# Temperature Effects in *SmartSpice* LEVEL=6

Ferroelectric Capacitance Model

From Ramtron International Corporation

Introduction

Implementation of a new ferroelectric capacitance model
from Ramtron International Corporation into ** SmartSpice**
was first described in the April 2002 issue of SILVACO

*Simulation Standard*. This model utilizes a new concept of double distribution of domain reversal voltages. The temperature effects were not detailed in the previous article. This application note discusses the implementation of the temperature effects and updates the device syntax.

Features

The updated ferroelectric model is invoked in ** SmartSpice**
by setting LEVEL=6 in the capacitance model card. This model differs from
its predecessor (model FCAP LEVEL=5) in that the ferroelectric capacitor
is regarded as a non-linear capacitor with Polarization-Voltage (P-V)
hysteresis loop, however the biases in the ferroelectric materials are
reversed at reversal voltages with double distributions. As compared with
the LEVEL=5 model, the LEVEL=6 model demonstrates the following improvements:
more accurate simulations of ferroelectric hysteresis loops and sub-loops,
improved voltage pulse responses, faster simulation speed (up to six times
faster), and added temperature dependence.

Ferroelectric Capacitor Element

** SmartSpice** device statement syntax:

Note: Device syntax is updated from that published in
the April 2002 *Simulation Standard*

Cxxx n1 n2 mname <V0=val> <P0=val> <A=val>

Cxxx: |
Capacitor element name; must begin with "C." |

n1,
n2: |
Positive and negative terminal node names, respectively. |

mname: |
Model name (must be ferroelectric capacitor model). |

V0: |
Initial voltage across the ferroelectric capacitor (V). Default is 0.0. |

P0: |
Initial polarization (mC/cm2) from positive node (n1) to negative node (n2). Default is 0.0. |

A
(AREA): |
Capacitor area (m2). Default is 1.0E-12. |

One difference to note is that the LEVEL=5 ferroelectric
capacitor uses the unit-less parameter, IP, for initial polarization while
the LEVEL=6 ferroelectric capacitor uses the initial polarization parameter,
P0, in µC/cm^{2}. The input for the capacitor size in the
LEVEL=6 model is the capacitor area, and can be specified using either
A or AREA in m^{2}.

Temperature Effects in LEVEL=6 Ferroelectric Capacitance Model

* SmartSpice* model syntax:

.MODEL mname C LEVEL=6 <parameter=value> …

mname: |
Model name. |

C: |
Specifies capacitance model. |

LEVEL=6: |
FRMC model. |

parameter: |
Any model parameter name. |

The model parameters were documented in the April 2002
*Simulation Standard* article with the exception of the temperature
parameters. Table 1 shows a complete list of the model parameters including
the updated default parameter values as well as the temperature coefficient
parameters.

LEVEL=6 FERROELECTRIC
CAPACITOR MODEL PARAMETERS |
|||

Parameter |
Description |
Units |
Default |

VMAX | Maximum voltage | V | 3.898e+00 |

PMAX | Maximum polarization at VMAX | µC/cm^{2} |
3.787e+01 |

KPMAX | 1st order temperature coefficient of PMAX | -8.803e-03 | |

K2PMAX | 2nd order temperature coefficient of PMAX | V | -8.616e-05 |

VSAT | Saturated model point | V | 2.452e+00 |

VCR | Minimum voltage for domain switching | 4.903e-01 | |

AS1 | Curve fitting parameter | 1.348e+00 | |

BS1 | Curve fitting parameter | 1.174e+00 | |

CS1 | Curve fitting parameter | 1.634e+00 | |

AS2 | Curve fitting parameter | -1.085e+00 | |

BS2 | Curve fitting parameter | 1.444e+00 | |

CS2 | Curve fitting parameter | 1.859e+00 | |

DS0 | Curve fitting parameter | 5.513e-01 | |

AU1 | Curve fitting parameter | 1.457e+00 | |

BU1 | Curve fitting parameter | 1.432e+00 | |

CU1 | Curve fitting parameter | 1.377e+00 | |

AU2 | Curve fitting parameter | -1.109e+00 | |

BU2 | Curve fitting parameter | 1.820e+00 | |

CU2 | Curve fitting parameter | 1.574e+00 | |

DU0 | Curve fitting parameter | 5.695e-01 | |

LEVEL=6 FERROELECTRIC
CAPACITOR MODEL PARAMETERS:Temperature Coefficients |
|||

KAS1 | 1st order temperature coefficient of AS1 | -3.178e-03 | |

KBS1 | 1st order temperature coefficient of BS1 | -1.970e-03 | |

KCS1 | 1st order temperature coefficient of CS1 | -4.562e-03 | |

KAS2 | 1st order temperature coefficient of AS2 | 3.074e-03 | |

KBS2 | 1st order temperature coefficient of BS2 | -2.539e-03 | |

KCS2 | 1st order temperature coefficient of CS2 | -4.343e-03 | |

KDS0 | 1st order temperature coefficient of DS0 | -1.869e-04 | |

KAU1 | 1st order temperature coefficient of AU1 | -4.090e-03 | |

KBU1 | 1st order temperature coefficient of BU1 | -2.641e-03 | |

KCU1 | 1st order temperature coefficient of CU1 | -4.944e-03 | |

KAU2 | 1st order temperature coefficient of AU2 | 4.495e-03 | |

KBU2 | 1st order temperature coefficient of BU2 | -4.626e-03 | |

KCU2 | 1st order temperature coefficient of CU2 | -4.637e-03 | |

KDU0 | 1st order temperature coefficient of DU0 | -4.621e-04 | |

K2AS1 | 2nd order temperature coefficient of AS1 | 3.423e-05 | |

K2BS1 | 2nd order temperature coefficient of BS1 | -3.860e-06 | |

K2CS1 | 2nd order temperature coefficient of CS1 | 2.176e-05 | |

K2AS2 | 2nd order temperature coefficient of AS2 | -3.725e-05 | |

K2BS2 | 2nd order temperature coefficient of BS2 | -8.596e-06 | |

K2CS2 | 2nd order temperature coefficient of CS2 | 1.689e-05 | |

K2DS0 | 2nd order temperature coefficient of DS0 | 1.575e-06 | |

K2AU1 | 2nd order temperature coefficient of AU1 | 4.337e-05 | |

K2BU1 | 2nd order temperature coefficient of BU1 | -4.328e-06 | |

K2CU1 | 2nd order temperature coefficient of CU1 | 1.882e-05 | |

K2AU2 | 2nd order temperature coefficient of AU2 | -5.218e-05 | |

K2BU2 | 2nd order temperature coefficient of BU2 | -4.039e-06 | |

K2CU2 | 2nd order temperature coefficient of CU2 | 1.254e-05 | |

K2DU0 | 2nd order temperature coefficient of DU0 | 2.099e-06 |

Table 1. Complete list of the model
parameters including the updated default

parameter values as well as the temperature coefficient parameters.

NOTE: All blank cells indicate a number with no units.

Simulation Results

The improved accuracy of the LEVEL=6 model
compared to the LEVEL=5 model was documented in the April 2002 *Simulation
Standard *article. Here we show comparison of the simulated vs. measured
results at three different temperatures to validate the temperature modeling.
The test circuit used is shown in Figure 1.

Figure 1. Test circuit for ferroelectric capacitor

simulations. (Sawyer-Tower circuit)

Temperature effects for the ferroelectric capacitor model are calculated in the following form for all model parameters:

AS1

_{eff}= AS1 + KAS1 * (TEMP – TNOM) +

K2AS1 * (TEMP – TNOM)^{2}

Figures 2, 3, and 4 show measured and simulated hysteresis loops at 3V and 5V, for temperatures of 27?C, 60?C, and 90?C, respectively. The input stimulus for these results was a sinusoidal voltage waveform at 10 KHz. This shows very close agreement between simulation and measurement at temperature.

Figure 2. Measured (red) and simulated (blue)
hysteresis loops at 27?C.

[Courtesy of Ramtron International Corporation]

Figure 3. Measured (red) and simulated (blue)
hysteresis loops at 60?C.

[Courtesy of Ramtron International Corporation]

Figure 4. Measured (red) and simulated (blue)
hysteresis loops at 90?C.

[Courtesy of Ramtron International Corporation]

Conclusions

The new ferroelectric capacitor model implemented
in ** SmartSpice** as LEVEL=6, has been shown to accurately simulate
hysteresis loops at various temperatures. This model based on double distributions
of domain reversal voltages has shown advantages over the LEVEL=5 model
as described in the April 2002

*Simulation Standard*article. In this article, we have presented details of the implementation of temperature effects, comparison of simulation results to measured data, and updated the device syntax.

*SILVACO gratefully acknowledges Ramtron
International Corporation for the development of the ferroelectric capacitance
model and the data presented here.*

**References**

- "Polarization Reversal Kinetics in Ferroelectric Liquid Crystals", Proceedings of the Sixth International Meeting on Ferroelectricity, Kobe 1985, Yoshihiro Ishibashi, Japanese Journal of Applied Physics,vol. 24 Suppl. 24-2, 126 (1985)
*Simulation Standard*Volume 12, Silvaco International, April 2002*ATLAS Users Manual,*Silvaco International. December 2002.