JP2008124075A - Ion implantation simulation method, simulator, and simulation program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To estimate with higher accuracy an arsenic concentration profile formed within a semiconductor substrate through high energy ion implantation using zero tilt angle by utilizing an analysis model (Dual-Pearson function). <P>SOLUTION: Projection range, dispersion, and weighting coefficient of the first Pearson function indicating a random element of impurity concentration profile are extracted on the basis of the shape of the maximum concentration 31 of the actual impurity concentration profile. Projection range and dispersion of the second Pearson function indicating a channeling element of impurity concentration profile can be calculated by reducing the projection range and dispersion of the first Pearson function with a specified rate. When the same impurity is implanted in different implantation energy, projection range and dispersion are extracted under the condition that these are reduced with reduction of the implantation energy and a degree of strain, a degree of sharpness, and a weighting coefficient are extracted under the condition that these are increased with reduction of the implantation energy. The degree of strain and the degree of sharpness are extracted on the basis of a shape of the tail part 32 of the actual impurity concentration profile. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to an ion implantation simulation method, an ion implantation simulator, and an ion implantation simulation program, and in particular, when an impurity is introduced into silicon with a high energy of 300 keV to 600 keV at a tilt angle of zero degree using the ion implantation method. The present invention relates to an ion implantation simulation method for predicting an impurity concentration profile, an ion implantation simulator, and an ion implantation simulation program.

  In a process simulator such as TSUPREM4 (trade name) that is widely used in general, an analysis model is used to predict the concentration distribution (impurity concentration profile) of impurities introduced into a semiconductor substrate. The analysis model approximately predicts the impurity concentration profile measured by SIMS (Secondary Ion Mass Spectrometry) or the like using a distribution function such as a Gaussian function or a Pearson function.

For example, the Pearson function uses four parameters (hereinafter referred to as Pearson function parameters) of the projection range Rp, variance ΔRp, skewness γ, and kurtosis β, as shown in Equations 1 to 6, and the substrate surface. To the impurity concentration profile at the position of the depth y. In Equations 1 to 6, f (v) is a function indicating the impurity concentration at the position of v = y−R _p . The projection range Rp is a parameter indicating the peak position (depth at which the maximum concentration is obtained) of the impurity concentration profile. The variance ΔRp is a parameter indicating the spread of the impurity concentration profile in the vicinity of the projection range Rp. The skewness γ is a parameter indicating the degree of distortion (symmetry) in the depth direction of the impurity concentration profile. The kurtosis β is a parameter indicating the sharpness of the impurity concentration profile.

  In actual ion implantation, some implanted impurities proceed in a direction along a specific crystal axis. In the direction along the specific crystal axis, the impurity can easily pass between the crystal lattices without colliding with atoms and electrons, so that the impurity enters deeper than usual. This phenomenon is called channeling, and causes a new impurity profile f2 (y) due to a channeling component separately from the normal impurity profile f1 (y). Therefore, as shown in Equation 7, a technique is used in which an impurity profile is expressed by a Dual-Pearson function f3 (y) in which two Pearson functions are associated with a weighting coefficient D.

The Pearson function parameters (R _p , ΔR _p , γ, β) are stored in a database or the like as a data table associated with injection energy for each injection material. When performing ion implantation simulation (impurity profile prediction), Pearson function parameters corresponding to the implantation material and implantation energy are read from the data table. The read Pearson function parameters are substituted into the above formulas 1 to 6. The impurity concentration profile is calculated by multiplying the distribution function by the implantation dose. As a technique for improving the accuracy of impurity implantation simulation using such a Pearson function, a technique for changing a Pearson function parameter depending on the implantation dose of the impurity has been proposed (see, for example, Patent Document 1). .

In recent years, in a solid-state imaging device including a photodiode, a structure in which arsenic ions are implanted in a relatively narrow region around the photodiode has been proposed in order to improve the number of charges that can be accumulated in the solid-state imaging device. In this structure, arsenic is ion-implanted with an implantation energy of 300 keV to 600 keV. Also, in the ion implantation, in order to efficiently implant arsenic into a narrowly limited region of the silicon single crystal substrate, the tilt angle of the silicon single crystal substrate at the time of ion implantation is zero degrees (impurity of impurities with respect to the surface of the silicon single crystal substrate). The incident angle is set to 90 degrees. When ion implantation is performed on a silicon single crystal substrate at a tilt angle of zero degree, channeling is likely to occur. In particular, when ion implantation is performed at a high implantation energy such as 300 keV to 600 keV, charing occurs remarkably, so that the channeling component cannot be ignored. Therefore, in order to obtain the arsenic ion implantation conditions capable of obtaining desired characteristics by simulation, it is desirable to perform an impurity concentration profile simulation using the Dual-Pearson function f3 (y) as described above.
JP 7-62533 A

  The above-described Pearson function parameters are calibrated for each injection material and injection energy so as to reproduce an actual impurity concentration profile (hereinafter referred to as an actual measurement value) acquired by SIMS or the like. Usually, the Pearson function parameters are calibrated by mathematically fitting each Pearson function parameter so that the Pearson function and the actual measurement value match. Therefore, it is difficult to prepare a Pearson function parameter data table for all injection conditions. In addition, ion implantation at a tilt angle of zero degrees is not employed in a normal semiconductor device manufacturing process because of a large variation in impurity profile after implantation. That is, ion implantation is not performed at a tilt angle of zero degree, such as when an impurity region that does not spread in a direction parallel to the surface of the semiconductor substrate is formed in a narrow region of the semiconductor substrate, such as the solid-state imaging device described above. Used only when not obtaining In that sense, it can be said that ion implantation with a tilt angle of zero degrees corresponds to a special application. For this reason, a process simulator such as TSUPREM4 (trade name), which is widely used in general, does not provide a Pearson function parameter that can accurately represent an impurity concentration profile formed by ion implantation with a tilt angle of zero degrees. .

  Also, the Pearson function parameter data table generally prepared in the process simulator is calibrated independently for each impurity concentration profile formed under each implantation condition. That is, even when the same implantation material is ion-implanted into the semiconductor substrate with different implantation energies, the Pearson function parameters at each implantation energy are individually calibrated with respect to the corresponding actually measured values. For this reason, there is no physical consistency in the injection energy dependency between the Pearson function parameters, and the physical basis for the value of the Pearson function parameters becoming dilute. In the impurity concentration profile calculated using such Pearson function parameters that do not have physical consistency, it becomes difficult to perform qualitative evaluation based on the dependence on implantation energy.

  The present invention has been proposed in view of the above-described conventional circumstances. Even when arsenic ions are implanted with a tilt angle of zero degrees and high implantation energy, impurities can be accurately detected using an analytical model. An object of the present invention is to provide an ion implantation simulation method, an ion implantation simulator, and an ion implantation simulation program capable of predicting a concentration profile.

  In order to achieve the above object, the present invention employs the following technical means. The present invention provides a first distribution function f1 and a first distribution function f1 having parameters of at least a projection range and a dispersion (spread of an impurity concentration profile near the projection range) of an impurity introduced into a semiconductor substrate by ion implantation. This is an ion implantation simulation method that predicts a distribution function f2 of 2 based on a combined distribution function f3 = D × f1 + (1−D) × f2 combined by a weighting coefficient D. Here, the first distribution function is a distribution function that represents a random component of the impurity concentration profile, and the second distribution function is a distribution function that represents a channeling component of the impurity concentration profile.

  First, the projection range and variance of the first distribution function and the weighting coefficient are extracted based on the shape of the maximum concentration portion of the actual impurity concentration profile. Here, the maximum density portion refers to a region near the maximum density point. Further, the projection range and dispersion can be extracted by performing mathematical fitting so that the distribution based on the combined distribution function matches the actual impurity concentration profile.

  Next, a projection range of the second distribution function is calculated based on the extracted projection range of the first distribution function. Also, the variance of the second distribution function is calculated based on the extracted variance of the first distribution function.

  The impurity concentration profile is calculated by the combined distribution function to which the parameters and weighting coefficients obtained as described above are applied.

  In the above configuration, the projection range and dispersion of the distribution function (second distribution function) of the channeling component are calculated based on the projection range and dispersion of the distribution function (first distribution function) of the random component. A correlation can be established between the distribution function of the component and the distribution function of the channeling component. As a result, it is possible to provide a physical consistency between the two distribution functions such that the channeling component has a smaller ability to block the ion-implanted impurities than the random component.

  In the above configuration, the projection range of the second distribution function can be calculated by increasing the projection range of the corresponding first distribution function at a specific rate. The variance of the second distribution function at each implantation energy can be calculated by increasing the variance of the corresponding first distribution function at a specific rate. Thus, by setting the projection range and the variance of the first distribution function and the second distribution function to a constant ratio, the number of parameters for fitting can be reduced and the calibration can be simplified.

  Further, when extracting the projection range and dispersion of the first distribution function for the actual impurity concentration profile of each semiconductor substrate into which the same impurity is implanted with different implantation energies, the projection range for each implantation energy and The dispersion is extracted under conditions that decrease as the implantation energy decreases. Thereby, the projection range and dispersion are in a state having physical consistency with the implantation energy. For this reason, it becomes possible to perform a highly accurate ion implantation simulation.

  In addition, when extracting the weighting coefficient for the actual impurity concentration profile of each semiconductor substrate in which the same impurity is implanted with different implantation energy, the weighting coefficient for each implantation energy increases as the implantation energy decreases. Is extracted under the following conditions. As a result, the weighting coefficient can have physical consistency with a phenomenon in which the nuclear stopping power due to the elastic collision becomes smaller as the injection energy increases. For this reason, it becomes possible to perform a highly accurate ion implantation simulation.

  The distribution function may further include skewness and kurtosis as parameters. In this case, the skewness and kurtosis of the first distribution function are the shape of the tail portion in the actual impurity concentration profile in a state where the obtained projection range, dispersion, and weighting coefficient are applied to the composite distribution function. Can be extracted. At this time, the skewness and kurtosis of the second distribution function can be constant values. As a result, it is possible to perform ion implantation simulation with higher accuracy in consideration of skewness and kurtosis. When extracting the skewness and kurtosis of the first distribution function with respect to the actual impurity concentration profile of each semiconductor substrate into which the same impurity is implanted with different implantation energy, the skewness and kurtosis at each implantation energy are It is preferable that the extraction be performed under conditions that increase as the implantation energy decreases. As a result, since the skewness and kurtosis are in a state of physical consistency with the implantation energy, it is possible to perform a more accurate ion implantation simulation. Note that a Dual-Pearson function can be used as the composite distribution function.

  In addition, another ion implantation simulation method according to the present invention uses a first distribution function f1 having a projection range, dispersion, skewness, and kurtosis as parameters for a concentration profile of impurities introduced by ion implantation, and The second distribution function f2 is predicted based on the combined distribution function f3 = D × f1 + (1−D) × f2 combined by the weighting coefficient D. The first distribution function is a distribution function that represents a random component of the impurity concentration profile, and the second distribution function is a distribution function that represents a channeling component of the impurity concentration profile.

  In this ion implantation simulation method, first, the projection range and dispersion of the first distribution function, and the weighting coefficient, the shape of the maximum concentration portion in the actual impurity concentration profile of each semiconductor substrate into which impurities are introduced with different implantation energies. Based on the above, extraction is performed for each implantation energy under the condition that the value becomes smaller as the implantation energy becomes smaller. Next, the projection range of the second distribution function is increased for each implantation energy by increasing the projection range of the first distribution function extracted for each implantation energy by a specific ratio regardless of the implantation energy. Calculated. The variance of the second distribution function is calculated for each implantation energy by increasing the variance of the first distribution function extracted for each implantation energy at a specific rate regardless of the implantation energy.

  The skewness and kurtosis of the first distribution function can be obtained from the tail portion in the actual impurity concentration profile of each semiconductor substrate under the situation where the extracted projection range, variance, and weighting coefficient are applied to the composite distribution function. Based on the shape, extraction is performed for each implantation energy under conditions where the implantation energy decreases as the implantation energy decreases.

  The parameters of the first distribution function, the parameters of the second distribution function, and the weighting coefficient at the implantation energy requested to be predicted are the parameters of the first distribution function at the implantation energy obtained as described above, the second It is calculated based on the parameter of the distribution function and the weighting coefficient. The impurity concentration profile at the required implantation energy is predicted by the combined distribution function to which the calculated parameters and weighting coefficients are applied.

  In this configuration, the distribution function of the random component and the distribution function of the channeling component have physical consistency, and the projection range, dispersion, skewness, kurtosis, and weighting coefficient have physical consistency. It becomes a state with energy dependence. Therefore, it is possible to perform ion implantation simulation with higher accuracy.

  On the other hand, in another aspect, the present invention can provide an ion implantation simulator that implements the above-described ion implantation simulation method. That is, in the ion implantation simulator according to the present invention, the parameter setting unit sets each parameter of the first distribution function, each parameter of the second distribution function, and a weighting coefficient for any implantation energy requested to be predicted. And set it unambiguously. The profile calculation unit calculates the impurity concentration profile based on the uniquely set parameters of the first distribution function, the parameters of the second distribution function, and the weighting coefficient.

  Here, the parameter setting unit may set the projection range and dispersion of the first distribution function to a value that decreases as the injection energy decreases, and sets the weighting coefficient to a value that increases as the injection energy decreases. it can. The parameter setting unit is a value obtained by increasing the projection range and dispersion of the second distribution function at each implantation energy at a specific rate regardless of the implantation energy. Can be set to The parameter setting unit may set the skewness and kurtosis of the first distribution function to values that increase as the implantation energy decreases. At this time, the skewness and kurtosis of the second distribution function can be constant values. Furthermore, from another viewpoint, the present invention can also provide a program that causes a computer to execute the ion implantation simulation method.

  In the present invention, the projection range of the distribution function in the profile of the random component and the projection range of the distribution function in the channeling component, and the variance of the distribution function in the profile of the random component and the variance of the distribution function in the channeling component have a correlation, respectively. ing. As a result, a physical phenomenon that the random component has a higher ability to stop the ion-implanted impurities than the channeling component can be incorporated into the analysis model. For this reason, the concentration profile of the implanted impurity can be predicted with high accuracy.

  In addition, since the projection range and dispersion are reduced as the implantation energy decreases, and the weighting coefficient is extracted as a value that increases as the implantation energy decreases, physical consistency with the implantation energy dependency of the impurity concentration profile is extracted. Can be given. Thereby, in this invention, an impurity concentration profile can be uniquely set with respect to arbitrary implantation energy. For example, even when ion implantation is performed into a silicon substrate with a tilt angle of zero degrees and a high implantation energy such as 600 keV, the impurity concentration profile can be predicted with high accuracy.

  In particular, the ratio of the projection range of the distribution function in the random component to the projection range of the distribution function in the channeling component, and the ratio of the distribution function distribution in the random component to the distribution function dispersion in the channeling component are related to the implantation energy. If they are the same, the number of parameters of the distribution function for fitting can be reduced, and the calibration can be simplified.

  Further, by increasing the skewness and kurtosis of the distribution function in the random component as the implantation energy decreases, the influence of channeling becomes relatively large as the implantation energy decreases, and at the same time, impurity scattering is reduced. Consistency with the physical phenomenon of becoming smaller can be provided. Thereby, the impurity concentration profile can be predicted with higher accuracy.

  Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings. In the following, the present invention is embodied as an example of calculating an impurity concentration profile when arsenic ions are implanted into a silicon substrate. FIG. 1 is a schematic functional block diagram of the ion implantation simulator of this embodiment.

  The ion implantation simulator 10 includes a parameter setting unit 11, a parameter management unit 12, and a profile calculation unit 13. The profile calculation unit 13 calculates an impurity concentration profile by substituting the Pearson function parameters into the first Pearson function and the second Pearson function. Here, the first Pearson function represents an impurity concentration profile of a random component in which ions implanted into the single crystal substrate are scattered in a random direction by elastic collision with the crystal lattice, and the second Pearson function represents a channeling component. Represents the impurity concentration profile. At this time, the specific gravity of each of the first Pearson function and the second Pearson function is expressed by the weighting coefficient D shown in Equation 7 so that the total amount matches the injection dose.

Pearson function parameters used for impurity concentration profile calculation are set by the parameter setting unit 11. The parameter setting unit 11 reads the Pearson function parameters from the parameter management unit 12 according to the injection conditions such as the injection energy and the injection dose. The parameter management unit 12 corresponds to each parameter of the first Pearson function and the second Pearson function (projection range Rp, variance ΔRp, skewness γ, kurtosis β) and weighting coefficient D for each injection condition. The attached database is stored. In the following, the Pearson function parameters of the first Pearson function are denoted as Rp ₁ , ΔRp ₁ , γ ₁ , β _1, and the Pearson function parameters of the second Pearson function are denoted as Rp ₂ , ΔRp ₂ , γ ₂ , β ₂ And the weighting factor is denoted as D. The parameter management unit 12 includes a storage device such as an HDD (Hard Disk Drive).

  When performing the ion implantation simulation, the user inputs the implantation conditions directly via the input unit 21 or in a file state that can be recognized by the ion implantation simulator 10. The input injection conditions are held in the condition storage unit 22 constituted by, for example, a memory or an HDD. When the injection conditions are held in the condition storage unit 22, the parameter setting unit 11 reads data (in this case, injection energy and injection dose) necessary for setting the Pearson function parameters from the condition storage unit 22. The parameter setting unit 11 reads and holds each Pearson function parameter corresponding to the input injection energy from the parameter management unit 12 based on the read data.

The profile calculation unit 13 substitutes each Pearson function parameter held in the parameter setting unit 11 for the first and second Pearson functions (Dual-Pearson function), thereby obtaining the Dual-Pearson distribution at the input injection energy. Calculate. The profile calculation unit 13 first substitutes Pearson function parameters (Rp ₁ , ΔRp ₁ , γ ₁ , β ₁ ) for the _first Pearson function. Then, the integral value C ₁ of the first Pearson function in the range where the depth y is from zero to infinity is calculated. Next, the profile calculation unit 13 uses the Pearson function parameters (Rp ₂ , ΔRp ₂ , γ ₂ , β ₂ ) as the second Pearson function, and the integrated value C _{2 in} the range from the depth y to zero to infinity is C. Substituting under a condition satisfying ₁ × D = 1−C ₂ × (1-D), a normalized Dual-Pearson distribution is calculated. By multiplying the Dual-Pearson distribution by the implantation dose amount, an impurity concentration profile under the required implantation conditions is calculated and output via the output unit 23 by display display, data file output, or the like. The profile matching unit 14, the projection range / dispersion calculation unit 15, and the actual measurement value storage unit 16 will be described later.

  The Pearson function parameters stored in the parameter management unit 12 are extracted by performing calibration (hereinafter referred to as calibration) prior to the execution of the simulation, as in the past. FIG. 2 is a flowchart showing a calibration process performed in the ion implantation simulator 10 of the present invention. FIG. 3 is a schematic diagram of an impurity concentration profile formed by ion implantation.

  The calibration is performed by collating the impurity concentration profile calculated by reading the Pearson function parameter, which is the initial value, by the profile calculation unit 13 with the actual impurity concentration profile. Such collation can be performed, for example, by matching the two by the least square method using Pearson function parameters as variables. Hereinafter, the impurity concentration profile calculated by the profile calculation unit 13 is expressed as a predicted value, and the actual impurity concentration profile is expressed as an actually measured value.

As described above, the first and second Pearson function parameters and the weighting coefficient D are obtained for each injection energy. In the present embodiment, actual measurement values are obtained from a silicon substrate (hereinafter referred to as a sample substrate) in which arsenic (As) is implanted with different implantation energies at a tilt angle of zero degree. Here, three types of sample substrates are used. The conditions (implantation energy and implantation dose) of each sample substrate are (300 keV, 2.1E12 atoms / cm ² ), (400 keV, 2.1E12 atoms / cm ² ), and (600 keV, 2.1E12 atoms / cm ² ), respectively. . The actual measurement value is measured by SIMS or the like and stored in the actual measurement value storage unit 16 (see FIG. 1) via the input unit 21.

In the calibration process, first, the projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D of the first Pearson function are calibrated. In the case of ion implantation of impurities, if the implantation material is the same, it is considered that the peak depth (projection range) of the impurity concentration profile approaches the surface of the semiconductor substrate as the implantation energy decreases. As a result, it is considered that the scattering of the ion-implanted impurities is reduced and the spread of the distribution in the vicinity of the projection range is reduced. Therefore, calibration of Rp _1, dispersed .DELTA.Rp ₁ projected range is projected range as implantation energy decreases Rp _1, is dispersed .DELTA.Rp ₁ is a prerequisite to be smaller.

  Further, the energy of the impurity ions implanted into the semiconductor substrate is lost due to the loss due to the nuclear stopping ability and the electron stopping ability, and the impurity ions stop at the position where all the energy is lost. Nuclear stopping power is energy loss due to elastic scattering between implanted ions and crystal lattice (silicon atoms), and electron stopping power is due to the interaction (electron excitation) between implanted ions and electron clouds (electron cloud of silicon atoms). The resulting energy loss.

  The nuclear stopping power gradually decreases as the injection energy increases, and the electron stopping power increases gradually as the injection energy increases. That is, as the implantation energy increases, the ratio of impurity ions that lose energy due to elastic scattering and stop is reduced among all implanted impurity ions. As described above, the first Pearson function represents the concentration distribution of impurity ions that are stopped by the nuclear stopping power. For this reason, the calibration of the weighting coefficient D is based on the premise that the weighting coefficient D becomes smaller as the injection energy increases.

In the present embodiment, in the sample substrate group, calibration of the projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D is performed in descending order from the sample substrate having a high implantation energy. As a result, the projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D that satisfy the above preconditions are extracted.

  The parameter setting unit 11 first sets each Pearson function parameter of the first Pearson function and an initial value of the weighting coefficient D. As the initial value set at this time, a value that does not deviate from a commonly used value is used. For example, the default parameter values of the process simulator TSUPREM4 described above can be used.

  The profile calculation unit 13 substitutes the initial value set by the parameter setting unit 11 into a function obtained by multiplying the first Pearson function (the above formulas 1 to 6) and the weighting coefficient D, and the predicted value of the function is set. The calculation is performed (S21 in FIG. 2). The projection range / dispersion matching unit 141 (see FIG. 1) of the profile matching unit 14 calculates an error (in this case, a mean square error) between the actual measurement value and the predicted value whose injection energy is 600 keV. The error is obtained particularly for the maximum concentration portion 31 of the actual impurity concentration profile by limiting the error calculation range or the like. The maximum density portion 31 is an area near the maximum density point as shown in FIG.

Next, the parameter setting unit 11 changes the values of the projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D based on the error calculated by the projection range / dispersion collating unit 141 (at this time, the skewness γ ₁ and kurtosis β ₁ is fixed). The profile calculation unit 13 uses the Pearson function parameter after the change to calculate the predicted value again using a function obtained by multiplying the first Pearson function and the weighting coefficient D. The projection range / dispersion collating unit 141 calculates an error between the predicted value and the actually measured value. By repeating the above processing, the projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D that minimize the error are extracted as optimum values representing the measured value of the implantation energy 600 keV. The projection range Rp ₁ and the variance ΔRp ₁ are parameters that govern the shape of the maximum density portion 31. Therefore, by performing calibration based on the error of the maximum density portion 31, the projection range Rp ₁ and the dispersion are almost independent of the values of the skewness γ ₁ and the kurtosis β ₁ that mainly determine the profile of the tail portion. An optimum value of ΔRp ₁ can be determined (S22 in FIG. 2).

Next, the parameter setting unit 11 performs calibration for the actually measured value when the implantation energy is 400 keV (FIG. 2, S23No → S21). At this time, the initial value can be used as the initial value of the calibration. Here, however, the optimum value of the projection range Rp _{1 and} the optimum value of the variance ΔRp ₁ obtained with respect to the measured value of 600 keV described above are used. The optimum value of the weighting coefficient D is used as the initial value. As for the skewness γ ₁ and the kurtosis β ₁ , values that do not deviate from commonly used values are used as in the case of 600 keV described above.

The profile calculation unit 13 calculates a predicted value using a function obtained by multiplying the first Pearson function and the weighting coefficient D by the initial value set by the parameter setting unit 11. The projection range / dispersion collating unit 141 calculates an error in the maximum concentration unit 31 between the predicted value and the actually measured value of the injection energy of 400 keV. Then, similarly to the case where the implantation energy is 600 keV, the parameter setting unit 11 changes the values of the projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D based on the error (distortion γ ₁ , kurtosis) β ₁ is fixed). In this case, the parameter setting unit 11, Rp ₁ and dispersed .DELTA.Rp ₁ projected range changes the value of the dispersion .DELTA.Rp ₁ and Rp ₁ projected range in a range smaller than the optimum value at 600 keV. Further, the weighting coefficient D is changed in a range larger than 600 keV. The profile calculation unit 13 calculates a predicted value using a function obtained by multiplying the first Pearson function and the weighting coefficient D using the Pearson function parameter after the change, and the projection range / dispersion matching unit 141 calculates the predicted value. Calculate the error from the measured value. These processes are repeated, and the projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D that minimize the error are extracted as optimum values representing the actual measured value with an injection energy of 400 keV (S 22 in FIG. 2).

Since, even for the measured values when the injection energy is 300 keV, the projected range Rp _1, dispersion .DELTA.Rp _1, and the calibration of the weighting coefficient D is performed in the same manner, Rp ₁ projected range for each implantation energy, An optimum value of the variance ΔRp ₁ and the weighting coefficient D is obtained. The projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D thus determined satisfy the above-mentioned preconditions. The optimum values of the projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D are stored in the parameter management unit 12 in association with the injection energy.

When acquisition of the optimum values of the projection range Rp ₁ , variance ΔRp ₁ , and weighting coefficient D is completed, the projection range Rp ₂ and variance ΔRp ₂ of each parameter of the second Pearson function are set (S 23 Yes in FIG. 2). → S24). Here, the projection range Rp ₂ is calculated based on the projection range Rp ₁ of the first distribution function, and the variance ΔRp ₂ is calculated based on the variance ΔRp ₁ of the first distribution function. Accordingly, it is possible to correlate the projection range of the distribution function in the random component and the projection range of the distribution function in the channeling component, and the variance of the distribution function in the random component and the variance of the distribution function in the channeling component. The random component loses energy by both the above-described nuclear stopping power and electron stopping power, and the channeling component loses energy only by the electron stopping power. For this reason, it is considered that the random component is a component that has a larger ability to block impurities implanted by ion implantation than the channeling component. In the present embodiment, the ratio of the projection range between the random component and the channeling component is almost constant even when the injection energy is reduced, and the ratio of the dispersion between the random component and the channeling component reduces the injection energy. In some cases, it is considered to be almost constant. This is based on the physical phenomenon that the projection range Rp and the dispersion ΔRp change almost linearly with the implantation energy. For this reason, in this embodiment, Rp ₁ = k ₁ Rp ₂ (0 <k ₁ <1), ΔRp ₁ = k ₂ ΔRp ₂ (0 <k ₂ <1), and the projection range Rp ₂ and the variance ΔRp ₂ Determine. In addition, by setting the projection range and dispersion of the second Pearson function based on the projection range and dispersion of the first Pearson function in this way, the number of parameters of the distribution function for fitting can be reduced. Calibration can also be simplified.

The values of k ₁ and k ₂ can be set as follows. First, the profile calculator 13 determines that Rp ₁ = k ₁ Rp ₂ (0 <k ₁ <1), ΔRp ₁ based on the optimal value of the projection range Rp _{1 and} the optimal value of the variance ΔRp _{1 on} a specific sample substrate. = K ₂ ΔRp ₂ (0 <k ₂ <1), and the initial value of the second Pearson function is set. The projection range / dispersion matching unit 141 calculates an error between the predicted value and the impurity concentration profile in the random component of the specific sample substrate. In the present embodiment, an error in the vicinity of the boundary between the maximum density portion 31 and the tail portion 32 in FIG. 3 (region where the tail portion of the profile starts to stand out) is calculated. Based on the error, the parameter setting unit 11 changes the values of k ₁ and k ₂ . The parameter setting unit 11 sets the values of k ₁ and k ₂ that minimize the error to the projection range / dispersion calculation unit 15 (see FIG. 1) as optimum values. Here, k ₁ = 0.5 and k ₂ = 0.3.

The projection range / dispersion calculation unit 15 reads the optimal value of the projection range Rp ₁ of the first Pearson function obtained for each condition stored in the parameter management unit 12. By multiplying the optimum value of the read projection range Rp ₁ by k ₁ , the projection range / variance calculation unit 15 calculates the projection range Rp ₂ of the second Pearson function. The calculated projection range Rp ₂ of the second Pearson function is stored in the parameter management unit 12 in association with the injection energy. Similarly, the projection range / dispersion calculation unit 15 multiplies the optimal value of the _first Pearson function variance ΔRp ₁ obtained for each condition stored in the parameter management unit 12 by k ₂ . The variance ΔRp 2 of the Pearson function of ₂ is calculated. The calculated variance ΔRp ₂ is stored in the parameter management unit 12 in association with the injection energy. Thereby, the optimum values of the projection range Rp ₂ and the variance ΔRp ₂ of the second Pearson function corresponding to each implantation energy are obtained.

As described above, when the setting of the projection range Rp ₂ and variance ΔRp ₂ of the second Pearson function is completed, the skewness γ ₁ and the kurtosis β ₁ are subsequently calibrated. When the implantation energy is reduced, the influence of impurities entering the substrate deeply due to channeling becomes relatively large. Thus, the impurity concentration profile is considered to have a shape with a skirt. The skewness γ becomes 0 when the distribution is symmetric with respect to the peak position, and becomes positive when the skirt is drawn on the deep side. For this reason, in the calibration of the skewness γ ₁ and the kurtosis β ₁ , it is assumed that the skewness γ ₁ increases as the implantation energy decreases. Further, when the implantation energy is reduced, it is considered that the impurity scattering in the substrate at the time of ion implantation becomes small and the impurity concentration profile becomes a sharper shape. The kurtosis β increases as the distribution becomes sharper. For this reason, in the calibration of the skewness γ ₁ and the kurtosis β ₁ , it is also assumed that the kurtosis β ₁ increases as the implantation energy decreases. In the present embodiment, calibration of the skewness γ ₁ and the kurtosis β ₁ is performed in descending order with respect to the implantation energy in the sample substrate group. Thereby, the skewness γ ₁ and the kurtosis β ₁ that satisfy the above preconditions are extracted. In the calibration of the skewness γ ₁ and the kurtosis β ₁ , the projection ranges Rp ₁ and Rp ₂ and the variances ΔRp ₁ and ΔRp ₂ are fixed to the corresponding optimum values described above.

Furthermore, in the present embodiment, in the calibration of the skewness γ ₁ and the kurtosis β ₁ of the _first Pearson function, the skewness γ ₂ and the kurtosis β ₂ of the _second Pearson function are set to constant values, and γ ₂ > γ ₁ and β ₂ <β ₁ . This is because the channeling component is a component that receives energy loss only by the electron stopping power, and thus it is considered that a profile with a broad tail is maintained even when the injection energy is different. Although not particularly limited, in this embodiment, the skewness γ ₂ = 1.7 and the kurtosis β ₂ = 3.5.

The parameter setting unit 11 first sets initial values of the skewness γ ₁ and the kurtosis β ₁ . As the initial value to be set, a value that does not deviate from a commonly used value is used. At this time, the projection ranges Rp ₁ and Rp ₂ , the variances ΔRp ₁ and ΔRp ₂ , and the weighting coefficient D are fixed to the corresponding optimum values, that is, the optimum values obtained for the actually measured value of 600 keV. The profile calculation unit 13 calculates a predicted value using the Dual-Pearson function based on the initial value set by the parameter setting unit 11 (S25 in FIG. 2). The skewness / kurtosis matching unit 142 (see FIG. 1) of the profile matching unit 14 calculates an error between the predicted value and the actually measured value of the injection energy 600 keV. The error is obtained particularly for the tail portion of the actual impurity concentration profile by limiting the error calculation range or the like. As shown in FIG. 3, the tail portion 32 is a region deeper than the maximum concentration portion 31 with respect to the surface of the silicon substrate, and a deviation from the normal distribution occurs. Therefore, an error in skewness and kurtosis expressing a deviation from the normal distribution can be obtained from the tail portion 32.

The parameter setting unit 11 changes the values of the skewness γ ₁ and the kurtosis β ₁ based on the error calculated by the skewness / kurtosis matching unit 142. The profile calculation unit 13 calculates a predicted value using the Dual-Pearson function using the Pearson function parameter after the change. The skewness / kurtosis matching unit 142 calculates an error between the predicted value and the actually measured value. Repeating the above processing, skewness gamma ₁ and kurtosis beta ₁ that the error is minimized, the implantation energy is extracted as the optimum value of the skewness gamma ₁ and kurtosis beta ₁ representing the measured value of 600 keV ( FIG. 2 S26).

Next, the parameter setting unit 11 calibrates the actual measurement value when the implantation energy is 400 keV (FIG. 2, S27 No → S25). At this time, the initial value can also be used as the initial value of the calibration. Here, the optimum value of the skewness γ _{1 and} the optimum value of the kurtosis β ₁ obtained with respect to the measured value of 600 keV described above are used here. Use as initial value. The projection range Rp ₁ , the variance ΔRp ₁ , and the weighting coefficient D are fixed to the corresponding optimum values, that is, the optimum values obtained with respect to the actually measured value where the implantation energy is 400 keV, as in the case of 600 keV described above. The

The profile calculation unit 13 calculates a predicted value using the Dual-Pearson function based on the initial value set by the parameter setting unit 11. The skewness / kurtosis matching unit 142 calculates an error in the tail unit 32 between the predicted value and the actually measured value of the injection energy of 400 keV. Then, similarly to the case where the implantation energy is 600 keV, the parameter setting unit 11 changes the values of the skewness γ ₁ and the kurtosis β ₁ based on the error. In this case, the parameter setting unit 11, skewness gamma ₁ and kurtosis beta ₁ is in a range larger than the optimum value varying the skewness gamma ₁ and kurtosis beta ₁ in 600 keV. The profile calculation unit 13 calculates a predicted value by the Dual-Pearson function using the Pearson function parameter after the change, and the skewness / kurtosis matching unit 142 calculates an error between the predicted value and the actually measured value. The above processing is repeated, and the skewness γ ₁ and the kurtosis β _{1 at} which the error is minimized are extracted as optimum values representing the actually measured value with the injection energy of 400 keV (S 26 in FIG. 2).

Thereafter, the calibration of the skewness γ ₁ and the kurtosis β ₁ is similarly performed on the actually measured value with the implantation energy of 300 keV, and the optimum values of the skewness γ ₁ and the kurtosis β ₁ at each implantation energy are obtained. It is done. The skewness γ ₁ and the kurtosis β ₁ thus obtained satisfy the above-mentioned preconditions. The optimum values of the skewness γ ₁ and the kurtosis β ₁ are stored in the parameter management unit 12 in association with the injection energy. Then, when the optimum values of the skewness γ ₁ and the kurtosis β ₁ corresponding to all the actual measurement values are extracted, the calibration is completed (S27 Yes in FIG. 2).

An example of the optimum value of the Pearson function parameter obtained as described above is shown in FIG. The parameter table 41 in FIG. 4 shows each Pearson function parameter acquired for each sample substrate. As shown in FIG. 4, the projection ranges Rp ₁ and Rp ₂ and the dispersions ΔRp ₁ and ΔRp ₂ become smaller as the implantation energy decreases. Further, the projection range Rp ₂ and the variance ΔRp ₂ of the channeling component are larger at a fixed rate than the projection range Rp ₁ and the variance ΔRp _{1 of} the random component regardless of the injection energy. Further, the values of the skewness γ ₁ and the kurtosis β ₁ become larger as the implantation energy decreases, and the values of the skewness γ ₂ and the kurtosis β ₂ become constant values regardless of the implantation energy. ing. Further, the weighting coefficient D increases as the injection energy decreases. That is, each Pearson function parameter having continuity with respect to the implantation energy is acquired.

  5 to 7 show an ion implantation simulator using measured values of a sample substrate into which arsenic is ion-implanted with a tilt angle of zero degree at implantation energies of 300 keV, 400 keV, and 600 keV, and the Pearson function parameters shown in FIG. It is a figure which shows the calculated estimated value. 5 to 7, the origin in the depth direction of the impurity concentration profile data is the silicon surface at the time of ion implantation. From FIG. 5, it can be understood that when the implantation energy is 300 keV, a predicted value 52 corresponding to the actually measured value 51 is obtained. Moreover, it can be understood from FIG. 6 that when the implantation energy is 400 keV, a predicted value 62 that matches the actual measured value 61 is obtained. Furthermore, it can be understood from FIG. 7 that even when the implantation energy is 600 keV, a predicted value 72 that matches the measured value 71 is obtained.

  When the calibration is completed as described above, the ion implantation simulator 10 shown in FIG. 2 can perform an ion implantation simulation under an arbitrary implantation condition (particularly, an arbitrary high implantation energy condition). FIG. 8 is a flowchart showing processing performed by the ion implantation simulator 10 during the ion implantation simulation. At this time, the range of the injection energy that can be predicted is the range described in the injection parameter table. In the present embodiment, as shown in FIG. 4, the minimum energy is 300 keV to the maximum energy is 600 keV.

  When the injection conditions such as the injection energy and the injection dose are input via the input unit 21, the injection conditions are held in the condition storage unit 22 (S81 in FIG. 8). The parameter setting unit 11 reads the injection energy from the condition storage unit 22. When the Pearson function parameter that matches the read injection energy is stored in the parameter management unit 12, the parameter setting unit 11 reads the parameter from the parameter management unit 12 and holds it (S82 Yes → S86 in FIG. 8).

  When the Pearson function parameter that matches the read injection energy is not stored in the parameter management unit 12, the parameter setting unit 11 reads and holds the Pearson function parameter before and after the requested injection energy from the parameter management unit 12 (FIG. 8 S82No → S83). The parameter setting unit 11 performs linear interpolation of each read parameter, calculates and holds a Pearson function parameter corresponding to the requested injection energy (S84 in FIG. 8).

  When the Pearson function parameter corresponding to the injection energy requested to be predicted is held in the parameter setting unit 11 as described above, the profile calculation unit 13 represents each Pearson function parameter held in the parameter setting unit 11 as shown in Equation 7. Substituting into the Dual-Pearson function, the normalized Dual-Pearson distribution at the input injection energy is calculated. Further, the profile calculation unit 13 calculates an impurity concentration profile under the required implantation conditions by multiplying the Dual-Pearson distribution by the implantation dose amount, and outputs it to the output unit 23.

  As described above, according to the ion implantation simulator 10 of the present embodiment, the parameter setting unit 11, the parameter management unit 12, the profile calculation unit 13, the profile matching unit 14, the projection range / dispersion calculation unit 15, and the actual measurement value storage unit. The parameter defining unit 20 configured by 16 can unambiguously set each parameter of the first and second Pearson functions with respect to an arbitrary injection energy requested to be predicted. Further, by using the Pearson function parameter group acquired by the ion implantation simulation method of the present embodiment, the impurity concentration profile after ion implantation is predicted using the Pearson function, such as TSUPREM4, which is generally widely used. Even in a standard ion implantation simulator, the Pearson function parameters can be uniquely set for any implantation energy that has been predicted.

  The parameter setting unit 11, the profile calculation unit 13, the parameter collation unit 14, and the projection range / dispersion calculation unit 15 are, for example, hardware including a dedicated calculation circuit, a processor, and a memory such as a RAM and a ROM. And software stored in the memory and operating on the processor.

  In addition, a program for causing a computer to execute such an ion implantation simulation procedure uses a telecommunication line such as the Internet or stores it in a computer-readable recording medium, so that a related party or a third party Can be provided. For example, a program command is expressed by an electric signal, an optical signal, a magnetic signal, etc., and the signal is placed on a carrier wave and transmitted, so that the program is provided on a transmission medium such as a coaxial cable, copper wire, or optical fiber Can do. As a computer-readable recording medium, optical media such as CD-ROM and DVD-ROM, magnetic media such as a flexible disk, and semiconductor memory such as flash memory and RAM can be used.

  The high energy implantation of arsenic performed at the tilt angle of zero degree is composed of, for example, a high concentration P-type impurity layer, an N-type charge storage layer, a silicon substrate, or a well from the silicon substrate surface side in the manufacturing process of the solid-state imaging device The present invention is applied to ion implantation for forming an N-type charge storage layer of a photodiode (light receiving portion) made of a P-type layer. By comparing the impurity concentration profile predicted by the above simulation method with the desired impurity concentration profile to be formed in the semiconductor substrate, it is possible to predict the ion implantation conditions capable of forming the desired impurity profile. For this reason, a semiconductor device having desired characteristics can be easily manufactured by performing ion implantation of impurities under predicted implantation conditions.

  As described above, in the present invention, the projection range of the distribution function of the random component and the projection range of the distribution function of the channeling component, and the variance of the distribution function of the random component and the variance of the distribution function of the channeling component are correlated. Have. As a result, a physical phenomenon that the random component has a higher ability to stop the ion-implanted impurities than the channeling component can be incorporated into the analysis model. Further, the weighting coefficient D is extracted as a value that decreases as the injection energy increases. As a result, it is possible to incorporate into the analysis model a physical phenomenon in which the nuclear stopping power due to elastic scattering gradually decreases as the injection energy increases, and the influence of the electron stopping power gradually increases. For this reason, it is possible to predict the concentration profile of the ion-implanted impurity using a tilt angle of zero degrees with high accuracy.

  In addition, since the projection range and dispersion are extracted as values that become smaller as the implantation energy decreases, the dependence of the impurity concentration profile on the implantation energy can be physically matched. Thereby, in this invention, an impurity concentration profile can be uniquely set with respect to arbitrary implantation energy.

  In particular, the ratio between the projection range of the distribution function of the random component and the projection range of the distribution function of the channeling component, and the ratio of the distribution function of the random component and the distribution function of the channeling component depend on the implantation energy. If they are the same, the number of parameters of the distribution function for fitting can be reduced, and the calibration can be simplified.

  Furthermore, by increasing the skewness and kurtosis as the implantation energy decreases, the effect of channeling becomes relatively large as the implantation energy decreases, and at the same time the scattering of impurities decreases. And consistency. Thereby, the impurity concentration profile can be predicted with higher accuracy.

  The above-described embodiments do not limit the technical scope of the present invention, and various modifications and applications other than those already described are possible within the scope of the present invention. For example, the case where arsenic ions are implanted into the silicon substrate has been described above, but the material for the implantation material and the semiconductor substrate is arbitrary. Corresponding Pearson function parameters may be obtained in advance, and these materials may be designated as injection conditions. Further, the distribution function is not limited to the Pearson function, and other distribution functions having at least the projection range and the dispersion as parameters can be applied.

  The present invention can predict the impurity concentration profile of arsenic formed in a semiconductor substrate by high energy ion implantation of 300 keV to 600 keV with high accuracy using an analytical model, using a tilt angle of zero degree. It is useful as a simulation method or simulator for predicting an impurity concentration profile.

Schematic functional block diagram showing an ion implantation simulator of one embodiment of the present invention The flowchart which shows the calibration process of one Embodiment of this invention Schematic diagram illustrating calibration according to an embodiment of the present invention The figure which shows an example of the data table of the Pearson function parameter of one Embodiment of this invention The figure which shows the actual value corresponding to the predicted value calculated by one Embodiment of this invention. The figure which shows the actual value corresponding to the predicted value calculated by one Embodiment of this invention. The figure which shows the actual value corresponding to the predicted value calculated by one Embodiment of this invention. The flowchart which shows the ion implantation simulation of one Embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Ion implantation simulator 11 Parameter setting part 12 Parameter management part 13 Profile calculation part 14 Profile collation part 15 Projection range and dispersion | distribution calculation part 16 Actual value storage part 20 Parameter prescription | regulation part 21 Input part 22 Condition storage part 23 Output part 31 Maximum density | concentration Part 32 tail part 41 data table

Claims (14)

A first distribution function f1 representing a random component of an impurity concentration profile, and a channeling component of the impurity concentration profile, wherein the impurity concentration profile introduced by ion implantation into the semiconductor substrate has at least a projection range and dispersion as parameters. In the ion implantation simulation method for predicting the second distribution function f2 expressing the following distribution based on the combined distribution function f3 = D × f1 + (1−D) × f2 combined by the weighting coefficient D:
Extracting the projection range and variance of the first distribution function and the weighting factor based on the shape of the maximum concentration part in the actual impurity concentration profile;
Calculating a projection range of the second distribution function based on the extracted projection range of the first distribution function;
Calculating a variance of the second distribution function based on the variance of the extracted first distribution function;
Calculating an impurity concentration profile by a composite distribution function applying the obtained parameters and weighting factors;
An ion implantation simulation method characterized by comprising:   The projection range of the second distribution function is calculated by increasing the projection range of the corresponding first distribution function by a specific ratio regardless of the implantation energy, and the variance of the second distribution function is The ion implantation simulation method according to claim 1, wherein the ion implantation simulation method is calculated by increasing the variance of the corresponding first distribution function at a specific rate regardless of the implantation energy.   When the projection range and dispersion of the first distribution function are extracted from the actual impurity concentration profile of each semiconductor substrate into which the same impurity is implanted with different implantation energies, the projection range and dispersion for each implantation energy are extracted. The ion implantation simulation method according to claim 1, wherein the ion extraction is performed under a condition that decreases as the implantation energy decreases.   When the weighting coefficient is extracted from the actual impurity concentration profile of each semiconductor substrate in which the same impurity is implanted with different implantation energy, the weighting coefficient for each implantation energy increases as the implantation energy decreases. The ion implantation simulation method according to claim 1, wherein the ion implantation simulation is performed under conditions. The first and second distribution functions include skewness and kurtosis as parameters;
The skewness of the first distribution function based on the shape of the tail portion in the actual impurity concentration profile under the situation where the obtained projection range, variance, and weighting coefficient are applied to the composite distribution function. The ion implantation simulation method according to claim 1, further comprising a step of extracting the kurtosis and the kurtosis.   6. The ion implantation simulation method according to claim 5, wherein the skewness and kurtosis of the second distribution function are constant values.   When extracting the skewness and kurtosis of the first distribution function with respect to the actual impurity concentration profile of each semiconductor substrate implanted with the same impurity at different implantation energies, the skewness and kurtosis for each implantation energy 7. The ion implantation simulation method according to claim 5 or 6, wherein the ion implantation is extracted under a condition that increases as the implantation energy decreases.   6. The ion implantation simulation method according to claim 5, wherein the composite distribution function is a Dual-Pearson function. A first distribution function f1 and an impurity representing a random component of an impurity concentration profile, in which a concentration profile of an impurity introduced into a semiconductor substrate by ion implantation is a parameter of projection range, dispersion, skewness, and kurtosis In an ion implantation simulation method for predicting a second distribution function f2 representing a channeling component of a concentration profile based on a combined distribution function f3 = D × f1 + (1−D) × f2 combined by a weighting coefficient D.
Based on the shape of the maximum concentration portion in the actual impurity concentration profile of each semiconductor substrate into which impurities are introduced with different implantation energies, the projected range and dispersion of the first distribution function are reduced as the implantation energy decreases. Extracting for each implantation energy under the condition of, and extracting the weighting factor under conditions that increase as the implantation energy decreases;
The projection range of the first distribution function extracted for each implantation energy is increased at a specific rate regardless of the implantation energy, thereby calculating the projection range of the second distribution function for each implantation energy. Steps,
Calculating the variance of the second distribution function for each implantation energy by increasing the variance of the first distribution function extracted for each implantation energy at a specific rate regardless of the implantation energy;
Applying the obtained projection range, variance and weighting coefficient to the composite distribution function, and setting the skewness and kurtosis of the second distribution function to constant values, the actual impurity concentration profile of each semiconductor substrate Extracting the skewness and kurtosis of the first distribution function based on the shape of the tail portion for each implantation energy under the condition that the value increases as the implantation energy decreases;
Based on the parameters of the first distribution function, the parameters of the second distribution function, and the weighting coefficients obtained at the respective implantation energies, the parameters of the first distribution function at the implantation energy requested to be predicted, Calculating each parameter of the distribution function of 2 and a weighting coefficient;
Predicting an impurity concentration profile at the required implantation energy by a composite distribution function to which the calculated parameters and weighting coefficients are applied;
An ion implantation simulation method characterized by comprising: A first distribution function f1 and an impurity representing a random component of an impurity concentration profile, in which a concentration profile of an impurity introduced into a semiconductor substrate by ion implantation is a parameter of projection range, dispersion, skewness, and kurtosis In an ion implantation simulator for predicting a second distribution function f2 representing a channeling component of a concentration profile based on a combined distribution function f3 = D × f1 + (1−D) × f2 distribution function combined by a weighting coefficient D.
Means for unambiguously setting each parameter of the first distribution function, each parameter of the second distribution function, and the weighting coefficient with respect to any injection energy requested to be predicted;
Means for calculating an impurity concentration profile based on each parameter of the first distribution function set uniquely, each parameter of the second distribution function, and a weighting coefficient;
An ion implantation simulator comprising:   The setting means sets the projection range and dispersion of the first distribution function to a value that decreases as the injection energy decreases, sets the weighting coefficient to a value that increases as the injection energy decreases, The projection range and dispersion of the second distribution function at the implantation energy are set to values obtained by increasing the projection range and dispersion of the corresponding first distribution function at a specific rate regardless of the implantation energy. Ion implantation simulator.   The ion implantation simulator according to claim 10 or 11, wherein the setting means sets the skewness and kurtosis of the first distribution function to values that increase as the implantation energy decreases.   The ion implantation simulator according to claim 10, wherein the composite distribution function is a Dual-Pearson function. A first distribution function f1 and an impurity representing a random component of an impurity concentration profile, in which a concentration profile of an impurity introduced into a semiconductor substrate by ion implantation is a parameter of projection range, dispersion, skewness, and kurtosis Causes the computer to execute a process of predicting the second distribution function f2 representing the channeling component of the density profile based on the combined distribution function f3 = D × f1 + (1−D) × f2 distribution function combined by the weighting coefficient D. In the ion implantation simulation program,
In the computer,
Based on the shape of the maximum concentration portion in the actual impurity concentration profile of each semiconductor substrate into which impurities are introduced with different implantation energies, the projection range and dispersion of the first distribution function become smaller as the implantation energy decreases. And extracting the weighting factor for each implantation energy under conditions that increase as the implantation energy decreases; and
Calculating the projected range of the second distribution function for each implantation energy by increasing the extracted projection range of the first distribution function at a specific rate regardless of the implantation energy;
Calculating the variance of the second distribution function for each implantation energy by increasing the variance of the extracted first distribution function at each implantation energy at a specific rate regardless of the implantation energy;
Applying the obtained projection range, variance and weighting coefficient to the composite distribution function, and setting the skewness and kurtosis of the second distribution function to constant values, the actual impurity concentration profile of each semiconductor substrate Extracting the skewness and kurtosis of the first distribution function based on the shape of the tail portion for each implantation energy under conditions where the implantation energy decreases, and
Based on the parameters of the first distribution function, the parameters of the second distribution function, and the weighting coefficients obtained at the respective implantation energies, the parameters of the first distribution function at the implantation energy requested to be predicted, Calculating each parameter of the distribution function of 2 and a weighting coefficient;
Predicting an impurity concentration profile at the required implantation energy by a composite distribution function to which the calculated parameters and weighting coefficients are applied;
An ion implantation simulation program characterized in that

Images