JP2010103402A - Method of generating ion implantation distribution and simulation thereof - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of generating an ion implantation distribution and a simulation thereof which can accurately reproduce actual ion implantation distribution, over a range extending from an energy level of as low as 1 keV, to an energy level of as high as several MeVs. <P>SOLUTION: When a locus of implantation ions is calculated by the Monte Carlo method to generate an ion implantation distribution, an electron stopping power S<SB>e</SB>with respect to implantation ions is expressed by a combination of an electron stopping power S<SB>eL</SB>of the Lindhard model, and an electron stopping power S<SB>e-mB</SB>, corresponding to a modification of the electron stopping power S<SB>eB</SB>of the Bethe model. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

The present invention relates to an ion implantation distribution generating method and simulator relates setting manner of the electronic stopping power S _e for generating a high ionic implantation distribution accuracy over a wide energy range by Monte Carlo simulation.

  In a silicon integrated circuit device, introduction of impurities into a silicon substrate is generally performed by ion implantation. In the process construction of such a silicon integrated circuit device, it is necessary to determine ion implantation conditions for obtaining a necessary element structure, and such ion implantation conditions are determined by simulation.

  Conventionally, commercialized simulators predict such an ion implantation profile in a silicon substrate based on an enormous ion implantation database. This ion implantation database is a set of parameters for an analytical function such as a Gaussian function, a joint half Gaussian function, a Pearson function, a dual Pearson function, or a tail function.

  These analytical models are only for representing ion implantation profiles and are not based on physical evidence. Therefore, when there is little experimental data regarding ion implantation distribution, there is a problem that it is impossible to predict with high accuracy.

  In recent years, various ions such as C, N, and F have been used to suppress temporary diffusion associated with an annealing process in a later process, and a theoretical prediction of the profile of these ions is required.

In order to meet such a demand, Monte Carlo is known as a means for theoretically predicting the ion implantation distribution into the amorphous layer. This interaction between the incident ions and the substrate, based on the physics of nuclear stopping power S _n and the electronic stopping power S _e, in which continue to track the trajectory of the incident ions.

In other words, it is assumed that the interaction between the incident ion and the substrate consists of two mechanisms, one is the interaction between the ion and the nucleus of the substrate atom, and the other is the interaction between the ion and the electron of the substrate atom. an action, the former corresponds to the nuclear stopping power S _n, the latter corresponds to the electronic stopping power S _e. Such an interaction mechanism is directly implemented in Monte Carlo simulation in SRIM and other Monte Carlo simulators (see, for example, Non-Patent Document 1).

This theory is also effective in a general case where ions are implanted into an arbitrary substrate, and the accuracy can be further improved by tuning the electron stopping power. FIG. 15 shows a calculation model in which ions having mass number M ₁ , atomic number Z ₁ , energy T _1i (velocity v _1i ) interact with atoms having mass number M ₂ and atomic number Z ₂ constituting the substrate. Energy T _2f , scattering angle Φ, velocity of ions after interaction ν _1i , and substrate atom velocity ν _2i ,
T _2f / T _1i = 2M ₂ ν _2i ² sin ² (Φ / 2) / [(1/2) M ₁ ν _1i ² ]
= (4M ₂ / M ₁ ) {[M ₁ v _1i / (M ₁ + M ₂ )] ² / ν _1i ² }
× sin ² (Φ / 2)
= [4M ₂ M ₁ / (M ₁ + M ₂ ) ² ] sin ² (Φ / 2) (1)
It is expressed.

つまり、注入されたイオンは、核との相互作用により、
ΔＥ_ｎ＝Ｔ_２ｆ
のエネルギーを失う。 Here, assuming that the distance between the ions and the substrate atoms is r, the collision parameter is b, and the potential energy is V (r), the transfer energy T _2f is obtained as the following equation (2).

In other words, the implanted ions are interacted with the nucleus,
ΔE _n = T _2f
Lose energy.

ここで、半径ｂの円周上の位置、即ち角度θは、Ｒａｎｄ（ｎ）をｎが０から１の間の乱数とすると、
θ＝２πＲａｎｄ（ｎ）
の関係から求まる。 Further, the scattering angle Φ accompanying the interaction is expressed by the following formula (3).

Here, the position on the circumference of the radius b, that is, the angle θ is Rand (n), where n is a random number between 0 and 1,
θ = 2πRand (n)
It is obtained from the relationship.

なお、ρ＝ｒ／ａｕである。 Further, as the potential energy V (r), for example, the potential energy of the following Ziegler-Litmark-Biersak (ZLB) is used (for example, see Non-Patent Document 2).
V (r) = (e ² Z ₁ Z ₂ / r) f (ρ) (4)
However,

Note that ρ = r / au.

This determines the energy and direction after the collision. Next, the same calculation is newly repeated with the implantation energy, and the ion trajectory is traced to obtain the ion distribution profile.
Since this Monte Carlo simulation follows each trajectory of particles, it is necessary to perform tens of thousands or more calculations in order to reduce statistical errors.

There is such a Monte above the important physical parameters of Carlo simulation ions and electrons stopping power S _e that corresponds to the interaction between the electrons of the substrate atoms, as the standard model for this is shown by the following formula (6) The thing of Lindhard (Linthard) is known (for example, refer nonpatent literature 3).

According to such a Lindhard model, a relatively good prediction can be made when the implantation energy is in the range of several tens of keV. Note that in the equation (6), although the addition of _{r e} a fitting parameter for each atom, the original electronic stopping power _{S eL} of Lindhard corresponds to _r e = 1.

Electronic stopping power _{S eL} in this Lindhard model assumes the interaction between the electron cloud and the substrate atom ions. However, since the electron cloud associated with the ions is stripped in the high energy region, the assumption does not hold, and therefore there is a problem that the approximation becomes very bad in the high energy region.

The critical velocity v _c corresponding to the application limit of such a model is given by assuming that v ₀ is the Bohr velocity.
v _c = Z ₁ ^2/3 v ₀ (7)
It is represented by Therefore, the critical energy E corresponding to the application limit of the model is
^{_{E = (M 1/2)}} v c 2 = (M 1/2) (Z 1 2/3 v 0) 2 ··· (8)
It becomes. Incidentally, the critical energies for B, P, and As are 2 MeV, 10 MeV, and 29 MeV, respectively. In recent years, ion implantation has been performed with an energy of MeV order for the formation of a well region, but the Lindhard model cannot be applied in such an energy region.

但し、平均電子励起エネルギーＩは、経験的に下記の式（１０）で表される。

On the other hand, a Bethe model is known as a dedicated model for a high energy region (see, for example, Non-Patent Document 4). Electronic stopping power S _eB in this model of Bethe, the density of the N substrate atoms, electron mass m _e, when the average electron excitation energy I, represented by the following formula (9).

However, the average electron excitation energy I is empirically represented by the following formula (10).

In this Bethe model, it is assumed that the implanted ions are completely stripped of the electron cloud, and this is effective when the ion implantation rate is equal to or higher than the critical velocity v _c represented by the above equation (9). It becomes.

  Therefore, Ziegler proposed a model of Lindhard's model in the low energy region and a model close to the Bethe model in linear response theory in the high energy region, and connected them, and many of them for many combinations And proposed an electron stopping power model in a wide energy range (for example, see Non-Patent Document 3 above).

なお、式（１１）における係数Ｃ_１，Ｃ_２，Ｃ_３，Ｃ_４は、各基板種毎にテーブルに与えられている。 Ziegler empirically represents the electron stopping power S _e ¹ by the following formula (11), where S _e ¹ is the electron stopping power when hydrogen ions are implanted into various substrates.

Note that the coefficients C ₁ , C ₂ , C ₃ , and C ₄ in Equation (11) are given to the table for each substrate type.

なお、式（１２）におけるζ_Ｚ１ ² は、電子雲の剥奪の程度を表している（必要ならば、上述の非特許文献３参照）。 The electronic stopping power _{S e} atomic number for ions of _{Z 1} is expressed by the following equation (12).

Note that ζ _Z1 ² in equation (12) represents the degree of electron cloud deprivation (see Non-Patent Document 3 above if necessary).

なお、式（１３）におけるＥ_ｃはモデルを切り替える臨界エネルギーであり、
Ｅ_ｃ／Ｍ_１＝２５ｋｅＶ／ａｍｕ ・・・（１４）
で表される。したがって、臨界エネルギーＥ_ｃにおける電子阻止能Ｓ_ｅ ^Z1（Ｅ_ｃ）は、式（１２）から、下記の式（１５）で表される。

Ziegler sets the relationship represented by the following formula (13) as the electron stopping power S _e ^Z1 (E) in the low energy region.

Incidentally, _{E c} in equation (13) is a critical energy for switching the model,
E _c / M ₁ = 25 keV / amu (14)
It is represented by Therefore, the electron stopping power S _e ^Z1 (E _c ) at the critical energy E _c is expressed by the following formula (15) from the formula (12).

As is clear from Equation (13), the electron stopping power S _e ^Z1 of the Ziegler model is proportional to E ^0.45 in the low energy region, which is similar to the electron stopping power S _eL of the Lindhard model. It shows energy dependence.
SRIM-2003, http: // www. srim. org / J. et al. F. Ziegler, J. et al. P. biersack, and U.S. Litmark, The stopping and range of ions in solid, Pergamom, 1985 J. et al. Lindhard, and M.M. Scharff, Phys / Rev. , Vol. 124, no. 1, 1961, p. 128 H. A. Bethe, Ann. Phys. (Leipzig) Vol. 5, 1930, p. 325

  However, the Ziegler model has a problem that its handling is complicated, and there is a problem that quantitativeness is not verified by experimental data. As will be described later, when collating with the experimental data by SIMS, the deviation from the experimental data by SIMS becomes large in the high energy region.

  In recent years, ion implantation is performed at a low energy of about 1 keV in order to form a shallow junction, but there is a problem that the accuracy of the Lindhard model in such a low energy region has not been verified. . This is because there is no physical problem in ion implantation at a low energy of about 1 keV, but the resolution limit in SIMS necessary for verification affects.

  Therefore, an object of the present invention is to accurately reproduce an actual ion implantation distribution from a low energy region of about 1 keV to a high energy region of several MeV.

From one aspect of the present invention, the trajectory of the implanted ions an ion implantation distribution generating method for calculated generate an ion implantation distribution by Monte Carlo method, the electronic stopping power S _e for the implanted ions, fitting parameter a r _e , Z ₁ is the atomic number of the implanted ions, Z ₂ is the atomic number of the atoms constituting the substrate, M ₁ is the mass number of the implanted ions, and E is the incident energy. There is provided an ion implantation distribution generation method characterized by a combination of an electron stopping power S _eL and a modified electron stopping power S _{e-mB obtained} by correcting the electron stopping power S _eB of the _{Bethe model} .

In another aspect of the present invention, there is provided a simulator having a function of generating an ion implantation distribution by calculating a locus of implanted ions by a Monte Carlo method. simulator is provided, characterized by employing a capacity S _e.

  According to the disclosed ion implantation distribution generation method and simulator, an actual ion implantation distribution can be accurately reproduced from a low energy region of about 1 keV to a high energy region of several MeV.

Referring now to FIGS. 1 to 11, will be explained an ion implantation distribution generation method according to the embodiment of the present invention, prior to, using the electronic stopping power S _eL of Lindhard with fitting parameters r _e Examine the suitability of Monte Carlo simulation. As the nuclear stopping power S _n using a nuclear stopping power S _n used in the conventional Monte Carlo simulation.

  First, in order to examine the suitability of Monte Carlo simulation, a sample was prepared, ions were implanted, and the distribution was measured by SIMS. As a sample, an α-Si film having a thickness of about 1 μm was formed at 550 ° C. by a low pressure chemical vapor deposition method (LPCVD method) on a single crystal Si substrate to obtain a sample for ion implantation. A sample was also prepared in which Ge was ion-implanted into crystalline Si to form an amorphous layer.

  The ion implantation distribution in such an α-Si film is almost the same as the ion implantation distribution in the surface and near the peak value, so that the difference in the distribution of the tail part affected by the ion channeling is different. In order to compare with the simulation results for the amorphous film, the ion implantation profile in single crystal Si was also used.

  In addition, the SIMS measurement detects only secondary ions from a narrow central region by providing an electronic gate mechanism to avoid the edge effect among secondary ions emitted by raster scanning of primary ions. Thus, an ion implantation profile was created. The measured ion implantation profile was calibrated using a surface shape measuring instrument (4 Dektak 2A: trade name manufactured by ULVAC), and the concentration scale was adjusted by the actual ion dose.

  Recently, the basic SIMS measurement mechanism has been elucidated, and the accuracy of the ion distribution profile of shallow junctions by ion implantation at a low acceleration energy such as 1 keV, which has been suspected in the past, has been improved. It is expensive.

FIG. 1 is an explanatory diagram of a measurement result by SIMS and a simulation result by a Monte Carlo simulator when ions of B, P, and As are implanted into α-Si with an acceleration energy of 80 keV. In this _simulation, a r e = 1.0, uses an original electronic stopping power _{S eL} of Lindhard. As shown in FIG. 1, in the case of As and P, a good agreement between the SIMS data and the simulation result is seen, but in the case of B, a large difference is seen between the SIMS data and the simulation result.

2, in order to eliminate the deviation of the SIMS data and the simulation result of B ion is an explanatory diagram of an ion implantation profile when varying the fitting parameters r _e. As shown in FIG. 2, the ion implantation profile becomes shallower as the fitting parameter r _e becomes larger. When r _e = 1.5, the SIMS data and the simulation result are in good agreement with the entire profile.

3 to 8, there is shown a comparison of the ion implantation profile when optimized fitting parameters r _e to various ions. FIG. 3A shows a profile when 1 × 10 ¹⁵ cm ⁻² B ions are implanted into α-Si at 40 keV, 80 keV, and 160 keV, respectively. In the case of B ions, r _e = 1.55 is the optimum value. FIG. 3B shows a profile when 1 × 10 ¹⁵ cm ⁻² of C ions are implanted into single crystal Si at 40 keV, 80 keV, and 160 keV, respectively. In the case of C ions, r _e = 1.5 is the optimum value, and although there is a divergence at the tail, it can be said that the overall match is good.

FIG. 4A shows a profile when 1 × 10 ¹⁵ cm ⁻² of N ions are implanted into single crystal Si at 40 keV, 80 keV, and 160 keV, respectively. In the case of N ions, r _e = 1.4 is the optimum value, and although there is a divergence at the tail, it can be said that the overall match is good. FIG. 4B shows a profile when 1 × 10 ¹⁵ cm ⁻² F ions are implanted into single-crystal Si at 40 keV, 80 keV, and 160 keV, respectively. In the case of F ions, r _e = 1.0 is the optimum value, and although there is a divergence at the tail portion, it can be said that the overall match is good.

FIG. 5A shows a profile when 1 × 10 ¹⁵ cm ⁻² of Si ions are implanted into single-crystal Si at 20 keV, 40 keV, 80 keV, and 160 keV, respectively. In the case of Si ions, r _e = 1.25 is an optimum value, and although there is a divergence at the tail portion, it can be said that the overall match is good. FIG. 5B shows a profile when 1 × 10 ¹⁵ cm ⁻² of P ions are implanted into α-Si at 40 keV, 80 keV, and 160 keV, respectively. In the case of P ions, r _e = 1.2 is the optimum value.

FIG. 6A shows a profile when 1 × 10 ¹⁵ cm ⁻² Ga ions are implanted into single-crystal Si at 20 keV. In the case of Ga ions, r _e = 1.0 is the optimum value, and although there is a divergence at the tail, it can be said that the overall match is good. FIG. 6B shows a profile when Ge ions of 1 × 10 ¹⁵ cm ⁻² are implanted into single crystal Si at 20 keV, 40 keV, and 80 keV, respectively. In the case of Ge ions, r _e = 1.0 is the optimum value, and although there is a divergence at the tail portion, it can be said that the overall match is good.

FIG. 7A shows a profile when 1 × 10 ¹⁵ cm ⁻² As ions are implanted into α-Si at 40 keV, 80 keV, and 160 keV, respectively. In the case of As ions, r _e = 1.0 is the optimum value. FIG. 7B shows a profile when 1 × 10 ¹⁵ cm ⁻² In ions are implanted into single crystal Si at 10 keV, 20 keV, 40 keV, 80 keV, and 160 keV, respectively. In the case of In ions, r _e = 1.0 is the optimum value.

FIG. 8A shows a profile when 1 × 10 ¹⁵ cm ⁻² of Sb ions are implanted into single crystal Si at 10 keV, 20 keV, 40 keV, 80 keV, and 160 keV, respectively. In the case of Sb ions, r _e = 1.0 is the optimum value.

FIG. 8 (b) summarizes the optimum value of the fitting parameter r _e in each ion in the periodic form. As apparent from FIG. 8 (b), as as r _e is the atomic number is increased in the same cycle, therefore, it decreases as going to the right in the figure, also, atomic number increases in the same genus, therefore, the period It turns out that it becomes small as becomes large.

From this result, in the range of several 10keV~ hundreds 10 keV, by optimizing the fitting parameters r _e for each ion, it has been confirmed that it is possible to obtain the ion implantation profile in alpha-Si by Monte Carlo simulation.

Next, the reproducibility of the ion implantation profile in a shallow junction by low energy ion implantation near 1 keV will be examined. FIG. 9A shows a profile when 1 × 10 ¹⁵ cm ⁻² B ions are implanted into single-crystal Si at 0.3 keV, 0.5 keV, 1 keV, and 3 keV, respectively. Again, good agreement between the SIMS data and the simulation results is seen when r _e = 1.55.

FIG. 9B shows a profile when 1 × 10 ¹⁵ cm ⁻² As ions are implanted into single-crystal Si at 1 keV and 3 keV, respectively. Again, when r _e = 1.0, there is a relatively good agreement between the SIMS data and the simulation results.

These results, fitting parameters r _e is no implantation energy dependence was found to take the ion species-specific values. Accordingly, in the energy range of 0.3keV~ hundred 10 keV, by optimizing the fitting parameters _{r e,} as can be predicted with high ion implantation profile accuracy by Monte Carlo simulation using the electronic stopping power _{S eL} of Lindhard I understand that The optimum value of the fitting parameter r _e of each ion is obtained from the measurement results of the SIMS, it is stored as a database in advance Monte Carlo simulator.

  Next, the validity of the simulation in the high energy region near 1 MeV will be examined. FIG. 10A shows the ion implantation profile of B ions in each model, and FIG. 10B shows the ion implantation profile of P ions in each model. Here, for the sake of convenience, a model ion implantation profile (θ = 1.45) proposed by the present invention is also shown.

  As described above, in the high energy region, the profile according to the Lindhard model is greatly different from the profile according to the Bethe model. The profile by the Ziegler model is originally a compromise of the two models by the Ziegler model, so it is close to the Lindhard model in the low energy region and close to the Bethe model in the high energy region.

However, as will be described later, the Ziegler model has a large deviation from SIMS data in the high energy region, so that a highly accurate profile cannot be predicted. Therefore, the present inventor has an electronic stopping power Se for implanted ions, and electrons stopping power _{S eL} of Lindhard model represented by the above formula (6), fixes an electron blocking that fixes the electronic stopping power _{S eB} of Bethe model We propose to express it in combination with the capability _Se-mB .

In this case, the corrected electron stopping power S _e-mB is a corrected electron blocking represented by the following formula (16) in which the value below the peak value of the electron stopping power _SeB of the Bethe model is a constant value equal to the peak value. The function _Se-mB is used.

なお、この修正電子阻止能Ｓ_ｅ-ｍＢは結果的に、Ｂｉｅｒｓａｃｋ（ビールザック）が提案しているモデルを簡略化した式になっている（必要ならば、Ｊ．Ｐ．Ｂｉｅｒｓａｃｋ，ａｎｄ Ｌ．Ｇ．Ｈａｇｇｍａｒｋ，Ｎｕｃｌｅａｒ Ｉｎｓｔ．Ａｎｄ Ｍｅｔｈ．，ｖｏｌ．１７４（１９８０），ｐ．２５７ 参照）。 Alternatively, the corrected electron stopping power S _e-mB represented by the following formula (17) is used as the corrected electron stopping power S _e-mB .

As a result, this modified electron stopping power _Se-mB is a simplified expression of the model proposed by Biersack (if necessary, JP Biersack, and L. G. Haggmark, Nuclear Inst. And Meth., Vol. 174 (1980), p.257).

Next, the corrected electron stopping power S _e-mB and the Lindhard model electron stopping power _SeL are combined in the form represented by the following equation (18) using θ as a fitting parameter.

Thus, the simulation can be performed analytically by combining the modified electron stopping power Se _-mB and the Lindhard model electron stopping power _SeL . The electronic stopping power _{S e} bound in this case, the electronic stopping power _{S eL} next Lindhard model in the low energy region, the high-energy side and fix the electronic stopping power S _e-mB of Bethe.

11 (a) is modified according to formula (16) electronic stopping power S _e-mB, electron stopping power _{S eL} of Lindhard model, and is a view comparatively showing the electronic stopping power _{S e} of the present invention . Here, as the electronic stopping power S _e of the present invention shows a case of fitting parameters θ three you 1,1.45,2. This θ represents empirically the degree of transition from the Lindhard model to the Bethe model.

FIG. 11 (b) shows a case where the electronic stopping power S _e of the present invention is applied to an ion implantation profile prediction of B ions. Here shows the profile when injected into the single-crystal Si and B ions of 1 × 10 ¹³ cm ^-2 at 2000 keV (= 2 MeV), fitting parameters _{r e} is the 1.55 as described above.

  As is apparent from FIG. 11B, when θ is 1, the profile is deeper than the actually measured value, and when θ is 2, the profile is shallower than the actually measured value, and good agreement is obtained when θ = 1.45. It was observed. Note that θ = 1 corresponds to the above-described Biersack model, and therefore the accuracy of profile prediction by the Biersack model is inferior to that of the present invention in the high energy region.

Thus, in the present invention, the modified electron stopping power Se _-mB and the Lindhard model electronic stopping power _SeL are combined so that an analytical simulation is possible, and the number of parameters is small, so that A highly accurate ion implantation profile can be generated by simulation.

Based on the above, the ion implantation distribution generation method according to the first embodiment of the present invention will be described with reference to FIGS. In the first embodiment of the present invention, in the above formula (18), θ = 1.45 and theta = 1.55 as B ions, set the fitting parameters _{r e} 1.55 for the P ions and As ions A simulation was performed. In each figure, a profile based on the Lindhard model and a profile based on the Ziegler model are also shown.

FIG. 12A shows an ion implantation profile of B ions when θ = 1.45. Here, B ions of 1 × 10 ¹³ cm ⁻² are formed into single crystal Si at 400 keV, 1200 KeV, and 2000 keV, respectively. The profile when injected is shown. As is clear from FIG. 12A, at 400 keV, both models have good agreement with the SIMS data.

  However, the difference between the Lindhard model and the Ziegler model from SIMS data increases as the energy increases to 1200 keV and 2000 keV. In comparison between the Lindhard model and the Ziegler model, the Ziegler model is slightly closer to SIMS data, but it is understood that the actual profile cannot be predicted. On the other hand, the ion implantation profile according to the model of the present invention was in good agreement with the SIMS data at each implantation energy except for the tail distribution.

FIG. 12B shows an ion implantation profile of B ions when θ = 1.55. Here, B ions of 1 × 10 ¹³ cm ⁻² are formed into single crystal Si at 400 keV, 1200 KeV, and 2000 keV, respectively. The profile when injected is shown. Also in this case, the result is the same as the case of FIG. 12A in which θ = 1.45.

FIG. 13A shows an ion implantation profile of P ions when θ = 1.45. Here, 1 × 10 ¹³ cm ⁻² of P ions are converted into single crystal Si at 400 keV, 1200 KeV, and 2000 keV, respectively. The profile when injected is shown. Again, as described above, the simulation was performed to set the fitting parameters r _e to 1.2.

  As is clear from FIG. 13A, at 400 keV, all models have good agreement with SIMS data. However, in the Ziegler model, the deviation from SIMS data increases as the energy increases to 1200 keV and 2000 keV, and in the case of P ions, it is inferior to the Lindhard model. On the other hand, the ion implantation profile according to the model of the present invention was in good agreement with the SIMS data at each implantation energy except for the tail distribution. As described above, this is because the critical energy for P is 10 MeV, and the critical energy is not reached at 2 MeV (= 2000 keV).

FIG. 13B shows an ion implantation profile of P ions when θ = 1.55. Here, 1 × 10 ¹³ cm ⁻² of P ions are converted into single crystal Si at 400 keV, 1200 KeV, and 2000 keV, respectively. The profile when injected is shown. Also in this case, the result is the same as in the case of FIG. 13A in which θ = 1.45.

FIG. 14 shows an As ion implantation profile when θ = 1.55. In this example, 1 × 10 ¹³ cm ⁻² As ions are implanted into single crystal Si at 300 keV, 600 KeV, and 1000 keV, respectively. Shows the profile. Again, as described above, it was simulated by setting the fitting parameters r _e to 1.0.

  As is clear from FIG. 14, in the case of As, both models have good agreement with the SIMS data. This is also because the critical energy for As is 29 MeV as described above, and the critical energy is not reached at 2 MeV.

Thus, in the first embodiment of the present invention, since the coupling as described above formula (18) the electronic stopping power S _e of θ as fitting parameters, in a wide energy range of 0.3keV~ number MeV, It became possible to generate ion implantation distribution with high accuracy regardless of ion species.

  In the first embodiment, the fitting parameter θ is set to 1.45 or 1.55. However, this value is not absolute, and a lot of data will be accumulated in the future to improve the fitting accuracy. This may change slightly.

It is explanatory drawing of the measurement result by SIMS at the time of ion-implanting B, P, and As to (alpha) -Si, and the simulation result by a Monte Carlo simulator. Is an explanatory view of an ion implantation profile of B ion in the case of varying the fitting parameters r _e. It is a comparison figure of the SIMS data of the ion implantation profile of B ion and C ion, and a simulation result. It is a comparison figure with SIMS data of the ion implantation profile of N ion and F ion, and a simulation result. It is a comparison figure of SIMS data of the ion implantation profile of Si ion and P ion, and a simulation result. It is a comparison figure of SIMS data of the ion implantation profile of Ga ion and Ge ion, and a simulation result. It is a comparison figure of SIMS data of the ion implantation profile of As ion and In ion, and a simulation result. Is an illustration of the optimum values of the fitting parameters r _e in comparison diagram and each ion of the SIMS data and the simulation results of ion implantation profiles of Sb ion. It is a comparison figure with SIMS data and the simulation result in the low energy area | region of B ion and As ion. It is an ion implantation profile of B ion and P ion in each model. It is an illustration of the application of the electronic stopping power S _e of comparison diagram with the invention of the electronic stopping power to the ion implantation profile prediction of B ions. It is a comparison figure of the ion implantation profile of B ion by each model. It is a comparison figure of the ion implantation profile of P ion by each model. It is a comparison figure of the ion implantation profile of As ion by each model. It is a calculation model.

Claims (6)

An ion implantation distribution generation method for generating an ion implantation distribution by calculating a locus of implanted ions by a Monte Carlo method,
Wherein for implanted ions electrons stopping power S _e, fitting parameters r _e, the Z ₁ implanted ions of the atomic number, atomic number of the atoms of Z ₂ constituting the substrate, the mass number of the M ₁ implanted ions, incident E In the case of energy, the electron stopping power _SeL of the _Linthard model represented by the following formula:
A method for generating an ion implantation distribution, characterized in that the electron stopping power S _eB of the _{Bethe model} is represented by a combination with a modified electron stopping power S _e-mB .

Wherein the electronic stopping power S _e of the implanted ions, the θ as a fitting parameter, the ion implantation distribution generating method according to claim 1, characterized in that expressed by the following equation.

As the modified electronic stopping power S _e-mB, q the elementary charge, vacuum permittivity of .epsilon.0, electron mass m _e, when the average electron excitation energy I, energy electron stopping power S _eB of the Betemoderu ion implantation distribution generating method according to claim 1 or 2, characterized in that a modified electronic stopping power S _e-mB represented by the following formula was replaced with a fixed value of the position eE _r with low energy side.

The ion implantation distribution generation method according to claim 3, wherein the energy position eE _r is a peak energy position in the electron stopping power _SeB of the _{Bethe model} . A simulator having a function of generating an ion implantation distribution by calculating a locus of implanted ions by a Monte Carlo method,
Wherein for the implanted ions as electron stopping power S _e, fitting parameters r _e, Z ₁ of implanted ions atomic number, atomic number of the atoms of Z ₂ constituting the substrate, the mass number of the M ₁ implanted ions, incident E In the case of energy, the electron stopping power _SeL of the _Linthard model represented by the following formula:
Simulator, characterized in that employing the electronic stopping power S _e expressed by the combination of the modified electronic stopping power S _e-mB that fix electronic stopping power S _eB of Betemoderu.

For Fitting parameters r _e in the electronic stopping power S _eL of the lint Hult model, characterized in that it contains an optimized value from the measured data obtained by secondary ion mass spectrometry for each ion species as a database The simulator according to claim 5.

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