Role of Surface Steps in Thin Film Growth and Properties Studied by Leem
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Mat. Res. Soc. Symp. Proc. Vol. 355 ©01995 Materials Research
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Figure 2: A monoatomic step is modeled as two opposed, semi-infinite apertures for calculating LEEM step contrast. (see text for full description).
Figure 1: LEEM image of defects at the W(1 10) surface, including monoatomic steps (dark lines) and dislocations (bright lines) [electron energy E = 11.7 eV; step height ao = 2.23 A; electron phase shift = 57r/2].
LEEM Step Contrast It is generally understood that step contrast in LEEM arises from interference of the electron waves reflected from terraces on opposite sides of a step. This interference occurs as a result of the phase shift, 4, of the electron wave across a step. Phase shift which is determined by the path length difference is accordingly given by 4o= 22t (2ao/l), where X is the electron wavelength and ao is the step height. Since the wavelength of electrons in the low energy regime appropriate for LEEM is on the order of the step height, large phase shifts across a step can be achieved which can be easily manipulated by small changes in imaging electron energy. Despite the importance of surface steps and the basic understanding of their imaging in LEEM, step contrast in LEEM has not been fully explored until recently [7]. In this recent work, an analytical, wave-optical model has been developed which permits a quantitative evaluation of steps with LEEM. This model and its predictions of step contrast which depend upon imaging electron energy and image defocus are described next. A monoatomic surface step is modeled as two opposed straight edge apertures which are shifted by the step height, ao , perpendicular to the surface and unshifted parallel to the surface (fig. 2). The LEEM reflection geometry is then mapped onto a transmission problem by replacing the real source with virtual sources below the surface. Two virtual sources must be used - one for each aperture - in order to maintain the original path lengths from the single real source to the two terraces. Step contrast is calculated as the interference of the Fresnel diffracted waves from the two aperture edges. This model is an adaptation and extension of Kastler's work on optical interference [9]. This wave-optical model predicts a rich interference phenomena caused by a surface step. Presence of wave interference in a plane beyond the step corresponds physically to the observation of step contrast upon defocus. In planes further removed from the step, the interference pattern appears broader. This is also seen in experiment with increasing defocus. 236
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Distance from the step (ao) Figure 3: Step contrast calculated for several values of electron wave phase shift, step. The parameter a0 is the step height.
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Step contrast calculated for several values of phase shift, i.e. elec
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