JP2609698B2 - Prediction method of directivity and film thickness distribution of evaporation material - Google Patents

Description

TECHNICAL FIELD The present invention relates to a method of predicting the directivity and film thickness distribution of an evaporated substance obtained by a vacuum vapor deposition method.

[Prior Art] As a conventional method for predicting the directivity of a vaporized substance obtained by a vacuum deposition method, for example, Vacuum, 36 , 346 (198
6) (Vacuum, 36 , 346 (1986)), there is a method using the Monte Carlo method.

On the other hand, as a conventional method for predicting the film thickness distribution of the vaporized substance obtained by the vacuum evaporation method, for example, Journal of Vacuum Science and Technology, B3 , 53.
1 (1985) (J. Vac. Sci. Technol., B3, 531 (1985)), the crucible is meshed,
There is a method of calculating the film thickness distribution by establishing a matrix equation of 1000 dimensions or more in the real space and solving it.

[Problems to be Solved by the Invention] In any of the above methods, even a single calculation requires a large amount of calculation time, and it is extremely extremely difficult to obtain a large amount of calculation data required for designing a vacuum evaporation apparatus. It was difficult.

An object of the present invention is to greatly reduce the calculation time required for calculating the directivity and the film thickness distribution of an evaporating substance obtained by a vacuum evaporation method, and to obtain a large amount of calculation data necessary for designing a vacuum evaporation apparatus. It is to provide a practical calculation method of.

[Means for Solving the Problems] The above-mentioned problem is solved by a method for predicting the directivity of a deposition material obtained by a vacuum deposition method, wherein a process in which a deposition material in a deposition source jumps out of a deposition source is f (z, φ). = Ψ (z, φ) + ∬k (z, φ; z ', φ') f
(Z ′, φ ′) r ₀ dz′dφ ′ Described as a two-variable integral equation, and the integral equation is transformed into a variable. The integral equation of the variable is expressed by By substituting And solving the matrix equation.

[Operation] As shown in FIG. 3, the wall surface in the evaporation source is designated by cylindrical coordinates. By catching the process in which the deposition material in the deposition source jumps out of the deposition source as a Markov process, the following type of two-variable integral equation can be obtained.

f (z, φ) = φ (z, φ) + ∬k (z, φ; z ′, φ ′) f
(Z ', φ') r 0 dz'dφ ' This Zeit shoe lift fur Fizuiku, 66, 471 (1930) ( Z.Phys., 66, 471 (1930)) 1 variable integral Clasing discussed in This is an extension of the equation, and is a basic equation that holds in more general cases. Subsequent suitable variable transformation, for example, Z = 1/2 {(T + r ₀ tanδcosφ) x + T−r ₀ tanδcos
φ} reconverts the above integral equation into the following normalized form.

Subsequently, the solution is developed using a suitable orthogonal function system, for example, Chebyshev polynomials and trigonometric functions.

By substituting this into the above integral equation and using orthogonality,
The following matrix equation is obtained.

Generally, M and N may be about 15 to 25 and about 5 to 7, respectively.
Therefore, the above matrix equation is usually less than 200 dimensions. The computation time required to solve this equation is a few seconds. on the other hand,
In the Monte Carlo method and the matrix equation method based on the mesh decomposition of the real space, a single calculation takes several hours. Thus, using this method, it is possible to significantly reduce the calculation time required to calculate the directivity and film thickness distribution of the vaporized substance obtained by the vacuum evaporation method, and it is necessary to design the vacuum evaporation apparatus. A large amount of calculation data can be easily obtained.

[Embodiment] As one embodiment of the present invention, a method of calculating the angular distribution of the vaporized substance ejected from the evaporation source will be described with reference to the drawings.
FIG. 1 shows an example of a system configuration for implementing the present invention. 1 is a host computer which performs various information processing, 2 is a TSS which has a keyboard and a graphic display device and communicates with the host computer 1 interactively via an appropriate line.
Terminals 3, 3 are storage devices for storing information created using the TSS terminal 2, and 4 is a line printer for output. FIG. 2 is a schematic view of a vapor deposition apparatus targeted in the present invention. After the vacuum chamber 5 is evacuated to 10 ⁻³ Pa or less by a vacuum pump (not shown) connected to the vacuum chamber 5, the evaporation material 7 in the crucible evaporation source 6 is heated by an appropriate method to melt, evaporate, and evaporate. It becomes the substance vapor 8 and is deposited on the substrate 9. In order to calculate the angular distribution of the vaporized substance vapor 8, the coordinate system shown in FIG. 3 is introduced on the crucible type vaporization source 6. The physical condition of the crucible can be designated by 10: crucible diameter 2r ₀ , 11: liquid surface depth T, 12: crucible inclination δ. FIG. 5 is a flowchart schematically showing the processing performed by the host computer 1 in the present invention. Of these, the process 17 is the third by the operator.
The parameters r ₀ , T, and δ shown in the figure are input from the TSS terminal, the processes 18, 19, and 20 are processes by the host computer, and the process 22 is a display by a graphic display device or an output to a line printer or a storage device Writing.
The operator sets the TS of the parameters r ₀ , T, and δ shown in FIG.
When input from the keyboard of the S terminal 2, the host computer 1
Is the matrix element Ψ _ij , Are generated and stored in the storage device 4, and then the above-described matrix equation is solved. Subsequently, the directivity of the vaporized substance is calculated in step 20, and the calculation method is as follows. First, the contribution D ₁ of the evaporated substance jumping out of direct evaporation source from the evaporation material 7 in the crucible-type evaporation source 6 by a well-known geometric methods. Next, without jumping directly out of the evaporation source from the evaporation substance 7 in the crucible-type evaporation source 6, one time on the wall surface of the evaporation source
The contribution D _{2 of the} evaporating substance that is emitted after being reflected more than once is given by D ₂ = {P (θ, φ, z ′, φ ′) f (z ′, φ ′) dz′d
Obtained from the relational expression φ '. Where P (θ, φ, z ′, φ ′)
Is a coefficient obtained by a well-known geometric method, and f (z,
φ) is the distribution function obtained in the present invention. From the above, the angle distribution obtained is D = D ₁ + D ₂ . FIG. 6 is an example of directivity output obtained by the present invention. The parameters used for the calculation are T = 1, 2r ₀ = 1, and δ = 45 °. HITAC M280 was used as a computer. The calculation time was about 6 minutes, including calculation of matrix elements and graphics. For comparison, the calculation time required to solve the same physical situation using the same computer by the mesh decomposition method of the real space described above is when the wall surface of the crucible type evaporation source is roughly divided into 100 in both z and φ directions. However, it is estimated to be about 186 hours, and the superiority of the present invention is clear.

As another embodiment of the present invention, a method of calculating a film thickness distribution when an evaporating substance jumping out of an evaporation source is deposited on a substrate 9 will be described with reference to the drawings. FIG. 1 shows an example of a system configuration for implementing the present invention. 1 is a host computer that performs various information processing, 2 is a TSS terminal that has a keyboard and a graphic display device, and communicates with the host computer 1 in an interactive manner via an appropriate line, and 3 is an information created using the TSS terminal 2. The storage device 4 for storing is a line printer for output. FIG. 2 is a schematic diagram of a vapor deposition apparatus targeted by the present invention. After the vacuum chamber 5 is evacuated to 10 ^-3 Pa or less by a vacuum pump (not shown) connected to the vacuum chamber 5, the evaporation material 7 in the crucible evaporation source 6 is heated by an appropriate method to melt, evaporate, and evaporate. The material vapor 8 is deposited on the substrate 9. In order to calculate the film thickness distribution when the vaporized substance vapor 8 is deposited on the substrate 9, the coordinate system shown in FIG. 3 and the parameters shown in FIG. 4 are introduced on the crucible type evaporation source 6. The physical condition of the crucible is 10: crucible diameter 2
r ₀ , 11: liquid surface depth T, 12: crucible inclination δ. The positional relationship between the crucible type evaporation source 6 and the substrate 9 is 1
3: the coordinates of the substrate center O, 14: the normal vector n of the substrate, 15: the coordinates of the liquid surface center C, 16: the vector 1 of the central axis of the crucible evaporation source. FIG. 5 is a flowchart showing the outline of the processing performed by the host computer 1 in the present invention. Of these, processing 17 is input by the operator from the TSS terminal of the parameters r ₀ , T, δ, O, n, C and l shown in FIGS. 3 and 4, processing 18, 19 and 21 are processing by the host computer, Process 22 is display by a graphic display device, output to a line printer, or writing to a storage device. The operator uses the parameter r shown in Figs.
_{When 0} , T, δ, O, n, C, l and the coordinates of the point P on the substrate 9 for which the film thickness is to be calculated are input from the keyboard of the TSS terminal 2, the host computer 1 calculates the matrix elements Ψ _ij , Is generated, the above-described matrix equation is solved, and the film thickness distribution of the evaporated substance is calculated. The calculation method is as follows. First, the contribution t ₁ from the evaporation material that directly jumps out of the evaporation source from the evaporation material 7 in the crucible type evaporation source 6 is obtained by a known geometric method. Next, the contribution t _{2 of the} evaporating substance that is not reflected directly from the evaporating substance 7 in the crucible-type evaporating source 6 but at least once on the wall surface of the evaporating source without jumping out of the evaporating source and then jumps out is represented by t ₂ = ∬T (P; z, φ) f (z, φ) dzdφ Here, T (P; z, φ) is a coefficient obtained by a known geometric method, and f (z, φ) is a distribution function obtained in the present invention. Therefore, the film thickness at P obtained is t = t ₁
+ A t _2. By performing the above procedure for various points P on the substrate, a film thickness distribution can be obtained. FIG. 7 is an output example of the film thickness distribution obtained by the present invention. HITAC as a computer
M280 was used. The calculation time was about 10 minutes, including calculation of matrix elements and graphics. For comparison, the calculation time required to solve the same physical situation using the same computer by the mesh decomposition method of the real space described above is the case where the wall of the crucible type evaporation source is roughly divided into 100 in both z and φ directions. But about 186
Estimated time, the advantage of the present invention is clear.

[Effects of the Invention] According to the present invention, the calculation time required for calculating the directivity and the film thickness distribution of the evaporated substance obtained by the vacuum evaporation method can be greatly reduced.

[Brief description of the drawings]

FIG. 1 is a diagram showing a system configuration for implementing the present invention. FIG. 2 is a schematic diagram of a vapor deposition apparatus which is the object of the present invention. FIG. 3 is a schematic diagram of an evaporation source. FIG. 4 is a diagram showing a positional relationship between the evaporation source and the substrate. FIG. 5 is a flowchart of a process performed by the host computer in the present invention. FIG. 6 is a diagram showing the directivity output obtained by the present invention. FIG. 7 is a diagram showing the output of the film thickness distribution obtained by the present invention. DESCRIPTION OF SYMBOLS 1 ... Host computer, 2 ... TSS terminal, 3 ... Storage device, 4 ... Line printer, 5 ... Vacuum chamber, 6 ...
… Evaporation source, 7 ... Evaporation material, 8 ... Evaporation material vapor, 9 ...
… Substrate, 10 …… Evaporation source radius, 11 …… Depth of liquid level, 12 ……
Inclination of evaporation source, 13: coordinates of substrate center C, 14: normal vector of substrate, 15: center of liquid surface, 16: vector of central axis of evaporation source, 17: input step of geometric information, 18 ... step of generating matrix elements, 19 ... step of solving a matrix equation, 20 ... step of calculating angular distribution, 21 ... step of calculating thickness distribution, 22 ... output step.

 ──────────────────────────────────────────────────続 き Continuation of front page (56) References H, "Diffusion at the vacuum- solid and gas-solid interface: Some matters." (1988) Diffus Interfaces: Microsoc Concepts-P. 67−69

Claims (1)

(57) [Claims] 1. A method for predicting the directivity of a deposition material obtained by a vacuum deposition method, wherein a process in which a deposition material in a deposition source jumps out of the deposition source is represented by f (z, φ) = ψ (z, φ) + ∬k (z, φ; z ', φ') f
(Z ′, φ ′) r ₀ dz′dφ ′ Described as a two-variable integral equation, and the integral equation is transformed into a variable. Where the variable-converted integral equation is By substituting And estimating the directivity of the evaporated substance by solving the above integral equation by solving the matrix equation.