JP2910626B2 - Sputtering system optimization method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a method for optimizing a sputtering apparatus, and more particularly to a method for optimizing parameters of a sputtering apparatus by simulation.

[0002]

2. Description of the Related Art Along with the miniaturization of semiconductor devices, embedding of fine holes has become a problem, and to cope with this problem, it is necessary to optimize a sputtering apparatus. However, when optimizing a sputtering apparatus, there is a problem in terms of cost and TAT in actually developing the apparatus and performing an experiment.

Therefore, optimization of a sputtering apparatus using simulation has been studied. Conventionally, as a technique related to such simulation, for example, “H. Yamada et.al., 1994 IEDM Tech. Dig., pp553-55
6 "discloses a shape simulation technology using the Monte Carlo method.

In the shape simulation technique disclosed in the above document, first, the position at which particles are emitted from a target of a sputtering apparatus is determined by assuming that the number of emitted particles is proportional to the erosion of the target. The angle is determined using random numbers assuming the cos rule, and the energy of the emitted particles is determined by a rejection method assuming a Thompson distribution.

Next, the collision position is determined by using the mean free path and the Poisson distribution, and the trajectory of the particle after the collision is determined by the classical dynamic formula of the central force field using a hard sphere model. Also,
The trap determination to the collimator and the device side wall is performed.

Further, the trajectory of the particles calculated as described above is extracted in a specific area on the wafer. The sputter shape is calculated using a two-dimensional string model by determining the three-dimensional shadow effect from the extracted trajectory using the axial symmetry of the through hole.

[0007]

In the shape simulation technique using the Monte Carlo method described above, the analysis is performed assuming that the apparatus conditions such as erosion and emission angle distribution have already been given. Therefore, when examining optimization of a sputtering apparatus using this simulation technique, it is necessary to determine the optimum conditions of the sputtering apparatus by performing a simulation in which values such as erosion and emission angle distribution are changed as parameters.

However, in the conventional shape simulation technique using the Monte Carlo method, it is necessary to generate a certain number of particles or more in terms of structure. For one apparatus condition, for example, EWS (Engineering Workstation)
Approximately 2 hours of calculation time were required using. Therefore, there is a serious problem that it takes a very long calculation time to obtain the optimum conditions of the sputtering apparatus by changing the apparatus parameters.

[0009] The present invention has been made in view of the above circumstances, and in determining the optimum parameters of a sputtering apparatus for embedding through holes using simulation,
An object of the present invention is to provide a method for optimizing a sputtering apparatus, which can obtain an apparatus optimizing condition in a short calculation time.

[0010]

In order to achieve the above object, a method for optimizing a sputtering apparatus according to the present invention comprises the steps of: It is characterized by including.

Calculating the trajectory of the particles emitted from the target; Extracting the trajectory on a wafer.
Calculating the embedded shape or film thickness of the through-hole as a function of a coefficient representing the occurrence probability of the trajectory. A step of obtaining the coefficient by using a linear programming method based on a condition for optimizing a through hole filling shape or a film thickness. Obtaining an optimum parameter of the sputtering apparatus from the coefficient. Here, the process of calculating the trajectory of a particle refers to the position of the particle.
The time-dependent change of the position and speed into the equation of motion of Newtonian mechanics
Therefore, calculate and calculate Poisson the frequency of collision with other particles on the way.
The speed change before and after the collision is determined
Refers to the process of calculating using the central force field of dynamics. Orbit
The step of extracting on C means that the particles calculated by the above method
The intersection between the trajectory of the wafer and the plane containing the upper surface of the wafer.
The value of the coordinates of the point was specified in advance to be extracted on the wafer
It is determined whether or not the coordinates are within the coordinates of the area.
In this case, it refers to the process of recording the speed of the orbit. Through hole
The process of calculating the embedded shape or film thickness of
Cross-section of through-hole with string points on top
And the trajectory of the particle at each string point
Aiming, aiming trajectory is indicated by other string points
Calculate whether it does not intersect with the displayed shape, and if it does
Ignores its trajectory as a shadow has occurred
If they do not intersect, string in the direction of the particle trajectory.
Filling through holes by moving
Refers to the process of calculating the embedded shape. Also, here,
Vertical movement distance of the moving point (vertical
Calculate the film thickness from the distance moved to

In the method of optimizing a sputtering apparatus according to the present invention, a shape simulation technique using a Monte Carlo method is used, and the following methods (1) to (3) are used. Use a flow to calculate the trajectory of particles, a flow to calculate the shape or film thickness by adding the expression probability of each trajectory as a weight, and a flow to calculate each expression probability from conditions for optimizing the shape or film thickness. Accordingly, it is possible to obtain the optimum parameters of the sputtering apparatus by simulation in a short calculation time.

(1) After calculating each trajectory (i), a probabilistic weight (ai) is assigned to it. Here, ai corresponds to device parameters such as erosion and emission angle distribution. (2) Simulation of device optimization conditions including shape, film thickness, etc., as a function of ai. (3) From the results and the optimum conditions of the apparatus, ai is calculated by a linear programming method to obtain the optimum apparatus parameters.

Steps (1) to (4) in the method for optimizing a sputtering apparatus of the present invention can be carried out, for example, by the following steps (see FIG. 2).

Calculating the trajectory of the particles emitted from the target; Step 1: A step of calculating a position at which sputtered particles are emitted from the target, an emission angle and energy of the particles (S1 in FIG. 2). Step 2: A step of obtaining the collision position of the particles using the mean free path and the Poisson distribution, and obtaining the trajectory of the particles after the collision using a hard sphere model from the classical dynamic formula of the central force field (FIG. 2S2). Step 3: A step of determining whether the particles are trapped on the collimator and the device side wall (S3 in FIG. 2).

A step of extracting the trajectory on a wafer. Step 4: a step of extracting the trajectory of the sputtered particles in a specific area on the wafer and recording the three-dimensional velocity of the particles entering the specific area on the wafer in a trajectory file (S4 in FIG. 2).

Calculating a buried shape or a film thickness of the through hole as a function of a coefficient representing a probability of occurrence of the trajectory. Step 5: Classify the sputtered particles according to the range from which the particles are emitted on the target, and use the trajectory of the particles emitted from each target area to determine the cross-sectional shape of the through hole using a string model. (S5 in FIG. 2). Step 6: Step of calculating various film thicknesses from the result of step 5 (S6 in FIG. 2). Step 7: A step of calculating various film thicknesses for all target ranges (S7 in FIG. 2).

A step of obtaining the coefficient from a condition for optimizing the shape or film thickness of the through hole by using a linear programming method. Step 8: A step of formulating various conditional expressions and an objective function G (ai) using the coefficient ai representing the depth of the erosion as an unknown value while representing the probability of appearance of particles in each target range (S8 in FIG. 2). Step 9: A step of finding a set of ai that maximizes G (ai) using linear programming (S9 in FIG. 2).

A step of obtaining an optimum apparatus parameter from the coefficient. Step 10: Apply a to the shape calculated for each target area
A step of calculating an optimized shape by multiplying by i and adding them up to obtain an optimum parameter of the sputtering apparatus (S10 in FIG. 2).

[0020]

EXAMPLES The present invention will be specifically described below with reference to examples, but the present invention is not limited to the following examples.

Embodiment 1 A method for optimizing a sputtering apparatus according to a first embodiment of the present invention is schematically shown in FIG. 1 and FIG.
This will be described with reference to the flowchart shown in FIG.

Calculating the trajectory of the particles emitted from the target. For example, the target 101 is divided into three parts (target range (i = 1 to 3)) at equal intervals in the radial direction of the target. Then, using the Monte Carlo method, the trajectory of the particle 10
Calculate 2. That is, the position where sputtered particles are emitted from the target, the emission angle and energy of the particles are calculated (S1). Next, the collision position is obtained using the mean free path and the Poisson distribution, and the trajectory of the particle after the collision is obtained from the classical dynamic formula of the central force field using a hard sphere model (S
2). Further, a trap is determined for the collimator and the device side wall (S3).

The step of calculating the trajectory of each sputtered particle emitted from the target of the sputtering apparatus, taking into account the collision with the background gas particles, the collimator, and the trapping on the side wall of the apparatus.

Extracting the trajectory on the wafer. 1 cm square area at the center of the wafer and 1 cm at the edge of the wafer
The particle trajectory 102 is extracted in the corner area (S4). The particle trajectory 102 also includes data on the position from which the sputtered particles are emitted.

In the step, the trajectory of the sputtered particle calculated in the step is extracted in a specific area on the wafer, and the three-dimensional velocity of the particle entering the specific area on the wafer is recorded in the trajectory file. This is the step of performing

Calculating a buried shape or a film thickness of the through hole as a function of a coefficient representing a probability of occurrence of the trajectory. In the shape calculation unit, based on the trajectory file extracted at the center of the wafer, the trajectory 102
And the three-dimensional shadow effect is determined by using the trajectory of the particles emitted from each target area (i) using the axial symmetry of the through-hole 103, so that the cross section of the through-hole 103 is determined. The shape is calculated using a string model (S5). From the results, the upper film thickness Tcti (104) at the wafer center and the lower film thickness Tcbi
(105) is calculated. In addition, by the same method as above, the upper film thickness Teti is calculated from the trajectory extracted at the wafer edge.
(106) The lower film thickness Tebi (107) is calculated (S6). This is applied to all target ranges (i = 1 to
Step 3) is performed (S7).

In the step, particles entering the trajectory file are classified according to the range from which the particles are emitted on the target, and various film thicknesses are calculated by a string model using the trajectory for each range. This is the step of performing

A step of obtaining the coefficient by using a linear programming method based on a condition for optimizing the shape or film thickness of the through hole. At the same time as expressing the probability of appearance of particles in each target range (i), the coefficient ai representing the depth of erosion is set as an unknown value, and a conditional expression in which the thickness of the upper portion of the through hole is constant is as follows: Σai × Tcti = 1.0 1) Σai × Teti = 1.0 (2) Conditional expression that probability is positive, ai ≧ 0 (i = 1 to 3) (3) and objective function G (ai), G (ai) = Σai × Tcbi + Σai × Tebi (4) is formulated (S8). Since the expressions (1) to (4) are linear combinations of ai, G (ai) is calculated using linear programming.
Is determined (S9).

In the step, the coefficient a is set to the film thickness for each range.
i is multiplied and added over the entire range, and the objective function G (ai) is set so that the film thickness becomes constant at each point on the wafer and the erosion depth becomes positive. This is a step of obtaining a set of ai that maximizes G (ai) using ai as an unknown number, utilizing that G (ai) is a linear combination.

A step of obtaining an optimum apparatus parameter from the coefficient. The optimized shape is calculated by multiplying the shape calculated for each target range by ai and adding them together, thereby obtaining the optimum parameters of the sputtering apparatus (S10).

The step (1) is a step of actually calculating and confirming the shape from the obtained ai to obtain the optimum parameters of the sputtering apparatus.

The thickness of the upper part of the through hole in the equations (1) and (2)
Is constant for each target range (i)
All trajectories emitted are contacted (without shadowing)
To the top of the contact (wafer surface).
The film thickness is constant at the center and the edge of the wafer.
The same film thickness from within the wafer surface due to the wafer process
Is it necessary to create devices with equal characteristics?
Therefore, both equations are set to the same value, and a constant value is set to 1 for convenience.
You. Ai is physically proportional to the erosion depth.
Since it is an example amount, it is always positive, and the value of the expression (3)
Case is required. Further, the objective function G (a) in equation (4)
i) Contact holes located at the center and the edge of the wafer
This is the sum of the lower film thickness at the bottom of
The larger the value, the better, for the following reason. sand
In other words, the thicker the film thickness at the bottom of the contact hole, the thicker
The likelihood of poor contact at the bottom of the contact
This is because a stable device can be manufactured. However,
As the contact hole aspect ratio increases,
The bottom film thickness formed by the sputtering method is thin,
Since the problem is to increase the thickness, Equation (1),
While satisfying the conditions of (2) and (3), G in Expression (4) is satisfied.
Sum of film thickness at bottom of contact hole defined in (ai)
Is to maximize
Optimizes film thickness. " In the optimization method of the present embodiment, the particle trajectory calculation using the Monte Carlo method only needs to be performed once by regarding the appearance probability of the particles as the constant ai. A great advantage is obtained that it can be reduced by a factor of one.

That is, in the prior art, S5, S7,
There is no step like S8, S9, S10, and the thickness calculation (S6) is performed using all the extracted orbits.
Therefore, in order to express the appearance probability ai handled in S8 in the conventional technique, ai is used when the particles are released in S1.
When the value of ai is changed, it is necessary to recalculate all the trajectories and film thicknesses each time, and it is enormous to change the set of ai to obtain the optimum value. It took a lot of calculation time. In contrast,
In the optimization method of the present embodiment, the probability of appearance of particles is determined by a constant ai
Thus, it is possible to calculate the orbit and the film thickness required for determining ai only once.

[Embodiment 2] A method of optimizing a sputtering apparatus according to a second embodiment of the present invention will be described with reference to the schematic diagram shown in FIG.

Calculating the trajectory of the particles emitted from the target. As the emission angle of the particles emitted from the target 301, a range divided into three at equal intervals (angular range (i = 1 to 1)
3)) is specified. Next, in the same procedure as in the first embodiment, the trajectory 302 of the particle is calculated using the Monte Carlo method.

Extracting the trajectory on the wafer. The trajectory 302 is extracted in the same procedure as in the first embodiment. The extracted trajectory 302 also includes data on the angle at which the particles are emitted.

Calculating a buried shape or a film thickness of the through hole as a function of a coefficient representing a probability of occurrence of the orbit. In the first embodiment, the same calculation as the film thickness calculation at the center and the end of the wafer performed in each target range (i) is performed in each angle range (i). That is, the cross-sectional shape of the through hole 303 is calculated using a string model, and from the result, the upper film thickness Tcti (304), the lower film thickness Tcbi (305), the upper film thickness Teti (306),
The lower film thickness Tebi (307) is calculated. This is performed for all the angle ranges (i = 1 to 3).

A step of obtaining the coefficient by using a linear programming method from a condition for optimizing the shape or film thickness of the through hole. At the same time as expressing the probability of appearance of particles in each emission angle range (i) and the coefficient ai representing the emission angle distribution as an unknown number, ai that optimizes the conditional expression is obtained by the same method as in the first embodiment. In step 1, target
By dividing into multiple in the radial direction, multiple targets
When the range of the credit is specified (when the invention of claim 3 is applied)
Ai) is the probability of appearance of particles in each target range.
Rate (= coefficient representing erosion depth). Also,
In step 1, the particles released from the target
By splitting the emission angle into multiple, multiple angle ranges
If specified (when the invention of claim 4 is applied),
ai is a coefficient representing the emission angle distribution.
You. Therefore, ai is the probability of particle appearance in each target range.
The procedure for setting the rate is to release ai from the target as it is.
This is achieved by using a coefficient that expresses the angle distribution.
You.

A step of obtaining optimum device parameters from the coefficients. The optimized shape is calculated by multiplying the shape calculated for each target range by ai and adding them together, thereby obtaining the optimum parameters of the sputtering apparatus.

According to the optimizing method of this embodiment, as in the first embodiment, the calculation time can be greatly reduced as compared with the prior art, and the emission angle distribution which cannot be achieved in the first embodiment can be optimized. It can be performed.

[0041]

According to the method for optimizing a sputtering apparatus according to the present invention, when the optimum parameters of a sputtering apparatus for embedding a through hole are obtained by simulation,
Device optimization conditions can be obtained in a short calculation time.
That is, the method for optimizing a sputtering apparatus according to the present invention determines the trajectory occurrence probability ai by using a linear programming method, and thereby optimizes the bottom coverage by changing the apparatus conditions such as erosion and emission angle distribution in a short time. It has a great advantage that it can be obtained by:

[Brief description of the drawings]

FIG. 1 is a schematic diagram showing erosion optimization performed in a first embodiment.

FIG. 2 is a flowchart showing an outline of a flow of the first embodiment.

FIG. 3 is a schematic diagram showing optimization of an emission angle distribution performed in a second embodiment.

[Explanation of symbols]

 101 Target 102 Particle trajectory 103 Through hole 104 Wafer central upper film thickness 105 Wafer central lower film thickness 106 Wafer upper film thickness 107 Wafer lower film thickness 301 Target 302 Particle trajectory 303 Through hole 304 Wafer central upper film thickness 305 Wafer Central lower layer thickness 306 Wafer edge upper layer thickness 307 Wafer edge lower layer thickness

Continuation of the front page (56) References JP-A-9-249969 (JP, A) JP-A-5-29257 (JP, A) JP-A-10-306371 (JP, A) March 28 to 31, 1995 Program (28a-TF-2) announced in writing at the 42nd Federation of Applied Physics held at Tokai University Shonan Campus (58) Field surveyed (Int.Cl. ⁶ , DB name) C23C 14/00-14/58 G06F 17/50 H01L 21 / 203,21 / 285

Claims (4)

(57) [Claims] 1. A method for calculating, by simulation, an optimum parameter of a sputtering apparatus for embedding a through hole, a step of calculating a trajectory of a particle emitted from a target, and a step of extracting the trajectory on a wafer. Calculating the embedded shape or film thickness of the through hole as a function of a coefficient representing the occurrence probability of the trajectory,
A step of obtaining the coefficient by using a linear programming method from the conditions for optimizing the embedded shape or film thickness of the through hole,
Obtaining an optimum parameter of the sputtering apparatus from the coefficient. 2. A position where sputtered particles are emitted from a target, a step 1 for calculating an emission angle and energy of the particles, and a collision position of the particles is obtained by using a mean free path and a Poisson distribution. Step 2 for finding the trajectory from the classical dynamic formula of the central force field using a hard sphere model
And performing a step of calculating the trajectory of the particles emitted from the target by performing the collimation of the particles and the trap determination to the side wall of the apparatus, and extracting the trajectories of the sputtered particles in a specific region on the wafer,
The step of recording the three-dimensional velocities of the particles entering a specific area on the wafer in a trajectory file is performed by extracting the trajectories on the wafer by the step 4. Step 5: Classify according to whether or not the target area has been emitted, and calculate the cross-sectional shape of the through hole using a string model using the trajectory of the particle emitted from each target area.
Step 6 of calculating various film thicknesses from the results of Step 5 and Step 7 of calculating various film thicknesses for all target ranges, thereby embedding the through holes as a function of a coefficient representing the probability of occurrence of the orbit. Perform the process of calculating the shape or film thickness, and at the same time represent the appearance probability of particles in each target range,
Step 8 of formulating various conditional expressions and an objective function G (ai) with the coefficient ai representing the depth of erosion as an unknown number, and ai at which G (ai) is maximized by using a linear programming method
The step of obtaining the coefficient by using the linear programming method based on the condition for optimizing the buried shape or the film thickness of the through-hole, and multiplying the shape calculated for each target range by ai 2. A step of calculating an optimized shape by adding them up and obtaining an optimum parameter of the sputtering apparatus in the step 10 to obtain an optimum apparatus parameter from the coefficient.
The method for optimizing the sputtering apparatus described in the above. 3. The method according to claim 2, wherein in step 1, a plurality of target ranges are specified by dividing the target into a plurality in the radial direction, and a particle trajectory is calculated using a Monte Carlo method. . 4. The sputter according to claim 2, wherein in step 1, a plurality of angular ranges are designated by dividing an emission angle of particles emitted from the target into a plurality, and a trajectory of the particles is calculated using a Monte Carlo method. Equipment optimization method.