JP5347493B2 - Ion implantation distribution generation method and simulation apparatus - Google Patents

Description

The present invention relates to an ion implantation distribution generation method and a simulation apparatus. For example, the proportional coefficient ξ of a parameter L that represents the spread of a tail when an ion implantation distribution is generated using a tail function proposed by the present inventor. _It relates to a configuration for giving _L a physical meaning.

  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. In this LSS theory, approximation is necessary when solving the integral equation. In the models proposed so far, the projection R _p of the ion range in the injection direction is not a problem, but the standard deviation ΔR _p of the distribution is There is a problem that accuracy is greatly reduced or calculation is not possible.

  Therefore, the present inventors have proposed a tail function from the conventional dual Peason function as a function used when constructing a database. By using this tail function, the parameter of the Peason distribution that is currently used as a standard is analytically obtained for the first time, and a unique parameter set can be made with fewer parameters (for example, Patent Document 1 or Non-Patent Document). 2).

  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.

On the other hand, in recent years, attempts have been made to construct MOSFETs, particularly p-channel MOSFETs, with Si _1-x Ge _x having higher mobility than Si.
JP 2002-118073 A J. et al. Lindhart, M .; Scharff, H.M. Schott, Mat. Fts. Med. Dan. Vid. Sclsk, vol. 33, pp. 1-39, 1963 K. Suzuki and R.K. Sudo, Solid-State Electronics, Vol. 44, pp. 2253, 2000

However, up to now, an abundant database has been constructed for Si or Ge, but there is a problem that a specific simulation method and database have not been sufficiently developed for Si _1-x Ge _x .

Moreover, even if the simulation method for Si or Ge is applied to Si _1-x Ge _x as it is, some models used in the conventionally proposed simulation are treated empirically and physically There is a problem that there are some things that are meaningless.

Ion implantation parameter L representing the spread of the tail of the distribution of the R _max maximum range of the ion, when the R _p and the projection of the ions, but almost successful proportional to (R _{max -R p),} the proportionality There is a problem that the coefficient ξ _L has a poor physical meaning. Furthermore, there is a problem that it is unclear what parameter dependency this proportional coefficient ξ _L has.

Therefore, an object of the present invention is to give a physical meaning to the proportional coefficient ξ _L of the parameter L representing the tail spread of the ion implantation distribution in the tail function.

From one aspect of the present invention, 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 ) As the distribution function of the channeling part, when the ion implantation distribution is generated from the tail function N (x) represented by the following formula (1), the ions extracted from the ion distribution in the amorphous layer The parameter R _p representing the projection of the range injection direction, the standard deviation ΔR _{p of} the distribution, the parameter γ representing the left-right asymmetry of the implanted ion distribution, and the parameter β representing the peak sharpness of the implanted ion distribution are represented by R _{p of the} tail function. , ΔR _p , γ, β and
When R _max is the maximum ion range, the proportional coefficient ξ _L in the parameter L representing the tail spread of the ion implantation distribution defined by L = ξ _L (R _max −R _p ) is expressed as A, r _s. Is the coefficient, M ₁ is the mass number of ions, M ₂ is the mass number of atoms constituting the substrate, E is the energy of the ions, and E ₁ is the energy at which the electron stopping power and the nuclear stopping power are equal. An ion implantation distribution generation method as described in 2) is provided.
N (x) = (Φ- Φ chan) n a (x) + Φ chan n c (x) ··· (1)
However, n _a (x) and n _c (x) are the 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
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 ) / L] ^a }

  From another viewpoint, there is provided a simulation apparatus that executes a calculation based on the calculation formula relating to the above-described ion implantation distribution generation method.

According to the disclosed ion implantation distribution generation method and simulation apparatus, the proportional coefficient ξ _L of the parameter L representing the tail spread of the ion implantation distribution in the tail function can be associated with the ion scattering angle θ _av . As a result, the proportionality coefficient ξ _L has a physical meaning, so that a lot of experimental data can be unified.

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 ion having the mass number M ₁ proceeds in the x direction while interacting with the nucleus and electrons of the atom having the mass number M ₂ constituting the substrate. At this time, the atom having the mass number M ₂ constituting the substrate is also affected by the interaction, and this causes damage to the substrate.

Figure 2 is an explanatory view of the parameters at the ion implantation, ions of mass number M ₁ is shows a state in which it is implanted into the substrate consists of an element of the mass number 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, the lateral extent When R _T, as is apparent from the figure,
R _T ² = (Δy) ² + (Δz) ² (4)
It becomes.

Therefore, the lateral spread ΔR _pt of the ions is
^{_{ΔR pt = (R T 2/}} 2) 1/2 ··· (5)
Define in. Also, the standard deviation of the distribution is 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 distribution with a tail by the parameter L representing the tail spread of the ion implantation distribution. Note that about 10 ¹⁶ cm ⁻³ is SIMS background noise.

The tail function N (x) of the higher hierarchy proposed by the present inventor will be described with reference to FIG.
N (x) is the depth direction of the substrate, x is the dose of ions to be implanted, Φ _chan is the channel dose, n _a (x) is the amorphous part distribution function, and n _c (x) is The distribution function of the channeling part is
N (x) = (Φ- Φ chan) n a (x) + Φ chan n c (x) ··· (6)
It is represented by

However, n _a (x) and n _c (x) are parameters R _p representing the projection of h _ma (x) and h _mc (x) in the implantation direction of the ion range, standard deviation ΔR _{p of the} distribution, and implantation. In order to guarantee the continuity of the expression at x = x _T , the parameter γ representing the left-right asymmetry of the 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 If the coefficient is
n _a (x) = h _ma (x) (7)
n _c (x) = h _mc (x): x <x _T (8 ₁ )
n _c (x) = κ [h _mc (x) + h _TC (x)]: x> x _T (8 ₂ )
The peak concentration position is represented by x _pc , L is a parameter representing the tail spread of the ion implantation distribution, α is a parameter representing the shape of the tail spread, and η is a coefficient. _TC (x) is
h _TC (x) = h _mc (x _pc ) exp {− (lnη) [(x−x _pc ) / L] ^a } (9)
It is represented by 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 N (x) according to the proposal is represented by the sum of two Peason functions.

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), as [Delta] R _p, gamma, beta, moment parameters _{R p} in the amorphous layer, [Delta] R _p, gamma , Β is adopted as it is. The coefficient η in h _TC (x) is η = 1000 here.

In this case, the moment parameters R _p , ΔR _p , γ, and β in the amorphous layer may be values obtained by actual measurement, but here are obtained from the extended LSS theory (see Japanese Patent Application No. 2008-0669509 if necessary). R _p , ΔR _p , γ, and β are used. The LSS theory has an advantage that the energy dependence of the distribution moment can be immediately calculated if the injection conditions are determined without tracking the particle trajectory.

After using the parameters R _p , ΔR _p , γ, and β defined in this way, the parameters L, α, and Φ _chan related to the tail function crystal are extracted by fitting the measured values by SIMS to be arbitrary. Build a unique database with very little.

なお、式（１０）におけるＺ_１，Ｚ_２はそれぞれ入射イオンの質量数、基板構成原子の質量数である。また、係数ｒ_ｅはフィッティングパラメータである。 The electronic stopping power S _e may be used electron stopping power S _e in a model of Rintoharuto, or may be used an improved electronic capability in combination with an electronic stopping power of the Bethe. Here, the electron stopping power S _e (see, for example, Non-Patent Document 1) in the Linthard model represented by the following formula (10) is used.

In the formula (10), Z ₁ and Z ₂ are the mass number of the incident ions and the mass number of the atoms constituting the substrate, respectively. The coefficient _{r e} is the fitting parameter.

なお、式（１１）におけるフィッティングパラメータｒ_ｅとして、各入射イオン種毎に図４に示したＳｉ及びＧｅについての数値を用い、Ｓｉ_１-ｘＧｅ_ｘに対して特別の値を用いるものではい。 The sum in the case, as in the following equation (11), at a ratio corresponding to the composition ratio x by dividing the _{Z 2} in Si and Ge applying this electronic stopping power _{S e} the Si _1-x Ge _x Represented by

Incidentally, yes those as fitting parameters _{r e} in equation (11), using the numerical values of the Si and Ge shown in FIG. 4 for each incident ion species, using special values for Si _1-x Ge _x .

Further, the nuclear stopping power S _n , the second-order energy disturbance coefficient Ω _n ² and the third-order energy disturbance coefficient Λ _n ² are _{expressed by the} following equations (12) to (14) used in the extended LSS theory. S _n , Ω _n ² and Λ _n ² are also applied to Si _1-x Ge _x . In addition, the coefficient μ in the equations (12) to (14) is μ = M ₂ / M ₁ .

Next, the atomic concentration N of the unit cell of the substrate is _expressed by the following formula (n) _where ρ is the atomic density of the substrate, N _avo is the Avogadro constant, and M _Si and M _Ge are the mass numbers of _Si and _Ge , respectively. 15).

なお、図５は、基板の原子密度ρの組成比ｘ依存性を図示したものである。 In this case, the lattice constant a of Si _1-x Ge _x having the composition ratio x is
a = 0.002733x ² + 0.01992x + 0.5431 [nm] (16)
Given in. In addition, since Si _1-x Ge _x having a diamond crystal structure has 8 atoms per unit lattice regardless of the composition ratio x, the atomic density of the substrate is expressed by the following formula (17). .

FIG. 5 shows the composition ratio x dependency of the atomic density ρ of the substrate.

Next, a parameter L representing the tail spread of the ion implantation distribution, that is, the channeling tail length 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 equation (18), where N is the ion dose, S _e (E) is the electron stopping power, and E is the implantation energy.

Moreover, as also shown in FIG. 3, L is from a channeling length when relative to the projection R _p of the injection direction of the projected range of the ion, the xi] _L and proportional constant,
L = ξ _L (R _max −R _p ) (19)
The present inventor has already proposed that (see Japanese Patent Application No. 2008-059070 if necessary).

In this equation (19), the channeling ions are on average farther from the nucleus than in the case of electron interaction in the amorphous state, that is, the electron stopping power in this case is in the amorphous layer. On the other hand, it is empirically expressed by the proportional constant ξ _L that it is different from the effective one, and that L is not physically strictly defined but qualitatively represents the channeling length.

Here, L is obtained from SIMS data, while R _max and R _p are obtained from the above-mentioned extended LSS theory, and the proportional coefficients ξ are assigned by substituting the obtained L, R _max , R _p into the above equation (19). Evaluate _L.

FIG. 6 is a diagram showing the evaluation result of ξ _L. Here, the implantation obtained by fitting the measured value by tail and the tail function when three types of ions of B, P, and As are implanted into the Si substrate. It shows energy dependence. As is apparent from FIG. 6, the dependence of the implantation energy varies depending on the type of ions, and ξ _L = 0.5 to 1.5 in the range of 20 keV to 80 keV. Further, in each ion, the proportionality coefficient ξ _L gradually increases as the energy increases.

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 7 is a schematic illustration of a nuclear stopping power S _n and the electronic stopping power S _e, the value by Although there are energy E ₁ that matches the nuclear stopping power S _n and the electronic stopping power S _e ionic species Will be different.

FIG. 8 is an explanatory diagram of the dependence of the proportionality constant ξ _{L on} the normalized implantation energy (E / E ₁ ). The dependence on impurities is almost clear and the dependence is almost universal. In this case, although there is variation, ξ _L is smaller than ₁ when E / E ₁ is smaller than 1, and ξ _L is larger than ₁ when E / E ₁ is larger than 1.

However, as is apparent from FIG. 8, the dependence is slightly different for each ion species, and the proportionality constant ξ _L decreases as the ion mass decreases. On the other hand, the deviation of the proportional constant xi] _L for the proportionality constant xi] _L and Ge to Si is greater as the mass of the ion is increased. In more detail, when the substrate is Ge, the proportionality constant ξ _L is always lower than that of Si. In other words, it appears that there is a weak substrate dependency.

The physical meaning of this dependency is further examined. First, when ions are greatly scattered before channeling, the channeling path is different from the incident direction of ions. Therefore, since the parameter L is the length projected in the ion incident direction, the proportional coefficient ξ _L becomes small.

なお、式（２０）における係数ｒ_ｓは、ある一定エネルギー領域におけるＳ_ｎ／（Ｓ_ｅ＋Ｓ_ｎ）の平均値であり、係数ｒ_ｓは０〜１の範囲となる。 Therefore, as the relationship between the projection R _p of about about R and Fei Fei, introducing equation (20) below.

The coefficient r _s in the equation (20) is an average value of S _n / (S _e + S _n ) in a certain constant energy region, and the coefficient r _s is in the range of 0-1.

なお、この平均散乱角θ_ａｖは厳密にはエネルギー依存性を有しているが、ここでは簡略化のために無視する。 Here, the projected range as a result of scattering in Figure 1 above in consideration of the relationship between the projection R _p of about R and flight, defining a mean scattering angle theta _av the following equation (21).

The average scattering angle θ _av is strictly energy dependent, but is ignored here for the sake of simplicity.

Further, in the above formula (21), as Si _1-x Ge _x having a composition ratio x as the mass number M ₂ of the atoms of the substrate,
M ₂ = 28.09 (1-x) + 72.61x (22)
Is used.

On the other hand, when the electron stopping power of the channeling ions becomes smaller than the average electron stopping power of the substrate, the proportionality coefficient ξ _L increases. Further, when the nuclear stopping power becomes dominant at low incident energy, the interaction with the nucleus is unavoidable, and the proportional coefficient ξ _L becomes small. Such a characteristic is a physical meaning for explaining the energy dependency of the proportional coefficient ξ _L described above.

In the above extended LSS theory by the present inventor, such energy dependency of the proportional coefficient ξ _L is expressed semi-empirically by the following equation (23).
ξ _L = λ (Z ₂ ) In (1000E / E ₁ ): E / E ₁ ≧ 1/1000 (23 ₁ )
ξ _L = 0: E / E ₁ <1/1000 (23 ₂ )
However, λ (Z ₂ ) is a coefficient indicating the substrate dependence. In the case of the Si substrate and the Ge substrate,
λ (Z ₂ = 14: Si) = 0.1485 (24)
λ (Z ₂ = 32: Ge) = 0.1080 (25)
It is.

なお、式（２６）におけるパラメータＡは定数である。 Here, in order to give more accurate and physical meaning by the proportional coefficient ξ _L , the above-described average scattering angle θ _av is used to express the equation (26).

Note that parameter A in equation (26) is a constant.

It can be understood from this equation (26) that the proportional coefficient ξ _L decreases as the mass number M ₂ of the constituent atoms of the substrate increases and as the mass number M ₁ of the incident ions decreases. This larger mass number M ₂ of the substrate constituent atoms of, and to express physical phenomenon that is ions greatly scattered as the mass number M ₁ of the incident ions is small projective R _p of the projected range is reduced Will be.

FIG. 9 and FIG. 10 are plots obtained by calculating the locus of 50 ions by the Monte Carlo method when B ions and As ions are implanted into the Si substrate and the Ge substrate, respectively.
As is clear from FIG. 9, the trajectory of B ions in the Ge substrate is equal to or longer than the trajectory of B ions in the Si substrate.

However, the trajectory of B ions in the Ge substrate is bent at a high angle by repeating many times of scattering, which corresponds to a large scattering angle θ _av . As a result, the final point of the trajectory, that is, the B ion implantation depth in the Ge substrate is shallower than the implantation depth in the Si substrate.

On the other hand, as is apparent from FIG. 10, the locus of As ions in the Ge substrate is shorter than the locus of As ions in the Si substrate. Therefore, it is understood that the scattering angle θ _av is small in any substrate. . Therefore, the dependency of the proportionality coefficient ξ _{L on} the mass number M ₂ of the constituent atoms of the substrate becomes remarkable when the mass number M ₁ is B, which is relatively smaller than As.

FIG. 8 described above is an explanatory diagram of the normalized injection energy dependence of the proportionality constant ξ _L when the parameters r _s and A in equation (26) are r _s = 0.2 and A = 0.18, respectively. In the case of B having a small mass number M _1, the dependence on the mass number M ₂ is increased.

Next, the parameter α representing the shape of the tail spread of the ion implantation distribution will be examined.
FIG. 11 is an explanatory diagram of the dependence of the parameter α on the implantation energy. Here, it is obtained by fitting the measured value by tail and the tail function when three types of ions of B, P, and As are implanted into the Si substrate. The dependence on injection energy is shown. As is apparent from the figure, the dependence of the implantation energy varies depending on the type of ions.

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 with ₁ .

FIG. 12 is an explanatory diagram of the dependence of the parameter α on the normalized injection energy (E / E ₁ ). Although variation is seen in the case of P, E / E ₁ is also a good measure for delimiting the phenomenon in this case. It has become. That is, if E / E ₁ is smaller than 1, α = 1, and if E / E ₁ is larger than _1, α = 2.

Therefore, the dependence of the parameter α shown in FIG. 12 on the normalized injection energy (E / E ₁ ) varies abruptly when α is E / E ₁ = 1.
α (E) = 1 + 1 / {1+ (E ₁ / E) ⁴ } (27)
It is expressed empirically.

Next, the channel dose amount Φ _chan will be examined. FIGS. 13 to 15 are explanatory diagrams of the dose dependency of the channel dose Φ _chan when B, P, and As are implanted into the Si substrate, respectively. In either case, the measured values by SIMS are shown when the implantation energy is 20 keV, 40 keV, 80 keV, and 160 keV.

In this case, as the dose Φ increases, Φ _chan increases proportionally, and the channel dose Φ _chan tends to saturate at a certain dose. There is almost no influence of incident energy on the dose dependency.

Considering this feature, the channel dose Φ _chan is considered to be related to the accumulation of damage accompanying ion implantation. When the dose amount Φ is small, the damage region formed by each ion can be considered to be independent, so the ion trajectory does not depend on the accumulation of damage. Therefore, the channel dose amount Φ _chan is considered to be proportional to the dose amount Φ. However, when the dose Φ is further increased, the damaged regions overlap and eventually cover the entire surface, and as a result, the channel dose Φ _chan is saturated at a high dose.

Therefore, expressing the dependency of Φ _{chan on} the dose Φ as a universal relationship,
Φ _chan = r _chan Φ: r _chan Φ <Φ _chansat (28 ₁ )
Φ _chan = Φ _chansat : r _chan Φ> Φ _chansat (28 ₂ )
It expresses. Note that r _chan is set to 1 when expressed in a simplified manner.

As is apparent from FIGS. 13 to 15, the saturation state varies for each ion species or for each substrate. Therefore, the mass M _{1 of} each ion is normalized by the mass M ₂ of the atoms constituting the substrate so that universal injection energy dependence can be obtained regardless of the type of ions and the type of substrate, and the following equation (29 ).
Φ _chansat = 3.3 × 10 ¹³ (M ₁ / M ₂ ) ^-1.06 cm ^-2 (29)

In the embodiment of the present invention, the above relational expression is incorporated into a simulation apparatus, and various parameters L, α, and Φ _chan are obtained by fitting with SIMS data for each predetermined implantation energy. A database in which the obtained parameters L, α, and Φ _chan are combined with the parameters R _p , ΔR _p , γ, and β used in this relational expression is constructed, and the constructed database is stored in the simulation apparatus. Based on this database, ion distributions for various ion species, substrates, and implantation energies are generated.

但し、式（３０）におけるｍはΔＲ_ｐｔの勾配であり、また、ΔＲ_ｐｔ０＝ΔＲ_ｐｔ（Ｒ_ｐ）である。 Further, in the LSS theory, since the lateral spread ΔR _pt of ions can be obtained together, ΔR _pt (x) is expressed by the following equation (30), and ΔR _pt0 is added to the database set. A two-dimensional ion distribution can be generated.

However, m in the equation (30) is a gradient of ΔR _pt , and ΔR _pt0 = ΔR _pt (R _p ).

  Further, it is possible to cope with ion types, substrate types, and implantation energies that are not in the database by interpolation and extrapolation thereof.

As described above, in the embodiment of the present invention, the parameter L has physical meaning by associating the proportional coefficient ξ _L of the parameter L representing the tail spread of the implanted ion distribution with the scattering angle θ _av. it can.

Further, since the proportionality coefficient ξ _L has a physical meaning, it is possible to unify a lot of experimental data and improve the matching accuracy with SIMS data. The other parameters alpha, for [Phi _chan, except the values of the coefficient parameters previously proposed alpha, is basically the same as [Phi _chan.

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. Here, as a substrate for actual measurement by SIMS, a substrate is prepared by growing a Si _1-x Ge _x layer having a thickness of 300 nm on a Si substrate by a low pressure chemical vapor deposition method (LPCVD method). B, P, and As are ion-implanted with various implantation energies into this substrate under the conditions that the tilt angle is 7 ° and the rotation angle is 0 °.

In this case, the Ge composition ratio x of the Si _1-x Ge _x layer was evaluated by the Rutherford backscattering (RBS) method. FIG. 16 is an explanatory diagram of measurement results obtained by the RBS method. By comparing measurement data and simulation results, the Ge composition ratio x of the Si _1-x Ge _x layer used in the example is 0.16,. 25, 0.35. In the following figures, only data of x = 0.16 and x = 0.35 are displayed for easy understanding of the explanation.

Since the detected He ions are scattered by atoms closer to the surface as the energy is higher, the position of Si indicated by the arrow in FIG. 16 is the interface position between the Si substrate and the Si _1-x Ge _x layer. is there. Further, the position of Ge indicated by an arrow corresponds to He ions scattered by collision with Ge on the surface of the Si _1-x Ge _x layer.

When measuring the ion distribution by SIMS, Cs ⁺ is used as the primary ion, and when the measurement target is As, the irradiation energy is 1 keV, the incident angle is 0 °, and As ⁺ is detected as the secondary ion. To obtain the ion distribution. When the measurement target is P, the irradiation energy is 1 keV, the incident angle is 45 °, and P ⁺ is detected as a secondary ion. When the measurement target is B, the irradiation energy is 1 keV, and the incident angle is At 20 °, B ⁺ is detected as secondary ions.

FIGS. 17 to 19 are ion implantation distribution diagrams when B, P, and As are implanted into the Si substrate and the Ge substrate, respectively. Here, the simulation values are compared with the actual measurement values by SIMS. (A) of each figure is the case where ions are implanted at 1 × 10 ¹³ cm ⁻² at an implantation energy of 20 keV, and (b) in each figure is implantation of 1 × 10 ¹⁵ cm ⁻² at an implantation energy of 20 keV. Is the case. The background noise in SIMS data is 10 ¹⁶ cm ^{−3 to} 10 ¹⁷ cm ⁻³ .

In each figure, the peak position of the ion implantation distribution, i.e., R _p is shallower with increasing composition ratio x. Further, the channeling tail is slightly suppressed as the composition ratio x increases when the dose is 1 × 10 ¹³ cm ⁻² . On the other hand, when the dose amount is 1 × 10 ¹⁵ cm ⁻² , the composition ratio x dependency is ambiguous, which is considered to be due to the resolution of SIMS.

20 to 22 are explanatory views of the energy dependence of each B, electron stopping power of P and As _{S e} and nuclear stopping power _{S n.} As shown in FIG. 20, in the case of B, the nuclear stopping power S _n increases with increasing composition ratio x in the low energy region, which is inversely related in the high energy region. The degree of increase is somewhat increased with increasing nuclear stopping power S _n composition ratio x in the 20keV is slight.

On the other hand, the electron stopping power _Se always decreases as the composition ratio x increases. Since in the 20keV a predominant direction of the electronic stopping power S _e, the total stopping power decreases constantly with increasing composition ratio x in all energy regions. Therefore, the reason why R _p in FIG. 17 becomes shallow as the composition ratio x increases cannot be well explained from the viewpoint of stopping power.

Further, as shown in FIG. 21, in the case of P is approximately the same for the nuclear stopping power _{S n} and the electronic stopping power _{S e} both the composition ratio in the 20 keV x. Therefore, also in this case, the reason why R _p in FIG. 18 becomes shallow as the composition ratio x increases cannot be well explained from the viewpoint of stopping power.

Further, as shown in FIG. 22, in the case of As is larger with an increase in the nuclear stopping power S _n and the electronic stopping power S _e both the composition ratio x, this case, R in the above FIG. 19 _This corresponds to an event in which _p becomes shallower as the composition ratio x increases.

FIG. 23 to FIG. 25 are explanatory diagrams of energy dependence of the range R, projection R _p , and lateral spread ΔR _pt of B, P, and As, respectively. Here, the value evaluated by pseudo crystal LSS (QCLSS) is shown.

  In this case, the range R corresponds to the tendency of total stopping power. That is, as is clear from the comparison between FIG. 23 and FIG. 20, in the case of B, the total stopping power decreases as the composition ratio x increases, so that the range R increases as the composition ratio x increases. . In the case of P, the range R increases as the composition ratio x increases. On the other hand, in the case of As, as is clear from the comparison between FIG. 25 and FIG. 22, the total stopping power increases with the increase in the composition ratio x, so that the range R decreases conversely with the increase in the composition ratio x. .

In the case of B or P, the lateral spread ΔR _pt increases with an increase in the composition ratio x, which is relatively small in mass number, as is apparent from the above equation (26). In the case of B or P, this corresponds to an increase in the scattering angle θ _av as the composition ratio x increases.

26 and 27 are ion implantation distribution diagrams of B ions, in which B ions having a dose of 1 × 10 ¹⁵ cm ⁻² are implanted into Si substrate and Ge substrate with implantation energy of 20 keV, 40 keV, and 80 keV, respectively. It is an ion implantation distribution diagram. Here, the result of simulation using Φ _chansat shown in the above equation (27) is shown, and good agreement with the measured data of SIMS is seen.

FIG. 28 to FIG. 33 are examples of the database constructed as described above. Here, B, P, As are represented by Si, Si _0.9 Ge _0.1 , Si _0.8 Ge _0.2 , Si _0.6 Ge _0.4 , Si _0.2 Ge _0.8 , and parameters R _p , ΔR _p , γ, β, L, α, ΔR _pt0 , m when implanted into Ge are shown.

  By constructing such a database, it becomes possible to stably set ion implantation conditions when designing a silicon integrated circuit device. In addition, by mounting the above functions as a program in a simulation apparatus, it is possible to provide a simulation apparatus that can easily determine 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 an illustration of a set value of r _e. It is an illustration of the composition ratio x dependency of the atomic density ρ of the Si _1-x Ge _x layer. It is explanatory drawing of the evaluation result of (xi) _L. It is a schematic illustration of a nuclear stopping power S _n and the electronic stopping power S _e. It is explanatory drawing of the injection energy dependence of proportionality constant (xi) _L. It is explanatory drawing of the locus | trajectory of ion at the time of implanting B ion to Si substrate and Ge substrate. It is explanatory drawing of the locus | trajectory of ion at the time of implanting As ion to Si substrate and Ge substrate. 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 amount dependence of channel dose amount (PHI) _chan when B is inject | poured into Si substrate. It is explanatory drawing of the dose amount dependence of channel dose amount (PHI) _chan when P is inject | poured into Si substrate. It is explanatory drawing of the dose amount dependence of channel dose amount (PHI) _chan when As is inject | poured into Si substrate. It is explanatory drawing of the measurement result by RBS method. It is an ion implantation distribution diagram when B is implanted into a Si substrate and a Ge substrate. It is an ion implantation distribution diagram when P is implanted into a Si substrate and a Ge substrate. It is an ion implantation distribution diagram when As is implanted into a Si substrate and a Ge substrate. It is an illustration of the energy dependence of the electronic stopping power SS _e and nuclear stopping power S _n of B. It is an illustration of the energy dependence of the electronic stopping power S _e and nuclear stopping power S _n of P. It is an illustration of the energy dependence of the electronic stopping power S _e and nuclear stopping power S _n of As. Projected range of B R, is an illustration of the energy dependence of the projection R _p, lateral spread [Delta] R _pt. As P range of the R, it is an illustration of the energy dependence of the projection R _p, lateral spread [Delta] R _pt. As As Fei R, it is an illustration of the energy dependence of the projection _{R p,} lateral spread [Delta] R _pt. It is an ion implantation distribution diagram when B is implanted into a Si substrate. It is an ion implantation distribution diagram when B is implanted into a Ge substrate. The B constructed by the ion implantation distribution generating method of the present invention _{Si, Si} 0.9 _{Ge 0.1,} a configuration example of a database showing the respective parameters when injected into Si 0.8 _{Ge 0.2.} Ion implantation distribution generating method _Si 0.6 _Ge 0.4 was constructed B by the present _invention, Si _{0.2 Ge 0.8,} a configuration example of a database showing the respective parameters when injected into Ge. The P constructed by ion implantation distribution generating method of the present invention _{Si, Si} 0.9 _{Ge 0.1,} a configuration example of a database showing the respective parameters when injected into Si 0.8 _{Ge 0.2.} It is a structural example of the database which shows each parameter in the case of implanting P constructed by the ion implantation distribution generation method of the present invention into Si _0.6 Ge _0.4 , Si _0.2 Ge _0.8 , and Ge. It is a structural example of the database which shows each parameter in the case of implanting As constructed by the ion implantation distribution generation method of the present invention into Si, Si _0.9 Ge _0.1 , and Si _0.8 Ge _0.2 . Ion implantation distribution generating method _Si 0.6 _Ge 0.4 of As constructed by the present _invention, Si _{0.2 Ge 0.8,} a configuration example of a database showing the respective parameters when injected into Ge.

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 (1), the projection of the ion range extracted from the ion distribution in the amorphous layer in the implantation direction is The parameter R _p representing the distribution, the standard deviation ΔR _{p of} the distribution, the parameter γ representing the left-right asymmetry of the implanted ion distribution, and the parameter β representing the sharpness of the peak of the implanted ion distribution as R _p , ΔR _p , γ, β of the tail function While using
When R _max is the maximum ion range, the proportional coefficient ξ _L in the parameter L representing the tail spread of the ion implantation distribution defined by L = ξ _L (R _max −R _p ) is expressed as A, r _s. Is the coefficient, M ₁ is the mass number of ions, M ₂ is the mass number of atoms constituting the substrate, E is the energy of the ions, and E ₁ is the energy at which the electron stopping power and the nuclear stopping power are equal. 2) A method for generating ion implantation distribution.
N (x) = (Φ- Φ chan) n a (x) + Φ chan n c (x) ··· (1)
However, n _a (x) and n _c (x) are the 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)
nc (x) = h _mc (x): x <x _T
nc (x) = κ [h _mc (x) + h _TC (x)]: x> x _T
And the peak concentration position is represented by 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 ) / L] ^a }

The coefficient A and the coefficient r _s, the implanted ion implantation distribution generating method according to claim 1, wherein using the same value for all combinations of type and atoms constituting the substrates of ions. When the substrate is composed of a plurality of types of atoms, when M _2i is the mass number of each atom and n _i is the number of atoms per unit volume of each atom, M ₂ is represented by the following formula (3). The ion implantation distribution generation method according to claim 1, wherein M _2av is used.

The ion implantation distribution generation method according to claim _1, wherein the substrate is Si _1-y Ge _y (where 0 ≦ y ≦ 1). 5. A simulation apparatus that executes a calculation based on a calculation formula relating to the ion implantation distribution generation method according to claim 1. By executing the calculation based on the calculation formula, a combination of R _p , ΔR _p , γ, β, L, and a previously obtained for each ion type and each substrate type at an arbitrarily determined energy is stored as a database. The simulation apparatus according to claim 5.

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