  In this work, we analyze the ferroelectric (FE) domain-wall (DW) induced
negative capacitance (NC) effect in Metal-FE-Insulator-Metal (MFIM) and
Metal-FE-Insulator-Semiconductor (MFIS) stacks. Our analysis is based on 2D
phase field simulations. Considering HZO as the FE material, we study 180 FE
domain formation in MFIM and MFIS stacks and their voltage-dependent DW motion.
Our analysis signifies that, when FE is in multi-domain (MD) state with
soft-DW, the stored energy in the DW leads to non-hysteretic NC effect in FE,
which provides an enhanced charge response in the MFIM stack, compared to
Metal-Insulator-Metal. According to our analysis, the DW-induced NC effect
yields local negative permittivity in FE in the domain and DW regions, which
leads to an average negative effective permittivity in FE. Furthermore, we show
that the NC trajectory of FE is dependent on its thickness, the gradient energy
coefficient and the in-plane permittivity of the underline DE material but not
on the DE thickness. Similar to MFIM, MFIS also exhibits an enhancement in the
overall charge response and the capacitance compared to MOS capacitor. At the
same time, the MD state of FE induces non-homogenous potential profile across
the underlying DE and semiconductor layer. In the low voltage regime, such
non-homogenous surface potential leads to the co-existence of electron and hole
in an undoped semiconductor, while at higher voltages, the carrier
concentration in the semiconductor becomes electron dominated. In addition, we
show that with FE being in the 180 MD state, the minimum potential at FE-DE
interface and hence, the minimum surface potential in the semiconductor, does
not exceed the applied voltage (in-spite of the local differential
amplification and charge enhancement).
