Modifications and Additions to the Ferroelectric Model in Atlas

In the Fall Release 1996 Silvaco International introduced a ferroelectric module as part of the Atlas device simulation framework. Development work has continued on this module in order to better meet our customers needs. This article reports two modifications to the existing module which are now available in Atlas.

1. Unsaturated Polarization

It is well understood that in the static or DC state the permittivity of a ferroelectric material is given by

 

where E is the electric field, D is the displacement vector, ef is the ferroelectric permittivity and Pd is the position dependent dipole polarization.

The derivative of the dipole polarization with respect to electric field is given by:

where Psat is the position dependent saturated dipole polarization. A numeric integration of this function is carried out in Atlas to calculate the position dependent dipole polarization. In the previous release we have assumed that the dipole polarization is saturated. The Ferroelectric model has now been modified to allow the simulation of unsaturated polarization loops as follows.

For saturated loop polarization, the function G is unity, which corresponds to the default model. If the user specifies the parameter UNSAT.FERRO on the models statement, the function G can take a more general form suitable for the simulation of unsaturated loops. In this case, G is given by:

 

where z =+1 for increasing fields and z =-1 for decreasing fields.

This modification to the dipole polarization results in a small but yet significant change in the device simulations. Figures 1 and 2 illustrate this for a one-dimensional MFS capacitor structure where the gate voltage is swept from -5V to +0.5V. The polarization curve is therefore simulated beginning from a saturated position and finishes on an unsaturated position on the polarization curve. Figure 1 shows that with the default model the reverse sweep from +0.5V to -5V the polarization is miscalculated. With the extension of the model to unsaturated regions, shown in Figure 2, the polarization is now correctly calculated for any applied gate voltage sweep.

Figure 1. Simulated polarization plot using the
default model that illustrates the inaccuracies which
arise by assuming saturated polarization.

 

Figure 2. Simulated polarization plot which illustrates that
the new improved model for polarization does not require
a saturated hysteresis curve tobe traced.

 

2. High Frequency Response

Under AC conditions the Ferroelectric material properties can allow the effect of the dipole polarization to have reduced influence on the dielectric permittivity. This effect can be important as, for instance, capacitance C-V curves are normally calculated using a 1 MHz AC signal. It has been suggested that the field dependent polarization has a reduced contribution to the total permittivity, while the hysteresis remains the same. To include this effect the FERRODAMP parameter has been added to the solve statement. This parameter may have an integer value between 0 and 1, where 0 corresponds to no field dependent polarization and 1 corresponds to the full effect. To illustrate this effect the capacitance curves of the previous MOS capacitor are shown in Figure 3 and 4. The ferrodamp parameter has been used to illustrate that different C-V curves can be obtained. Recent publications seem to indicate that the C-V curve shown in Figure 4 is more realistic. [1]

Figure 3. In Figure 2a simulated C-V curve
which assumes a dc behavior for permittivity.

 


Figure 4. Simulated C-V curve which assumes a high
frequency ac, or linear dielectric, behavior for
permittivity. This shows that Atlas can differentiate
between low and high frequency behavior.

 

 

References

[1] J-S Lyu et al,
"Metal-Ferroelectric Semiconductor Field-Effect Transistor (MFSFET) for Single Transistor Memory by Using Poly-Si Source/Drain and BaMgF4 Dielectric",
IEDM 1997, p. 496.