EVAPORATION CHARACTERISTICS OF …downloads.hindawi.com/journals/apec/1984/697139.pdfElectrocomp....

Eiectrocornponent Science and Technology. 1984, Vol. 11, pp. 175-183 (C) 1984 Gordon and Breach Science Publishers, lnc0305-3091/84/1102-0175 $18.50/0 Printed in Great Britain

EVAPORATION CHARACTERISTICS OFELECTRON BEAM GUN HEATED SOURCES

PAUL C. BAYNES and T. NAGARAJANDepartment ofNuclear Physics, University ofMadras, A.C. College Campus, Madras 600 025, India

(Received April 20, 1 983; in final form July 6, 1983)

Exact expressions for the thickness profile of thin films deposited using electron beam gun heatedsources are obtained in terms of the source-substrate geometry. Calculations based on conical andcylindrical indentations show the latter to be more realistic. Self-masking effects at the source aretaken into account.

1. INTRODUCTION

The thickness of thin films using EBG heated sources decreases with increasing angle ofemission 0, at a rate more rapid than cos20.1’2 An empirical relation was proposed byGraper to describe the same. Szilagyi tried to explain this theoretically but failed to doso as his functions f(r) and g(r) depend on parameters that are not well known. Further,his assumption of a cone source implies a cos20 dependence in the umbral region of depo-sition, as will be shown in this paper. This however is not borne out by Graper’s workwhich indicates self-masking effects being effective even at small emission angles. Hence ahollow cylindrical source has also been investigated. Further, while the emission charac-teristics based on the source-substrate geometry have been investigated for a number ofsource shapes,4 no such work has been reported for the EBG source (other than a preli-minary report by us ).

2. THEORY

2.1 Cone Source:

Consider the source of radius R and height H to consist of a stack of rings whose radiivary from 0 to R. Each ring is assumed to be an array of small area surface sources. Theemission characteristic of the cone is obtained by integrating over the characteristic forthe rings. From Figure two regions of deposition may be identified:

(i) The Umbral (unshadowed) region where x/z < R/H(ii) The Penumbral region x/z > R/H where only a part of the cone emits towards thepoint P(x, o, z), i.e., P sees varying fractions of the rings of which the cone is composed.The fraction varies from unity at h H to zero at some cut-off height ho. h is the heightof the ring of radius r, from the apex.

The emission characteristic for a ring array of small area surface sources is given by4

(z-h)a ((z-h) +x +r)TpR m/prr

(((z_h)2 + x + r: ) 4xr)3/a (1)

175

176

Region 1" x/R < z/H

P.C. BAYNES AND T. NAGARAJAN

The emission characteristic of the cone is

H

Tpc f TpR dho

(2)

Since h and r , z,

TpR m/pnZ2

(z2 + x2)2

Thus

Tpc m/prrZ2

(Z2 + X2 )2H (4)

Region 2" x/R > z/H

Here, one must evaluate the fraction fR a ring that ’sees’ P, as well as the cut-off heightho. Referring to Figure 2, if SJ is the portion of the ring that sees P, then

fR SJ/2rrr r//rr (5)

ForSJ < 1 r/ COS-1 (1- 2f)

r n- Cos-1 (2f-1)

where

f EH/EI H/h (h- ho)/(H ho)

Now when r/= zr/2, f 1A and fR 1/2. The height of the corresponding ring

hv 2Hho/(H + ho) (6)

as easily obtained from Figure 1.Further, since

tan 0o (x R)/(z H)

(R + (R/H)ho)/(H ho)

Therefore

ho H(x- R)- R(z- H)H(x- R) + R(z- H)

EVAPORATION CHARACTERISTICS OF EBG HEATED SOURCES 177

Z AOBZ QOP=OZ YLC-Oo

FIGURE Geometry of cone source.

E

FIGURE 2 Evaluation of fR.

Thus the thickness at point P is evaluated from"

This gives

H

TPC "]hi0

fR TpR dh

178 P.C. BAYNES AND T. NAGARAJAN

Tpc9i’2 (z2 + X2)2

COS-1 (1- 2f)dh + (zr-COS-1 (2f-1))dhv ho by2

Since R z and sin20 < we get,

m z2Tpc

0r (z + x)z (H- (ho H)v) (8)

2.2 Cylindrical source:

As in the case of the cone, the cylinder is assumed to consist of a stack of rings on a discbase. The cylinder is characterised by a radius R and height H. Referring to Figure 3 onecan identify three regions 0 < 0 < a, a < 0 < 6 and 6 < 0 < rr/2. a defines the region inwhich no self-shadowing occurs. In the second region part of the base and part of the sidecontribute. In the third region varying fractions of the side only contribute towards Tp.

p" p’ P(m,o,z)

P (x’, o, z) A(-R,O, H) 6C =hoQ(a::,y,H) B (R,O,H) AC:H

0’(323,y,o) C (-R, O, O) E C hD R,O,O) CD:2R

FIGURE 3 Geometry of cylindrical source.


Thus if CR and CB are the emission characteristics of the ring and base and fR, fB thefractions of the ring and base that emit towards the point P(x, o, z) we have"

HCR dh + CB in region (1)

fR CR dh + f CB in region (2)

fR CR dhho

in region (3)

(9)

The emission characteristic for a ring array of small area surface sources is given by"Eq. (9)" i.e.

m z2Ca (10)

;r (z + x)

The emission characteristic of the base is that of a small area surface source i.e.

m z2CB

On (z2 + x2)2(11)

Region (1) 0 < 0 < a. Using "Eqs (9 and 10)" in (8) we have

m z2Tp

)2(H+I) (12)

or (z + x

Region (2) a < 0 < 6. We must first evaluate fR, fB and ho. The expressions obtainedfor fR earlier "(Eq. 5)" are valid for this case also. When r/= r/2, the emitting fraction ofthe ring is also 1/2. i.e.

fR =f=1/2.

From Figure 3

f (h ho)/(H ho) (13)

and

hv (H + ho)/2 (14)

Further since

tan 0 o 2R/( H ho)

(x + R)/(z- ho)


we have

(x + R) 2Rzho H (15)

(x- R) (x- R)

To evaluate lB. This is easily done once the area of intersection of the locus of Q’ whichis the projection of PQ on the XY plane, as Q is moved on the upper surface of the cylin-der, keeping P fixed (Figure 4) with the basal plane of the cylinder is known. The locusturns out to be a circle of radius RB centred at (- A, O) where

A xH/(z-H) and B z/(z-H) (16)

Referring to Figure 5, the area of intersection is

A A1 + A:

TL OL

TJ OK

y dx

where T - (- A, O), O (O, O), L -+ (xi, O) J - (- (A- RB), O) and K -+ (- R, O).x is the abscissa of the points of intersection of the two circles. One thus obtains:

A R:( B Sin- ((xi + A)/RB) + Sin-1 (xi/R) + rr/2 (B+ 1)) (17)

(o,o,o)

p (:,o,z)

a

Q’ ,/(:,,y,,o)

FIGURE 4 Evaluation of the locus of Q’.

EVAPORATION CHARACTERISTICS OF EBG HEATED SOURCES

Z181

with

FIGURE 5 Evaluation of fB.

R(1-B2) + A2)xi 2A

Using "Eq. 17)"

(18)

fB A/rr R2 (19)

Thus the emission from the fraction towards P is

ie.

TpB fB CB

Z2

(z2 + x2)2(Sin-1 (xi/R) R2 Sin-1 ((xi + A)/RB) + rr/2(B2 + 1)) (20)

Similarly the emission from the rings gives

m z2 (H-ho) ( (H+ho)TPR

p,tr2 (z2 + x2)2 2rr +

(H- ho)

(H + ho) )Cs-1(H ho)

2(- hoH)V

(H- ho)

Using "Eqs. (20 and 21)", the thickness of the deposit at P is

Tp TpR + TpB (22)


It should be noted that in this region, < ho < 0, implying that ho is not the cut-offheight, the latter being equal to zero.

Region (3,) 6 < 0 < zr/2. As before using "Eqs. (5, 10, 13 and 14)" in (9), we get

Tp m z2 ((H-ho))On (z2 + x2)2 2(23)

All the above expressions have been obtained for deposition onto a planar substrate. Ifhowever the substrate is spherical and concentric with the source, the substitution zCos 0 and Cos 0 z/(z2 + x2)’/2 must be made. is the radius of the sphere.

The angles a and are given by

a tan-1 (R/z)

tan-1 (2R/H- R/z) (24)

for planar substrates, and

a tan-1R/

(1 (R/))v2

6 2tan-1 (-CosT+((+RCos3’)(-RCos7))y2 ]Sin3’ + R Cos 7

for spherical substrates. When - R and H, the same values are obtained from"Eqs. (24 and 25)" for a and i.

3. RESULTS AND DISCUSSION

Polar plots of Graper’s experimental data and his empirical equation are shown inFigures (6, 7, 8) along with typical curves obtained on the cone source and cylindricalsource models. From Graper’s work we note that the thickness profile is smooth and hasa greater than Cos0 dependence on the emission angle. Further, the CosZ0 region if itexists, should be very close to 0 O. i.e., self-masking effects at the source are effectiveover the whole region. The cone source model however shows a large region of Cos20dependence, implying that no self-masking effects occur, in this region. There is a sharptransition to the shadowed region of deposition. The curve in no way resembles theexperimentally obtained profile. On the other hand, all the properties of the experimentalcurve are reproduced by the cylindrical source model. For example, the data for deposi-tion at 105 A/S fit well with R 0.4 cm and H 0.3 cm.

CONCLUSION

Exact expressions for the thickness profile of EBG heated sources are obtained assuminghollow conical and cylindrical sources. The latter reproduce experimental results verywell.


f.O0

FIGURE 6 Polar Plot of Graper’s result.

1.00

O.OC0.00FIGURE 7 Polar Hot of the evaporation

characteristics for a cone source.

FIGURE 8

1.0030"

O.OC0O(3 I.(0

Polar Plot of the evaporation characteristics for a cylindrical source.

REFERENCES

1. E.B. Graper, "Distribution and apparent source geometry of electron-beam heated evaporationsources" J. Vac. Sci. TechnoI. 10, 100 (1973).

2. R. Hill, "Evaporated aluminium films: a review of techniques and improvements" (AirceTemescal, Berkeley, Calif., 1971).

3. M. Szilagyi, "Model for describing emission characteristics of electron-beam evaporation sources"Electrocomp. Sci. and TechnoL 6, 9 (1979).

4. L. Holland, Vacuum Deposition of Thin Films Chapman and Hall, London, (1970) p. 153.5. Paul C. Baynes and T. Nagarajan, "Evaporation characteristics of electron beam gun heated

sources" Nucl. Phys. and Solid State Phys. (lndiaj 24C, 565 (1981).

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