JPH10294293A - Sputter device simulation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce a track calculation time of sputter particle by calculating a deposit film shape from angle distribution of a track of extracted sputter particle when energy of sputter particle is smaller than average energy of particle following Maxwell distribution of temperature inside a sputter device. SOLUTION: Relative velocity of Ti sputter particle and Ar background gas particle is obtained, collision energy is obtained from the relative velocity and velocity of Ti sputter particle after collision is calculated. In the process, energy of sputter particle after collision is calculated from velocity of Ti sputter particle and is compared to average energy of Ar background gas particle following Maxwell distribution of device gas temperature. When energy after collision of Ti sputter particle is smaller than average energy of Ar background gas particle, it is judged whether or not Ti sputter particle is extracted on a wafer, a track of sputter particles required for angle distribution calculation is calculated and a deposit configuration is calculated using an extracted track 121.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for simulating a sputtering apparatus, and more particularly to a method for simulating a sputtering apparatus for calculating collision with a background gas by a Monte Carlo method.

[0002]

2. Description of the Related Art With the increase in the number of mounted elements in a semiconductor integrated circuit device, there is an urgent need to develop a technique for embedding a conductive film in a miniaturized contact hole.

[0003] In order to solve this problem, it is necessary to develop a sputtering apparatus. Simulation techniques have been developed for the purpose of improving the efficiency of the development of a sputtering apparatus.
As this kind of simulation technology, for example, literatures (H. Yamada et al., I.E.D.M., (199
4), pp. As described in 553 to 556), a method of calculating a trajectory in an apparatus and calculating a shape using a string model is known.

The prior art of the simulation of the sputtering apparatus will be schematically described below with reference to a flowchart shown in FIG.

First, Ti sputter particles are generated from the Ti target surface at a probability proportional to the erosion distribution (step 301), and uniform random numbers e1 and e2 are used to return numbers in the range of 0 to 1 with the same probability. The horizontal angle Φ (Φ = 2π · e1) and the vertical angle θ ｛θ = acos ((e2) 1/2)｝ are obtained, and the emission energy Ee and the velocity Vs of the Ti sputtered particles Vs = (2Ee / m) ^1/2 is determined by a rejection method using uniform random numbers e3 and e4 so as to follow the Thompson distribution. Here, the uniform random number is a random number that returns a number in the range of 0 to 1 with the same probability.

[0006] The velocity Vg of the Ar background gas particles according to the Maxwell distribution of the device gas temperature is determined by the uniform random numbers e5 and e5.
6, using the Box-Muller method

[0007]

(Equation 1)

(Step 302), the relative velocity Vrel = Vs−V between the Ti sputtered particles and the Ar background gas particles.
g is obtained by vector calculation. Here, Vg ′ is Bo
Since these values are determined simultaneously due to the nature of the x-Muller (box-Muller) method, they are used in the next calculation of the velocity of Ar background gas particles. The collision energy E is obtained from the relative velocity Vvel (step 303).

[0009] In addition, Lenard-J between Ti-Ar
Assuming a ones (Leonard-Jones) two-body potential, the calculation of the central force field in classical mechanics shows that at each collision energy E, the relationship between the scattering angle の in the traveling direction before and after the collision as seen from the center of gravity and the collision parameter b is calculated. Then, assuming the scattering angle χ and the linearity of the collision parameter b, the collision radius bmax is determined (step 301), and the relationship between the collision energy E and the collision radius bmax is tabulated.

The table 320 is created only once before the Monte Carlo calculation, and is referred every time the collision between the sputtered particles and the background gas is calculated by the Monte Carlo method.

Next, using the uniform random number e7, the collision parameter at the collision energy E is obtained by b = bmax · e7 (step 305), and the scattering angle よ り is obtained by the scattering angle χ = π · b / bmax. The energy loss κ at the scattering angle χ is calculated from the theory of the central force field in classical mechanics, and the direction and velocity of the Ti sputtered particles after collision are calculated (step 30).
6).

At the same time, the collision radius is calculated by calculating the mean free path λ0 from bmax, assuming a Poisson distribution, and using the uniform random number e8, the distance dL = λ0 · Vrel until the Ti sputtered particle causes the next collision. │1n (e8) │ is calculated (step 307).

By these calculations, the trajectory of the Ti sputtered particles after the collision is calculated.

Thus, the trajectory of the particles is repeatedly calculated until the particles reach the side wall of the apparatus or the wafer (step 310).

Finally, the trajectory of the Ti sputtered particles is extracted in a certain area on the wafer, and the shape is calculated using the result by using a string model or the like (step 322).

[0016]

In the above-mentioned conventional simulation technique, when calculating the trajectory of a sputtered particle in a high pressure region where collisions occur 5 or more times, the energy of the sputtered particle emitted from the target is reduced by the collision. If lost and the mean free path becomes small relative to the size of the device, a number of collision calculations will need to be performed until they are extracted or trapped on the wafer (see the determination of steps 308, 309).

Therefore, to calculate the trajectory of about 10 million particles statistically required by the Monte Carlo method, 190 MI
50 on EWS (Engineering Workstation) of PS (Million Instrutions Per Second)
It takes time and is not practical.

Therefore, the present invention has been made in view of the above problems, and an object of the present invention is to provide a simulation method for shortening the time required for calculating the trajectory of sputtered particles in a sputtering apparatus. .

[0019]

In order to achieve the above object, a simulation method according to the present invention is directed to a method for simulating a sputtering apparatus for forming a deposited film shape of a contact hole. Emitting particles, (b) calculating collisions between the sputtered particles and a background gas,
(C) Maxwell (Ma) at the temperature in the sputtering apparatus
xwell) The average energy of the particles according to the distribution and the energy of the sputtered particles are compared. If the energy of the sputtered particles is smaller, the presence or absence of extraction in the extraction area on the wafer is determined using the expected angle. A determining step; and (d) calculating a deposited film shape from the angular distribution of the trajectories of the extracted sputtered particles.

[0020]

Embodiments of the present invention will be described below. The simulation method of the present invention comprises the steps of (a)
To (b).

(A) In a simulation of a sputtering apparatus for forming a deposited film shape of a contact hole, sputter particles are emitted from a target of the sputtering apparatus.

(B) Calculate the collision between the sputtered particles and the background gas.

(C) Maxwe of the temperature in the sputtering apparatus
The average energy of the particles according to the 11 distribution and the energy of the sputtered particles are compared, and if the energy of the sputtered particles is smaller, the presence or absence of extraction in the extraction area on the wafer is determined from the expected angle.

(D) The shape of the deposited film is calculated from the angular distribution of the orbits of the extracted sputtered particles.

In the embodiment of the present invention configured as described above, the sputtered particles having the same energy or less as the background gas particles according to the Maxwell distribution are extracted from the expected angle in the extraction region on the wafer. Is determined.

That is, in the embodiment of the present invention, calculation of collision of sputtered particles whose mean free path is smaller than the size of the apparatus can be omitted, so that orbit calculation can be performed in a short time. The processing in each of the above steps is preferably implemented by a program, and is realized by executing the program in an information processing device such as an EWS (Engineering Workstation) as described later.

[0027]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram showing an embodiment of the present invention;

FIG. 1 is a flowchart for explaining the outline of a sputtering apparatus simulation method according to one embodiment of the present invention.

In this embodiment, for example, the trajectory of the sputtered particles is calculated by the following procedure using the Monte Carlo method.

First, Ti sputtered particles are generated from the Ti target surface with a probability proportional to the erosion distribution (step 101), and uniform random numbers e1 and e2 which return numbers in the range of 0 to 1 with the same probability are used. , Horizontal angle Φ
(Φ = 2π · e1), vertical angle θ {θ = acos
((e2) 1/2)}, the emission energy Ee and the velocity Vs of the Ti sputtered particles Vs = (2Ee / m) 1 /
2 according to the Thompson distribution, one random random number e3,
Determined by the rejection method using e4. Here, the uniform random number is a random number that returns a number in the range of 0 to 1 with the same probability.

Further, Ar background gas particles are generated according to the Maxwell distribution of the device gas temperature (step 10).
2). That is, the velocity Vg of the Ar background gas particles according to the Maxwell distribution of the device gas temperature is determined by the Box-Muller method using uniform random numbers e5 and e6.

[0032]

(Equation 2)

Then, the relative velocity Vrel = Vs−Vg between the Ti sputtered particles and the Ar background gas particles is obtained from the bearing calculation. Here, Vg ′ is Box-Muller
Since it is a value determined simultaneously due to the nature of the method, it is used in the next calculation of the velocity of Ar background gas particles.

The collision energy E is determined from the relative speed Vrel (step 103).

Also, Leard-Jo between Ti-Ar
Assuming a two-body potential, a calculation of the central force field in classical mechanics was performed to find the relationship between the scattering angle の between the traveling direction before and after the collision as viewed from the center of gravity and the collision parameter b at each collision energy E. The collision radius bmax is calculated assuming the linearity of
4).

This table 120 is created only once before the Monte Carlo calculation, and is referred every time the collision between the sputtered particles and the background gas is calculated by the Monte Carlo method.

Next, using the uniform random number e7, the collision parameter b at the collision energy E is determined by b = bmax · e7 (step 105). The scattering angle χ is calculated from the scattering angle χ = π · b / bmax. The energy loss κ at the scattering angle χ is calculated from the central force field theory of classical mechanics (step 10).
6) Calculate the velocity of the Ti sputtered particles after collision.

At this time, from the speed of the Ti sputtered particles,
The energy Eaft of the sputtered particles after collision is calculated (step 107), and the average energy Egas of Ar background gas particles according to the Maxwell distribution of the device gas temperature (= kT /
4π) (step 108).

Energy E after collision of sputtered Ti particles
If aft is smaller than the average energy Egas of the Ar background gas particles, it is determined whether or not Ti sputtered particles are extracted on the wafer as follows (step 1).
12, 113).

First, as shown in FIG. 2, starting from the collision point 1 of the Ti sputtered particle and using uniform random numbers e8 and e9, a horizontal angle Φ ′ (Φ ′ = 2π · e8) and a vertical angle Φ ′ are obtained. (Θ ′ = π · e9), and a trajectory 3 for extraction determination is generated.

Next, the intersection of the trajectory 3 with the upper surface of the wafer for the extraction determination is calculated, and if the intersection is within the sputter particle extraction region, it is determined that the extraction is performed in the extraction region 2 on the wafer. Then, the trajectory of the Ti sputtered particles after the collision is recorded in a file.

If the intersection is not within the extraction region, it is determined that the trajectory of the Ti sputtered particles is trapped on the side wall of the apparatus or on the wafer. As a result, the extraction determination is performed at a rate proportional to the prospective angle 2 looking into the extraction area 2 from the collision point 1.

On the other hand, when the energy Eaft after collision of the Ti sputtered particles is larger than Egas, the collision radius b
The mean free path λ0 is calculated from the max, the Poisson distribution is assumed, and the distance dL = λ0 · Vrel · | 1n (e10) | Then, the trajectory of the Ti sputtered particles after the collision is calculated (step 109). Further, repeated collision calculations are performed until the particle trajectory is extracted in the extraction area on the wafer or trapped on the side wall of the apparatus or on the wafer.

In this way, the angle distribution calculation
The trajectory of about 10 million sputtered particles is calculated, and the extracted trajectory 121 is used to calculate the deposition shape using a string model or the like (step 122).

At this time, the trajectory calculation time of the sputtered particles by the Monte Carlo method is about 3 hours with an EWS of 190 MIPS because the collision calculation after losing energy is omitted, which is much larger than the conventional simulation technology. This is a practical calculation time that has been reduced.

[0046]

According to the present invention, since the extraction judgment is performed by calculating the expected angle with respect to the extraction region without performing the subsequent collision calculation for the sputtered particles having reduced energy, the calculation related to the calculation of the trajectory of the sputtered particles is performed by the conventional method. About 20 of technology
It can be performed in about one-half the calculation time.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating an outline of a sputtering apparatus simulation method according to an embodiment of the present invention.

FIG. 2 is a diagram for explaining one embodiment of the present invention;
It is a schematic diagram which shows calculation of extraction determination.

FIG. 3 is a flowchart illustrating an outline of a conventional sputtering apparatus simulation method.

[Description of Signs] 1 Collision point 2 Extraction area on wafer 3 Trajectory for extraction judgment 4 Estimated angle

Claims (2)

[Claims] 1. A method for simulating a sputter device for forming a deposited film shape or the like of a contact hole, comprising: (a) discharging sputter particles from a target of the sputter device; and (b) collision of the sputter particles with a background gas. (C) Maxwell (Ma) of the temperature in the sputtering apparatus.
xwell) The average energy of the particles according to the distribution and the energy of the sputtered particles are compared, and if the energy of the sputtered particles is small, the presence or absence of extraction in the extraction region on the wafer is determined using the expected angle. Steps,
And (d) calculating the shape of the deposited film from the angular distribution of the orbits of the extracted sputtered particles. (A) a process for emitting sputtered particles from a target; (b) a process for calculating the collision between the sputtered particles and a background gas; and (c) an energy after the collision of the sputtered particles is calculated. And comparing the average energy of the gas particles according to the Maxwell distribution of the temperature with the energy of the sputtered particles. If the energy of the sputtered particles is smaller,
A process of judging the presence or absence of extraction in the extraction region on the substrate by using an expected angle in which the extraction region on the substrate is viewed from the collision point; (d) On the other hand, when the energy of the sputtered particles is larger Calculates the distance until the next collision of the sputtered particles, calculates the trajectory of the sputtered particles after the collision, and the trajectory of the particles is extracted in the extraction area on the substrate, or on the side wall of the apparatus or on the substrate. The above-described processes (a) to (d) of the process of repeatedly calculating collision until trapped, and the process of calculating the deposited film shape from the angular distribution of the trajectory of the extracted sputtered particles are executed by the information processing device. A recording medium on which a program for performing a simulation of a sputtering apparatus is recorded.