  In this paper we proclaim excellent variation control in
Hf$_{0.5}$Zr$_{0.5}$O$_2$ based ferroelectric films obtained by germination of
large ferroelectric domain via extended duration of thermal annealing. 10nm
thick Hf$_{0.5}$Zr$_{0.5}$O$_2$ based ferroelectric capacitors with TiN as
bottom and top electrodes are fabricated and characterized. The duration of
rapid thermal annealing (RTA) is varied to observe its effect on crystal
formation and device electrical properties at 700C. The device to device
variation in terms of coercive voltage and peak capacitance are reduced from
0.4V to 0.01V and from 2*$10^{-5}$nF/cm$^2$ to 4*$10^{-6}$nF/cm$^2$,
respectively, by increasing the RTA duration. High resolution transmission
electron micrograph clearly shows large and uniform ferroelectric domains with
RTA of 180 seconds. Extended duration of RTA likely allows uniform crystal to
form, which mitigates the stochasticity of the distribution of ferroelectric
and paraelectric domains, and deterministic switching has been infused. This
improvement paves the way for implementing Hf$_{0.5}$Zr$_{0.5}$O$_2$ based
deeply scaled devices for memory and steep slope device applications.
