Imaging Surface Topography using Lloyd’s Mirror in Photoemission Electron Microscopy

We use Lloyd’s mirror to modulate electron photoemission in photoemission electron microscopy. This results in the projection of Lloyd’s fringes on to three-dimensional (3D) surface objects. An iterative reconstruction method is used to correct for distortions in the fringe pattern due to the cathode immersion lens, thereby providing a quantitative interpretation of surface shape. It is therefore possible to extract 3D height information directly from a two-dimensional, plan-view image. The technique is of sufficient intensity and contrast to study real-time changes in surface topography and we apply the method to study unusual contact-line dynamics during the reactive wetting of metal droplets.

Figure 1

(a) Lloyd’s mirror PEEM geometry for imaging a surface cluster. (b) Schematic of photoelectrons emitted at various points on the surface cluster, which are accelerated by the electric field $E_0$. The electrons are focused by the lens $L$ onto the PEEM screen $D$. Electric field perturbations, arising from surface roughness $h(x,y)$, affect the photoelectron trajectories (1), (2), and (3), giving rise to fringe shifts $S_x^{(i)}$ ($i=1,2,3$).

Figure 2

Schematic cross section of a reactive liquid Ga droplet on GaAs (001). Here ${\theta }_t$ and ${\theta }_b$ denote the partial contact angles, ${\sigma }_{\mathrm{SV}}$, ${\sigma }_{\mathrm{LV}}$, and ${\sigma }_{\mathrm{SL}}$ are the energies of the solid-vacuum, liquid-vacuum, and solid-liquid interfaces, respectively.

Figure 3

(a) PEEM image of a liquid Ga droplet (at $620°\mathrm{C}$) on a GaAs (001) substrate showing Lloyd’s fringes. (b) Simulation of the photoemission signal intensity $I$ as a function of the height $z$ for an ideal monochromatic point source with $\lambda =253.65\mathrm{nm}$ (solid line), and an aperture $R/d=0.025$ incoherently filled with polychromatic sources ($\overline{\lambda }=253.65\mathrm{nm}$, $\Delta \lambda =20\mathrm{nm}$) (dashed line). In both cases $\alpha =16°$. The arrow in (a) indicates multiple reflections (see text).

Figure 4

(a) Enlargement of the Ga droplet region corresponding to the framed box in Fig. 3a. (b) Intensity line trace $I_F$ measured along the solid white line. (c) An interpolated first approximation to the quasi-1D shape function $h(x)$. This is based on the application of Eq. (5) to the bright Lloyd’s fringe positions, indicated by the solid squares. (d) Reconstructed shape function obtained by an iterative method based on the inverse Hilbert transform of Eq. (7). This facilitates the calculation of the undistorted bright fringe lateral positions, from which the partial contact angle of the Ga droplet is determined (${\theta }_t\approx 22°$). The shaded portion denotes the range of reconstructions based on successively removing bright Lloyd fringes (7) and (8), respectively. This shows that the number of fringes does not significantly influence the reconstructed contact-line region.