Abstract

Emission characteristics of real vapor sources are analyzed on the basis of experimental results. It is found that some real sources have complex emission behaviors that agree only with a model that assumes a virtual surface instead of the real one.

© 1999 Optical Society of America

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References

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  1. L. Holland, Vacuum Deposition of Thin Films (Wiley, New York, 1956).
  2. H. K. Pulker, Coatings on Glass (Elsevier, Amsterdan, 1984).
  3. A. Musset, I. C. Stevenson, “Thickness distribution of evaporated films,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE1270, 287–291 (1990).
    [CrossRef]

Holland, L.

L. Holland, Vacuum Deposition of Thin Films (Wiley, New York, 1956).

Musset, A.

A. Musset, I. C. Stevenson, “Thickness distribution of evaporated films,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE1270, 287–291 (1990).
[CrossRef]

Pulker, H. K.

H. K. Pulker, Coatings on Glass (Elsevier, Amsterdan, 1984).

Stevenson, I. C.

A. Musset, I. C. Stevenson, “Thickness distribution of evaporated films,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE1270, 287–291 (1990).
[CrossRef]

Other (3)

L. Holland, Vacuum Deposition of Thin Films (Wiley, New York, 1956).

H. K. Pulker, Coatings on Glass (Elsevier, Amsterdan, 1984).

A. Musset, I. C. Stevenson, “Thickness distribution of evaporated films,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. SPIE1270, 287–291 (1990).
[CrossRef]

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Figures (24)

Fig. 1
Fig. 1

General geometrical configuration of a source–substrate system. The surfaces of the source and the substrate are represented by F(x, y, z) and S(x 1, y 1, z 1), respectively.

Fig. 2
Fig. 2

Planar rectangular vapor source.

Fig. 3
Fig. 3

Spherical meniscus concave and convex vapor sources.

Fig. 4
Fig. 4

Lobule of emission of a spherical concave source with a directivity pattern t 1. The solid curve represents the shape of the vapor cloud in the vicinity of the source; as the substrate is placed farther away, the distribution becomes similar to that produced by an elemental surface source (dashed curve).

Fig. 5
Fig. 5

Ellipsoidal meniscus concave and convex vapor sources.

Fig. 6
Fig. 6

Lobule of emission of a concave ellipsoidal source with a directivity pattern t 1. The vapor cloud becomes asymmetrical as we approach the source (solid curve). As we move away from the source, the vapor cloud behaves very much the same as an elemental area source.

Fig. 7
Fig. 7

Planar horizontal disk substrate.

Fig. 8
Fig. 8

Vertical cylindrical substrate.

Fig. 9
Fig. 9

Thickness distribution on the flat (dashed curve) and curved (solid curve) surfaces of the cylinder (R = 22 and h p = 32 cm) as a function of radius and height, respectively. Both distributions are normalized with respect to a central point on a flat surface. Source placed in the origin.

Fig. 10
Fig. 10

Spherical dome-shaped substrate.

Fig. 11
Fig. 11

Normalized thickness distribution along the perimeter l(z 1). An elemental surface source is placed at the origin. The parameters of the dome are r s = 28, k = 4, h = 32 cm.

Fig. 12
Fig. 12

Horizontal cylindrical substrate (drum vacuum chamber).

Fig. 13
Fig. 13

Normalized thickness distribution along the circle y = 0 (dashed line) and along a line x = 0 (solid curve) on the surface of the cylinder (r c = 22; length, 64; k = 28 cm).

Fig. 14
Fig. 14

Truncated-cone substrate.

Fig. 15
Fig. 15

Normalized thickness distribution along the line c(z 1). The parameters of the conical fixture are ρ0 = 5, h 1 = 5, h = 30, c 1 = 28 cm.

Fig. 16
Fig. 16

Substrate holder, calotte of plane sectors.

Fig. 17
Fig. 17

Vectors defined to scan the surface of a sector of a calotte fixture.

Fig. 18
Fig. 18

Normalized thickness distribution along the line l 1 (dotted–dashed curve) and along the symmetry axis (solid curve) on the surface of a sector oriented with an angle ψ = 30°. The dashed curve indicates the distribution along the symmetry axis but oriented to ψ = 120°. The difference is due to the asymmetry of the extended source, which is placed at the origin. The parameters of the substrate according to Fig. 16 are R = 30.5, h 1 = 38.7, ρ = 7, and h = 8.3 cm. The axes of the planar elliptical source are a = 0.5, b = 8 cm.

Fig. 19
Fig. 19

Experimental thickness distribution produced by a rectangle source with magnesium fluoride (x direction, a = 0.25 cm; y direction, b = 1 cm) on a planar disk substrate (h p = 32 cm). In this case the scale factor is q s = 2/32, and the source behaves as an elemental surface. The evaporation parameters are pressure 5 × 10-5 mbar, rate 1 Å/s.

Fig. 20
Fig. 20

Distribution produced by an ellipsoidal concave source on a flat disk with the same configuration as in Fig. 19. The solid curve with spheres represents the measured thickness, and the dashed curve the the theoretical fit. In this case the dimensions of the source are a = 0.5, b = 1.5, and c = 0.2 cm. The material used in this experiment is a composite Balzers material called dimo (zirconium suboxide), which is evaporated reactively at an oxygen pressure of 2 × 10-4 mbar and a rate of 0.5 Å/s. The material melts to evaporate.

Fig. 21
Fig. 21

Virtual surface source that fits the emission pattern of the experimental example with dimo. The parameters of such a source are a = 0.5, b = 5, c = 1.5 cm.

Fig. 22
Fig. 22

Emission lobule of the ellipsoidal source given in Fig. 21 (heavy curves) compared with that of an elemental surface source where t ∝ cos θ (thin curve); t = 142.5t 0 - 20.t 1 + 2500t 5 - 2577t 7.

Fig. 23
Fig. 23

Experimental thickness distribution produced by an electron gun equipped with a spiral sweep pattern, with hafnium dioxide (base pressure, 5 × 10-5 mbar; rate, 5 Å/s). The dimensions of the source are, radius of crucible, 0.7 cm; rectangular spot of the beam, a = 0.3, b = 0.8 cm.

Fig. 24
Fig. 24

Distribution measured in x and y directions on a conical dome (indicated by arrows). Crucible radius, r = 0.7 cm; rectangular spot, a = 0.3 cm, b = 0.8 cm.

Equations (46)

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t=j=0m ajtj,
tjr1=Px, ycosj θr, r1cos ϕr, r1Ax, y|r-r1|2dxdy.
tjr1=Px, yvjr, r1ur, r1Ax, y|r-r1|j+3dxdy.
Fx, y, z=z=0,
vr, r1=z1,
Ax, y=1.
x-a, a,  y-b, b.
x-a1-y2/b21/2, a1-y2/b21/2,  y-b, b.
Fx, y, z=x2+y2+z+-1ph02-rf2=0.
vr, r1=-1p+1rfxx-x1+yy-y1+z+-1ph0z-z1,
Ax, y=1+x2+y2rf2-x2-y21/2.
x-rf2-h02-y21/2, rf2-h02-y21/2, y-rf2-h021/2, rf2-h021/2.
Fx, y, z=x2a2+y2b2+z+-1ph02c2-1=0,
vr, r1=-1p+1xx-x1a2+yy-y1b2+z+-1ph0z-z1c2x2a4+y2b4+z+-1ph02c41/2,
Ax, y=1+c2x2/a4+y2/b41-x2/a2-y2/b21/2.
x-a1-y2/b2-h02/c21/2,  a1-y2/b2-h02/c21/2, y-b1-h02/c21/2, 1-h02/c21/2.
c=|z0+-1ph0|,
b=y01-h02/c21/2,
a=x01-h02/c21/2.
Sx1, y1, z1=z1-hp=0,
ur, r1=z1-z.
Sx1, y1, z1=x12+y12-R2=0,
ur, r1=1Rx1x1-x+y1y1-y.
Sx1, y1, z1=x12+y12+z1-k2-rs2=0,
ur, r1=1rsx1x1-x+y1y1-y+z1-kz1-z.
lz1=rs arccosz1-krs,
Sx1, y1, z1=x12+z1-k2-rc2=0,
ur, r1=1rcx1x1-x+z1-kz1-z.
Sx1, y1, z1=x12+y12-ρ0+h-z1cot θ2=0,
ur, r1=x1x1-x+y1y1-y+q-pz1z1-zx12+y12+q-pz121/2,
θ=arcsinh1/c1,
p=cot2 θ,
q=ρ0 cot θ+h cot2 θ.
cz1=h-z1sin θ,
uψ=Rcos ψıˆ+Rsin ψjˆ+h1kˆ,
wψ=R cosψ+θıˆ+R sinψ+θjˆ+h1kˆ,
vψ=ρcos ψıˆ+ρsin ψjˆ+hkˆ,
tψ=ρ cosψ+θıˆ+ρ sinψ+θjˆ+hkˆ.
aψ=uψ-vψ,
bψ=uψ-wψ,
sˆψ=a×b|a×b|.
l1ψ, q1=u+q1w-u,
l2ψ, q2=v+q2t-v.
r1ψ, q3, q=l1ψ, q+q3l2ψ, q-l1ψ, q
t=224.5t0-82.9t2-1050t5+1118t6
t=142.5t0-20.3t1+2500t3-2577t5.

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