Chapter 14
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Quantitative Analysis of a Laser Interferometer Waveform Obtained During Oxygen Reactive-Ion Etching of Thin Polymer Films B. C. Dems, P. D. Krasicky, and F. Rodriguez School of Chemical Engineering, Olin Hall, Cornell University, Ithaca, NY 14853
A rigorous analysis of a laser interferometer waveform, obtained during oxygen Reactive-Ion Etching (RIE) of thin polymer films, was developed and used to measure the polymer refractive index to within 2-3%. This in turn allowed the in situ etch rate to be measured without any prior knowledge of the polymer's physical properties. Film "roughening", imparted to the film surface during RIE, was assessed semi-quantitatively through an amplitude reduction factor, which accounts for any diffuse character at the plasma/polymer interface. Amplitude reduction factors measured for films etched at 5mTorr were near unity (smooth surface) and invariant with respect to incident RF power over the range 0.125-0.75 Watts/cm . However, amplitude reduction factors decreased with incident RF power at 35mTorr, indicating greater roughening. Scanning Electron Micrographs showed roughness correlation lengths of etched films to be on the order of 0.10.2µm. 2
Laser interferometry i s used extensively i n the integrated c i r c u i t and t h i n f i l m processing industries. I t i s well-suited f o r endpoint detection and in situ etch rate monitoring during the plasma processing of t h i n polymer films. The q u a l i t a t i v e features of the laser interferogram can also shed l i g h t on physical changes occurring at any p a r t i c u l a r time i n the process. This paper describes a rigorous analysis of an interferogram which allows the polymer's r e f r a c t i v e index to be calculated d i r e c t l y from the waveform. This i n turn allows in situ etch rate determination without p r i o r knowledge of the polymer film's physical properties. The analysis also allows the degree of surface roughening imparted to the f i l m during plasma processing to be assessed on a r e l a t i v e basis. The analysis i s r e s t r i c t e d to (a) process etch gases which do not contain film-forming pre-cursors and (b) non-absorbing polymer films which remain homogeneous at a l l times. 0097-6156/89/0412-0234$06.00A) ο 1989 American Chemical Society
Reichmanis et al.; Polymers in Microlithography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
14.
DEMS ET AL»
235
Laser Interferometer Waveform
Background A model for the type of thin f i l m system r e a l i z e d i n Reactive-Ion Etching (RIE) i s shown i n Figure 1. The polymer f i l m i s labeled as region #2, the substrate as #3, and the plasma environment as #1. The polymer-substrate (2-3) interface i s assumed to be sharp and smooth, but the plasma-polymer (1-2) interface may be d i f f u s e or rough. Unpolarized l i g h t of vacuum wavelength λ i s incident upon the system from region #1 at an angle ϋ r e l a t i v e to the normal. The system's o v e r a l l reflectance R i s given by (1), Λ
R
_
β
I
r
r
23 + 2 f r r c o s ^ + f r
I
0
2
12
23
2
.
2
12
(
r
J
1 + 2fr r cos^ + f ^ r f a 23
where I and I are the incident and r e f l e c t e d l i g h t i n t e n s i t i e s , respectively. The r's with subscripts are Fresnel r e f l e c t i o n c o e f f i c i e n t s for sharp, smooth interfaces between the regions denoted, while f i s a reduction factor for r e f l e c t i o n from the plasma-polymer (1-2) interface and accounts for spreading of the interface into a t r a n s i t i o n region. R i s a periodic function of the f i l m thickness d through the phase function φ - φ +Φ\, which includes the phase delay (2), Q
2
φ
2
2
1
- (4*d/A)(n| - n^sin ^) '
2
(2)
associated with passage of l i g h t through the f i l m to the substrate and back, as well as any additional phase s h i f t φ introduced by the t r a n s i t i o n region. When the 1-2 interface i s p e r f e c t l y sharp and smooth, then f - 1, φ - 0, and the maximum value of the p e r i o d i c a l l y o s c i l l a t i n g reflectance equals the reflectance of the bare substrate a f t e r the f i l m i s completely removed. The o p t i c a l e f f e c t of f < 1 i s a reduction i n amplitude of o s c i l l a t i o n of R from what i t would be for an otherwise sharp, smooth i n t e r f a c e . For a sharp, smooth f i l m with φ - 0, the f i n a l reflectance maximum occurs j u s t as f i l m removal i s completed. With a t r a n s i t i o n region, f and φ axe constant i f t h i s region maintains f i x e d size and shape, but are expected to vary once the region begins to collapse into the substrate near the endpoint of f i l m removal. An observable e f f e c t of f and φ varying i s the end-point according to the laser interferogram occurring s l i g h t l y before the f i n a l extrapolated reflectance maximum. The shape of the R versus time curve near the endpoint can provide clues to the shape of the r e f r a c t i v e index p r o f i l e through the t r a n s i t i o n region (Figure 2). In RIE, f i l m roughening i s expected from ion bombardment of the exposed surface. Roughening of the 1-2 interface can produce an amplitude reduction i n reflectance o s c i l l a t i o n s s i m i l a r to that due to diffuseness provided the laser beam i s s u f f i c i e n t l y wide compared to the roughness c o r r e l a t i o n length. But scattering from the rough interface also deflects energy out of the specular directions and introduces additional corrections into R. As a f i r s t approximation, these corrections can be neglected and the interferometer waveform for RIE analyzed using a modified version of d i f f u s e interface t r a n s i t i o n layer theory. χ
ί
χ
χ
χ
Reichmanis et al.; Polymers in Microlithography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
236
POLYMERS IN MICROLITHOGRAPHY
Figure 2
Waveform Dependence on Concentration P r o f i l e Near the End-Point
Reichmanis et al.; Polymers in Microlithography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
14.
DEMS ET AL.
237
Laser Interferometer Waveform a s
r
When | r | f ° most polymer films dissolving i n solvents, R i s well-approximated by a power series i n r to f i r s t order : 1 2
1 2
R » r§
3
+ 2fr r (l-rf )cos^ 1 2
2 3
(3)
3
Physically, this amounts to considering emerging rays whose h i s t o r i e s involve no more than one r e f l e c t i o n from the 1-2 interface (figure 1). R i s then a purely sinusoidal function of φ (and of f i l m thickness d), o s c i l l a t i n g about the value R - r . The factor f reduces the o s c i l l a t i o n amplitude symmetrically about R - R , f a c i l i t a t i n g straightforward c a l c u l a t i o n of polymer r e f r a c t i v e index from quantities measured d i r e c t l y from the waveform (3). When | r | i s not small, as i n the plasma etching of thin polymer films, the f i r s t order power series approximation i s inadequate. For example, for a plasma/poly(methylmethacrylate)/silicon system, r = -0.196 and r = -0.442. The waveform for a uniformly etching f i l m i s no longer purely sinusoidal i n time but contains other harmonic components. In addition, amplitude reduction through the f factor does not preserve the v e r t i c a l median R making the f i l m r e f r a c t i v e index calculation non-trivial. Figure 3 i s a sketch of a t y p i c a l waveform obtained during an oxygen/RIE process. Referring to this figure, l e t R be the extreme values of R when the t r a n s i t i o n layer i s present. Let R± be the corresponding values i f the interface were sharp ( f l ) . These values can be i d e n t i f i e d by setting cos^ — ±1 i n equation 1 which gives, Q
2 3
0
1 2
1 2
2 3
Q
±
s
R
=Γ
±
Γ Ζ 3
±
F R I 2
I 1 ± fr
U
r
±
r
1 2
Λ
(4)
J
2 3
i2r J 2 3
Remember that R£ - r f , the reflectance of the bare substrate medium. As before, l e t R be the value of R for which cos^-0 i n equation 1, 3
Q
R„
= r [
„2 r
"
,
f2„2 f
1 2
2
1 + f r
2 2
ι
r
(6)
2 3
J
Note that the points on the waveform f o r which R=R are equally spaced along φ for uniformly decreasing f i l m thickness, making them i d e n t i f i a b l e . The plasma i t s e l f contributes to the measured intensity. This contribution, defined as R , must be subtracted from the reflectance values before any calculations are made. R i s measured by extinguishing the plasma and measuring the corresponding reduction i n intensity. When f=l, the d i r e c t l y measurable r a t i o x° - (R_/R£) f o r normal or near normal incidence can be used to determine n , from the known value of n and n . At normal incidence, Q
p
p
%
2
x
3
Reichmanis et al.; Polymers in Microlithography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
POLYMERS IN MICROLITHOGRAPHY
238
ο _
, n
In
λ
y ^J
(7a)
- ni
3
+
3
I n n,
(7b)
J
+ n|
3
Solving f o r ng i n terms of x° y i e l d s , n* + n
ι
ng
Il " n'
3
1
J
-η
Λ
(8)
In
3
J
- τι
Λ
For unpolarized l i g h t , this r e l a t i o n i s a very good approximation for incidence angles ϋ < 15°. When f < 1, the observed r a t i o i s χ - (IL_/R ) < x°. I f r were small, then the fact that f would compress the waveform symmetrically about the value ^ could be used to f i n d x°, and hence ng. Note that this analysis would also immediately determine f because equation 3 would apply, and f would be the amplitude reduction factor f o r the reflectance o s c i l l a t i o n s . But i f r i s not small, then a more careful analysis i s needed. Consider the quantities A R s |R - R ° 1 , which denote the s h i f t s i n the extreme values of R due to spreading of the interface. Using equations 4 and 5, these can be written as Λ
1/2
+
1 2
1 2
1 / S
, / 2
±
,/2
±
V A
(1
- f ) r ( l - rj ) 1 2
(9)
3
(1 ± f r r ) ( l ± r r ) 1 2
2 3
1 2
2 3
One then finds
f _
Ί -
1
( I
I AR? J
+
1
f r i 2 r 2 3
1 - fr r 1 2
J
2 3
r
1
I
r
r
+ i2 23 1 -r r 1 2
(10) 2 3
J
If the r i g h t side of equation 10 were known or could be estimated reasonably well, the equation could then be used to f i n d R2. from normalized values of R , R£, and IL, which are available experimentally. I f (1 - f ) were small, then the f r a c t i o n a l s h i f t s AR /R+ would also be small, and vice-versa, so that the r a t i o of s h i f t s could be written as +
±
( A
R
+
)
~
(
R
+
) ( AR?
(11) )
But the r i g h t side of equation 10 i s not known a p r i o r i . A crude approximation might be to set i t equal to unity, and equation 11 would then give (AfL/AR ) « (R_/R ) +
+
,/2
- x
Reichmanis et al.; Polymers in Microlithography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
12
< >
14.
DEMSETAL.
239
Laser Interferometer Waveform
This crude approximation gives a rather simple r e s u l t but i s probably not accurate enough for most purposes. However, i t turns out that the quantities on the right side of equation 10 can be obtained from a more careful analysis of the interferometer waveform. And once these quantities are known, n can then be found d i r e c t l y from them without recourse to equations 11 or 12. Consider the general form of the reflectance R from equation 1, namely 2
a
R •
W
h
e
r
e
a » r
2
2
2
2
r
+ f r
3
+
c
c o s
f ( ^> ï [ b + c(cos
