PC4259 Chapter 5 Surface Processes in Materials Growth & Processing Homogeneous nucleation: solid (or liquid) clusters nucleated in a supersaturated vapor of pressure P 0 Thermodynamic driving force --- free energy change per unit volume of condensed phase: ΔG v = -nkT ln (P 0 / P ∞ ) (P ∞ : equilibrium vapor pressure over solid, n: solid atomic density) When a growing sample is nearly in equilibrium with vapor, nucleation and growth is mainly governed by thermodynamics

Formation of spherical cluster of radius r : energy increase due to surface energy 4πr 2 γ, so total energy change:  G r r crit Critical cluster radius: Energy barrier: ΔG homo (r) = (4πr 3 /3)ΔG v + (4πr 2 )γ When r > r crit, the cluster becomes thermodynamically stable

Heterogeneous nucleation: clusters are formed on a substrate (Cluster/substrate interface energy  int, substrate surface energy  s ) Truncated sphere of contact angle: When  s   int + ,  = 0, complete wetting When  int   s + ,  = 180˚, spherical ball without any wetting Free energy barrier for stable nucleation:  G het =  G homo (2 + cos  )(1 - cos  ) 2 /4 Hetero-nucleation barrier is significantly lower than that of homo-nucleation in general! θ = cos -1 [(γ s - γ int )/γ]

Epitaxy: Crystalline film growth on a crystalline substrate in a unique lattice orientation relationship Growth proceeds as atomic layers stacking up sequentially Three growth modes γ int ≤ γ s – γ f γ int ≤ γ s – γ f with misfit γ int ≥ γ s – γ f

Stranski-Krastanov growth of Ge on Si(001) 3D islands formation ~ 3.5 ML Ge, 475°C, (110nm) 2 huts pyramids Wetting layer ~ 2.5 ML Ge, 475 °C, (44nm) 2 4% lattice mismatch between Ge & Si

Atomic Processes in Nucleation & Growth Adsorption, diffusion, incorporation, nucleation, desorption, coarsening Si islands on Si(001)

Thermal activated process, hopping frequency: Atomic Diffusion on Terrace Diffusivity: Diffusion barriers of Rh on Rh surfaces Anisotropic diffusion

Migration of cluster on surface

Fractal islands obtained in hit-and-stick or diffusion-limited- aggregation (DLA) growth Equilibrium island shape determined by step free energy anisotropy Islands grow in relatively compact shape at a raised T

Atom detachment makes small islands unstable. At given T & F, there is a critical island size i to which addition of just 1 atom makes it stable Fe on Fe(100) growth at F = ML/s,  = 0.07 ML but different T. E diff = 0.45 eV & i = 1 from lnN vs 1/T Island density N & deposition amount  are related as: where:

Island size distributions: N s density of islands of size s, so: Average island size: Scaling function:

Coarsening of islands Island coalescence: merging of islands in contact Ostwald ripening: vapor of smaller islands absorbed by larger ones Gradient of vapor pressure generates atomic flux towards larger island Kelvin effect:

4 stages in sub-ML nucleation & growth: 1.Low coverage (L), nucleation dominates 2.Intermediate coverage (I), island density approaches saturation 3.Aggregation (A), island density saturates 4.Coalescence (C), island density decreases Variation of density of islands (n x ) & adatoms (n 1 )

Inter-layer atomic transport in growth Layer-by-layer growth requires sufficient inter-layer atomic transport Ehrlich-Schwoebel barrier E ES : additional barrier for adatom jumps down a step edge due to less neighbors than at a regular terrace site

Insufficient inter-layer transport leads to multilayer growth & a rough surface If inter-layer atomic motion is completely forbidden, the coverage of first layer  1 satisfies: Coverages of upper layers  n, n = 2, 3…, can be found in similar way (see Homework 9.1)

Step-flow growth: atoms quickly migrate to step edges instead of island nucleation, film growth proceeds as the advancement of existing steps Three kinetic growth modes: Phase diagram

Monitoring growth morphology STM & AFM: high resolution for atomic details for both homo- and hetero-epitaxy; but interrupt growth, time consuming and limited sample size (~ 1 cm 2 ) AES: for heteroepitaxy, monitoring film & substrate peak intensities. Different intensity variation characters in different growth modes If layer-by-layer: If island growth, nearly linear variations

Reflection high-energy electron diffraction (RHEED) For real-time surface monitoring in molecular beam epitaxy 1. Surface reconstruction 2. Period in layer-by-layer growth 3. 2D or 3D growth

RHEED Pattern RHEED in MBE System Surface reconstruction Streaky diffraction pattern from a flat surface

Rough vs. Smooth Surface Rough & 3D: Spotty pattern Smooth & 2D Streaky pattern

RHEED Intensity Oscillation When electron waves from neighboring atomic layers interfere destructively 1 oscillation cycle = 1 ML For precise growth rate & film thickness control

Modification of Growth Morphology by Surfactant General surfactant: adsorbed layer modifies surface thermodynamic properties, e.g. surface tension, friction coefficient, sticking power Surfactant in film growth: adsorbed impurities which facilitate, thermodynamically or kinetically, the growth proceed in a desired mode, normally layer-by-layer Surfactant should keep floating on surface so it is not consumed in growth, so surfactant should have a low surface energy, e.g. Sb (  ~ 0.6 J/m 2 )

Surfactant based on thermodynamics  Film is covered with 1 ML of surfactant with a lower   Deposited atoms exchange position with surfactant atoms in order to reduce   Floating surfactant layer keeps film surface smooth

Surfactant based on kinetics Some surfactant atoms tend to decorate step edges; deposited atoms can take the sites of surfactant atoms and push them outward, an effectively lower E ES Some surfactant atoms act as nucleation centers to form a large density of islands with small size. Atoms deposited later easily attach to island edges instead of nucleation of upper-layer islands. Such film surface appears rough at small scale but smooth at large scale. surfactant