E59 · Surface spectromicroscopy

LEEM: Surface Reflection & Diffraction

Sweep low-energy electrons across a two-domain surface. Select a reflected order to form an image, inspect stored region intensity curves and record a separate micro-LEED pattern with a field aperture. Find contrast reversals and the energy where a diffracted order can propagate.

Imaged order $\text{—}$

Selected nominal landing energy $\text{—}$

Stored region image counts $\text{—}$

Phase A / B recorded contrast $\text{—}$

Separate micro-LEED counts $\text{—}$

First-order propagation threshold: phase A $\text{—}$

Assumed image FWHM $\text{—}$

Total image-stack exposure $\text{—}$

Experiment target $\text{—}$

Predict · select · explain

Can one diffracted beam isolate a surface domain?

Stored nominal landing energy

E_0

25\,\mathrm{eV}

Source-energy standard deviation

\sigma_E

0.15\,\mathrm{eV}

Contrast-aperture reciprocal radius

q_a

1.2\,\mathrm{\mathring A^{-1}}

Imaged order: 0 BF, 1 A, 2 B

0

Exposure per energy step

t

0.4\,\mathrm{s}

Field-aperture center: horizontal

x_s

-1.5\,\mathrm{\mu m}

Field-aperture center: vertical

y_s

0\,\mathrm{\mu m}

Selected-area radius

r_s

0.6\,\mathrm{\mu m}

Target: select the phase-A first order above 22 eV with a reciprocal aperture radius from 0.2 to 0.5 inverse angstrom. Keep source spread at or below 0.3 eV, select only phase A, acquire more than 500 region counts and obtain recorded domain contrast above 0.8. A bright-field image cannot complete this dark-field task.

Lossless attractive-slab teaching model, not a real-material dynamical LEED calculation or thickness reconstruction. Both domains have an assumed 3 angstrom square lattice; thicknesses are 0.6 and 1 nanometre and rotations are 0 and 30 degrees. Their relative surface-potential offsets are 0 and 0.4 eV. Gaussian source-energy averaging is applied before recording. Total elastic reflectivity comes from the exact symmetric slab solution; an invented partition sends 40 percent into four first orders when propagation is allowed. Grid-normalized reciprocal kernels conserve that elastic probability. A contrast aperture creates independent LEEM image counts; the micro-LEED data are a separate exposure with that aperture retracted and a real-space field aperture. Selected-area spectroscopy sums stored LEEM pixels. The image stack has 0.5 eV steps and 0.2 micrometre pixels. The 18 keV relay, spatial-width law and representative rays are schematic. Inelastic absorption, multiple-scattering crystal intensities, growth kinetics and real lens fields are omitted. Below the local landing threshold, mirror reflection occurs before the surface.

Physics tutorial

LEEM: Surface Reflection & Diffraction

BackgroundSweep low-energy electrons across a two-domain surface. Select a reflected order to form an image, inspect stored region intensity curves and record a separate micro-LEED pattern with a field aperture. Find contrast reversals and the energy where a diffracted order can propagate.

Why it mattersTarget: select the phase-A first order above 22 eV with a reciprocal aperture radius from 0.2 to 0.5 inverse angstrom. Keep source spread at or below 0.3 eV, select only phase A, acquire more than 500 region counts and obtain recorded domain contrast above 0.8. A bright-field image cannot complete this dark-field task.

Start with the essentials

Focus question: Can one diffracted beam isolate a surface domain?
One-sentence intuition: The diffraction-plane contrast aperture and real-space field aperture perform different selections. Energy-dependent intensity is a measurement that needs a scattering model, not a direct height map.

Core mathematical model

Propagating diffraction order

E_\perp=E_0-\frac{\hbar^2|\mathbf G|^2}{2m_e}

At normal incidence an elastic order requires nonnegative perpendicular kinetic energy. A relative surface potential changes local landing energy.

Symmetric attractive slab

R=\frac{\eta\sin^2(qd)}{1+\eta\sin^2(qd)}

The exactly soluble lossless slab has an attractive 10 eV well; the phase inside the film produces reflectivity oscillations.

Mismatch and internal wave number

\begin{aligned}\eta&=\frac{V_0^2}{4E(E+V_0)}\\q&=\frac{\sqrt{2m_e(E+V_0)}}{\hbar}\end{aligned}

Thickness, local energy and source-energy averaging set different intensity curves. No unique real-material thickness inversion follows.

Common difficulties

Brightness needs a model

Typical misconceptionA bright region directly reveals its physical cause.

Better mental modelThe diffraction-plane contrast aperture and real-space field aperture perform different selections. Energy-dependent intensity is a measurement that needs a scattering model, not a direct height map.

Run the experiment

01
Predict contrast reversal
In bright field, move through the energy stack and compare the two recorded domain curves.
What to observe: The brighter domain changes with energy; brightness alone does not label thickness.
02
Select an order and a region
Choose the phase-A dark-field preset. Move the field aperture from the left to the right domain.
What to observe: The image selects an angular order; the independent micro-LEED exposure selects a real-space region.
03
Check propagation and precision
Compare closed-order, wide-aperture, mirror and low-count presets.
What to observe: A closed order stays dark. A wide aperture mixes domains, while low counts undermine an otherwise correct selection.