  Ferroelectricity in sputtered undoped-HfO$_2$ is attractive for composition
control for low power and non-volatile memory and logic applications. Unlike
doped HfO$_2$, evolution of ferroelectricity with annealing and film thickness
effect in sputter deposited undoped HfO$_2$ on Si is not yet reported. In
present study, we have demonstrated the impact of post metallization annealing
temperature and film thickness on ferroelectric properties in dopant-free
sputtered HfO$_2$ on Si-substrate. A rich correlation of polarization with
phase, lattice constant, and crystallite size and interface reaction is
observed. First, anneal temperature shows o-phase saturation beyond 600 oC
followed by interface reaction beyond 700 oC to show an optimal temperature
window on 600-700 oC. Second, thickness study at the optimal temperature window
shows an alluring o-phase crystallite scaling with thickness till a critical
thickness of 20 nm indicating that the films are completely o-phase. However,
the lattice constants (volume) are high in the 15-20 nm thickness range which
correlates with the enhanced value of 2Pr. Beyond 20 nm, crystallite scaling
with thickness saturates with the correlated appearance of m-phase and
reduction in 2Pr. The optimal thickness-temperature window range of 15-20 nm
films annealed at 600-700 oC show 2Pr of ~35.5 micro-C/cm$^2$ is comparable to
state-of-the-art. The robust wakeup-free endurance of ~$10^$8 cycles showcased
in the promising temperature-thickness window has been identified
systematically for non-volatile memory applications.
