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Scattering of x-ray and synchrotron radiation by porous semiconductor structures.

1. Introduction

Regardless of the considerable interest in nano- and mesoporous crystalline materials, the physics of diffraction of x-rays on these materials has been studied insufficiently. This is associated with both the absence of stable and guaranteed simulation specimens for the investigations and also with the complicated description of the processes of scattering in porous structures.

For example, one of the special features of diffraction on these objects is that, regardless of the relatively high (>80%) porosity and the size of the pores expressed in units of nanometres, the 'skeleton', remaining from the monocrystalline material, may cause dynamic scattering of radiation [1, 2].

At the same time, the scattering on such objects is characterised by a strong diffusion component. In addition, it is also necessary to take into account the effects of low-angle scattering of x-ray radiation on the boundaries of the pores.

At present, there are no detailed theoretical models for describing scattering of these structures. Therefore, various quantitative characteristics of the structures, such as thickness L, porosity P, the degree of coherence of the crystals [f.sub.c], the profiles of the distribution of electronic density [rhp](z) and deformation d(z) of the lattice, surface roughness, the geometrical dimensions of the pores, the surface morphology and other parameters, have not been extracted from the conventional x-ray diffraction methods.

In the study, investigations were carried out into the special features of the diffraction of x-ray and synchrotron radiation on single-layer and multilayer porous structures InP (001) with different types of pores. Special attention is given to the possibilities of numerical characterisation of the parameters of the pores on the basis of the analysis of sections and charts of the two-dimensional distribution of the intensity of diffraction reflection--reciprocal space mapping (RSM) around the node of the reciprocal lattice.

2. Experiments

Investigations were carried out on the standard substrates InP (001)

(Sn ~ [10.sup.18] [cm.sup.-3]). The porous layers with the thickness of ~0.5-2.5 [micro]m and the multilayer structures were produced by anodising using the technology described in [3]. Two types of pores formed in the subsurface layers of the specimen: along the normal to the surface (TO-pores) and under the angle a to the surface--crystallographically oriented (KO-pores).

The x-ray diffraction investigations of the 004 reflection were carried out by the method of the diffraction reflection curves (DRC) and the sections of the node of the reciprocal lattice (TRD spectra). The diagram of positioning of the crystals taking into account the crystallographic special features of the specimens is shown in Fig. 1. The study was carried out using copper radiation. The primary beam was formed by a slit monochromator (M) (with triple reflection 004 Ge and directed to the investigated specimen either from the side of the polar (110) or non-polar face (1-10) by selecting the azimuthal angle [phi]. In recording the TRD spectra the crystal-analyser (A) was in the form of Ge (004). The diffraction curves obtained for the investigated specimens for the two azimuthal angles [phi] = 0[degrees] and 90[degrees] are shown in Fig. 2 and 3. The RSM charts from the single porous layers (Fig. 4) were recorded in a BEDE diffractometer ([lambda] = 0.154 nm) and those from the multilayer porous structures were recorded using synchrotron radiation (wavelength X = 0.12398 nm in station E2 (DESY, Hamburg)) using a Mythen positional detector.




3. Experimental results and discussion

Fig. 3 shows the two-crystal DRC (curve 1) obtained from the specimen with the TO-pores. It can be seen that the resultant interference pattern consists of wide humps and fine oscillations around the main Bragg peak. The almost symmetric shape of the curves in Fig. 3 shows that the layers of the porous InP (001) are not subjected to deformation, characteristic of the layers of porous silicon.

The sections of the 004 node produced from the same specimen in the direction normal (curve 2) and along (curve 3) the surface of the specimen greatly differ. The 'tails' of the curve 2 show fine-period oscillations, indicating the existence of the coherently scattering layer with the thickness [L.sub.nop] = ([lambda][gamma]h) [DELTA][theta]sin2[[theta].sub.B] ~ 0.5 [micro]m ([[theta].sub.B] = 31.7[degrees] for the 004 InP reflection), yh is the directing cosine. The fraction of the coherently scattering crystals is associated with the amplitude of oscillations and can be determined by the simulation of the theoretical reflection curve. The good agreement between the experimental and theoretical curves was obtained at the static Debye-Waller factor f = exp (-W) [approximately equal to] 0.26 for the specimen with the TO-pores. Transferring to analysis of the curve 3, it should be mentioned that the position of the secondary maxima in the form of 'shoulders' makes it possible to determine only the mean distance L between the pores.

In order to construct the model of the pores and determine the parameters of the pores and morphology, it is necessary to analyse a series of the RSM sections. For this purpose, DRC curves were recorded for the specimens with the KO-pores (Fig. 4) at different azimuthal positions with respect to the angle. It can be seen that on the curves obtained with the non-zero position of the crystal-analyser in addition to the wide diffusion scattering (DS) with two 'shoulders' there are also additional peaks: the main peak (MP), the pseudo-peak (PS) from the crystal-analyser, and the maximum (MB) in the area of the pseudo-peak (PM) from the crystal-monochromator.

The size of the pores on the surface of the specimen is inversely proportional to the width of the diffraction maximum at the exact Bragg angle: [l.sub.x] [approximately equal to] [lambda]/2[DELTA][theta]sin [[theta].sub.B]. In the case of relatively high porosity (P [greater than or equal to] 50%) there maybe a short-range order in the distribution of the pores leading to the formation of additional maxima on the intensity of diffusion scattering reflected in the form of symmetrically distributed 'shoulders'. The intensity and width of these 'shoulders' are determined by the correlation parameters, and by the dimensions and orientation of the porous interlayer.

The analysis of the type of pores shows that the mean distance between the points along the surface L = 2[pi]/[q.sub.x] ~ 140 nm, and the size of the pores is [l.sub.x] [approximately equal to] 90 nm. The mean size of the 1 1s in the depths of the layer can be obtained from the analysis of the section of the RSM. On the basis of the investigated model and the kinetic approximation we can use the expression [l.sub.z] [approximately equal to] [lambda]/2[DELTA][[theta].sub.z] cos[[theta].sub.B], where [DELTA][[theta].sub.B] is the width of the peak in the section along [q.sub.z] (Fig. 4). Consequently, for the longitudinal dimensions of the pores we obtain [l.sub.z] [approximately equal to] 1250 nm.

Analysis of the DRC spectra explains the transformation of the intensity distribution of diffusion scattering in the case of the deviation of the pores in the diffraction plane, to determine the type of pores, and from the angular position of the 'shoulders' determine the mean angle of inclination of the pores in relation to the surface of the specimen (in the case of KO-pores in Fig. 4 the angle is 56[degrees]). The physical reason for the low-angle Bragg (MB) scattering is associated with the initial diffusion of the primary beam in intersection of a large number of boundaries and can be used for determining the number of these boundaries [4].


The experimental and theoretical charts RSM for the specimens of InP (004) with the KO-pores in a single porous layer and in a multilayer structure are shown in Figs. 5 and 6, respectively. The charts (Fig. 5) show the distinctive azimuthal dependence on the position of the specimen. There are areas with increased intensity--'strands', positioned under a certain angle to the direction [q.sub.z]. These 'strands' are the Fourier images of the shape of the scattering object of the boundaries or of the projections onto the scattering plane. In particular, these boundaries are represented by the walls of the crystallographically oriented pores. It should be mentioned that the scattering, caused only by the TO-pores, does not show any significant azimuthal dependence. The RSM charge obtained from the multilayer porous structure are more complicated and do not permit the previously described unambiguous interpretation. The model [5] was used for different numerical calculations of the RSM (Fig. 6c, d) and for obtaining structural parameters (Table 1).

Thus, it was shown in the investigations that the analysis of diffusion scattering from the porous systems can be used for the nondestructive diagnostics of these systems. However, in the case of multilayer porous systems without taking into account apriori information and the data, for example, those obtained in electron microscopy, there may be an ambiguity in the determined parameters and this has been evidently reflected in the large value of their dispersion (Table 1).




[1.] A. A. Lomov, D. Bellet, and G. Dolino, Phys. Status Solidi B, 190, 219 (1995).

[2.] D. Buttard, D. Bellet, G. Dolino, and T. Baumbach, J. Appl. Phys., 83, No. 11, 5814 (1998).

[3.] D. Nohavica, P. Gladkov, J. Zelinka et al., Proceedings Conf. NaNo 04 (Brno, Czech Republic: 2004), p. 176.

[4.] A. A. Lomov, V. A. Bushuev and V. A. Karavanskii, Kristallografiya, 45, No. 5, 915 (2000).

[5.] V. I. Punegov and A. A. Lomov, Pis'ma v ZhTF, 34, No. 6, 30 (2008).

A.A. Lomov

Institute of Crystallography, Russian Academy of Science, Leninskii Prospekt 59. 119333 Moscow, Russia
Table 1. The parameters of the pores in the multilayer porous
structure InP (001), restored on the basis of mathematical analysis of
the RSM charts in the vicinity of the 004 reflection, E = 10 keV

                   Mean parameters of pores and their dispersion

Radius of          Length             Radius               Deviation
inclines           of inclined        of vertical          of the num-
pores [R.sub.KO]   pores [l.sub.KO]   (apores [R.sub.TO]   ber of pores
([sigma]), nm      nm                 ([sigma]), nm

40(15)             60(20)                 40(15)               200(80)

                   Mean parameters of pores and their dispersion

Radius of          Lateral                Lateral quasi-
inclines           quasi-                 period
pores [R.sub.KO]   period [T.sub.[100]]   [T.sub.[1-100]] ([sigma]), nm
([sigma]), nm      ([sigma]), nm

40(15)             0.4                    160(50)

                   Mean parameters of pores and their dispersion
Radius of
pores [R.sub.KO]   [alpha], ([degree])
([sigma]), nm

40(15)             56(10)
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Author:Lomov, A.A.
Publication:Physics of Metals and Advanced Technologies
Article Type:Report
Geographic Code:4EXRU
Date:Jan 1, 2010
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