JP5277668B2 - Ion implantation distribution generation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To eliminate arbitrariness of a moment parameter and to expand application type and application range, in relation to an ion implantation distribution generation method. <P>SOLUTION: When it is assumed that (x), &Phi;, &Phi;<SB>chan</SB>, n<SB>a</SB>(x) and n<SB>c</SB>(x) are the depth direction of a substrate, the dose amount of ions to be implanted, and the channel dose amount, a distribution function of an amorphous part, and a distribution function of a channeling part, respectively, this method generates an ion implantation distribution by using moment parameters extracted from the ion distribution in an amorphous layer such as a parameter R<SB>p</SB>expressing projection in the implantation direction of ion range, a standard deviation &Delta;R<SB>p</SB>of R<SB>p</SB>, a parameter &gamma; expressing asymmetrical nature of an implanted ion distribution, and a parameter &beta; expressing sharpness of a peak of the implanted ion distribution as R<SB>p</SB>, &Delta;R<SB>p</SB>, &gamma; and &beta; of a tail function, respectively, when the ion implantation distribution is generated from the tail function N (x) expressed by expression: N (x)=(&Phi;+&Phi;<SB>chan</SB>)n<SB>a</SB>(x)+&Phi;<SB>chan</SB>n<SB>c</SB>(x). In this case, n<SB>a</SB>(x) and n<SB>c</SB>(x) are expressed by n<SB>a</SB>(x)=h<SB>ma</SB>(x), n<SB>c</SB>(x)=h<SB>mc</SB>(x): x&lt;xT when h<SB>ma</SB>(x) and h<SB>mc</SB>(x) are Pearson functions having the moment parameters Rp, &Delta;R<SB>p</SB>, &gamma; and &beta;, xT=Rp+&Delta;R<SB>p</SB>, and &kappa; is a proportional constant. <P>COPYRIGHT: (C)2009,JPO&amp;INPIT

Description

  The present invention relates to a method for generating an ion implantation distribution, and in particular, a moment pattern for generating an ion implantation distribution using a tail function proposed by the present inventor is uniquely determined, and universal for each moment parameter. It is related to a configuration for enhancing the extensibility of the theory assuming the relationship.

At present, an ion implantation method is generally used as an impurity introducing means in a silicon integrated circuit device.
In ion implantation, since ion distribution after implantation is important, an ion implantation database is constructed in order to generate distributions corresponding to various ion implantation conditions.

  The distribution of impurities implanted by such ion implantation can be obtained by a SIMS (secondary ion mass spectrometer), but it is realistic to actually measure the ion implantation distribution under a wide variety of ion implantation conditions by SIMS. is not.

  Therefore, the behavior of ions implanted into the substrate is theoretically predicted, and the Monte Carlo method and LSS (Lindhart, Scharff, Schott) theory are known (see, for example, Non-Patent Document 1). .

For example, the Monte Carlo method is a means for theoretically predicting the ion implantation distribution into the amorphous layer, and the interaction between the incident ions and the substrate is based on the physics of (nuclear stopping power, electron stopping power), The trajectory of incident ions is tracked.
This theory is also effective in the general case where ions are implanted into an arbitrary substrate.

  Also, LSS theory provides an integral equation to be followed by ions based on the same physics. This theory has the feature that even if the injection conditions are determined without tracking the particle trajectory, the energy dependence of the distribution moment can be calculated immediately.

On the other hand, the present inventors proposed a tail function from the conventional dual Peason function as a function used when constructing a database. By using this tail function, a unique parameter set can be made with fewer parameters (see, for example, Patent Document 1).
JP 2002-118073 A J. et al. Lindhart, M .; Scharff, H.M. Schott, Mat. Fts. Medd. Dan. Vid. Sclsk, vol. 33, pp. 1-39, 1963

  However, since the above-mentioned Monte Carlo method follows each trajectory of particles (implanted ions), it is necessary to perform tens of thousands or more calculations in order to reduce the statistical error, which requires a lot of time.

In the LSS theory, approximation is necessary when solving the integral equation. In the models proposed so far, the projection R _{p in} the injection direction of the ion range is not a problem, but is the standard deviation of the projection R _p. There is a problem that ΔR _p is remarkably reduced in accuracy or cannot be calculated.

Therefore, the present inventor has proposed an analytical model that accurately calculates up to R _p , ΔR _p , γ, and β, and can first analytically determine the parameters of the Peason distribution currently used as a standard. did.

However, what is actually used in the LSI process is not an amorphous substrate but a crystal substrate.
Therefore, when theoretically predicting the distribution in the crystal substrate, there are many unsolved problems such as defects introduced along with ion implantation, their accumulation, and the relationship between the accumulated defects and channeling. Exists.

  In addition, the tail function proposed by the present inventors also has the problem that the third-order parameter γ representing the left-right asymmetry of the implanted ion distribution and the fourth-order parameter β representing the sharpness of the peak of the implanted ion distribution exist. There is.

  Therefore, when constructing the database, the change has been suppressed so as not to fluctuate as much as possible when extracting the parameters γ and β. However, such restrictions are not physically meaningful, and the arbitraryness of this value has been a problem.

  Therefore, an object of the present invention is to uniquely define a moment pattern when an ion implantation distribution is generated using a tail function, and to increase the extensibility of the theory by assuming a universal relationship for each moment parameter.

From one aspect of the present invention, x is the depth direction of the substrate, Φ is a dose of ions to be implanted, Φ _chan is a channel dose, n _a (x) is an amorphous part distribution function, and n _c (x ) As the distribution function of the channeling part, when generating the ion implantation distribution from the tail function N (x) represented by the following equation, the moment parameter extracted from the ion distribution in the amorphous layer, parameters R _p representing the projection of the injection direction of the projected range, standard deviation [Delta] R _p of R _p, parameters representing the asymmetry of the implanted ion distribution gamma, R of the tail function parameter β representative of the sharpness of the peak of implanted ion distribution _An ion implantation distribution generation method for use as _p , ΔR _p , γ, and β is provided.
N (x) = (Φ + Φ chan) n a (x) + Φ chan n c (x)
Where n _a (x) and n _c (x) are Pearson functions having the same moment parameters R _p , ΔR _p , γ, β as h _ma (x), h _mc (x), x _T = R _p + ΔR _p , where κ is a proportional coefficient,
n _a (x) = h _ma (x)
n _c (x) = h _mc (x): x <x _T
n _c (x) = κ [h _mc (x) + h _TC (x)]: x> x _T
And the peak concentration position is x _pc , L is a parameter representing the tail spread of the ion implantation distribution, and α (a is used for convenience in h _TC (x)) is the tail of the ion implantation distribution. The parameter representing the shape of the spread of η, where η is a coefficient,
h _TC (x) = h _mc (x _pc ) exp {− (lnη) [(x−x _pc ) ^a / L]}

From another viewpoint, x is the depth direction of the substrate, Φ is the dose of ions to be implanted, Φ _chan is the channel dose, n _a (x) is the distribution function of the amorphous part, and n _c (x ) Is a distribution function of the channeling part, when generating an ion implantation distribution from a tail function N (x) represented by the following formula, R _p is a parameter representing the projection of the ion range in the implantation direction, ΔR _p is the standard deviation of R _p , γ is a parameter representing the left-right asymmetry of the implanted ion distribution, β is a parameter representing the sharpness of the peak of the implanted ion distribution, ξ is a proportional coefficient, and R _max is the maximum ion range. In this case, the parameter L representing the tail spread of the ion implantation distribution of the tail function is expressed as L = ξ (R _max −R _p )
An ion implantation distribution generation method is provided that performs calculations assuming that
N (x) = (Φ + Φ chan) n a (x) + Φ chan n c (x)
Where n _a (x) and n _c (x) are Pearson functions having the same moment parameters R _p , ΔR _p , γ, β as h _ma (x), h _mc (x), x _T = R _{When p} + ΔR _p and κ are proportional coefficients, n _a (x) = h _ma (x)
n _c (x) = h _mc (x): x <x _T
n _c (x) = κ [h _mc (x) + h _TC (x)]: x> x _T
The peak concentration position is represented by x _pc , a ( _note that a is used for h _TC (x) for convenience) is a parameter representing the shape of the tail spread of the ion implantation distribution, and η is a coefficient. ,
h _TC (x) = h _mc (x _pc ) exp {− (lnη) [(x−x _pc ) ^a / L]}

Furthermore, from another viewpoint, a simulator having a function of generating a Pearson distribution using R _p , ΔR _p , γ, β, L, a, and Φ _chan extracted by the above-described ion implantation distribution generation method is provided. Is done.

According to the disclosed ion implantation distribution generation method, the moment parameter of the tail function can be determined remarkably uniquely, and parameters L, α, and Φ _chan related to the tail function crystal are measured by using the determined parameter. This makes it possible to construct a unique database.

In addition, by introducing appropriate assumptions regarding the parameters L, α, and Φ _chan , a universal relationship can be set between the parameters and the ion implantation conditions. The theory can be extended and applied to implanted ions or various implantation energies.

Here, an embodiment of the present invention will be described with reference to FIGS.
FIG. 1 is a conceptual explanatory diagram of a collision phenomenon associated with ion implantation.
As shown in the figure, the ions of mass M ₁ proceed in the x direction while interacting with the atomic nuclei and electrons of the mass M ₂ constituting the substrate.
At this time, the atom of the mass M ₂ constituting the substrate is also affected by the interaction, and this causes damage to the substrate.

FIG. 2 is an explanatory diagram of each parameter in ion implantation, and shows a state where ions of mass M ₁ are implanted into a substrate composed of an element of mass M ₂ .
Ions travel through the substrate in the x direction while interacting with the atomic nuclei and electrons that make up the substrate, and when the line integral of the trajectory of the ions is defined as the range R, the projection of the implantation direction is represented by R. _p , where R _T is the lateral spread, as is clear from the figure,
R _T ² = (Δy) ² + (Δz) ² (1)
It becomes.

Therefore, the lateral spread ΔR _pt of the ions is
^{_{ΔR pt = (R T 2/}} 2) 1/2 ··· (2)
Define in.
Further, the standard deviation of the projection R _p is defined as ΔR _p, and the maximum projection of the ion range is defined as R _max .

FIG. 3 is a schematic explanatory diagram of a one-dimensional distribution of implanted ions. Here, the relationship with a tail function proposed by the present inventor will be described.
The implanted ions have a peak in the projection R _p and have a tailed distribution by a parameter L representing the tail spread of the ion implantation distribution.
Further, α is a parameter representing the shape of the tail spread of the ion implantation distribution.

Next, the tail function N (x) of the higher hierarchy proposed by the present inventor will be described. N (x) is a function of x in the depth direction of the substrate, a dose amount of ions to be implanted, Φ _chan Is the channel dose, n _a (x) is the distribution function of the amorphous part, and n _c (x) is the distribution function of the channeling part,
N (x) = (Φ + Φ chan) n a (x) + Φ chan n c (x) ··· (3)
It is represented by
However, n _a (x) and n _c (x) are parameters R _p and R _p of standard deviation ΔR _p representing projection of h _ma (x) and h _mc (x) in the implantation direction of the ion range, When the parameter γ representing the left-right asymmetry of the implanted ion distribution, the Pearson function having the parameter β representing the sharpness of the peak of the implanted ion distribution, x _T = R _p + ΔR _p , κ is a proportional coefficient,
n _a (x) = h _ma (x) (4)
n _c (x) = h _mc (x): x <x _T (5 ₁ ) n _c (x) = κ [h _mc (x) + h _TC (x)]: x> x _T. (5 ₂₎
In expressed, and the peak concentration position x _pc, parameter representing the spread of the tail of the ion implantation distribution L, and the coefficient parameters η of the α representing the shape of the spread of the tail, the lower hierarchy tail function h _TC (X) is
h _TC (x) = h _mc (x _pc ) exp {− (lnη) [(x−x _pc ) ^a / L]} (6)
In h _TC (x), the parameter α representing the shape of the tail spread of the ion implantation distribution is denoted by a for convenience.

Therefore, the tail function according to the proposal is represented by the sum of two Peason functions.
However, as shown in FIG. 4, even in the tail function, the parameters are not unique, and in particular, there is arbitraryness regarding the tail part of the distribution function n _a (x) representing the main part.

FIG. 5 is an ion implantation distribution diagram when B is implanted into crystalline Si and α-Si. The distribution shape in α-Si when B ions of 1 × 10 ¹⁵ cm ⁻² are implanted is crystalline Si. It can be seen that the distribution in the vicinity of the middle peak is well approximated.

FIG. 6 is an ion implantation distribution diagram when As is implanted into crystalline Si and α-Si. Also in this case, the distribution shape in α-Si when 1 × 10 ¹⁵ cm ⁻² As ions are implanted. However, it can be seen that the distribution in the vicinity of the peak in the crystalline Si is well approximated.

Therefore, in the embodiment of the present invention, the moment parameters R _p that defines the distribution function n _a representative of the main part _{(x), ΔR p, γ} , as a beta, moment in the amorphous layer parameter R _p, [Delta] R _p , Γ, and β are employed as they are.

In this case, as the moment parameters R _p , ΔR _p , γ, β in the amorphous layer, measured values by SIMS may be used, or R _p , ΔR _p , γ, obtained from the Monte Carlo method or LSS theory. β may be used.
In the LSS theory, since the energy dependence of the distribution moment can be immediately calculated if the injection conditions are determined without tracking the trajectory of the particles, R _p , ΔR _p , γ, β calculated from the LSS theory It is desirable to use
However, the accuracy of ΔR _p , γ, and β varies depending on the accuracy of analysis.

As described above, the moment parameter is remarkably unique by using the actually measured value or the simulated value as the moment parameters R _p , ΔR _p , γ, β that define the distribution function n _a (x) representing the main part. Determined.

Using such uniquely defined parameters R _p , ΔR _p , γ, and β, parameters L, α, and Φ _chan related to the tail function crystal are extracted by fitting the measured values by SIMS. Build a unique database with very little arbitraryness.

In addition, when the parameters R _p , ΔR _p , γ, and β obtained from the Monte Carlo method or LSS theory are used, the Monte Carlo method or LSS theory can simultaneously obtain the lateral spread ΔR _pt of the ions. This lateral spread ΔR _pt is also adopted in the database.

Next, referring to FIGS. 7 to 15, semi-experience in which parameters L, α, and Φ _chan related to the tail function crystal are not actually measured, but a universal relationship is set between each parameter and ion implantation conditions. A method of obtaining from a typical model formula will be described.
Here, we examine the dependence of these parameters on the implantation conditions from the data of the ion implantation distribution in the Si or Ge crystal substrate, grasp the dependence phenomenologically, find the continuous or universal relationship for ions, I try to express it with a semi-empirical model formula.

First, the parameter L representing the tail spread of the ion implantation distribution, that is, the length of the channeling tail is examined.
As shown in FIG. 3 above, it is considered that the ions that reach the innermost part of the substrate interact only with electrons without interacting with nuclei.
That is, the depth R _max at which ions reach is expressed by the following formula (7), where N is the ion dose, S _e (E) is the electron stopping power, and E is the implantation energy.

Similarly, as shown in FIG. 3, since L is the channeling length based on the projection R _p of the ion range in the implantation direction, ξ _L is a proportional constant,
L = ξ _L (R _max −R _p ) (8)
The present invention proposes that
The channeling ions are on average farther from the nucleus than in the case of electron interactions in the amorphous state, which means that the electron stopping power in this case is different from that effective for the amorphous layer. , L is not physically strictly defined but only qualitatively represents the channeling length, which is empirically expressed as a proportionality constant.

FIG. 7 is an explanatory diagram of the dependence of the proportionality constant ξ _{L on} the implantation energy. Here, the measured values and tail functions by SIMS when three types of ions B, P and As are implanted into the Si substrate are fitted. The injection energy dependence obtained in this way is shown.
As is apparent from the figure, the dependence of the implantation energy varies depending on the type of ions.

Therefore, as universal implantation energy dependency regardless of the type of ion is obtained, it is standardized by matching the energy E ₁ of the injection energy E a nuclear stopping power S _n and the electronic stopping power S _e for each ion species Tried.
Figure 8 is a schematic illustration of a nuclear stopping power S _n and the electronic stopping power S _e, the value by the energy E ₁ is present ionic species that matches the nuclear stopping power S _n and the electronic stopping power S _e is Will be different.

FIG. 9 is an explanatory diagram of the dependence of the proportional constant ξ _{L on} the normalized implantation energy (E / E ₁ ), which is almost universally dependent on impurities.
In this case, although there is variation, ξ _L is almost 1 when E is equal to E _1, and monotonously decreases when it is smaller than E ₁ .

This can be interpreted qualitatively as follows.
The ion implantation distribution is considered that if the implantation energy E is sufficiently larger than the energy E _{1 at} which the electron stopping power _Se and the nuclear stopping power _Sn are the same, the ions almost interact only with electrons before reaching R _p. It is done.
This case qualitatively matches the physical background connecting L and R _max discussed above.

However, when the energy E becomes smaller than E ₁ , the possibility of reaching the tail portion without interaction with the nucleus decreases. This case is different from the assumed situation. However, the effect is expressed using the same form with ξ _L having energy dependence.

  Although illustration is omitted, in more detail, when the substrate is Ge, the substrate is always on the lower side compared to Si. In other words, it appears that there is a weak substrate dependency. The physical meaning of this dependency is unknown.

Here, in summary, the proportionality constant ξ _L shown in FIG.
ξ _L = λ (Z ₂ ) In (1000 E / E ₁ ): E / E ₁ ≧ 1/1000 (9 ₁ ) ξ _L = 0: E / E ₁ <1/1000 (9 ₂ ) Express semi-empirically.
However, λ (Z ₂ ) is a coefficient indicating the substrate dependence, and in the case of the Si substrate,
λ (Z ₂ = 14: Si) = 0.1485 (10)
It is.
Note that the suffix ₂ of Z ₂ is for performing notation in accordance with the fact that the mass of atoms constituting the substrate is M ₂ in FIG.

In addition, other substrates are also determined by various SIMS based on actual measurement values and simulation results.
For example, when the substrate is composed of a plurality of types of atoms such as a compound semiconductor substrate such as GaAs, the average value Z _2av is used as Z ₂ . The average value Z _2av is expressed by the following formula (11) when it is assumed that n _i types of substrate atoms are included in the unit substrate constituent atoms.

Next, the parameter α representing the shape of the tail spread of the ion implantation distribution will be examined.
FIG. 10 is an explanatory diagram of the dependency of the parameter α on the implantation energy. In this example, the measured values by the SIMS and the tail function when the three types of ions B, P, and As are implanted into the Si substrate and the Ge substrate are fitted. The injection energy dependency obtained by the above is shown.
As is apparent from the figure, the dependence of the implantation energy on the type of ions is different, and in the case of P, the dependence on the substrate is also observed.

Accordingly, again as universal implantation energy dependency is obtained regardless of the type and the type of substrate ions, matching the energy E of the injection energy E a nuclear stopping power S _n and the electronic stopping power S _e for each ion species I tried to standardize by ₁ .

FIG. 11 is an explanatory diagram of the dependence of the parameter α on the normalized injection energy (E / E ₁ ). Although variation is observed in the case of P, E / E ₁ is also a good measure for delimiting the phenomenon. It has become. That is, if E is smaller than E ₁ , the tail portion becomes exponential, and if it is larger, it has a Gauss shape, and has a universal dependence on impurities and the substrate.

Since the dependence of the parameter α shown in FIG. 11 on the normalized implantation energy (E / E ₁ ) varies abruptly when E / E ₁ = 1,
α (E) = 1 + 1 / {1+ (E ₁ / E) ⁴ } (13)
It is expressed empirically.

Next, the channel dose amount Φ _chan will be examined.
FIG. 12 is an explanatory diagram of the dose dependency of the channel dose Φ _chan when B is implanted into the Si substrate. Here, the implantation energy when B is implanted into the Si substrate is 10 keV, 20 keV, 40 keV, The measured values by SIMS when 80 keV and 160 keV are shown.
In this case, roughly divided into a region saturated with a region [Phi _chan is proportional to [Phi. Although there is some variation on the high dose side, at a high dose, Φ _chan has a substantially constant saturation value Φ _chansat regardless of energy.

Figure 13 is an explanatory view of the dose dependence of the channel dose [Phi _chan in the case of implanting P to Si substrate, wherein the implantation energy when implanting P on Si substrate 30 keV, 70 keV, the 180keV The measured value by SIMS is shown.
Also in this case, Φ _chan can be roughly divided into a region that is proportional to Φ and a region that is saturated, and at a high dose, Φ _chan has a substantially constant saturation value Φ _chansat regardless of energy.

FIG. 14 is an explanatory diagram of the dose dependence of the channel dose Φ _chan when As is implanted into the Si substrate. Here, the implantation energy when As is implanted into the Si substrate is 20 keV, 40 keV, 80 keV, The measured value by SIMS in the case of 160 keV is shown.
Also in this case, Φ _chan can be roughly divided into a region that is proportional to Φ and a region that is saturated, and at a high dose, Φ _chan has a substantially constant saturation value Φ _chansat regardless of energy.

Considering FIG. 12 to FIG. 14 together, it is considered that the channel dose Φ _chan is related to the accumulation of damage accompanying ion implantation.
When the dose Φ is small, the damage region formed by each ion can be considered to be independent, so Φ _chan is considered to be proportional to Φ.
When the dose Φ is further increased, the damage areas overlap and finally the entire surface is covered. In other words, if the intermediate region is ignored, there can be considered a dose region where each ion independently forms a damaged region and a region where the damaged region is saturated.

However, even if the general tendency is the same, the saturation state varies for each ion species or for each substrate as it is, so here again, universal implantation energy dependence is obtained regardless of the type of ions and the type of substrate. As described above, an attempt was made to normalize the mass M _{1 of} each ion with the mass M ₂ of atoms constituting the substrate.

FIG. 15 is an explanatory diagram of the M ₁ dependence of Φ _chansat of various ions in a Si substrate and a Ge substrate, and an inversely proportional universal correlation was seen in the log-log graph.
Therefore, expressing the dependency of Φ _chan as a universal relationship,
Φ _chan = r _chan Φ: r _chan Φ <Φ _chansat (14 ₁ ) Φ _chan = Φ _chansat : r _chan Φ> Φ _chansat (14 ₂ )
It expresses.
Note that r _chan is set to 1 when expressed in a simplified manner.

In addition, the M ₁ dependence of Φ _chansat is
Φ _chansat = 4.9 × 10 ¹³ (M ₁ / M ₂ ) ^−1.088 cm ⁻² (15) It is expressed in common for both Ge and Si substrates.

なお、ここで単位基板構成原子内にｉという基板原子がｎ_i 個含まれているとしている。 Further, when the substrate is composed of a plurality of types of atoms such as a compound semiconductor, an average value M _2av expressed by the following formula (16) is used as M ₂ .

Here, it is assumed that n _i substrate atoms are included in the unit substrate constituent atoms.

  As described above, in the embodiment of the present invention, since a universal relationship is set between each parameter and the ion implantation conditions, even for ion species and implantation energy that are not actually handled, It becomes possible to apply by interpolation and extrapolation.

Based on the above, the ion implantation distribution generation method according to the first embodiment of the present invention will be described next with reference to FIGS.
Here, the present inventors have extended the LSS theory to third-order perturbation by using moment parameters R _p , ΔR _p , γ, and β that define the distribution function n _a (x) representing the main part of the tail function described above. Use the calculated value.

FIG. 16 is an ion implantation distribution diagram when B is implanted into the Si substrate. Here, a simulation value is compared with an actual measurement value by SIMS.
In the figure, the dose amount of B is three types of doses of 10 ¹³ cm ⁻² , 10 ¹⁴ cm ⁻² , and 10 ¹⁵ cm ⁻² , and the implantation energy is two types of implantation energy of 20 keV and 80 keV. The results of six ion implantation conditions are shown.
As is apparent from the figure, there is a discrepancy with the actual measurement value obtained by SIMS in the portion where the peak value falls, but in the tail portion, there is a satisfactory agreement with a satisfactory level.

FIG. 17 is an ion implantation distribution diagram when P is implanted into the Si substrate. Here, the simulation value is also compared with the actual measurement value by SIMS.
In the figure, the dose amount of P is set to three types of doses of 1 × 10 ¹³ cm ⁻² , 3 × 10 ¹⁴ cm ⁻² , and 1 × 10 ¹⁶ cm ⁻² , and the implantation energy is set to two types of 30 keV and 70 keV. The results for a total of six ion implantation conditions are shown as implantation energy.
In this case as well, there was a discrepancy with the actual measured value by SIMS in the portion that fell from the peak value, but satisfactory agreement was seen in the tail portion to a satisfactory degree.

FIG. 18 is an ion implantation distribution diagram when As is implanted into a Si substrate. Here, a simulation value is compared with an actual measurement value by SIMS.
In the figure, the dose amount of As is three types of dose amounts of 10 ¹³ cm ⁻² , 10 ¹⁴ cm ⁻² , and 10 ¹⁵ cm ⁻² , and the implantation energy is two types of implantation energy of 20 keV and 80 keV. The results of six ion implantation conditions are shown.
In this case as well, there was a discrepancy with the actual measured value by SIMS in the portion that fell from the peak value, but satisfactory agreement was seen in the tail portion to a satisfactory degree.

FIG. 19 is a configuration example of a database when B constructed by the above-described ion implantation distribution generation method is implanted into a Si substrate.
By constructing such a database, it becomes possible to stably set ion implantation conditions when designing a silicon integrated circuit device.

Next, with reference to FIGS. 20 to 24, the ion implantation distribution generation method according to the second embodiment of the present invention will be described.
Here, the simulation results by the pseudo-crystal LSS (QCLSS) theory improved by the present inventor using the parameters obtained by universalizing the ion implantation conditions using the above formulas (7) to (16) are shown.

FIG. 20 is an ion implantation distribution diagram when B is implanted into the Si substrate. Here, a simulation value based on the QCLSS theory is compared with an actual measurement value based on SIMS.
In the figure, the dose amount of B is three types of doses of 10 ¹³ cm ⁻² , 10 ¹⁴ cm ⁻² , and 10 ¹⁵ cm ⁻² , and the implantation energy is two types of implantation energy of 20 keV and 80 keV. The results of six ion implantation conditions are shown.
As is apparent from the figure, good agreement was found between the simulation value and the actual measurement value by SIMS, although it was not perfect.

FIG. 21 is an ion implantation distribution diagram when P is implanted into the Si substrate. Here, the simulation value based on the QCLSS theory is compared with the actual measurement value based on SIMS.
In the figure, the dose amount of P is set to three types of doses of 1 × 10 ¹³ cm ⁻² , 3 × 10 ¹⁴ cm ⁻² , and 1 × 10 ¹⁶ cm ⁻² , and the implantation energy is set to two types of 30 keV and 70 keV. The results for a total of six ion implantation conditions are shown as implantation energy.
As is clear from the figure, although there was some divergence in the tail portion, good agreement was observed between the simulation value and the measured value by SIMS.

FIG. 22 is an ion implantation distribution diagram when As is implanted into the Si substrate. Here, the simulation value based on the QCLSS theory is compared with the actual measurement value based on SIMS.
In the figure, the dose amount of As is three types of dose amounts of 10 ¹³ cm ⁻² , 10 ¹⁴ cm ⁻² , and 10 ¹⁵ cm ⁻² , and the implantation energy is two types of implantation energy of 20 keV and 80 keV. The results of six ion implantation conditions are shown.
As is apparent from the figure, good agreement was found between the simulation value and the actual measurement value by SIMS, although it was not perfect.

FIG. 23 is an ion implantation distribution diagram when In is implanted into the Si substrate. Here, the simulation value based on the QCLSS theory is compared with the actual measurement value based on SIMS.
In the figure, there are three types of dose amounts of In, 5 × 10 ¹² cm ⁻² , 1 × 10 ¹⁴ cm ⁻² , and 1 × 10 ¹⁵ cm ⁻² , and two types of implantation energy, 20 keV and 80 keV. The results for a total of six ion implantation conditions are shown as implantation energy.
As is apparent from the figure, good agreement was found between the simulation value and the actual measurement value by SIMS, although it was not perfect.

FIG. 24 is an ion implantation distribution diagram when Sb is implanted into the Si substrate. Here, the simulation value based on the QCLSS theory is compared with the actual measurement value based on SIMS.
In the figure, the dose amount of Sb is 3 × 10 ¹² cm ⁻² , 1 × 10 ¹⁴ cm ⁻² , and 1 × 10 ¹⁵ cm ⁻² , and the implantation energy is two types of 20 keV and 80 keV. The results for a total of six ion implantation conditions are shown as implantation energy.
As is apparent from the figure, good agreement was found between the simulation value and the actual measurement value by SIMS, although it was not perfect.

Considering the results of FIGS. 20 to 24 together, it can be seen that, though not completely, a wide range of injection conditions can be handled uniformly and expressed almost quantitatively.
Therefore, by adopting L, α, and Φ _chan thus obtained as universal relationships as parameters of the tail function shown in Example 1, a database in a wide range of injection conditions can be created without directly referring to actual measurement values. Can be built.

Further, as shown in FIG. 20 to FIG. 24, the L, α, and Φ _chan obtained as universal relationships are adopted as the values of moment parameters in the amorphous using the main part of the tail function. Regardless of this, by adopting it as a general tail function parameter, the ion implantation distribution under a wide range of implantation conditions can be handled uniformly.

  By mounting these functions as a program in the simulator, it is possible to provide a simulator that can easily obtain the ion implantation distribution under a wide range of implantation conditions.

It is a conceptual explanatory drawing of the collision phenomenon accompanying ion implantation. It is explanatory drawing of each parameter in ion implantation. It is a typical explanatory view of a one-dimensional distribution of implanted ions. It is explanatory drawing of the non-uniqueness of the parameter in a tail function. It is an ion implantation distribution diagram when B is implanted into crystalline Si and α-Si. It is an ion implantation distribution diagram when As is implanted into crystalline Si and α-Si. It is explanatory drawing of the injection energy dependence of proportionality constant (xi) _L. It is a schematic illustration of a nuclear stopping power S _n and the electronic stopping power S _e. Normalized implantation energy proportional constant ξ _L (E / E ₁₎ is an illustration of dependencies. It is explanatory drawing of the injection energy dependence of parameter (alpha). Normalized implantation energy parameters α (E / E ₁₎ is an illustration of dependencies. It is explanatory drawing of the dose dependence of channel dose amount (PHI) _chan at the time of inject | pouring B into Si substrate. It is explanatory drawing of the dose amount dependence of channel dose amount (PHI) _chan at the time of inject | pouring P into Si substrate. It is explanatory drawing of the dose amount dependence of channel dose amount (PHI) _chan at the time of inject | pouring As to Si substrate. Si is a variety of M ₁ dependent illustration of [Phi _Chansat ions substrate and Ge in the substrate. It is an ion implantation distribution diagram when B is implanted into a Si substrate. It is an ion implantation distribution diagram when P is implanted into a Si substrate. It is an ion implantation distribution diagram when As is implanted into a Si substrate. It is a structural example of the database in the case of implanting B constructed by the ion implantation distribution generation method of the present invention into a Si substrate. It is an ion implantation distribution diagram when B is implanted into a Si substrate. It is an ion implantation distribution diagram when P is implanted into a Si substrate. It is an ion implantation distribution diagram when As is implanted into a Si substrate. It is an ion implantation distribution diagram when In is implanted into a Si substrate. It is an ion implantation distribution diagram when Sb is implanted into a Si substrate.

Claims (6)

x is the depth direction of the substrate, Φ is the dose of ions to be implanted, Φ _chan is the channel dose, n _a (x) is the distribution function of the amorphous part, and n _c (x) is the distribution function of the channeling part Then, when the ion implantation distribution is generated from the tail function N (x) represented by the following equation, the parameter R represents the projection of the ion range extracted from the ion distribution in the amorphous layer in the implantation direction. _p, the standard deviation [Delta] R _p of R _p, parameters representing the asymmetry of the implanted ion distribution gamma, R _p of the tail function parameter β representative of the sharpness of the peak of implanted ion distribution, [Delta] R _p, gamma, ion used as β Injection distribution generation method.
N (x) = (Φ + Φ chan) n a (x) + Φ chan n c (x)
Where n _a (x) and n _c (x) are Pearson functions having the same moment parameters R _p , ΔR _p , γ, β as h _ma (x), h _mc (x), x _T = R _p + ΔR _p , where κ is a proportional coefficient,
n _a (x) = h _ma (x)
n _c (x) = h _mc (x): x <x _T
n _c (x) = κ [h _mc (x) + h _TC (x)]: x> x _T
And the peak concentration position is x _pc , L is a parameter representing the tail spread of the ion implantation distribution, a is a parameter representing the shape of the tail spread of the ion implantation distribution, and η is a coefficient.
h _TC (x) = h _mc (x _pc ) exp {− (lnη) [(x−x _pc ) ^a / L]} 2. The ion implantation distribution generation method according to claim 1, wherein the parameter extraction from the ion distribution in the amorphous layer is obtained from calculation of the ion distribution in the amorphous layer by either the Monte Carlo method or the LLS theory. The ion implantation distribution generation method according to claim 2, wherein the parameter extracted by calculation from the ion distribution in the amorphous layer includes a parameter ΔR _pt of a lateral spread of ions. After fixing R _p , ΔR _p , γ, and β, parameters of the tail function, which are parameters of the tail spread of the ion implantation distribution, a parameter L representing the shape of the tail spread of the ion implantation distribution, and _4. The ion implantation distribution generation method according to any one of claims 1 to 3, wherein the channel dose amount Φ _chan is extracted from experimental data. x is the depth direction of the substrate, Φ is the dose of ions to be implanted, Φ _chan is the channel dose, n _a (x) is the distribution function of the amorphous part, and n _c (x) is the distribution function of the channeling part Then, when generating the ion implantation distribution from the tail function N (x) represented by the following equation, R _p is a parameter representing the projection of the ion range in the implantation direction, and ΔR _p is the standard deviation of R _p . , Γ is a parameter representing the left-right asymmetry of the implanted ion distribution, β is a parameter representing the sharpness of the peak of the implanted ion distribution, ξ is a proportional coefficient, and R _max is the maximum ion range, the ions of the tail function The parameter L representing the tail spread of the injection distribution is
L = ξ (R _max −R _p )
An ion implantation distribution generation method that performs calculations assuming that
N (x) = (Φ + Φ chan) n a (x) + Φ chan n c (x)
Where n _a (x) and n _c (x) are Pearson functions having the same moment parameters R _p , ΔR _p , γ, β as h _ma (x), h _mc (x), x _T = R _p + ΔR _p , where κ is a proportional coefficient,
n _a (x) = h _ma (x)
n _c (x) = h _mc (x): x <x _T
n _c (x) = κ [h _mc (x) + h _TC (x)]: x> x _T
And the peak concentration position is x _pc , a is a parameter representing the shape of the tail spread of the ion implantation distribution, and η is a coefficient.
h _TC (x) = h _mc (x _pc ) exp {− (lnη) [(x−x _pc ) ^a / L]} The calculation is performed assuming that ξ depends on E / E ₁ , where E is ion implantation energy and E ₁ is an energy at which the nuclear stopping power and electron stopping power of the substrate are equal. Ion implantation distribution generation method.

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