| Science Home | Future students | Current students | Postgraduate | Research | Staff | Contact us |
| Staff directory | A-Z index | Site map |
| Science Home | Future students | Current students | Postgraduate | Research | Staff | Contact us |
| Staff directory | A-Z index | Site map |
Two-Dimensional Crystal-Lattice Strain Reconstruction with Nanometre Spatial ResolutionIon implantation is still widely used technique for the production of microelectronics devices. An effective control on the doped ions concentration distribution and stresses introduced by the impurities in the semiconductor crystal lattice is, thus, critical point of the technology enhancement. In the case of ion implantation without a mask the introduced atoms and radiation defects distribution is homogeneous along the sample surface and the methods of calculation of this distribution into the crystal depth are highly developed. However, in real microelectronics structures the implantation is being carried out usually through a special mask in order to form a desirable topology of the device. Thus, the introduced atom and point defect distribution is expected to be affected by stresses under the mask edges. X-ray diffraction is very useful non-destructive method of the crystal-structure characterisation. There were attempts to characterise the crystal lattice deformations under the oxide mask edge using X-ray topography (see, for instance, [1]). However, the imaging of the diffraction contrast is useless for the quantitative analysis of the observed data. Meanwhile, the diffraction contrast on the rocking curve from the crystal with one oxide strip on the surface is very weak to be analysed quantitatively. The best way to observe strong diffraction contrast from the crystal with the localised strains on the surface is to form periodic surface superstructure with a big number of the same strip edges [2]. Recently we have demonstrated that two-dimensional (2D) lattice distortions in near-surface layers of ion-implanted silicon crystals can be mapped with nanometre depth resolution from high-resolution x-ray diffraction data collected at a synchrotron source [3-4]. The maps show the distribution of lattice distortion perpendicular to the surface as a function of lateral position and depth in crystals implanted with 300 and 100 keV B+ ions. The samples were masked prior to the implantation with a one-dimensional 0.5 microns thick surface oxide film pattern with a 5.83 microns period and 4 microns open regions. The reconstructed profiles demonstrate 2D changes of the interplanar distances in a thin damaged layer of 1.5 and 0.6 microns thick, respectively. They show that the surface mask destroys the implanted ions channelling along the 111-axis perpendicular to the crystal surface and overlapping of the deformation peaks under the mask. From the previous study we know that the thermal annealing leads to reduction of diffraction contrast and eventually, its disappearance, after some critical temperature at which large defects clusters are formed [5]. To analyse the influence of the thermal annealing on the ions and defects distribution under the influence of the surface mask pattern we treated the samples studied in [4], by high temperature heating at 1000 C for 15 min. The present page presents some of the results of the analysis of 2D strain profiles in the 100 keV boron implanted samples before [4] and after [6] thermal annealing at 1000 C for 15 min. [1] Blech, I. A. & Meieran, E. S. J. of Appl. Physics, 38, 7 (1967). Strain Map Reconstruction ProcedureThe Fourier coefficients of the susceptibility of the distorted crystal: (1), where  is the Fourier coefficient of the ideal crystal susceptibility corresponding to the reciprocal lattice vector h. If the displacements are periodic in x with period a, then  can be expanded into a Fourier series with respect to x:  (2), where  (3). We have a continuum of different distributions of susceptibility
and the corresponding continuum of different displacement fields  (4), where  is the projection of the vector-field  onto the reciprocal lattice vector h. In the case of symmetric distortions with  it is possible to reduce the ambiguity of the choice of N+1 arbitrary real constants  (relative phases) to the choice of N signs  , each  . This reduction exploits the existence of the perfect crystal substrate under the thin damaged layer. After such a reduction formula (3) can be rewritten as  (5), with  . Thus, we have  different 2D profiles of susceptibility corresponding to different choices of the signs , and corresponding profiles , obtained from the given set of 1D Fourier harmonics ,  .
(AFTER: Nikulin, Gureyev, Stevenson et.al., J. Appl. Cryst., 28, 803 (1995)).  (a)  (b) 2D deformation profiles reconstructed for the Si(111) crystal implanted with 100 keV boron ions through a periodic oxide mask pattern (a) and annealed at 1000 C for 15 min (b). The relative phases of 11 satellite reflections were determined with the sequential trial method.  Table of results of two-dimensional deformation profiles reconstructed for the Si(111) crystals implanted with 100 & 300 keV boron ions through a periodic oxide mask pattern. |