Exploratory analysis of the breakdown spots spatial distribution in metal gate/high-K/III-V stacks using functional summary statistics

The breakdown spots spatial distribution in MgO dielectric films deposited on InP was investigated using functional summary statistics for point patterns. The analysis involved five estimators: the empty space function F(r), the nearest neighbor distance distribution function G(r), the van Lieshout-Baddeley function J(r), the Ripley's function K(r) and the pair correlation function g(r). In order to illustrate the consequences of considering a large or a small number of spots on the summary statistics, a comparative study on capacitors with different gate areas was carried out. Even though this paper deals with metal gate/MgO/InP stacks exclusively, the methods discussed here can be easily applied to any device exhibiting similar point pattern structures.