JP3102472B2 - Ion implantation simulation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a method for simulating a semiconductor manufacturing process, and more particularly to a method for simulating ion implantation.

[0002]

2. Description of the Related Art A Monte Carlo ion implantation simulation method is described in Ryo Dan, "Process Device Simulation Technique", p60, 1990.
In this method, the type and relative position of the atom (nucleus) that the ion moving next in the substrate collides with are determined by random numbers, and the traveling direction and the motion of the ion after scattering are determined from the impact parameter P shown in FIG. It calculates energy. The energy loss due to electron scattering is L
It is calculated by SS theory or the like. When calculating by LSS theory, the energy due to electron scattering is an amount proportional to the moving distance and velocity of the ions.

The above-described simulation method corresponds to a calculation method for an amorphous substrate because the position of an atom (nucleus) to which ions collide next is determined by random numbers. A Monte Carlo ion implantation simulation method for a substrate having a crystal structure is described in M.S. Posselt, “Comp
outer simulation of ion im
plantation into crystalli
ne targets ”, Nuclear Instrument
Uments and Methods in Physs
ics Research B64 (1992) pp7
06-710. According to this, in ion implantation simulation for a substrate having a crystal structure, it is necessary to determine the nucleus to which ions will collide next by searching from the crystal lattice existing in the substrate. 3A is divided into unit cells (unit cells) having a diamond structure as shown in FIG.
The cells are classified into two types of cells, (b) and (c), and then it is determined which type of cell is present in FIGS. 3 (b) and (c). They are looking for the next nucleus that the ion will bombard from one type of cell.
M. In the literature of Posselt et al., The maximum value P _max of the impact parameter when an ion collides with an atom is calculated using the atomic density N per unit volume.

[0004] _{^{πP 2 max = N -2/3 (1}} )

[0005] _Pmax is the radius of a sphere having the same volume as the volume occupied by one atom.
It becomes smaller than the cell size of (b) and (c). Therefore, the range of searching for the nucleus where the ions collide is as shown in FIG.
The range of the cells (b) and (c) may be used. However, increasing P _max is closer to the actual condition, and the calculation accuracy is improved. In fact, depending on the literature,
In some cases, _Pmax is set to 5 Å, which is close to the lattice constant. In such a case, when searching for a nucleus that collides with the ion, it is necessary to search for an atom inside the sphere having a radius of P _max or more around the ion (or the atom closest to the ion). (FIG. 4).

[0006]

The problem is that, as shown in FIG. 4, when the number of atoms to be searched for colliding nuclei is large, the calculation time for the search becomes long, so that ion implantation is difficult. The time required for the simulation increases. The reason is that in order to find the next nucleus to collide with, it is necessary to calculate the distance to the collision for all target atoms.

[0007]

SUMMARY OF THE INVENTION It is an object of the present invention to reduce the calculation time of the Monte Carlo ion implantation simulation for a crystal structure substrate.

[0008]

According to the ion implantation simulation method of the present invention, means for judging whether data for shortening the calculation time is registered (FIG. 1, S1).
(FIG. 9, P1), means for taking out the unit cell and dividing it into small cells (FIG. 1, S2) (FIG. 9, P2), ions from one of the divided cells θ _i to θ _{i + 1} , φ _{j to} φ _{j + 1}
Means (FIG. 7 (b)) for obtaining a figure representing the trajectory of the ion when it flies in an arbitrary direction, and setting an appropriate range of space around the divided cells.
Means for finding and placing nuclei within _max (Fig. 8)
Means for registering, among all the nuclei arranged by the above means, those in which a sphere having a radius P _max from the nucleus intersects with the figure representing the ion trajectory, for the combination of the target cell and the angular range (FIG. S5), for all combinations of the divided cells and the angular range, a process of obtaining a trajectory of ions emerging from the cell, a process of arranging nuclei around the cell, and a nucleus among the arranged nuclei Means for registering the one where the sphere centering on the trajectory of the ion intersects (Fig. 1,
S6), means (FIG. 1, S7) for calculating in which of the divided cells the ions to be subjected to the scattering calculation are present, and the directions of the ions to be calculated are divided. Means (S8 in FIG. 1) for calculating in which angular range the directions are present, and the nuclei registered in the angular range including the cell where the ions are present and the direction in which the ions are traveling are taken out, and A means (FIG. 1, S9) for calculating which nucleus of the ion collides with the ion, a means (FIG. 1, S10) for performing a scattering calculation when the ion collides with the nucleus calculated by the above means, Means for calculating the nuclei that collide and performing the scattering calculation until the ions are stopped (FIG. 1, S11), and means for performing the processing until the implanted ions are stopped for a predetermined number of ions (FIG. 1, S12) Having.

Further, according to the ion implantation simulation method of the present invention, after dividing a unit cell into cells, means for classifying the divided cells into those requiring data registration and those requiring no data registration based on the symmetry of the unit cell (see FIG. 9, P3) and data registration processing for obtaining a figure representing a locus of ions when ions fly from one cell in any direction of θ _i to θ _{i + 1} and φ _{j to} φ _{j + 1.} Data registration means (P4 in FIG. 9) for only necessary cells and processing for setting an appropriate range of space around the cell and finding and arranging nuclei within _Pmax from the set space Means (P5 in FIG. 9) for only the cells that need to be performed, means for determining the trajectory of ions emerging from the cell for a combination of the cell and the angle range, and means for arranging nuclei around the cell. And of the placed nucleus And means for performing only for cells in the treatment of a sphere centered on the nucleus to register what intersects the trajectory of the ions must be data registration (Fig. 9, P7),
After calculating in which of the divided cells the ion to be subjected to the scattering calculation is located, if the calculated cell is classified as a cell that does not require data registration, Means (P9 in FIG. 9, P9) for finding a cell that substitutes for the cell and moving the position and direction of the ion to a cell classified as requiring data registration by using symmetry (FIG. 9, P9); After taking out the nuclei registered in the angular range that includes the cell and the direction in which the ions travel, and calculating which of these nuclei will collide with the ions, if the above means, the position and direction of the ions are symmetrically moved. In this case, there is provided means (FIG. 9, P12) for symmetrically moving the calculated position of the nucleus in the direction opposite to that performed by the above means.

In the present invention, when the range in which ions exist and the range in which the direction in which ions travel exist are determined,
Since the number of nuclei to be determined as to whether or not ions collide is limited, the calculation time for determining the nuclei to collide is reduced.

According to the second aspect of the present invention, the amount of data that needs to be registered is reduced in consideration of the symmetry of the unit cell of the crystal.

[0012]

Next, a first embodiment of the present invention will be described in detail with reference to the drawings. FIG. 1 is a flowchart of the first embodiment of the present invention.

First, in S1, it is determined whether data for shortening the calculation time of the simulation is registered. If not registered, data is registered by performing steps S2 to S6. If it has already been registered, the calculation of the ion implantation simulation is performed in S7 to S12. Subsequently, if no data is registered in S1, a unit cell (including a unit cell (including a basic unit cell)) determined for the crystal structure in S2 is taken out, and the unit cell taken out as shown in FIG. Is divided into cells. The division of the unit cell is performed by dividing each side at equal intervals as shown in FIG. 5A (Δr ₁ , Δ
r ₂ and Δr ₃ are intervals when each side is divided). Here, the unit cell is written as a cube, but the unit cell does not necessarily need to be a cube or a box, and the angles α, β, and γ shown in FIG. May not be equal.

Subsequently, in S3, the azimuths θ and φ are divided at equal intervals as shown in FIG. 5B, and the divided angles are respectively 0, θ,..., Θ _i ,. 0, φ ₁ , ..., φ
_j ,..., 2π. Thereafter, for one of the cells divided in S2, ions existing in this cell flew in any direction within the range of azimuth angles θ _{i to} θ _{i + 1} and φ _{j to} φ _{j + 1} . In this case, a figure representing a locus through which ions pass is obtained. The figure representing this trajectory is obtained by the following method. First, FIG.
(A), the semi-straight line hl when the azimuth angle is _{θ = θ i, φ = φ} j, can when the phi while fixing the theta is changed from phi _j to phi _{j + 1} Find the surface lhi.
In addition, the other three surfaces khj, lhk, and ihj shown in FIG. Subsequently, a three-dimensional figure hlkji surrounded by the four surfaces obtained above is obtained. Subsequently, for all the sides on the target cell, the ions pass through the space (the oblique line in FIG. 7B) through which the three-dimensional figure passes when the three-dimensional figure moves so that the vertex h moves on the side. Let it be a figure representing a trajectory.

Subsequently, in S4, a space of an appropriate range is set around the cell (in FIG. 8, a space surrounded by a plane separated by a distance d from the cell), and a space set as shown in FIG. , All the nuclei within the maximum value _{Pmax of the} collision coefficient are obtained and arranged.

Subsequently, in S5, of all the nuclei arranged in S4, a sphere having a radius P _max centered on the nucleus is formed in S3.
Search for a thing that intersects with the figure representing the trajectory obtained in or the thing that the nucleus itself is included in the figure of the trajectory.
Register for the combination of the current target cell and angle range. However, for example, as shown in FIG. 7 (b), when all ions moving from inside the cell collide with another atom (here, atom a) before colliding with atom b, Do not register atom b.

Subsequently, in S6, S3, S4, and S5 are repeated, and the corresponding nucleus is registered with respect to all the combinations of the divided cells and the angle range in the unit cell, and the flow proceeds to S7.

Subsequently, in the processing of S1, if data for shortening the calculation time is registered, or after the processing of S6 is completed, the ions to be calculated by executing S7 are divided by S2. Calculates in which of the cells are located. In this case, since each side of the unit cell is divided at equal intervals, the number of the cell in which the ion exists can be determined by dividing the coordinate of the ion by the interval at the time of division.

Subsequently, in S8, it is calculated in which angular range the direction of the ion to be calculated exists in the divided directions. At this time, since the angles are divided at equal intervals, the angles θ and φ representing the traveling directions of the ions are used.
Are divided angles θ _i (i = 1, 2, 3,...), Φ
_j (j = 1, 2, 3,...), the angle θ _{i + 1} −θ is obtained by dividing the angles θ and φ representing the traveling direction of the ions. _i , φ _{j + 1} −φ _j to obtain the value.

Subsequently, in S9, the coordinate positions of the nuclei registered with respect to the combination of the cell and the angle range calculated in S7 and S8 are taken out, and which of these nuclei the ion first collides with is selected. Is calculated.

Subsequently, in S10, the scattering calculation when the ions collide with the nuclei calculated in S9 is performed.

Subsequently, in S11, S7, S8, S9, S
Step 10 is repeated until the ions come to rest.

Subsequently, in S12, S7 to S11 are repeated to perform an implantation calculation for a predetermined number of ions.

Next, a second embodiment of the present invention will be described in detail with reference to the drawings. FIG. 9 shows a flow of the second embodiment of the present invention.

First, at P1, it is determined whether data for shortening the calculation time is registered. If not registered, proceed to P2. If registered, proceed to P8. Subsequently, when the process proceeds from P1 to P2, S2 of the first embodiment is performed.
Similarly to the above, the unit cell is taken out and divided into small cells.

Subsequently, in P3, the cells divided in P2 are classified into those requiring data registration and those not requiring data registration in consideration of the symmetry of the unit cell. For example, an example in the case of silicon is as follows. Assuming that the cube shown in FIG. 10A is a silicon unit cell, the silicon unit cell is plane-symmetric with respect to the plane opqr. Therefore, the unit cell is restored from one of the solids bounded by this plane using symmetry. it can. Further, the atomic nucleus that collides with the ion having the velocity existing in one of the three-dimensional bodies is at the plane symmetric position with the atomic nucleus that collides with the ion having the plane symmetric position and the velocity vector in the plane opqr. Therefore, the cells for which data needs to be registered are cells that overlap with the hatched portions in FIG. Since the unit lattice of the silicon crystal has several planes symmetrical in addition to the plane opqr in FIG. 10A, the shaded portion in FIG. Can be changed to a smaller area that can be restored to This is shown in FIGS. 10 (b) to 10 (f). When the cells for which data needs to be registered are obtained from the shaded area in FIG. 10A, the number of cells is about 比 べ as compared with the case where no symmetry is used. Further, when it is obtained from the shaded area in FIG. 10F, it is 1/24.

Subsequently, at P4, for one of the cells classified as having to register data at P3, ions existing in the cell are in the angular range θ _{i to} θ _{i + 1} , φ _j to φ
A figure representing the trajectory of ions when traveling in an arbitrary direction of _{j + 1} is obtained by the same method as in S3 of the first embodiment.

Subsequently, in P5, a space within an appropriate range is set around the cell handled in P4, and the nuclei within _Pmax from the set space are determined and arranged, similarly to S4 of the first embodiment. I do.

Subsequently, at P6, as in S5 of the first embodiment, of all the nuclei arranged at P5, a sphere having a radius _Pmax centered on the nucleus intersects with the figure representing the trajectory obtained at P4. The object or the nucleus itself is searched for in the trajectory figure, and the nucleus is registered with respect to the combination of the cell and the angle range which are currently targeted.

Subsequently, at P7, P4, P5, and P6 are repeated, and the corresponding nucleus is registered for the combination that requires data registration classified at P3, and the program proceeds to P8.

Subsequently, the process proceeds to P8 at P1 or
After the process of 7, in P8, as in S7 of the first embodiment, it is calculated in which of the cells divided in P2 the ions to be calculated are present.

Subsequently, at P9, the cell calculated at P8 is P
If the cell is classified as a cell that does not require data registration in step 3, a cell that substitutes for this cell is determined based on symmetry. In addition, the position and direction of the ions are moved to cells classified as requiring data registration by utilizing symmetry. Regarding a method of finding a cell that substitutes for a cell that does not need to be registered, here, the cell that needs to be registered is shown in FIG.
(R), Δr ₁ , Δr in FIG.
₂ and Δr ₃ will be described by taking as an example a case where Δr ₁ = Δr ₂ = Δr ₃ . FIG. 11 is a diagram of FIG. 10B as viewed from above. When the ion exists in the region b (2) in FIG. 11, the position and the direction vector of the ion are moved to a mirror-symmetric position of a plane vx where the unit cell is plane-symmetric,
Move to cell (1) where data is registered. When the ions are present in the region (3) of the region d, the position and the direction vector of the ions are first symmetrically moved with respect to the plane wy and then symmetrically moved with respect to the plane vx. Can be moved to the position (1). When the ion exists in the region d (4), the position and the direction vector of the ion are symmetrically moved with respect to the plane wy to move to the position (1) in which data is similarly registered. Can be done.

Subsequently, in P10, it is determined in the same angular range as that of S8 in the first embodiment that the direction of the ion to be calculated or the direction of the ion moved in P9 exists in which angular range of the divided directions. Calculate by method.

Subsequently, at P11, P8 (or P9), P8
The nuclei registered in the cell and the angular range calculated in 10 are taken out, and it is calculated which of these nuclei the ion collides with.

Subsequently, in P12, when the position and direction of the ion are symmetrically moved in P9, the position of the nucleus calculated in P11 is moved by the operation opposite to the symmetric movement performed in P9.

Subsequently, at P13, P11 (or P12)
The scattering calculation is performed when the ion to be calculated collides with the nucleus calculated in.

Subsequently, at P14, P8 to P13 are repeated until the ions come to rest.

Subsequently, in P15, P8 to P14 are repeatedly performed to perform an injection calculation for a predetermined number of ions.

[0039]

According to the present invention, when the range in which the ions are present and the range in which the direction in which the ions travel are determined, the number of nuclei to be determined whether or not the ions collide is determined. Is limited, the calculation time for determining the nucleus to collide is reduced, and the time required for the simulation can be reduced.

According to the second aspect of the present invention, the amount of data that needs to be registered is reduced by considering the symmetry of the unit cell of the crystal, so that the amount of memory required by the computer is reduced. Can be reduced.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a first embodiment of an ion implantation simulation method according to the present invention.

FIG. 2 is an explanatory diagram showing a state where ions collide with an atomic nucleus.

FIG. 3 is a perspective view showing a state in which a unit cell is divided in order to search for an atomic nucleus that collides with ions in the related art, and FIG. 3 (a) is divided into FIGS. 3 (b) and 3 (c). Here is an example.

FIG. 4 is an explanatory view showing a state of searching for an atomic nucleus that collides with ions.

5A and 5B are perspective views showing how a unit lattice and an angle representing a direction are divided, and FIGS. 5A and 5B are FIGS.
It is an example of dividing into (c).

FIG. 6 is a perspective view showing a unit lattice that is not a cube (or a rectangular parallelepiped).

FIG. 7 is a perspective view showing a figure representing a trajectory when ions jump out of a cell, and the figure is obtained in the order of FIGS. 7 (a) and 7 (b).

FIG. 8 is an explanatory view showing a state where nuclei are arranged around a cell.

FIG. 9 is a flowchart showing a second embodiment of the ion implantation simulation method according to the present invention.

FIG. 10 is a perspective view showing a state in which a silicon unit cell is cut along a plane that is plane-symmetric and a region is reduced.
The area is reduced in the order of 0 (a) to FIG. 10 (f).

FIG. 11 is an explanatory view showing a state in which the position and direction of ions are moved by utilizing the symmetry of a silicon unit cell.

Claims (4)

(57) [Claims] 1. Step S2 of taking out a unit cell and dividing it into small cells; and azimuth angles θ _i to か_ら from one of the cells divided in step S2.
theta _{i + 1,} if the flew ionic any direction within a range of φ _j ~φ _{j + 1,} and step S3 to determine a graphic representing a locus ion passes, around the cells treated in step S3 Set an appropriate range of space and set the maximum impact parameter from the set space.
Step S for finding and arranging nuclei within the value _Pmax
And step S5 of registering, among all the nuclei arranged in step S4, a sphere having a radius P _max from the nucleus that intersects the figure obtained in step S3 for the combination of the target cell and the angle range; Step S6 for performing the processing of steps S3, S4 and S5 for all the combinations of the divided cells and the angle range.
Step S7 of calculating in which cell among the cells divided in step S2 the ion for which the scattering calculation is to be performed is present, and step S7 for calculating the direction of the ion for which the scattering calculation is to be performed. Step S8 for calculating in which angular range the cell exists, and the cells calculated in steps S7 and S8 and the nuclei registered in the angular range are taken out, and which of these nuclei the ions collide with is extracted. Step S9 for calculating the following equation; Step S10 for performing scattering calculation when ions collide with the nucleus calculated in Step S9; and Step S11 for performing the processing of Steps S7, S8, S9 and S10 until the ions come to rest. Step S1 in which the processes of steps S7, S8, S9, S10 and S11 are performed for a predetermined number of ions.
2. An ion implantation simulation method, comprising: 2. A step P2 of taking out the unit cell and dividing it into small cells, and a step P3 of classifying the cells divided in step P2 into those that need to be registered and those that do not need to register data based on the symmetry of the unit cell. azimuth θ _i ~θ _{i + 1} from one need a certain cell of the classified data registered in step P3, if the flew ionic any direction within a range of φ _j ~φ _{j + 1,} this Step P4 for obtaining a figure representing the trajectory through which ions pass, and setting an appropriate range of space around the cell treated in Step P4, and setting the maximum impact parameter from the set space.
Step P for finding and placing nuclei within the value _Pmax
5 and, among all the nuclei arranged in Step P5, a step in which a sphere having a radius P _max from the nucleus intersects with the figure obtained in Step P4 is registered for the combination of the target cell and the angle range, Steps P4 and P4 are performed on all combinations of cells and angle ranges that need to be registered in step P3.
Step P7 for performing the processes of Steps 5 and P6, Step P8 for calculating which of the cells divided in Step P2 contains an ion to be subjected to the scattering calculation, and Cell calculated for Step P8 Is classified as a cell that does not require data registration in step P3, a cell that substitutes for this cell is obtained from the symmetry, and the position and direction of the ion are determined using the symmetry in step P3. Step P9 of symmetrically moving the cells classified as necessary, and calculating in which angular range of the divided directions the ions to be subjected to the scattering calculation or the ions moved in step P9 Step P10, and taking out the nuclei registered in the cell and the angle range calculated in Step P8 or Step P9 and Step P10, Step P11 for calculating which of these nuclei the ions will collide with. If the position and direction of the ions are symmetrically moved in Step P9, the calculated positions of the nuclei are converted to Step P11.
Step P1 of symmetrically moving in the opposite direction to that performed in
2, step P13 for performing scattering calculation when ions collide with the nucleus calculated in step P11 or P12, and steps P8, P9, P10, P11, P12 and P1.
Step P14 of performing the processing of Step 3 until the ions stop.
Steps P8, P9, P10, P11, P12, P13
A step P15 of performing the processes of P14 and P14 for a predetermined number of ions. 3. A step S1 for determining whether or not data for shortening the calculation time is registered is added before the step S2. If the data is not registered, the process proceeds to the step S2. 2. The ion implantation simulation method according to claim 1, wherein the process proceeds to step S7 if the information is already registered. 4. A step P1 for judging whether data for shortening calculation time is registered is added before the step P2, and if the data is not registered, the process proceeds to the step P2, and the data is 3. The ion implantation simulation method according to claim 2, wherein the process proceeds to step P8 when the ion implantation has already been registered.