JPH11163280A - Method for simulating ferroelectric - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enable to accurately perform a ferroelectric simulation, by calculating polarization inversion amount per unit time by subtracting product of the polarization inversion amount and a second polarization inversion speed factor from product of non inversion polarization amount and first polarization inversion speed factor. SOLUTION: First, rectangular wave pulse of pulse voltage is applied to a ferroelectric capacitor and a curve of variation with time of polarization amount is obtained by measurement (Pa1). Also, polarization inversion amount per unit time when rectangular wave pulse of pulse voltage is applied to the ferroelectric capacitor is integrated with time to obtain a curve of variation with time according to the ferroelectric simulation (Pa2). These operations are repeated with changing variables until the difference between the curve of variation with time of polarization amount according to the measurement and that according to the ferroelectric simulation reaches the specified value or smaller. Then a ferroelectric simulation is performed to calculate polarization inversion amount per unit time corresponding to the voltage applied to the ferroelectric capacitor.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a ferroelectric simulation method.

[0002]

2. Description of the Related Art In recent years, ferroelectric non-volatile memories utilizing polarization hysteresis characteristics of ferroelectrics have been actively developed, and capacitors using ferroelectrics as capacitor thin films,
A simulation method for a circuit including a so-called ferroelectric capacitor has become important.

FIG. 5 is a configuration diagram of a polarization hysteresis curve measuring device in a conventional ferroelectric simulation method.

In FIG. 5, 1 is a ferroelectric capacitor,
2 is a sense capacitor, 3 is an arbitrary voltage waveform generator, and 4 is an oscilloscope. 1a is a first electrode of the ferroelectric capacitor 1, and 2a is a first electrode of the sense capacitor 2. The capacitance of the sense capacitor 2 is known.

FIG. 6 is a configuration diagram of a ferroelectric capacitor in a conventional ferroelectric simulation method. The ferroelectric capacitor 1 includes a large number of ferroelectrics 11.

FIG. 7 is a flowchart of a conventional ferroelectric simulation method. FIG. 8 is a diagram showing a polarization hysteresis curve measured by a conventional ferroelectric simulation method.

Hereinafter, a conventional ferroelectric simulation method will be described with reference to FIGS.

First, in a step P1, the first electrode 1a of the ferroelectric capacitor 1 is
, A trapezoidal wave voltage pulse is applied, and the oscilloscope 4 measures the potential change of the first electrode 2a of the sense capacitor 2 to measure the capacitance of the sense capacitor 2 and the measured potential change of the first electrode 2a of the sense capacitor 2. , A polarization hysteresis curve 21 is obtained. Next, in step P2, a database containing the values of the polarization hysteresis curve voltage and the polarization amount is created. In step P3, a ferroelectric simulation is performed, and a polarization amount corresponding to the voltage applied to the ferroelectric capacitor 1 is obtained with reference to a database.

[0009]

However, the above-mentioned conventional configuration has the following disadvantages.

The polarization hysteresis curve shown in FIG. 8 is a relationship between the voltage applied to the ferroelectric capacitor and the amount of polarization of the ferroelectric capacitor, and does not take into account the speed at which the polarization is inverted. Therefore, it is impossible to accurately perform a ferroelectric simulation in which the speed at which the polarization is inverted is important, as in the circuit design of a ferroelectric nonvolatile memory. Further, in the ferroelectric simulation method shown in FIG. 7, it is not possible to obtain the characteristic fluctuation of the ferroelectric capacitor due to the repetition of the voltage application. Therefore, it cannot be used for predicting the reliability of the ferroelectric nonvolatile memory.

In view of the above problems, the present invention provides a ferroelectric simulation capable of accurately performing a ferroelectric simulation in which the speed of polarization inversion is important, which is necessary for circuit design of a ferroelectric nonvolatile memory. It is another object of the present invention to provide a ferroelectric simulation method capable of obtaining a characteristic change of a ferroelectric capacitor due to repetition of voltage application and capable of predicting the reliability of a ferroelectric nonvolatile memory.

[0012]

In order to achieve this object, a ferroelectric simulation method according to the present invention uses a voltage applied to a ferroelectric to determine a total polarization amount and an uninverted polarization amount. And the polarization inversion amount per unit time is calculated by subtracting the product of the already-inverted polarization amount and the second polarization inversion speed coefficient from the product of the non-inversion polarization amount and the first polarization inversion speed coefficient. And a process.

Thus, the speed at which the polarization of the ferroelectric is reversed, that is, the amount of polarization reversal per unit time can be calculated for an arbitrary applied voltage waveform, and the circuit of the ferroelectric nonvolatile memory can be calculated. It is possible to accurately perform a ferroelectric simulation in which the speed at which the polarization required for the design is reversed is important.

Further, according to the ferroelectric simulation method of the present invention, the amount of polarization reversal per unit time of one ferroelectric capacitor composed of a plurality of ferroelectrics is determined by calculating the first polarization reversal rate coefficient or the second At least one of the polarization inversion rate coefficients different from each other is calculated from the sum of the polarization inversion amounts per unit time.

Thus, for a ferroelectric capacitor composed of a large number of polarization regions, the speed at which the polarization of the ferroelectric is reversed, that is, the amount of polarization reversal per unit time, is calculated for an arbitrary applied voltage waveform. This makes it possible to accurately perform a ferroelectric simulation in which the speed of inversion of the polarization required for the circuit design of the ferroelectric nonvolatile memory is important.

Further, according to the ferroelectric simulation method of the present invention, the absolute value of the amount of polarization reversal per unit time is integrated over time to calculate the integrated amount of polarization reversal, A step of calculating the total amount of polarization is provided.

Thus, it is possible to obtain a change in the characteristics of the ferroelectric substance due to the repetition of the voltage application, and it is possible to predict the reliability of the ferroelectric nonvolatile memory.

[0018]

(Embodiment 1) A polarization hysteresis curve measuring apparatus in a ferroelectric simulation method according to a first embodiment of the present invention measures a polarization hysteresis curve in a conventional ferroelectric simulation method. Same as the device.

FIG. 1 is a flowchart of a ferroelectric simulation method according to the first embodiment of the present invention.

FIG. 2 is a diagram showing a time change curve of the polarization amount in the ferroelectric simulation method according to the first embodiment of the present invention.

In FIG. 2, 101, 102, 103
Is the pulse voltage of the square wave voltage pulse, 1 shown by the solid line
Reference numerals 04, 105, and 106 denote time-varying curves of the measured polarization amounts at the pulse voltages 101, 102, and 103 of the rectangular-wave voltage pulses, and 107 and 108 indicated by broken lines, respectively.
Reference numeral 109 denotes a pulse voltage of the rectangular wave voltage pulse.
It is a time change curve of the amount of polarization by ferroelectric simulation in 1,102,103.

The polarization reversal amount DP per unit time of the ferroelectric capacitor 1 is expressed by the following formula: DP = ΣDPi (Equation 1), based on the polarization reversal amount DPi of the i-th ferroelectric substance 11 per unit time.

The polarization reversal amount DPi of the i-th ferroelectric substance 11 per unit time is determined by the polarization reversal rate coefficients RAi and Ri.
DPi = RAi × PAi−RBi × PBi (Equation 2) is represented by Bi, the unreversed polarization PAi, and the already reversed polarization PBi.

The total amount of polarization Pi of the i-th ferroelectric substance 11 is represented by the following equation: Pi = PAi + PBi (Equation 3)

The polarization reversal rate coefficient RAi is determined by the voltage V applied to the i-th ferroelectric substance 11 and the variables AAi and BAi that change depending on the temperature. RAi = exp (AAi × V + BAi) 4) It is represented by.

The polarization reversal rate coefficient RBi is determined by the voltage V applied to the i-th ferroelectric substance 11 and the variables ABi and BBi that vary depending on the temperature. RBi = exp (ABi × V + BBi) 5) is represented by

The ferroelectric simulation method according to the first embodiment of the present invention will be described below.

First, in step Pa1, rectangular wave voltage pulses of pulse voltages 101, 102, and 103 are applied to the ferroelectric capacitor 1, and time-varying curves 104, 105, and 106 of the amount of polarization by actual measurement are obtained. In the process Pa2, the pulse voltages 101 and 10 are applied to the ferroelectric capacitor 1.
The polarization change amount DP per unit time when the rectangular wave voltage pulses of 2, 103 are applied is temporally integrated, and the time change curve 10 of the polarization amount by the ferroelectric simulation is obtained.
7, 108 and 109 are obtained. Variables AAi, ABi, B
By changing Ai and BBi, the time change curves 104, 105, and 106 of the polarization amount by actual measurement and the time change curves 107, 108, and 10 of the polarization amount by the ferroelectric simulation.
Step Pa2 is repeated until the difference from No. 9 becomes equal to or less than a predetermined value. In step Pa3, a ferroelectric simulation is performed to calculate a polarization reversal amount DP per unit time corresponding to the voltage applied to the ferroelectric capacitor 1.

In the ferroelectric simulation according to the first embodiment of the present invention, the change in the amount of polarization is obtained by the time integration of the amount of polarization inversion per unit time. As in the case of design, a ferroelectric simulation in which the speed at which the polarization is inverted is important can be accurately performed. Further, since the change in the polarization amount of the ferroelectric capacitor 1 is obtained by the sum of the changes in the polarization amounts of the plurality of ferroelectrics 11, the time change of the polarization amount by the actual measurement of the ferroelectric capacitor 1 can be obtained with high accuracy. Can be reproduced by ferroelectric simulation.

In the first embodiment of the present invention, the ferroelectric capacitor 1 is subjected to the ferroelectric simulation in the step Pa3. However, the ferroelectric capacitor 1 is manufactured by the same manufacturing process as that of the ferroelectric capacitor 1. Needless to say, a ferroelectric simulation can be similarly performed for any circuit configuration including another ferroelectric capacitor.

(Equation 4) and (Equation 5) are examples of a method of calculating the polarization inversion rate coefficients RAi and RBi, and the first embodiment of the present invention is not limited to this.

(Embodiment 2) The polarization hysteresis curve measuring device in the ferroelectric simulation method according to the second embodiment of the present invention is the same as the polarization hysteresis curve measuring device in the conventional ferroelectric simulation method. is there.

FIG. 3 is a flowchart of a ferroelectric simulation method according to the second embodiment of the present invention.

FIG. 4 is a diagram showing a time change curve of the polarization amount after an AC voltage stress is applied in the ferroelectric simulation method according to the second embodiment of the present invention.

In FIG. 4, 204, 2
Reference numerals 05 and 206 denote time-varying curves of the measured polarization amount at the pulse voltages 101, 102, and 103 of the rectangular wave voltage pulses, and 207, 208, and 209 indicated by broken lines.
Are the pulse voltages 101, 10 of the rectangular wave voltage pulse, respectively.
5 is a time change curve of a polarization amount by a ferroelectric simulation in Nos. 2 and 103.

The temporal integration amount SPi of the polarization inversion occurring in the ferroelectric material 11 is obtained by integrating the absolute value of the polarization inversion amount DPi per unit time of the ferroelectric material 11 with respect to time.

After the i-th ferroelectric substance 11 has undergone the polarization inversion by the time integration amount SPi of the polarization inversion, the total polarization quantity PSi of the i-th ferroelectric substance 11 is the total polarization quantity in its initial state. PSi = Pi × SRi ^SPi ( ^Equation 6) represents Pi, the decrease coefficient SRi of the total polarization amount, and the temporal integration amount SPi of the polarization inversion.

Hereinafter, a ferroelectric simulation method according to the second embodiment of the present invention will be described.

First, in step Pb1, pulse voltages 101, 102, and 10 are applied to the ferroelectric capacitor 1 in the initial state.
Then, a rectangular wave voltage pulse of No. 3 is applied, and time-varying curves 104, 105, and 106 of the polarization amount by actual measurement are obtained. Process Pb
In 2, an AC voltage stress is applied to the ferroelectric capacitor 1. In step Pb3, the pulse voltages 101 and 10 are applied to the ferroelectric capacitor 1 after the application of the AC voltage stress.
2, 103 rectangular wave voltage pulses are applied to obtain time-dependent curves 204, 205, and 206 of the amount of polarization by actual measurement.
In the process Pb4, the polarization reversal amount DP per unit time when the rectangular wave voltage pulse of the pulse voltage 101, 102, 103 is applied to the ferroelectric capacitor 1 is integrated over time, and the polarization by the ferroelectric simulation is obtained. Time-varying curves 107, 108, 109, 207, 208,
209. Variables AAi, ABi, BAi, BB
i, SRi are changed, and the time-varying curves 104, 105, 106, 204, 205, 206 of the polarization amount by the actual measurement.
Step Pb4 is repeated until the difference between the time variation curves 107, 108, 109, 207, 208, and 209 of the polarization amounts obtained by the ferroelectric simulation becomes equal to or smaller than a predetermined value. In step Pb5, a ferroelectric simulation is performed to calculate a polarization reversal amount DP per unit time corresponding to the voltage applied to the ferroelectric capacitor 1.

In the ferroelectric simulation according to the second embodiment of the present invention, since the change in the amount of polarization is obtained by the time integration of the amount of polarization inversion per unit time, the circuit design of the ferroelectric nonvolatile memory is performed. As described above, it is possible to accurately perform a ferroelectric simulation in which the speed at which the polarization is inverted is important. Further, since the change in the polarization amount of the ferroelectric capacitor 1 is obtained by the sum of the changes in the polarization amounts of the plurality of ferroelectrics 11, the time change of the polarization amount by the actual measurement of the ferroelectric capacitor 1 can be obtained with high accuracy. Can be reproduced by ferroelectric simulation. Further, the total amount of polarization of the ferroelectric 11 after the application of the AC voltage stress is made a function of the time integration amount of the polarization inversion, so that the reliability of the ferroelectric nonvolatile memory can be predicted.

In the second embodiment of the present invention, the ferroelectric capacitor 1 is subjected to the ferroelectric simulation in step Pb5. However, the ferroelectric capacitor 1 was manufactured by the same manufacturing process as that of the ferroelectric capacitor 1. Needless to say, a ferroelectric simulation can be similarly performed for any circuit configuration including another ferroelectric capacitor.

[0042]

As described above, according to the present invention, the change in the amount of polarization is obtained by the time integration of the amount of polarization inversion per unit time. Therefore, it is possible to accurately perform a ferroelectric simulation in which the speed at which the polarization is inverted is important.

Further, according to the present invention, the change in the amount of polarization of the ferroelectric capacitor is obtained by summing the change in the amount of polarization of a plurality of ferroelectrics. Therefore, it is possible to accurately reproduce the time-dependent change in the polarization amount of the ferroelectric capacitor composed of polycrystal.

[Brief description of the drawings]

FIG. 1 is a flowchart of a ferroelectric simulation method according to a first embodiment of the present invention.

FIG. 2 is a diagram showing a time change curve of a polarization amount in the ferroelectric simulation method according to the first embodiment of the present invention.

FIG. 3 is a flowchart of a ferroelectric simulation method according to a second embodiment of the present invention.

FIG. 4 is a diagram showing a time change curve of a polarization amount after an AC voltage stress is applied in a ferroelectric simulation method according to a second embodiment of the present invention.

FIG. 5 is a configuration diagram of an apparatus for measuring a polarization hysteresis curve in a conventional ferroelectric simulation method.

FIG. 6 is a configuration diagram of a ferroelectric capacitor in a conventional ferroelectric simulation method.

FIG. 7 is a flowchart of a conventional ferroelectric simulation method.

FIG. 8 is a diagram showing a polarization hysteresis curve measured by a conventional ferroelectric simulation method.

[Explanation of symbols]

 Reference Signs List 1 ferroelectric capacitor 2 sense capacitor 3 arbitrary voltage waveform generator 4 oscilloscope 11 ferroelectric

──────────────────────────────────────────────────続 き Continued on the front page (51) Int.Cl. ⁶ Identification code FI H01L 29/788 29/792 // G06F 17/00

Claims (5)

[Claims] A step of distributing a total polarization amount to an uninverted polarization amount and an already-inverted polarization amount by a voltage applied to the ferroelectric, and determining a polarization inversion amount per unit time by the uninverted polarization amount. A step of subtracting the product of the already-inverted polarization amount and the second polarization inversion velocity coefficient from the product of the first polarization inversion velocity coefficient to calculate the ferroelectric substance. 2. A semiconductor device comprising: a plurality of ferroelectrics;
The amount of polarization inversion per unit time of the two ferroelectric capacitors is determined by calculating two or more polarization inversion amounts per unit time in which at least one of the first polarization inversion speed coefficient or the second polarization inversion speed coefficient is different. 2. The ferroelectric simulation method according to claim 1, further comprising a step of calculating by a sum. 3. The method according to claim 1, further comprising the step of calculating at least one of the first polarization inversion velocity coefficient and the second polarization inversion velocity coefficient as a function of a voltage applied to the ferroelectric. The ferroelectric simulation method according to claim 1 or 2, wherein 4. The method according to claim 1, further comprising the step of calculating at least one of the first domain inversion rate coefficient and the second domain inversion rate coefficient as a function of the temperature of the ferroelectric. The ferroelectric simulation method according to claim 1. 5. A step of calculating an integrated polarization inversion amount by temporally integrating the absolute value of the polarization inversion amount per unit time, and a step of calculating the total polarization amount as a function of the integrated polarization inversion amount. The ferroelectric simulation method according to any one of claims 1 to 4, further comprising: