JPH11297952A - Cosmic ray neutron software error rate calculation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an accurate guideline for manufacturing a semiconductor device which is strong against cosmic ray neutron software errors, by calculating the cosmic ray neutron software error rate of the semiconductor device based on a charge quantity collected on the surface of an element region from all small regions. SOLUTION: The element region of a semiconductor device is divided into a plurality of small regions in a depth direction, and a process of calculating a potential difference between each small region and the adjacent small regions is executed. Based on the potential difference, a process of calculating a probability that a carrier generated in each small region moves to the adjacent small regions by a cosmic ray neutron, a process of calculating a charge quantity collected on the surface of the element region by small region, by multiplying a probability that the carrier, which is generated in each small region by the cosmic ray neutron, reaches the surface of the element region by the charge quantity generated in each small region by the cosmic ray neutron, and a process of calculating the sum of the charge quantities collected on the surface of the element region by small region, are executed. Thus, the charge quantity collected on the surface of the element region from all the small regions can be accurately calculated.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of calculating a cosmic ray neutron soft error rate which is an index for predicting a cosmic ray neutron soft error resistance of a semiconductor device.

[0002] Soft errors are one of the factors that impair the reliability of semiconductor devices. This is a phenomenon in which electron-hole pairs caused by ions generated by decay of radioactive elements or nuclear reactions due to cosmic ray neutrons in a semiconductor device cause malfunction of the semiconductor device.

[0003] Among soft errors, soft errors due to cosmic ray neutrons are extremely difficult to prevent because the neutrons that cause them are cosmic ray origins. Therefore,
The cosmic ray neutron soft error can only be dealt with by optimizing the impurity concentration distribution (element structure) in the element region. To that end, the difference in cosmic ray neutron soft error resistance due to the difference in impurity concentration distribution in the element region Needs to be accurately predicted.

[0004] A cosmic ray neutron soft error rate is an index for predicting cosmic ray neutron soft error resistance. This is because the cosmic-ray neutrons, which give rise to the amount of charge collected on the surface (diffusion layer) of the element region due to the nuclear reaction between the cosmic-ray neutrons and the atoms in the element region, and the atoms in the element region The probability of occurrence of a nuclear reaction is defined as the probability of occurrence of a nuclear reaction between a cosmic ray neutron, which is a source of charge equal to or more than an arbitrary amount of charge, and atoms in the element region.

[0005]

2. Description of the Related Art Conventionally, as a method of calculating a cosmic ray neutron soft error rate, a sensitive volume (sensitivity volume) method is used.
The ive-volume method has been proposed. this is,
This is a method in which the amount of carriers generated per unit volume by primordial nuclear reaction between cosmic ray neutrons and atoms in the element region is stored as a database, and the cosmic ray neutron soft error rate is calculated by giving the element volume. .

[0006]

The cosmic ray neutron soft error rate gives rise to the amount of charge collected on the surface of the device region due to a nuclear reaction between the cosmic ray neutrons and atoms in the device region. Probability of nuclear reaction between cosmic ray neutrons and atoms in the element region, defined as the probability of nuclear reaction between cosmic ray neutrons and the atoms in the element region, which give a charge of more than an arbitrary amount of charge In order to calculate the cosmic ray neutron soft error rate with high accuracy, it is necessary to consider the impurity concentration distribution in the element region.

However, the sensitive volume method is
The cosmic ray neutron soft error rate is calculated by simply giving the volume of the element region to the carrier generation amount per unit volume due to neutron nuclear reaction in the element region held as a database, and the impurity concentration distribution of the element region is calculated. Since it was not taken into account, there was a problem that the cosmic ray neutron soft error rate could not be calculated with high accuracy.

In view of the foregoing, the present invention can calculate the cosmic ray neutron soft error rate with high accuracy, and can provide an accurate guideline for producing a semiconductor device resistant to cosmic ray neutron soft error. It is an object of the present invention to provide a cosmic ray neutron soft error rate calculation method.

[0009]

According to the present invention, a cosmic ray neutron soft error rate calculation method according to a first aspect of the present invention divides an element region of a semiconductor device into a plurality of small regions in a depth direction, Calculating the probability that carriers generated in each small region move to adjacent small regions; and calculating the probability that carriers generated in each small region by cosmic ray neutrons move to adjacent small regions. Calculating the probability that carriers generated in the region reach the surface of the element region; and calculating the probability that carriers generated in each small region by cosmic ray neutrons reach the surface of the element region. Calculating the amount of charge collected on the surface of the region, and calculating the cosmic ray neutron soft error rate of the semiconductor device based on the amount of charge collected on the surface of the element region from all small regions. Is that include and.

According to the first aspect of the present invention, an element region of a semiconductor device is divided into a plurality of small regions in a depth direction, and carriers generated in each small region by cosmic ray neutrons move to an adjacent small region. The probability that carriers generated in each small region by cosmic ray neutrons reach the surface of the element region is calculated based on this probability, so the carriers generated in each small region by cosmic ray neutrons are calculated. The probability of reaching the surface of the element region can be calculated with high accuracy.

Then, the step of calculating the amount of charge collected from all the small regions to the surface of the element region based on the probability that carriers generated in each small region by cosmic ray neutrons reach the surface of the element region is executed. Therefore, the amount of charges collected on the surface of the element region from all the small regions can be calculated with high accuracy. Therefore, the cosmic ray soft error rate of the semiconductor device can be calculated with high accuracy.

[0012] In the present invention, the cosmic ray neutron soft error rate calculation method of the second invention is the first invention, wherein the probability that carriers generated in each small area by cosmic ray neutrons move to an adjacent small area is calculated. In the process, the impurity concentration distribution inside each small region is approximated to be constant, and for each small region, a potential difference between adjacent small regions is calculated.Based on the potential difference between the adjacent small regions, each cosmic ray neutron is used. Calculating the probability that carriers generated in a small region will move to an adjacent small region if they do not recombine, and recombining when carriers generated in each small region by cosmic ray neutrons pass through each small region The process of calculating the probability of not disappearing, and the probability that carriers generated in each small region by cosmic ray neutrons will move to adjacent small regions if they do not recombine, It is that raw to carrier and a step of multiplying the probability of not disappear by recombination in the case of passing through the respective small regions.

According to the second aspect of the present invention, the step of approximating the impurity concentration distribution inside each small region to be constant and calculating the potential difference between each small region and the adjacent small region is executed. In addition, the impurity concentration distribution of the element region can be reflected as a potential difference between the small regions.

Then, based on the potential difference between the adjacent small regions, the step of calculating the probability of moving to the adjacent small regions when carriers generated in each small region due to cosmic ray neutrons do not recombine is executed. If the carriers generated in each small region due to cosmic ray neutrons do not recombine, the probability of moving to an adjacent small region can be calculated with high accuracy.

Further, if the carriers generated in each small region by the cosmic ray neutrons do not recombine, the probability that the carriers generated in each small region by the cosmic ray neutrons are changed to the probability of moving to the adjacent small region. Since the process of multiplying the probability of not disappearing by recombination when passing through is performed,
The probability that carriers generated in each small region due to cosmic ray neutrons move to the adjacent small region can be calculated with high accuracy.

In the present invention, the cosmic ray neutron soft error rate calculation method of the third invention is characterized in that in the first or second invention,
The process of calculating the probability that carriers generated in each small region by cosmic ray neutrons reach the surface of the element region is based on the probability that carriers generated in each small region by cosmic ray neutrons move to adjacent small regions. The method includes a step of tracking the movement of carriers generated in each small region between the small regions by the line neutrons by the Monte Carlo method.

According to the third aspect of the present invention, based on the probability that carriers generated in each small region by cosmic ray neutrons move to adjacent small regions, the number of carriers generated in each small region by cosmic ray neutrons is determined. Since the step of tracking the movement between the small regions by the Monte Carlo method is performed, the probability that carriers generated in each small region by cosmic ray neutrons reach the surface of the element region can be calculated with high accuracy.

In the present invention, the cosmic ray neutron soft error rate calculation method according to the fourth invention is the method according to the first, second or third invention, wherein the amount of charge collected on the surface of the element region from all the small regions is calculated. Calculating the amount of charge generated in each small region by cosmic ray neutrons, based on the amount of charge generated by cosmic ray neutrons calculated in advance for each depth from the surface of the element region, The probability that carriers generated in each small area by cosmic ray neutrons reach the surface of the element area is multiplied by the amount of charge generated in each small area by cosmic ray neutrons, and collected on the surface of the element area for each small area. And calculating a total amount of charges collected on the surface of the element region for each small region.

According to the fourth aspect of the present invention, according to the fourth aspect, the cosmic ray neutrons are applied to each small area based on the amount of charge generated by the cosmic ray neutrons calculated for each depth from the surface of the element region in advance. Since the step of calculating the amount of generated charge is executed, the amount of charge generated in each small region by cosmic ray neutrons can be calculated with high accuracy.

The probability that carriers generated in each small area by cosmic ray neutrons reach the surface of the element area is multiplied by the amount of electric charge generated in each small area by cosmic ray neutrons, thereby obtaining an element for each small area. The step of calculating the amount of charge collected on the surface of the region and the step of calculating the sum of the amount of charge collected on the surface of the element region for each small region are executed. Can be calculated with high accuracy.

According to a fifth aspect of the present invention, there is provided the cosmic ray neutron soft error rate calculation method according to the first, second, third or fourth aspect, wherein the cosmic ray neutron soft error rate of the semiconductor device is calculated. The method includes a step of multiplying the amount of charge collected from all the small regions to the surface of the element region by a constant.

[0022]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In one embodiment of the present invention,
First, the element region of the semiconductor device whose cosmic ray neutron soft error rate is to be calculated is divided into a plurality of small regions in the depth direction, and the impurity concentration distribution inside each small region is approximated to be constant (see FIG. 1). .

In FIG. 1, a broken line A1 shows an example of an actual impurity concentration distribution of the element region, and a solid line A2 divides the element region into a plurality of small regions in the depth direction and distributes the impurity concentration of each small region. Shows the impurity concentration distribution of the element region when is approximated to be constant.

Next, for each small region, the potential difference between the adjacent small region and the adjacent small region is calculated by Equation 1 based on the impurity concentration difference between the small region and the adjacent small region. Incidentally, .DELTA.V _ab potential difference, k _B is Boltzmann (Boltzmann) constant, T is the absolute temperature, q is the electron charge, N _a is an impurity concentration in the region a between the small region a and the small region b, N _b region Impurity concentration.

[0025]

(Equation 1)

Next, it is assumed that carriers generated due to a nuclear reaction between cosmic ray neutrons and atoms in the element region are in a thermal equilibrium state and follow a Boltzmann distribution. Paying attention, using the Boltzmann distribution function, the (j-1) th area which is a small area on both sides and j + 1
Calculate the percentage of carriers with energy that can overcome the potential difference with the th region.

Here, assuming that the potential difference between the j-th sub-region and the j-1st or j + 1-th sub-region is δV, the ratio P of carriers having energy enough to overcome this potential difference δV is as follows: It can be calculated by Equation 2.

[0028]

(Equation 2)

Therefore, the probability that the carrier generated in the j-th sub-region can move to the (j-1) -th or j + 1-th sub-region can be calculated by using this ratio P in consideration of the direction of movement of the carrier. Yes, but j-1 and j +
Considering the magnitude relationship of the potential difference with the first small region, the following five cases can be classified.

(1) As shown in FIG. 2, the case where the potential of the (j-1) th and (j + 1) th subregions is lower than the potential of the jth subregion.

In this case, since there is no potential barrier, the carriers N _tot generated in the j-th small area are not _{limited to} the j-1st small area on the front side and the j + 1-th small area on the back side. Can also move with equal probability.

[0032] That is, the probability PA _j ^f to j-th carriers generated in small areas is moved to the j-1 th small region is as shown in equation 3, the probability to move to the j + 1 th small region P
A _j ^b is as shown in Expression 4.

[0033]

(Equation 3)

[0034]

(Equation 4)

(2) As shown in FIG. 3, the potential of the (j-1) th small area is lower than the potential of the jth small area, and j + 1
The case where the potential of the 小 th small area is higher than the potential of the j 番 目 th small area.

In this case, a carrier that does not have enough energy to cross the potential barrier between it and the (j + 1) th small region must move to the (j-1) th small region, and its probability is 1 Yes, carriers having energy enough to cross the potential barrier between the (j + 1) th subregion can move to either subregion.
The movement probabilities are each 各 々.

Therefore, the number of carriers that do not have enough energy to cross the potential barrier between the (j + 1) th sub-region is set to N _low and the energy enough to cross the potential barrier between the (j + 1) th sub-region. Assuming that the number of carriers having is N _high , the probability PA _j ^f that the carrier generated in the j-th small area moves to the j−1-th small area becomes as shown in Expression 5, and the j + 1-th small area becomes The probability PA _j ^b of moving to the region is as shown in Expression 6. Note that N _low , N
The relative ratio of _high can be easily calculated using Equation 2.

[0038]

(Equation 5)

[0039]

(Equation 6)

(3) As shown in FIG. 4, the potential of the (j-1) th small area is higher than the potential of the jth small area, and j + 1
The case where the potential of the n-th small area is lower than the potential of the j-th small area.

In this case, a carrier that does not have energy enough to cross the potential barrier between it and the (j-1) th small region must move to the (j + 1) th small region, and its probability is 1 Yes, carriers having energy enough to cross the potential barrier between the (j-1) th small region can move to the (j-1) th small region and the (j + 1) th small region. , Their movement probabilities are 1 /
It becomes 2.

Therefore, the number of carriers not having enough energy to cross the potential barrier between the (j-1) th subregion and the potential barrier between the (j-1) th subregion is set to N _low . only the number of carriers with the energy when the N _high is the probability PA _j ^f of carriers generated in the j-th small region is moved to (j-1) -th small region is as shown in Equation 7, The probability PA _j ^{b of} moving to the (j + 1) th small area is as shown in Expression 8. Note that N _low , N
The relative ratio of _high can be easily calculated using Equation 2.

[0043]

(Equation 7)

[0044]

(Equation 8)

(4) As shown in FIG. 5, the potential of the (j-1) th small area is higher than the potential of the jth small area, and j + 1
The case where the potential of the small region is higher than the potential of the (j-1) th small region.

In this case, a carrier having no energy enough to cross the potential barrier between the (j-1) th sub-region and the (j-1) -th sub-region. They cannot move and rejoin.

Further, carriers having energy enough to cross the potential barrier between the (j-1) th small region but not having enough energy to cross the potential barrier between the (j + 1) th small region are , J-1st small area only.

A carrier having energy enough to cross the potential barrier between the (j + 1) th small region is j
Since it is possible to move to both the -1st small area and the j + 1th small area, the movement probability is １ ／ each.

Therefore, the number of carriers having no energy enough to exceed the potential barrier between the (j-1) th subregion and the potential barrier between the (j-1) th subregion is set to N _low . The number of carriers that have only energy but do not have enough energy to cross the potential barrier between the (j + 1) th subregion is N _mid , the number of carriers that can only cross the potential barrier between the (j + 1) th subregion. When the number of carriers with an energy and N _{hi gh,} probability carriers generated in the j-th small region is moved to (j-1) -th small region P
A _j ^f is as shown in Expression 9, and the probability PA _j ^{b of} moving to the (j + 1) th small area is as shown in Expression 10. Note that the relative ratio of N _low , N _mid , and N _high can be easily calculated using _Equation 2.

[0050]

(Equation 9)

[0051]

(Equation 10)

(5) As shown in FIG. 6, the potential of the (j + 1) th small area is higher than the potential of the jth small area, and j−1
The case where the potential of the small region is higher than the potential of the (j + 1) th small region.

In this case, a carrier having no energy enough to cross the potential barrier between it and the (j + 1) th small area moves to both the (j-1) th small area and the (j + 1) th small area. Not be able to do so and rejoin.

A carrier having energy enough to cross the potential barrier between the (j + 1) th small region but not having enough energy to cross the potential barrier between the (j-1) th small region is , J + 1-th sub-region only.

The carriers having energy enough to cross the potential barrier between the (j-1) th small region are j
Since it is possible to move to both the −1st small area and the j + 1th small area, the probability is １ ／ for each.

Therefore, the number of carriers having no energy enough to cross the potential barrier between the (j + 1) th small region is set to N _low , and the energy enough to cross the potential barrier between the (j + 1) th small region is set to N _low . N _mid , the number of carriers that have the energy but do not have enough energy to cross the potential barrier between the j-1st subregion and the number of carriers that can cross the potential barrier between the j-1st subregion. When the number of carriers with an energy and N _{hi gh,} probability carriers generated in the j-th small region is moved to (j-1) -th small region P
A _j ^f is as shown in Equation 11, the probability PA _j ^b to move j + 1-th small region is as shown in Equation 12. Note that the relative ratio of N _low , N _mid , and N _high can be easily calculated using _Equation 2.

[0057]

[Equation 11]

[0058]

(Equation 12)

[0059] In this manner, for all the small regions obtained by dividing the element region, and the probability PA _j ^f that carriers generated by nuclear reactions with atoms of cosmic ray neutron element regions flows on the surface side of the element region , The probability PA _j ^b flowing on the back side of the element region is calculated.

Next, in the calculation of the carrier movement probability up to now, the effect of reducing the amount of collected charges due to the recombination of the moving carriers has been neglected, so that the effect of disappearance due to the recombination of the carriers is incorporated.

Here, assuming that the time required for the carrier to advance by Δx is Δt and the diffusion coefficient is D, Expression 13 holds from the diffusion equation, and the diffusion coefficient D is given by Expression 14, so that Δt is Equation 15 is obtained.

[0062]

(Equation 13)

[0063]

[Equation 14]

[0064]

(Equation 15)

Here, assuming that the recombination time of the carrier is τ, the probability F that the carrier does not disappear by recombination while passing through one small area is expressed by the following equation (16), where Δx is the width of the small area. Can be.

[0066]

(Equation 16)

Therefore, this probability F is calculated as the movement probability PA _j ^f , P
_Aj ^b is evenly multiplied, and the movement probability PB _j ^f (= j−
PB _j ^b (= probability of movement to the (j + 1) th small area) and PB _j ^b (= movement probability to the first small area) are calculated.

However, the recombination time τ mentioned here is not necessarily the same as that included in the device simulation, but it is better to look at it as a kind of fitting parameter, and ultimately optimize it with experimental data. .

Next, the carrier in the j-th small region N _Oj number is generated, movement probability PB _j ^f, based on the PB _j ^b, carriers which have been generated out of the adjacent small regions, j-1 th small It is determined whether to move to the area, or to the (j + 1) th small area, or to disappear by recombination.

This determination condition is performed by repeating the procedure shown in Expression 17 using a uniform random number R. Then, the movement of the generated carriers between the small regions is tracked, and the number of carriers that have reached the surface of the element region is counted.

[0071]

[Equation 17]

[0072] That is, the random number R is, in the case of 0 ≦ R ≦ PB _j ^f is the carrier of the moving object is moved in (j-1) -th small region, PB _j ^f <of ^{_{R ≦ PB j f + PB j}} b In this case, the carrier to be moved is moved to the (j + 1) th small area, and PB _j ^f +
If PB _j ^b <R, the next carrier is determined. By repeating this procedure, the movement of carriers between the small regions is tracked, and the number of carriers that have reached the surface of the element region is counted.

Here, assuming that the number of carriers finally reaching the surface of the element region is N _j , the ratio P _j of collected carriers is as shown in Expression 18. Therefore, this ratio is calculated for all the small areas.

[0074]

(Equation 18)

Next, the amount of charge Q _j generated in each small area can be calculated by the conventional sensitive volume method.
That is, based on the amount of charge generated by cosmic ray neutrons calculated for each depth from the surface of the element region in advance, the amount of charge Q _j generated in each small region by cosmic ray neutrons
Can be calculated, the charge amount Q _tot collected on the surface of the element region among all the generated charges is calculated by _Expression 19, and the charge amount Q _tot is calculated.
Calculate cosmic ray neutron soft error rate by multiplying _tot by a constant.

[0076]

[Equation 19]

Here, FIGS. 7, 9 and 11 show examples of the actual impurity concentration distribution in the element region of the semiconductor device, and FIGS. 8, 10 and 12 respectively show FIGS. FIG.
FIG. 9 is a diagram showing experimental values of cosmic ray neutron soft error rates of semiconductor devices having the impurity concentration distribution shown in FIG.

In FIGS. 8, 10, and 12, the horizontal axis represents the collected charge, the vertical axis represents the cosmic ray neutron soft error rate, and the vertical axis represents the rate at which a certain charge or more is collected. The integration is shown on an arbitrary scale, and the broken line B
Reference numerals 1, B2, and B3 indicate experimental values of the cosmic ray neutron soft error rate, and solid lines C1, C2, and C3 indicate calculated values of the cosmic ray neutron soft error rate according to the embodiment of the present invention. However, the hitting parameter τ in Equation 16 is set to 0.1 μsec.
It is calculated as

As described above, according to one embodiment of the present invention, the element region of the semiconductor device is divided into a plurality of small regions in the depth direction, and the impurity concentration distribution inside each small region is approximated to be constant. Since the process of calculating the potential difference δV between adjacent small regions is performed for each small region, the impurity concentration distribution of the element region can be reflected as the potential difference δV between the small regions.

Further, based on the potential difference δV from the adjacent small region, if carriers generated in each small region due to cosmic ray neutrons do not recombine, the probability of moving to the adjacent small region, P
Since the process of calculating A _j ^f and PA _j ^b is executed, the probability PA that the carriers generated in each sub-region due to cosmic ray neutrons will move to the adjacent sub-region if they do not recombine.
_j ^f and PA _j ^b can be calculated with high accuracy.

Further, a step of calculating a probability F that carriers generated in each small region by cosmic ray neutrons do not disappear by recombination when passing through each small region, and a step of calculating the probability F of carriers generated in each small region by cosmic ray neutrons. probability PA _j ^f to move to the adjacent small areas when not recombine, the PA _j ^b, probability does not disappear by recombination when carriers generated in each small region by cosmic ray neutrons passing through each small region F Is carried out, the probability PB that carriers generated in each small area by cosmic ray neutrons move to the adjacent small area is obtained.
_j ^f and PB _j ^b can be calculated with high accuracy.

Further, the probability PB _j ^f , PB jf that the carriers generated in each small region by cosmic ray neutrons move to the adjacent small region
Based on the _j ^b , a step of tracking the movement of carriers generated in each small region by cosmic ray neutrons between the small regions by the Monte Carlo method is executed, so that the carriers generated in each small region by the cosmic ray neutrons are generated in the element region. the probability P _j reaching the surface of the can be accurately calculated.

[0083] Further, based on the amount of charge generated by cosmic ray neutrons are calculated for each depth from the surface of the advance element region, calculating a charge amount Q _j generated in each small region by cosmic ray neutron because There is executed, it is possible to calculate high accuracy the amount of charge Q _j generated in each small region by cosmic ray neutron.

Further, the probability P _j that carriers generated in each small region by cosmic ray neutrons reach the surface of the element region is _expressed by:
Calculating a charge amount P _j · Q _j collected on the surface of the element region for each small region by multiplying the charge amount Q _j generated in each small region by cosmic ray neutrons; Sum of electric charges collected on the surface of the element region ΣP _j · Q _j
Is calculated, the amount of charge Q _tot collected on the surface of the element region from all the small regions can be calculated with high accuracy.

As described above, according to the embodiment of the present invention, the amount of charge Q _tot collected on the surface of the element region from all the small regions can be calculated with high accuracy. Can be calculated with high accuracy,
An accurate guideline for producing a semiconductor device resistant to cosmic-ray neutron soft errors can be provided.

[0086]

As described above, according to the present invention, the amount of electric charge collected on the surface side of the element region can be calculated with high accuracy, so that the cosmic ray neutron soft error rate with high accuracy can be calculated. And provides an accurate guideline for producing a semiconductor device resistant to cosmic-ray neutron soft errors.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining an embodiment of the present invention (an example of an actual impurity concentration distribution of an element region and an impurity concentration distribution of each small region by dividing an element region into a plurality of small regions in a depth direction). FIG. 9 is a diagram showing an impurity concentration distribution in an element region when is approximated to be constant.

FIG. 2 is a diagram for explaining an embodiment of the present invention (a diagram for explaining a probability of a carrier generated in a small region by a cosmic ray neutron to move to an adjacent small region).

FIG. 3 is a diagram for explaining an embodiment of the present invention (a diagram for explaining a probability of a carrier generated in a small region by a cosmic ray neutron to move to an adjacent small region).

FIG. 4 is a diagram for explaining an embodiment of the present invention (a diagram for explaining a probability of a carrier generated in a small region by a cosmic ray neutron to move to an adjacent small region).

FIG. 5 is a diagram for explaining an embodiment of the present invention (a diagram for explaining a probability of a carrier generated in a small region by a cosmic ray neutron to move to an adjacent small region).

FIG. 6 is a diagram for explaining an embodiment of the present invention (a diagram for explaining a probability of a carrier generated in a small region by a cosmic ray neutron to move to an adjacent small region).

FIG. 7 is a diagram for explaining an embodiment of the present invention (a diagram showing an example of an actual impurity concentration distribution in an element region);

FIG. 8 is a diagram for explaining an embodiment of the present invention (a diagram showing experimental values of cosmic ray neutron soft error rates and calculated values according to an embodiment of the present invention).

FIG. 9 is a diagram for explaining an embodiment of the present invention (a diagram showing an example of an actual impurity concentration distribution in an element region).

FIG. 10 is a diagram for explaining an embodiment of the present invention (a diagram showing experimental values of cosmic ray neutron soft error rates and calculated values according to an embodiment of the present invention).

FIG. 11 is a diagram for explaining an embodiment of the present invention (a diagram showing an example of an actual impurity concentration distribution in an element region).

FIG. 12 is a diagram for explaining an embodiment of the present invention (a diagram showing experimental values of cosmic ray neutron soft error rates and calculated values according to an embodiment of the present invention).

[Explanation of symbols]

A1 Example of actual impurity concentration distribution of element region A2 Impurity concentration distribution of element region when element region is divided into a plurality of small regions in the depth direction and impurity concentration distribution of each small region is approximated to be constant B1 to B3 Experimental value of cosmic ray neutron soft error rate C1 to C3 Calculated value of cosmic ray neutron soft error rate according to one embodiment of the present invention

Claims (5)

[Claims] A step of dividing an element region of a semiconductor device into a plurality of small regions in a depth direction and calculating a probability that carriers generated in each of the small regions by cosmic ray neutrons move to an adjacent small region; Based on the probability that carriers generated in each small region by line neutrons move to adjacent small regions, calculating the probability that carriers generated in each small region by the cosmic ray neutrons reach the surface of the element region, Based on the probability that carriers generated in each small region by the cosmic ray neutrons reach the surface of the element region, calculating the amount of charge collected on the surface of the element region from all the small regions, Calculating a cosmic ray neutron soft error rate of the semiconductor device based on the amount of electric charge collected on the surface of the element region from the small region of the cosmic ray. Neutron soft error rate calculation method. 2. The step of calculating the probability that carriers generated in each small region by cosmic ray neutrons move to an adjacent small region includes the step of: approximating the impurity concentration distribution inside each small region to be constant; Calculating the potential difference between the adjacent small area, and moving to the adjacent small area if the carriers generated in each small area by the cosmic ray neutrons do not recombine based on the potential difference between the adjacent small area. A step of calculating a probability; a step of calculating a probability that carriers generated in each small region by the cosmic ray neutrons will not disappear by recombination when passing through each small region; If carriers that do not recombine move to adjacent small regions, the probability that the carriers generated in each small region by the cosmic ray neutrons will be recombined when passing through each small region. Multiplying the probability of non-extinction by a cosmic ray neutron soft error rate according to claim 1. 3. The step of calculating the probability that carriers generated in each small region by the cosmic ray neutrons reach the surface of the element region, wherein the carriers generated in each small region by the cosmic ray neutrons are located in adjacent small regions. 3. The cosmic ray according to claim 1, further comprising a step of tracking, by a Monte Carlo method, the movement of the carrier generated in each of the small areas by the cosmic ray neutrons, based on a probability of the movement. Neutron soft error rate calculation method. 4. The step of calculating the amount of charge collected on the surface of the element region from all of the small regions is generated by cosmic ray neutrons that are calculated in advance for each depth from the surface of the element region. Calculating the amount of charge generated in each small region by cosmic ray neutrons based on the amount of charge; and calculating the probability that carriers generated in each small region by the cosmic ray neutrons reach the surface of the element region. A step of calculating the amount of charge collected on the surface of the element region for each small region by multiplying the amount of charge generated in each small region by line neutrons; Calculating a total amount of collected electric charges. 4. The method according to claim 1, further comprising the step of calculating a cosmic ray neutron soft error rate. 5. The method according to claim 1, wherein the step of calculating the cosmic ray neutron soft error rate of the semiconductor device includes a step of multiplying the amount of charge collected on the surface of the element region from all the small regions by a constant. The method for calculating a cosmic ray neutron soft error rate according to claim 1, 2, 3, or 4.