of the coordination octahedron by about O.lLO.12 8, from the crystalline to the amorphous state. 4.2.2. Ti-Ti distance. As mentioned above, the Ti-Ti contribution disappears progressively as the niobium content increases. This is observed either for
(b)
Energy
( eV)
-
5000
4950
4960
4970
4980 4990 Enorgy(w) -4
5000
500
Fig. 5. Ti K edge XANES spectra for films (a) and crystalline samples (b) [smoothing window = 2.3 eV for (a) and 2.1 eV for (b)].
Amorphous
thin films of (Ti, Nb)O,
1215
solid solutions
titanium on one side and a niobium neighbour on the other side. Hence, a superposition of the incoming waves from the two metallic atoms is expected. In order to determine the resultant signal, we performed a simulation of the EXAFS part with the following classical formula: kX(k) = $
A(k)exp(-202k2)
x exp -2 f sin(2kR + 4(k))
‘V
(
0.45
0.3
0,03
1
0
Energy Fig. 6. Second derivatives
(eV)
of the spectra
shown in Fig. 5(a).
the amorphous films or the crystalline samples (follow peaks denoted A, B, C). Therefore, because the crystalline phases exhibit the same phenomenon, this cannot be explained by the structural disorder above but by the Nb-Ti substitutional disorder which takes place in both phases. In Fig. 9, disappearance of the A peak between x = 0.2 and x = 0.4 is observed. This peak is representative of the metallic neighbours along the c-axis. In this direction, for x = 0.3, the mean configuration consists of a central titanium atom surrounded by a
>
with A(k) and 4(k) expressed by the analytical forms from [9]. (N.B. the curved wave correction would not change the conclusions drawn below as the signal taken into account here is for k > 4 A-‘.) The results are shown in Fig. 10. In Fig. 10(a), the Ti contribution appears at R = 2.54 %, (instead of the crystallographic distance R = 2.96 A) with a magnitude of 50; in Fig. IO(b) the Nb backscatter contribution is shifted less and appears at R = 2.68 A with almost the same magnitude. Lastly, in Fig. IO(c) the full contribution exhibits two less wide peaks, one at 2.29A with a magnitude of 23 and another one at 2.81 8, with a magnitude of 30. This implies that both signals are partly in phase opposition and never separated. Moreover, a simulation performed on the third shell (Fig. 11) exhibits the same phenomenon; but it is worth noting that, if it appears at 3.14 8, for the pure Ti contribution, it splits into a peak at 2.91 A with a magnitude of 34 and at 3.42 8, with a magnitude of 44. Therefore, a part of the third shell signal (for R = 2.91 A) IS mixed with the second shell signal which appears at R = 2.81 A. This precludes any computation of each component separately and leads eventually to a consideration of the whole signal between 2~ R <4A. Thus, we have explained the disappearance of the A peak in Fig. 9, the appearance of the C peak at the same time and the broadening of the B peak. This stands for the crystalline samples but also for the amorphous layers, although, in this last case, the structural disorder smoothes the structure. 5. CONCLUSION
In spite of the problem encountered above, we have deduced some interesting information about the structure of amorphous (Ti, Nb)02 solid solutions by X-ray absorption.
Table 1. Energy peak positions of the features in Fig. 6 x/peak
A,
Al
B
c
TiO, x = 0.3 x = 0.45 x = 0.6
4966.8 4966.4 4966.2 4966.2
4970.4 4970.4 4970.2 4069.6
4975.8 4976.2 4976.6 4976.2
(C,) 4982.6 (C,) 4987.2 4983.2 4983.2 4983.2
F. PICARD-LAGNEL et al.
1216
125
4
distance
yi)
Fig. 7. Fourier transforms of the EXAFS signal recorded by the ReflEXAFS method on the amorphous films.
From the energy shift of prepeak AZ. we deduce that a partial electron transfer from Nb to ‘Ii takes
place, as was the case in the crystalline analogues [ 121. The edge exhibits simpler structures in the amorphous layers: this indicates that the coordination octahedron is almost regular. This is proved by the study of the polarized Ti K edge in TiOz [13]. Moreover, the examination of both the XANES structures and of the EXAFS titanium-oxygen signal yields the conclusion that the TiO, octahedron does not change much but does decrease slightly in size (-2 x IO-* A) when the niobium content increases. This behaviour is completely different in the crystalline case for which the octahedron is distorted with two long distances and increases in size (f5 x 10e2 A). For s e 0.8, the difference in titanium-
oxygen distances between the two phases amounts to about 0.1 A. As a matter of fact, it is understandable that the amorphism which leads to an isotropic state gives rise to regular octahedra but it is difficult to understand the decrease in its size with the Nb content. In the crystalline phase, the TiO, octahedron is held extended and the NbO, one compressed by the crystalline forces. On the contrary, in the amorphous state, bending or dangling bonds allow a relaxation of the coordination sphere, thus the size should be independent of its surroundings. We expected that metal-metal interactions, such as antiferromagnetic coupling [14], would be destroyed by the structural disorder. This seems to be confirmed by the electron transport properties [l]. However, it
Amorphous thin &nms of (Ti, Nb)O, solid solutions
distance (II )
-
Fig. 8. Fourier transforms af the EXAFS signal recorded by the electron detection method on the amorphous films. 150
0
h
t i
u
P y t
130
0
-130
0
4
% distance (I )
___I+
Fig. 9. Fourier transforms of the EXAFS signal recorded by the transmission method cm the crystalline solid solutions.
F. PICARD-LAGNEL et al.
1218 (a)
(4
50
Ti - Nb
(b)
-5o-501
.
1 :.
,
I
.
0
,
4 distance
(cl
8 (8)
-
Fig. 11. (a) Pure Ti third shell contribution. R = 3.57 A; o = 8 x 10-r A; (b) third shell contribution composed of four titanium and four niobium backscatters. Ti-Ti
-Nb
REFERENCES 1. Lagnel F., Poumellec B. and Picard C., Phys. Status Solidi (6) 151 (1989). 2. Poumellec B., Lagnel F., Marucco J.-F. and Touzelin B., Phys. Status Solidi (b) 133, 371 (1986). 3. Lagnel F., Poumellec B., Thomas J. P., Ziani A., Gasgnier M., Marucco J.-F. and Picard C., Thin Solid Films 173 (1989).
4. Bosio L., Cortes R., Defrain A. and Froment
M.,
J. electroanal. Chem. 180, 265 (1984).
Fig. 10. Fourier transforms of the simulation of the metallic neighbour contributions parallel to the c-axis. R = 2.96 A; o = 5 x IO-‘& i. = 8 A. (a) Ti-Ti contribution; (b) Ti-Nb contribution; and (c) superposition of both contributions. was not possible to confirm this phenomenon by EXAFS study. This problem is inherent in the treatment of some solid solutions by X-ray absorption. Finally, we should mention that a new program for the treatment of the X-ray reflectivity has been written for this study (see Appendix). Acknowledgments-We are grateful to G. Tourillon from LURE for the records of the photoemitted electron detection spectra and to J. M. Andre from Lab. de ChimiePhysique de Paris VI for useful and very interesting discussions and advices.
5. Poumellec B., Cortes R., Lagnel F., Comput. Phys. Commun. (submitted). 6. Tourillon G., Dartyge E., Fontaine A., Lemonnier M. and Bartol F., Phys. Left. A21, 251 (1987). 7. Lagnel F., These de Doctorat en Sciences, Orsay, No. 586 (1988). 8. Poumellec B. and Cortes, R. J. appl. Crystallogr. 22,295 (1989).
9. Teo B. K., Lee P. A., Simons A. L., Eisenberger P. and Kincaid B. M., J. Am. them. Sot. 99, 3854 (1977). 10. Natoli C. R., in EXAFS and NES III (Edited by K. 0. Hodgson, B. Hedman and J. E. Penner), p. 38. Springer, Hahn (1984). II. Poumellec B., Marucco J.-F. and Touzelin B., Phys. Rev. B35, 2284 (1987). 12. Poumellec B., Marucco J.-F., Gales B. and Touzelin B., J. de Phys. Colloque Cl, Supplement No. 2 825. (1986). 13. Poumellec B., Cortes R., Tourillon G. and Berthon J., Phys. Rev. (submitted). 14. Poumellec B., These de Doctorat d’Etat, Orsay (1986).
Amorphous
thin films of (Ti, Nb)O,
solid solutions
APPENDIX
Flow diagram of jogging
1219
F. PICARD-LAGNEL et al.
1220
First calibration
Yes 1 + arc tan
k3
Oscillatory part
1 :
Analytical transformation
Kramers-Kronig transformation Oscillatory part
1
v Is the estimation fiLEI satisfactory
I
]
p(Ej computation
PU3 computation
of 7
1
Return to jogging
Flow diagram of ReflEXAFS subroutine
J. Phys. Chew. So/ids Vol. 50. No. 12. pp. 1211-1220. 1989 Printed in Great Britam.
STUDY OF AMORPHOUS THIN FILMS OF (Ti, Nb)O, SOLID SOLUTIONS BY X-RAY ABSORPTION AT THE TiK EDGE F. PICARD-LAGNPL,~
B.
PouMELLEct and R. CORTES$
jURA D-0446, Laboratoire des Composes non-stoechiometriques, Bat. 415, Universite Paris&d, 91405 Orsay Cedex, France fCNRS, Laboratoire Physique des Liquides et Electrochimie, ESPCI, 10, Rue Vauquelin, 75005 Paris, France (Received 29 March 1989; accepted 13 July 1989)
Abstract-As the (Ti, Nb)O, amorphous thin films cannot be prepared under a self-supported form, we have recorded the X-ray reflectivity. A new program which allows extraction of the X-ray absorption from the reflectivity is briefly described. The correction of the anomalous dispersion effect is effective, particularly near the edge within 200eV. Hence, it has allowed a comparison between the amorphous layers and the crystalline analogues for which the X-ray absorption has been recorded by transmission. In the amorphous state, the TiO, group is smaller than in the crystalline state because of the relaxation of the crystallographic constraints. The oxygen coordination octahedron is almost regular in the films. On the other hand, in both cases, an electron transfer takes place from Nb to Ti. Keywords: Amorphous
material, thin films, (Ti, Nb)O,, X-ray absorption, Ti K edge.
1. INTRODUCTION Amorphous Ti, _JNb,02 solid solutions (0 < x ,< 1) exhibit interesting electrical properties: the resistivity in the amorphous range is low and close to that of the high temperature crystalline phases [l]. This feature is rather scarce in amorphous oxides. It can be explained by the absence of antiferromagnetic coupling in the amorphous state which gives rise to a high conductivity. In order to interpret the electron transport properties in the amorphous phases, information about the electronic density of states or the local structure around the metallic atoms is useful and has led us to begin a study of the X-ray absorption fine structures. A previous X-ray absorption study carried out on related crystalline solid solutions [2] at the titanium K edge brought the following information: the chemical shift of the Ti K edge spectra indicates a partial electronic transfer between 3d Ti and 4d Nb. This implies that the levels of titanium and niobium are nearly at the same energy (the energy difference is of the order of 0.1 eV). Analysis of the prepeaks shows a decrease of the crystal field splitting when the niobium content increases. This is related to screening by the d electrons and the increase of the oxygen-metal bond length. Finally, the change of the shape of the Ti spectra with changing niobium content is due to a continuous modification around the titanium in going from TiOz to NbOz and can be interpreted in terms of disordered solid solutions. The aim of this paper is to show how the structural disorder related to the amorphous state modifies the
above conclusions. Hence, analysis of the XANES at the Ti K edge will bring information about changes in the electronic density of states and analysis of the EXAFS changes about the neighbourhood of the titanium atom, especially the metallic neighbourhood which governs the electron transport properties. 2. EXPERIMENTAL
The method of sample preparation is described in [3]. Films were obtained by RF sputtering of oxide targets in an argon atmosphere. The first idea was the preparation of 10-20 pm thick films in order to record the absorption spectra by transmission. However, mismatch of the thermal expansion coefficient between the layer and the substrates did not allow one to obtain self-supported samples. Consequently, we decided to use a few 1000 h; thick films deposited on silica or on float glass substates. Then, the absorption related spectra were recorded by reflection or electron detection. An extended description of the X-ray reflection spectrum technique (ReflEXAFS technics) can be found in [4]. The relevant parameter is the glancing angle which ranges from 2 to 10 m rad at the Ti K edge. Smoothness of the surface is also required. This question will be analysed in [S] where the program that computes the absorption from the reflectivity data is described. The electron detection method is described in [6]. The photon beam strikes the sample surface at a 45”
1211
5 (Kapton or NaCl).
1212
F. PICARD-LAGNEL et al.
angle. The extracted electrons ionize the helium atoms. A cathode, placed perpendicular to the beam and kept at a potential of 100 V, collects the ions. In this case, the quality of the sample surface is not important; moreover the recorded signal is proportional to the absorption. These experiments were useful in order to check whether the absorption extraction procedure from the reflectivity measurements was correct or not. Spectra were recorded at Lure, Orsay, at the Ti K edge (_ 4975 eV) with a Si (3 11) monochromator and glass mirrors for harmonic rejection. The slit entrance was 100pm wide in the ReflEXAFS configuration and 1 mm in the electron detection method. An initial investigation in the laboratory was made to record the reflectivity vs the glancing angle RE(0) at constant energy. This enables one to check the sample surface quality and the density of the layer (at 8028 eV for example [7]) or to compute the initial critical angle (i.e. 0, at 4900eV). Then, R,(E) spectra were recorded from 4900eV up to 5500eV for various values of 0/O,. ranging from 0.2 to 0.9.
beginning of the EXAFS one, up to 200 eV from the edge. Specifically, the greatest alteration occurs at the edge where the first maximum shows up. As a matter of fact, the spectrum recorded under the smallest glancing angle is the least distorted and approximates the true absorption; but, in that case, noise becomes important because the XAS modulation decreases with angle [7] whereas the absolute reflectivity increases. Therefore, it is necessary to correct the X-ray reflectivity spectra so that the comparison between different samples be valid. 3.1.2. The solution. The computation of the correction is obtained by the inversion of the Fresnel equation (1) giving the reflectivity R(B
’
E) _ (s!n 8 - u+)~+ a2 - (sm 8 + ~2~)~+ al
with ai = -!- ((sin2 Q - 0:)’ + 4p2)* + (4p2)“’ 4 + (sin’ 0 - Qf)li2
3. DATA
TREATMENT
3.1. Computation of the absorption from the reflectivity spectra 3.1.1. The problem. As a rough estimate, a reflectivity spectrum vs energy has the same shape as an absorption spectrum, except that the edge is reversed and values of the reflectivity range between 0 and 1. However, the shape of a reflectivity spectrum depends on the glancing angle. For the sake of clarity, in Fig. 1, normalized spectra are displayed (the EXAFS part from 5200 up to 5500 eV is the same for all the spectra). An increase of 6 gives rise to an enhancement of the whole XANES spectrum and of the
R(E)-R(4950) 3 R(5200LRI49501 :;-..._
Fig.
1. Dependence
of the normalized glancing angle.
reflectivity
on the
where 8 represents the glancing angle, 0, the critical angle, E the energy, h and c are the usual constants; the absorption b and the dispersion 6 are related to the refractive index n by n = 1 - 6 - @I. Hence, the reflectivity depends on the energy through /? and 6
R(Q,E) = Rut 836). The inversion on /I leads to b = fi(0,6, R). R and 0 are known but the whole determination of p requires the knowledge of 6 at each energy. Now 6, especially the anomalous dispersion, is often unknown. This difficulty is overcome by the fact that p and 6 are related by the Kramers-Kronig transformation. Therefore, it is possible to determine b by iterative computation, provided some constants such as the normal dispersion curve are imposed. The flow diagram of the program is given in the Appendix. Details of the procedures will be supplied in [5] but are available from [8]. The program is named JOGGING II. 3.1.3. The ejkiency. Figure 2 shows the efficiency of the method when the full dispersion curve is taken into account. As in all computational procedures containing integral transformations, the curve is noisy at the part where the correction is large. Nevertheless, it is clear that the absorption spectrum is well restored when it is compared with curve (b) which has been obtained on the same sample by the electron detection method.
Amorphous
thin films of (Ti, Nb)O,
1213
solid solutions Ti-0 L .::.
3r
..
:
?;i
’
b
a
4 Distance
4950
5000 Energy
(eV)
-
3.2. Treatment of the EXAFS
signal
3.2.1. Foreword. As a result of the superposition of the metal-oxygen and the metal-metal shells in the Fourier transform, it was impossible to extract experimental values for the phases and amplitudes of the EXAFS signal. On the other hand, the previous analysis of the crystalline TiO, EXAFS has shown that the theoretical values of Teo et al. [9] are not very applicable to these compounds. Therefore, in this paper, we discuss only the Fourier transforms and not the fits. We shall go further in the future by recording the polarized spectra. Indeed, this method allows one to cancel the Ti-Ti shell parallel to the c-axis. 3.2.2. Observations. The insertion of a smoothing procedure on the EXAFS signal before the Fourier transform improves its readability. Nevertheless, when the target atom is very diluted in the absorbing bulk, this procedure is going to be inoperative. This effect is shown in Figs 7 and 8, specifically for x = 0.8, when the Fourier transform of the ReflEXAFS spectrum is compared with one of the electron detection spectra: the first peak relative to the metal-oxygen shell is almost the same in both spectra whereas differences are appreciable for larger radii; because these spectra were recorded from the same sample, the differences arise from the noise which is greater in the ReflEXAFS method than in the electron detection one. Lastly, we have observed that no correction is required for the weak EXAFS modulations. On the other hand, concerning the metal-oxygen shell, the first oscillations are rather large and, in this case, the dispersion effect is active and implies a distortion of the first peak in the Fourier transform.
-
Fig. 3. Fourier transform of TiO, EXAFS signal: the full curve is relative to the film (~9= 0.9 0,) and the dotted one to the crystalline sample.
Fig. 2. Illustration of the efficiency of the dispersion correction method: curve (a) obtained from the reflectivity with only a normal dispersion correction; curve (a’) is for the full
dispersion correction; curve (b) is obtained on the same sample by the photoelectron detection method.
(A)
4. ABSORPTION
4.1.
SPECTRUM
ANALYSIS
XANES
4.1.1. TiO, . Despite the drastic preparation conditions used, the TiOz films were partially crystalline [3]. In fact, the edge (specifically for 0 = 0.8 0,) exhibits the feature of a crystalline sample, i.e. well structured prepeaks, bump in the middle of the edge and three peaks after the edge. The comparison of the Fourier transforms between crystalline TiO, and the film confirms this fact (Fig. 3). The second and third neighbours are similarly distant although the disorder leads to less separated bands. On the contrary, the first shell radius is shorter in film than in the crystal, i.e. by ~5 x lO-=A.
4950
5000 Energy
Fig. 4. TiO, film absorption spectra t7 = 0.28,. and 0.80, (smoothing
(eV) for two glancing angles: window = 2.3 eV).
F.
1214
PICARD-LAGNELet
Figure 4 shows the absorption spectra for two glancing angles: 0 = 0.20, and 0.88,. A shift of the main maximum (relative to the prepeak) is clearly seen and corresponds to a variation of the titaniumoxygen shell distance. Using Natoli’s relation [lo] and the coefficient published in [ll], a shortening of 6 x 10m2A from 0.8 to 0.28, is deduced. Besides, the smaller the glancing angle, the smaller the X-ray penetration depth. Therefore, this titanium-oxygen distance variation probably arises from a larger disordered layer at the film surface. 4.1.2. Ti, _xNb,02(x # 0). XANES spectra are displayed in Fig. 5 [Fig. 5(b) is from a previous study [2]]. The main differences between the two phases are clearly perceptible: -firstly, the magnitude of the prepeak transitions, i.e. the A, intensity, is independent of x for the amorphous films where the modulation disappears for the crystalline solid solutions; -secondly, the modulations after the edge are weaker for the amorphous phases and seem to be dependent on the niobium content. Particularly, the C, feature has almost disappeared and for x = 0.8, only one C peak seems to be present. Quantitative information is available from the analysis of the second derivative spectra in Fig. 6 and Table 1. The A, peak shifts from TiO, to x = 0.8 by about 0.6 eV. This value corresponds to the one previously observed in the crystalline analogues (0.7 eV) [2]. The A,-A, difference seems to be almost constant around 3.8 eV but the A, transition is rather weakly defined. The B, C and D features do not shift appreciably for x # 0 indicating that the Ti coordina-
al.
tion octahedron does not change much in size and shape, contrary to the crystalline phases. 4.2. EXAFS analysis In the absence of a good table of phases and amplitudes, changes in distance were measured by the shifts of the maxima of the imaginary part in the Fourier transform. Figures 7-9 show the Fourier transforms of the amorphous films recorded by reflection, by electron detection and of the crystalline solid solutions recorded by transmission. At a first glance, compared with the titaniumoxygen peak amplitude (i.e. we assume six oxygen neighbours in the first shell), we see a decrease of the second and third peak representative of the metallic neighbours, either in the films or in the crystalline samples. However, the decrease or the complexity of the 2-3 A part of the Fourier transform is larger in the amorphous films. 4.2.1. Titanium-oxygen distance. From Fig. 7 or Fig. 8, a sudden variation of the Ti-Q distance (3.3 x 10e2 A) is detected from x = 0 to x = 0.3 and then the change is small from x = 0.3 to x = 0.8 (i.e. < 1.7 x 10e2 A). From Fig. 9, a reverse behaviour is observed: the Ti-O distance increases by about 5 x 10e2A. On the other hand, a comparison of Figs 7-9 for x around 0.5 yields a reduction in the size of the coordination octahedron by about O.lLO.12 8, from the crystalline to the amorphous state. 4.2.2. Ti-Ti distance. As mentioned above, the Ti-Ti contribution disappears progressively as the niobium content increases. This is observed either for
(b)
Energy
( eV)
-
5000
4950
4960
4970
4980 4990 Enorgy(w) -4
5000
500
Fig. 5. Ti K edge XANES spectra for films (a) and crystalline samples (b) [smoothing window = 2.3 eV for (a) and 2.1 eV for (b)].
Amorphous
thin films of (Ti, Nb)O,
1215
solid solutions
titanium on one side and a niobium neighbour on the other side. Hence, a superposition of the incoming waves from the two metallic atoms is expected. In order to determine the resultant signal, we performed a simulation of the EXAFS part with the following classical formula: kX(k) = $
A(k)exp(-202k2)
x exp -2 f sin(2kR + 4(k))
‘V
(
0.45
0.3
0,03
1
0
Energy Fig. 6. Second derivatives
(eV)
of the spectra
shown in Fig. 5(a).
the amorphous films or the crystalline samples (follow peaks denoted A, B, C). Therefore, because the crystalline phases exhibit the same phenomenon, this cannot be explained by the structural disorder above but by the Nb-Ti substitutional disorder which takes place in both phases. In Fig. 9, disappearance of the A peak between x = 0.2 and x = 0.4 is observed. This peak is representative of the metallic neighbours along the c-axis. In this direction, for x = 0.3, the mean configuration consists of a central titanium atom surrounded by a
>
with A(k) and 4(k) expressed by the analytical forms from [9]. (N.B. the curved wave correction would not change the conclusions drawn below as the signal taken into account here is for k > 4 A-‘.) The results are shown in Fig. 10. In Fig. 10(a), the Ti contribution appears at R = 2.54 %, (instead of the crystallographic distance R = 2.96 A) with a magnitude of 50; in Fig. IO(b) the Nb backscatter contribution is shifted less and appears at R = 2.68 A with almost the same magnitude. Lastly, in Fig. IO(c) the full contribution exhibits two less wide peaks, one at 2.29A with a magnitude of 23 and another one at 2.81 8, with a magnitude of 30. This implies that both signals are partly in phase opposition and never separated. Moreover, a simulation performed on the third shell (Fig. 11) exhibits the same phenomenon; but it is worth noting that, if it appears at 3.14 8, for the pure Ti contribution, it splits into a peak at 2.91 A with a magnitude of 34 and at 3.42 8, with a magnitude of 44. Therefore, a part of the third shell signal (for R = 2.91 A) IS mixed with the second shell signal which appears at R = 2.81 A. This precludes any computation of each component separately and leads eventually to a consideration of the whole signal between 2~ R <4A. Thus, we have explained the disappearance of the A peak in Fig. 9, the appearance of the C peak at the same time and the broadening of the B peak. This stands for the crystalline samples but also for the amorphous layers, although, in this last case, the structural disorder smoothes the structure. 5. CONCLUSION
In spite of the problem encountered above, we have deduced some interesting information about the structure of amorphous (Ti, Nb)02 solid solutions by X-ray absorption.
Table 1. Energy peak positions of the features in Fig. 6 x/peak
A,
Al
B
c
TiO, x = 0.3 x = 0.45 x = 0.6
4966.8 4966.4 4966.2 4966.2
4970.4 4970.4 4970.2 4069.6
4975.8 4976.2 4976.6 4976.2
(C,) 4982.6 (C,) 4987.2 4983.2 4983.2 4983.2
F. PICARD-LAGNEL et al.
1216
125
4
distance
yi)
Fig. 7. Fourier transforms of the EXAFS signal recorded by the ReflEXAFS method on the amorphous films.
From the energy shift of prepeak AZ. we deduce that a partial electron transfer from Nb to ‘Ii takes
place, as was the case in the crystalline analogues [ 121. The edge exhibits simpler structures in the amorphous layers: this indicates that the coordination octahedron is almost regular. This is proved by the study of the polarized Ti K edge in TiOz [13]. Moreover, the examination of both the XANES structures and of the EXAFS titanium-oxygen signal yields the conclusion that the TiO, octahedron does not change much but does decrease slightly in size (-2 x IO-* A) when the niobium content increases. This behaviour is completely different in the crystalline case for which the octahedron is distorted with two long distances and increases in size (f5 x 10e2 A). For s e 0.8, the difference in titanium-
oxygen distances between the two phases amounts to about 0.1 A. As a matter of fact, it is understandable that the amorphism which leads to an isotropic state gives rise to regular octahedra but it is difficult to understand the decrease in its size with the Nb content. In the crystalline phase, the TiO, octahedron is held extended and the NbO, one compressed by the crystalline forces. On the contrary, in the amorphous state, bending or dangling bonds allow a relaxation of the coordination sphere, thus the size should be independent of its surroundings. We expected that metal-metal interactions, such as antiferromagnetic coupling [14], would be destroyed by the structural disorder. This seems to be confirmed by the electron transport properties [l]. However, it
Amorphous thin &nms of (Ti, Nb)O, solid solutions
distance (II )
-
Fig. 8. Fourier transforms af the EXAFS signal recorded by the electron detection method on the amorphous films. 150
0
h
t i
u
P y t
130
0
-130
0
4
% distance (I )
___I+
Fig. 9. Fourier transforms of the EXAFS signal recorded by the transmission method cm the crystalline solid solutions.
F. PICARD-LAGNEL et al.
1218 (a)
(4
50
Ti - Nb
(b)
-5o-501
.
1 :.
,
I
.
0
,
4 distance
(cl
8 (8)
-
Fig. 11. (a) Pure Ti third shell contribution. R = 3.57 A; o = 8 x 10-r A; (b) third shell contribution composed of four titanium and four niobium backscatters. Ti-Ti
-Nb
REFERENCES 1. Lagnel F., Poumellec B. and Picard C., Phys. Status Solidi (6) 151 (1989). 2. Poumellec B., Lagnel F., Marucco J.-F. and Touzelin B., Phys. Status Solidi (b) 133, 371 (1986). 3. Lagnel F., Poumellec B., Thomas J. P., Ziani A., Gasgnier M., Marucco J.-F. and Picard C., Thin Solid Films 173 (1989).
4. Bosio L., Cortes R., Defrain A. and Froment
M.,
J. electroanal. Chem. 180, 265 (1984).
Fig. 10. Fourier transforms of the simulation of the metallic neighbour contributions parallel to the c-axis. R = 2.96 A; o = 5 x IO-‘& i. = 8 A. (a) Ti-Ti contribution; (b) Ti-Nb contribution; and (c) superposition of both contributions. was not possible to confirm this phenomenon by EXAFS study. This problem is inherent in the treatment of some solid solutions by X-ray absorption. Finally, we should mention that a new program for the treatment of the X-ray reflectivity has been written for this study (see Appendix). Acknowledgments-We are grateful to G. Tourillon from LURE for the records of the photoemitted electron detection spectra and to J. M. Andre from Lab. de ChimiePhysique de Paris VI for useful and very interesting discussions and advices.
5. Poumellec B., Cortes R., Lagnel F., Comput. Phys. Commun. (submitted). 6. Tourillon G., Dartyge E., Fontaine A., Lemonnier M. and Bartol F., Phys. Left. A21, 251 (1987). 7. Lagnel F., These de Doctorat en Sciences, Orsay, No. 586 (1988). 8. Poumellec B. and Cortes, R. J. appl. Crystallogr. 22,295 (1989).
9. Teo B. K., Lee P. A., Simons A. L., Eisenberger P. and Kincaid B. M., J. Am. them. Sot. 99, 3854 (1977). 10. Natoli C. R., in EXAFS and NES III (Edited by K. 0. Hodgson, B. Hedman and J. E. Penner), p. 38. Springer, Hahn (1984). II. Poumellec B., Marucco J.-F. and Touzelin B., Phys. Rev. B35, 2284 (1987). 12. Poumellec B., Marucco J.-F., Gales B. and Touzelin B., J. de Phys. Colloque Cl, Supplement No. 2 825. (1986). 13. Poumellec B., Cortes R., Tourillon G. and Berthon J., Phys. Rev. (submitted). 14. Poumellec B., These de Doctorat d’Etat, Orsay (1986).
Amorphous
thin films of (Ti, Nb)O,
solid solutions
APPENDIX
Flow diagram of jogging
1219
F. PICARD-LAGNEL et al.
1220
First calibration
Yes 1 + arc tan
k3
Oscillatory part
1 :
Analytical transformation
Kramers-Kronig transformation Oscillatory part
1
v Is the estimation fiLEI satisfactory
I
]
p(Ej computation
PU3 computation
of 7
1
Return to jogging
Flow diagram of ReflEXAFS subroutine