Ferroelectric capacitor

In a short-circuited ferroelectric capacitor with a metal-ferroelectric-metal (MFM) structure, a charge distribution of screening charges forms at the metal-ferroelectric interface so as to screen the electric displacement of the ferroelectric. Due to these screening charges, there is a voltage drop across the ferroelectric capacitor with screening in the electrode layer that can be obtained using the Thomas-Fermi approach as follows:[1]

${\displaystyle V=E_{f}d+E_{e}\left(2\lambda \right)}$

Here ${\displaystyle d}$ is the film thickness, ${\displaystyle E_{f}={\frac {V+8\pi P_{s}a}{d+\epsilon _{f}\left(2a\right)}}}$ and ${\displaystyle E_{e}={\frac {\epsilon _{f}}{\epsilon _{e}}}E_{f}-{\frac {4\pi }{\epsilon _{e}}}P_{s}}$ are the electric fields in the film and electrode at the interface, ${\displaystyle P_{s}}$ is the spontaneous polarization, ${\displaystyle a={\frac {\lambda }{\epsilon _{e}}}}$, and ${\displaystyle \epsilon _{f}}$ & ${\displaystyle \epsilon _{e}}$ are the dielectric constants of the film and the metal electrode.

With perfect electrodes, ${\displaystyle \lambda =0}$ or for thick films, with ${\displaystyle d\gg a}$ the equation reduces to:

${\displaystyle V=E_{f}d\Rightarrow E_{f}={\frac {V}{d}}}$

• Ferroelectricity
• Ferroelectric RAM

• FeRAM Tutorial