JP4593766B2 - Ferroelectric film evaluation method, ferroelectric film evaluation apparatus, and storage medium - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for evaluating ferroelectric characteristics of a ferroelectric film, which is a constituent member of a semiconductor element such as a capacitor, a ferroelectric film evaluation apparatus, a semiconductor device manufacturing method, and a storage medium.
[0002]
[Prior art]
In recent years, Pb (Zr _1-x Ti _x ) O _Three Ferroelectric materials such as (PZT) are attracting attention. Also, FeRAM (Ferroelectric Random Access Memory) using PZT as a capacitor material has already been put into practical use.
[0003]
Conventionally, the following method is used to measure the ferroelectric characteristics of a ferroelectric film made of PZT or the like.
That is, first, a sample having a structure in which a ferroelectric film is sandwiched between a pair of electrodes is formed.
Next, a voltage is applied to the electrode of this sample, and the hysteresis of polarization with respect to the electric field of the ferroelectric is measured.
Then, the ferroelectric strength of the ferroelectric film is evaluated based on the magnitude of the measured value.
[0004]
From the ferroelectricity of the ferroelectric film thus examined, the electrical characteristics of the semiconductor element having the ferroelectric film are estimated.
[0005]
[Problems to be solved by the invention]
By the way, when a ferroelectric material such as PZT is used as a memory component such as FeRAM or DRAM (Dynamic Random Access Memory), the number of elements is unstable compared to conventional dielectric materials, and the manufacturing process and electrode material Depending on the case, an element such as oxygen or lead may be separated from the ferroelectric film to change the composition ratio.
Then, the ferroelectricity of the ferroelectric film changes, and in extreme cases, the ferroelectricity may be lost.
[0006]
Even if the ferroelectricity of a ferroelectric film of a semiconductor element in the course of manufacturing is examined and used for process control or screening of defective products, the conventional method cannot examine the ferroelectricity without electrodes. For this reason, conventionally, it was necessary to form electrodes on both sides of the ferroelectric film even if the ferroelectricity of the ferroelectric film itself was to be investigated.
[0007]
Accordingly, an object of the present invention is to evaluate the ferroelectric characteristics of a ferroelectric film, which is an element constituent element, even in the absence of an electrode. For example, the manufacturing yield can be improved by recovering the ferroelectricity of the ferroelectric film during the manufacturing process. A highly reliable ferroelectric film evaluation method, a ferroelectric film evaluation apparatus, a semiconductor device manufacturing method, and a storage medium are provided.
[0008]
[Means for Solving the Problems]
As a result of intensive studies, the present inventor has conceived the following aspects of the invention.
[0009]
The ferroelectric film evaluation method of the present invention pays attention to the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction when determining the ferroelectric characteristics of the ferroelectric film.
[0010]
Then, the presence / absence of splitting of the diffraction peak is determined, and if it is split, the polarization value is calculated based on the position of each diffraction peak, and if it is not split, the half width of a predetermined diffraction line is estimated. The polarization value is calculated by performing diffraction peak separation based on the half width.
[0013]
More specifically, when the crystal structure of the ferroelectric is tetragonal, the (h00) / (0k0) / (00l) diffraction lines or h = k = 1 are excluded from the ferroelectric film (hkl). ) Diffracted lines and half-widths of (hhh) diffracted lines are detected, and when the crystal structure of the ferroelectric is orthorhombic, (h00) / (0k0) / (001) diffraction of the ferroelectric film When the half-width of the (hkl) diffraction line and (hhh) diffraction line excluding the line or h = k = 1 is detected, and the crystal structure of the ferroelectric is rhombohedral, hh) / (− hh) diffraction lines or half-widths of (h00) diffraction lines and (h00) diffraction lines excluding diffraction lines in which any two of h, k, and l are 0,
The ferroelectric characteristics of the ferroelectric film are determined based on the detected half widths.
[0014]
As another specific example, when the crystal structure of the ferroelectric is a tetragonal crystal, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or h = k = 1 is used. If only the half-value width of the (hkl) diffraction line is detected and the crystal structure of the ferroelectric is orthorhombic, the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or When only the half width of the diffraction line except h = k = 1 is detected and the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) of the ferroelectric film. Only half-value widths of diffraction lines except for diffraction lines or diffraction lines in which any two of h, k, and l are 0 (hkl) are detected, and based on the detected half-value widths, the ferroelectric film Determine ferroelectric properties.
[0015]
As yet another specific example, when the crystal structure of the ferroelectric is a tetragonal crystal, (h00) / (0k0) / (00l) diffraction lines or h = k = 1 is excluded from the ferroelectric film. (Hkl) When diffraction lines are measured and the diffraction peaks are separated, the lattice constants of the a-axis and c-axis are obtained based on the positions of the respective diffraction peaks, the polarization value is calculated from the lattice constants, and the diffraction peaks Are not separated from each other, the half-value width of the diffraction line that does not include the polarization value information is estimated from the half-value width of the (hhh) diffraction line of the ferroelectric film, and the ferroelectric film based on the half-value width is estimated. Diffraction peak separation of (h00) / (0k0) / (001) diffraction lines or (hkl) diffraction lines excluding h = k = 1 is performed, and the lattice constants of the a axis and c axis are based on the respective diffraction peak positions. And calculate the polarization value from the lattice constant before the ferroelectric When the crystal structure is orthorhombic, (h00) / (0k0) / (001) diffraction lines or diffraction lines excluding h = k = 1 (hkl) are measured and the diffraction peaks are separated. When the diffraction peaks are not separated, the lattice constants of the a-axis, b-axis and c-axis are obtained based on the respective diffraction peak positions, and the polarization value is calculated from the lattice constants. The half-value width of the diffraction line that does not include the polarization value information is estimated from the half-value width of the (hhh) diffraction line of the film, and (h00) / (0k0) / (00l) of the ferroelectric film based on the half-value width. ) Separate diffraction peaks of diffraction lines except for diffraction lines or h = k = 1 (hkl), and obtain lattice constants of a-axis, b-axis and c-axis based on the respective diffraction peak positions, and from the lattice constants The polarization value is calculated, and the crystal structure of the ferroelectric is rhombohedral In other words, the diffraction peak of the ferroelectric film is measured by excluding the (hhh) / (− hhh) diffraction line or the diffraction line in which any two of h, k, and l are 0 (hkl), and the diffraction peak is When the diffraction peaks are separated, the lattice constants of the a-axis and the α angle are obtained based on the respective diffraction peak positions, the polarization value is calculated from the lattice constants, and when the diffraction peaks are not separated, the ferroelectric film The half width of a diffraction line that does not include polarization value information is estimated from the half width of the (h00) diffraction line of (h00), and the (hhh) / (− hhh) diffraction line of the ferroelectric film or the The diffraction peaks of h, k, and l except for the diffraction line where any two are 0 (hkl) are separated, and the lattice constants of the a axis and α angle are obtained based on the respective diffraction peak positions. The polarization value is calculated from the lattice constant.
[0016]
As yet another specific example, when the crystal structure of the ferroelectric is a tetragonal crystal, (h00) / (0k0) / (00l) diffraction lines or h = k = 1 is excluded from the ferroelectric film. (Hkl) For diffraction lines, when the peaks are separated, the a-axis and c-axis lattice constants are calculated from the respective peak positions, and the polarization values are calculated from the lattice constants. When the peaks are not separated, Estimate the half-value width of the diffraction line that does not contain polarization value information from the half-value width at a high temperature at which the half-value width does not change due to temperature rise, and perform peak separation based on the half-value width. The a-axis and c-axis lattice constants are calculated from the position, and the polarization value is calculated from these lattice constants. When the crystal structure of the ferroelectric is orthorhombic, (h00) / (0k0) of the ferroelectric film ) / (00l) diffraction lines or = For diffraction lines excluding k = l (hkl), when the peaks are separated, the a-axis, b-axis, and c-axis lattice constants are calculated from the respective peak positions, and the polarization values are calculated from the lattice constants. However, when the peaks are not separated, the half-value width of the diffraction line not including the polarization value information is estimated from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise, and based on the half-value width. When the peak separation is performed, the lattice constants of the a-axis, b-axis, and c-axis are calculated from the respective peak positions, and the polarization value is calculated from the lattice constant. When the crystal structure of the ferroelectric is rhombohedral, When (hkl) / (− hh) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding diffraction lines in which any two of h, k, l are 0 are separated from each other Its each peak The a-axis and α-angle lattice constants are calculated from the position, and the polarization value is calculated from the lattice constant. When the peaks are not separated, the polarization is determined from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise. The half-value width of the diffraction line that does not contain value information is estimated, peak separation is performed based on the half-value width, and the lattice constants of the a-axis and α-angle are calculated from each peak position, and polarization is performed from this lattice constant. Calculate the value.
[0017]
As still another specific example, when the crystal structure of the ferroelectric is tetragonal, (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or h = k = l (Hkl) diffraction lines are detected, and when the ferroelectric crystal structure is orthorhombic, (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or h = k = When (hkl) diffraction lines excluding l are detected, and the crystal structure of the ferroelectric is rhombohedral, (hhh) / (-hhh) diffraction lines of the ferroelectric film or h, k, (hkl) diffraction lines excluding diffraction lines in which any two of l are 0 (hkl) are detected, and when the crystal structure of the ferroelectric is cubic, (hkl) diffraction lines of the ferroelectric film And the amount of crystals and the magnitude of strain in each of the crystal groups are measured.
[0018]
The present invention is also directed to an evaluation apparatus including means for realizing each evaluation method and a computer-readable storage medium including each evaluation method as a program.
[0019]
In the ferroelectric film evaluation method (evaluation apparatus) of the present invention, the ferroelectric characteristics of the ferroelectric film are examined using X-ray diffraction. In X-ray diffraction, the length of a crystal lattice (lattice constant) can be known by detecting the position of a diffraction peak that has appeared.
[0020]
On the other hand, the ferroelectric film has spontaneous polarization, and the occurrence of this spontaneous polarization causes the lattice constant to extend in the direction in which it occurs. That is, the ferroelectric characteristics of the ferroelectric film can be known by measuring the change in lattice constant due to the occurrence or disappearance of spontaneous polarization.
[0021]
As described above, in the present invention, the ferroelectric characteristics of the formed ferroelectric film can be directly examined, and the local detection is possible regardless of the surface or the film thickness direction. The ferroelectric characteristics of a ferroelectric film formed during the manufacture of an element or the like can be evaluated in a fine and multifaceted manner.
[0022]
Furthermore, in the present invention, when the ferroelectric film has a crystal group consisting of a plurality of crystals having different orientations, the measurement is performed by rotating the ferroelectric film, whereby the ratio of each crystal and each crystal It is possible to know the ferroelectric characteristics.
[0023]
Further, in the method of manufacturing a semiconductor device of the present invention, X-ray diffraction is used to examine the ferroelectric characteristics of the ferroelectric film to determine whether it is good or bad. On the other hand, a process for recovering the ferroelectricity by introducing oxygen or lead into the ferroelectric, or a lot process in which the film forming conditions are corrected is performed. By these steps, the manufacturing yield can be improved.
[0024]
DETAILED DESCRIPTION OF THE INVENTION
DESCRIPTION OF EMBODIMENTS Hereinafter, preferred embodiments to which the present invention is applied will be described in detail with reference to the drawings.
[0025]
(First embodiment)
1 to 3 are flow charts showing the ferroelectric film evaluation method according to the present embodiment in order of steps.
In this embodiment, for the sake of convenience, the ferroelectric film evaluation method will be described in order of steps, but an evaluation apparatus for realizing the evaluation method is also disclosed. This evaluation device includes a normal X-ray diffractometer and a device for measuring the appearance peak position (counter, Position Sensitive Proportional Counter (PSPC), photograph, imaging plate (IP), etc.). As will be described later, it is configured to be driven by a program of a storage medium storing the evaluation method.
[0026]
In evaluating the ferroelectric characteristics of the formed ferroelectric film, first, the crystal structure of the ferroelectric substance of the ferroelectric film is specified (step S1). The crystal structure is classified into four types: tetragonal, orthorhombic, rhombohedral and cubic.
[0027]
If the crystal structure is tetragonal in step S1, it is determined whether or not the (h00) / (0k0) / (001) diffraction lines of the ferroelectric film can be measured (step S11).
[0028]
If the measurement is possible in step S11, (h00) / (0k0) / (00l) diffraction lines are measured by a method such as 2θ / ω scan (step S21).
[0029]
Subsequently, in step S21, it is determined whether or not diffraction peak separation is recognized (step S22). Here, when peak separation is recognized, the lattice constants of the a axis and the c axis are immediately calculated based on the respective diffraction peak positions (step S12). On the other hand, when peak separation is not recognized, the following steps are executed.
[0030]
First, (hhh) diffraction lines of the ferroelectric film are measured by a technique such as 2θ / ω scan (step S23).
[0031]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the (hhh) diffraction line of the ferroelectric film (step S24).
[0032]
Subsequently, the calculated half-width of the (hhh) diffraction line is converted into a half-width at the position of (h00) / (0k0) / (00l) diffraction line (step S25).
[0033]
Subsequently, using the calculated half-width at the position of the (h00) / (0k0) / (001) diffraction line, fitting to the (h00) / (0k0) diffraction line and the (00l) diffraction line by a 2-Gauss function is performed. Peak separation is performed (step S26).
[0034]
Then, the lattice constants of the a axis and the c axis are calculated from the separated diffraction peak positions (step S12).
[0035]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis and c-axis (step S2), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on the polarization value (step S3). .
[0036]
If the (h00) / (0k0) / (001) diffraction line of the ferroelectric film cannot be measured in step S11, the diffraction line except for h = k = 1 is measured by a method such as 2θ / ω scan. (Step S31).
[0037]
Subsequently, it is determined in step S31 whether or not diffraction peak separation is recognized (step S32). Here, when peak separation is recognized, the lattice constants of the a axis and the c axis are immediately calculated based on the respective diffraction peak positions (step S12). On the other hand, when peak separation is not recognized, the following steps are executed.
[0038]
First, (hhh) diffraction lines of the ferroelectric film are measured by a method such as 2θ / ω scan (step S33).
[0039]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the (hhh) diffraction line of the ferroelectric film (step S34).
[0040]
Subsequently, using the calculated half-width of the (hhh) diffraction line, h = k = 1 is removed (hkl) and the half-width at the position of the diffraction line is converted (step S35).
[0041]
Subsequently, using the calculated half width at the position of the diffraction line excluding h = k = 1 (hkl), a multi-Gaussian function such as 2 gauss, 3 gauss is added to the diffraction line excluding h = k = l (hkl). Peak separation is performed by fitting with a function (step S36).
[0042]
Then, the a-axis and c-axis lattice constants are calculated based on the separated diffraction peak positions (step S12).
[0043]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis and c-axis (step S2), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on the polarization value (step S3). .
[0044]
If the crystal structure is orthorhombic in step S1, it is determined whether or not the (h00) / (0k0) / (001) diffraction lines of the ferroelectric film can be measured (step S13).
[0045]
If the measurement is possible in step S13, the (h00) / (0k0) / (00l) diffraction lines are measured by a method such as 2θ / ω scan (step S41).
[0046]
Subsequently, it is determined whether or not separation of diffraction peaks is recognized in step S41 (step S42). Here, when peak separation is recognized, the lattice constants of the a-axis, b-axis, and c-axis are immediately calculated based on the respective diffraction peak positions (step S14). On the other hand, when peak separation is not recognized, the following steps are executed.
[0047]
First, (hhh) diffraction lines of the ferroelectric film are measured by a method such as 2θ / ω scan (step S43).
[0048]
Subsequently, the half-value width of the diffraction line is calculated from the measurement result of the (hhh) diffraction line of the ferroelectric film (step S44).
[0049]
Subsequently, the calculated half-width of the (hhh) diffraction line is converted into a half-width at the position of (h00) / (0k0) / (00l) diffraction line (step S45).
[0050]
Subsequently, using the calculated half width at the position of the (h00) / (0k0) / (001) diffraction line, the (h00) diffraction line, the (0k0) diffraction line, and the (00l) diffraction line are expressed by a 3 Gauss function. Peak separation is performed by fitting (step S46).
[0051]
Then, the lattice constants of the a-axis, b-axis, and c-axis are calculated based on each separated diffraction peak position (step S14).
[0052]
Thereafter, the value of strain is obtained from the calculated lattice constants of the a-axis, b-axis, and c-axis (step S2), the polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on this value ( Step S3).
[0053]
If the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film cannot be measured in step S13, the diffraction lines excluding h = k = 1 (hkl) are measured by a method such as 2θ / ω scanning. (Step S51).
[0054]
Subsequently, it is determined whether or not separation of diffraction peaks is recognized in step S51 (step S52). Here, when peak separation is recognized, the lattice constants of the a-axis, b-axis, and c-axis are immediately calculated based on the respective diffraction peak positions (step S14). On the other hand, when peak separation is not recognized, the following steps are executed.
[0055]
First, the (hh) diffraction line of the ferroelectric film is measured by a technique such as 2θ / ω scan (step S53).
[0056]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the (hhh) diffraction line of the ferroelectric film (step S54).
[0057]
Subsequently, using the calculated half-width of the diffraction line (hhh), h = k = 1 is removed (hkl), and the half-width at the position of the diffraction line is converted (step S55).
[0058]
Subsequently, using the calculated half-value width at the position of the diffraction line excluding h = k = l (hkl), a multi-Gaussian function such as 3 gauss or 6 gauss is used for the diffraction line excluding h = k = l (hkl). Peak separation is performed by fitting with a function (step S56).
[0059]
Then, the lattice constants of the a-axis, b-axis, and c-axis are calculated based on each separated diffraction peak position (step S14).
[0060]
Thereafter, the value of strain is obtained from the calculated lattice constants of the a-axis, b-axis, and c-axis (step S2), the polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on this value ( Step S3).
[0061]
If the crystal structure is rhombohedral in step S1, it is determined whether or not the (hhh) / (− hh) diffraction line of the ferroelectric film can be measured (step S15).
[0062]
If the measurement is possible in step S15, (hhh) / (-hhh) diffraction lines are measured by a technique such as 2θ / ω scan (step S61).
[0063]
Subsequently, in step S61, it is determined whether or not diffraction peak separation is recognized (step S62). Here, when peak separation is recognized, the lattice constants of the a axis and the α angle are immediately calculated based on the respective diffraction peak positions (step S16). On the other hand, when peak separation is not recognized, the following steps are executed.
[0064]
First, the (h00) diffraction line of the ferroelectric film is measured by a method such as 2θ / ω scan (step S63).
[0065]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the (h00) diffraction line of the ferroelectric film (step S64).
[0066]
Subsequently, the calculated half-width of the (h00) diffraction line is converted into a half-width at the position of the (hhh) / (− hh) diffraction line (step S65).
[0067]
Subsequently, using the calculated half width at the position of the (hhh) / (− hhh) diffraction line, peak separation is performed by fitting the (hhh) diffraction line and the (−hhh) diffraction line with a 2-Gaussian function (step) S66).
[0068]
Then, the lattice constants of the a axis and α angle are calculated based on the separated diffraction peak positions (step S16).
[0069]
Thereafter, a strain value is obtained from the calculated lattice constant of the a axis and α angle (step S2), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on the polarization value (step S3). .
[0070]
If the (hhh) / (− hhh) diffraction line of the ferroelectric film cannot be measured in step S15, a diffraction line in which any two of h, k, and l are 0 by a method such as 2θ / ω scan. Exclude (hkl) diffraction lines are measured (step S71).
[0071]
Subsequently, in step S71, it is determined whether or not diffraction peak separation is recognized (step S72). Here, when peak separation is recognized, the lattice constants of the a axis and the α angle are immediately calculated based on the respective diffraction peak positions (step S16). On the other hand, when peak separation is not recognized, the following steps are executed.
[0072]
First, the (h00) diffraction line of the ferroelectric film is measured by a method such as 2θ / ω scan (step S73).
[0073]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the (h00) diffraction line of the ferroelectric film (step S74).
[0074]
Subsequently, using the calculated half-width of the (h00) diffraction line, a diffraction line where any two of h, k, and l are 0 is excluded (hkl) and converted to a half-width at the position of the diffraction line. (Step S75).
[0075]
Subsequently, any two of h, k, and l are calculated using the half width at the position of the diffraction line except for the diffraction line in which any two of h, k, and l are 0 (hkl). Peak separation is performed by fitting with a multi-Gaussian function, for example, 2 gauss, 3 gauss, and 4 gauss functions, to the diffracted lines excluding the diffracted line having zero (hkl) (step S76).
[0076]
Then, the lattice constants of the a axis and α angle are calculated based on the separated diffraction peak positions (step S16).
[0077]
Thereafter, a strain value is obtained from the calculated lattice constant of the a axis and α angle (step S2), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on the polarization value (step S3). .
[0078]
If the crystal structure is cubic in step S1, the polarization value is calculated as 0 because no distortion occurs (step S17).
[0079]
According to the present embodiment, it is possible to evaluate the ferroelectric characteristics of the ferroelectric film, which is an element constituent member, even in the absence of an electrode for applying an electric field that has been considered essential in the past. Thus, the ferroelectricity of the ferroelectric film can be recovered and the manufacturing yield can be improved.
[0080]
(Second Embodiment)
4 to 6 are flowcharts showing the evaluation method of the ferroelectric film according to the present embodiment in the order of steps.
In the present embodiment, as in the first embodiment, the ferroelectric film evaluation method (evaluation apparatus) will be described in the order of steps. However, this technique is suitable when the half-value width of the diffraction peak changes depending on the temperature. Is different from the first embodiment.
[0081]
When evaluating the ferroelectric characteristics of the formed ferroelectric film, first, the ferroelectric crystal structure of the ferroelectric film is specified (step S101). The crystal structure is classified into four types: tetragonal, orthorhombic, rhombohedral and cubic.
[0082]
If the crystal structure is tetragonal in step S101, it is determined whether or not the (h00) / (0k0) / (001) diffraction lines of the ferroelectric film can be measured (step S111).
[0083]
When the measurement is possible in step S111, (h00) / (0k0) / (00l) diffraction lines are measured by a method such as 2θ / ω scan (step S121).
[0084]
Subsequently, in step S121, it is determined whether or not diffraction peak separation is recognized (step S122). Here, when peak separation is recognized, the lattice constants of the a axis and the c axis are immediately calculated based on the respective diffraction peak positions (step S112). On the other hand, when peak separation is not recognized, the following steps are executed.
[0085]
First, the (h00) diffraction line of the ferroelectric film is measured by a method such as a 2θ / ω scan under a high temperature condition (paraelectric phase) such that the half-value width of the diffraction peak does not change due to temperature rise. (Step S123).
[0086]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the (h00) diffraction line of the ferroelectric film (step S124).
[0087]
Subsequently, using the calculated half-width of the (h00) diffraction line, peak separation is performed by fitting a 2-Gauss function in the (h00) / (0k0) diffraction line and the (00l) diffraction line (step S125).
[0088]
Then, the lattice constants of the a-axis and the c-axis are calculated based on each separated diffraction peak position (step S112).
[0089]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis and c-axis (step S102), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on the polarization value (step S103). .
[0090]
If the (h00) / (0k0) / (001) diffraction line of the ferroelectric film cannot be measured in step S111, the diffraction line except for h = k = 1 is measured by a technique such as 2θ / ω scan. (Step S131).
[0091]
Subsequently, in step S131, it is determined whether or not diffraction peak separation is recognized (step S132). Here, when peak separation is recognized, the lattice constants of the a axis and the c axis are immediately calculated based on the respective diffraction peak positions (step S112). On the other hand, when peak separation is not recognized, the following steps are executed.
[0092]
First, the diffraction lines except for h = k = 1 of the ferroelectric film (hkl) are removed by a technique such as 2θ / ω scan under the condition that the temperature is high enough that the half width of the diffraction peak does not change due to the temperature rise. Measurement is performed (step S133).
[0093]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the diffraction line excluding h = k = 1 of the ferroelectric film (hkl) (step S134).
[0094]
Subsequently, using the calculated half-value width of the diffraction line excluding h = k = 1 (hkl), peak separation is performed by fitting on the diffraction line excluding h = k = 1 (hkl) (step S135).
[0095]
Then, the lattice constants of the a-axis and the c-axis are calculated based on each separated diffraction peak position (step S112).
[0096]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis and c-axis (step S102), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on the polarization value (step S103). .
[0097]
If the crystal structure is orthorhombic in step S101, it is determined whether the (h00) / (0k0) / (001) diffraction lines of the ferroelectric film can be measured (step S113).
[0098]
If the measurement is possible in step S113, the (h00) / (0k0) / (00l) diffraction lines are measured by a technique such as 2θ / ω scan (step S141).
[0099]
Subsequently, in step S141, it is determined whether or not diffraction peak separation is recognized (step S142). Here, when peak separation is recognized, the lattice constants of the a-axis, b-axis, and c-axis are immediately calculated based on the respective diffraction peak positions (step S114). On the other hand, when peak separation is not recognized, the following steps are executed.
[0100]
First, the (h00) diffraction line of the ferroelectric film is measured by a technique such as 2θ / ω scan under the condition that the temperature is high enough that the half width of the diffraction peak does not change due to the temperature rise (step S143).
[0101]
Subsequently, the half-value width of the diffraction line is calculated from the measurement result of the (h00) diffraction line of the ferroelectric film (step S144).
[0102]
Subsequently, using the calculated half-width of the (h00) diffraction line, peak separation is performed by fitting a 3 gauss function in the (h00) diffraction line, the (0k0) diffraction line, and the (00l) diffraction line (step S145). .
[0103]
Then, the lattice constants of the a-axis, b-axis, and c-axis are calculated based on the separated diffraction peak positions (step S114).
[0104]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis, b-axis, and c-axis (step S102), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on this value ( Step S103).
[0105]
If the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film cannot be measured in step S113, the diffraction line except for h = k = 1 is measured by a method such as 2θ / ω scan. (Step S151).
[0106]
Subsequently, in step S151, it is determined whether or not diffraction peak separation is recognized (step S152). Here, when peak separation is recognized, the lattice constants of the a-axis, b-axis, and c-axis are immediately calculated based on the respective diffraction peak positions (step S114). On the other hand, when peak separation is not recognized, the following steps are executed.
[0107]
First, the diffraction lines except for h = k = 1 of the ferroelectric film (hkl) are removed by a technique such as 2θ / ω scan under the condition that the temperature is high enough that the half width of the diffraction peak does not change due to the temperature rise. Measurement is performed (step S153).
[0108]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the diffraction line excluding h = k = 1 of the ferroelectric film (hkl) (step S154).
[0109]
Subsequently, using the calculated half-value width of the diffraction line excluding h = k = 1 (hkl), peak separation is performed by fitting in the diffraction line excluding h = k = 1 (hkl) (step S155).
[0110]
Then, the lattice constants of the a-axis, b-axis, and c-axis are calculated based on the separated diffraction peak positions (step S114).
[0111]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis, b-axis, and c-axis (step S102), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on this value ( Step S103).
[0112]
If the crystal structure is rhombohedral in step S101, it is determined whether or not the (hhh) / (− hh) diffraction line of the ferroelectric film can be measured (step S115).
[0113]
If the measurement is possible in step S115, (hhh) / (-hhh) diffraction lines are measured by a technique such as 2θ / ω scan (step S161).
[0114]
Subsequently, in step S161, it is determined whether or not diffraction peak separation is recognized (step S162). Here, when peak separation is recognized, the lattice constant of the a axis and the α angle is immediately calculated based on each diffraction peak position (step S116). On the other hand, when peak separation is not recognized, the following steps are executed.
[0115]
First, (hhh) diffraction lines of the ferroelectric film are measured by a technique such as 2θ / ω scan under the condition that the temperature is high enough that the half width of the diffraction peak does not change due to the temperature rise (step S163).
[0116]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the (hh) diffraction line of the ferroelectric film (step S164).
[0117]
Subsequently, using the calculated half-width of the (hhh) diffraction line, peak separation is performed by fitting a 2-Gauss function in the (hhh) diffraction line and the (−hhh) diffraction line (step S165).
[0118]
Then, the lattice constant of the a axis and the α angle is calculated based on each separated diffraction peak position (step S116).
[0119]
Thereafter, a strain value is obtained from the calculated lattice constant of the a axis and the α angle (step S102), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on the polarization value (step S103). .
[0120]
If the (hhh) / (− hhh) diffraction line of the ferroelectric film cannot be measured in step S115, the diffraction line in which any two of h, k, and l are 0 is removed by a method such as 2θ / ω scan. (Hkl) A diffraction line is measured (step S171).
[0121]
Subsequently, in step S171, it is determined whether or not diffraction peak separation is recognized (step S172). Here, when peak separation is recognized, the lattice constant of the a axis and the α angle is immediately calculated based on each diffraction peak position (step S116). On the other hand, when peak separation is not recognized, the following steps are executed.
[0122]
First, any two of h, k, and l of the ferroelectric film are 0 by a technique such as 2θ / ω scan under the condition that the temperature is high enough that the half width of the diffraction peak does not change due to the temperature rise. A diffraction line excluding a certain diffraction line (hkl) is measured (step S173).
[0123]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the diffraction line excluding the diffraction line in which any two of h, k, and l of the ferroelectric film are 0 (hkl) (step S174).
[0124]
Subsequently, any two of h, k, and l are zero using the half-value width of the diffraction line excluding the diffraction line in which any two of the calculated h, k, and l are zero (hkl). Peak separation is performed by fitting on the diffraction lines excluding the diffraction lines (hkl) (step S175).
[0125]
Then, the lattice constant of the a axis and the α angle is calculated based on each separated diffraction peak position (step S116).
[0126]
Thereafter, a strain value is obtained from the calculated lattice constant of the a axis and the α angle (step S102), a polarization value is calculated from the strain value, and the ferroelectric film is evaluated based on the polarization value (step S103). .
[0127]
When the crystal structure is a cubic crystal in step S101, since no distortion occurs, the polarization value is calculated as 0 (step S117).
[0128]
According to the present embodiment, it is possible to evaluate the ferroelectric characteristics of the ferroelectric film, which is an element constituent member, even in the absence of an electrode for applying an electric field that has been considered essential in the past. Thus, the ferroelectricity of the ferroelectric film can be recovered to improve the manufacturing yield.
[0129]
(Third embodiment)
7 to 9 are flowcharts showing the evaluation method of the ferroelectric film according to the present embodiment in the order of steps.
This embodiment is a technique suitable for application when a plurality of different orientations exist in the ferroelectric film.
[0130]
When evaluating the ferroelectric characteristics of the formed ferroelectric film, first, a profile is obtained by a technique such as χ scan, and the ferroelectric film is separated into a plurality of crystal groups having different orientations (step S201).
[0131]
Subsequently, the obtained profile is integrated for each orientation, and the ratio of each crystal group is calculated (step S202).
[0132]
Subsequently, the ferroelectric crystal structure of the ferroelectric film is specified for each separated crystal group (step S203). The crystal structure is classified into three types: tetragonal, orthorhombic and rhombohedral.
[0133]
If the crystal structure is tetragonal in step S203, it is determined whether or not the (h00) / (0k0) / (001) diffraction lines of the ferroelectric film can be measured (step S211).
[0134]
If the measurement is possible in step S211, (h00) / (0k0) / (00l) diffraction lines are measured by a technique such as 2θ / ω scan (step S221).
[0135]
Subsequently, in step S221, it is determined whether or not diffraction peak separation is recognized (step S222). Here, when peak separation is recognized, the lattice constants of the a axis and the c axis are immediately calculated from the respective diffraction peak positions (step S212). On the other hand, when peak separation is not recognized, the following steps are executed.
[0136]
First, (hhh) diffraction lines of the ferroelectric film are measured by a technique such as 2θ / ω scan (step S223).
[0137]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the (hh) diffraction line of the ferroelectric film (step S224).
[0138]
Subsequently, the calculated half-width of the (hhh) diffraction line is converted into a half-width at the position of (h00) / (0k0) / (00l) diffraction line (step S225).
[0139]
Subsequently, using the calculated half-width at the position of the (h00) / (0k0) / (001) diffraction line, fitting to the (h00) / (0k0) diffraction line and the (00l) diffraction line by a 2-Gauss function is performed. Peak separation is performed (step S226).
[0140]
Then, the lattice constants of the a axis and the c axis are calculated from the separated diffraction peak positions (step S212).
[0141]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis and c-axis (step S204), a polarization value is calculated from the strain value, and based on this, the ferroelectric of the crystal group of the ferroelectric film is calculated. The characteristics are evaluated (step S205).
[0142]
If the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film cannot be measured in step S211, the diffraction line except for h = k = 1 is measured by a method such as 2θ / ω scan. (Step S231).
[0143]
Subsequently, in step S231, it is determined whether or not diffraction peak separation is recognized (step S232). Here, when peak separation is recognized, the lattice constants of the a axis and the c axis are immediately calculated based on the respective diffraction peak positions (step S212). On the other hand, when peak separation is not recognized, the following steps are executed.
[0144]
First, the (hh) diffraction line of the ferroelectric film is measured by a method such as 2θ / ω scan (step S233).
[0145]
Subsequently, the half-value width of the diffraction line is calculated from the measurement result of the (hhh) diffraction line of the ferroelectric film (step S234).
[0146]
Subsequently, using the calculated half-width of the (hhh) diffraction line, h = k = 1 is removed (hkl), and the half-width at the position of the diffraction line is converted (step S235).
[0147]
Subsequently, peak separation is performed by fitting in the diffraction line excluding h = k = l (hkl) using the half width at the position of the diffraction line excluding h = k = 1 (hkl) (step S236). .
[0148]
Then, the a-axis and c-axis lattice constants are calculated based on the separated diffraction peak positions (step S212).
[0149]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis and c-axis (step S204), a polarization value is calculated from the strain value, and based on this, the ferroelectric of the crystal group of the ferroelectric film is calculated. The characteristics are evaluated (step S205).
[0150]
If the crystal structure is orthorhombic in step S203, it is determined whether the (h00) / (0k0) / (001) diffraction lines of the ferroelectric film can be measured (step S213).
[0151]
If the measurement is possible in step S213, the (h00) / (0k0) / (001) diffraction lines are measured by a method such as 2θ / ω scan (step S241).
[0152]
Subsequently, in step S241, it is determined whether or not diffraction peak separation is recognized (step S242). Here, when peak separation is recognized, the lattice constants of the a-axis, b-axis, and c-axis are immediately calculated from the respective diffraction peak positions (step S214). On the other hand, when peak separation is not recognized, the following steps are executed.
[0153]
First, (hhh) diffraction lines of the ferroelectric film are measured by a method such as 2θ / ω scan (step S243).
[0154]
Subsequently, the half width of the diffraction line is calculated from the measurement result of the (hh) diffraction line of the ferroelectric film (step S244).
[0155]
Subsequently, the calculated half-width of the (hhh) diffraction line is converted into a half-width at the position of (h00) / (0k0) / (00l) diffraction line (step S245).
[0156]
Subsequently, using the calculated half-width at the position of the (h00) / (0k0) / (001) diffraction line, the (h00) diffraction line, the (0k0) diffraction line, and the (00l) diffraction line are expressed by a 2-Gauss function. Peak separation is performed by fitting (step S246).
[0157]
Then, the a-axis, b-axis, and c-axis lattice constants are calculated based on the separated diffraction peak positions (step S214).
[0158]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis, b-axis, and c-axis (step S204), a polarization value is calculated from the strain value, and based on this, the crystal group of the ferroelectric film is calculated. The ferroelectric characteristics are evaluated (step S205).
[0159]
If the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film cannot be measured in step S213, the diffraction line except for h = k = 1 is measured by a method such as 2θ / ω scan. (Step S251).
[0160]
Subsequently, in step S251, it is determined whether or not diffraction peak separation is recognized (step S252). Here, when peak separation is recognized, the lattice constants of the a-axis, b-axis, and c-axis are immediately calculated based on the respective diffraction peak positions (step S214). On the other hand, when peak separation is not recognized, the following steps are executed.
[0161]
First, (hhh) diffraction lines of the ferroelectric film are measured by a method such as 2θ / ω scan (step S253).
[0162]
Subsequently, from the measurement result of the (hhh) diffraction line of the ferroelectric film, the half width of the diffraction line is calculated (step S254).
[0163]
Subsequently, using the calculated half-width of the diffraction line (hhh), h = k = 1 is removed (hkl) and the half-width at the position of the diffraction line is converted (step S255).
[0164]
Subsequently, using the calculated half-value width at the position of the diffraction line excluding h = k = 1 (hkl), peak separation is performed by fitting on the diffraction line excluding h = k = l (hkl) (step S256). .
[0165]
Then, the a-axis, b-axis, and c-axis lattice constants are calculated based on the separated diffraction peak positions (step S214).
[0166]
Thereafter, a strain value is obtained from the calculated lattice constants of the a-axis, b-axis, and c-axis (step S204), a polarization value is calculated from the strain value, and the ferroelectric film of the ferroelectric film is calculated based on this value. The characteristics are evaluated (step S205).
[0167]
If the crystal structure is rhombohedral in step S203, it is determined whether the (hhh) / (− hh) diffraction line of the ferroelectric film can be measured (step S215).
[0168]
If the measurement is possible in step S215, (hhh) / (-hhh) diffraction lines are measured by a technique such as 2θ / ω scan (step S261).
[0169]
Subsequently, it is determined whether or not separation of diffraction peaks is recognized in step S261 (step S262). Here, when peak separation is recognized, the lattice constant of the a axis and the α angle is immediately calculated based on each diffraction peak position (step S216). On the other hand, when peak separation is not recognized, the following steps are executed.
[0170]
First, the (h00) diffraction line of the ferroelectric film is measured by a method such as 2θ / ω scan (step S263).
[0171]
Subsequently, from the measurement result of the (h00) diffraction line of the ferroelectric film, the half width of the diffraction line is calculated (step S264).
[0172]
Subsequently, using the calculated half-width of the (h00) diffraction line, the half-width at the position of the (hhh) / (− hh) diffraction line is converted (step S265).
[0173]
Subsequently, using the calculated half width at the position of the (hhh) / (− hhh) diffraction line, peak separation is performed by fitting the (hhh) diffraction line and the (−hhh) diffraction line with a 2-Gaussian function (step) S266).
[0174]
Then, the lattice constant of the a axis and the α angle is calculated based on each separated diffraction peak position (step S216).
[0175]
Thereafter, a strain value is obtained from the calculated lattice constant of the a axis and the α angle (step S204), a polarization value is calculated from the strain value, and based on this, the ferroelectric of the crystal group of the ferroelectric film is calculated. The characteristics are evaluated (step S205).
[0176]
If the (hhh) / (− hhh) diffraction line of the ferroelectric film cannot be measured in step S215, a diffraction line in which any two of h, k, and l are 0 by a method such as 2θ / ω scan. Exclude (hkl) diffraction lines are measured (step S271).
[0177]
Subsequently, in step S271, it is determined whether or not diffraction peak separation is recognized (step S272). Here, when peak separation is recognized, the lattice constant of the a axis and the α angle is immediately calculated based on each diffraction peak position (step S216). On the other hand, when peak separation is not recognized, the following steps are executed.
[0178]
First, the (h00) diffraction line of the ferroelectric film is measured by a method such as 2θ / ω scan (step S273).
[0179]
Subsequently, from the measurement result of the (h00) diffraction line of the ferroelectric film, the half width of the diffraction line is calculated (step S274).
[0180]
Subsequently, using the calculated half-value width of the (h00) diffraction line, a diffraction line in which any two of h, k, and l are 0 is excluded (hkl) and converted to a half-value width at the position of the diffraction line. (Step S275).
[0181]
Subsequently, any two of h, k, and l are calculated using the half width at the position of the diffraction line except for the diffraction line in which any two of h, k, and l are 0 (hkl). Peak separation is performed by fitting on the diffraction lines excluding the diffraction line having zero (hkl) (step S276).
[0182]
Then, the lattice constant of the a axis and the α angle is calculated based on each separated diffraction peak position (step S216).
[0183]
Thereafter, a strain value is obtained from the calculated lattice constant of the a axis and the α angle (step S204), a polarization value is calculated from the strain value, and based on this, the ferroelectric of the crystal group of the ferroelectric film is calculated. The characteristics are evaluated (step S205).
[0184]
If the crystal structure is cubic in step S201, the polarization value is calculated as 0 because no distortion occurs (step S217).
[0185]
According to the present embodiment, the ferroelectric characteristics of the ferroelectric film, which is an element constituent member, are evaluated together with the ratio for each crystal group even in the absence of an electrode for applying an electric field, which has been considered essential in the past. For example, it is possible to improve the manufacturing yield by restoring the ferroelectricity of the ferroelectric film during the manufacturing.
[0186]
Even in the case where the ferroelectric film has a plurality of crystal groups as in the present embodiment, the evaluation suitable for the case where the half-value width of the diffraction peak changes depending on the temperature as in the second embodiment. It is possible to introduce a method.
[0187]
The evaluation methods of the first to third embodiments described above can also be applied to a method for manufacturing a semiconductor device such as DRAM or FeRAM. In this case, for the semiconductor element in the element manufacturing process, the ferroelectric film is examined for quality at the stage of forming the ferroelectric film, and when it is determined to be defective, the condition is corrected and the lot is flowed or the semiconductor used for the determination Ferroelectric properties can be recovered by performing a process such as annealing in an oxygen atmosphere on the elements in the same lot as the elements. This realizes a significant improvement in manufacturing yield.
[0188]
(Fourth embodiment)
In the present embodiment, a computer-readable storage medium that stores the evaluation methods according to the first to third embodiments as a program is disclosed. Furthermore, the evaluation apparatus according to the first to third embodiments is configured to be driven by a program of the storage medium.
[0189]
FIG. 10 is a schematic diagram showing an internal configuration of a general personal user terminal device.
In FIG. 10, reference numeral 1200 denotes a computer PC. The PC 1200 includes a CPU 1201, executes device control software stored in the ROM 1202 or the hard disk (HD) 1211, or supplied from the floppy disk drive (FD) 1212, and collects all devices connected to the system bus 1204. To control.
[0190]
The CPU 1201, the ROM 1202, or the hard disk (HD) 1211 of the PC 1200 includes steps S1 to S76 in the first embodiment, steps S101 to S175 in the second embodiment, and steps S201 to S276 in the third embodiment. It is stored as a program, and the evaluation apparatus is driven based on this.
[0191]
A RAM 1203 functions as a main memory, work area, and the like for the CPU 1201. A keyboard controller (KBC) 1205 controls instruction input from a keyboard (KB) 1209, a device not shown, or the like.
[0192]
Reference numeral 1206 denotes a CRT controller (CRTC) which controls display on a CRT display (CRT) 1210. A disk controller (DKC) 1207 is a hard disk (boot program (start program: a program that starts execution (operation) of personal computer hardware and software)), a plurality of applications, editing files, user files, a network management program, and the like. HD) 1211 and floppy disk (FD) 1212 are controlled.
[0193]
Reference numeral 1208 denotes a network interface card (NIC) that exchanges data bidirectionally with a network printer, another network device, or another PC via the LAN 1220.
[0194]
According to the present embodiment, by driving the evaluation apparatus using the storage medium, the ferroelectric film, which is an element constituent member, even in the absence of an electrode for applying an electric field that has been considered essential in the past The ferroelectric characteristics of the ferroelectric film can be evaluated. For example, the ferroelectricity of the ferroelectric film can be recovered during the manufacturing process to improve the manufacturing yield.
[0195]
【Example】
Hereinafter, examples for more specifically disclosing the present invention will be described.
[0196]
Example 1
FIG. 11 is a cross-sectional view of the sample used in Example 1.
This sample is formed on a Si substrate 10 with SiO. ₂ A film 11, a Ti film 12, and a lower Pt electrode 13 are sequentially formed, and a PZT film 14 having a thickness of about 200 nm is formed on the lower Pt electrode 13.
[0197]
FIG. 12 is a characteristic diagram showing a temperature change of the half width of the PZT (200) / (020) / (002) diffraction peak of the sample shown in FIG.
Thus, the half-value width of the PZT (200) / (020) / (002) diffraction peak changes greatly with changes in temperature.
[0198]
This change in the half width depends on the change in the polarization value. The polarization value becomes 0 at a sufficiently high temperature, and the width of the PZT (200) / (020) / (002) diffraction line becomes a constant value accordingly.
[0199]
The full width at half maximum of the PZT (200) / (020) / (002) diffraction line is a full width at half maximum depending on the crystal grain size other than the polarization value and the resolution of the measuring apparatus. By using this, it is possible to extract only the information on the polarization value.
[0200]
FIG. 13 is a characteristic diagram showing a change in temperature of a polarization value obtained from a PZT (200) / (020) / (002) diffraction peak.
First, the PZT (200) / (020) / (002) diffraction at each temperature using the half-value width of the PZT (200) / (020) / (002) diffraction peak that is high enough to eliminate the polarization value. The peaks are separated by fitting the PZT (200) / (020) diffraction line and the PZT (002) diffraction line with a 2-Gauss function.
[0201]
Next, the a-axis and c-axis lattice constants are calculated from the peak positions of the obtained PZT (200) / (020) diffraction line and PZT (002) diffraction line.
[0202]
Further, the polarization value is calculated from the lattice constant according to the following equation (1). Since A in the equation (1) is a constant, the polarization value can be obtained from the lattice constant by examining the value in PZT in advance.
P = A (c / a-1) ^0.5 ... (1)
Here, P is a polarization value, A is a constant, c is a lattice constant of the c axis, and a is a lattice constant of the a axis.
[0203]
(Example 2)
In this example, the ferroelectric characteristics of the ferroelectric film were evaluated using the same sample as in Example 1 shown in FIG.
[0204]
FIG. 14 is a characteristic diagram showing the temperature change of the half width of the PZT (111) diffraction peak of the sample shown in FIG.
The full width at half maximum of the PZT (200) / (020) / (002) diffraction peak changes greatly with temperature change, but the full width at half maximum of the PZT (111) diffraction peak shows almost no change in temperature.
[0205]
The PZT (111) diffraction peak that does not show a temperature change is considered to contain no polarization value information, so it depends on the crystal grain size and the resolution of the measuring device from the half-value width of the PZT (111) diffraction peak. The full width at half maximum (which does not include polarization value information) is extracted.
[0206]
From the half-value width of the PZT (111) diffraction line that does not include the polarization value information, to the half-value width of the PZT (200) / (020) / (002) diffraction line when the polarization value is 0, the following formula ( 2) Convert using the formula.
[0207]
Using the half width of the PZT (200) / (020) / (002) diffraction line obtained from the equation (2), the PZT (200) / (020) / (002) diffraction line when the polarization value is not 0 is obtained. Peak separation is performed by fitting the PZT (200) / (020) diffraction line and the PZT (002) diffraction line with a 2-Gauss function.
[0208]
Next, the lattice constants of the a-axis and c-axis are calculated from the peak positions of the obtained PZT (200) / (020) diffraction line and PZT (002) diffraction line, and the polarization is further calculated from the lattice constant according to the equation (1). Calculate the value. Since A in the equation (1) is a constant, the polarization value can be obtained from the lattice constant by examining the value in PZT in advance.
W ₂ = W ₁ cos (2θ ₁ / 2) / cos (2θ ₂ / 2) ... (2)
Where W ₂ Is the half width of the PZT (200) / (020) / (002) diffraction line when the polarization value is 0, W ₁ Is the half width of the PZT (111) diffraction line, 2θ ₁ Is the peak position of the PZT (111) diffraction line, 2θ ₂ Represents the peak position of the PZT (200) / (020) / (002) diffraction line.
[0209]
(Example 3)
FIG. 15 is a cross-sectional view of the sample used in Example 3.
This sample is formed on a Si substrate 10 with SiO. ₂ Membrane 11, IrO ₂ A film 15 and a lower Pt electrode 13 are sequentially formed, and a PZT film 16 having a thickness of about 260 nm is formed on the lower Pt electrode 13.
[0210]
FIG. 16 shows the results of electrical measurement (Qsw value / 2 to P (polarization value)) of four samples with different ratios of Zr and Ti of PZT and half of PZT (100) / (010) / (001) diffraction peaks. The value width is plotted.
When the half-value width of the PZT (111) or PZT (222) diffraction line that does not depend on the polarization value hardly changes for each sample (the crystal grain size does not change), the polarization value by electrical measurement as shown in FIG. ) / (010) / (001) diffraction peak half-width correlation diagram is prepared in advance, and the PZT (h00) / (0k0) / (001) diffraction peak half-value width is referred to as the polarization value. Can be requested.
[0211]
Example 4
FIG. 17 is a cross-sectional view of a sample used in Example 4.
This sample is formed on a Si substrate 10 with SiO. ₂ Membrane 11, IrO ₂ A film 15 and a lower Pt electrode 13 are sequentially formed, and a PLCSZT film (PbLaCaSrZrTiO) formed on the lower Pt electrode 13 to a thickness of about 150 nm. _Three ) 17.
[0212]
18 is a characteristic diagram obtained by performing χ scan at the PLCSZT (100) diffraction peak position and background position in the sample of FIG. 17, and FIG. 19 is a profile of χ scan at the PLCSZT (100) diffraction peak position of FIG. FIG. 5 is a characteristic diagram obtained by subtracting a profile of χ scan at the background position.
The sample of FIG. 17 includes three crystals: (111) -oriented crystal ((111) -oriented crystal), (100) -oriented crystal ((100) -oriented crystal), and non-oriented crystal. It can be seen that there are kinds of crystal groups.
[0213]
FIG. 20 shows that the 2θ / ω scan is performed while changing χ by 5 °, and each profile is 2θ = 19.76 ° of each profile (the peak top of the profile obtained by the 2θ / ω scan of χ = 0 °). FIG. 6 is a map around a PZT (100) diffraction peak, normalized by the intensity at position).
[0214]
Since the structure of the sample in FIG. 11 is a tetragonal crystal, the 2θ / ω profile in the vicinity of χ = 55 ° indicating the structure of the (111) -oriented crystal has a PLCSZT (001) diffraction peak and a PLCSZT (100) / (010) diffraction. Peaks overlap and widen.
[0215]
However, the 2θ / ω profile in the vicinity of χ = 0 ° indicating the structure of the (100) -oriented crystal and the 2θ / ω profile in the vicinity of χ = 20 ° indicating the structure of the non-oriented crystal are profiles obtained at χ = 55 °. The width is narrower than that, and the peak top position is also shifted to a high angle.
[0216]
This is because the profile from the (100) -oriented crystal and the non-oriented crystal is the lower of the PLCSZT (001) diffraction peak and the PLCSZT (100) / (010) diffraction peak from the (111) -oriented crystal at χ = 55 °. This is because the PLCSZT (001) diffraction peak appearing at the corner disappears and only the PLCSZT (100) / (010) diffraction peak appearing at the high angle remains.
[0217]
That is, the structure of the (111) oriented crystal is a tetragonal crystal, but the structure of the (100) oriented crystal and the non-oriented crystal is a cubic crystal, and the (111) oriented crystal has a polarization and functions as a memory. It can be seen that the oriented crystal and the non-oriented crystal have no polarization and do not function as a memory.
[0218]
19 and 20, the integral value of the profile from the (111) oriented crystal, the integral value of the profile from the (100) oriented crystal, and the integral value of the profile from the non-oriented crystal are obtained. The ratio of the crystal group can be calculated.
[0219]
Further, the PLCSZT (001) diffraction peak and the PLCSZT (100) / (010) diffraction peak are separated, the lattice constant is obtained from each peak position, and further, the strain is calculated, whereby the polarization value can be converted. . That is, it becomes possible to obtain the polarization value and the ratio of the crystal for each crystal group.
[0220]
(Example 5)
FIG. 21 is a cross-sectional view of a sample used in Example 5.
This sample is formed on a Si substrate 10 with SiO. ₂ A film 11, a Ti film 12, and a lower Pt electrode 13 are sequentially formed, and a PZT film 18 having a thickness of about 260 nm is formed on the lower Pt electrode 13.
[0221]
FIG. 22 shows a χ scan at the PZT (100) diffraction peak position and the background position in the sample of FIG. 21, and a χ scan profile at the background position from the χ scan profile at the PZT (100) diffraction peak position. FIG.
The sample in FIG. 21 includes three crystals: (111) -oriented crystal ((111) -oriented crystal), (100) -oriented crystal ((100) -oriented crystal), and non-oriented crystal. It can be seen that there are kinds of crystal groups.
[0222]
FIG. 23 shows a 2θ / ω scan near the PZT (100) diffraction peak at χ = 0 ° ((100) oriented crystal), χ = 20 ° (non-oriented crystal), χ = 55 ° ((111) oriented crystal). It is the characteristic view which performed.
The 2θ / ω profile at χ = 55 ° showing the structure of the (111) oriented crystal shows a shoulder from the low angle PZT (001) diffraction and a peak from the high angle PZT (100) / (010) diffraction.
[0223]
However, the 2θ / ω profile of χ = 0 ° indicating the structure of the (100) -oriented crystal and the 2θ / ω profile of χ = 20 ° indicating the structure of the non-oriented crystal are different from the profile obtained at χ = 55 °. The shoulder from the low angle PZT (001) diffraction disappears and only the peak from the high angle PZT (100) / (010) diffraction is seen.
[0224]
Thereby, the structure of the (111) -oriented crystal is a tetragonal crystal, but the structure of the (100) -oriented crystal and the non-oriented crystal is a cubic crystal, and the (111) -oriented crystal has polarization and functions as a memory. 100) It can be seen that oriented crystals and non-oriented crystals have no polarization and do not function as a memory.
[0225]
From the measurement data of FIG. 19 and FIG. 20, the integral value of the profile from the (111) oriented crystal, the integral value of the profile from the (100) oriented crystal, the profile from the non-oriented crystal, and the integral value of the The ratio of each crystal group can be calculated.
[0226]
Further, the PZT (001) diffraction peak and the PZT (100) / (010) diffraction peak are separated, the lattice constant is obtained from each peak position, and further, the strain is calculated, whereby the polarization value can be converted. .
That is, it becomes possible to obtain the polarization value for each crystal group and the ratio of the crystals.
[0227]
In each of the above embodiments, the case where the ferroelectrics are PZT and PLCSZT has been described. However, PZT includes all of La, Sr, Ca, Ba, Mn, P, Bi, etc. or some elements therein. Even if it is out, it can be applied.
Further, it can be similarly applied to ferroelectrics other than PZT.
[0228]
Furthermore, the present invention can be applied to a high dielectric material as long as spontaneous polarization occurs at a temperature below the Curie point temperature.
[0229]
In the first embodiment, the polarization value is calculated by the equation (1) when the polarization value is obtained from the lattice constant. However, other equations may be used as necessary.
[0230]
In each embodiment, peak separation was performed by fitting with a 2 Gauss function. However, if necessary, other functions such as a Lorentz function may be used, and the number of peaks such as a 3 Gauss function and a 4 Gauss function may be increased. It doesn't matter.
[0231]
In each of the examples, all the samples are in a state where there is no upper electrode on the ferroelectric film. However, the upper electrode and other thin films may be attached.
Further, the sample may be in the form of a chip or any other shape.
[0232]
Furthermore, in Examples 4 and 5, the (100) / (010) / (001) diffraction peaks were used when determining the crystal orientation ratio, but orientation separation may be performed using other diffraction peaks.
[0233]
Hereinafter, various aspects of the present invention will be collectively described as supplementary notes.
[0234]
(Appendix 1) When determining the ferroelectric properties of a ferroelectric film,
By X-ray diffraction, paying attention to the diffraction peak for each ferroelectric crystal structure of the ferroelectric film,
If the diffraction peaks are split, calculate the polarization value based on each diffraction peak position,
A method for evaluating a ferroelectric film, wherein a diffraction peak is not split, a half-value width of a predetermined diffraction line is estimated, and a polarization value is calculated by performing diffraction peak separation based on the half-value width .
[0235]
(Appendix 2) When determining the ferroelectric properties of a ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction, and using the half-value width of the first diffraction peak as an index,
When the half width of the first diffraction peak does not change in temperature, the half width is used to calculate the polarization value by separating the second diffraction peak that always changes in temperature,
When the half-value width of the first diffraction peak changes with temperature, the half-value width of the second diffraction peak in the high temperature region is used to calculate the polarization value by separating the second diffraction peak. A characteristic evaluation method of a ferroelectric film.
[0236]
(Appendix 3) When determining the ferroelectric properties of a ferroelectric film,
By classifying the ferroelectric crystals of the ferroelectric film into different crystal groups by X-ray diffraction, focusing on the diffraction peaks for each crystal structure for each crystal group, the amount of crystals and the magnitude of strain are determined. A method for evaluating a ferroelectric film, comprising measuring.
[0237]
(Appendix 4) In determining the ferroelectric properties of a ferroelectric film,
By classifying the ferroelectric crystals of the ferroelectric film into different crystal groups by X-ray diffraction, focusing on the diffraction peak for each crystal structure for each crystal group,
If the diffraction peaks are split, calculate the polarization value based on each diffraction peak position,
When the diffraction peak is not split, estimate the half width of a predetermined diffraction line, perform diffraction peak separation based on the half width, calculate the polarization value, and calculate the amount of crystals in each crystal group and A method for evaluating a ferroelectric film, comprising measuring the magnitude of strain.
[0238]
(Additional remark 5) Each said crystal structure is a tetragonal crystal, an orthorhombic crystal, a rhombohedral crystal, and a cubic crystal, The polarization value is calculated about each of these said crystal structures, Any of the additional marks 1-4 characterized by the above-mentioned. The method for evaluating a ferroelectric film according to claim 1.
[0239]
(Appendix 6) An inspection apparatus for determining the ferroelectric characteristics of a ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
If the diffraction peaks are split, calculate the polarization value based on each diffraction peak position,
When the diffraction peak is not split, a half-value width of a predetermined diffraction line is estimated, and a polarization value is calculated by performing diffraction peak separation based on the half-value width, thereby evaluating the ferroelectric film .
[0240]
(Appendix 7) An evaluation apparatus for determining the ferroelectric characteristics of a ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction, and using the half-value width of the first diffraction peak that is substantially constant in the high temperature region as an index
When the half width of the first diffraction peak does not change in temperature, the half width is used to calculate the polarization value by separating the second diffraction peak that always changes in temperature,
When the half width of the first diffraction peak changes with temperature, the polarization value is calculated by separating the second diffraction peak using the half width of the second diffraction peak in the high temperature region. An apparatus for evaluating a ferroelectric film characterized by the following.
[0241]
(Appendix 8) An evaluation apparatus for determining the ferroelectric characteristics of a ferroelectric film,
By classifying the ferroelectric crystals of the ferroelectric film into different crystal groups by X-ray diffraction, focusing on the diffraction peaks for each crystal structure for each crystal group, the amount of crystals and the magnitude of strain are determined. A method for evaluating a ferroelectric film, comprising measuring.
[0242]
(Supplementary note 9) An evaluation apparatus for determining the ferroelectric characteristics of a ferroelectric film,
By classifying the ferroelectric crystals of the ferroelectric film into different crystal groups by X-ray diffraction, focusing on the diffraction peak for each crystal structure for each crystal group,
If the diffraction peaks are split, calculate the polarization value based on each diffraction peak position,
When the diffraction peak is not split, estimate the half width of a predetermined diffraction line, perform diffraction peak separation based on the half width, calculate the polarization value, and calculate the amount of crystals in each crystal group and An apparatus for evaluating a ferroelectric film, characterized by measuring the magnitude of strain.
[0243]
(Additional remark 10) Each said crystal structure is a tetragonal crystal, an orthorhombic crystal, a rhombohedral crystal, and a cubic crystal, The polarization value is calculated about each of these said crystal structures, Any of the additional marks 5-9 characterized by the above-mentioned. The method for evaluating a ferroelectric film according to claim 1.
[0244]
(Appendix 11) In determining the ferroelectric characteristics of the ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
When the crystal structure of the ferroelectric is a tetragonal crystal, the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 and (hhh) ) Detect half-width of diffraction line,
When the crystal structure of the ferroelectric is orthorhombic, (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 (and hh) Detect the half width of the diffraction line,
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. The half-width of the (hkl) diffraction line and (h00) diffraction line excluding
A method for evaluating a ferroelectric film, comprising determining a ferroelectric characteristic of the ferroelectric film based on the detected half widths.
[0245]
(Supplementary Note 12) When determining the ferroelectric characteristics of a ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
When the crystal structure of the ferroelectric is a tetragonal crystal, the half-value width of the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 Only detect
When the crystal structure of the ferroelectric is orthorhombic, the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or the half of the diffraction line excluding h = k = 1 (hkl) Detect only the price range,
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. (Hkl) except the half-width of the diffraction line is detected,
A method for evaluating a ferroelectric film, comprising determining a ferroelectric characteristic of the ferroelectric film based on the detected half widths.
[0246]
(Supplementary Note 13) In determining the ferroelectric characteristics of the ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
When the crystal structure of the ferroelectric is tetragonal,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 are measured and the diffraction peaks are separated, the diffraction peaks thereof are separated. The lattice constants of the a-axis and c-axis are obtained based on the position, the polarization value is calculated from the lattice constant, and when the diffraction peak is not separated, the polarization value is calculated from the half-value width of the (hh) diffraction line of the ferroelectric film. The half-width of the diffraction line not including the above information is estimated, and the (h00) / (0k0) / (00l) diffraction line or h = k = 1 is excluded from the ferroelectric film based on the half-width (hkl). ) Separating diffraction peaks of diffraction lines, obtaining lattice constants of the a-axis and c-axis based on the respective diffraction peak positions, calculating a polarization value from the lattice constants,
When the crystal structure of the ferroelectric is orthorhombic,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 are measured and the diffraction peaks are separated, the diffraction peaks thereof are separated. Based on the position, the lattice constants of the a-axis, b-axis, and c-axis are obtained, the polarization value is calculated from the lattice constant, and when the diffraction peaks are not separated, the half of the (hh) diffraction line of the ferroelectric film The half-value width of the diffraction line that does not include the polarization value information is estimated from the value range, and the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or h = k = l based on the half-value width. (Hkl) The diffraction peaks of the diffraction lines are removed, the lattice constants of the a-axis, b-axis and c-axis are obtained based on the respective diffraction peak positions, and the polarization value is calculated from the lattice constants.
When the crystal structure of the ferroelectric is rhombohedral,
The (hhh) / (− hhh) diffraction line of the ferroelectric film or the (hkl) diffraction line excluding the diffraction line in which any two of h, k, and l are 0 are measured, and the diffraction peak is separated. If the diffraction peak is not separated, the lattice constant of the a axis and the α angle is obtained based on the position of each diffraction peak, and the polarization value is calculated from the lattice constant. h00) The half-value width of the diffraction line that does not include the polarization value information is estimated from the half-value width of the diffraction line, and the (hhh) / (− hhh) diffraction line or h, The diffraction peaks of the diffraction lines excluding the diffraction line in which any two of k and l are 0 (hkl) are separated, and the lattice constants of the a axis and the α angle are obtained based on the respective diffraction peak positions. Ferroelectric film characterized by calculating polarization value from lattice constant Evaluation method.
[0247]
(Supplementary Note 14) In determining the ferroelectric characteristics of the ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
When the crystal structure of the ferroelectric is tetragonal,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1, when the peaks are separated, an a-axis is formed from each peak position. And the c-axis lattice constant, and the polarization value is calculated from the lattice constant. When the peaks are not separated, the polarization value information is obtained from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise. Estimate the half-value width of the diffraction lines not included, perform peak separation based on the half-value width, calculate the a-axis and c-axis lattice constants from the respective peak positions, and calculate the polarization value from this lattice constant. ,
When the crystal structure of the ferroelectric is orthorhombic,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1, when the peaks are separated, an a-axis is formed from each peak position. The b-axis and c-axis lattice constants are calculated, and the polarization value is calculated from the lattice constant. When the peaks are not separated, the polarization value is calculated from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise. The half-value width of the diffraction line not including the above information is estimated, peak separation is performed based on the half-value width, and the lattice constants of the a-axis, b-axis, and c-axis are calculated from the respective peak positions, and this lattice constant is calculated. Calculate the polarization value from
When the crystal structure of the ferroelectric is rhombohedral,
When (hkl) / (− hh) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding diffraction lines in which any two of h, k, l are 0 are separated from each other Then, the a-axis and α-angle lattice constants are calculated from the respective peak positions, and the polarization values are calculated from the lattice constants. When the peaks are not separated, the half-value width does not change due to the temperature rise. The half-value width of a diffraction line that does not contain polarization value information is estimated from the half-value width, peak separation is performed based on the half-value width, and the lattice constants of the a axis and the α angle are calculated from the respective peak positions. A method for evaluating a ferroelectric film, wherein a polarization value is calculated from the lattice constant.
[0248]
(Additional remark 15) When judging the ferroelectric characteristic of a ferroelectric film,
By classifying the ferroelectric crystals of the ferroelectric film into different crystal groups by X-ray diffraction, focusing on the diffraction peak for each crystal structure for each crystal group,
When the crystal structure of the ferroelectric is tetragonal, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or the diffraction lines excluding h = k = 1 (hkl) are detected. ,
When the crystal structure of the ferroelectric is orthorhombic, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or the diffraction lines excluding h = k = 1 (hkl) are detected. And
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. (Hkl) diffraction lines except
When the crystal structure of the ferroelectric is cubic, the (hkl) diffraction line of the ferroelectric film is detected,
A method for evaluating a ferroelectric film, comprising measuring the amount of crystal and the magnitude of strain in each of the crystal groups.
[0249]
(Supplementary Note 16) An inspection apparatus for determining ferroelectric characteristics of a ferroelectric film by X-ray diffraction,
Paying attention to the diffraction peak for each ferroelectric crystal structure of the ferroelectric film,
When the crystal structure of the ferroelectric is tetragonal, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 and (hhh) ) Detect half-width of diffraction line,
When the crystal structure of the ferroelectric is orthorhombic, (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 (and hh) Detect the half width of the diffraction line,
When the crystal structure of the ferroelectric is rhombohedral, (hhl) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. The half-width of the (hkl) diffraction line and (h00) diffraction line excluding
An inspection apparatus for a ferroelectric film, comprising means for determining a ferroelectric characteristic of the ferroelectric film based on the detected half-value widths.
[0250]
(Supplementary Note 17) An inspection apparatus for determining ferroelectric characteristics of a ferroelectric film by X-ray diffraction,
Paying attention to the diffraction peak for each ferroelectric crystal structure of the ferroelectric film,
When the crystal structure of the ferroelectric is a tetragonal crystal, the half-value width of the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 Only detect
When the crystal structure of the ferroelectric is orthorhombic, the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or the half of the diffraction line excluding h = k = 1 (hkl) Detect only the price range,
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. (Hkl) except the half-width of the diffraction line is detected,
An inspection apparatus for a ferroelectric film, comprising means for determining a ferroelectric characteristic of the ferroelectric film based on the detected half-value widths.
[0251]
(Supplementary Note 18) An inspection apparatus for determining ferroelectric characteristics of a ferroelectric film by X-ray diffraction,
Paying attention to the diffraction peak for each ferroelectric crystal structure of the ferroelectric film,
When the crystal structure of the ferroelectric is tetragonal,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 are measured and the diffraction peaks are separated, the diffraction peaks thereof are separated. The lattice constants of the a-axis and c-axis are obtained based on the position, the polarization value is calculated from the lattice constant, and when the diffraction peak is not separated, the polarization value is calculated from the half-value width of the (hh) diffraction line of the ferroelectric film. The half-width of the diffraction line not including the above information is estimated, and the (h00) / (0k0) / (00l) diffraction line or h = k = 1 is excluded from the ferroelectric film based on the half-width (hkl). ) Separating diffraction peaks of diffraction lines, obtaining lattice constants of the a-axis and c-axis based on the respective diffraction peak positions, calculating a polarization value from the lattice constants,
When the crystal structure of the ferroelectric is orthorhombic,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 are measured and the diffraction peaks are separated, the diffraction peaks thereof are separated. Based on the position, the lattice constants of the a-axis, b-axis, and c-axis are obtained, the polarization value is calculated from the lattice constant, and when the diffraction peaks are not separated, the half of the (hh) diffraction line of the ferroelectric film The half-value width of the diffraction line that does not include the polarization value information is estimated from the value range, and the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or h = k = l based on the half-value width. (Hkl) The diffraction peaks of the diffraction lines are removed, the lattice constants of the a-axis, b-axis and c-axis are obtained based on the respective diffraction peak positions, and the polarization value is calculated from the lattice constants.
When the crystal structure of the ferroelectric is rhombohedral,
The (hhh) / (− hhh) diffraction line of the ferroelectric film or the (hkl) diffraction line excluding the diffraction line in which any two of h, k, and l are 0 are measured, and the diffraction peak is separated. If the diffraction peak is not separated, the lattice constant of the a axis and the α angle is obtained based on the position of each diffraction peak, and the polarization value is calculated from the lattice constant. h00) The half-value width of the diffraction line that does not include the polarization value information is estimated from the half-value width of the diffraction line, and the (hhh) / (− hhh) diffraction line or h, The diffraction peaks of the diffraction lines excluding the diffraction line in which any two of k and l are 0 (hkl) are separated, and the lattice constants of the a axis and the α angle are obtained based on the respective diffraction peak positions. Ferroelectric film characterized by calculating polarization value from lattice constant Inspection equipment.
[0252]
(Supplementary note 19) An inspection apparatus for determining ferroelectric characteristics of a ferroelectric film by X-ray diffraction,
Paying attention to the diffraction peak for each ferroelectric crystal structure of the ferroelectric film,
When the crystal structure of the ferroelectric is tetragonal,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1, when the peaks are separated, an a-axis is formed from each peak position. And the c-axis lattice constant, and the polarization value is calculated from the lattice constant. When the peaks are not separated, the polarization value information is obtained from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise. Estimate the half-value width of the diffraction lines not included, perform peak separation based on the half-value width, calculate the a-axis and c-axis lattice constants from the respective peak positions, and calculate the polarization value from this lattice constant. ,
When the crystal structure of the ferroelectric is orthorhombic,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1, when the peaks are separated, an a-axis is formed from each peak position. The b-axis and c-axis lattice constants are calculated, and the polarization value is calculated from the lattice constant. When the peaks are not separated, the polarization value is calculated from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise. The half-value width of the diffraction line not including the above information is estimated, peak separation is performed based on the half-value width, and the lattice constants of the a-axis, b-axis, and c-axis are calculated from the respective peak positions, and this lattice constant is calculated. Calculate the polarization value from
When the crystal structure of the ferroelectric is rhombohedral,
When (hkl) / (− hh) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding diffraction lines in which any two of h, k, l are 0 are separated from each other Then, the a-axis and α-angle lattice constants are calculated from the respective peak positions, and the polarization values are calculated from the lattice constants. When the peaks are not separated, the half-value width does not change due to the temperature rise. The half-value width of a diffraction line that does not contain polarization value information is estimated from the half-value width, peak separation is performed based on the half-value width, and the lattice constants of the a axis and the α angle are calculated from the respective peak positions. An apparatus for inspecting a ferroelectric film, wherein a polarization value is calculated from the lattice constant.
[0253]
(Supplementary Note 20) An inspection apparatus for determining ferroelectric characteristics of a ferroelectric film by X-ray diffraction,
Before classifying the ferroelectric crystals of the ferroelectric film into different crystal groups, paying attention to the diffraction peak for each crystal structure for each crystal group,
When the crystal structure of the ferroelectric is tetragonal, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or the diffraction lines excluding h = k = 1 (hkl) are detected. ,
When the crystal structure of the ferroelectric is orthorhombic, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or the diffraction lines excluding h = k = 1 (hkl) are detected. And
When the crystal structure of the ferroelectric is rhombohedral, (hhl) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. (Hkl) diffraction lines except
When the crystal structure of the ferroelectric is cubic, the (hkl) diffraction line of the ferroelectric film is detected,
An inspection apparatus for a ferroelectric film, which measures the amount of crystal and the magnitude of strain in each of the crystal groups.
[0254]
(Supplementary Note 21) A computer-readable program storing a program for determining ferroelectric characteristics of a ferroelectric film by focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction Storage medium,
The program is
When the crystal structure of the ferroelectric is a tetragonal crystal, the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 and (hhh) ) Detect half-width of diffraction line,
When the crystal structure of the ferroelectric is orthorhombic, (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 (and hh) Detect the half width of the diffraction line,
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. The half-width of the (hkl) diffraction line and (h00) diffraction line excluding
A storage medium characterized in that the ferroelectric characteristic of the ferroelectric film is determined based on the detected half-value widths.
[0255]
(Supplementary Note 22) Computer-readable storage of a program for determining ferroelectric characteristics of a ferroelectric film by focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction Storage medium,
The program is
When the crystal structure of the ferroelectric is a tetragonal crystal, the half-value width of the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 Only detect
When the crystal structure of the ferroelectric is orthorhombic, the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or the half of the diffraction line excluding h = k = 1 (hkl) Detect only the price range,
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. (Hkl) except the half-width of the diffraction line is detected,
A storage medium characterized in that the ferroelectric characteristic of the ferroelectric film is determined based on the detected half-value widths.
[0256]
(Supplementary Note 23) A computer-readable program storing a program for determining ferroelectric characteristics of a ferroelectric film by focusing on a diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction. Storage medium,
The program is
When the crystal structure of the ferroelectric is tetragonal,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 are measured and the diffraction peaks are separated, the diffraction peaks thereof are separated. The lattice constants of the a-axis and c-axis are obtained based on the position, the polarization value is calculated from the lattice constant, and when the diffraction peak is not separated, the polarization value is calculated from the half-value width of the (hh) diffraction line of the ferroelectric film. The half-width of the diffraction line not including the above information is estimated, and the (h00) / (0k0) / (00l) diffraction line or h = k = 1 is excluded from the ferroelectric film based on the half-width (hkl). ) Separating diffraction peaks of diffraction lines, obtaining lattice constants of the a-axis and c-axis based on the respective diffraction peak positions, calculating a polarization value from the lattice constants,
When the crystal structure of the ferroelectric is orthorhombic,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 are measured and the diffraction peaks are separated, the diffraction peaks thereof are separated. Based on the position, the lattice constants of the a-axis, b-axis, and c-axis are obtained, the polarization value is calculated from the lattice constant, and when the diffraction peaks are not separated, the half of the (hh) diffraction line of the ferroelectric film The half-value width of the diffraction line that does not include the polarization value information is estimated from the value range, and the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or h = k = l based on the half-value width. (Hkl) The diffraction peaks of the diffraction lines are removed, the lattice constants of the a-axis, b-axis and c-axis are obtained based on the respective diffraction peak positions, and the polarization value is calculated from the lattice constants.
When the crystal structure of the ferroelectric is rhombohedral,
The (hhh) / (− hhh) diffraction line of the ferroelectric film or the (hkl) diffraction line excluding the diffraction line in which any two of h, k, and l are 0 are measured, and the diffraction peak is separated. If the diffraction peak is not separated, the lattice constant of the a axis and the α angle is obtained based on the position of each diffraction peak, and the polarization value is calculated from the lattice constant. h00) The half-value width of the diffraction line that does not include the polarization value information is estimated from the half-value width of the diffraction line, and the (hhh) / (− hhh) diffraction line or h, The diffraction peaks of the diffraction lines excluding the diffraction line in which any two of k and l are 0 (hkl) are separated, and the lattice constants of the a axis and the α angle are obtained based on the respective diffraction peak positions. Calculates the polarization value from the lattice constant A storage medium characterized by that.
[0257]
(Supplementary Note 24) A computer-readable program storing a program for determining the ferroelectric characteristics of a ferroelectric film by focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction Storage medium,
The program is
When the crystal structure of the ferroelectric is tetragonal,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1, when the peaks are separated, an a-axis is formed from each peak position. And the c-axis lattice constant, and the polarization value is calculated from the lattice constant. When the peaks are not separated, the polarization value information is obtained from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise. Estimate the half-value width of the diffraction lines not included, perform peak separation based on the half-value width, calculate the a-axis and c-axis lattice constants from the respective peak positions, and calculate the polarization value from this lattice constant. ,
When the crystal structure of the ferroelectric is orthorhombic,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1, when the peaks are separated, an a-axis is formed from each peak position. The b-axis and c-axis lattice constants are calculated, and the polarization value is calculated from the lattice constant. When the peaks are not separated, the polarization value is calculated from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise. The half-value width of the diffraction line not including the above information is estimated, peak separation is performed based on the half-value width, and the lattice constants of the a-axis, b-axis, and c-axis are calculated from the respective peak positions, and this lattice constant is calculated. Calculate the polarization value from
When the crystal structure of the ferroelectric is rhombohedral,
When (hkl) / (− hh) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding diffraction lines in which any two of h, k, l are 0 are separated from each other Then, the a-axis and α-angle lattice constants are calculated from the respective peak positions, and the polarization values are calculated from the lattice constants. When the peaks are not separated, the half-value width does not change due to the temperature rise. The half-value width of a diffraction line that does not contain polarization value information is estimated from the half-value width, peak separation is performed based on the half-value width, and the lattice constants of the a axis and the α angle are calculated from the respective peak positions. A storage medium characterized in that a polarization value is calculated from the lattice constant.
[0258]
(Supplementary Note 25) The ferroelectric crystals of the ferroelectric film are classified into different crystal groups by X-ray diffraction, and attention is paid to the diffraction peak for each crystal structure for each crystal group. A computer-readable storage medium storing a program for determining ferroelectric characteristics,
The program is
When the crystal structure of the ferroelectric is tetragonal, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or the diffraction lines excluding h = k = 1 (hkl) are detected. ,
When the crystal structure of the ferroelectric is orthorhombic, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or the diffraction lines excluding h = k = 1 (hkl) are detected. And
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. (Hkl) diffraction lines except
When the crystal structure of the ferroelectric is cubic, the (hkl) diffraction line of the ferroelectric film is detected,
A storage medium characterized in that it measures the amount of crystal and the magnitude of strain in each crystal group.
[0259]
(Supplementary Note 26) When manufacturing a semiconductor device including a capacitor in which a lower conductor film and an upper conductor film face each other with a capacitance insulating film interposed therebetween,
16. A method of manufacturing a semiconductor device, wherein a ferroelectric film whose ferroelectric characteristics are determined by the evaluation method according to any one of appendices 1 to 5 and 11 to 15 is used as the capacitive insulating film.
[0260]
(Supplementary note 27) The semiconductor device manufacturing method according to supplementary note 26, wherein after determining the ferroelectric characteristics of the ferroelectric film, the timely conditions are corrected.
[0261]
(Supplementary note 28) The method for manufacturing a semiconductor device according to supplementary note 26, wherein after the ferroelectric characteristic of the ferroelectric film is determined, a process for recovering the ferroelectric characteristic in a timely manner is performed.
[0262]
(Supplementary note 29) When the three-dimensional structure exists in the ferroelectric film, a flat region is prepared, the region is inspected, and the ferroelectric characteristics of the ferroelectric film are determined. The evaluation method according to any one of 5, 11 to 15.
[0263]
【The invention's effect】
According to the present invention, the half-value width and peak position of a ferroelectric film peak are detected using X-ray diffraction, and the presence or absence of ferroelectricity of the ferroelectric film or the strength of spontaneous polarization is determined based on the result. Therefore, the ferroelectricity of the ferroelectric film can be evaluated without an electrode for applying an electric field, which has been considered essential in the conventional method.
[0264]
Further, according to the present invention, it is possible to evaluate the ferroelectricity of an element being manufactured in an actual element manufacturing process. In addition, when the device in the actual device manufacturing process is checked for good or bad ferroelectricity, if it is determined to be defective, the conditions are corrected and the lot is run, or the device in the same lot as the device used for the determination is annealed in an oxygen atmosphere. It is possible to recover the ferroelectric characteristics by performing a process such as performing a process. As a result, the production yield can be improved.
[Brief description of the drawings]
FIG. 1 is a flowchart showing a ferroelectric film evaluation method according to a first embodiment in order of steps.
FIG. 2 is a flowchart illustrating the ferroelectric film evaluation method according to the first embodiment in order of steps, following FIG. 1;
FIG. 3 is a flowchart illustrating the ferroelectric film evaluation method according to the first embodiment in order of steps, following FIG. 2;
FIG. 4 is a flowchart showing a ferroelectric film evaluation method according to a second embodiment in order of steps.
FIG. 5 is a flowchart illustrating the ferroelectric film evaluation method according to the second embodiment in order of steps, following FIG. 4;
FIG. 6 is a flowchart illustrating the ferroelectric film evaluation method according to the second embodiment in order of steps, following FIG. 5;
FIG. 7 is a flowchart showing a ferroelectric film evaluation method according to a third embodiment in order of steps.
FIG. 8 is a flowchart illustrating the ferroelectric film evaluation method according to the third embodiment in order of steps, following FIG. 6;
FIG. 9 is a flowchart illustrating the ferroelectric film evaluation method according to the third embodiment in order of steps, following FIG. 8;
FIG. 10 is a schematic diagram showing an internal configuration of a personal user terminal device according to a third embodiment.
11 is a cross-sectional view of a sample used in Examples 1 and 2. FIG.
FIG. 12 is a characteristic diagram showing a temperature change of a half width of a PZT (200) / (020) / (002) diffraction peak.
FIG. 13 is a characteristic diagram showing a temperature change of a polarization value obtained from a PZT (200) / (020) / (002) diffraction peak.
FIG. 14 is a characteristic diagram showing a temperature change of a half width of a PZT (111) diffraction peak.
15 is a cross-sectional view of a sample used in Example 3. FIG.
FIG. 16 is a correlation diagram between polarization values and half-value widths of PZT (100) / (010) / (001) diffraction peaks.
17 is a cross-sectional view of a sample used in Example 4. FIG.
FIG. 18 is a characteristic diagram obtained by performing χ scan at the PLCSZT (100) diffraction peak position and the background position.
19 is a characteristic diagram obtained by subtracting the χ scan at the background position from the χ scan at the PLCCSZT (100) diffraction peak position in FIG. 18;
FIG. 20 is a map around a PLCCSZT (100) diffraction peak obtained by performing 2θ / ω scan while changing χ.
21 is a cross-sectional view of a sample used in Example 5. FIG.
FIG. 22 is a characteristic diagram obtained by subtracting the χ scan at the background position from the χ scan at the PZT (100) diffraction peak position.
FIG. 23 shows a 2θ / ω scan near the PZT (100) diffraction peak at χ = 0 ° ((100) oriented crystal), χ = 20 ° (non-oriented crystal), and χ = 55 ((111) oriented crystal). FIG.
[Explanation of symbols]
10 Si substrate
11 SiO ₂ film
12 Ti film
13 Lower Pt electrode
14, 16, 18 PZT film
15 IrO ₂ film
17 PLCSZT film

Claims (8)

An evaluation apparatus for determining ferroelectric characteristics of a ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
If the diffraction peaks are split, calculate the polarization value based on each diffraction peak position,
When the diffraction peak is not split, a half-value width of a predetermined diffraction line is estimated, and a polarization value is calculated by performing diffraction peak separation based on the half-value width, thereby evaluating the ferroelectric film . An evaluation apparatus for determining ferroelectric characteristics of a ferroelectric film,
By classifying the ferroelectric crystals of the ferroelectric film into different crystal groups by X-ray diffraction, focusing on the diffraction peak for each crystal structure for each crystal group,
If the diffraction peaks are split, calculate the polarization value based on each diffraction peak position,
When the diffraction peak is not split, estimate the half width of a predetermined diffraction line, perform diffraction peak separation based on the half width, calculate the polarization value, and calculate the amount of crystals in each crystal group and An apparatus for evaluating a ferroelectric film, characterized by measuring the magnitude of strain. When determining the ferroelectric properties of a ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
When the crystal structure of the ferroelectric is a tetragonal crystal, the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 and (hhh) ) Detect half-width of diffraction line,
When the crystal structure of the ferroelectric is orthorhombic, (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 (and hh) Detect the half width of the diffraction line,
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. The half-width of the (hkl) diffraction line and (h00) diffraction line excluding
A method for evaluating a ferroelectric film, comprising determining a ferroelectric characteristic of the ferroelectric film based on the detected half widths. When determining the ferroelectric properties of a ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
When the crystal structure of the ferroelectric is a tetragonal crystal, the half-value width of the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 Only detect
When the crystal structure of the ferroelectric is orthorhombic, the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or the half of the diffraction line excluding h = k = 1 (hkl) Detect only the price range,
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. (Hkl) except the half-width of the diffraction line is detected,
A method for evaluating a ferroelectric film, comprising determining a ferroelectric characteristic of the ferroelectric film based on the detected half widths. When determining the ferroelectric properties of a ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
When the crystal structure of the ferroelectric is tetragonal,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 are measured and the diffraction peaks are separated, the diffraction peaks thereof are separated. The lattice constants of the a-axis and c-axis are obtained based on the position, the polarization value is calculated from the lattice constant, and when the diffraction peak is not separated, the polarization value is calculated from the half-value width of the (hh) diffraction line of the ferroelectric film. The half-width of the diffraction line not including the above information is estimated, and the (h00) / (0k0) / (00l) diffraction line or h = k = 1 is excluded from the ferroelectric film based on the half-width (hkl). ) Separating diffraction peaks of diffraction lines, obtaining lattice constants of the a-axis and c-axis based on the respective diffraction peak positions, calculating a polarization value from the lattice constants,
When the crystal structure of the ferroelectric is orthorhombic,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1 are measured and the diffraction peaks are separated, the diffraction peaks thereof are separated. Based on the position, the lattice constants of the a-axis, b-axis, and c-axis are obtained, the polarization value is calculated from the lattice constant, and when the diffraction peaks are not separated, the half of the (hh) diffraction line of the ferroelectric film The half-value width of the diffraction line that does not include the polarization value information is estimated from the value range, and the (h00) / (0k0) / (00l) diffraction line of the ferroelectric film or h = k = l based on the half-value width. (Hkl) The diffraction peaks of the diffraction lines are removed, the lattice constants of the a-axis, b-axis and c-axis are obtained based on the respective diffraction peak positions, and the polarization value is calculated from the lattice constants.
When the crystal structure of the ferroelectric is rhombohedral,
The (hhh) / (− hhh) diffraction line of the ferroelectric film or the (hkl) diffraction line excluding the diffraction line in which any two of h, k, and l are 0 are measured, and the diffraction peak is separated. If the diffraction peak is not separated, the lattice constant of the a axis and the α angle is obtained based on the position of each diffraction peak, and the polarization value is calculated from the lattice constant. h00) The half-value width of the diffraction line that does not include the polarization value information is estimated from the half-value width of the diffraction line, and the (hhh) / (− hhh) diffraction line or h, The diffraction peaks of the diffraction lines excluding the diffraction line in which any two of k and l are 0 (hkl) are separated, and the lattice constants of the a axis and the α angle are obtained based on the respective diffraction peak positions. Ferroelectric film characterized by calculating polarization value from lattice constant Evaluation method. When determining the ferroelectric properties of a ferroelectric film,
Focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction,
When the crystal structure of the ferroelectric is tetragonal,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1, when the peaks are separated, an a-axis is formed from each peak position. And the c-axis lattice constant, and the polarization value is calculated from the lattice constant. When the peaks are not separated, the polarization value information is obtained from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise. Estimate the half-value width of the diffraction lines not included, perform peak separation based on the half-value width, calculate the a-axis and c-axis lattice constants from the respective peak positions, and calculate the polarization value from this lattice constant. ,
When the crystal structure of the ferroelectric is orthorhombic,
When (h00) / (0k0) / (001) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding h = k = 1, when the peaks are separated, an a-axis is formed from each peak position. The b-axis and c-axis lattice constants are calculated, and the polarization value is calculated from the lattice constant. When the peaks are not separated, the polarization value is calculated from the half-value width at a high temperature at which the half-value width does not change due to the temperature rise. The half-value width of the diffraction line not including the above information is estimated, peak separation is performed based on the half-value width, and the lattice constants of the a-axis, b-axis, and c-axis are calculated from the respective peak positions, and this lattice constant is calculated. Calculate the polarization value from
When the crystal structure of the ferroelectric is rhombohedral,
When (hkl) / (− hh) diffraction lines of the ferroelectric film or (hkl) diffraction lines excluding diffraction lines in which any two of h, k, l are 0 are separated from each other Then, the a-axis and α-angle lattice constants are calculated from the respective peak positions, and the polarization values are calculated from the lattice constants. When the peaks are not separated, the half-value width does not change due to the temperature rise. The half-value width of a diffraction line that does not contain polarization value information is estimated from the half-value width, peak separation is performed based on the half-value width, and the lattice constants of the a axis and the α angle are calculated from the respective peak positions. A method for evaluating a ferroelectric film, wherein a polarization value is calculated from the lattice constant. When determining the ferroelectric properties of a ferroelectric film,
By classifying the ferroelectric crystals of the ferroelectric film into different crystal groups by X-ray diffraction, focusing on the diffraction peak for each crystal structure for each crystal group,
When the crystal structure of the ferroelectric is tetragonal, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or the diffraction lines excluding h = k = 1 (hkl) are detected. ,
When the crystal structure of the ferroelectric is orthorhombic, the (h00) / (0k0) / (00l) diffraction lines of the ferroelectric film or the diffraction lines excluding h = k = 1 (hkl) are detected. And
When the crystal structure of the ferroelectric is rhombohedral, (hhh) / (− hhh) diffraction lines or diffraction lines in which any two of h, k, and l are zero. (Hkl) diffraction lines except
When the ferroelectric crystal structure is cubic, the (hkl) diffraction line of the ferroelectric film is detected, and the amount of crystal and the magnitude of strain in each crystal group are measured. A method for evaluating a ferroelectric film. A computer-readable storage medium storing a program for determining the ferroelectric characteristics of a ferroelectric film by focusing on the diffraction peak for each ferroelectric crystal structure of the ferroelectric film by X-ray diffraction There,
A storage medium for executing the procedure of the ferroelectric film evaluation method according to any one of claims 3 to 7 .

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