JP2583620B2 - Calculation method of film thickness distribution - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for calculating a film thickness distribution of a thin film obtained by a sputtering device using a highly directional beam (hereinafter, referred to as a sputtering device). .

[Conventional technology]

FIG. 1 shows an outline of a sputtering apparatus which is an object of the calculation method according to the present invention. In the figure, a beam source 2 is:
It has a hole B composed of an electrode for extracting Ar ions and the like with high directivity, and the high directivity beam 3 protrudes from the hole B. The highly directional beam 3 is applied to a target 4 made of a desired film forming material.
To sputter the film-forming material. The sputtered film forming material 5 is formed on the wafer 6.

FIG. 2 is a schematic diagram in which portions necessary for film thickness calculation in the sputtering apparatus are extracted. Point Q on wafer 6
To calculate the thickness of the thin film formed on
Multiple integration must be performed.

t (θ) = ∬f (x, y) I (x, y) dxdy (1) where x, y is a rectangular coordinate system on the target 4,
I (x, y) is the beam intensity at point (x, y), f
(X, y) is the probability that atoms sputtered at the point (x, y) reach the unit area including the point Q and are formed into a film. The integration area is the entire target 4.

Conventionally, in order to calculate the expression (1), coordinate conversion is performed and displayed in polar coordinates, and t (θ) = ∬f (r cos θ r sin θ) I (r cos θ r sin θ) rdrdθ Is calculated by the trapezoidal rule, and then the convergence calculation is performed on the integral of r until the desired accuracy is reached. In addition, those related to this kind of calculation method include, for example, Journal of Vacuum Science,
And Technology, B3, 531 (1985) (J. Vac. Sci. Tec
hnol., B3 , 531 (1985)).

[Problems to be solved by the invention]

In the above prior art, since the convergence calculation of the double integral is performed,
Was spending a lot of calculation time.

SUMMARY OF THE INVENTION An object of the present invention is to provide a method for calculating a film thickness distribution which significantly reduces the calculation time and guarantees a practically sufficient accuracy.

[Means for solving the problem]

The above object is achieved by the following means. On a plane (ξ = 0) orthogonal to the beam center axis, the intensity distribution of the highly directional beam can be well approximated by the following Gaussian distribution.

Here, 2σ ₀ ² = l ² tan ² θ ₀ , and 1 is the distance ▲
▼ ₀ and θ ₀ are divergence angles (that is, angles until the beam intensity becomes 1 / e with respect to the beam center axis direction) (see FIG. 2). The point P _{0 at} which the beam center axis intersects with the target is defined as the origin (0,0). Therefore, when the target is tilted by the angle ξ, the intensity distribution on the target is calculated by a well-known geometric calculation. Becomes here, It is. Then I (x, y) Write here, It is. The following well-known formula is used.

Where δ (x) and δ (y) are Dirac delta functions, It is. From equation (1), the contribution of beam source B to the film thickness distribution is By the way, in the case of a highly directional beam, the divergence angle θ _{0 of the} beam is small (<10 °), and σ ₀ ² is also small. Therefore, if equation (5) is regarded as an expansion with respect to σ ₀ ² , t (θ) = f (0,0) + σ ₀ ² ζ + O (σ ₀ ⁴ ) (6) _{Since 0} ⁴ ) only contributes on the order of 0.01%, it can be omitted in the film thickness distribution calculation.
Note that J (x, y) also depends on σ ₀ , Is obtained. The film thickness can be calculated by using the equations (6) and (7). In the case where the calculation accuracy is not so required (10%) or less, it is possible to substitute only the first term of the equation (6).

[Action]

Since σ ₀ is sufficiently small for a highly directional beam, O (σ ₀ ⁴ ) can usually be ignored in the expansion of equation (6). Therefore, the double integration in the expression (1) is replaced with the sum of at most four terms in the expressions (6) and (7), and it is clear that the processing is speeded up.

〔Example〕

Next, embodiments of the present invention will be described with reference to the drawings. First
FIG. 1 is a diagram schematically showing a sputtering apparatus which is an object of the calculation method according to the present invention, FIG. 2 is a diagram showing parameters used in the above calculation method, and FIG. 3 is a diagram showing a system configuration for implementing the present invention. FIG. 4 is a flowchart of a process performed by the host computer, FIG. 5 is a diagram showing a comparison of calculation results, FIG. 6 is a diagram showing parameters of another embodiment, and FIG. FIG. 8 is a flowchart showing the output of the film thickness distribution obtained in the above embodiment.

In FIG. 1, after a vacuum chamber 1 is evacuated to 10 ⁻³ Pa or less by a vacuum pump (not shown) connected thereto, a highly directional beam 3 is emitted from an ion beam source 2. The highly directional beam 3 collides with the target 4 and generates sputtered particles 5. Sputtered particles 5
Reaches the wafer 6 and forms a thin film.

FIG. 2 schematically shows a portion necessary for calculating the film thickness in FIG. 1 described above. The coordinate system (x, y, z) is set as shown in the figure, the inclination of the target 4 with respect to the beam center axis is ξ, and the unit normal vector of the wafer 6 is The position vector of the point Q of interest on the wafer is With the normal of target 4 And the distance between the beam source 2 and the target center and the distance between the target center and Q are 1 and L, respectively.
And

FIG. 3 shows an example of a system configuration for implementing the present invention. In FIG. 3, 7 is a host computer for performing various information processing, 8 is a TSS terminal which has a keyboard and a graphic display device and communicates with the host computer 1 in an interactive manner through an appropriate line, and 9 is a TSS terminal. A storage device for storing information created by using the device is a line printer for output.

FIG. 4 is a flowchart schematically showing the processing performed by the host computer 7 in the test calculation for showing the superiority of the present invention. Among them, the processing 11 is a part where the operator inputs the geometric information shown in FIG.
Reference numeral 13 denotes processing by the host computer, t ₁ (Q) is the film thickness calculation by the convergence calculation of the conventional method, and t ₂ (Q) is the film thickness calculation by the present invention. The processing 14 is display by a graphic display device, output to a line printer, or writing to a recording device.

FIG. 5 is a diagram comparing the calculation results of the film thickness distribution obtained by the procedure of FIG. 4 above, wherein t ₁ (Q), t _1
2 (Q) shows the calculation results according to the conventional method and the present invention, respectively. CPU time is also shown to show the superiority of the present invention. The parameters used for the calculation are l = 200 mm, L = 300 m
m, ξ = 45 ゜, β = 45 ゜, And The angle distribution of the sputtered particles follows the cosine distribution. in this case, And therefore It is. According to the present invention, an accuracy result with a calculation error of -0.0557% is obtained at a processing speed of about 7570 times as compared with the conventional method. The above calculation accuracy is too high for practical use, and the advantage of the present invention is clear.

Figure 6 is a diagram showing the respective parameters of the other embodiments, the physical conditions in the apparatus, an ion source diameter D _B, the ion extraction electrode spacing a, the focal length f, the distance between the ion source and the target L _B , target diameter D _T , distance L _W between target and wafer, wafer diameter D _W , and angle α shown in the figure,
Specified by β and γ.

FIG. 7 is a flowchart schematically showing the processing performed by the host computer 7 in the present embodiment. Among them, process 11 parameters D _B shown in FIG. 6 by the _{operator, a, f, L B,} D T, L W, D W, α, β, inputs from TSS terminal 8 of gamma, processing 12, Processes 13, 14, and 15 are processing by the host computer 7, and process 16 is display by a graphic display device, output to a line printer, or writing to a storage device. When the operator inputs the parameters shown in FIG. 6 from the keyboard of the TSS terminal 8, the host computer 7 sends the parameters on the target 4 corresponding to the extraction electrodes B _i (i = 1,..., N). Generate Subsequently, lattice points P on the wafer 6 are generated,
The film thickness t (P) at P This is performed for a desired number of lattice points P on the wafer 6. When all calculations are completed, the calculation results are stored in the storage device 9.

FIG. 8 is a diagram showing an output example of the film thickness distribution obtained by this embodiment. Parameters used for the calculation D _B = 100,
a = 6, f = 400, L B = 300, D T = 100, L W = 200, D W = 15
0, α = 60 °, β = 0 °, γ = −30 °, and HITACM680H was used as the host computer 7. The required calculation time was about 10 seconds including graphics. For comparison, the calculation time for performing the conventional calculation on the same physical situation using the same computer is estimated to be about 13 hours even when roughly divided, and the advantage of the present invention is clear.

〔The invention's effect〕

As described above, the method of calculating a film thickness distribution according to the present invention is a method of calculating a film thickness distribution of a thin film obtained by a sputtering method using a highly directional beam. Is a point P (x,
y) Sputtering of atoms in the vicinity, the probability that the atoms reach a unit area including the point Q on the wafer to form a film (x,
y), the point P ₀ = P where the beam center axis intersects the target
Value f (0,0) at (0,0) and derivative By using a calculation formula including one or all of them, the time required to calculate the film thickness distribution of the evaporated substance obtained by the sputtering method can be greatly reduced (more than 5000 times). It is extremely useful for optimization of

[Brief description of the drawings]

FIG. 1 is a diagram schematically showing a sputtering apparatus which is an object of the calculation method according to the present invention, FIG. 2 is a diagram showing parameters used in the above calculation method, and FIG. 3 is a system configuration for implementing the present invention. FIG. 4, FIG. 4 is a flowchart of a process performed by the host computer, FIG. 5 is a diagram showing a comparison of calculation results, FIG. 6 is a diagram showing parameters of another embodiment, and FIG. FIG. 8 is a diagram showing a flow chart of the process, and FIG. 8 is a diagram showing the output of the film thickness distribution obtained in the above embodiment, where (a) is a contour diagram and (b) is a three-dimensional diagram. 2 ... High directional beam source, 3 ... Beam 4 ... Target, 6 ... Wafer

Claims (2)

(57) [Claims] In a method for calculating a film thickness distribution of a thin film obtained by a sputtering method using a highly directional beam, a beam emitted from a point B on a highly directional beam source is converted to a point P (x, y) Sputtering of atoms in the vicinity, the probability f (x, y) of the atoms reaching a unit area including the point Q on the wafer and forming a film, the point P ₀ = P where the beam center axis intersects the target Value f (0,0) at (0,0) and derivative A method for calculating a film thickness distribution, wherein the calculation is performed using a calculation formula including one or all of the above. 2. The above f (0,0) and differential value Are given by 1 according to the angle す formed by the target normal with respect to the beam center axis, the beam divergence angle θ ₀ , and the distance 1 between the point B and the point P ₀ . And the following expression 2. The method for calculating a film thickness distribution according to claim 1, wherein the calculation is performed by: