Film Nucleation and Growth Section IV Film Nucleation and Growth © 1998, Angus Rockett
Nucleation © 1998, Angus Rockett Nucleation is a process of reversibly adding atoms to a small cluster until the cluster becomes stable. Cluster energy rises initially (as r2) and then decreases (as r3). When the cluster is large enough that it is unlikely to disappear, nucleation is said to have occurred. 2.0 surface energy The critical radius r* 1.5 1.0 The nucleation energy barrier, E* 0.5 Cluster Energy (Arbitrary Units) 0.0 a “nucleus” -0.5 volume energy Substrate -1.0 -1.5 -2.0 1 3 5 7 9 11 Cluster Size (atoms)
Nucleation © 1998, Angus Rockett The nucleation rate, R, is the number of nucleation events per second which occur in a given population. Typically: R = rNa e -E*/kT Thus, higher energy barriers and lower temperatures delay nucleation. r: an attempt frequency (constant) N: the number of atoms/unit area E*: the nucleation barrier k: Boltzmann’s constant T: Temperature a: the effective reaction order Cluster Energy (Arb. Units) Cluster size (nm) -2.0 -1.5 -1.0 -0.5 0.5 1.0 1.5 2.0 1 2 2.5 3 3.5 The gray curve shows the effect of atomic diffusion barriers on the energy curve.
© 1998, Angus Rockett Nucleation As atoms stick to the surface a population grows which eventually leads to nucleation of a layer. Film Thickness Nucleation Delay Higher concentrations of adatoms decrease the nucleation delay. Time (sec) or Dose (Monolayers) Epitaxial growth on the same substrate does not require nucleation.
Growth Once nuclei have been formed these grow by collection of atoms and transfer of atoms between the nuclei, and coalesce by moving as a unit until two nuclei meet. Arriving atoms Transfer among nuclei & coalescence The rate at which nuclei grow depends on both the local atom density and the rate of supply of atoms by diffusion or arrival. Substrate Surface diffusion A step edge on a nearly flat surface acts as an infinite size nucleus. © 1998, Angus Rockett
Atomic-scale phenomena affecting nucleation & growth Fast Ions & Neutrals (and sometimes electrons) Thermal Species Adsorb Diffuse Desorb Coalesce into clusters Cluster growth Create preferential nucleation sites Disrupt small clusters Increase effective adatom mobilities Heat the surface Substrate © 1998, Angus Rockett
Strong chemical bonding © 1998, Angus Rockett Adsorption Incident atoms or molecules must lose energy to bond. Energy barriers may block transfer to stronger bonding structures. Strong chemical bonding Weak chemical bonding van der Waals bonding Core repulsion 0.2 0.4 0.6 0.8 1 Zero interaction Energy (Arb. Units) Energy barrier to strong bonding Not all states shown may be present for a given system 1 1.5 2 2.5 Distance above the surface (Arb. Units)
Adsorption: Sticking Coefficient © 1998, Angus Rockett Adsorption: Sticking Coefficient Some species stick only where a reactive site is available. If the adsorbing species stays on this site a limited time a steady state partial coverage results. Total arrival rate: r Adsorption Probability: Reflection or very weak adsorption occurs at previously covered sites (~ 0). Desorption after average Reflection time Even on an open site the probabilityis less than 1.0 Surface Coverage: At steady state: = r
Adsorption with Reaction Chemical bonding during adsorption may require clearing a surface site. Example: SiH4 adsorption on a hydrogen covered surface. Significant reaction where unsaturated dangling bonds are present. Little reaction where the surface bonds are saturated with hydrogen. © 1998, Angus Rockett
Desorption rdes = Cn r0 e-G/kT © 1998, Angus Rockett Desorption Atoms may leave a surface alone or in groups. Desorption from chemically different areas proceeds at different rates Associative desorption involves multiple atoms and is concentration dependent Simple desorption is thermally activated and concentration independent 200 400 600 800 1000 1200 rdes = Cn r0 e-G/kT Desorption Rate rdes: the desorption rate T: Temperature G: the desorption energy C: adatom concentration k: Boltzmann’s constant r0: the desorption attempt rate n: the desorption reaction order. 50 100 150 200 250 300 Temperature
Surface Diffusion D = D0 e-E/kT © 1998, Angus Rockett Surface Diffusion Atoms move on simple surfaces by a series of jumps over energy barriers. The flux is given by Fick’s Law, F = -D dC/dx. Barrier height is modified around surface steps and impurities. The diffusivity, D: Diffusion over individual barriers is given by: D = D0 e-E/kT Atoms spend the most time in the deepest energy minima. Energy, E D0: an attempt frequency (constant) E: the energy barrier for a given hop k: Boltzmann’s constant T: Temperature Position, x A typical surface diffusion energy profile.
Surface Diffusion Diffusion can be anisotropic if the surface structure lacks symmetry. For example, on a reconstructed surface: Slow diffusion across surface channels Fast diffusion along surface channels Anisotropic diffusion produces asymmetric island growth on the surface. © 1998, Angus Rockett
Surface and Interface Structure Thin films grow on substrates in such a way that they minimize interface energy. Critical points are: the structures of the substrate and film lattices, surface and interfacial energies [s, f , i,], bonding configurations of substrate and film, the relative sizes of the substrate and film lattices. diamond fcc f s i 3-fold coordinated 6-fold coordinated tension compression © 1998, Angus Rockett
Grain Orientation in Polycrystals Deposition on patterned substrates yields different microstructures for different orientations with respect to the incident flux. Grains grow at similar rates leading to columns Incident atom flux distribution Poor quality underdense columnar structure. Acceptable quality dense columnar microstructure © 1997, Angus Rockett
Grain Orientation in Polycrystals Polycrystalline films grown on amorphous substrates tend to have close packed planes outward. This maximizes atomic density on the initial surface and minimizes surface energy. Thus fcc metals tend to have a (111) preferred orientation and bcc metals tend to have a (110) preferred orientation. Substrate This result is modified in some cases by: The structure of a crystalline substrate / local epitaxy Adsorbates on the substrate Energetic particle bombardment © 1998, Angus Rockett
Grain Structure in Polycrystals As growth of polycrystalline films proceeds, some grains grow at the expense of others. This may lead to a change in texture with thickness. Grains with the fast growing orientation Substrate Slower-growing grains Growth rate differences due to: Lower surface energies Slower resputtering under ion bombardment Higher reaction rate on some surface planes (in CVD) © 1998, Angus Rockett
Surface Reconstruction Most clean surfaces change their structure to: reduce the number of dangling bonds, minimize unpaired electrons in dangling bonds. The simplest reconstruction to understand is the Si (100) surface. Dangling bonds occur in pairs. Each is half filled with electrons. Dangling bonds are filled. New bonds are made. These bonds act as hinges. © 1998, Angus Rockett
Epitaxy Growth of a single crystal on another single crystal with a specific alignment relation. 1000 Amorphous: atoms can not move even a few atomic spacings. Amorphous 100 Single crystals require longer range atomic motion. Growth Rate (arbitrary units) Islanded surface Flat: only in a narrow process window. Slower growth of single crystals also typically reduces stacking faults Polycrystalline 10 Flat surface Single crystal 1 "Hot" "Cold" Inverse temperature (1/T) The boundaries on this diagram are typically vague and depend on the length scale considered. © 1998, Angus Rockett
Heteroepitaxy: Layer Morphology The morphology of a heteroepitaxial layer depends on the change in surface energy and lattice constant. 2-dimensional layers 0.2 0.1 0.0 -0.1 2-dimensional layer + islands Surface energy increases Fractional change in surface energy 1 2 3 4 5 6 % change in lattice constant 3-dimensional islands Surface energy increases © 1998, Angus Rockett
Heteroepitaxy The growth of one material on a chemically different single crystal substrate. Strained: Epitaxial layer has the substrate lattice spacing in the plane, different out of the plane. Unstrained: Epitaxial layer has its own lattice spacing. © 1998, Angus Rockett
Heteroepitaxy Lattice strain is relieved at a critical thickness where the elastic strain energy equals the interface energy increase upon strain relief. Lattice strain energy per unit area increases linearly with increasing thickness energy The energy per unit area of defects associated with lattice mismatch (misfit dislocations) increases as the logarithm of thickness. thickness 2 b: Burger’s Vector : Poisson’s Ratio : Dislocation core radius : Angles defining the dislocation f: The misfit strain. h b ( 1 - c o s ) Critical thickness: h = l n [ c ] c 8f ( 1 + ) c o s b © 1998, Angus Rockett
© 1998, Angus Rockett Impurity Segregation Impurities tend to redistribute across surfaces and interfaces and near crystallinity defects. Atoms whose concentrations increase at surfaces: Large atoms (relative to the matrix) Atoms that reduce the surface energy (surfactants) Attracted to the surface Concentration Rejected from the surface Atoms whose concentration decreases at surfaces: Atoms that increase the surface energy. 2 4 6 8 Depth (atomic layers)
Residual Stress in Thin Films Two effects on residual stress: Growth stress is intrinsic to the process and varies with deposition conditions such as rate. Thermal stress Growth stress Deposition Temperature (T/T ) m 1 Total Stress Film Stress (Arbitrary Units) Thermal stress is intrinsic to the two materials in contact and varies with the temperature. Tm: melting temperature © 1998, Angus Rockett