  We analyze the distributions of electric potential and field, polarization
and charge, and the differential capacitance of a silicon
metal-oxide-ferroelectric field effect transistor (MOSFET), in which a gate
insulator consists of thin layers of dielectric SiO2 and weak ferroelectric
HfO2. It appeared possible to achieve a quasi-steady-state negative capacitance
of the HfO2 layer, C_(HfO_2 )<0, if the layer thickness is close to the
critical thickness of the size-induced ferroelectric-paraelectric phase
transition. The quasi-steady-state negative capacitance, being a very
slow-varying transient state of the ferroelectric, corresponds to a positive
capacitance of the whole system, and so its appearance does not break any
thermodynamic principle. Implementation of the quasi-steady-state negative
capacitance C_ins of the gate insulator can open the principal possibility to
reduce the MOSFET subthreshold swing below the critical value, and to decrease
the gate voltage below the fundamental Boltzmann limit. However, we failed to
found the parameters for which C_ins is negative in the quasi-steady states;
and thus, the negative C_(HfO_2 ) cannot reduce the subthreshold swing below
the fundamental limit. Nevertheless, the increase in C_ins, related with
C_(HfO_2 )<0, can decrease the swing above the limit, reduce device heating
during the operation cycles, and thus contribute to further improvements of the
MOSFET performances.
