Where two crystalline solids meet and bond together the atoms or molecules will form an interface structure, the most general example being grain boundaries in polycrystalline materials. For such boundaries between identical materials the misorientation between the two crystals determines the interface structure. We can distinguish between rotational misfit, twist, and bending misfit, tilt. Usually the boundaries have both tilt and twist misfit and are buried deeply inside solids and therefore difficult to study. However, semiconductor wafers can be bonded together with predetermined orientations and with ideal covalent bonds [1]. Using this technique combined with the intense X-ray beams at moderately high energy (23 keV) available at the ESRF, it has been possible to take detailed measurements of the atomic structure of the interface of bonded silicon crystals as a function of both twist and tilt angles.

Apart from being an ideal model system for grain boundaries, the interface of bonded silicon wafers are also of interest for potential applications of practical value. Determined by the chosen twist and/or tilt orientations, periodic elastic modulations are induced in the region around the interface and this can give rise to novel electronic and optical properties. Further, by a special technique, a wafer may be thinned down to the extent that the elastic modulation from a bonded interface may reach through the entire wafer to the external surface thus inducing a modulated surface structure with a periodicity given by the twist and/or tilt misfit.

The silicon wafers are bonded as follows: Standard 350 µm thick wafers are dipped in HF acid removing the native oxide layer and resulting in hydrogen terminated surfaces. In a clean room the wafers are contacted and finally they are annealed above 1000°C to achieve covalent bonding at the interface [2].

Figure 103 shows a pair of bonded crystals with twist angle and with thickness t of the modulated interface. Measurements at the ESRF, performed at beamline ID32, have shown that the thickness t of the modulated interface varies from a few Å to several hundreds Å, and the functional form of the elastic modulation can be quite accurately determined. In Figure 104 the left panel shows the reciprocal lattice, parallel to the interface of the bonded crystals turned by the angle q from each other. The circles show the (h, k)-coordinates of bulk Bragg points of the two crystals whereas the crosses correspondingly show where the diffraction signal from the modulated elastic deformation may be observed. By measuring the scattering intensity at many of these cross-positions both harmonic and anharmonic terms of the deformation-waves are determined. The line shape of the decay of the elastic deformation away from the interface is measured in diffraction scans perpendicular to the interface.

The width (fwhm) of such diffraction profiles varies dramatically with the twist angle q as shown in Figure 105. This width can be translated into the thickness t of the interface, also given in the figure. By line shape analysis, the decay function of the harmonic component of the elastic deformation is proven to be exponential and the interface thickness t is determined as the double exponential decay length.

The experimental results are in good agreement with an idealised model for the interface, where all the deformations are described by a lattice of dislocations located in the interface. In Figure 105 the full line is calculated using this model. For twist angles smaller than 8 degrees the thickness is inversely proportional to and this holds at least down to the smallest angles studied, = 0.2 degree. For > 8 degrees t becomes a few atomic layers independent of .

References
[1] M. Nielsen, R. Feidenhans'l, P.B. Howes, F. Grey, K. Rasmussen, J. Vedde, Surf. Sci. Lett., 442, 989 (1999).
[2] S. Weichel, F. Grey, K. Rasmussen, M. Nielsen, R. Feidenhans'l, P.B. Howes, J. Vedde, Appl Phys. Lett., 76, 70 (2000).

Authors
M. Nielsen (a), R. Feidenhans'l (a), P.B. Howes (a, b), S. Weichel (c), F. Grey (c), M. Poulsen (c), J. Vedde (d).

(a) Risø National Laboratory, Roskilde (Denmark)
(b) Now at University of Leicester (UK)
(c) Mikroelektronik Centret, Technical University of Denmark (Denmark)
(d) TOPSIL Semiconductor Materials A/S, Frederikssund (Denmark)