JP2871588B2 - Simulation method of ion implantation process - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a simulator for a manufacturing process used for designing a semiconductor device, and more particularly to a method for simulating a distribution of implanted ions in an ion implantation process.

[0002]

2. Description of the Related Art The prior art of this type of ion implantation Monte Carlo simulation is as follows.
No. 4823, (2) Literature (SH Yang, et al.,
“A MoreEfficient Approach for Monte Carlo Simulat
ion of Deeply-Channeled Impanted Profiles in Singl
e-Crystal Silicon ”, NUPAD V, June 5, 1994, pp.97-1
00, Fig. 1-2).

It is industrially important to design a high-performance semiconductor device in a short time and at low cost. The electrical characteristics of a semiconductor can be arbitrarily designed by doping with an impurity, but it is not easy to directly measure the impurity distribution.

In addition, if the impurity distribution in a certain impurity introduction process can be accurately predicted in advance by computer simulation or the like before actually producing a prototype, useless trial production can be omitted.

In particular, ion implantation technology has conventionally been the mainstream for impurity introduction. As a precise simulation method of this ion implantation process, the movement of attentional ions in a target material is calculated by using a pseudo random number on a computer. There is a Monte Carlo method for simulation calculation. In recent years, the progress of Monte Carlo simulation of ion implantation has made it possible to calculate implantation into a crystalline semiconductor, and has been widely used.

However, in the conventional Monte Carlo simulation, the concentration of the implanted ions is represented by the number of sampled particles. Therefore, in a region where the concentration is low, the number of sampled particles decreases and the accuracy of the concentration distribution deteriorates. There is.

As a countermeasure, if the number of sampling particles is increased, the accuracy is improved, but the calculation time is greatly increased.

On the other hand, for example, Japanese Unexamined Patent Publication No.
No. 23, or the literature (SHYang, et al., “AM
ore Efficient Approach for Monte Carlo Simulation
ofDeeply-Channeled Impanted Profiles in Single-Cry
stal Silicon ”, NUPAD V, June 5, 1994, pp.97-100, F
The method described in ig. 1-2) etc. increases the overall calculation time by examining a place where the concentration accuracy is poor and partially re-performing the calculation from that place or its vicinity with a different random number sequence. This is to reduce the burden. In addition,
Japanese Patent Application Laid-Open No. 6-84823 discloses that a cross section orthogonal to an injection plane is divided into a plurality of cells of equal volume, and particles having a predetermined concentration weight are calculated by a Monte Carlo method at an initial stage. Injection trial calculation of particles with a concentration lower than the concentration weight for cells having a low concentration is carried out, and by repeating these steps continuously, particles having a low concentration The ion implantation process simulation has been proposed in which the distribution of the low concentration region can be grasped with high accuracy by the penetration of.

[0009]

The above-described conventional Monte Carlo simulation of ion implantation is intended to reduce the burden of simply increasing the number of sampling particles from the beginning and re-performing all high-precision calculations.

However, even in this case, in which part of the calculated result the accuracy of the density is insufficient,
It is necessary to judge where to start recalculation, etc.In particular, in order to judge that the accuracy of the concentration is insufficient, the concentration must be calculated. Spend time and require preliminary calculations.

In the case of two-dimensional and three-dimensional calculations,
Calculating the concentration alone requires a considerable amount of sampling, and even the preliminary calculations are already very burdensome.

In other words, the conventional method certainly contributes to reducing the load of the subsequent calculation for a certain calculation result, but the labor and calculation time required for the preliminary calculation required for this. Is still a heavy burden.

Accordingly, the present invention has been made in view of the above circumstances, and an object of the present invention is to perform the above-described preliminary calculation for the Monte Carlo ion implantation simulation with a large computer load. It is an object of the present invention to provide a simulation method that can eliminate the need to spend time and improve the accuracy.

[0014]

In order to achieve the above-mentioned object, the present invention provides a method for improving statistical properties in a Monte Carlo simulation calculation process of an ion implantation process. Ion implantation characterized by performing an operation of making a predetermined number of copies and distributing weights according to the number of copies, and performing this copy generation operation based on a distribution function of the flight distance of the ions in a three-dimensional space and in a plurality of stages. A method for simulating a process is provided.

[0015]

Embodiments of the present invention will be described below. The embodiment of the present invention increases only the number of sampling of ions having a long flight distance in order to improve the variation of the distribution which is a problem of the Monte Carlo simulation of the ion implantation process. In the simulation calculation process, as an operation of improving the statistical property, an operation of making a plurality of copies in the middle of calculation of the trajectory of the calculated virtual particles (ions) and distributing weights according to the number of copies is performed. This operation is performed in multiple stages based on the distribution of the flight distance of the ions in the three-dimensional space of the ions.

When the target substrate is composed of a plurality of media, a copy generating operation is performed based on a distribution function constructed after scaling the flight distance of ions by the average energy loss of each target medium.

Next, the principle of the embodiment of the present invention will be described. In the Monte Carlo calculation, the fact that the accuracy of the calculation result, that is, the concentration of the implanted ions here is poor, means that the number of sampling particles at the evaluation point is insufficient.

In order to improve the accuracy of the implanted ion concentration, when sampling and calculating ions implanted from the surface, the number of ions reaching that (evaluation location) may be increased. You can't tell if you can get to that place until you calculate it.

However, in the distribution of the implanted ions, in most cases, the variation at the bottom of the distribution becomes a problem. That is, if ions having a long range reaching a deep position are sampled preferentially, the number of samplings in the distribution can be effectively increased.

In the method according to the embodiment of the present invention, this operation of increasing the number of sampled particles is performed based on the flight distance distribution of the implanted ions.

The number of samplings at a place where the concentration distribution of the implanted ions is present, whereas the distribution of the flight distance of the ions has no place dependence when only one kind of medium is implanted. If there are a plurality of media, if they are standardized by an amount specific to the media, location dependency is almost eliminated. That is, even in the two-dimensional and three-dimensional calculations, the distribution function of the flight distance can be obtained with a very small number of samplings as compared with the calculation of the concentration distribution.

The distribution of the flight distance may be approximated, and can be updated while being calculated.

As described above, according to the embodiment of the present invention, the dispersion of the implanted ion distribution can be suppressed and the accuracy can be improved with little need for the preliminary calculation required by the conventional method.

Next, embodiments of the present invention will be described in more detail with reference to the drawings. FIG. 1 is a flowchart for explaining the processing operation of the embodiment of the present invention.

Referring to FIG. 1, first, in step S1, initial sample particles N are read.

Next, during the calculation of the trajectory of the implanted ions, a parameter N _c indicating how many copies are to be made and a parameter N _s indicating how many operations to make a copy are to be applied are read (step S 2).

Further, during the calculation of the trajectory of the implanted ions, the parameter L (N _s ) indicating at which flight distance the copy should be made is read by the number of application stages N _s (step S 3). However, since L (N _s ) is sequentially updated later during calculation, an appropriate value may be stored.

After that, steps S5 to S9 are performed in the same manner as the procedure of the ion implantation simulation by the ordinary Monte Carlo method. That is, the weight W of the particles is initially set to 1, the implantation energy and the implantation location are initialized (step S6), and the electronic element performance is calculated (step S6).
7) The nuclear element capability is calculated (step S8), and the inter-scatter distance S is calculated (step S9).

Next, an operation of normalizing the flight distance of the ions by the average energy loss amount in each material is performed (step S).
10), the standardized flight distance S of the _ions is stored as an amount L _ion obtained by accumulating (accumulating) (step S)
11 L _ion ← L _ion + S). This amount L _ion is initialized, for example, in step S6 and the like.

The point in time when this L _ion reaches each value of the preset L (N _s ) (ie, the point in time when L _ion > L (N _s ))
Then, in step S13, _Nc copies are made with the same particle energy, position, and traveling direction at that time. At this time, the weight W of each copy is reduced by the number _{Nc of} copies (W ← W / _Nc ).

Each copy particle is calculated in the same manner as a normal sampling particle, but each copy particle is calculated as a different trajectory because a pseudo random number sequence generated on a computer is different for each copy particle. . Since the flight distance of the copy is also stored, the copy particles may be further divided and copied.

As shown in step S14, the sampling particles are to have stopped in its place when it becomes smaller than the sufficiently small value E _d where that energy moves to the calculation of the next particle (Step S15 i ← i + 1).

As shown in the determination process of step S16 (whether or not the remainder of i by N _g is 0), at the time when N _g sampled particles are calculated, the index L for performing the particle multiplication operation is obtained.
(N _s ) is updated (step S17).

The index L in step S17
The update operation of (N _s ) may update the distribution of the _ion of the particles calculated so far and change the distribution to an appropriate position. An appropriate position is, for example, 1 point from the peak position of the distribution of L _ion.
A position where the value decreases to / 2, 1/4, 1/8 or the like is selected according to the desired number of stages. Further, the value of N _g may be a minimum number that enables the distribution of the flight distance to be formed by a simple approximation function.

The simulation ends when all the copy particles generated in the middle have been calculated and all the initial sample particles from which the copy has been made have been calculated. Then, the concentration distribution of the implanted ions is obtained from the position of the sample particles including the copy and the weight of each sample particle.

[0036]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In order to explain the above-mentioned embodiment of the present invention in more detail, specific embodiments will be described below with reference to the drawings.

FIG. 2 shows, by way of comparison, that phosphorus in crystalline silicon is reduced by 30 k by a conventional method which does not follow the method of the present invention.
FIG. 14 shows the results of ion implantation Monte Carlo simulation (ion implantation profile) when implanting at eV. In the simulation shown in FIG. 2, the number of sampled particles was 2000, and a workstation (EWS4800 manufactured by NEC) was used.
The calculation time in () and () was 338 seconds.

FIG. 3 shows the result (ion implantation profile) of applying the present invention to the same simulation of the ion implantation process conditions.

In the embodiment of the present invention, the initial number of particles corresponding to step S1 shown in FIG. 1 is 1000, and the Gaussian distribution is used as an approximate function form of the flight distance distribution of the ions used also in step S17. Also was 100 N _g in step S16. Further, in step S2, and the _{N c = 2, N s =} 4. Further, in step S3, a position which is reduced to 1/2 from the peak value of the Gaussian distribution which approximates the distribution of the ion flight distance as L (N _s ) is recursively calculated as N _s (= 4). Stage, applied.

After the simulation calculation, the final number of sampled particles increased to 1808 due to the multiplication effect. The calculation time of the simulation was 331 seconds at the same workstation as the comparative example, which was almost the same as that of FIG. 2 which is the calculation of the conventional method.

As shown in FIG. 2, the calculation results of the comparative example, the concentration of implanted ions, from where about 10 ¹⁶ cm ^-2, the concentration distribution of the implanted ions is has become a major noise variation However, in FIG. 3 showing the calculation results according to the example of the present invention, 10 ¹⁵ cm ⁻² to 10 ¹⁴ cm ⁻²
The dispersion of the distribution is suppressed to a low concentration, and a highly accurate calculation result is obtained.

In order to improve the precision by one or two digits, it is conventionally required to increase the number of particles by one or two digits, that is, to increase the calculation time corresponding to the increase in the number of particles.
According to the present embodiment, this is not necessary. That is, according to the present embodiment, it is possible to substantially increase the calculation efficiency by 10 to 100 times.

Here, for example, as a conventional technique,
JP-A-6-84823 and International Conference Proceedings
Comparing methods such as AH Yang's paper described in NUPADV, pp. 97-100, these conventional methods are first shown in FIG.
The calculation is performed as described above, and after re-calculation is performed after judging where the accuracy is insufficient, the calculation time is inevitably increasing.

FIG. 4 shows a calculation result obtained by performing the same calculation as that of FIG. 3 of the embodiment of the present invention by the conventional method after performing the preliminary calculation of FIG. 2 for comparison. In this case, the calculation time required 286 seconds in addition to 338 seconds required for the preliminary calculation in FIG.

On the other hand, in the method of this embodiment, there is no need to perform any preliminary calculation, and the accuracy of the solution can be improved by one or two digits in the same calculation time as in FIG.

Next, as a second embodiment of the present invention, FIG.
An example in which the present invention is applied to a two-dimensional calculation of ion implantation into a multi-medium structure by the same calculation method as described above will be described below.

FIG. 5A shows the structure to be calculated and the calculated distribution of implanted ions. 1.0 μm depth, 0.4 width
In a structure in which an amorphous silicon mask having a thickness of 0.1 μm and a width of 0.2 μm is present on a surface of a single-crystal silicon having a thickness of μm, arsenic (As) is applied at 80 keV and a dose of 1 × 10 ¹³ c.
The step of m ⁻² injection was calculated according to the processing flow of FIG.

In the processing flow shown in FIG. 1, as in step S10, when calculating the inter-scattering flight distance, weighting (normalization) was performed with the average energy loss in the material.

FIG. 5B shows the depth distribution of implanted ions immediately below the amorphous silicon mask when the weighting operation in step S10 is not performed and when the weighting operation is performed in step S10 in the processing flow of FIG.

If the weighting operation in step S10 is not performed, the distribution has sharply dropped.
This is because the number of particles is insufficient, and when the weighting operation in step S10 is performed, a smooth distribution is obtained.

[0051]

As described above, according to the ion implantation process simulation method according to the present invention, it is possible to eliminate the previously required preliminary calculation and calculate the ion distribution without increasing the simulation calculation time. This has a remarkable effect that the precision of the result can be improved, for example, by a factor of 10 or more (one digit) or more.

This is because, in the present invention, the accuracy of the entire simulation calculation result is not simply increased by the number of sampling particles, but the accuracy of the calculation result is insufficient. An operation of multiplying only the number of particles is performed, and this operation is performed based on a place-independent amount, which is a flight distance in three-dimensional space of the implanted ions normalized by an average energy loss in the medium, By configuring the flight distance distribution to be automatically updated during the calculation, the number of sampling particles near the base of the distribution can always be multiplied regardless of the calculation result of the implanted ion distribution. This is due to improved accuracy by eliminating unnecessary calculations.

[Brief description of the drawings]

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

FIG. 2 is a diagram showing, as a comparative example, a simulation result of phosphorus ion implantation into crystalline silicon by a conventional general ion implantation process simulation method by the Monte Carlo method.

FIG. 3 is a diagram showing a simulation result according to an embodiment of the present invention under the same ion implantation conditions as in FIG. 2;

FIG. 4 is a diagram illustrating a calculation result in a case where a calculation is performed to the same level of accuracy as in FIG. 3 by a conventional method after performing a simulation whose results are illustrated in FIG. 2;

FIG. 5 is a diagram for explaining a second embodiment of the present invention, and is a diagram showing a calculation result obtained by performing a two-dimensional calculation.

Claims (3)

(57) [Claims] In a Monte Carlo simulation calculation process of an ion implantation process, as an operation for improving statistical properties,
The ion particles are subjected to an operation of making a predetermined number of copies in the middle of the trajectory of the ion particles and distributing weights according to the number of copies, and performing the copy generation operation on the distribution function of the flight distance of the ions in the three-dimensional space. A simulation method of an ion implantation process, wherein the simulation is performed at a plurality of stages based on the above. 2. When the target substrate is composed of a plurality of media,
2. The simulation of the ion implantation process according to claim 1, wherein the copy generation operation is performed based on a distribution function configured after normalizing the flight distance of ions by an average energy loss of each target medium. Method. 3. In the copy generating operation, when the flight distance of an ion on a flight trajectory exceeds a predetermined distance,
The method according to claim 1, wherein one or more copy particles having the same energy, position, and direction as the ion particles are generated.