Supplementary Material: Extraction of Landau coefficients for Antiferroelectric from experimental Polarization versus Electric Field curves

An Anti-Ferroelectric Gated Landau Transistor to Achieve sub 60mV/dec Switching at Low Voltage and High Speed

Supplementary Material:

Extraction of Landau coefficients for Antiferroelectric from experimental Polarization versus Electric Field curves

The Landau model has shown to be in agreement with phase transitions in AFE [18, 19]. The energy density () for an AFE can be formulated as

+ . (S1)
At E=0 equilibrium conditions dictate; for =0;
(S2)
Also as −>0; ; where is linear dielectric susceptibility of the material. This results in a condition of
(S3)

At E=Ec, the coercive field the diverges and −>0 with

corresponding =.Ec.
=0 (S4)
For any ferroelectric material Ec, saturation polarization and can be experimentally measured through conventional Polarization versus Electric Field loop, is extracted, the material parameters and can then be obtained simply from three linear equations S2, S3 and S4. For Hafnium silicate based system [14] the values of Ec=1e8V/m, Ps=16.5μC/cm2 and =; these values can change accordingly with the dopant species used to stabilize the orthorhombic phase in hafnium oxide.

Acknowledgement
We gratefully acknowledge discussions with M. Masuduzzaman and M. Abdul Wahab. This work was supported in part through the NCN-NEEDS program, which is funded by the National Science Foundation, contract 1227020-EEC, and by the Semiconductor Research Corporation. K. Karda acknowledges Micron technology for continuing education support; Dr. Haitao Liu, TCAD and Emerging Memory research team at Micron technology for insightful discussions