Atoms arrive from an effusion-cell beam at flux F (atoms per site per second) and land on a substrate grid. Whether the film grows flat, layer by layer, or as rough 3-D mounds depends on how far an adatom can hop before it gets buried — its surface diffusion length, which grows with substrate temperature T through an Arrhenius hopping rate.
D(T) = D0 · exp(−E_d / k_B T) (adatom surface diffusion)
σ(t)² = ⟨h²⟩ − ⟨h⟩² (r.m.s. surface roughness)
I_RHEED ∝ exp(−4σ²) (kinematic specular intensity)
- Flux F — deposition rate. Higher flux buries adatoms before they find a step edge, favoring roughening; lower flux gives more time to diffuse.
- Temperature — sets the diffusion search radius. Low T ≈ 300 K: atoms stick where they land (random ballistic deposition), building rough, fractal-looking 3-D islands — Volmer–Weber-like growth. High T ≈ 900-1000 K: atoms hop to the nearest unfilled site of the current layer, completing it before the next one nucleates — Frank–van der Merwe layer-by-layer growth.
- Roughness σ — the standard deviation of the height map, in monolayers (ML). It rises as a layer nucleates and falls again as that layer fills in, which is exactly what drives the oscillation below.
- RHEED intensity — real MBE reactors fire a grazing electron beam at the growing film and watch the specularly reflected spot. A flat surface reflects strongly; a half-filled, rough layer scatters diffusely and the spot dims. Because σ oscillates once per completed monolayer in the layer-by-layer regime, the RHEED intensity oscillates too — each full period is literally a stopwatch for one atomic layer, which is how real MBE labs count layers in situ.
Real-world relevance: this diffusion-vs-burial competition is exactly what a materials scientist tunes when growing a quantum-well or topological-insulator film by MBE — the wrong temperature or flux turns an atomically flat interface into a rough one, degrading the electronic properties the deposition was meant to engineer.