Multi-step trap-assisted tunneling in Al-doped HfO₂ used in advanced 2.5D metal-insulator-metal capacitors

Abstract

Leakage currents through back-end dielectric layers critically affect the performance and reliability of modern electronic devices. In particular, high- dielectrics, such as HfO⁠, used in backend-integrated decoupling capacitors, exhibit significant trap-assisted leakage currents. This study investigates the leakage of Al-doped HfO in advanced 2.5D metal–insulator–metal capacitors across a wide temperature range of 77–448 K. It was found that Fowler–Nordheim tunneling dominates at fields exceeding 5 MV/cm, while trap-assisted tunneling (TAT) governs the leakage in the intermediate field range. A multi-step TAT model, parameterized by the trap concentration and trap spacing of the dielectric, is employed to analyze the leakage behavior. The model successfully separates the dependence of the leakage current on the field, linked to the trap spacing, and on the temperature, attributed to an energy barrier for trap-to-trap tunneling. At higher temperatures, the conduction complies with a uniform trap distribution with a trap spacing of nm and an energy barrier of eV, in agreement with a measured trapped electron concentration of cm⁠. As the temperature decreases toward 77 K, quantum mechanical tunneling becomes dominant, necessitating the presence of trap clusters. Our findings demonstrate that the leakage cannot be described by a single conduction mechanism over the entire temperature range; instead, the framework provides a more comprehensive understanding of the interplay between the field and temperature in governing the leakage behavior.