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Sinusoidal modulation of a thin film of Nb on sapphire
PHYSICA ELSEVIER
Physica B 198 (1994) 63-65
Sinusoidal modulation of a thin film of N b on sapphire A. Gibaud*, D.F. Mc-Morrow, R.A. C o w l e y Clarendon Laboratory, Parks Road, OX13PU Ox]brd, UK
The aim of this paper is to present the results of a high-resolution X-ray experiment on the in-plane and out-of-plane structures of a thin film (400 ~,) of niobium deposited on a sapphire substrate. The Nb sapphire system is interesting to study because it is the most appropriate system to grow epitaxial films of rare earth and 3d metals. It has indeed been shown that BCC Nb (1 10) can be epitaxially grown on (1 1 20) sapphire. The in-plane epitaxial relationship between Nb (110) and A1203 (1120) is [l 10] N b / / [ 0 0 0 1 ] A1203 and [ 1 1 2 ] N b / / [ 1 0 1 0 ]
a crystallographic direction (CD) which is at an angle of 7 with respect to the SD. A typical pattern is shown in Fig. 3. It is composed of the 1 10 Nb and of the 1 1 2 0 sapphire Bragg reflections and of a series of fringes which result from the interferences between the electric fields at the top and bottom parts of the finite film. The longitudinal location of the fringes is consistent with the composition obtained from the reflectivity. However, a more surprising effect arises from the fact that the fringes are not located along the CD but lie along a streak parallel to the SD. In addition, a transverse scan across the Nb 1 10 Bragg reflection reveals, as shown in Fig. 4, a complex structure composed of
A1203.
The small angle scattering results of the niobium deposited on the sapphire substrate allow the determination of the out-of-plane structure of the film in the direction normal to its average surface (surface direction, denoted SD). As shown in Fig. 1 and evidenced by the fit quality, the pattern is well interpreted by the system sapphire/Nb/niobium oxide in which the Nb film is about 417 A thick and is covered by a 13 A thick oxide layer the thickness of which is slowly time dependent. The observation of oscillations up to 0.6 A - 1 is consistent with very sharp interfaces. At high angle of diffraction as shown schematically in Fig. 2 the miscut angle 7 of the sapphire and the nearly perfect epitaxy of the niobium on the sapphire provide a diffraction pattern located along
* Corresponding author; Permanent address: Facult6 des Sciences, Universit6 du Maine, URA 807 CNRS, 72017, Le Mans Cedex, France.
- a very narrow (q < 0.004 °) central component, - a broad diffuse component having a Lorentzian square line shape A lDif(qx ) -=
(1 + ~2q~)2,
a pair of satellites symmetrically distributed at qx = 0.0034 ,~,- 1.
-
The origin of the broad diffuse component is related to a correlated in-plane disorder of the niobium atom network with a correlation function given by
C(r)-
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0921-4526(93) E0499-7
(h(O)h(r)) (h2(0))
= (1 + ~cr)e-K'.
64
A. Gibaud et al./ Physica B 198 (1994) 63-65
0
0
[...,
E--
(1]
-2
Z
~2 [-
-3
z
Z
-1 -2
Z
O
-4
-3
0
0 ..2
o ,..2
-5
-4
-6
-5
I
2.5
-7 0.0
0.1
0.2
0.3
Q
[A-']
0.4
I
~
2.6
2.7
0.5
Fig. 1. Results of the reflectivity measurements.
Q
I_
2.8
IX-1]
Fig. 3. High angle scattering results showing the sharp 1 1 7.0 sapphire and the 110 Bragg peaks with the characteristic fringes.
CD -1
Z Z
0.000
-2
q~ -3
© --4 -0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Qx[£ 1] Fig. 2. Schematic representation of the sapphire surface with the Nb film on top of it.
Fig. 4. Transverse scan through the Nb l T 0 Bragg peak showing the narrow 1 T 0 Bragg peak, the broad diffuse component and the satellites.
The correlation length ( = 1/• gives the extent over which the atomic arrangement of the Nb atoms is well ordered, and was found to be 72 A, but it was slightly varying according to the in-plane direction in which the qx scan was performed. Let us point out that the Lorentzian square line shape results from the integration over the vertical resolution of the instrument of the Fourier transform of the correlation function (for more details, see Refs. [1, 2-]).
The presence of the sharp satellites is not always observed and depends strongly upon the crystallographic direction in which the scan is performed in the same way as does the miscut angle. Their intensity is very weak if compared to that of the main central peak and subsequently it was difficult to observe higher-order satellites. In the grazing incidence study of the step-step correlations on a Si (0 0 1) surface by Renaud et al. [3], similar satellites have been successfully interpreted as coming from
A. Gibaud et al./Physica B 198 (1994) 63-65
the crystal truncation rod (CTR) of the Bragg reflections located above and below the investigated Bragg reflection. Their location was related to the miscut angle of the silicon. Let us recall that the miscut angle which defines the angle between the SD and the CD is related to the length of the terraces at the surface of the sample. To describe the number, the location and the intensity of the satellites, we have assumed that the Nb atomic displacements are identical to those produced by a frozen acoustic phonon propagating along [1 1 2] and polarized along [1 1 0]. In these directions, denoted x and z, respectively, the Nb atomic positions are x = na, z = Uzsin(qa na + ~p) + pc, where qa is the wave vector of the modulation, Uz is the amplitude of the oscillations and p and n are the positions of the Nb atoms along x and z. The scattered amplitude is given by N1
laragg =
65
sin2(N1 Qxa/2) sin2 ( N a Qzc/2) sin2(Qxa/2) sin2(Qzc/2) '
Qz2 uz2 sin2(Nla(Qx +_ qa)/2) sin2(N3Qzc/2) 4 sin2(a(Qx _+ qa)/2) sin2(Qzc/2)
/Sat -- - -
and the total intensity is given by I = Iaragg + /Sat q'- IDif"
Figure 4 is a fit to the data with A = 1830,i, Uz=0.07,~, 4=72,~, N l a = 15000,~ and N 3 c = 417 ,~. As a conclusion, let us stress that possible origins for the sunusoidal modulation of the film are the presence of regular steps and terraces at the sapphire surface together with the lattice mismatch in the z direction between Nb and sapphire, a huge roughness along the direction parallel to the sapphire steps which will produce an average sinusoi'dal electron density in the Nb film. This work was supported by a joint grant of the CNRS and the Royal Society. All the calculations were performed with help of the Matlab software.
N3
A = ~
~ eiQxnae iQz(pc+uzsin(q~na+tp)). n = l p=l
References
Introducing in this calculation the Bessel functions of order 0 and 1 which are not negligible, we end up with a scattering cross-section containing the Bragg and the satellite contributions given by
[1] D.F. Mc Morrow, R.A. Cowley, A. Gibaud, R. Ward and M.R. Wells, Appl. Phys. Lett., to be submitted. [2] A. Gibaud, D.F. Mc Morrow, R.A. Cowley, R. Ward and R. Wells, Phys. Rev. B, to be submitted. [3] G. Renaud, P.H. Fuoss, J. Bevk and B. Freer, Phys. Rev. B 45 (1992) 9192.
Physica B 198 (1994) 63-65
Sinusoidal modulation of a thin film of N b on sapphire A. Gibaud*, D.F. Mc-Morrow, R.A. C o w l e y Clarendon Laboratory, Parks Road, OX13PU Ox]brd, UK
The aim of this paper is to present the results of a high-resolution X-ray experiment on the in-plane and out-of-plane structures of a thin film (400 ~,) of niobium deposited on a sapphire substrate. The Nb sapphire system is interesting to study because it is the most appropriate system to grow epitaxial films of rare earth and 3d metals. It has indeed been shown that BCC Nb (1 10) can be epitaxially grown on (1 1 20) sapphire. The in-plane epitaxial relationship between Nb (110) and A1203 (1120) is [l 10] N b / / [ 0 0 0 1 ] A1203 and [ 1 1 2 ] N b / / [ 1 0 1 0 ]
a crystallographic direction (CD) which is at an angle of 7 with respect to the SD. A typical pattern is shown in Fig. 3. It is composed of the 1 10 Nb and of the 1 1 2 0 sapphire Bragg reflections and of a series of fringes which result from the interferences between the electric fields at the top and bottom parts of the finite film. The longitudinal location of the fringes is consistent with the composition obtained from the reflectivity. However, a more surprising effect arises from the fact that the fringes are not located along the CD but lie along a streak parallel to the SD. In addition, a transverse scan across the Nb 1 10 Bragg reflection reveals, as shown in Fig. 4, a complex structure composed of
A1203.
The small angle scattering results of the niobium deposited on the sapphire substrate allow the determination of the out-of-plane structure of the film in the direction normal to its average surface (surface direction, denoted SD). As shown in Fig. 1 and evidenced by the fit quality, the pattern is well interpreted by the system sapphire/Nb/niobium oxide in which the Nb film is about 417 A thick and is covered by a 13 A thick oxide layer the thickness of which is slowly time dependent. The observation of oscillations up to 0.6 A - 1 is consistent with very sharp interfaces. At high angle of diffraction as shown schematically in Fig. 2 the miscut angle 7 of the sapphire and the nearly perfect epitaxy of the niobium on the sapphire provide a diffraction pattern located along
* Corresponding author; Permanent address: Facult6 des Sciences, Universit6 du Maine, URA 807 CNRS, 72017, Le Mans Cedex, France.
- a very narrow (q < 0.004 °) central component, - a broad diffuse component having a Lorentzian square line shape A lDif(qx ) -=
(1 + ~2q~)2,
a pair of satellites symmetrically distributed at qx = 0.0034 ,~,- 1.
-
The origin of the broad diffuse component is related to a correlated in-plane disorder of the niobium atom network with a correlation function given by
C(r)-
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0921-4526(93) E0499-7
(h(O)h(r)) (h2(0))
= (1 + ~cr)e-K'.
64
A. Gibaud et al./ Physica B 198 (1994) 63-65
0
0
[...,
E--
(1]
-2
Z
~2 [-
-3
z
Z
-1 -2
Z
O
-4
-3
0
0 ..2
o ,..2
-5
-4
-6
-5
I
2.5
-7 0.0
0.1
0.2
0.3
Q
[A-']
0.4
I
~
2.6
2.7
0.5
Fig. 1. Results of the reflectivity measurements.
Q
I_
2.8
IX-1]
Fig. 3. High angle scattering results showing the sharp 1 1 7.0 sapphire and the 110 Bragg peaks with the characteristic fringes.
CD -1
Z Z
0.000
-2
q~ -3
© --4 -0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Qx[£ 1] Fig. 2. Schematic representation of the sapphire surface with the Nb film on top of it.
Fig. 4. Transverse scan through the Nb l T 0 Bragg peak showing the narrow 1 T 0 Bragg peak, the broad diffuse component and the satellites.
The correlation length ( = 1/• gives the extent over which the atomic arrangement of the Nb atoms is well ordered, and was found to be 72 A, but it was slightly varying according to the in-plane direction in which the qx scan was performed. Let us point out that the Lorentzian square line shape results from the integration over the vertical resolution of the instrument of the Fourier transform of the correlation function (for more details, see Refs. [1, 2-]).
The presence of the sharp satellites is not always observed and depends strongly upon the crystallographic direction in which the scan is performed in the same way as does the miscut angle. Their intensity is very weak if compared to that of the main central peak and subsequently it was difficult to observe higher-order satellites. In the grazing incidence study of the step-step correlations on a Si (0 0 1) surface by Renaud et al. [3], similar satellites have been successfully interpreted as coming from
A. Gibaud et al./Physica B 198 (1994) 63-65
the crystal truncation rod (CTR) of the Bragg reflections located above and below the investigated Bragg reflection. Their location was related to the miscut angle of the silicon. Let us recall that the miscut angle which defines the angle between the SD and the CD is related to the length of the terraces at the surface of the sample. To describe the number, the location and the intensity of the satellites, we have assumed that the Nb atomic displacements are identical to those produced by a frozen acoustic phonon propagating along [1 1 2] and polarized along [1 1 0]. In these directions, denoted x and z, respectively, the Nb atomic positions are x = na, z = Uzsin(qa na + ~p) + pc, where qa is the wave vector of the modulation, Uz is the amplitude of the oscillations and p and n are the positions of the Nb atoms along x and z. The scattered amplitude is given by N1
laragg =
65
sin2(N1 Qxa/2) sin2 ( N a Qzc/2) sin2(Qxa/2) sin2(Qzc/2) '
Qz2 uz2 sin2(Nla(Qx +_ qa)/2) sin2(N3Qzc/2) 4 sin2(a(Qx _+ qa)/2) sin2(Qzc/2)
/Sat -- - -
and the total intensity is given by I = Iaragg + /Sat q'- IDif"
Figure 4 is a fit to the data with A = 1830,i, Uz=0.07,~, 4=72,~, N l a = 15000,~ and N 3 c = 417 ,~. As a conclusion, let us stress that possible origins for the sunusoidal modulation of the film are the presence of regular steps and terraces at the sapphire surface together with the lattice mismatch in the z direction between Nb and sapphire, a huge roughness along the direction parallel to the sapphire steps which will produce an average sinusoi'dal electron density in the Nb film. This work was supported by a joint grant of the CNRS and the Royal Society. All the calculations were performed with help of the Matlab software.
N3
A = ~
~ eiQxnae iQz(pc+uzsin(q~na+tp)). n = l p=l
References
Introducing in this calculation the Bessel functions of order 0 and 1 which are not negligible, we end up with a scattering cross-section containing the Bragg and the satellite contributions given by
[1] D.F. Mc Morrow, R.A. Cowley, A. Gibaud, R. Ward and M.R. Wells, Appl. Phys. Lett., to be submitted. [2] A. Gibaud, D.F. Mc Morrow, R.A. Cowley, R. Ward and R. Wells, Phys. Rev. B, to be submitted. [3] G. Renaud, P.H. Fuoss, J. Bevk and B. Freer, Phys. Rev. B 45 (1992) 9192.