Abstract
To describe charge-polarization coupling in the nanostructure formed by a thin HfxZr1-xO2 film with single-layer graphene as the top electrode, we develop the "effective"Landau-Ginzburg-Devonshire model. This approach is based on the parametrization of the Landau expansion coefficients for polar (ferroelectric) and antipolar (antiferroelectric) orderings in thin Hf1-xZrxO2 films from a limited number of polarization-field curves and hysteresis loops. The Landau expansion coefficients are nonlinearly dependent on the film thickness, h, and Zr/[Hf+Zr] ratio, x, in contrast to h-independent and linearly-x-dependent expansion coefficients of classical Landau energy. We explain the dependence of the Landau expansion coefficients by the strong nonmonotonic dependence of the polar properties on the Hf1-xZrxO2 film thickness, grain size, and surface energy. The proposed Landau free energy with five effective expansion coefficients, which are interpolation functions of x and h, describes the continuous transformation of polarization dependences on applied electric field and hysteresis loop shapes induced by changes to x and h in the range 0 < x < 1 and 5 nm < h < 35 nm. Using the effective free energy, we demonstrate that polarization of Hf1-xZrxO2 films influences the graphene conductivity strongly, and the full correlation between the distribution of polarization and charge carriers in graphene is revealed. In accordance with our modeling, polarization of the 5-25-nm-thick Hf1-xZrxO2 films, which are in ferroelectriclike or antiferroelectriclike states for chemical compositions of 0.35 ≤ x ≤ 0.95, determine the concentration of carriers in graphene and can control its field dependence. The result is promising for the creation of next-generation Si-compatible nonvolatile memories and graphene-ferroelectric FETs, because the working voltages applied to the Hf1-xZrxO2 film (which acts as a gate) can be relatively low (less than 2 V). These low voltages are sufficient to induce the pronounced hysteresis of ferroelectric polarization in the Hf1-xZrxO2 gate, which, due to strong electric coupling, induces hysteresis of the graphene charge.
Original language | English |
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Article number | 054007 |
Journal | Physical Review Applied |
Volume | 20 |
Issue number | 5 |
DOIs | |
State | Published - Nov 2023 |
Funding
The authors are very grateful to the referees for constructive suggestions and useful discussions. This work was partially supported by the Center for 3D Ferroelectric Microelectronics (3DFeM), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, under Award No. DE-SC0021118. This work was partially supported by the U.S. Department of Energy, Office of Science User Facility. A.N.M. is supported by the Ministry of Science and Education of Ukraine (Grant No. PH/23-2023, “Influence of size effects on the electrophysical properties of graphene-ferroelectric nanostructures”) at the expense of the external aid instrument of the European Union for the fulfillment of Ukraine’s obligations in the Framework Program of the European Union for scientific research and innovation “Horizon 2020.” A.N.M. is very grateful to Dr. Yuri Zagorodny for useful discussions.
Funders | Funder number |
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center for 3D Ferroelectric Microelectronics | |
European Union for scientific research and innovation “Horizon 2020 | |
U.S. Department of Energy | |
Office of Science | |
Basic Energy Sciences | DE-SC0021118 |
European Commission | |
Ministry of Education and Science of Ukraine | PH/23-2023 |