List of Symbols

$A_\mathrm{down}$ 		 Area in the PE Diagram with Down Oriented Dipoles 

$A_\mathrm{up}$ 		 Area in the PE Diagram with Up Oriented Dipoles 

$C_B$ 		 Bitline Capacity

$C_F$ 		 Ferroelectric Capacitor

$C_S$ 		 Sense Capacitor

$d$ 		 Width

$D$ Electric Displacement

$E$ 		 Electric Field 

$E_a$,$E_b$ 		 Operating Points of the Electric Field

$E_c$ 		 Coercive Field

$E_{i}$,$E_{k}$ 		 Electric Field at the Grid Point i, k

$E_{i,x}$$E_{i,y}$ x- and y-Component of the Electric Field at the Grid Point i

$E_{ik}$ 		 Electric Field between the Grid Points i and k

$E_{ik,x}$,$E_{ik,x}$ 		 x- and y-Component of the Electric Field between the Grid Points i and k

$E_\mathrm{d}$ Transition Field in the Down Direction

$E_\mathrm{old}$ 		 Electric Field of the Previous Operating Point

$E_\mathrm{stat}$ 		 Static Electric Field


$E_\mathrm{turn}$ 		 Turning Point Electric Field

$E_\mathrm{u}$ Transition Field in the Up Direction

$E_1$ Electric Field of the Current Operating Point

$E_{1,\perp}$ 		 Orthogonalized Field


$f(E \pm E_c,k)$ 		 Hysteresis Shape Function

$f_{\mathrm{loc},\parallel}$ Subcycle Parallel to the Electric Field

$f_{\mathrm{loc},\perp}$ Subcycle Orthogonal to the Electric Field

$F(E_u,E_d)$ 		 Distribution Function of the Transition Fields

$G$ 		 Total Free Energy

$I$ 		 Electrical Current

$I_d$ 		 Drain Current

$I_0$ 		 Initial Current

$k$ 		 Subcycle Parameter

$k_\mathrm{nonlin}$ Parameter of the Nonlinear Transient Polarization Term


$p_n$ 		 Dipole Moment of the nth Dipole

$p_m,n$ Dipole Moment of the nth Dipole in the mth Row


$P$ Polarization

${P}_\mathrm{ef}$,${P}_\mathrm{pol}$ Transient Polarization Components  

$P_\mathrm{nonlin}$ Nonlinear Transient Polarization

$P_\mathrm{off}$ Subcycle Parameter

$P_\mathrm{old}$ 		 Polarization of the Previous Operating Point

$P_\mathrm{stat}$ 		 Static Polarization 

$P_\mathrm{turn}$ 		 Turning Point Polarization 

$P_\mathrm{Ferro}$ 		 Hysteretic Polarization

$P_\mathrm{Part}$ Dipole Polarization

$P_\mathrm{Rem}$ 		 Remanent Polarization

$P_S$ 		 Spontaneous Polarization

$P_\mathrm{Sat}$ 		 Saturation Polarization

$P_\mathrm{turn}$ 		 Turning Point Polarization 

$P_0$ Polarization in the Domain Center

${P}_{\parallel}$ 		 Polarization Parallel to the Electric Field

${P}_{\perp}$ 		 Polarization Orthogonal to the Electric Field

$P_1$ Current Polarization 

$P_{\mathrm{old},\parallel}$ Previous Parallel  Component of the Polarization

$P_{\mathrm{old},\perp}$ Previous Orthogonal Component of the Polarization


$P_{1,\parallel}$ Current Parallel  Component of the Polarization

$P_{1,\perp,init}$ Initial Guess to the Current Orthogonal Component of the Polarization

$P_{1,\perp}$ Current Orthogonal Component of the Polarization


$R_f$ 		 Series Resistance of the Ferroelectric Capacitor

$R_i$ 		 Input Resistanc of the Digitizer

$s_h$ 		 Sign Flag


$t$ 		 Time

$t_\mathrm{cryst}$ 		 Crystal Thickness

$\Delta t$ 		 Time-step

$T$ 		 Temperature

$T_\mathrm{C}$ 		 Curie Temperature

$V$ 		 Volume

$V_g$ 		 Gate Voltage

$V_\mathrm{i}$ 		 Input Voltage

$V_\mathrm{out}$ 		 Output Voltage

$V_t$ 		 Threshold Voltage

$V_B$ 		 Bulk Voltage

$V_D$ 		 Drain Voltage

$V_DD$ 		 Supply Voltage

$V_S$ 		 Source Voltage


$w$ 		 Shape Parameter

$W_\mathrm{dip}$ 		 Dipole Energy

$W_E$ Depolarization Energy

$W_W$ 		 Wall Energy

$vec{X}$ Space Coordinate

$\alpha$ 		 Angle

$\alpha,\beta$ 		      Parameters for the Free Energy Model


$\chi$ 		  Susceptibility

$\epsilon_r$ 		      Relative Permittivity

$\epsilon_0$ 		 Vacuum permittivity

$\epsilon^*$ Constant Depending on the Permitivity


$\gamma$ 		  Viscosity Coefficient


$\Phi_i$, $\Phi_k$ 		 Potenial at Grid Point i,k

$\rho$ Space Charge Density

$\sigma$ 		   Electric Conductivity

$\sigma_\mathrm{Wall}$ Wall Energy Density 

$\tau_1$, $tau_2$ 		  Time Constants

$\tau_\mathrm{ef}$ Relaxation Time of the Electric Field

$\tau_\mathrm{pol}$ Relaxation Time of the Polarization