For Regime I, the growth rate on the front laterally, referred to as g, is the rate-determining step (RDS) and exceeds the secondary nucleation rate, i. In this instance of g >> i, monolayers are formed one at a time so that if the substrate has a length of L and thickness, b, the overall linear growth can be described through the equation
and the rate of nucleation in specific can further be described by
with K equal to
where
This shows that in Region I, lateral nucleation along the front successfully dominates at temperatures close to the melting temperature, however at more extreme temperatures other forces such as diffusion can impact nucleation rates.
In Regime II, the lateral growth rate is either comparable or smaller than the nucleation rate g ≤ i, which causes secondary (or more) layers to form before the initial layer has been covered. This allows the linear growth rate to be modeled by
Using the assumption that g and i are independent of time, the rate at which new layers are formed can be approximated and the rate of nucleation in regime II can be expressed as
with K equal to about 1/2 of the K from Regime I,
Lastly, Regime III in the L-H model depicts the scenario where lateral growth is inconsequential to the overall rate, since the nucleation of multiple sites causes i >> g. This means that the growth rate can be modeled by the same equation as Regime I,
where G is the prefactor for Regime III and can be experimentally determined through applying the Lauritzen–Hoffman Plot.