JP2007258488A - Insulation film dielectric breakdown lifetime estimation method - Google Patents

Abstract

The first dielectric breakdown life is correctly estimated even when the dielectric breakdown detectable in actual measurement is not necessarily the first dielectric breakdown.
A Weibull plot is performed for each of a plurality of samples belonging to a sample group having different areas to obtain a dielectric breakdown life and a Weibull slope with a predetermined cumulative failure rate, and a sample area of each Weibull slope is obtained. M value which shows the dependence with respect to is calculated | required. Based on the correlation between the m-value and the Weibull slope of the dielectric breakdown lifetime up to the first dielectric breakdown in the sample calculated in advance, the Weibull slope of the dielectric breakdown lifetime up to the first dielectric breakdown in the sample to be evaluated is obtained. From the area dependency of each Weibull slope, an area a in which the Weibull slope of the dielectric breakdown life in the sample to be measured becomes the Weibull slope of the dielectric breakdown life until the first dielectric breakdown in the sample to be evaluated is obtained. Each dielectric breakdown lifetime is plotted against the area, and the dielectric breakdown lifetime in the area a is obtained.
[Selection] Figure 7

Description

  The present invention relates to a method for estimating a dielectric breakdown lifetime of an insulating film, particularly a gate insulating film, a capacitive insulating film, an interlayer insulating film, etc. used in a semiconductor element.

2. Description of the Related Art In recent years, the gate insulating film has been made thinner with higher integration, higher functionality, and higher speed of semiconductor integrated circuit devices. As a gate insulating film, a silicon oxide film (SiO ₂ ) or a silicon oxide film (SiOxNy) into which nitrogen has been introduced has been used conventionally, but the physical film thickness has reached, for example, about 2 nm or less. In such a film thickness region, the amount of leakage current increases, and the standard value required for the device cannot be satisfied.

For this reason, gate insulating films using new high dielectric constant materials, such as hafnium-based materials (HfOx, HfSiOx, HfAlOx, HfOxNy, etc.) have been proposed. The physical film thickness required to obtain the capacity is required to be 2 nm or less. In general, a laminated structure of a high dielectric constant film and a silicon oxide film (SiO ₂ , SiOxNy) or a silicon nitride film (Si ₃ N ₄ ) is employed.

  In order to guarantee the dielectric breakdown lifetime of the gate insulating film, it is generally performed to evaluate the dependency of the dielectric breakdown lifetime on the stress voltage and estimate the dielectric breakdown lifetime under the actual operating voltage. For this purpose, it is indispensable to detect and detect the occurrence of dielectric breakdown. However, it is difficult to detect dielectric breakdown in the region where the physical film thickness or the equivalent film thickness is thin. If the occurrence of dielectric breakdown cannot be correctly detected, the estimated life obtained by statistically processing the result is not correct. Therefore, a method for correctly detecting the occurrence of dielectric breakdown has been studied.

K. Okada, H. Ota, T. Horikawa, Y. Tamura, T. Sasaki, T. Aoyama, F. Ootsuka, and A. Toriumi: "Importance of Leakage Current Noise Analysis for Accurate Lifetime Prediction of High-k Gate Dielectrics ", Solid State Devices and Materials (SSDM), (2005) pp.248-249. M.A. Alam and R.K. Smith, "A Phenomenological Theory of Correlated Multiple Soft-Breakdown Events in Ultra-thin Gate Dielectrics," Proceedings of International Reliability Physics Symposium, 2003, pp. 406-411. J. Sune and E. Wu, "Statistics of Successive Breakdown Events for Ultra-thin Gate Oxides," Proceedings of IEDM Tech. Digest, 2002, pp. 147-150. R. Degraeve, G. Groeseneken, R. Bellens, M. Depas, HE Maes: "A consistent model for the thickness dependence of intrinsic breakdown in ultra-thin oxides", Int. Elec. Dev. Meeting (1995) pp.863 -866.

  However, even when dielectric breakdown can be detected using various methods, it is not clear whether the dielectric breakdown reflects the first (first) breakdown in the sample.

  This is because a sufficient increase in leakage current cannot be obtained even if dielectric breakdown occurs due to thinning of the gate insulating film thickness or low stress voltage. As a result, the first dielectric breakdown occurs. This is because the second and third dielectric breakdowns occur in another local region even after the occurrence in a certain local region in the insulating film. Thus, since the increase in the leakage current due to the first breakdown is not sufficient, the detection is not easy. In some cases, the second and third breakdowns are mistaken as the first breakdown. There is a risk.

  As described above, the expected dielectric breakdown lifetime is estimated by statistically processing the lifetime obtained by actual measurement. This statistical processing is performed by measuring the first lifetime in each sample. Since it is premised on the first dielectric breakdown life defined as the time until dielectric breakdown occurs, the estimated result is unreliable if a non-first dielectric breakdown lifetime is used as in the above-mentioned misunderstanding. It will be a thing.

  Therefore, it is required to realize a method for performing a correct lifetime estimation by processing a dielectric breakdown lifetime that may be misidentified and obtained by measurement.

  The present invention has been made in view of the above problems, and in a semiconductor element having a gate insulating film, it is determined whether or not the dielectric breakdown lifetime obtained by actual measurement reflects the first dielectric breakdown lifetime, It is an object of the present invention to provide a method for estimating the first dielectric breakdown lifetime from the actually measured value of the non-first dielectric breakdown lifetime.

In order to solve the above-mentioned problem, the dielectric breakdown lifetime estimation method of the insulating film of the present invention comprises a plurality of sample groups having the same area, wherein a plurality of sample areas are configured to be different from each other. Measure the time until electrical breakdown is detected for each sample by applying electrical stress to each sample, perform a Weibull plot for each sample group, and each sample group from each Weibull plot Each time until the cumulative failure rate determined in advance is determined as a dielectric breakdown lifetime, a first step for obtaining a Weibull slope, and the Weibull slope of each sample group obtained in the first step The second step for determining the m-value indicating the dependence on the area, and the dielectric breakdown lifetime that has been derived in advance until the first breakdown occurs in the sample Based on the correlation between the Weibull slope and the m value, a third step of obtaining a Weibull slope (beta ₁₎ of the dielectric breakdown lifetime up to the first dielectric failure occurred in the evaluation target sample, obtained in the second step Due to the area dependency of the Weibull slope of each sample group, the Weibull slope with the lifetime until the dielectric breakdown is detected in the sample to be measured causes the first dielectric breakdown in the sample to be evaluated obtained in the third step. A fourth step for determining the virtual unit cell area equivalent to the Weibull slope (β ₁ ) of the dielectric breakdown lifetime up to and the dielectric breakdown lifetime of each sample group determined in the first step with respect to the area of each sample Fifth step for obtaining the dielectric breakdown lifetime of the measured sample in the virtual unit cell area obtained in the fourth step Having.

  Note that there is no problem in applying the present invention even if the plurality of samples are provided on the same wafer or provided on different wafers. Further, “previously derived” in the third step is a description defining “correlation”. Furthermore, the “evaluation target sample” in the third step is an expression intended to be a sample including each sample in the first step. Further, the “sample to be measured” in the fourth step is an expression distinguished from the sample to be evaluated with the intention of not having the same area as the sample to be evaluated in the third step. A sample having the same area as the sample to be evaluated may be included.

  In the method for estimating a dielectric breakdown lifetime of an insulating film according to the present invention, the m value obtained in the second step is the slope of the Weibull slope of each sample group obtained in the first step (the area is logarithm, and the Weibull slope is Slope when plotted with a straight line).

In the third step, the correlation between the Weibull slope of the dielectric breakdown lifetime until the first dielectric breakdown occurs in the sample and the slope m value is n in the sample. The first breakdown occurs in the sample with n-dependence of the Weibull slope (β _n ) of the breakdown life until the first breakdown occurs (the slope when n is logarithm and β _n is plotted as a straight line) It is preferable to obtain this by comparing the change in dielectric breakdown lifetime due to the Weibull slope with the slope m value obtained in the second step.

  In the dielectric breakdown lifetime estimation method of the present invention, in the third step, the correlation between the Weibull slope of the dielectric breakdown lifetime until the first breakdown occurs in the sample and the slope m value is derived. It is preferable to obtain the n dependence of the Weibull slope of the dielectric breakdown lifetime until the n-th dielectric breakdown occurs in the sample, which is necessary for the purpose, by a percolation simulation method.

  In the dielectric breakdown lifetime estimation method of the insulating film of the present invention, the Weibull slope of the dielectric breakdown lifetime until the first breakdown occurs in the sample may be obtained by actual measurement.

  According to the method for estimating the dielectric breakdown lifetime of an insulating film according to the present invention, the dielectric breakdown life of an insulating film in a certain sample may not necessarily be the first dielectric breakdown that can be detected in actual measurement. In some cases, there is provided a method for correctly estimating the first dielectric breakdown lifetime that occurs, and the dielectric breakdown lifetime of the gate insulating film can be determined more easily and accurately.

  Hereinafter, the lifetime of the insulating film and the method for estimating the Weibull slope in one embodiment of the present invention will be described with reference to the drawings.

  FIGS. 1A and 1B simply show the cross-sectional shapes of samples used for the measurement of data shown below, and show MOS capacitors and MOSFETs, respectively.

In FIG. 1A, a gate insulating film 2 made of an SiO ₂ film 2a and an HfAlOx film 2b is formed on a silicon substrate 1, and a gate electrode 3 made of polysilicon is formed thereon. The gate electrode 3 is implanted with phosphorus or boron as an impurity. The HfAlOx film 2b is a high dielectric constant film (high-k film), and the SiO ₂ film 2a is called an interlayer film (Interlayer (IL) film) or a lower insulating film. The MOSFET of FIG. 1B has a source 4 and a drain 5 formed in addition to the gate structure similar to that of FIG.

Since the gate insulating film 2 has a laminated structure of a high dielectric constant film and a SiO ₂ film and is not necessarily limited to an oxide, it should be expressed strictly as MIS instead of MOS. Even in the case of an insulating film formed of a laminated structure or an insulating film other than an oxide, it is expressed as MOS. Therefore, in the present invention, even when expressed as MOS, it is not limited to oxide. Although a laminated structure of a high dielectric constant film and a SiO ₂ film is used here, the method of the present invention can be applied to a silicon oxide film that has been used conventionally.

FIG. 2 shows an example in which a stress gate voltage of −3.6 V is applied (constant voltage stress) to a sample formed on an N-type substrate and having the MOS transistor structure shown in FIG. The time-dependent change of stress gate current (absolute value) is shown. The thickness of the gate insulating film at this time is HfAlOx / SiO ₂ = 1.7 / 1.6 nm (according to TEM observation).

  The arrows in the figure indicate the vicinity of the boundary that divides the curve into two regions having different inclinations. The gate length (L) and gate width (B) of the transistor in each sample are entered in the figure. In each sample, the change in the amount of gate current is small in the region of several tens of seconds or less, and then the current increases. In the sample of B / L = 100/100 μm, the gate current changes smoothly, but becomes rough as the gate area decreases.

  For example, this is considered to reflect the occurrence of dielectric breakdown because the behavior of the current amount is noisy in a sample of B / L = 20/2 μm. That is, as described above, the increase in current at the time of dielectric breakdown is reduced by reducing the thickness or reducing the stress voltage. On the other hand, the initial current is increased by reducing the thickness. The clear current increase behavior observed in the thick gate insulating film is not observed, and it is presumed that it is difficult to detect the dielectric breakdown (see Non-Patent Document 2).

Therefore, the vertical axis is not the current amount, but the current amount I _G normalized by the initial current amount I _G0 , that is, the normalized stress current I _G (t) / I _G0 (where I _G is the gate current, t is FIG. 3 shows the result of plotting the stress time and I _{G0 as} the initial current amount) against the stress time.

  Since the initial current amount is proportional to the gate area, the occurrence of dielectric breakdown can be detected more easily by plotting the normalized stress current, and the detection becomes easier as the gate area is smaller. Specifically, as can be seen from FIG. 3, a sharp change is not observed in a sample with a large area of B / L = 100/100 μm, but samples with relatively small B / L = 20/2 and 20/10 μm. Then, a steep current increase behavior can be observed at the time indicated by the arrows. It is also clear that after a steep current increase behavior (first breakdown), multiple breakdowns (nth breakdown) have occurred. Here, the first dielectric breakdown and the n-th dielectric breakdown are phenomenologically the same, but their occurrence time and location are different.

  The stress time when the first dielectric breakdown obtained in this way is detected is defined as the dielectric breakdown lifetime in the sample. Further, when no clear current increase behavior was observed as in the sample of B / L = 100/100 μm in FIG. 3, the stress time when the current amount reached the minimum value was defined as the dielectric breakdown life. However, a steep current increase behavior is often observed in a sample with B / L = 100/100 μm as well as other samples.

  FIG. 4 shows the results of Weibull plotting of dielectric breakdown lifetimes in various area samples thus obtained (stress voltage is −3.1 V). The waibit (W) on the vertical axis is given by the following equation (1), where F is the cumulative failure rate up to a certain time.

W = ln (-ln (1-F)) (1)
In FIG. 4, the Weibull slope (β) for each area sample is also entered.

  As can be seen from FIG. 4, the gate area increases and the Weibull slope increases. It is known that the Weibull slope generally does not depend on the gate area, and the area-dependent expression shown in FIG. 4 is abnormal.

  The reason why such an area-dependent abnormality occurs is described below.

  Each sample is considered to be a set of virtual unit cells having an area a, and the lifetime of the unit cell under a certain stress condition (the ratio at which W = 0 when a large number of samples are measured (the cumulative defect rate is about 63.3%). 2%), where η is the life expectancy that breakdown is statistically expected to occur in the sample, and β is the Weibull slope, the breakdown of the breakdown occurring up to a certain stress time t in the sample of area S The number of occurrences n is given by the following equation (2).

n (S, t) = N (S) · F (t) = S / a · [1-exp {-(t / η) ^β }] (2)
Here, N is the number of unit cells in the sample. The total current amount I at an arbitrary reference voltage is expressed as follows using an initial current density J ₀ , a current density variation ΔJ ₀ that increases on the entire gate surface due to stress application, and a current amount I _BD per one dielectric breakdown. It is given by equation (3). Here, since dielectric breakdown is a phenomenon in the local region, it should be noted that the current amount is not the current density but the other current component is the current density.

I (S, t) = (J ₀ + ΔJ (t)) · S + n (S, t) · I _BD (3)
As indicated by the arrows in FIG. 3, the breakdown is observed because the second term on the right side of the equation (3), where the current increases due to the breakdown, is due to a factor other than the breakdown. It can be considered that the time is larger than the first term on the right side of a certain equation (3). Therefore, if the dielectric breakdown life detected in the actual measurement is T _BD , the relationship of equation (4) is derived from equation (3).

(J ₀ + ΔJ (T _BD )) · S = n (S, T _BD ) · I _BD (4)
From the equations (4) and (2), the following equation (5) is obtained.

(J ₀ + ΔJ (T _BD )) · S = S / a · F (T _BD ) · I _BD (5)
Therefore, when dielectric breakdown is detected in T _BD by actual measurement, n dielectric breakdowns corresponding to the cumulative defect rate F (T _BD ) expressed by the following formulas (6) and (7) have already occurred. Therefore, it cannot be observed due to the influence of a large initial current or the like.

F (T _BD ) = a · (J ₀ + ΔJ (T _BD )) / I _BD (6)
n (S, T _BD ) = N (S) · F (T _BD ) = S · (J ₀ + ΔJ (T _BD )) / I _BD (7)
From the equation (6), the T _BD value at which W = 0, that is, F to 63.2%, does not depend on the gate area S, and from the equation (7), the dielectric breakdown lifetime T _BD obtained by actual measurement. It can be seen that the number n of dielectric breakdowns already occurring at the time of is proportional to the gate area.

Here, if the first breakdown Weibull slope is β ₁ and the nth breakdown Weibull slope is β _n , it is known that β _n increases as n increases (Non-Patent Document 2). Non-Patent Document 3).

FIG. 5A shows the result of simulating the change of the Weibull slope by n by a method called percoration simulation (see Non-Patent Document 4). Assuming that β ₁ is 1.0, n is 1 The simulation is changed up to 1000. It can be seen that the slope increases as n increases.

FIG. 5B shows a graph in which such n dependence of β _n is simulated for various β _{1 and} plotted against n. beta _n slope strongly depends on the beta ₁ has (logarithm n, beta _n substantially shows a linear relationship when plotted in a straight line), therefore, the beta ₁ from a change in beta _n with changes in n value It is possible to estimate.

  In FIG. 5 (a), the lifetime value when the Wibit is 0 (W = 0) increases as the n value increases, but this is the case with the sample of the same area, and in FIG. Although the n value is increased by offsetting the well-known effect that the lifetime value when the wibit is 0 (W = 0) as the gate area increases is offset by the effect of the area scaling, The lifetime value when the Y bit is 0 (W = 0) is substantially constant.

FIG. 6 is a plot of β _n obtained from the data shown in FIG. 4 against the gate area (upper horizontal axis) and compared with the simulation result, which is in good agreement with the case of β ₁ = 0.6. ing. Since the n value is proportional to the gate area as shown in equation (7), the slope when β _n is plotted against the gate area is plotted against the n value as shown in FIG. It becomes equal to the inclination when In the sample used in FIG. 6, β ₁ coincides with the actually measured β value in the sample having the minimum area shown in FIG. 4, but the actually measured β value in the sample having the minimum area used in the actual measurement seems to be larger than β _1. The same sample can be handled in the same manner.

  FIG. 7 shows the flow of the semiconductor device evaluation method in this embodiment.

First, in step (a) of FIG. 7, a time T until electric breakdown is detected by applying electrical stress to a plurality of, for example, 50 samples having an area S ₁ is measured, and a Weibull plot is obtained. Do. From this Weibull plot, the time when Wibit W = 0 (cumulative failure rate ˜63.2%), that is, the dielectric breakdown lifetime T _BD (S ₁ ) and Weibull slope β (S ₁ ) are obtained.

Next, in step (b), the same processing as in step (a) is performed on the samples of areas S ₂ and S ₃ , and the respective Weibull slopes β (S ₂ ), β (S ₃ ) and dielectric breakdown are performed. The lifetimes T _BD (S ₂ ) and T _BD (S ₃ ) are acquired.

Next, in step (c), step (a), obtained in (b) beta a (S _n) was plotted against the logarithm of S _{n (n} = 1,2,3), obtains the slope m .

Next, in step (d), based on the correlation between the Weibull slope β ₁ of the lifetime until the first dielectric breakdown occurs in the sample previously obtained by percolation simulation and the slope m value. The first dielectric breakdown occurs in the measurement sample (this sample is a sample to be evaluated from now on, including each sample of the above-mentioned areas S _{1 to} S ₃ , and these are all the same sample except for different areas) Find the Weibull slope β ₁ of the life until.

Next, in step (e), an area a in which β (S) is equivalent to β ₁ obtained in step (d) is obtained from a plot of β (S _n ) obtained in step (c) against S _n . .

Finally in step (f), the step (a), obtained in obtained in (b) eta the (S _n) plotted against the S _{n (n} = 1,2,3), Step (e) A dielectric breakdown lifetime T _BD in the area a is obtained, and this is defined as η.

By the above method, the area a of the virtual unit cell, the true Weibull slope β ₁ and the dielectric breakdown lifetime value η with respect to the occurrence of dielectric breakdown in the virtual unit cell are obtained. These values are parameters relating to the first dielectric breakdown that occurs in one sample, and by using these values, it is possible to estimate the correct lifetime and statistical variation.

As described above, the smaller the gate area is, the easier the detection is in a sample having an area a or less. Therefore, the first breakdown can be detected when the gate area is equal to or less than the area a. Can be said to be the first dielectric breakdown. Therefore, in a sample having an area a or less, the Weibull slope is β ₁ regardless of the area.

  From the above, when the Weibull slopes match between samples of various areas used for evaluation, it is possible to determine that the correct Weibull slope and life are obtained in actual measurement.

From the a and β ₁ obtained by the above method, the dielectric breakdown lifetime value T _BD until the first dielectric breakdown occurs in the sample of the area S is converted into the area based on the following equation (8). The Weibull slope is β ₁ .

η · a ^{1 / β1} = T _BD · S ^{1 / β1} (8)
As for the size of the area of the sample, it is not always necessary to measure three types as described above, and if the measurement is performed on at least two types (plurality) of sizes, the same processing is performed. Is possible.

  Further, in the present embodiment, the estimation is performed by comparing the actual measurement result and the percolation simulation result in step (d) of FIG. 7, but the comparison with the result by another simulation method or the sample Of dielectric breakdown occurring first in the sample and the Weibull slope are clearly obtained, and the nth (n = 1, 2, 3,...) Dielectric breakdown life and measurement of the Weibull slope are shown. It is also possible to contrast the results.

  In the present embodiment, a method for evaluating the dielectric breakdown lifetime and its Weibull slope has been shown, but the total amount of electrons or holes injected up to the dielectric breakdown and its Weibull slope can also be handled in the same manner. is there.

  As described above, according to the present embodiment, the dielectric breakdown lifetime, the Weibull slope, and the area dependence thereof that can be detected in actual measurement are obtained even in a sample in which it is difficult to detect the first dielectric breakdown that occurs in the sample. The lifetime of the first dielectric breakdown generated in the sample by comparing with the simulation or the actual measurement result about how the Weibull slope of the n-th (n = 2, 3, 4,...) Changes, and its It is possible to estimate the Weibull slope.

  The dielectric breakdown lifetime estimation method of the insulating film according to the present invention correctly corrects the dielectric breakdown lifetime of an insulating film in a sample even when the dielectric breakdown detectable in actual measurement may not necessarily be the first dielectric breakdown. The method of estimating the lifetime of the second dielectric breakdown and the Weibull slope is provided, and the lifetime of the gate insulating film can be obtained more easily and accurately, which is useful for methods such as evaluating the dielectric breakdown lifetime of the gate insulating film. It is.

(A) The figure which shows the cross-sectional shape of the capacitor structure sample used for evaluation in embodiment of this invention (b) The figure which shows the cross-sectional shape of the transistor structure sample used for the evaluation Stress when applying -3.6V stress gate voltage (constant voltage stress) to each sample with various gate areas and the MOS transistor structure shown in Fig. 1 (b) formed on N-type substrate Diagram showing the change over time in gate current (absolute value) A graph in which the data shown in FIG. 2 is plotted with the value (normalized stress current) obtained by normalizing the current amount with the initial current amount on the vertical axis. Diagram showing Weibull plot of dielectric breakdown lifetime in various area samples (A) simulating the n dependence of FIG. (B) beta _n indicating the result of simulating the change due n Weibull slope for various beta ₁ by Pako configuration simulation, the results plotted against n Illustration A plot of β _n obtained from the data shown in FIG. 4 against the gate area (upper horizontal axis) and compared with the simulation results 1 is a flowchart showing a method for evaluating a semiconductor device according to a first embodiment.

Explanation of symbols

1 silicon substrate 2 gate insulating film 2a SiO ₂ film 2b HfAlOx film 3 gate electrode 4 source 5 drain
V _G gate voltage
I _G gate current
T _BD breakdown life
b Weibull slope with breakdown life
n Number indicating the order of dielectric breakdown that occurred in the same sample (n = 1, 2, 3, ...)
b Weibull slope of the lifetime of dielectric breakdown that occurs the first time in _one sample
b Weibull slope of the lifetime of dielectric breakdown that occurs n times in the _n sample
S _1, S _2, S ₃ gate area
B Gate width
L Gate length
W Wibit

Claims (5)

Sample groups consisting of a plurality of samples having the same area are formed by differentiating the areas of the samples from each other, and an electrical stress is applied to each sample to detect dielectric breakdown for each sample. Is measured for each sample group, the Weibull plot is performed for each sample group, and the time until the cumulative defect rate determined in advance for each sample group from each Weibull plot is defined as the dielectric breakdown lifetime. A first step for obtaining a Weibull slope,
A second step of determining an m value indicating the dependence of the Weibull slope of each sample group determined in the first step on the area;
Based on the correlation between the m-value and the Weibull slope of the dielectric breakdown lifetime until the first dielectric breakdown occurs in the sample, the insulation until the first dielectric breakdown occurs in the sample to be evaluated A third step for determining the Weibull slope (β ₁ ) of the fracture life;
Based on the area dependency of the Weibull slope of each sample group obtained in the second step, the Weibull slope of the life until the dielectric breakdown in the sample to be measured is detected is the same as that in the evaluation target sample obtained in the third step. A fourth step for determining a virtual unit cell area equivalent to the Weibull slope (β ₁ ) of the dielectric breakdown lifetime until the first dielectric breakdown occurs;
The dielectric breakdown lifetime of each sample group determined in the first step is plotted against the area of each sample, and the first breakdown in the sample to be measured in the virtual unit cell area determined in the fourth step is And a fifth step of obtaining a dielectric breakdown lifetime until the dielectric breakdown lifetime occurs.   2. The m value obtained in the second step is a slope of the Weibull slope of each sample group obtained in the first step with respect to the area (a logarithm of the area and a slope when the Weibull slope is plotted as a straight line). The dielectric breakdown lifetime estimation method of an insulating film as described in 2. In the third step,
The correlation between the Weibull slope of the dielectric breakdown life until the first dielectric breakdown occurs in the sample and the slope m value is calculated until the nth dielectric breakdown occurs in the sample. Weibull of dielectric breakdown life until the first breakdown occurs in the sample of n-dependence of the Weibull slope (β _n ) of the dielectric breakdown life of the sample (slope when β is logarithm and β _n is plotted as a straight line) The method for estimating a dielectric breakdown lifetime of an insulating film according to claim 1 or 2, wherein the method is obtained by comparing a change due to a slope and the slope m value obtained in the second step. In the third step,
Insulation until the n-th dielectric breakdown occurs in the sample, which is necessary for deriving the correlation between the Weibull slope of the dielectric breakdown life until the first dielectric breakdown occurs in the sample and the slope m value 4. The dielectric breakdown lifetime estimation method for an insulating film according to claim 1, wherein the n dependence of the Weibull slope of the breakdown lifetime is obtained by a percolation simulation method.   The dielectric breakdown lifetime estimation of the insulating film according to any one of claims 1 to 3, wherein a Weibull slope of a dielectric breakdown lifetime until the first dielectric breakdown occurs in the sample calculated in advance is obtained by actual measurement. Method.

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