Detailed characterization of supported eutectic droplets using photoemission electron microscopy

Pt-Ge eutectic alloy droplets are scrutinized by microscopic analysis of electrons excited by 4.9-eV photons. Using only the work function and contact angle as fitting parameters, we determine the exact droplet shape that reproduces the experimental electron emission profile. The local inclination of the droplets' surface plays a decisive role in the generated emission profile. Intensity variations at the illuminated side of the eutectic droplets are a consequence of standing waves in the electromagnetic field responsible for excitation. Intensity variations at the nonilluminated side are ascribed to a diffraction pattern of the photons after their interaction with the droplet.

Figure 1

Frame from a PEEM movie showing eutectic PtGe droplets on Ge(110). Illumination direction is along the red arrow. Field of view is $150\mu \mathrm{m}$. The irregularly shaped bright feature next to droplet 4 is due to a defect in the microchannel plates of the detector.

Figure 2

Profile of a spherical cap with radius $R$ and a contact angle $\alpha$ of the eutectic PtGe droplet along the red line in Fig. 1. The illuminated part of the droplet-vacuum interface is indicated by the dark blue line. Photoelectrons originate also from a thin skin (fading blue rim, exaggerated for clarity).

Figure 3

(a)–(d) Measured and calculated intensities along the optical plane of incidence through the droplets (1)–(4), respectively, in Fig. 1. The blue circles represent the experimental data, the solid blue lines are the fits using Eq. (6) with $\alpha ={20}^{\circ }$ and $m=5.5$ in (a) and $\alpha ={18}^{\circ }$ and $m=4.5$ in (b)–(d). The dotted black line and the dashed-dot green line in (a) are the calculated contributions without the ${sin}^m\varphi$ term for the surface and the thin bulklike shell, respectively, with the red dashed line being their sum. The solid gray lines are calculations of the diffraction patterns behind the droplet (see the text). (e) Cross-sectional profile of droplet (1). The five red dots in the lower panel are experimentally determined points of the droplet's surface (see the text).

Figure 4

(a) Construction of the standing wave interference pattern of the photon intensity (see the text). Solid and dashed lines correspond to constructive and destructive interference, respectively. (b) and (c) Radially averaged intensity profile, obtained for droplets 1 and 2 from Fig. 1 and derived from the segments shown in the insets representing the illuminated sides as a function of distance from the leading edge. Again constructive and destructive interference are marked by solid and dashed lines.

Figure 5

Schematic of the diffraction geometry. The solid/dashed black line $l$ displays the optical axis of the problem. The droplet is treated as sphere with height $a$. The distance between the intersection point of the optical axis and the surface and the center axis of the spherical cap is $e$.

Figure 6

Measured and calculated intensities along the optical plane of incidence through the droplets encircled in the insets. The blue crosses represent the experimental data for the droplet encircled in the left inset, which is illuminated from the receding side. The red plusses represent the data for the droplet in the right inset, which is illuminated from the advancing side. The solid blue lines, which are virtually identical, are the fits using Eq. (6) with $\alpha =16.3^{\circ }$ and $m=4.5$.

Figure 7

LEEM I(V) measurements obtained on an eutectic droplet (blue squares), the surrounding area (red circles) and a pristine Ge(110) surface.