Mathematical description of atomic layer deposition and its application to the nucleation and growth of HfO2 gate dielectric layers

Abstract

Alternate gate dielectrics will be necessary for continued scaling in the microelectronics industry, and atomic layer deposition is a likely technology for growth of such films. A phenomenological mathematical model of atomic layer deposition has been developed and applied to a large body of HfO2 growth data. The model is based on classical chemical kinetics theory, and assumes that OH groups are the nucleation sites for film growth. Two differential equations, one describing the deposition rate of HfO2 per cycle, and another the creation rate of new OH groups per cycle, completely describe the atomic layer deposition process. The entire body of HfO2 growth data can be explained by the model: linear growth behavior in the presence of large initial OH concentrations such as are present on chemical oxides; the ∼17 steric hindrance factor for linear growth, based on the size of the tetrahedral HfCl4 molecule, and a combination of adsorption modes; initial parabolic growth behavior in the presence of small initial OH concentrations such as are present on hydrogen (H)-terminated Si; and the transition from nonlinear to linear growth behavior after about 80 cycles of growth on H-terminated Si. Although applied to HfO2, for which the largest body of nucleation and growth data for thin atomic layer deposited films on differently treated substrate surfaces exists, the model is completely general and can describe any atomic layer deposition process. This is a comprehensive model of the atomic layer deposition process.