Growth per cycle in atomic layer deposition: A theoretical model

Atomic layer deposition (ALD) is used in advanced applications where thin layers of materials with precise thickness down to the nanometer scale are needed. Growth of materials by ALD takes place through repeating the separate, saturating reactions of at least two gaseous reactants with a solid substrate. When surface saturation is systematically utilized, the growth obtained per ALD reaction cycle is a well-defined quantity that depends on i) the reactants used, ii) the ALD processing temperature, and iii) sometimes the substrate material. A model is derived to describe the growth per cycle in ALD as a function of the chemistry of the growth when compounds are used as reactants. Two main types of chemisorption may occur: i) ligand exchange reaction of the MLn reactant with surface "a" groups, where ligands are removed from the surface as gaseous aL, and ii) dissociation or association, where all parts of the MLn, reactant are attached to the surface. A simple mathematical model based on the mass balance of chemisorption relates the growth per cycle to the size of the MLn reactant and the chemisorption mechanisms involved. Steric hindrance of the ligands causes saturation of chemisorption if a limited number of bonding sites does not cause it. Because of the steric hindrance, the growth per cycle remains less than a monolayer. The applicability of the model is illustrated through several theoretical examples.