Kinetics of Polymer Etching in an Oxygen Glow Discharge - ACS

Chapter 13

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Kinetics of Polymer Etching in an Oxygen Glow Discharge Charles W. Jurgensen AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974

This paper is a critical review of the literature and a sum mary of my recent work on the etching kinetics of organic and organosilicon polymers in oxygen glow discharges. The most important application for etching polymers in oxygen glow discharges is the pattern transfer step in multi-layer lithogra phy. Anisotropic etching is required and observed in this appli cation; this suggests that bombardment-induced processes play a dominant role in the etching mechanism. The etching rate for a bombardment-induced mechanism is equal to the flux of bombarding particles times the average yield per particle. The simplest kinetic model for a bombardment-induced process assumes that the yield per bombarding particle depends only on its energy and its angle relative to the surface normal. This paper discusses etching results of organic and organosilicon polymers to determine the range of etching conditions where these results are consistent with this simplest kinetic assump tion.

Multi-Layer Lithography. T h e etching k i n e t i c s of organic a n d organosilicon polymers i n oxygen glow discharges is i m p o r t a n t because the oxygen "reac tive i o n e t c h i n g " ( 0 R I E ) behavior of these materials is the basis for the p a t t e r n transfer step i n m u l t i - l a y e r l i t h o g r a p h y [1,2]. Single-layer o p t i c a l l i t h o g r a p h y is now capable of half m i c r o n resolution o n p l a n a r , nonreflective substrates; however, thickness variations a n d reflections off t o p o g r a p h y are severe problems for single-layer resists o n reflective t o p o g r a p h i c substrates. These difficulties associated w i t h device t o p o g r a p h y are e l i m i n a t e d i n m u l t i layer l i t h o g r a p h y b y coating the substrate w i t h an organic p l a n a r i z i n g layer t h a t ideally provides a level, nonreflective surface o n w h i c h t o image. T h i s simplifies the i m a g i n g step, b u t a d d i t i o n a l processing steps are required t o 2

0097-6156/89/0412-0210$07.00A) ο 1989 American Chemical Society

Reichmanis et al.; Polymers in Microlithography ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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transfer the p a t t e r n t h r o u g h the p l a n a r i z i n g layer. T r i - l a y e r schemes use a c o n v e n t i o n a l resist to p a t t e r n an intermediate m a s k i n g layer w h i c h is subseq u e n t l y used to p a t t e r n the p l a n a r i z i n g layer d u r i n g the 0 R I E pattern transfer step; the m a s k i n g layer m a y be either an inorganic oxide [3], or an organosilicon p o l y m e r [4]. S i l i c o n (or another oxide precurser) is incorp o r a t e d i n t o the i m a g i n g layer i n bi-layer l i t h o g r a p h y [5,6,7] t o enable it to f u n c t i o n as the 0 R I E mask. Surface f u n c t i o n a l i z a t i o n schemes [8,9] achieve m u l t i - l a y e r performance i n a single resist layer b y selective incorp o r a t i o n of an 0 R I E resistant species i n t o the surface of the exposed resist film t o allow 0 R I E development of the latent image. T h e 0 R E E p a t t e r n transfer step is a c r i t i c a l process i n all these schemes; t h u s it is i m p o r t a n t to u n d e r s t a n d the factors c o n t r o l l i n g p o l y m e r e t c h i n g rates, selectivity, uniform i t y , anisotropy, a n d process latitudes. 2


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The Problem with Plasmas. P l a s m a processes are c h a r a c t e r i z e d b y m a n y i n d e p e n d e n t degrees of freedom i n c l u d i n g the rf-volt age, rf-frequency, pressure, gas c o m p o s i t i o n , gas flow rate, sample temperature, reactor geometry, magnetic field s t r e n g t h , a n d others. A l l these processing variables have an effect o n e t c h i n g rates, selectivity, u n i f o r m i t y , a n d anisotropy; b u t a fundam e n t a l i n t e r p r e t a t i o n of these effects requires t h a t one u n d e r s t a n d the effect of the processing variables o n the f u n d a m e n t a l variables s u c h as the r a d i c a l c o n c e n t r a t i o n , i o n flux, i o n energy d i s t r i b u t i o n , a n d others. P l a s m a s are not u n d e r s t o o d well enough to predict these f u n d a m e n t a l variables as a f u n c t i o n of the processing variables; t h u s one must use p l a s m a diagnostics t o determine the dependence of the f u n d a m e n t a l variables o n the processing v a r i ables. U n f o r t u n a t e l y p l a s m a diagnostics are themselves complex, a n d it is difficult to measure or estimate the r a d i c a l flux, i o n flux, i o n energy d i s t r i b u t i o n , i o n angular d i s t r i b u t i o n , energetic n e u t r a l flux, a n d other f u n d a m e n t a l variables. I n t e r p r e t i n g the results observed i n e m p i r i c a l studies is difficult because one never has complete i n f o r m a t i o n o n all these f u n d a m e n t a l v a r i ables. Bombardment-Induced Kinetics. T h e d i r e c t i o n a l i t y observed i n anisotropic p a t t e r n transfer processes results from the h i g h l y d i r e c t i o n a l angular d i s t r i b u t i o n of the energetic particles b o m b a r d i n g the surface being etched. In 0 glow discharges, these particles are O^" ions a n d the energetic n e u t r a l 0 p r o d u c t s of charge transfer collisions [10]. H i g h l y selective a n d anisotropic p a t t e r n transfer is r o u t i n e l y achieved i n m u l t i - l a y e r l i t h o g r a p h y ; this i n d i cates t h a t c h e m i c a l a n d p h y s i c a l processes are a c t i n g s y n e r g i s t i c l y because p u r e l y p h y s i c a l s p u t t e r i n g is not selective w h i l e p u r e l y c h e m i c a l e t c h i n g is not anisotropic. T h e e t c h i n g rate for a b o m b a r d m e n t - i n d u c e d process is equal to the b o m b a r d i n g particle flux times the y i e l d per b o m b a r d i n g p a r t i cle; thus, to characterize the k i n e t i c s of a bombardment-induced chemically-assisted e t c h i n g process, one must determine the y i e l d per b o m b a r d i n g particle as a f u n c t i o n of its mass, energy, angle relative t o the surface n o r m a l , the flux ratio of b o m b a r d i n g t o c h e m i c a l l y assisting species, sample temperature, a n d other f u n d a m e n t a l variables. If the c h e m i c a l l y 2

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POLYMERS IN MICROLITHOGRAPHY

assisting species is g r o u n d state oxygen molecules t h e n the b o m b a r d i n g to assisting flux ratio w i l l be low at t y p i c a l 0 R I E pressures, so the pressure m a y have l i t t l e effect o n the yields u n d e r these c o n d i t i o n s . T h e simplest b o m b a r d m e n t - i n d u c e d k i n e t i c m o d e l assumes t h a t the y i e l d per b o m b a r d i n g particle o n l y depends o n its energy a n d its angle relative t o the surface nor m a l . T h i s review w i l l seek to determine the range of e t c h i n g c o n d i t i o n s where t h i s simplest k i n e t i c a s s u m p t i o n is consistent w i t h p u b l i s h e d e t c h i n g results. T h e first section of this paper is a c r i t i c a l review of the literature o n the e t c h i n g k i n e t i c s of organic polymers i n 0 glow discharges. T h e second section of t h i s paper reviews the o x i d a t i o n k i n e t i c s of organosilicon polymers i n 0 glow discharges. Some i m p o r t a n t aspects of p o l y m e r e t c h i n g k i n e t i c s can not be learned b y etching p l a n a r samples. F o r example, the angle dependence of the y i e l d can not be d e t e r m i n e d except b y b o m b a r d i n g at off n o r m a l incidence or b y etching topographic substrates. T h e angle depen dence has not been d i r e c t l y s t u d i e d i n p o l y m e r e t c h i n g , b u t i t is p a r t i c u l a r l y i m p o r t a n t for u n d e r s t a n d i n g e t c h i n g profiles as discussed i n the final section of this paper.


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Organic Polymers Chemical Etching Regime. T a y l o r a n d W o l f [11], s t u d i e d the 0 plasma e t c h i n g rates o f m a n y organic polymers at h i g h pressure (.5 t o 1 torr) i n a barrel-type e t c h i n g system where the p h y s i c a l e t c h i n g component is negligi ble. P e d e r s o n [12] c o n d u c t e d a s i m i l a r s t u d y for C F and CF /0 discharges. T h e e t c h i n g rates observed i n these studies were strong func tions o f temperature, a n d the relative rates of different polymers v a r i e d more t h a n an order of m a g n i t u d e . These large v a r i a t i o n s were r a t i o n a l i z e d i n terms of c h e m i c a l properties s u c h as the c h a i n scission y i e l d . C o o k a n d B e n son [13,14] used electron paramagnetic resonance spectroscopy to s t u d y the o x i d a t i o n o f photoresist (novolac) d o w n s t r e a m from a microwave discharge. T h e y f o u n d t h a t the e t c h i n g rate is p r o p o r t i o n a l to the Ο a t o m concentra t i o n , a n d shows an A r r h e n i u s t e m p e r a t u r e dependence w i t h an a c t i v a t i o n energy of 11 k c a l / m o l e . Spenser et a l . [15] f o u n d the same a c t i v a t i o n energy i n a d o w n s t r e a m s t r i p p i n g system. 2

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Ion Beam Studies. G o k a n et a l . [16,17,18] s t u d i e d A r a n d 0 / i o n beam e t c h i n g (ΓΒΕ) rates of several organic polymers. Since c a r b o n has the s m a l lest s p u t t e r i n g y i e l d of the atoms present i n organic polymers, t h e y expected t h a t the relative A r s p u t t e r i n g rates w o u l d be inversely p r o p o r t i o n a l to the mass d e n s i t y of c a r b o n (density times mass fraction carbon) i n the p o l y m e r . T h e relative e t c h i n g rates v a r i e d b y a factor of 3, a n d were i n good agree ment w i t h the expected correlation. F u r t h e r m o r e , a better correlation was o b t a i n e d w h e n one carbon atom per oxygen a t o m i n a m o n o m e r u n i t was neglected i n c a l c u l a t i n g the c a r b o n mass density. T h e y c o n c l u d e d t h a t C = 0 groups have a higher s p u t t e r i n g y i e l d t h a n carbon atoms; this is rea sonable because C O is a stable molecule a n d one w o u l d expect its b i n d i n g energy t o the surface t o be m u c h smaller t h a n t h a t of a c a r b o n a t o m . T h e +


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O^" I B E rates were p r o p o r t i o n a l to but 15 times higher t h a n the A r I B E rates, a n d C O was the p r e d o m i n a n t carbon c o n t a i n i n g 0 I B E p r o d u c t . T h e 0 I B E yields [17] increased as the 0 c h a m b e r pressure increased, b u t s u r p r i s i n g l y the y i e l d decreased w i t h increasing b o m b a r d m e n t energy. A t the lowest pressure, the yields were 2 carbons per Ο2", i n d i c a t i n g t h a t b o t h Ο atoms reacted to form C O . T h i s is an example of the reactive i o n e t c h i n g m e c h a n i s m , b u t it is interesting to note t h a t this m e c h a n i s m was o n l y observed at their lowest c h a m b e r pressure ( 5 X 1 0 ~ t o r r ) . A s the 0 c h a m b e r pressure increased, the yields increased up to 6 carbons per 0 / at the highest pressure s t u d i e d (0.4 m t o r r ) . T h e y noted t h a t this c h a m b e r pressure was too low for charge transfer collisions to p l a y an i m p o r t a n t role i n increasing the flux of b o m b a r d i n g particles; t h u s t h e y c o n c l u d e d t h a t these y i e l d s resulted from an 0 chemically-assisted, b o m b a r d m e n t - i n d u c e d e t c h i n g m e c h a n i s m . T h e y were also able t o e x p l a i n the c o u n t e r i n t u i t i v e energy dependence of the yields i n terms of this m e c h a n i s m . A p p a r e n t l y t h e i r i o n source was not equipped w i t h accel-decel e x t r a c t i o n electrodes to prevent target electrons from flowing back to the source p l a s m a ; t h u s they c o u l d not i n d e p e n d e n t l y control acceleration voltage a n d beam c u r r e n t . T h e beam current increased r a p i d l y w i t h acceleration voltage, so the neutral-toion flux ratio (pressure to beam current ratio) decreased w i t h acceleration voltage. T h e y c o n c l u d e d t h a t the b o m b a r d m e n t - i n d u c e d c h e m i s t r y per i o n depends d i r e c t l y o n the neutral-to-ion flux ratio, a n d t h a t this dependence d o m i n a t e d the direct energy dependence w h e n the acceleration voltage was increased. 2

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These studies [16,17,18] are i m p o r t a n t because t h e y show t h a t g r o u n d state 0 can enhance polymer 0 / I B E yields, b u t they leave several i m p o r t a n t questions unanswered. W h a t is the energy dependence of the y i e l d at constant 0 pressure a n d beam current? W h a t happens w h e n the n e u t r a l to-ion flux ratio is increased b y more t h a n an order of m a g n i t u d e to the range t y p i c a l for 0 R I E p a t t e r n transfer processes? Does the y i e l d saturate w i t h increasing pressure at constant i o n flux a n d energy? D o the 0 molecules enhance the y i e l d b y a t h e r m a l spike m e c h a n i s m [19,20] or b y an enhanced s p u t t e r i n g m e c h a n i s m [21]? T h e c h e m i c a l l y e n h a n c e d s p u t t e r i n g m e c h a n i s m is a m o m e n t u m transfer collision cascade m e c h a n i s m where the p r o d u c t molecules leave the surface w i t h i n a picosecond of the collision a n d have a n o n - M a x w e l l i a n energy d i s t r i b u t i o n . T h e c h e m i c a l enhancement i n this m e c h a n i s m results from the chemical s t a b i l i t y of C O molecules w h i c h allows a C O molecule to be removed from the p o l y m e r c h a i n w i t h m u c h less energy t h a n w o u l d be required to remove a Ο Η χ r a d i c a l or C a t o m . T h e t h e r m a l spike m e c h a n i s m assumes t h a t the p r o d u c t molecules leave the sur face o n a time scale greater t h a n a picosecond w h i c h is the time required for the surface to reach local t h e r m a l e q u i l i b r i u m [19]. In this m e c h a n i s m , the p r o d u c t molecules have a modified M a x w e l l i a n energy d i s t r i b u t i o n at the (time v a r y i n g ) local surface temperature [19]. A low energy ( < 1000 e V ) ion penetrates « 4 0 A i n t o the surface; t h u s it deposits its energy i n t o the « 1 0 0 0 atoms t h a t are w i t h i n 40 A of the p o i n t where the i o n h i t . F o r a 500 e V i o n , this results i n a local temperature of « 5 0 0 0 ° K (roughly the 2

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t e m p e r a t u r e at the surface of the sun) w h i c h persists for tens of picoseconds. T h e c h e m i c a l enhancement i n this m e c h a n i s m results from t h e r m a l l y i n d u c e d reactions w i t h 0 adsorbed t o the surface a n d from t h e r m a l desorpt i o n of C O groups w h i c h m a y be formed w h e n 0 reacts w i t h the radicals t h a t m a y r e m a i n after a t h e r m a l spike has cooled. These mechanisms m a y be d i s t i n g u i s h e d b y measuring the p r o d u c t energy d i s t r i b u t i o n [19,20,21,22], b u t s u c h measurements have not been a t t e m p t e d i n p o l y m e r e t c h i n g . T h e most i m p o r t a n t d i s t i n c t i o n between these mechanisms is t h a t energy is a scalar q u a n t i t y while m o m e n t u m is a vector q u a n t i t y ; t h u s yields m a y be angle dependent for a m o m e n t u m transfer m e c h a n i s m , b u t must be nearly i n d e p e n d e n t of angle for a t h e r m a l spike m e c h a n i s m . P h y s i c a l s p u t t e r i n g yields are strongly angle dependent [22,23], b u t c h e m i c a l l y - e n h a n c e d b o m b a r d m e n t - i n d u c e d e t c h i n g y i e l d s are nearly i n d e p e n d e n t of angle i n the systems t h a t have been s t u d i e d to date [24,25,26]. T h e angle dependence was not d e t e r m i n e d i n G o k a n ' s 0 I B E studies [16,17,18]; however, it is relevant to the s i m u l a t i o n of p a t t e r n transfer processes as w i l l be discussed i n the final section of this paper. 2


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Role of Ο Atoms in Pattern Transfer Regime. O x y g e n atoms spontaneously etch polymers a n d are present u n d e r 0 R I E conditions, so it is i m p o r t a n t to determine i f t h e y have a significant effect on p o l y m e r 0 R I E rates u n d e r t y p i c a l e t c h i n g c o n d i t i o n s . H a r t n e y et a l . [27] measured the effect of power d e n s i t y a n d pressure o n organic p o l y m e r 0 R I E rates w h i l e using mass spec t r o m e t r y flux analysis to t r a c k the Ο a t o m p a r t i a l pressure. T h e i r organic p o l y m e r 0 R I E rate increased w i t h pressure, b u t the Ο a t o m p a r t i a l pres sure decreased w i t h pressure. T h i s experiment shows t h a t Ο atoms can not e x p l a i n the observed t r e n d , a n d suggests t h a t Ο atoms do not p a r t i c i p a t e i n the rate c o n t r o l l i n g step. S e l w y n [28] used laser-induced fluorescence t o measure the Ο a t o m c o n c e n t r a t i o n d i s t r i b u t i o n over a bare electrode, a n d over a p o l y i m i d e p o l y m e r sample i n a low pressure 0 / A r glow discharge. E t c h i n g rates increase w i t h bias voltage, b u t S e l w y n f o u n d t h a t the Ο atom c o n c e n t r a t i o n near the p o l y m e r surface decreased w i t h bias voltage. S e l w y n c o n c l u d e d t h a t the Ο atoms are not rate c o n t r o l l i n g , a n d suggested a d o m i n a n t role for b o m b a r d m e n t - i n d u c e d processes. T h e Ο a t o m c o n c e n t r a t i o n gradient increased w i t h bias voltage, w h i c h shows t h a t the Ο a t o m consump t i o n rate increases w i t h the e t c h i n g rate. S e l w y n [28] suggests t h a t b o m b a r d m e n t - i n d u c e d processes c o n t r o l the etching rate, w h i c h i n t u r n con trols the Ο a t o m c o n s u m p t i o n rate, a n d hence the c o n c e n t r a t i o n near the p o l y m e r surface. T h r e e studies of 0 R I E profiles [29,30,31] have reported t h a t Ο atoms can result i n lateral e t c h i n g rates ( u n d e r c u t t i n g ) as h i g h as 1 5 % of the v e r t i c a l e t c h i n g rate; moreover, this lateral e t c h i n g component is t e m p e r a t u r e sensitive (activation energy 2.1 k c a l / m o l e [30]). T h i s r a d i c a l i n d u c e d u n d e r c u t t i n g m a y be almost completely suppressed b y h o l d i n g the substrate at room temperature [29,30], or b y a d d i n g h y d r o c a r b o n s to the p l a s m a to reduce the Ο atom c o n c e n t r a t i o n [31]. 2

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Role of Bombardment in Pattern Transfer Regime. G o k a n et a l . [18] meas u r e d the relative 0 R I E rates of a series of polymers a n d f o u n d t h a t the R I E rates scaled inversely w i t h the mass density of c a r b o n as i n t h e i r I B E s t u d y (several materials deviated from the correlation). T h e relative R I E rates [18] v a r i e d b y a factor of 3 a n d do not show the large v a r i a t i o n s charac teristic of the r a d i c a l - i n d u c e d m e c h a n i s m [10]. These results s t r o n g l y sug gest a b o m b a r d m e n t - i n d u c e d m e c h a n i s m , b u t one can not d i r e c t l y a p p l y the I B E results to R I E conditions because I B E neutral-to-ion flux ratios are o r d ers of m a g n i t u d e lower t h a n u n d e r R I E c o n d i t i o n s .


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P a r a s z c z a k et a l . [32] s t u d i e d p o l y i m i d e e t c h i n g i n a d u a l rf-microwave e t c h i n g system. T h e y used a L a n g m u i r probe t o m o n i t o r the p l a s m a density, a n d used the 13.5 M H z rf power to c o n t r o l the sheath acceleration voltage while i n d e p e n d e n t l y c o n t r o l l i n g the p l a s m a density w i t h the microwave power source. In one experiment, t h e y v a r i e d the sheath acceleration voltage at constant p l a s m a density, a n d observed t h a t the e t c h i n g rate increased as the square root of voltage over the range from 15 to 160 V o l t s . T h e i o n flux is p r o p o r t i o n a l t o the p l a s m a density [33], so this experiment is performed at constant i o n flux; t h u s it determines the e t c h i n g y i e l d as a f u n c t i o n of b o m b a r d m e n t energy to w i t h i n a p r o p o r t i o n a l i t y factor. T h e y [32] noted t h a t the m o m e n t u m per b o m b a r d i n g particle varies as the square root of its energy, a n d argued t h a t the square root energy dependence i m p l i e s t h a t the rate c o n t r o l l i n g step is a p h y s i c a l s p u t t e r i n g ( m o m e n t u m transfer) process. I agree t h a t these results reflect the energy dependence of the y i e l d ; however, I do not. agree t h a t these results i m p l y t h a t the rate c o n t r o l l i n g step is a p h y sical s p u t t e r i n g process for the following reasons: (1) A straight line w i t h a positive intercept o n the rate axis fits this d a t a as well as t h e i r square root energy dependence. (2) P h y s i c a l s p u t t e r i n g yields do not scale as the square root of b o m b a r d m e n t energy [22]. I w i l l r e t u r n t o a discussion of the energy dependence after showing t h a t the results presented b y P a r a s z c z a k et a l . [32] are consistent w i t h the energy dependent yields reported b y Jurgensen a n d R a m m e l s b e r g [34]. In a second experiment, P a r a s z c z a k et a l . [32] observed t h a t the e t c h i n g rate increases l i n e a r l y w i t h the p l a s m a density w h e n the microwave power source is used to v a r y the p l a s m a density at constant sheath acceleration v o l tage. T h e y argued t h a t the Ο a t o m c o n c e n t r a t i o n is p r o p o r t i o n a l to the p l a s m a density a n d i n t e r p r e t e d the results of this experiment i n terms of a r a d i c a l - d o m i n a t e d m e c h a n i s m . T h e y d i d not measure the Ο a t o m concentra t i o n , a n d it is not clear w h y they abandoned the p h y s i c a l s p u t t e r i n g m e c h a n ism w h i c h they h a d used to e x p l a i n the acceleration voltage dependence. T h e i o n flux is p r o p o r t i o n a l to the p l a s m a density [33] (at constant electron t e m p e r a t u r e as reported i n this experiment); t h u s a linear increase i n e t c h i n g rate w i t h p l a s m a density can also be i n t e r p r e t e d i n terms of a b o m b a r d m e n t - i n d u c e d m e c h a n i s m . T h i s experiment shows t h a t the e t c h i n g rate is p r o p o r t i o n a l to the i o n flux at constant acceleration voltage; t h u s it implies t h a t the y i e l d is independent of the neutral-to-ion flux ratio under these e t c h i n g c o n d i t i o n s .


216


V i s s e r a n d de V r i e s [29] used an energy flux diagnostic to s t u d y the 0 R I E rates of novolac, polystyrene and p o l y m e t h y l m e t h a c r y l a t e ( P M M A ) i n a s y m m e t r i c parallel plate e t c h i n g system. T h e y reported t h a t the etching rates of the novolac a n d polystyrene are insensitive to temperature, b u t the e t c h i n g rate of P M M A at 150 ° C was three times its e t c h i n g rate at 4 0 C . T h e y d e t e r m i n e d t h a t the e t c h i n g reactions are exothermic for novolac, polystyrene, a n d for P M M A at 40 C ; however, the P M M A reaction becomes e n d o t h e r m i c at temperatures higher t h a n 100 C . A t low temperature, the P M M A e t c h i n g rate i n an A r p l a s m a was m u c h lower t h a n i n an 0 plasma, b u t at h i g h t e m p e r a t u r e the P M M A etched at the same rate b o t h plasmas. T h e y [29] c o n c l u d e d that P M M A etches b y a b o m b a r d m e n t - i n d u c e d oxidat i o n m e c h a n i s m at low temperatures, b u t at h i g h temperatures it etches b y c h a i n scission followed b y d e p o l y m e r i z a t i o n a n d evaporation of the monomer. 2

0

0


0

2

V i s s e r a n d de V r i e s [29] used i n s i t u t e m p e r a t u r e measurements a n d an energy balance to determine the rate at w h i c h b o m b a r d i n g particles deliver energy to the sample. T h e y d e t e r m i n e d e t c h i n g rates a n d energy deposition rates o n b o t h the powered a n d grounded electrodes as a f u n c t i o n of 0 pressure over the range from 1.3 to 12.5 P a . T h e novolac e t c h i n g rate increased w i t h pressure o n the powered electrode while it decreased w i t h pressure on the g r o u n d e d electrode; however, it was p r o p o r t i o n a l to the b o m b a r d m e n t energy flux o n b o t h electrodes. T h i s correlation is p l o t t e d as triangles on F i g . 1 where the lower three e t c h i n g rates were o b t a i n e d o n the g r o u n d e d electrode w h i l e the higher rates were o b t a i n e d on the powered electrode. T h e i r system is n o m i n a l l y an equal area system, but the powered electrode s t i l l developed a negative self bias; t h u s the difference i n e t c h i n g rates between the powered a n d g r o u n d e d electrodes p r i m a r i l y reflects the difference i n sheath acceleration voltages on these electrodes. T h i s energy flux diagnostic results i n a correlation t h a t s i m u l t a n e o u s l y accounts for the effect of pressure a n d acceleration voltage on p o l y m e r 0 R I E rates. T h e y conc l u d e d t h a t the p r o p o r t i o n a l i t y between e t c h i n g rates a n d the b o m b a r d m e n t energy flux implies t h a t the rate c o n t r o l l i n g step is a b o m b a r d m e n t - i n d u c e d process. 2

2

Jurgensen [10] has s h o w n t h a t the sheath thickness is o n the order of the mean free p a t h for charge transfer collisions under t y p i c a l 0 R I E c o n d i tions. T h u s the flux of energetic n e u t r a l products of charge transfer collisions is o n the order of the i o n flux, and charge transfer collisions c o n t r o l the ion energy d i s t r i b u t i o n at the electrode. Jurgensen a n d Shaqfeh [35] have presented a theory w h i c h uses measurements of the pressure, sheath t h i c k ness, a n d sheath voltage drop to estimate the flux a n d average b o m b a r d m e n t energy of ions, a n d of energetic n e u t r a l 0 p r o d u c t s of charge transfer collisions. Jurgensen a n d R a m m e l s b e r g [34] have a p p l i e d this t h e o r y to s t u d y the 0 R I E k i n e t i c s of a h a r d - b a k e d organic novolac p o l y m e r . T h e y s t u d i e d the effect of pressure, sheath voltage drop, rf frequency, sample temperature, a n d 0 flow rate o n 0 R I E rates (R), a n d o n the energy flux delivered b y b o m b a r d i n g particles ( Q ) . F i g u r e 2 shows the effect of pressure 2

2

2

2

2



13. JURGENSEN


200

400

600

Energy Flux F i g . 1.

800

1000

217

1200

2

(W/m )

T h e organic p o l y m e r e t c h i n g rate is a linear f u n c t i o n of the b o m b a r d m e n t energy flux as d e t e r m i n e d b y V i s s e r a n d de V r i e s [29] (triangles) a n d b y Jurgensen a n d R a m m e l s b e r g [34] (squares).

4.0

40 P F i g . 2.

60

100

(mtorr)

T h e organic p o l y m e r 0 R I E rate (filled points) t r a c k s the b o m b a r d m e n t energy flux (open points) as the pressure is v a r i e d at a constant 500 V self bias, a n d at 13.5 M H z . 2


218


o n the 0 R I E rate (filled points) a n d o n the b o m b a r d m e n t energy flux (open p o i n t s ) at 500 V self bias, 13.5 M H z , 20 S C C M 0 flow, a n d 20 C sample t e m p e r a t u r e . T h e e t c h i n g rates a n d energy fluxes i n F i g s . 2 a n d 3 are ratioed to the results at 10 m t o r r where the e t c h i n g rate is 0.1 w r a / m i n a n d the estimated energy flux is 110 W / m . N o t e t h a t the e t c h i n g rate t r a c k s the energy flux as reported b y V i s s e r a n d de V r i e s [29]. Jurgensen a n d R a m m e l s b e r g [34] also reported t h a t the e t c h i n g rate a n d b o m b a r d m e n t energy flux b o t h increased b y a factor of 2.5 w h e n the frequency was increased from 9 to 18 M H z at 10 m t o r r , a n d 500 V self bias. F i g u r e 3 shows the effect of self bias voltage o n the relative e t c h i n g rate (filled points) a n d b o m b a r d m e n t energy flux (open points) at 13.5 M H z a n d 10 m t o r r (squares) or 80 m t o r r (triangles). T h i s figure shows t h a t the e t c h i n g rate t r a c k s the b o m b a r d m e n t energy flux at b o t h pressures. T h e flow rate was v a r i e d from 5 to 100 seem, a n d the sample temperature was v a r i e d from 15 to 90 ° C , b u t neither of these variables h a d a significant effect of either the e t c h i n g rate or the b o m b a r d m e n t energy flux. T h e squares i n F i g . 1 show the correlation between e t c h i n g rate a n d energy flux, as reported b y Jurgensen a n d R a m melsberg [34]. These results s p a n the following range of parameter space: pressure from 5 to 80 m t o r r , self bias from 200 to 1000 volts, a p p l i e d power d e n s i t y (not an independent variable) from 0.1 to 1.4 W / c m , frequency from 9 t o 18 M H z , 0 flow rate from 5 to 100 seem, a n d sample temperature from 15 to 90 C . N o t e t h a t the e t c h i n g rate is a linear f u n c t i o n of the energy flux over t h i s entire range of e t c h i n g c o n d i t i o n s . 2

0

2


2

2

2

0

F i g u r e 1 shows t h a t the results reported b y Jurgensen a n d R a m m e l s b e r g [34] (squares) are i n qualitative agreement w i t h those r e p o r t e d b y V i s s e r a n d de V r i e s [29] (triangles), b u t the results of these studies do not overlay. J u r gensen a n d R a m m e l s b e r g [34] have discussed the differences i n reactor geometry a n d i n the methods used to estimate the b o m b a r d m e n t energy flux i n an a t t e m p t to u n d e r s t a n d w h a t is responsible for the q u a n t i t a t i v e differences between these studies. T h e y c o n c l u d e d t h a t the relative energy flux estimates s h o w n i n F i g s . 2 a n d 3 are accurate, b u t the absolute energy flux estimates (squares s h o w n i n F i g . 1) are low because the t h e o r y does not account for the effect of rf m o d u l a t i o n o n the electron d e n s i t y i n the sheath [35]. T h e correction for this effect w o u l d shift the squares i n F i g . 1 to the r i g h t towards the results presented b y V i s s e r a n d de V r i e s [29] (triangles). T h e y also argued t h a t energetic electrons m a y c o n t r i b u t e to the energy flux measured i n the s y m m e t r i c system used b y V i s s e r a n d de V r i e s [29]. In part i c u l a r energetic electrons are k n o w n [36] to b o m b a r d the counter-electrode where three of t h e i r results were o b t a i n e d (lower 3 triangles i n F i g . 1). E n e r getic electrons are expected to be less effective at i n d u c i n g c h e m i c a l reactions, so this c o u l d explain w h y these three d a t a points are shifted to the right of the results presented b y Jurgensen a n d R a m m e l s b e r g [34]. T h e above speculations m a y be tested b y direct c o m p a r i s o n between these methods of e s t i m a t i n g the i o n flux. Bombardment-induced Yields in Pattern Transfer Regime. V i s s e r a n d de V r i e s [29] e s t i m a t e d the sheath acceleration voltages i n t h e i r system, a n d


13. JURGENSEN


219

used the measured energy flux to estimate the i o n flux. F r o m the e t c h i n g rate a n d the i o n flux, t h e y d e t e r m i n e d t h a t the y i e l d per i o n was 3.6 mono mer u n i t s for the novolac [C^H^O^) at an estimated 500 V acceleration v o l tage. F o r this e t c h i n g c o n d i t i o n , the yields for novolac, polystyrene, a n d P M M A at 40 C were all about 30 carbons per b o m b a r d i n g i o n . T h i s y i e l d is 5 times larger t h a n the largest 0 I B E y i e l d reported b y G o k a n a n d E s h o [16], b u t t h i s is consistent w i t h G o k a n ' s finding t h a t the y i e l d increases w i t h the neutral-to-ion flux ratio. T h e results presented b y V i s s e r a n d de V r i e s [29] i m p l y t h a t the y i e l d is independent of the neutral-to-ion flux r a t i o i n the R I E pressure range, a n d this is consistent the results presented b y P a r a s z c z a k et a l . [32]. 0


2

F i g u r e 1 shows t h a t the e t c h i n g rate is nearly p r o p o r t i o n a l to the energy flux delivered b y b o m b a r d i n g particles; this implies t h a t b o m b a r d m e n t i n d u c e d processes c o n t r o l the e t c h i n g rate, a n d t h a t the y i e l d per i n c i d e n t particle is nearly p r o p o r t i o n a l to its energy. F i g u r e 4 shows the energy dependence of the c a r b o n a t o m y i e l d (squares) as d e t e r m i n e d b y Jurgensen a n d R a m m e l s b e r g [34] from the e t c h i n g rate a n d estimated t o t a l flux of ions a n d energetic neutrals. T h e triangles a n d right h a n d axis o n F i g . 4 are the e t c h i n g rates reported b y P a r a s z c z a k et a l . [32] as f u n c t i o n of sheath acceleration voltage at constant p l a s m a density. T h e i o n flux was constant i n P a r a s z c z a k ' s [32] experiment, so his e t c h i n g rates are p r o p o r t i o n a l t o the energy dependent y i e l d a n d it s h o u l d be possible to rescale his e t c h i n g rates to superimpose t h e m o n Jurgensen's [34] y i e l d t r e n d . T h e line s h o w n o n F i g . 4 is a linear least squares fit to the yields reported b y Jurgensen a n d R a m melsberg [34], b u t it is also a reasonable fit to the e t c h i n g rates reported b y P a r a s z c z a k et a l . [32]. T h u s the y i e l d s i n these studies show nearly the same energy dependence. Jurgensen's y i e l d extrapolates to a finite value of 3 ±2 carbons per 0 at zero b o m b a r d m e n t energy. S u b t r a c t i n g 2 carbons per b o m b a r d i n g 0 gives the i n d u c e d y i e l d per i n c i d e n t particle w h i c h extrapo lates t o zero at zero b o m b a r d m e n t energy ( w i t h i n e x p e r i m e n t a l error). F o r the rescaling factor chosen i n F i g . 4, P a r a s z c z a k ' s [32] results extrapolate to a y i e l d of 4.4 (f0.2) carbons per Ο £ at zero energy. T h i s implies t h a t Ο atoms induce half the etching rate at the lowest acceleration voltage i n P a r a s z c z a k ' s [32] s t u d y w h i c h agrees w i t h the a m o u n t of u n d e r c u t t i n g observed on t h e i r e t c h i n g profiles [32]. T h e e t c h i n g profiles observed i n Jurgensen's [37] system do not show any r a d i c a l i n d u c e d u n d e r c u t t i n g a n d w i l l be discussed i n the final section of this paper. 2

2

U n d e r t y p i c a l 0 R I E conditions, the i n d u c e d y i e l d is m u c h larger t h a n the 2 carbons removed b y the r e a c t i v i t y of an energetic 0 i o n or n e u t r a l . T h u s the t e r m "reactive i o n e t c h i n g " is a c t u a l l y a double misnomer. It implies t h a t the b o m b a r d i n g particles are Ο 2 ions, b u t the flux of energetic n e u t r a l p r o d u c t s of charge transfer collisions is r o u g h l y equal to the i o n flux u n d e r t y p i c a l 0 R I E conditions [10]. In a d d i t i o n , it i m p l i e s t h a t the reac t i v i t y is s u p p l i e d b y the b o m b a r d i n g i o n , b u t F i g . 4 shows t h a t the i n d u c e d y i e l d is m u c h larger t h a n t h i s reactive component. T h e m e c h a n i s m i m p l i e d b y the name "reactive ion e t c h i n g " was observed at the lowest pressures i n 2

2

2



220


0.0 100

F i g . 3.

200 300 400 500 600 Self-Bias (Volts)

700

800

T h e organic p o l y m e r 0 R I E rate (filled points) t r a c k s the energy deposition rate (open points) as the self bias voltage is v a r i e d at 13.5 M H z a n d 10 m t o r r (squares) or 80 m t o r r (triangles). 2

2000 R (A/mln) 1500 1000 500

100

F i g . 4.

150 200 Ë (eV)

250

300

350

T h e carbon atom y i e l d (squares a n d left h a n d axis) reported by Jurgensen a n d R a m m e l s b e r g [34], is c o m p a r e d to the e t c h i n g rate at constant p l a s m a density (triangles a n d right h a n d axis) reported b y P a r a s z c z a k et a l . [32]. T h e line is a linear least squares fit to the Jurgensen's [34] results.



13. JURGENSEN


221

G o k a n a n d E s h o ' s [17] 0 ^ I B E y i e l d s t u d y , b u t this m e c h a n i s m does not a p p l y u n d e r the " R I E " c o n d i t i o n s . T h e t e r m "reactive i o n e t c h i n g " not o n l y refers t o a p a r t i c u l a r (and incorrect) e t c h i n g m e c h a n i s m , b u t it is also used to refer t o a reactor geometry where the powered electrode is m u c h smaller t h a n the g r o u n d e d electrode a n d where the wafer sits o n the powered electrode. Jurgensen's [34] results were o b t a i n e d o n s u c h a system, b u t it is interesting t o note t h a t V i s s e r a n d de V r i e s [29], a n d P a r a s z c z a k et a l . [32] o b t a i n e d their results o n systems t h a t are not t r a d i t i o n a l l y called "reactive ion e t c h i n g " systems. Nevertheless, the results o b t a i n e d i n these three studies clearly indicate t h a t the same f u n d a m e n t a l m e c h a n i s m occurs i n a l l three reactor configurations. T h e b o m b a r d m e n t - i n d u c e d yields s h o w n i n F i g . 4 are so large t h a t it seems u n l i k e l y t h a t m o m e n t u m transfer c o u l d p l a y a d o m i n a n t role i n the e t c h i n g m e c h a n i s m . These yields are consistent w i t h a t h e r m a l spike m e c h a n i s m for the b o m b a r d m e n t i n d u c e d chemistry; i n this m e c h a n i s m , g r o u n d state oxygen molecules react w i t h b o m b a r d m e n t generated r a d i c a l sites o n the p o l y m e r to form c a r b o n y l groups w h i c h are later t h e r m a l l y desorbed from the hot microregion created b y a b o m b a r d i n g p a r t i c l e . T h i s m e c h a n i s m predicts t h a t the y i e l d increases w i t h b o m b a r d m e n t energy, a n d t h a t the y i e l d saturates w i t h increasing pressure at constant i o n energy a n d flux. T h i s s a t u r a t i o n effect was suggested i n the 0 I B E yield study presented b y G o k a n a n d E s h o [17], a n d is consistent w i t h the y i e l d being i n d e p e n d e n t of the neutral-to-ion flux ratio i n the R I E regime as f o u n d i n a l l the R I E studies [29,32,34]. T h e t h e r m a l spike m e c h a n i s m also i m p l i e s t h a t the y i e l d is nearly independent of angle w h i c h has i m p o r t a n t i m p l i c a t i o n s for m o d e l i n g e t c h i n g profiles. 2

Organosilicon Polymers General Considerations. I n 1980 T a y l o r a n d W o l f [11] noted t h a t d i m e t h y l siloxane has " n o appreciable" etching rate i n an 0 p l a s m a , a n d s u r m i s e d t h a t a t h i n < 1 0 0 A t h i c k S i 0 film formed o n top o f the p o l y m e r a n d protected it from further e t c h i n g . T h e p r i n c i p l e t h a t silicon (or another oxide former) c a n d r a s t i c a l l y reduce a polymer's 0 R I E rate is the basis for select i v i t y d u r i n g the 0 R I E p a t t e r n transfer step for m a n y m u l t i - l a y e r lithographic processing schemes i n c l u d i n g " s p i n o n glass" t r i - l a y e r schemes [4], bi-layer schemes [5,6,7], a n d surface f u n c t i o n a l i z a t i o n schemes [8,9]. L i n e w i d t h loss caused b y mask erosion is a serious concern for a l l these schemes, so it is i m p o r t a n t to u n d e r s t a n d organosilicon p o l y m e r 0 R I E kinetics. M o r e recently B u t h e r u s et a l . [38] have reported another a p p l i c a t i o n for 0 p l a s m a e t c h i n g of silicon c o n t a i n i n g polymers where the objective is t o form a t h i c k S i 0 layer ( > 2 0 0 0 A ) for use as a permanent dielectric between m e t a l levels i n m u l t i - l e v e l m e t a l i z a t i o n schemes. T h i s a p p l i c a t i o n requires r a p i d o x i d a t i o n of the organosilicon p o l y m e r , so it is also i m p o r t a n t t o unders t a n d organosilicon polymer o x i d a t i o n k i n e t i c s i n 0 glow discharges for this a p p l i c a t i o n . N o t e t h a t the oxide layer must protect the organosilicon polymer from further o x i d a t i o n i n the m a s k i n g a p p l i c a t i o n , w h i l e the entire layer 2

2

2

2

2

2

2

2



222

m u s t be r a p i d l y o x i d i z e d i n the dielectric a p p l i c a t i o n . F o u r e t c h i n g regimes have been observed for organosilicon polymers i n 0 glow discharges. T h e transient regime occurs d u r i n g the early stages of the e t c h i n g or o x i d a t i o n process w h i l e the oxide layer forms o n the surface of the p o l y m e r . T h e diffusion-controlled regime [38] occurs u n d e r conditions where s p u t t e r i n g is absent; i n this regime the oxide thickness a n d t o t a l t h i c k n e s s loss (initial t h i c k n e s s m i n u s t o t a l thickness of the oxide a n d polymer) scale as the square root of the e t c h i n g t i m e . T h e steady-state regime [39,40] occurs w h e n the s p u t t e r i n g rate balances the o x i d a t i o n rate s u c h t h a t the oxide t h i c k n e s s is i n d e p e n d e n t of t i m e (after the i n i t i a l transient), a n d the t o t a l thickness loss increases l i n e a r l y w i t h t i m e (after the i n i t i a l transient). F i n a l l y , the t o t a l t h i c k n e s s loss a n d the thickness of the p a r t i a l l y o x i d i z e d layer increase l i n e a r l y w i t h t i m e after an i n i t i a l transient i n the anomalous transport regime [40]. Before discussing the e x p e r i m e n t a l results, it is useful to present a simple k i n e t i c m o d e l w h i c h contains the transient, diffusion-controlled, a n d steady-state regimes as special cases.


2

Kinetics of Oxide Growth. T h e k i n e t i c m o d e l derived i n t h i s section is an extension of the D e a l - G r o v e [41] o x i d a t i o n m o d e l to i n c l u d e a loss t e r m t h a t accounts for oxide loss b y s p u t t e r i n g . T h i s m o d e l assumes t h a t the p l a s m a c o n d i t i o n s determine b o t h the oxygen r a d i c a l c o n c e n t r a t i o n o n the surface of the oxide layer, a n d the rate at w h i c h oxide is lost b y p h y s i c a l s p u t t e r i n g . S e c o n d l y , it assumes quasi-static diffusion of oxygen radicals across a u n i form oxide layer w i t h no r e c o m b i n a t i o n losses. F i n a l l y it assumes t h a t the oxygen radicals react b y first order k i n e t i c s at the polymer-oxide interface to f o r m oxide a n d volatile o x i d a t i o n p r o d u c t s w h i c h diffuse back t h o u g h the oxide t o escape. In the quasi-static a p p r o x i m a t i o n , the flux of radicals across the oxide layer is set equal t o t h e i r rate of c o n s u m p t i o n at the oxide-polymer interface [41] to o b t a i n D(Cs-Ci)

kC

s

where F is the Ο a t o m flux, k is the rate constant for the reaction between Ο atoms a n d p o l y m e r , C, is the Ο atom c o n c e n t r a t i o n at the polymer-oxide interface, D is the Ο a t o m diffusion coefficient i n the oxide, C$ is the Ο a t o m c o n c e n t r a t i o n o n the surface of the oxide (plasma side), a n d X is the oxide t h i c k n e s s . T h e rate at w h i c h the p o l y m e r is consumed is p r o p o r t i o n a l t o the Ο atom flux w h i c h yields

dt

{

{l + Xk/D)

)

where Ρ is the r e m a i n i n g t h i c k n e s s of the organosilicon p o l y m e r layer, t is t i m e , a n d ν is the v o l u m e of p o l y m e r removed per Ο a t o m . If the s t o i c h i o m e t r y of the o x i d a t i o n reaction is assumed to be

Ο Η βί α

β

η

Ο + ( 2 α + ν β+ Ί

Ζ

2η - η ) Ο

aC0

2

+ V2fiH Ο + ηβί0 2

t h e n the v o l u m e of p o l y m e r consumed per Ο a t o m is given b y


2

(3)

13. JURGENSEN


223

(12α+ β+28η+16η) ρ Ν (2α+Κβ+2η-η)

=

ρ

0

where p is the p o l y m e r density, a n d N silicon m a t e r i a l balance gives p

Q

is A v o g a d r o ' s n u m b e r .

Finally, a

where S is the S i 0 s p u t t e r i n g rate, a n d M is the ratio of the S i mass density in the p o l y m e r to the S i mass density i n the oxide. F o r the p o l y m e r compo s i t i o n s h o w n i n E q . 3, M is given b y


2

M = 7 ô — ς («) (12«+0+28*7+167 Κ χ where ρ is the density of the oxide layer. E q u a t i o n s 2 a n d 5 m a y be com b i n e d to o b t a i n a closed o r d i n a r y differential equation for the time depen dence of the oxide thickness οχ

dX

Mi/kCs

=

dt

(

1 + kX/D

J

T h e transient s o l u t i o n to E q . 7 w i l l be discussed i n the next section. E q u a t i o n 5 can also be d i r e c t l y integrated to relate the r e m a i n i n g p o l y m e r t h i c k ness to the time dependent oxide thickness P{t) a

n

a

r

e

t

= P

0

n

-

St/M

+ ( X - X{t))/M 0

(8)

e

where X d i n i t i a l oxide a n d p o l y m e r thicknesses. F i n a l l y , one m a y define the t o t a l thickness loss L(t) as the i n i t i a l thickness m i n u s the sum of the oxide a n d polymer thicknesses to o b t a i n 0

L(t)

= (X(t)-X ){l/M-1)+ 0

St/M

(9)

It is i m p o r t a n t to note t h a t E q s . 5, 8, and 9 were derived e n t i r e l y from a s i l i con m a t e r i a l balance a n d the assumption t h a t p h y s i c a l s p u t t e r i n g is the o n l y silicon loss m e c h a n i s m ; t h u s these equations are independent of the k i n e t i c assumptions i n c o r p o r a t e d i n t o E q s . 1, 2, a n d 7. T h i s is an i m p o r t a n t point because several of these k i n e t i c assumptions are questionable; for example, E q . 2 assumes a r a d i c a l d o m i n a t e d m e c h a n i s m for X= 0, b u t b o m b a r d m e n t i n d u c e d processes m a y dominate for s m a l l oxide t h i c k n e s s . M o r e o v e r , ballis tic transport is not i n c l u d e d i n E q . 1 , b u t this m a y be the d o m i n a n t t r a n sport m e c h a n i s m t h r o u g h the first « 4 0 A of oxide. F i n a l l y , the first « 4 0 A of oxide m a y be annealed b y the b o m b a r d i n g ions, so the diffusion coeffi cient m a y not be a constant t h r o u g h o u t the oxide layer. I n spite of these objections, E q . 2 is a three parameter k i n e t i c m o d e l ( k, C$, a n d D ), a n d it s h o u l d not be rejected u n t i l clear e x p e r i m e n t a l evidence shows t h a t a more complex k i n e t i c scheme is required. Transient Regime. E q u a t i o n 7 is separable a n d m a y be integrated t o o b t a i n the t i m e dependence of the oxide thickness. A s s u m i n g a finite s p u t t e r i n g rate, the result is


224


MuDC

s


X{t)-Xo

=

MvkDCs-

In

S

DS-

MvkDCs-

DS-

SkX

0

-

St

(10)

SkX{t)

W a t a n a b e a n d O h n i s h i [39] have proposed another m o d e l for the p o l y m e r c o n s u m p t i o n rate (in place of E q . 2) a n d have also integrated t h e i r m o d e l to o b t a i n the time dependence of the oxide thickness. T i m e dependent oxide t h i c k n e s s measurement i n the transient regime is the clearest w a y to test the k i n e t i c assumptions i n these models; however, neither m o d e l has been subj e c t e d t o e x p e r i m e n t a l verification i n the transient regime. E q u a t i o n 9 m a y be used to o b t a i n time dependent oxide thickness estimates from the time dependence of the t o t a l thickness loss, b u t s u c h results have not been p u b lished. H a r t n e y et a l . [42] have recently used variable angle X P S spectroscopy t o determine the t i m e dependence of the oxide t h i c k n e s s for t w o organosilicon polymers a n d several e t c h i n g c o n d i t i o n s . T h e y d i d not present k i n e t i c model fits to their results, nor d i d they compare t h e i r results t o time dependent thickness estimates from the m a t e r i a l balance ( E q . 9). M o r e research o n the transient regime is needed t o determine the v a l i d i t y of E q . 10 or the comparable result for the k i n e t i c model presented b y W a t a n a b e a n d O h n i s h i [39]. Diffusion Controlled Regime. B u t h e r u s et a l . [38] s t u d i e d p l a s m a o x i d a t i o n of polysiloxane i n a barrel etcher, and were able to convert several t h o u s a n d angstroms of polysiloxane to S i 0 i n « 2 0 m i n u t e s . T h e y observed t h a t the oxide t h i c k n e s s scales as the square root of t i m e , a n d c o n c l u d e d t h a t the rate c o n t r o l l i n g step i n this process is the diffusion of oxygen radicals t h r o u g h the oxide film. M o r e recently N a m a t s u [43] has also observed t h a t the oxide t h i c k n e s s scales as the square root of time u n d e r c o n d i t i o n s where the ion b o m b a r d m e n t energy is low. In terms of the k i n e t i c model presented earlier, the diffusion-controlled regime is described b y assuming 5 = 0 and kX/D » 1 i n E q . 7, a n d i n t e g r a t i n g to o b t a i n 2

X

2

-

x

2 0

= 2DMvC t s

(ll)

T h i s equation predicts t h a t the oxide thickness scales as the square root of the e t c h i n g time ( f o r X » X ) as observed e x p e r i m e n t a l l y [38,43]. N o t e t h a t D i n E q . 11 is the diffusion coefficient of oxygen radicals i n the oxide layer, not i n the p o l y m e r . T h e r a d i c a l c o n c e n t r a t i o n at the surface of the oxide is d e t e r m i n e d b y the p l a s m a c o n d i t i o n s . T h u s the o n l y p o l y m e r dependent p r o p e r t y i n E q . 11 is the p r o d u c t Mv w h i c h is d e t e r m i n e d e n t i r e l y b y the density a n d stoichiometric c o m p o s i t i o n of the p o l y m e r . T h i s constant increases w i t h the silicon content of the p o l y m e r s u c h t h a t Mv for a dimethylsiloxane is four times larger t h a n for a d i p h e n y l s i l o x a n e . N a m a t s u [43] observed t h a t the oxide accumulates more r a p i d l y o n methylsiloxane t h a n o n phenylsiloxane as p r e d i c t e d b y E q . 11; however, he d i d not interpret his results i n terms of this k i n e t i c m o d e l . N a m a t s u [43] also f o u n d t h a t the m o l e c u l a r weight a n d structure of several methylsiloxane polymers has a large effect o n the o x i d a t i o n rate i n the diffusion-controlled regime even t h o u g h the silicon a n d carbon contents of these polymers were s i m i l a r . T h i s result was not expected from E q . 11 because Mv o n l y depends on 0



13. JURGENSEN


225

c o m p o s i t i o n of the polymer a n d is independent of its m o l e c u l a r weight a n d detailed s t r u c t u r e . O n e can, however, rationalize N a m a t s u ' s [43] results i n terms of E q . 11 i f one assumes t h a t the molecular weight a n d p o l y m e r structure c a n affect the structure of the oxide a n d hence the diffusion coefficient i n the oxide. N a m a t s u [43] d i d not interpret his results i n terms of E q . 11, a n d has rejected the assumptions t h a t lead to this m o d e l . He argues t h a t the diffusion coefficient i n the polymer itself is i m p o r t a n t , a n d t h a t the t r e n d w i t h p o l y m e r structure reflects the t r e n d i n the diffusion coefficients i n the p o l y m e r . N a m a t s u [43] d i d not present measurements of diffusion coefficients i n his polymers, nor d i d he e x p l a i n how the oxide t h i c k n e s s could scale as the square root of time i f diffusion across the oxide layer is not the rate c o n t r o l l i n g step. N a m a t s u ' s [43] results are interesting regardless of how they are interpreted; they either indicate t h a t the oxide remembers the s t r u c t u r e of its p o l y m e r precurser (my i n t e r p r e t a t i o n ) , or t h a t the k i n e t i c assumptions leading to E q . 11 must be a b a n d o n e d i n the regime where they seem most reasonable ( N a m a t s u ' s i n t e r p r e t a t i o n ) . Etching Rates in Steady-State Regime. W a t a n a b e a n d O h n i s h i [39] proposed a steady-state R I E m o d e l for organosilicon p o l y m e r e t c h i n g ; i t assumes t h a t an oxide forms o n the surface of the p o l y m e r a n d reaches a steady-state t h i c k n e s s where the rate of silicon loss b y p h y s i c a l s p u t t e r i n g is balanced b y o x i d a t i o n of the u n d e r l y i n g organosilicon p o l y m e r . T h e i r k i n e t i c m o d e l was not based o n a microscopic m e c h a n i s m ; however, E q . 11 also predicts t h a t the oxide t h i c k n e s s w i l l reach a steady-state where the rate of o x i d a t i o n balances the s p u t t e r i n g losses. Jurgensen et a l . [40] p o i n t e d out t h a t steadystate e t c h i n g behavior is expected for any k i n e t i c m o d e l where the p o l y m e r o x i d a t i o n rate decreases as the oxide thickness increases. S u c h behavior is plausible because transport t h r o u g h the oxide layer is i n series w i t h oxidat i o n of the p o l y m e r . T h e steady-state e t c h i n g rate (R = S/M) is proport i o n a l to the s p u t t e r i n g rate of S i 0 a n d inversely p r o p o r t i o n a l to the mass density of silicon (density times mass fraction silicon) i n the p o l y m e r . T h i s result is a direct consequence of the silicon m a t e r i a l balance ( E q . 9) together w i t h the a s s u m p t i o n that the oxide thickness is i n d e p e n d e n t of t i m e i n the steady-state regime. W a t a n a b e a n d O h n i s h i [39] tested t h i s m o d e l for several silyl-styrene polymers a n d found t h a t it q u a n t i t a t i v e l y predicts the e t c h i n g rate of these materials under h i g h b o m b a r d m e n t energy 0 R I E conditions; however they observed significant deviations from p r e d i c t e d behavior under lower b o m b a r d m e n t energy 0 R I E c o n d i t i o n s . In a later s t u d y , G o k a n et a l . [44] f o u n d t h a t the steady-state m o d e l q u a n t i t a t i v e l y predicts the e t c h i n g rate of 12 organosilicon polymers u n d e r 0} I B E conditions for b o m b a r d m e n t energies greater t h a n 100 e V . In this same s t u d y , t h e y observed significant deviations from the steady-state model u n d e r 0 R I E conditions s i m i l a r to those where W a t a n a b e a n d O h n i s h i [39] observed s u c h deviations. Jurgensen et a l . [40] s t u d i e d the 0 R I E behavior a s i l y l novolac a n d t w o silyl-methacrylate polymers a n d observed quantitative agreement w i t h the steady-state model for all three polymers u n d e r h i g h bombardment energy ( > 2 5 0 eT^) etching conditions. At lower 2

2

2

2

2



226


b o m b a r d m e n t energies, the silyl-methacrylates exceeded the p r e d i c t e d etching rate, w h i l e the silyl-novolac c o n t i n u e d t o etch at the p r e d i c t e d rate d o w n t o 130 e V . H a r t n e y et a l . [42] recently f o u n d excellent agreement w i t h the p r e d i c t e d steady-state e t c h i n g rate for diphenylsiloxane based negative photoresist over a wide range of e t c h i n g conditions; however, t h e y observed steady-state etching rates twice as large as predicted for p o l y ( t r i m e t h y l s i l y l m e t h y l s t y r e n e ) ( P S M S ) a n d a c o p o l y m e r of t h i s m a t e r i a l w i t h c h l o r o m e t h y l s t y r e n e . I w i l l delay further discussion of the deviations from the steady-state model u n t i l after presenting surface analysis results. P h y s i c a l s p u t t e r i n g of the oxide layer is the rate c o n t r o l l i n g step i n the steady-state regime, so it is i m p o r t a n t to s t u d y S i 0 s p u t t e r i n g yields u n d e r 0 R I E c o n d i t i o n s to u n d e r s t a n d the effect of e t c h i n g c o n d i t i o n s o n select i v i t y i n m u l t i l a y e r l i t h o g r a p h y . Jurgensen a n d R a m m e l s b e r g [34] determ i n e d S i yields for a s i l y l novolac a n d for S i 0 from the measured s p u t t e r i n g rate (for S i 0 ) or steady-state e t c h i n g rate (for the novolac) a n d from the e s t i m a t e d flux of b o m b a r d i n g ions a n d energetic neutrals. F i g u r e 5 shows the S i y i e l d of the silyl novolac (squares) a n d of S i 0 (triangles) as a f u n c t i o n of the average b o m b a r d m e n t energy over the entire range of e t c h i n g c o n d i tions discussed earlier. T h e S i 0 s p u t t e r i n g y i e l d falls o n the same curve as the results for the s i l y l novolac as assumed i n the steady-state m o d e l . T h e least squares line s h o w n o n F i g . 5 is a fit to the silyl novolac results a n d i n d i cates an apparent s p u t t e r i n g t h r e s h o l d of 50 e V . F i g u r e 6 shows the experim e n t a l (squares) a n d expected (curve) s e l e c t i v i t y for e t c h i n g the an organic novolac p l a n a r i z i n g layer relative to the silyl novolac as a f u n c t i o n of the average b o m b a r d m e n t energy. T h e equation for the expected s e l e c t i v i t y is 2

2

2

2

2

2

SEL

b t

J

= — ^ ^(X p)opYsi V

(12)

c

where YQ is the energy dependent c a r b o n a t o m y i e l d s h o w n i n F i g . 4, Y$i is the energy dependent silicon a t o m y i e l d s h o w n i n F i g . 5, (XsiP)sP mass fraction of silicon times the density of the organosilicon p o l y m e r , a n d {XCP)OP the mass fraction of carbon times the density of the organic polymer. T h i s equation applies to a wide range of e t c h i n g c o n d i t i o n s a n d to other polymer-organosilicon p o l y m e r systems because the 0 R I E rate of most organic polymers scales inversely w i t h the mass density of c a r b o n [19,20,21], w h i l e the 0 R I E rate of m a n y organosilicon polymers scales inversely w i t h the mass density of silicon [39,40,42]. These results show t h a t one can i m p r o v e s e l e c t i v i t y b y r e d u c i n g the b o m b a r d m e n t energy; however, this is o n l y true as long as the organosilicon p o l y m e r continues to e t c h b y the steady-state m e c h a n i s m . 1 S

t

n

e

1 S

2

2

Steady-State Oxide Thickness. T h e steady-state e t c h i n g rate (R = S/M) does not c o n t a i n any of the k i n e t i c parameters; t h u s it does not c o n t a i n any i n f o r m a t i o n about the k i n e t i c s of the o x i d a t i o n process. In contrast, the steady-state oxide thickness is d e t e r m i n e d b y the k i n e t i c s of the t r a n s p o r t a n d o x i d a t i o n processes; t h u s one can learn about these processes b y s t u d y ing the steady-state oxide t h i c k n e s s . T h e silicon m a t e r i a l balance ( E q . 9)


13. JURGENSEN



• .08

-

.06

-

227

•

Δ

/ α

Y(Sl/0 ) 2

.04

.02

Λ

£ • 0

Δ

\/

ι

ι

ι

ι

I

50

100

150

200

250

300

Ë

F i g . 5.

(eV)

T h e silicon a t o m y i e l d of a s i l y l novolac (squares) a n d of S1O2 (triangles) are s h o w n as a f u n c t i o n of the average b o m b a r d m e n t energy. T h e line is a linear least squares fit to the s i l y l novolac results.

0

I

1

0

50

1

1

100

150 Ë

F i g . 6.

350

1

200

1

250

1

300

1 350

(eV)

T h e selectivity for etching the organic novolac relative to the s i l y l novolac is shown as a f u n c t i o n of the average b o m b a r d m e n t energy. T h e curve is based o n the least squares fits t o the y i e l d trends.



228


m a y be used to relate the steady-state oxide t h i c k n e s s to the i n i t i a l thickness loss d u r i n g the transient regime. Jurgensen et a l . [40] e s t i m a t e d the steadystate oxide t h i c k n e s s using this m e t h o d a n d b y d e p t h profiles based o n A r ion m i l l i n g w i t h g l a n c i n g angle X - r a y photoelectron spectroscopy ( X P S | . B o t h methods gave oxide thickness estimates i n the range from 30 to 50 A u n d e r conditions where steady-state model p r e d i c t e d the e t c h i n g rate. T h e observed steady-state oxide thickness was nearly independent of e t c h i n g con ditions a n d p o l y m e r silicon content. H a r t n e y et a l . [42] used variable angle X P S spectroscopy to measure the oxide thickness, a n d also o b t a i n e d thicknesses i n this range. These results [40,42] appear to conflict w i t h the results o b t a i n e d i n the diffusion-controlled regime where oxide f o r m a t i o n rates of several h u n d r e d A/min are observed [38,43]. In p a r t i c u l a r , the observed oxide t h i c k n e s s w o u l d appear to require S1O2 s p u t t e r i n g rates greater t h a n 100 A/min i n the steady-state regime; however, this is m u c h larger t h a n the observed [40,42] S i 0 s p u t t e r i n g rates w h i c h range from 2 to 30 A/min d e p e n d i n g on e t c h i n g c o n d i t i o n s . T h i s d i s c r e p a n c y implies t h a t energetic b o m b a r d m e n t plays an i m p o r t a n t role i n the steady-state regime i n a d d i t i o n to s p u t t e r i n g the oxide layer. B a g l e y et a l . [45] resolved this d i l e m m a b y s h o w i n g t h a t energetic i o n b o m b a r d m e n t renders these materials p e r m a n e n t l y resistant to o x i d a t i o n . T h e y propose t h a t i o n b o m b a r d m e n t compacts the oxide surface, d r a m a t i c a l l y r e d u c i n g diffusion coefficients i n the oxide layer. 2

T h e results presented b y B a g l e y et a l . [45] i m p l y t h a t the oxide diffusion coefficient is m u c h smaller i n the steady-state regime t h a n i n the diffusionc o n t r o l l e d regime where physical b o m b a r d m e n t is absent. It m a y be possible to account for this effect i n terms of the diffusive transport m o d e l presented earlier b y using a smaller oxide diffusion coefficient i n the steady-state regime. T o explore t h i s possibility, one m a y set dX/dt = 0 i n E q . 7 t o o b t a i n

Xss =

MukC

s

j

-

1

(13)

where Xss is the steady-state oxide t h i c k n e s s a n d the first t e r m i n the brackets is the r a t i o of the i n i t i a l e t c h i n g rate to the steady-state e t c h i n g rate a n d is m u c h larger t h a n one. T h i s t e r m equals the s e l e c t i v i t y , so E q . 13 predicts t h a t Xss is p r o p o r t i o n a l to the s e l e c t i v i t y w h i c h decreases w i t h b o m b a r d m e n t energy. Jurgensen et a l . [40] reported t h a t the steady-state oxide t h i c k n e s s is nearly independent of e t c h i n g c o n d i t i o n s , while H a r t n e y et al. [42] reported t h a t the oxide thickness increases w i t h b o m b a r d m e n t energy. E q u a t i o n 13 also predicts t h a t the steady-state oxide thickness increases w i t h the p o l y m e r ' s silicon content; however, Jurgensen et a l . [40] f o u n d t h a t the steady-state oxide thickness is nearly i n d e p e n d e n t of the s i l i con content. These failures show t h a t the diffusive t r a n s p o r t m o d e l is not v a l i d w h e n the sample is subjected to energetic Ο £ b o m b a r d m e n t ; this sug gests t h a t ballistic transport is the d o m i n a n t transport m e c h a n i s m i n the steady-state regime. T h e steady-state oxide t h i c k n e s s for a ballistic t r a n sport m e c h a n i s m is equal to the penetration d e p t h of the i m p l a n t e d oxygen [42]. T h i s m e c h a n i s m predicts t h a t the steady-state oxide t h i c k n e s s is


13. JURGENSEN


229

i n d e p e n d e n t of the silicon content of the p o l y m e r a n d increases w i t h b o m b a r d m e n t energy as f o u n d e x p e r i m e n t a l l y [40,42]. Anomalous Transport Regime. T h e characteristic signature of the steadystate e t c h i n g regime is a r a p i d i n i t i a l e t c h i n g rate (while the oxide layer forms) followed b y a m u c h slower constant e t c h i n g rate. T h i s e t c h i n g b e h a v i o r is always observed for h i g h silicon content organosilicon polymers u n d e r 0 R I E conditions; however, the p r e d i c t e d steady-state e t c h i n g rate appears to be a lower b o u n d w h i l e rates t h a t exceed t h i s p r e d i c t i o n are often observed under moderate bombardment energy etching conditions [39,40,42,44]. T h e p r e d i c t e d steady-state e t c h i n g rate was derived e n t i r e l y from a silicon m a t e r i a l balance a n d three assumptions: (1) T h e oxide t h i c k ness is constant (after the transient regime). (2) P h y s i c a l s p u t t e r i n g is the o n l y silicon loss m e c h a n i s m (after the transient regime). (3) T h e p h y s i c a l s p u t t e r i n g y i e l d is i d e n t i c a l to t h a t for S i 0 . A t least one of these assumptions must fail w h e n an organosilicon polymers etch faster t h a n p r e d i c t e d b y the steady-state m o d e l . Jurgensen et a l . [40] a n d H a r t n e y et a l . [42] have b o t h used surface analysis to determine w h i c h of these assumptions is failing. Jurgensen et a l . [40] used i o n m i l l i n g a n d g l a n c i n g angle X P S to d e p t h profile s i l y l m e t h a c r y l a t e samples t h a t h a d been etched at for various times u n d e r b o t h h i g h a n d low b o m b a r d m e n t energy e t c h i n g c o n d i t i o n s . A t h i g h b o m b a r d m e n t energy, the sample etched at the rate p r e d i c t e d b y the steadystate m o d e l , a n d after the i n i t i a l transient the oxide t h i c k n e s s was constant a n d equal to the value expected from the m a t e r i a l balance ( E q . 9). A f t e r the i n i t i a l transient at low b o m b a r d m e n t energy, the sample etched at twice the p r e d i c t e d rate a n d the oxide thickness c o n t i n u e d to increase. T h e a c c u m u l a t e d oxide t h i c k n e s s was i n excellent agreement w i t h the t h i c k n e s s p r e d i c t e d from the t o t a l thickness loss a n d the m a t e r i a l balance ( E q . 9). T h e y c o n c l u d e d t h a t the a s s u m p t i o n 1 was v i o l a t e d u n d e r c o n d i t i o n s where t h i s organosilicon p o l y m e r exceeded the p r e d i c t e d e t c h i n g rate. H a r t n e y et a l . [42] used variable angle X P S to determine the oxide t h i c k n e s s o n the s i l y l styrene p o l y m e r under conditions where it etched at twice the p r e d i c t e d rate. T h e y f o u n d t h a t the oxide thickness was constant after the i n i t i a l transient a n d c o n c l u d e d t h a t the p o l y m e r structure can affect the oxide s t r u c t u r e a n d its s p u t t e r i n g y i e l d (assumption 3 v i o l a t e d ) . T h i s conclusion appears to conflict w i t h G o k a n ' s [44] f i n d i n g t h a t a l l organosilicon polymers e t c h at the p r e d i c t e d steady-state e t c h i n g rate u n d e r I B E conditions.


2

2

T h e results o b t a i n e d i n these studies [40,42] a p p a r e n t l y conflict a n d lead t o opposite conclusions; however, the differences m a y result from different surface analysis methods, not from differences i n the samples s t u d i e d . J u r gensen et a l . [42] d e t e r m i n e d the silicon c o n c e n t r a t i o n as a f u n c t i o n of d e p t h b y i n t e g r a t i n g u n d e r the t o t a l silicon X P S peak i n c l u d i n g b o t h oxygen b o u n d a n d c a r b o n b o u n d s i l i c o n . T h i s procedure was used because bonds are b r o k e n a n d reform i n the i o n m i l l i n g process, so the c h e m i c a l b o n d i n g i n f o r m a t i o n m a y not be reliable i n i o n m i l l i n g - X P S d e p t h profiles. T h e y [40] also used this procedure to determine the carbon a n d oxygen c o n c e n t r a t i o n profiles. A f t e r a long low energy etch, the silicon a n d oxygen concentrations


230

POLYMERS IN MICROUTHOGRAPHY ο

were elevated to a d e p t h of 240 A while the c a r b o n c o n c e n t r a t i o n was depressed to t h i s d e p t h [40] (compared to an u n e t c h e d b u t A r sputtered sample); however, the X P S s p e c t r a also i n d i c a t e d t h a t at 2 4 0 A , the silicon a n d oxygen were b o t h b o u n d to c a r b o n . T h u s carbon is selectively o x i d i z e d a n d removed from the p o l y m e r w h i c h concentrates the silicon t h a t remains, b u t t h i s silicon m a y s t i l l be b o u n d to c a r b o n . In contrast, H a r t n e y et a l . [42] used v a r i a b l e angle X P S to determine the t h i c k n e s s of the layer where silicon was b o u n d to oxygen. T h i s m e t h o d w o u l d not detect the presence of a s i l i con e n r i c h e d layer unless the silicon was present as an oxide. T h u s these studies do not necessarily conflict w i t h each other, b u t m a y be giving t w o d i s t i n c t pieces of i n f o r m a t i o n .


+

T h e above i n t e r p r e t a t i o n implies t h a t c a r b o n b o u n d silicon is a c c u m u l a t i n g u n d e r the oxide layer w h e n the e t c h i n g rate exceeds the steady-state p r e d i c t i o n . T h e s p u t t e r i n g X P S d e p t h profiles [40], silicon m a t e r i a l balance [40] and angle resolved X P S thickness measurement [42] a l l agree t h a t 30 to 50 A of oxide are formed d u r i n g the i n i t i a l transient. T h e e t c h i n g rate i n the anomalous transport regime is constant after the i n i t i a l transient w h i c h i m p l i e s t h a t the a c c u m u l a t i n g silicon does not c o n t r i b u t e a d d i t i o n a l mass transfer resistance. T h i s is consistent w i t h the c o n c l u s i o n t h a t p h y s i c a l b o m b a r d m e n t can d r a m a t i c l y reduce a material's diffusivity [45], a n d w i t h the i n t e r p r e t a t i o n t h a t the p e n e t r a t i o n d e p t h is « 4 0 A . T h i s leads to the question of w h a t determines organosilicon p o l y m e r e t c h i n g rates u n d e r moderate b o m b a r d m e n t energy e t c h i n g c o n d i t i o n s . A reasonable w o r k i n g hypothesis assumes t h a t the mass transfer resistance i n the diffusionc o n t r o l l e d regime (D i n E q . 11) is equal to the mass transfer resistance of the m a t e r i a l w h i c h accumulates u n d e r the first « 4 0 A of oxide. O r g a n o s i l i c o n polymers w h i c h form good diffusion barriers i n the diffusion-controlled regime (low D i n E q . 11) are expected to etch b y the steady-state m e c h a n i s m i n moderate b o m b a r d m e n t energy e t c h i n g c o n d i t i o n s , w h i l e materials w h i c h form poor diffusion barriers i n the diffusion c o n t r o l l e d regime (high D i n E q . 11) are expected to e t c h b y the anomalous transport m e c h a n i s m i n moderate b o m b a r d m e n t energy e t c h i n g c o n d i t i o n s . T h i s hypothesis has not been care f u l l y tested, b u t i t appears t o be consistent w i t h the results presented i n several studies [39,40,42,43,44]. T h i s m e c h a n i s m differs from those proposed b y Jurgensen et a l . [40] (which i n v o l v e d k i n E q . 1), H a r t n e y et a l . [42] ( w h i c h i n v o l v e d Y$ - i n E q . 12), a n d N a m a t s u [43] (which i n v o l v e d D for the polymer); however i t is s i m i l a r to the m e c h a n i s m proposed b y G o k a n et a l . [44]. o

t

Bombardment Induced Pattern Transfer Models Jurgensen a n d Shaqfeh [46] have f o r m u l a t e d a k i n e t i c t h e o r y of interface e v o l u t i o n t o describe the t i m e e v o l u t i o n of e t c h i n g profiles i n b o m b a r d m e n t i n d u c e d glow discharge e t c h i n g processes. T h i s t h e o r y assumes t h a t an a x i s y m m e t r i c angular d i s t r i b u t i o n of energetic particles is i n c i d e n t o n the surface being etched, a n d t h a t the y i e l d per i n c i d e n t p a r t i c l e is a f u n c t i o n of its energy a n d angle relative to the surface n o r m a l . T h e e v o l u t i o n equation



13. JURGENSEN


231

t h a t results from these assumptions is i n t r a c t a b l e except i n t w o special cases where i t reduces to a p a r t i a l differential equation. F o r t u n a t e l y one of these special cases applies t o the p l a n a r i z i n g layer i n m u l t i l a y e r l i t h o g r a p h y , while the other applies to the m a s k i n g layer. O n e of these s i m p l i f i c a t i o n s is the case where the y i e l d is independent of angle as expected for the t h e r m a l spike m e c h a n i s m of b o m b a r d m e n t - i n d u c e d e t c h i n g . Shaqfeh a n d Jurgensen [47,37] have assumed t h a t this s i m p l i f i c a t i o n applies t o the p l a n a r i z i n g layer i n m u l t i - l a y e r l i t h o g r a p h y a n d have f o u n d t h a t the p r e d i c t e d e t c h i n g profiles are i n good agreement w i t h those observed e x p e r i m e n t a l l y for a t r i - l a y e r patt e r n transfer process. V i s s e r [unpublished results] has also o b t a i n e d some evidence t h a t 0 R I E yields are independent of angle b y e t c h i n g photoresist p a t t e r n s w i t h different w a l l angles. T h e rate c o n t r o l l i n g step for organosilicon polymers i n the steady-state regime is a p h y s i c a l s p u t t e r i n g process, a n d p h y s i c a l s p u t t e r i n g yields are strongly angle dependent [22,23]; therefore the above s i m p l i f y i n g a p p r o x i m a t i o n does not a p p l y to the m a s k i n g layer i n b i layer l i t h o g r a p h y . F o r t u n a t e l y , the m a s k i n g layer is not shadowed b y remote portions of the interface (it is raised a n d convex), a n d this allows our e v o l u t i o n equation [46] to be reduced to the h y p e r b o l i c conservation law discussed b y Ross [48]. A n a l y s i s of this case [48] shows t h a t facet edges (slope discontinuities) w i l l spontaneously develop w h e n the y i e l d is angle dependent. D r A . T a n a k a at N T T has m a n y beautiful (but u n p u b l i s h e d ) S E M s s h o w i n g the f o r m a t i o n a n d t i m e e v o l u t i o n of facets i n the m a s k i n g layer of a bi-layer system; however, the clearest p u b l i s h e d S E M s h o w i n g s u c h facets i n bi-layer l i t h o g r a p h y was presented b y S a i t o et a l . [49] (fig 10). T h i s p h e n o m e n o n has i m p o r t a n t i m p l i c a t i o n s for bi-layer p a t t e r n transfer processes because it implies t h a t some line w i d t h loss w i l l occur even w i t h a perfectly m o n o d i r e c t i o n a l angular d i s t r i b u t i o n a n d a perfect 90 degree w a l l angle i n the organosilicon resist layer. 2

Conclusions P h y s i c a l b o m b a r d m e n t plays a d o m i n a n t role i n the 0 reactive i o n etching p a t t e r n transfer step i n m u l t i - l a y e r l i t h o g r a p h y . T h e results of organic p o l y m e r 0 R I E a n d 0 I B E e t c h i n g studies are consistent w i t h a t h e r m a l spike m e c h a n i s m for the b o m b a r d m e n t - i n d u c e d c h e m i s t r y . T h e silicon atom y i e l d of organosilicon polymers i n the steady-state regime is equal to the S i 0 s p u t t e r i n g y i e l d for the same e t c h i n g c o n d i t i o n as assumed i n the steady-state e t c h i n g m o d e l . These yields show t h r e s h o l d behavior at low b o m b a r d m e n t energy, b u t this behavior is often o b s c u r e d because m a n y organosilicon polymers do not etch b y the steady-state m e c h a n i s m at low a n d intermediate b o m b a r d m e n t energies. These e t c h i n g results are being i n c o r p o r a t e d i n t o p a t t e r n transfer models [37,46,47] t h a t p r e d i c t e t c h i n g profiles a n d process latitudes i n m u l t i - l a y e r l i t h o g r a p h y . 2

2

2

2

Acknowledgments I t h a n k M a r k H a r t n e y , R o b e r t V i s s e r , A k i n o b u T a n a k a , E r i c Shaqfeh, M i k e V a s i l e , E i s a R e i c h m a n i s , a n d G a r y T a y l o r for s t i m u l a t i n g discussions.


232



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Kinetics of Polymer Etching in an Oxygen Glow Discharge - ACS

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