Evaluation of the differential capacitance for ferroelectric materials using either charge-based or energy-based expressions

Abstract

Differential capacitance is derived based upon energy, charge or current considerations, and determined when it may go negative or positive. These alternative views of differential capacitances are analyzed, and the relationships between them are shown. Because of recent interest in obtaining negative capacitance for reducing the subthreshold voltage swing in field effect type of devices, using ferroelectric materials characterized by permittivity, these concepts are now of paramount interest to the research community. For completeness, differential capacitance is related to the static capacitance, and conditions when the differential capacitance may go negative in relation to the static capacitance are shown.

Negative Capacitance in BaTiO3/BiFeO3 Bilayer Capacitors

“…However, the possibility of stable negative capacitances using ferroelectric materials has been controversial. According to the double-well energy landscape, based on the Landau theory, negative capacitances and negative differential capacitances in the individual ferroelectric material appear only in nonequilibrium conditions, and it is hard to be experimentally measured in the single- or multidomain ferroelectric materials. − For example, Krowne et al have measured 2185 ferroelectric capacitors and have shown no instance of negative capacitances in their database. Subsequently, it has been reported that the nonequilibrium negative capacitance can be stabilized by putting a dielectric capacitor in series with the ferroelectric capacitor. , For example, O’Neill et al have reported that the total capacitance of BaTiO 3 /SrTiO 3 bilayer capacitor is enhanced in a series combination of BaTiO 3 and SrTiO 3 capacitors, and the capacitance enhancement in the BaTiO 3 /SrTiO 3 bilayer capacitor indicates a stable state of negative capacitances in the BaTiO 3 capacitor.…”

Evidence of Negative Capacitance in Piezoelectric ZnO Thin Films Sputtered on Interdigital Electrodes

“…A key role in NC effects is also played by oxygen vacancies . These are often present in metal oxides like zinc oxide (ZnO), titanium oxide, and tantalum oxide and are believed to be responsible for the appearance of memristive phenomena. , From 2008, different theoretical works predicted the possibility of reducing the SS below the Boltzmann limit by using a ferroelectric insulator as gate oxide (Figure c). − It is shown that the interaction among electric dipoles of the ferroelectric gate oxide should provide, in principle, a positive feedback effect capable of implementing a step-up voltage transformer, that is, a voltage amplification that increases the channel potential more than that applied externally. This can reduce the SS without further increasing the external gate voltage.…”

Ferroelectric differential capacitance affected by stresses and strains and implications for use in electronic devices

“…Previously, it was shown that for useful electronic devices, especially those operating in a steady state fashion in the microwave frequency region and higher, that the use of negative differential capacitance effects in devices such as transistors, is highly unlikely. The studies were based upon energy considerations in the fields and extensive measurements of ferroelectric structures and upon additional considerations including current and charge. Here, attention is turned to another approach, based upon phenomenological thermodynamic physics using free energy expressions, to see what is possible by introducing strain, and not necessarily restricting operation to only steady state.…”