  Ferroelectric domain walls hold great promise for innovative applications in
ferroelectric devices. However, the underlying mechanisms behind the observed
giant conductance of charged domain walls remain poorly understood. Using a
first-principles approach that incorporates Boltzmann transport theory and the
relaxation time approximation, we determine the carrier concentration,
mobility, and conductivity of domain walls with head-to-head and tail-to-tail
polarization orientations. Our systematic exploration reveals that the
accumulation of carriers, particularly their concentration, plays a dominant
role in the domain wall conductance mechanism. However, the observed
conductance differences between head-to-head and tail-to-tail domain walls are
primarily due to differences in carrier mobility. The width of the domain wall
is a key factor determining the device scale. Our calculated domain wall width
is significantly smaller than previously reported values. This method, not
limited to a certain ferroelectric material, can be used for the optimization
and application development of various domain wall materials and devices.
