X-ray standing-wave technique as a source of complementary
information in structural characterization of thin surface layers
C. BOCCHI(1), P. FRANZOSI(1), R. M. IMAMOV(2), A. V. MASLOV(2)E. KH. MUKHAMEDZHANOV(2) and E. M. PASHAEV(2) (1) MASPEC-CNR Institute - I-43100 Parma, Italy
(2) A. V. Shubnikov’s Institute of Crystallography of Russian Academy of Sciences
Leninskiy pr. 59, 117333 Moscow, Russia, CIS
(ricevuto il 10 Settembre 1996; approvato il 22 Ottobre 1996)
Summary. — Lattice distortions in a 100 keV O1-implanted (001) InP crystal with
dose f 41015
atoms Ocm2, have been investigated by high-resolution X-ray
diffraction and X-ray standing-wave techniques. Besides direct analysis of equivalent strain and damage profiles, the use of photoelectrons in the X-ray standing-wave method provides valuable complementary information on completely disordered surface layers which is not accessible by conventional X-ray diffraction. By numerical simulation of the experimental X-ray diffraction and photoelectron yield profiles an amorphous surface layer of about 200 nm has been found.
PACS 61.10 – X-ray diffraction and scattering. PACS 73.20 – Surface and interface electron states.
1. – Introduction
Recently we investigated the effect on crystal structure of various dose Fe1 implantation in InP crystals. The structural investigation of the implanted layers was carried out by means of high-resolution X-ray diffraction (HRXRD) and X-ray standing-wave (XSW) techniques and the results were reported elsewhere [1]. From a methodological point of view the study demonstrated the great advantages of a joint use of HRXRD and XSW for characterization of thin surface layers.
Really the HRXRD method is extremely sensitive to even small lattice distortions and its spatial resolution improves in the kinematical domain with the increment of NDwN , where Dw is the angular deviation from the Bragg angle wB[2]. However, HRXRD only detects the intensity of diffraction scattering loosing all the information concerning the phase of diffracted wave which results in a certain ambiguity in the determination of the lattice distortion profile [3-5].
Though it is difficult for the XSW technique to reach the spatial resolution of HRXRD, but unlike conventional X-ray diffraction methods the XSW technique is sensitive to the phase of the diffracted wave. Thus it was supposed that experimental 65
C. BOCCHI, P. FRANZOSI, R. M. IMAMOV, ETC.
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data sets of HRXRD and XSW could be complementary to each other and the basic idea of the study was to use XSW data (in our case it was low–energy-loss photoelectron yield in condition of dynamical X-ray diffraction) for selection of the most appropriate strain and damage depth profile among those ones that were practically equivalent from the point of view of the intensity of kinematical X-ray diffraction.
The procedure for choosing the most appropriate profile included fit of the HRXRD experimental data starting from different initial profiles. All the strain and damage profiles that provided more or less satisfactory simulation of the HRXRD curves were then tested in the dynamical domain by comparing the calculated and experimental angular curves of photoelectron yield to obtain the closest to the true one. In fact in every sample there are numerous local mimina x2 which stands for the difference of experimental and calculated angular curves of diffraction scattering intensity. Examples of the effectiveness of the approach one may find elsewhere [11].
However, in some cases the proposed direct procedure for distortion profile examination may prove to be insufficient. It is especially true far from exact Bragg position where accurate measurements of X-ray diffraction scattering are hindered or rather time consuming due to low counting rate. Nevertheless even in that case XSW technique may provide complementary information which could be useful for structural characterization of thin surface layers.
The aim of the present paper is to illustrate the use of the XSW technique to get information on the crystal surface structure when the HRXRD experimental data prove to be insufficient. The experimental investigation was carried out on an InP crystal implanted with O1 ions.
2. – Experimental
HRXRD measurements were carried out by means of conventional computer-controlled triple-crystal diffractometer (TCD) using symmetric 004 reflections of CuKa1 radiation. The diffracted intensity was measured in the angular range of 2200GDwG900 seconds of arc where the diffraction scattering intensity exceeded 1027 in comparison with the one in the exact Bragg position. For each angular position Dw, the angular distribution of X-rays scattered by the sample was analyzed by scanning a third crystal (analyzer). Such experimental procedure allowed to separate elastic diffraction and diffuse scattering. More details of TCD measurements may be found in the literature [6].
The XSW measurements were carried out with a conventional diffractometer in a double-crystal (n , 2n) set-up in the dynamical domain 230 GDwG30 s of arc of the CuKa1 004 reflection. The sample was mounted inside the gas-flow proportional counter with the energy resolution of about 17% and nearly 100% effectiveness of photoelectron detection [7]. The energy spectrum of photoelectrons emitted by the InP crystal due to the absorption of CuKa1 radiation obtained by means of a gas proportional counter is shown in fig. 1. It is known that low–energy-loss electrons escape from the shallow depths close to the surface, whereas those that have lost significant part of their energy in inelastic collisions with the crystal atoms, originate mainly in the deeper layers. In the experiments we used two energy bands located in high- and low-energy sides of the spectrum. The high-energy band ( 7 .3 EEE7.8 keV)
Fig. 1. – Experimental photoelectron energy spectrum from InP crystal. Numbers 1 and 2 denote high- and low-energy bands used in the experiment. Arrows indicate main groups of electrons emitted due to absorption of CuKa1radiation.
contained mainly low–energy-loss InM photoelectrons. For such electrons a simple exponential function provides a satisfactory approximation of the probability function P of electron escape from different depths z in crystal [8], P(z) 4exp [2zOL], where L is a parameter. The small escape depth permits to avoid a significant averaging of the phase of the standing wave in the space-modificated subsurface area.
The low-energy band ( 0 .8 EEE1.3 keV) formed by the mixture of photo and Auger electrons of various origin with nearly linear probability function P(z) 4 1 2zOL [8] was also used. The values of parameter L for both cases were determined experimentally [1] in accordance with the technique proposed elsewhere [8]. For high-energy band L was found to be 0.031 mm, whereas for low-energy band it was estimated as 0.24 mm. The benefit of the use of two energy bands will become clear below.
The sample in study was a (001)-oriented InP crystal implanted at room temperature with O1ions. Implantation was carried out at 100 keV and the dose was
f 41015
atoms Ocm2, higher than the critical threshold for producing lattice amorphization f 46Q1014
atoms Ocm2, calculated on the basis of the conventional models [9].
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3. – Results and discussion
Carefully measured intensity of diffraction scattering in conventional semi-logarithmic scale is shown in fig. 2a).
Numerical simulation of scattering intensity angular curve was carried out using the concept of asymptotic Bragg diffraction (ABD) [2] also known as crystal truncation rod scattering [10]. The theory of asymptotic Bragg diffraction is based on kinematical approximation which is valid when the scattering amplitude is small NR(Dw)Nb1. The following well-known expression could be used for the description of ABD:
R(Dw) 4 ik 2 g0
0 Q xhexp [iqz] f (z) dz , (1) f (z) 4exp [2Ws(z) 2iW(z) ] , (2)where k 42pOl is the wavevector; g0 is the direction cosine of the incident beam;
q 4k[x01 sin ( 2 wB) Dw] Og0is the angular variable; x0 , his the Fourier component of the polarizability. The function f(z) describes the structural perfection of the crystal. Distortions in eq. (2) are represented by the so-called static Debye-Waller factor
Fig. 2. – CuKa1 radiation, 004 reflection. Experimental (dots) and calculated (solid) angular
curves of diffraction scattering intensity (a) and reduced intensity (b) from InP sample implanted with O1.
exp [2Ws(z) ] which stands for the local disorder and the phase W(z) 422pOdhQ
s
02Dd Odhds, where dhis the interplanar spacing in the substrate, which depends on the
lattice deformation in the surface layer.
Far from Bragg condition due to the multiplier exp [iqz] the integrand in (1) is a fast oscillating function with the period T 42pONqN. It is clear that fast oscillations of the integrand reduce the value of the scattering amplitude. Physically those oscillations reflect destructive interference of X-rays diffracted by crystal layers located at different depths. If the functions Ws(z) and W(z) change slowly at the
distances of the order of T, then for scattering amplitude it is possible to use the following asymptotic formula:
R(Dw) 4 ik 2 g0 xh f ( 0 ) q
k
1Og
1 qh
l
, (3)valid for Dw0bNDwN b wB, where Dw0 is the angular width of the Bragg peak. Formula (3) could be derived by integrating (1) by parts [2] and it implies that Bragg condition is not met at any depth.
Thus at high deviations from the exact Bragg position the intensity of diffraction scattering:
I(Dw) 4NR(Dw)N2P Nexp [2Ws( 0 ) 2iW(0) ]OqN24 exp [22 Ws( 0 ) ] Oq2.
(4)
Equation (4) shows that in asymptotic mode the diffracted intensity is directly proportional to the static Debye-Waller factor of the surface. It is plain to see from (4) as well that the angular curve of the so-called reduced intensity I(Dw) Dw2 is more informative than conventional plots of I(Dw) in semi-logarithmic scale. It should be noted that for correct interpretation of ABD data the curve of reduced intensity must be normalized in such a way that I(Dw) Dw2
K 1 when Dw K 60. Of course, the angular domain of dynamic scattering must not be considered. For a perfect crystal the reduced intensity is a constant, since I(Dw) P1ODw2. Vice versa in a crystal with a smooth interface between perfect substrate and amorphous film on top, I(Dw) Dw2
K 0 when Dw K6Q since in such a crystal f(0) 40. One may find elsewhere [2, 6, 11-13] examples of ABD method applied to surface crystal structure investigation.
The reduced intensity from the implanted InP crystal in study is shown in fig. 2b).
The fit of experimental reduced intensity profile started from different initial approximations. There were found several equivalent strain and damage profiles, proved to be rather close to each other. One of them which provided the minimum to x2 is shown in fig. 3. All of the discovered solutions including the depicted one display monotonous damage profiles that spread to a considerable depth of several quantity of a hundred nm. The damage of the surface proved to be considerable, since exp [2Ws( 0 ) ] B0.3. The strain was found to be negative (lattice contraction) and it
differs from zero in a subsurface region thinner than 200 nm.
However, direct examination of the obtained profiles in the dynamical domain resulted in obvious disagreement of calculated (dashed line in fig. 4) and experimental angular curve of photoelectron yield in high-energy band (dots in fig. 4). It proves that the discovered profile allows to obtain good description of the HRXRD experimental data, but it is not enough accurate to match the XRSW data in a region very close to the surface.
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Fig. 3. – Depth profiles of static Debye-Waller factor and lattice strain.
Nevertheless we managed to improve considerably the agreement between calculated and experimental angular curves of photoelectron yield by taking into account the following. The shape of experimental photoemission curve in the dynamical domain reminds the one of the rocking curve (fig. 4). This feature is specific to the yield from a completely disordered layer situated on top of a nearly perfect substrate. Really the yield from a disordered film is directly proportional to the sum of incident and diffracted wave intensities since the periodic structure of the standing-wave field formed by a perfect substrate cannot be revealed by the ensemble of randomly distributed absorbers (see ref. [14] and references therein). We carried out numerical simulations of the low–energy-loss photoelectron yield relying on the profile depicted in fig. 3 and amorphous layers of various thicknesses on top of the crystal. A good agreement (solid line in fig. 4) was obtained for a completely disordered layer whose thickness was not less than 60 nm.
To investigate a greater depth in the crystal, the photoelectrons in the low-energy band were collected. Despite of the considerable difference of the escape depths, the angular curves of the yield for the mentioned energy bands displayed complete coincidence. This implied that also in the case of low-energy band, most of electrons were produced in an amorphous layer. More careful numerical simulations allowed to conclude that the thickness of the amorphous layer was not less than
Fig. 4. – Experimental and calculated (solid, dashed lines) double-crystal CuKa1004 rocking
curves (triangles) and low-loss photoelectron yield angular profiles (dots). The solid-line graph of photoelectron yield was calculated assuming 60 nm thick amorphous layer on top of the crystal.
200 nm. Finiteness of the escape depths of photoelectrons did not permit a more precise determination of the amorphous layer thickness.
A reasonable question to be considered is whether it was possible to detect total damage of the surface by means of HRXRD only. We do not imply the possibility to detect an amorphous layer since the presence of a thin disordered film on top of a crystal is not «visible» for HRXRD as well as for other conventional X-ray diffraction methods. Was it possible to detect the interface between amorphous layer and crystal where scattering power of crystal matter drops to zero? The answer is positive and it is based on the behavior of the reduced intensity curve which sharply drops to zero on the low angle side
(
fig. 2b))
. However, to confirm this conclusion by direct simulation of HRXRD data, it should be necessary to extend the angular range of HRXRD measurements especially on the high angle side. Probably the failure of HRXRD in this particular case was due to the relative abruptness and thus the small thickness of the interface layer where exp [2Ws(z) ] changes from 0.3 to zero. Insufficient influence onscattering amplitude of this layer means that its thickness was considerably smaller than the period of oscillations T 42pONqN which at the deviation of 900 s of arc is about of 21.5 nm. It is plain to see however that measuring X-ray diffraction intensity beyond the limit of 900 s of arc could be a rather time-consuming operation, at least in comparison to the XSW measurements near exact Bragg position.
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4. – Conclusions
The present results demonstrate the advantages of joint use of XSW and HRXRD techniques. An investigation has been performed on a (001) InP crystal implanted with O1at a dose f 41015
atoms Ocm2, larger than the critical one for amorphization. It has been shown that the use of XSW techniques besides direct analysis of equivalent strain and damage profiles is able to provide valuable complementary information on completely disordered surface layers which is not accessible by conventional X-ray diffraction methods.
In addition to this, we have measured both low- and high-energy photoelectrons. By numerical simulation of the experimental X-ray diffraction and photoelectron yield profiles and amorphous surface layer of at least 200 nm has been found.
Based on the present result, we can conclude that the energy analysis in XSW technique allows one to determine the thickness of such disordered layers or, in the case of thick amorphous films, to show the low limit of their thickness.
* * *
The authors are grateful to Dr. C. SPAGGIARI(Istituto Donegani, Novara, Italy) who provided the sample.
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