JPH10189472A - Method and system for simulating semiconductor impurities - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enhance the convergence of parameters indicating the distribution of functions by performing approximate calculation of a person function for impurity concentration distribution of high dose or a person function for impurity concentration distribution of low dose and then determining the parameters of these functions. SOLUTION: Based on a first impurity concentration distribution data of high dose selected by a distribution selecting means 14, a first function setting means 15 calculates the initial values of four function parameters of first person function through approximate calculation of the person function. A second impurity concentration distribution data implanted with ions at a relatively low dose is selected for calculating the function parameters of a second person function. Subsequently, a second function setting means 16 distributes the selected second impurity concentration distribution data depending on predetermined function parameters of first person function. Second function parameters are set through approximate calculation of a distribution data from which random scattering components are removed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a semiconductor impurity simulation method for estimating the behavior of implanted ions in a semiconductor device manufacturing process and the final impurity concentration distribution from data on the concentration distribution of impurities implanted into a semiconductor substrate. Further, the present invention relates to a semiconductor impurity simulation apparatus suitable for performing the simulation method.

[0002]

2. Description of the Related Art Impurity simulations are used only to determine the concentration distribution of impurities implanted in a silicon substrate or the like with high accuracy, and then behave in subsequent heat treatment steps (annealing, oxidation, CVD, etc.) (relocation, etc.). Various types have been realized according to applications, such as estimation of the final impurity concentration distribution. The latter impurity simulation is incorporated into the process for each function of ion implantation and diffusion as part of the process simulation.
This form is the current mainstream of impurity simulation.

In this impurity simulation, a distribution parameter is extracted from impurity concentration distribution data at the time of ion implantation, and boundary conditions and the like are appropriately set. Under these conditions, a predetermined physical equation representing a diffusion phenomenon, for example, is obtained. And so on to find a solution. The impurity concentration distribution data in the depth direction of the substrate immediately after the implantation is usually obtained by SIMS.
(Secondary Ion Mass Spectroscopy) It can be obtained by actual measurement such as measurement, or calculation by modeling a physical phenomenon with high accuracy, such as Monte Carlo ion implantation simulation.

The extraction of the distribution parameters is performed by comparing the impurity concentration distribution immediately after the injection indicated by the data obtained by the above method with a predetermined function using the least squares method (such as Levenberg-Marquart method), and comparing the two. The parameters of the predetermined function are changed so as to increase the degree. Then, the parameter of the function having the highest degree of coincidence is output as the impurity concentration distribution parameter immediately after the implantation. The predetermined function used for this distribution parameter extraction is usually built in an impurity simulator, and specifically, a Gaussian distribution function,
There are Pearson distribution function, Dual-Pearson distribution function, and the like. In the recent trend of miniaturization of semiconductor devices, low-energy, low-dose ion implantation tends to greatly influence the element characteristics. The function that can reproduce the impurity concentration distribution in the depth direction of the substrate with the highest accuracy is Dual-Pears
It is an on function.

[0005] The Dual-Pearson function represents the term of the first Pearson function representing the concentration distribution of the randomly scattered impurities, and the concentration distribution of the impurities channeled deep into the substrate during ion implantation. 2nd Pearso
and n function terms. Therefore, Dual-Pears
When the distribution parameters are extracted using the on function, the impurity concentration distribution in the tail (channeling tail) due to channeling is well reflected, and as a result, ion implantation with low energy and low dose in which channeling is particularly problematic In the impurity simulation, the ion implantation concentration can be calculated with high accuracy.

[0006]

The injection dose in the Dual-Pearson function is distributed according to the first Pearson function at the ratio of the variable R, and according to the second Pearson function at the ratio of the complement 1-R of the variable. I have. Therefore, the degree of channeling usually depends on the parameter R of the Dual-Pearson function. It should be noted that the distribution shapes of the impurity concentration that differ greatly depending on the implantation energy mainly depend on the first and second Pearso.
n Depends on the four parameters of the function. It is known that the degree of the channeling also depends on the dose. To express this, the parameter R may be changed according to the implantation dose.

However, as described above, the Du at the time of the highest degree of coincidence with the impurity concentration distribution data having the same implantation energy and different implantation doses for ion implantation.
When the parameters of the al-Pearson function are extracted as the distribution parameters, the convergence of the parameters of the Dual-Pearson function is poor.
Of the parameters of the -Pearson function, the parameters of the distribution shape excluding the parameter R often do not match. In this case, even if the implantation energy is the same, it is necessary to prepare a number of parameters of the distribution shape, which not only lowers the calculation efficiency but also lowers the accuracy of each parameter,
-It is often difficult to use the Pearson function for a highly accurate impurity simulator.

[0008] The present invention has been made in view of such circumstances, and is based on dual-pea analysis based on impurity concentration distribution data obtained by measurement such as SIMS or calculation by Monte Carlo method.
When extracting a distribution parameter using the rson function, a highly reliable distribution parameter can be obtained because the convergence and accuracy of the parameter indicating the distribution shape of the function are good, and the efficiency and accuracy of the calculation using this can be improved. An object of the present invention is to provide an enhanced semiconductor impurity simulation method. It is another object of the present invention to provide a semiconductor impurity simulation apparatus suitable for this highly accurate simulation method.

[0009]

In order to solve the above-mentioned problems of the prior art, the present inventor extracts a distribution parameter from various impurity distribution data, compares the original impurity distribution with the extraction result, and makes a dual study. -We investigated the cause of the inconsistency of the parameters indicating the distribution shape of the Pearson function between different implantation doses. As a result, the impurity concentration distribution data serving as the basis for extracting the parameters of the Dual-Pearson function, that is, the impurity concentration distribution data obtained by SIMS or the like or by the Monde Carlo method is calculated by using the first Pearson function and the second Pearso function.
It has been found that the above problem tends to occur when measurement or calculation is not performed within the impurity concentration range (dynamic range) suitable for each of the n functions.

That is, when the impurity is ion-implanted at a high concentration, the impurity concentration distribution by the first Pearson function in the dual-Pearson function occupies most of the implanted dose, and the peak concentration of the impurity concentration distribution by the second Pearson function is: It was found that the concentration was lower by several orders of magnitude than the peak concentration of the impurity concentration distribution of the first Pearson function. Therefore, using the high-concentration impurity concentration distribution data,
When trying to extract the parameters of the Pearson function, the second
The distribution that depends on the Pearson function is almost buried in the noise level. When trying to forcibly correlate the distribution in this noisy state, the second
There is a possibility that the coincidence of the distribution is the highest with the parameter different from the true value of the parameter of the Pearson function, and this is considered to be the cause of poor parameter coincidence.

The dynamic range is, for example, SIM
When oxygen is used as the primary ion in S measurement, boron (B)
Is about 4 digits, arsenic (As) is about 3 digits, and phosphorus (P) is 3
Since it is of the order of magnitude, a drop in the detection concentration in SIMS measurement by several orders has a fatal effect on the measurement accuracy. On the other hand, the dynamic range in the ion implantation calculation of the Monte Carlo method can be increased according to the number of calculation points and the number of repetitions. For example, if the dynamic range is increased by one digit, the calculation time is required to be ten times, and several digits are required. Increasing the dynamic range of the computer causes an increase in computational cost, which is not realistic, and is not preferable in terms of effective use of computer resources.

The semiconductor impurity simulation method according to the present invention is based on such considerations and considerations. For example, the method for simulating impurities at the time of ion implantation indicated by input data obtained by SIMS measurement, impurity distribution calculation by Monte Carlo method, or the like. Dual-Pearson for impurity concentration distribution
The function is adjusted while appropriately changing the parameters, the parameter of the function having the highest degree of coincidence is extracted as a distribution parameter of the impurity concentration distribution at the time of the ion implantation, and the extracted distribution parameter is used for the semiconductor device. An impurity simulation method for a semiconductor device for estimating the behavior of impurities or final impurity distribution data in a manufacturing process, comprising: selecting data of at least two impurity concentration distributions differing only in a dose amount from the input data; For the first Pearson function or the second Pearson function constituting the Pearson function, an approximate calculation of the first Pearson function for the selected impurity concentration distribution with a high dose and the second Pe for the impurity concentration distribution with a low dose are performed.
Perform at least one of the approximate calculation of the arson function,
It is characterized in that at least one parameter of the first Pearson function and the second Pearson function is obtained.

As described above, since the first Pearson function and the second Pearson function have a complementary relationship with respect to the dose, the parameter extraction accuracy of the second Pearson function can be improved using this relationship. That is, in this case, in the present invention, after obtaining the parameter of the first Pearson function, the impurity concentration distribution data with a low dose is read out and distributed according to the parameter of the first Pearson function obtained earlier. The impurity concentration data having a distribution corresponding to the first Pearson function is subtracted from the impurity concentration distribution data having a low original dose, and the approximate calculation is performed on the impurity concentration distribution indicated by the subtracted data. Another feature is to obtain the parameters of the 2 Pearson function. By subtracting the data, distribution points due to random scattering at the time of ion implantation are removed, so that the degree of coincidence of the parameters of the second Pearson function is increased, and as a result, the extraction accuracy of the subsequent distribution parameters is improved. .

As described above, according to the impurity simulation method of the present invention, first, the first Pearson function and the second Pears function are used.
The impurity distribution data measured or calculated in the range of the impurity concentration suitable for each of the on functions is selected. That is, high dose impurity concentration distribution data is selected for the first Pearson function, and low dose impurity concentration distribution data is selected for the second Pearson function. Then, using the parameters of the function obtained with high precision from the impurity concentration distribution data in these optimum concentration ranges, for example, the initial value of the distribution parameter is obtained by the least square method or the like. Easy to converge to value.

On the other hand, the present inventor has found that, in the examination of the various impurity distribution data described above, the measured values of the impurity concentration distribution data obtained by the SIMS measurement vary due to noise, which deteriorates the consistency of the parameters. Got the view. That is, when the noise level of the SIMS measurement is high, only the impurity concentration distribution data near the peak concentration can be used due to the weight noise.
Dual using this limited range of impurity concentration distribution data
When the parameters of the -Pearson function are obtained, the accuracy of the extracted distribution parameters becomes low when the distribution parameters are extracted by the least square method or the like. The detection limit of measurement in SIMS measurement varies depending on measurement conditions and sample preparation conditions. For example, when oxygen is used for primary ions, B is 1
× 10 ¹⁵ / cm ² approximately, As is 1 × 10 ¹⁷ / cm ² approximately, P is a 1 × 10 ¹⁶ / cm ² approximately. Actual SIMS
In measurement, high accuracy data cannot be obtained up to this detection limit because, when a substrate is cut by sputtering to check the concentration distribution in the depth direction of the substrate, the surface state of the substrate and the initial effect of sputtering, or due to sputtering. This is because the noise effect becomes dominant on the low density side due to the shape effect of the concave portion.

In consideration of this detection limit, the present invention further performs data processing on each of a plurality of selected impurity concentration distribution data to reduce the dispersion of the impurity concentration distribution data, and then performs the approximate calculation. Another feature is to perform. As this data processing method, for example, using other impurity concentration distribution data which is expected to be almost the same on the low concentration side, the data is replaced only on the low concentration side (distribution synthesis), or a plurality of data under the same condition are replaced. A method of removing the noise component by taking an average, applying smoothing by predetermined signal processing, or the like can be appropriately selected. Such a method enables SIMS measurement with an accuracy close to the measurement limit, and as a result, the accuracy of parameter extraction is further improved.

According to the semiconductor impurity simulation apparatus of the present invention, the Dual-Pearson function is fitted to the impurity concentration distribution at the time of ion implantation indicated by the input data while appropriately changing its parameters, and the function of the function having the highest degree of coincidence is obtained. Parameter extracting means for extracting a parameter as a distribution parameter of the impurity concentration distribution at the time of the ion implantation, and using the extracted distribution parameter, estimating an impurity behavior or a final impurity distribution in a semiconductor device manufacturing process. A semiconductor impurity simulation apparatus having analysis means, further comprising distribution selection means for selecting data of at least two impurity concentration distributions differing only in dose amount from the input data, forming the Dual-Pearson function For the first Pearson function, the Performs approximate calculation for the amount is higher impurity concentration distribution, the first function setting means for obtaining a parameter of the first 1Pearson function, the Dual-Pearson
For the first Pearson function constituting the function, an approximate calculation is performed on the impurity concentration distribution having a low dose selected by the distribution selecting means, and at least one of the second function setting means for obtaining the parameter of the second Pearson function is used. It is characterized by having.

[0018]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a semiconductor impurity simulation apparatus and a simulation method according to the present invention will be described in detail with reference to the drawings. First, Dual-P
The earson function will be described. The Dual-Pearson function is a distribution function that accurately reflects the concentration distribution due to channeling during ion implantation, and is expressed by the following equation.

## EQU1 ## F (x) = DOSE × R × f1 (x, Rp1, σ1, γ)
1, β1) + DOSE × (1-R) × f2 (x, Rp2, σ2,
γ2, β2) where F (x) is a Dual-Pearson function, x is the coordinate in the depth direction of the substrate, and f1 and f2 are two normalized Pearson
A function, DOSE, is an implantation dose amount of the ion implantation, and R is a parameter indicating a ratio of f1 to the implantation dose. Also,
Rp1, σ1, γ1, β1 are parameters for determining the distribution shape of the first pearson function f1, and Rp2, σ2, γ2, β2 are parameters for determining the distribution shape of the second pearson function f2. Specifically, Rp1, Rp2 Is the projection range of the ion implantation, σ1 and σ2 are the standard deviations of the projection ranges Rp1 and Rp2, respectively, and γ1 and γ2 are the "skewness"
s) ", and β1 and β2 are" kurtosis "parameters representing the distribution shape near the peak.

As shown in the above equation, Dual-Pearson
The function F (x) is composed of two Pearson functions f1 and F2. The Pearson function f1 represents the concentration distribution of the randomly scattered impurities.
The n function f2 represents the concentration distribution of impurities channeled between substrate lattices. Thus, since two Pearson functions are combined, other Gauss functions, Pears functions
With the on function, the channeling tail of the impurity concentration distribution in the depth direction of the substrate during ion implantation, which is difficult to reproduce, can be expressed with high accuracy. By changing the ratio R occupied by the Pearson function f1 between different implantation doses according to the implantation dose, it is possible to express the implantation dose dependence of the degree of channeling.

FIG. 1 is a block diagram showing a schematic configuration of an impurity simulation apparatus according to the present invention. Impurity simulation device (simulator) in the present embodiment
Is calculated by an approximate calculation of the impurity concentration distribution data immediately after ion implantation obtained by actual measurement or calculation.
The parameters of the earson function F (x) (the above R, Rp1, σ1
, Γ1, β1, Rp2, σ2, γ2, β2), and by changing this initial value, the Dual-Pearson function F (x) is fitted to the impurity concentration distribution data immediately after the ion implantation. After extracting the distribution parameters and creating an ion implantation range table, setting boundary conditions and the like as appropriate, and then solving a predetermined physical equation or the like representing a diffusion phenomenon under these conditions, a semiconductor manufacturing process is performed. The purpose is to estimate the behavior (rearrangement) of impurities and the final impurity concentration distribution in the heat treatment.

The impurity simulator 1 roughly includes a preprocessor 2 that mainly performs various data processing and setting of conditions such as initial parameters of impurity concentration distribution data, and a main processor 3 that obtains a solution by taking a predetermined basic equation. And a post processor 4 for converting the result of the main processor 3 into a form conforming to a predetermined output format and outputting the result, giving data and conditions to each of the processors 2, 3, and 4, and storing means for accumulating calculation results 5 and
And a display device 6. Further, the SIMS measuring device 7 for actually measuring the impurity concentration distribution data immediately after the ion implantation and the ion implantation Monte Carlo simulator 8 for calculating the impurity concentration distribution data immediately after the ion implantation by calculation using a particle model are stored in the storage device 5 online. Or it is connected offline.

In the storage device 5, a database 9 for storing impurity concentration distribution data from the SIMS measuring device 7 or the ion implantation Monte Carlo simulator 8;
There is provided an ion implantation range table 10 in which distribution parameters of impurity concentration distribution data to be used in the simulation are tabulated and described for each implantation energy.

The preprocessor 2 includes a data processing unit 11 for performing a process for reducing the variation of the impurity concentration distribution data from the database 9, and the Dual-Pearson function F based on the impurity concentration distribution data after the data processing. (x) parameters (hereinafter referred to as function parameters)
And a parameter processing unit 12 for extracting the distribution parameters using the function parameters, and a range table creating means 13 for reflecting the extracted distribution parameters in the ion implantation range table 10. Although not particularly shown, the preprocessor 2 also includes an input unit that receives an operator's condition input, a unit that creates a process model from various data, and a unit that formulates conditions such as boundaries. The parameter processing unit 12 includes the distribution selection unit 1
4, a first function setting means 15, a second function setting means 16, and a parameter extracting means 17. These functions and operations will be described in the following simulation method.

Hereinafter, the impurity simulation method of the present invention will be described by way of an example in which the impurity concentration distribution data at the time of ion implantation is obtained by measurement by the SIMS measuring device 7 and stored in the database 9.
FIG. 2 is a follow chart showing the overall flow of the impurity simulation method. First, step ST1
The data processing means 11 shown in FIG.
Imports impurity concentration distribution data from In the case of the present embodiment, the impurity concentration distribution data to be taken in at least includes at least a pair of impurity concentration distribution data having the same implantation energy and different doses at the time of ion implantation, which is used for obtaining a function parameter.

In step ST2, the data processing section 11 performs data processing on the impurity concentration distribution data. As is well known, in the SIMS measurement, the secondary ions emitted from the substrate at the time of the primary irradiation of oxygen or the like are mass-analyzed while shaving the surface spot of the substrate by sputtering, and are thereby contained in the substrate. This is a method for analyzing trace impurities that can analyze the type and ratio (concentration) of elements in the depth direction of the substrate. The accuracy of the SIMS measurement on the low concentration side is degraded by the surface condition of the substrate, the initial effect of sputtering, the shape effect of the substrate recess (crater) by sputtering, and the like. The purpose of the data processing in step ST2 is to remove, from the impurity concentration distribution data obtained by the SIMS measurement, a portion (measurement noise component) that deteriorates the later parameter extraction accuracy.

FIGS. 3 to 5 are flowcharts showing the details of this data processing flow. Step ST2 in FIG.
In step ST21, data to be processed is selected from the acquired impurity distribution data, and in step ST21, the selected data is displayed on the display device 6 in FIG. Step ST
At 22, a data processing method is selected. That is,
The operator selects the processing method (S
When any one of T231 to ST235) is selected, the flow proceeds to the step of the selected processing method.

Hereinafter, each processing method will be specifically illustrated and described with reference to FIGS. 6 to 10 which schematically show the contents.

Synthesis of Impurity Distribution Data (ST231) As shown in FIG.
Is that the concentration on the substrate surface side does not change smoothly due to the influence caused by the SIMS measurement, that is, in the illustrated example, the surface state of the substrate, the initial effect of sputtering, and the like. In this process, other impurity concentration distribution data B which is expected to be equivalent to the impurity concentration distribution data A to be processed on the substrate surface side (or on the substrate deep side) is read out. A process for partially replacing the distribution data is performed. This makes it possible to remove such noise components from the impurity concentration distribution data A to be processed.

Averaging of a plurality of distributions (ST232) As shown in FIG. 7, this processing is performed, for example, on a plurality of measurement data (in FIG. 7, data C
And D) are averaged to calculate the processed data E. Thereby, in addition to reducing the variation of the ion implantation on the high concentration side of the distribution, the variation on the low concentration side of the deep portion of the substrate, which tends to greatly vary every measurement, is particularly reduced.

Smoothing (ST233) As shown in FIG. 8, this processing is effective when noise is present on the entire measurement data to be processed, and is performed by using a predetermined signal processing method or the like. Smoothing is applied. This makes it possible to obtain smoothed processed data.

Averaging of impurity distribution data (ST234) In this processing, as shown in FIG. 9, for example, the resolution is reduced in the depth direction of the substrate with respect to the measurement data to be processed to reduce the variation. It is alleviating.

Subjective correction (ST235) As shown in FIG. 10, this last processing is performed, as shown in FIG. 10, on a portion where a measurement error is liable to occur empirically, for example, a low-concentration portion on the substrate surface side or the substrate back side. Is corrected by extrapolation while the operator looks at the display device.

After performing such data processing, the post-processing data is displayed in step ST24 of FIG. 4, and it is determined in step ST25 whether or not the processing is completed.

If the determination in step ST25 is Yes, the data processing step is terminated. If the determination is No, the process proceeds to step ST25 in FIG. 5 to determine whether or not to process the previous data. If the determination in step ST25 is Yes, the previous data, that is, the measurement data after SIMS measurement in this case, is displayed on the display device 6 in the following step ST26. If the determination in step ST25 is No
If so, the data after processing is displayed in step ST27. In any case, the flow is returned to before step ST22 in FIG. 3, and the selection of the data processing and the data processing are repeated until it is determined in step ST25 in FIG. 2 that the processing is completed. By performing the data processing in such a procedure, it is possible to reduce in advance the variation of the impurity concentration distribution data used for calculating the function parameters of the Dual-Pearson function F (x), thereby reducing the noise component that affects the calculation accuracy. it can. Further, since the control for repeating the processing is performed, the noise component removing effect can be further enhanced by repeating the same processing a plurality of times or by arbitrarily combining different types of processing.

When the data processing process described in detail above is completed, in steps ST3 to ST6 of FIG. 2 that follow, the initial values of the function parameters of the second Pearson function f2 of the Dual-Pearson function F (x) are calculated. In a subsequent step ST7, the Dual-Pearson function F
The initial value of the function parameter of the first Pearson function f1 of (x) is set. The setting of these function parameters is performed in the parameter processing unit 12 of FIG.

Here, the outline of the process of calculating these two function parameters will be described in advance. The two function parameter calculation steps can be performed independently in parallel. However, in order to further increase the calculation accuracy, one function parameter is calculated and set, and the result is used to calculate the other function parameter. Preferably, the parameters are calculated. For this reason, in the present embodiment, first, the first Pe is used by using the high-dose impurity concentration distribution data in which the ratio of components due to random scattering during ion implantation is relatively high.
The initial value of the function parameter of the arson function f1 is set.
Then, when the impurity concentration distribution data of a low dose in which the ratio of the other channeling component is relatively high is distributed according to the first Pearson function f1 for which the function parameter has already been obtained, this distribution data is obtained. It can be regarded as a random scattering component of the impurity concentration distribution data of the dose. Therefore, distribution data by channeling the low dose impurity concentration distribution data can be obtained by subtracting this random scattering component from the original low dose impurity concentration distribution data. Therefore, the second Pearson is used by using the distribution data by this channeling.
When the distribution parameter of the function f2 is calculated, the calculation accuracy is improved. If the channeling component of the low-dose impurity concentration distribution data is considered to be absolutely high, for example, the ion implantation angle with respect to the substrate is not optimized, the second Pearson function f
Set the function parameters of 2 and use this result to
The function parameters of the arson function f1 can be calculated with high accuracy. In other words, the method using the above calculation results is to fit one of the distribution data in which either the channeling component or the random scattering component is considered dominant to a function representing the dominant component first. This is a method in which rough approximation is performed, and the accuracy of calculation of other function parameters based on this approximation is increased. By developing this idea, it is possible to repeatedly apply the same method to other function parameters again based on the function parameters with increased accuracy, and gradually improve the accuracy of the function parameters.

In the following, a specific procedure in this embodiment will be described. First, in step ST3, ion implantation is performed at a relatively high dose used for extracting a parameter of the first Pearson function f1 from measured data after data processing. The first
Is selected. The selection of the distribution data is performed by the distribution selecting means 14 in FIG.

In the next step ST4, Dual is performed based on the selected high-dose first impurity concentration distribution data.
-Initial values of four function parameters (Rp1, σ1, γ1, β1) of the first Pearson function f1 of the Pearson function are set as Pearso
Calculated from the approximate calculation of the n function. This approximate calculation is shown in FIG.
The method is performed by, for example, a method of calculating all the function parameters from a predetermined moment calculation, or a method of calculating the first Pearson function f1 by a Gaussian distribution (γ1 = 0, β1 = 3). After estimating the projection range Rp1 from the measurement data, the substrate depth (Rp1) at the most frequent location and the substrate depth extrapolated from the most frequent location of the measurement data by exp (−0.5) A known calculation method such as a method of estimating the standard deviation σ1 from the distance between the two can be selected. In addition, a method of calculating the matching degree (approximate calculation) by adjusting the function parameters to the distribution while changing the parameters of the function, and extracting a parameter having the highest matching degree, such as a least square method described in detail later, is adopted. You can also.

In the next step ST4, the first Pearson
In order to check whether the initial values of the parameters of the function f1 have been accurately calculated, the first impurity concentration distribution data used for calculating the initial values and the distribution data distributed according to the calculated initial values are overlapped. A graph is displayed on the screen of the display device 6. When the operator who sees this screen proceeds to step ST
If it is determined in step 6 that the accuracy of the initial value of the parameter is low, the process returns to step ST3 to select another impurity concentration distribution data and repeat the calculation of the initial value of the parameter in the same manner as described above. Become. If there is no problem with the initial value, the process proceeds to the next step ST7.

Step ST7 is the second Pearson function f2
The second impurity concentration distribution data which is used for calculating the function parameters (Rp2, .sigma.2, .gamma.2, and .beta.2) and is ion-implanted at a relatively low dose is selected. The following step ST8 is performed by the second function setting means 16 in FIG. First, the selected second impurity concentration distribution data is distributed according to the function parameters (Rp1, σ1, γ1, β1) of the first Pearson function f1 which have already been obtained. Then, this distribution data is subtracted from the original second impurity concentration distribution data, and the distribution data from which the random scattering component has been removed is subjected to the above-described approximate calculation (step ST).
3) is performed in a similar manner to obtain the second Pearson function f
The second function parameter (Rp2, σ2, γ2, β2) is calculated and set. For the above-mentioned reason, it is possible to obtain a function parameter with higher accuracy than when it is calculated independently.

In step ST9, the accuracy of the calculated function parameters is confirmed in the same manner as described above.
The selection of distribution data and the calculation of initial values of function parameters are repeated until it is determined that there is no problem in 10. Step ST
If it is determined in step 10 that there is no problem, the flow proceeds to the next step ST11.

Steps ST11 to ST15 are steps for extracting the parameters of the Dual-Pearson function by the method of least squares, and are executed by the parameter extracting means 17 of FIG. First, in step ST11, a plurality of impurity concentration distribution data having the same implantation energy and different implantation doses to be subjected to parameter extraction are selected from the impurity concentration distribution data taken in step S1.

In the next step ST12, using the initial value of the function parameter of the Dual-Pearson function obtained earlier, the parameter R of the Dual-Pearson function is adjusted for the impurity concentration distribution from which the parameter is to be extracted. A distribution shape corresponding to the implantation dose is obtained. Step S
At T13, the square error between the impurity concentration distribution data of the parameter extraction target distributed by the Dual-Pearson function and the corresponding impurity concentration data of the original parameter extraction target (measurement data) is obtained, and the sum is calculated. Then, in the next step ST14, the sum of the square errors is compared with the convergence condition e. If the result of this comparison indicates that the sum of the squared errors is greater than the convergence condition e, step ST15
Then, the parameter R of the Dual-Pearson function and the function parameter are updated using a non-linear least squares algorithm such as the Levenberg-Marquart method, and the process returns to step ST12 until the sum of the squared errors becomes smaller than the convergence condition e. Steps ST12 to ST15 are repeated. In step ST15, if the sum of the squared errors is smaller than the convergence condition e, the parameters of the optimal Dual-Pearson function are extracted, and the distribution parameters of the impurity concentration distribution data for parameter extraction are obtained. Become.

The distribution parameters thus obtained are as follows:
Although omitted in FIG. 2, it is output to the range table creating unit 13 in FIG. The range table creating unit 13 updates the contents of the ion implantation range table 10 in the storage device 5 as illustrated in, for example, FIG. The updated contents of the ion implantation range table 10 reflect the high extraction accuracy of the distribution parameters described above, and indicate the initial conditions for a more accurate simulation.

Then, in step ST16 of FIG.
A predetermined simulation is executed by the main processor 3 using the ion implantation range table 10. For example, after creating a process model of a semiconductor substrate region and setting boundary conditions (for example, conditions for precipitation), a predetermined basic equation such as a thermal diffusion equation is converted into a numerically calculable equation and standardized. After giving the initial condition to the formula, the calculation is repeated for each calculation point. And FIG.
, The respective calculation results are integrated and output according to a predetermined output format (step ST
17), the simulation ends.

The above-described simulation apparatus and simulation method of the present invention have the following effects. That is, in consideration of the fact that the ion implantation conditions in semiconductor manufacturing are generally optimized for channeling in setting the initial values of the function parameters, the initial values of the function parameters of the first Pearson function are determined as follows. By using the density distribution data, an initial value closer to the true value can be set. Also, the second
The initial values of the function parameters of the Pearson function are the initial values of the parameters of the first Pearson function that are close to the true values obtained earlier,
By using the impurity concentration distribution data implanted at a low dose, the initial value is set closer to the true value. As a result, highly accurate simulation parameters (for example, an ion implantation range table) can be obtained, and a simulation result in which the behavior of impurities in an actual device is well reflected can be obtained.

In particular, in the condition setting for each ion implantation energy as shown in FIG. 11, since a plurality of impurity concentration distribution data having different dose amounts are used for each implantation energy with the same function parameter setting, the doses are different. A function parameter is uniquely obtained for the impurity concentration distribution, and as a result, the distribution parameter also becomes close to the true value. The good convergence of this function parameter is
For example, a parameter indicating the distribution shape for each implantation energy may be one set, and the number of parameters to be prepared can be reduced. Therefore, there is an effect that the calculation efficiency and the effective use of the calculation environment are brought about. Further, by performing data processing for reducing the variation in advance on the impurity concentration distribution data used for calculating the function parameter, it is possible to further improve the accuracy.

In the description of the above embodiment, SIMS
Although the case of using the actual measurement data by the measurement method has been described, the calculation result by the ion implantation Monte Carlo simulator 8 in FIG. 1 and the impurity concentration distribution data obtained by other methods can be used. In the simulation of a particle model such as the Monte Carlo method, the calculation time is lengthened in order to obtain highly accurate data.
The use of the simulation method and apparatus for calculating a function parameter with high accuracy according to the present invention makes it possible to reduce the overall calculation time.

[0049]

As described above, according to the present invention,
When extracting distribution parameters using the Dual-Pearson function from impurity concentration distribution data obtained by SIMS measurement or Monte Carlo calculation, etc., the convergence and accuracy of parameters indicating the distribution shape of the function are high, so reliability is high. It is possible to obtain a distribution parameter with high reliability, and to provide a semiconductor impurity simulation method with improved calculation accuracy using the distribution parameter. Further, according to the present invention, it is possible to provide a semiconductor impurity simulation apparatus suitable for this highly accurate simulation method.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a schematic configuration of an impurity simulation apparatus according to an embodiment of the present invention.

FIG. 2 is a follow chart showing an overall flow of an impurity simulation method according to the embodiment of the present invention.

FIG. 3 is a flowchart showing a flow of data processing (ST2) in detail.

FIG. 4 is a flowchart following FIG. 3;

FIG. 5 is a flowchart showing a feedback loop of FIGS. 2 and 3;

FIG. 6 is an explanatory diagram schematically showing the contents of synthesis of impurity distribution data (ST231).

FIG. 7 is an explanatory diagram schematically showing the contents of averaging a plurality of distributions (ST232).

FIG. 8 is an explanatory diagram schematically showing the contents of smoothing (ST233).

FIG. 9 is an explanatory diagram schematically showing the contents of averaging of impurity distribution data (ST234).

FIG. 10 is an explanatory diagram schematically showing the contents of a subjective correction (ST235).

FIG. 11 is a diagram schematically illustrating the contents of an updated ion implantation range table.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Simulator (semiconductor impurity simulation device), 2 ... Preprocessor, 3 ... Main processor (analysis means), 4 ... Postprocessor, 5 ... Storage device, 6 ...
Display device, 7 SIMS measuring device, 8 ion implantation Monte Carlo simulator, 9 database, 10 ion implantation range table, 11 data processing unit, 12 parameter processing unit, 13 range table creation unit, 14 distribution Selection means, 15: first function setting means, 16: second function setting means, 17: parameter extraction means.

Claims (7)

[Claims] 1. A dual-Pearson function is fitted to an impurity concentration distribution at the time of ion implantation indicated by input data while appropriately changing parameters thereof, and a parameter of the function having the highest degree of coincidence is set at the time of the ion implantation. An impurity simulation method for a semiconductor device, wherein the input data is extracted as a distribution parameter of an impurity concentration distribution, and using the extracted distribution parameter, estimating an impurity behavior or a final impurity concentration distribution in a process of manufacturing the semiconductor device. At least 2 which differs only in dose
Selecting data of two impurity concentration distributions, for the first Pearson function or the second Pearson function constituting the Dual-Pearson function, an approximate calculation of the first Pearson function for the selected impurity concentration distribution having a high dose, and a selected dose. A semiconductor impurity simulation method for performing at least one of an approximate calculation of a second Pearson function and an approximate calculation of a second Pearson function for an impurity concentration distribution having a low amount to obtain at least one parameter of the first Pearson function and the second Pearson function. 2. After obtaining the parameters of the first Pearson function, the data of the impurity concentration distribution with the low dose is read out and distributed according to the parameters of the first Pearson function obtained earlier. The impurity concentration distribution data having a distribution corresponding to the function is subtracted from the original impurity concentration distribution data having a low dose, and the approximate calculation is performed on the impurity concentration distribution indicated by the subtracted data, thereby obtaining the second Pearson function. The semiconductor impurity simulation method according to claim 1, wherein the parameter is determined. 3. Data processing for reducing variation in the impurity concentration distribution data of the selected impurity concentration distribution data is performed on the impurity concentration distribution data for obtaining a parameter of the Dual-Pearson function. After doing
2. The semiconductor impurity simulation method according to claim 1, wherein the approximation calculation is performed. 4. The semiconductor impurity simulation method according to claim 1, wherein the data of the impurity concentration distribution at the time of the ion implantation is obtained from a measurement result of a secondary ion mass spectrometry. 5. The semiconductor impurity simulation method according to claim 1, wherein the data of the impurity concentration distribution at the time of the ion implantation is obtained from a calculation result of a Monte Carlo method. 6. A dual-Pearson function is fitted to the impurity concentration distribution at the time of ion implantation indicated by the input data while appropriately changing its parameter, and the parameter of the function having the highest degree of matching is determined at the time of the ion implantation. A parameter extracting means for extracting as a distribution parameter of the impurity concentration distribution of the semiconductor device, and an analyzing means for estimating a behavior of impurities or a final impurity distribution in a process of manufacturing a semiconductor device using the extracted distribution parameters. An impurity simulation apparatus, comprising: at least two different dose amounts from the input data.
Further comprising distribution selection means for selecting data of two impurity concentration distributions, and performing an approximate calculation on the impurity concentration distribution having a high dose selected by the distribution selection means for the first Pearson function constituting the Dual-Pearson function. , The first
For the first function setting means for obtaining the parameters of the Pearson function, and for the second Pearson function constituting the Dual-Pearson function, an approximate calculation is performed on the impurity concentration distribution having a low dose selected by the distribution selecting means,
And a second function setting means for obtaining a parameter of a Pearson function. 7. Data processing for reducing variation in the impurity concentration distribution data of the selected impurity concentration distribution data is performed on the impurity concentration distribution data for obtaining a parameter of the Dual-Pearson function. After doing
The semiconductor impurity simulation apparatus according to claim 6, further comprising a data processing unit that outputs the data to the first function setting unit or the second function setting unit.