ULTRASHORT HEAT TRANSIENTS IN METALS UNDER LASER IRRADIATION

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ULTRASHORT HEAT TRANSIENTS IN METALS UNDER LASER IRRADIATION

L.F. Donà Dalle Rose

To cite this version:

L.F. Donà Dalle Rose. ULTRASHORT HEAT TRANSIENTS IN METALS UNDER LASER IRRADIATION. Journal de Physique Colloques, 1983, 44 (C5), pp.C5-469-C5-479.

�10.1051/jphyscol:1983569�. �jpa-00223154�

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Colloque C5, supplement au nO1O, Tome 44, octobre 1983

ULTRASHORT HEAT TRANSIENTS I N METALS UNDER LASER IRRADIATION

L . F . Don2 d a l l e Rose

Unitd GNSM-CUR, Dipartirnento d i F i s i c a d e Z Z r U n i v e r s i t c i d e g Z i S t u d i d i Padova, i t a Z y

Resume - Entre l e s d i f f e r e n t s types de t r a n s i e n t de f l u x de chaleur, comportant l a fusion e t l l P b u l l i t i o n des e c h a n t i l l o n s m @ t a l l i q u e s , seuls ceux q u i

n ' o n t pas de termes c o n v e c t i f s peuvent @ t r e analyses quantitativemen?. La s t r u c t u r e de ces t r a n s i e n t s e s t d e c r i t e e t analysee 2 l ' a i d e de nombreux r e s u l t a t s experimentaux.

A b s t r a c t - Among the d i f f e r e n t types o f u l t r a s h o r t heat f l o w t r a n s i e n t s which i n v o l v e m e l t i n g and b o i l i n g o f metal samples, o n l y those n o t showing convective- t y p e e f f e c t s are amenable t o q u a n t i t a t i v e discussion. The s t r u c t u r e o f these t r a n s i e n t s i s described and discussed i n terms o f several experimental r e s u l t s .

1. I n t r o d u c t i o n

The u l t r a s h o r t h e a t t r a n s i e n t s i n metals ' I , as induced by d i r e c t e d and pulsed ener- gy beams, ranging between 5 4 100 ns i n d u r a t i o n (sometimes up t o 300 ns) and w h i t h i n 1 + 15 J/cm2 i n energy d e n s i t y , show considerable d i f f e r e n c e s i n t h e i r c h a r a c t e r i - zation. B a s i c a l l y , w i t h i n c r e a s i n g energy d e n s i t y , f o u r d i f f e r e n t regimes may be defined and e x p e r i m e n t a l l y studied: t r a n s i e n t s i n s o l i d phase, t r a n s i e n t s i n s o l i d and l i q u i d phase, t r a n s i e n t s i n v o l v i n g q u i e t v a p o r i z a t i o n and/or b o i l i n g from t h e l i q u i d phase, t r a n s i e n t s which i n v o l v e convective motion and v i o l e n t b o i l i n g o f the molten phase.

The heat f l o w t r a n s i e n t s a r e accompanied and r e l a t e d t o t r a n s i e n t s i n o t h e r r e l e - vant p h y s i c a l q u a n t i t i e s l i k e surface s t a t e , r e f l e c t i v i t y , s u r f a c e and b u l k tempe- r a t u r e , t r a n s p o r t p r o p e r t i e s o f embedded i m p u r i t i e s , o r m i x i n g a t t h e boundary of a l a y e r deposited over b u l k substrate. The r e f l e c t i v i t y t r a n s i e n t has a s p e c i a l importance, since i t determines t h e a c t u a l amount o f observed energy under pulsed l a s e r i r r a d i a t i n g (PLI) and t h e r e f o r e t h e main f e a t u r e s o f t h e associated heat f l o w t r a n s i e n t ( l i k e molten phase d u r a t i o n and maximum molten depth). U n f o r t u n a t e l y very few measurements a r e a v a i l a b l e about such a t r a n s i e n t . There i s a l s o an i n i - t i a l r e f l e c t i v i t y problem which depends on t h e surface p r e p a r a t i o n technique. For example, r o l l i n g o f the sample surface may cause scratches which under l a s e r i r r a d i a t i n g a c t as p r e f e r e n t i a l centres f o r l i g h t a b s o r p t i o n (see F i g . 1 ) . S i m i l a r events may occur on chemically ( p o l i s h e d and) p i t t e d surfaces, sometimes provoking even e a r l y h e a t i n g and l o c a l i z e d evaporation from t h e surface. I n o t h e r cases i m - p l a n t a t i o n o f species t o be s t u d i e d under m a t r i x heat t r a n s i e n t s may q u i t e a l t e r the i n i t i a l r e f l e c t i v i t y , as c l e a r l y shown by Fig. 2, where regions a,b,c a r e r e - s p e c t i v e l y v i r g i n surface, C r ( 7 a t % ) implanted region, C r implanted p l u s pulsed l a s e r t r e a t e d r e g i o n (ruby l a s e r , a t 3. J/cm2, 25 ns); r e g i o n d which was l a s e r t r e a t e d b u t n o t implanted does n o t show any p a r t i c u l a r f e a t u r e . Region c shows a w r i n k l e p a t t e r n , w i t h a c h a r a c t e r i s t i c wavelength ~ 4 0 pm, which i s probably due t o

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I

I

mechanism

Fig. 1 - Evidence f o r p r e f e r e n t i a l l i g h t absorption along r o l l i n g s c r a t c h e s i d vergin AR under PLI a t 3.5 J/cmZ, 15 ns (ruby l a s e r ) .Courtesy of Padua CNR-GNSI4 group on energy beam treatment o f m a t e r i a l s .

Fig. : 2 T r a n s i t i o n region of an AR sample from v i r g i n ( l e f t ) t o Cr implanted ( r i g h t ) a f t e r PLI with ruby l a s e r ; s e e main t e x t f o r d e t a i l s about region a , b , c , d . Ccurtesyof Padua CNR-GNSM group.

a l a s e r d i f f r a c t i o n p a t t e r n inducing melting only a t t h e l i g h t maxima; t h e absence of such a p a t t e r n i n region d c l e a r l y c a l l s f o r a g r e a t e r absorbed energy, i . e . a reduced r e f l e c t i v i t y , i n t h e implanted region. These and s i m i l a r observations demand a t t e n t i o n when adopting l i t e r a t u r e data about r e f l e c t i v i t y . Apart from d i r e c t (during t r a n s i e n t ) measurements, some i n d i r e c t methods have been discussed

t o assess t h e surface r e f l e c t i v i t y i n a given experiment, e i t h e r by l o o k i n g *) a t t h e c h a r a c t e r i s t i c f r i n g e s which s i g n t h e m e l t threshold, t h i s l a t t e r being then compared w i t h heat f l o w c a l c u l a t i o n s , o r by using a c a l o r i m e t r i c method 4, t o measure t h e t o t a l absorbed energy. This very method a l l o w s d e t e c t i o n o f r e f l e c t i - v i t y changes when passing from a s o l i d t o a l i q u i d sample s u r f a c e (e.g. a s l i g h t decrease, i n t h e case o f AR). An a d d i t i o n a l m e l t t h r e s h o l d i n d i c a t o r i s given by t h e damage ( i . e . xMIN) behaviour w i t h i n c r e a s i n g absorbed energy 5 y 6 ) , which shows a peak (due t o increased s l i p deformation a t m e l t t h r e s h o l d ) . F i n a l l y a consistency check about an e f f e c t i v e ( i .e. a l l o v e r t h e p u l s e d u r a t i o n ) r e f l e c t i v i t y assignment may be c a r r i e d o u t whenever a s e t o f i m p u r i t y p r o f i l e s (as implanted as w e l l as a f t e r t r a n s i e n t p r o f i l e s , a t several energy d e n s i t i e s ) a r e a v a i l a b l e . I t i s then g e n e r a l l y p o s s i b l e t o l o c a t e t h e m e l t t h r e s h o l d and, by means o f a combined s o l u - t i o n o f t h e heat and i m p u r i t y d i f f u s i o n equations, t o assign d e f i n i t e values t o t h e i m p u r i t y normal d i f f u s i o n c o e f f i c i e n t D. By now several d i f f u s i o n c o e f f i c i e n t s have been determined i n t h i s way 5 y 8 7 9 y 1 0 ) , th e i r value being %lo-' cmz/sec, which i s w i d e l y recognized s t h e t y p i c a l l i q u i d phase value, mainly on t h e basis o f o t h e r measurements 111, c a r r i e d o u t under conditons much nearer t o thermal e q u i l i - brium. An i n t e r e s t i n g p o i n t here concerns t h e d i f f u s i o n c o e f f i c i e n t dependence on t h e t r a n s i e n t absorbed energy, which i n t u r n may be r e l a t e d t o t h e temperature dependence o f t h e d i f f u s i o n process and t o t h e as y e t u n d e c i d e d question whether the c o e f f i c i e n t D increases l i n e a r l y o r e x p o n e n t i a l l y "I. For instance, Sb d i f - f u s i o n i n AR y e l d s ") a value D = 5 ~ 1 0 - ~ cm2/sec under a s i t u a t i o n where a h i g h average temperature i s achieved d u r i n g t h e t r a n s i e n t ( a c o n c e n t r a t i o n g r a d i e n t h i g h e r than usual might a l s o i n t r o d u c e c o r r e c t i o n s t o t h e l i n e a r t h e o r y ) . Some e a r l i e r determinations 1 2 5 1 3 ) p r o v i d e d values f o r D up t o 10-I cm2/sec. Such r a t h e r extreme r e s u l t s a r e now i n t e r p r e t e d as a piece o f evidence f o r convective type motions under P L I . This i s f u r t h e r supported (see Fig. 3 ) : i ) by t h e a f t e r t r a n s i e n t metal surface which shows q u i t e a rough aspect as compared t o t h e surface smooth- ness found a f t e r lower energy d e n s i t y t r a n s i e n t s (and which i n t u r n c o r r e l a t e w i t h D values f o r implanted i m p u r i t i e s equal t o QJIO-' cm2/sec) and i i ) by t h e deep i m p u r i t y p r o f i l e t a i l s which o f t e n extend we1 1 beyond t h e d e t e c t a b l e 1 im i t s , thus p r e v e n t i n g any check based on t h e conservation o f the t o t a l i m p u r i t y amount and a t t h e same time c o n f i r m i n g t h e general idea according t o which convective motions may q u i t e increase the depth over which a molten phase appears. The t r u e n a t u r e o f t h i s v i o l e n t , convective t y p e motion has n o t y e t been understood comple- t e l y , the main d i f f i u l t y being t h e q u i t e l o n g e r time scale needed i n conventional convective motion

'".

I n t h e f o l l o w i n g we s h a l l r e s t r i c t our discussion o n l y t o t r a n s i e n t s which e i t h e r r e l a t e t o simple h e a t i n g and me1 t i n g o f t h e i r r a d i a t e d metal (lower absorbed energy t r a n s i e n t s ) o r i n v o l v e q u i e t evaporation and/or b o i l i n g from the l i q u i d phase ( h i g h e r absorbed energy t r a n s i e n t s ) .

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Fig. 3 - Lower (aboveland h i g h e r (below) absorbed energy t r a n s i e n t e f f e c t s on t h e s t a t e o f a La implanted N i surface and on t h e La p r o f i l e (courtesy o f Padua CNR- GNSM group; see a l s o r e f . 10). Both t r a n s i e n t s were induced by a ruby l a s e r pulse, 16 ns Fwhm.

2. S t r u c t u r e o f t h e heat t r a n s i e n t 2.1. Lower absorbed energy t r a n s i e n t s

As i t i s w e l l known 1 5 ) , i n metals i t i s p o s s i b l e t o assume an istantaneous con- v e r s i o n i n t o heat o f t h e energy absorbed from t h e primary beam, a t l e a s t f o r t h e times under c o n s i d e r a t i o n here. Then the heat f l o w i s governed by t h e (unidimen- s i o n a l ) conduction equation

where C, p, K are t h e sample s p e c i f i c heat, d e n s i t y and thermal c o n d u c t i v i t y (depending on t h e temperature T, on t h e s t a t e , whether s o l i d o r molten, and pos s i b l y on t h e amount o f embedded i m p u r i t i e s and damage). Q ( x , t ) represents t h e source term. Equation (1) must be solved t o g e t h e r w i t h t h e boundary c o n d i t i o n s :

aT

p H f u / = K s o l

IX+

ⁱ

^c

plus, d u r i n g r e s o l i d i f i c a t i o n ,

x = - 1 ( T . - T )

B l M

Conditions (2a,b) takes i n t o account the e x t e r n a l bath a t T = T, ( o f t e n , b u t n o t always, room temperature), w h i l e c o n d i t i o n s (3a) and (3b) r e f e r t o t h e m e l t f r o n t (whenever i t shows up), more p r e c i s e l y t o i t s v e l o c i t y X, which v a r i e s i n such a way as t o conserve the balance o f i n g o i n g and outgoing heat f l u x (eq. 3a, where Hfus i s t h e l a t e n t heat o f fusion/resolidification) and which has t o s a t i s f y the undercool i n g c o n s t r a i n t as r e q u i r e d by c r y s t a l regrowth thermodynamics (eq. 3b, where Ti i s t h e l i q u i d - s o l i d i n t e r f a c e temperature and TM the m e l t i n g temperature;

6 i s a p r o p o r t i o n a l i t y constant). The constant B i s v e r y small i n e t a l s as com- pared t o t h e semiconductor case. According t o a simple argument 16T, t h e i n t e r - face undercooling obeys

Stefan (T _M - T. )/Ti ₁ * ^vres _{l v s}

Stefan .

where vs i s t h e metal sound v e l o c i t y and vres i s t h e r e s o l i d i f i c a t i o n v e l o c i t y as determined by t h e pure heat f l u x conservation ( i .e. eq. 3a which

a Stefan boundary problem i f a c t i n g alone). As a consequence since v

i n most c a l c u l a t e d t r a n s i e n t s i n metals, and vs 2.5000 m/sec, ATi ^?. 0.5 2 e o f TM, i,e. n e g l i g i b l e . The r e s o l i d i f i c a t i o n v e l o c i t y i n metals i s then c o n t r o l l e d o n l y by heat f l u x .

As a m a t t e r o f f a c t , heat t r a n s i e n t s i n metals may be c a l c u l a t e d by using appro- p r i a t e average values f o r C, p , K, which a r e s l o w l y v a r y i n g f u n c t i o n s o f T i n a given s t a t e ( s o l i d o r molten). Keeping i n t o account t h e i r a c t u a l v a r i a t i o n would o n l y change t h e r e s u l t s by some percents, w h i l e i n c r e a s i n g much t h e computer time.

Recent papers I 5 7 l 7 ) have described t h e d e t a i l e d n a t u r e o f t h e heat t r a n s i e n t a t lower absorbed energy. The source term may q u i t e i n f l u e n c e i t s s t r u c t u r e . Roughly speaking t h e molten phase d u r a t i o n may be d i v i d e d i n t o two subsequent stages, an e a r l i e r one which i s q u i t e warmer ( i t s average temperature being a t an i n t e r - mediate value between TM and t h e normal b o i l i n g temperature Teb) and a second one c h a r a c t e r i z e d by an almost constant temperature ( a c t u a l l y TM) a l l over t h e molten l a y e r . Depending on t h e used source ( i .e. w i t h l a s e r b u t n o t w i t h e-beam) t h e former stage i s a l s o c h a r a c t e r i z e d by very h i g h thermal g r a d i e n t s i n l i q u i d phase (up t o l o 7 "Kjcm). These two stages may be e x p e r i m e n t a l l y observed by l o o k i n g a t several p r o p e r t i e s o f i m p u r i t i e s embedded i n t h e h o s t metal sample through e i t h e r i m p l a n t a t i o n o r sandwiching o f a t h i n i m p u r i t y l a y e r . While normal d i f f u s i o n may occur d u r i n g both stages, t h e r e a r e o t h e r phenomena which are c h a r a c t e r i s t i c o f one stage o r t h e other. The f i r s t stage o f f e r s t h e unique combination o f h i g h c o n c e n t r a t i o n g r a d i e n t s (as due t o i o n i m p l a n t a t i o n o r m i x i n g o f a l a y e r e d s t r u c t u r e ) and extreme l i q u i d phase gradients: t h e i r product c o n t r o l s 18) a term i n t h e i m p u r i t y d i f f u s i o n equation which i s u s u a l l y n e g l i - g i b l e , b u t which may p l a y an observable r o l e i n some cases (Soret d i f f u s i o n ) . Appreciable e f f e c t s have been observed f o r Cu and Zn i n A t and Au i n N i . The second stage, on the o t h e r hand, ma be q u i t e a p t f o r i m p u r i t y p r e c i p i t a t i o n occurence; t h i s may be understood 15) by looking, f o r example, a t t h e A t - r i c h p o r t i o n o f the e q u i l i b r i u m phase diagram f o r t h e AR-Sb b i n a r y and by n o t i c i n g

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t h a t , f o r Sb c o n c e n t r a t i o n o f a few atomic p e r c e n t s , t h e t i m e spent by t h e c o o l i n g AR m o l t e n phase w i t h i n t h e temperature i n t e r v a l a s s o c i a t e d w i t h a two phase s t a t e ( i . e . l i q u i d p l u s AX-Sb p r e c i p i t a t e ) may be ong enough t o cause p r e c i p i t a t i o n i n c e r t a i n t r a n s i e n t s . A b e a u t i f u l experiment 4j which c o n t r o l l e d t h e second stage d u r a t i o n under P L I by a c t i n g on t h e ambient temperature To was a b l e t o show i n t h e v e r y case o f t h e AR(Sb) system, w i t h i n i t i a l Sb c o n c e n t r a t i o n equal t o 2. a t %, t h a t p r e c i p i t a t e n u c l e a t i o n and growth o c c u r r e d w i t h i n 15 ( + l o ) ns.

Another phenomenon which may t a k e p l a c e a l o n g b o t h stages, a t l o w e r absorbed ener- gies, i s i m p u r i t y s u r f a c e o x i d a t i o n . The c o r r e s p o n d i n g s u r f a c e peak has been de- t e c t e d i n t h a f t e r t r a n s i e n t p r o f i l e o f some i m p u r i t i e s i m p l a n t e d i n N i ; H f 20), La and Eu lo' a r e good examples i n t h i s r e s p e c t . F o r H f and La, l a s e r i r r a d i a t i n g i n Helium atmosphere o r under l o - ' t o r r vacuum,yields q u i t e a r e d u c t i o n i n t h e peak h e i g h t . I n a d d i t i o n t h e h e a t o f f o r m a t i o n o f La,O, and Hf,O, i s n e g a t i v e and much l a r g e r , i n a b s o l u t e value, t h a n NiO. T h i s means t h a t i n these cases s u r f a c e impu- r i t y o x i d a t i o n i s an e n e r g e t i c a l l y h i g h l y f a v o u r e d process, even though t h e e x a c t way, i n which i t a c t u a l l y develops a t h i g h temperatures, i s s u b j e c t t o a d e l i c a t e and as y e t n o t e x p l o r e d balance between t h e r e a c t i o n r a t e and t h e Le C h a t e l i e r p r i n c i p l e ( a b o u t exothermic r e a c t i o n s ) . Eu seems n o t t o be an a l t o g e t h e r d i f f e r e n t case, even though no check was performed on i t b y v a r y i n g t h e oxygen atmosphere l o ) . An i m p u r i t y s u r f a c e peak may be o r i g i n a t e d by s e v e r a l mech nisms: b e s i d e s u r f a c e o x i d a t i o n , i m p u r i t y s e g r e g a t i o n d u r i n g r e s o l i d i f i c a t i o n 13?, changes i n t h e reso- 1 i d i f i c a t i o n v e l o c i t y when t h e i m p u r i t y d i s t r i b u t i o n i s f l a t ''1, p r e f e r e n t i a l e v a p o r a t i o n o f t h e h o s t metal which causes i m p u r i t y enrichment o f t h e s u r f a c e l a y e r l o ) , and f i n a l l y d i f f e r e n t combination o f t h e t r a n s p o r t c o e f f i c i e n t s (normal and S o r e t d i f f u s i o n , segregation, s u r f a c e c a p t u r e r a t e , .. .) which may be used i n t h e e x p e r i m e n t a l p r o f i l e f i t t i n g procedure. Here we o n l y remind t h e reason why s e g r e g a t i o n e f f e c t s , which a r e so abundant i n p u l s e induced t r a n s i e n t s i n s i l i c o n , a r e n o t observed i n m e t a l s under s i m i l a r c o n d i t i o n s . T h i s i s due t o t h e f a c t t h a t t h e i m p u r i t y r e s i d e n c e t i m e ^{f r e s} a t t h e r e g r o w i n g i n t e r f a c e i s much t o o long, as compared t o t h e r e g r o w t h t i m e rreg, i n o r d e r t o a v o i d t r a p p i n g . As a consequence, i f D i i s t h e i m p u r i t y d i f f u s i o n c o e f f i c i e n t j u s t a t t h e regrowing i n t e r f a c e , t h e c o n d i t i o n f o r s e g r e g a t i o n t o occur:

(A b e i n g t h e monolayer c h a r a c t e r i s t i c l e n g h t ) , i s n o t s a t i s f i e d under P L I , s i n c e vres i s q u i t e h i g h as compared t o s i l i c o n ( t h i s b e i n g due t o t h e f a c t t h a t m e t a l s have h i g h e r thermal c o n d u c t i v i t y and l o w e r l a t e n t h e a t o f r e c r y s t a l l i z a t i o n ) . Estimates o f t h e r a t i o f r e s / f r e g g i v e 8 f o r Sn i n AR e f . 22) o r 62 f o r Eu i n N i ( r e f . 10). We may f i n a l l y q u o t e t h e f a c t 19y5y18*21y t h a t Sb,Cr,Cu,Sn, (and perhaps Pb) a l l show an e f f e c t i v e s e g r e g a t i o n c o e f f i c i e n t i n AR equal t o 1, even though t h e e q u i l i b r i u m s e g r e g a t i o n c o e f f i c i e n t i s e i t h e r v e r y l a r e (Sb,Cr)

1 8 ) o r v e r y small (Cu,Sn). A s i m i l a r statement h o l d s f o r Eu and La i n N i .

A f u r t h e r s u p p o r t t o t h e absence o f s e g r e g a t i o n i n m e t a l s under t h e p r e s e n t con- d i e i o n s i s t h e f a c t t h a t no c e l l s t r u c t u r e has y e t been observed, t h i s f a c t a g a i n b e i n g r e l a t e d t o t h e h i g h v v a l u e (see M u l l ins-Sekerka c r i t e r i o n 2 3 ) ) .

r e s

Other t o p i c s which m i g h t be discussed i n t h e p r e s e n t c o n t e x t o f t r a n s i e n t s t r u c t u r e a r e d e f e c t f o r m a t i o n i n s i n g l e c r y s t a l l i q u i d phase e p i t a x y and i m p u r i t y d e f e c t i n t e r a c t i o n . As t o them and t o t h e r e l a t e d q u e s t i o n o f m e t a s t a b l e s o l i d s o l u t i o n s see r e f . 10 and r e f e r e n c e s t h e r e i n .

2.2. Higher absorbed energy t r a n s i e n t s

I n these cases, t h e heat f l o w equation must s a t i s f y some a d d i t i o n a l boundary con- d i t i o n s . Denoting by S t h e instantaneous evaporating f r o n t p o s i t i o n w i t h respect t o a reference frame f i x e d i n t h e bulk o f t h e sample, then i t i s

H being t h e ( c o n s t a n t ) heat o f v a p o r i z a t i o n ; equation (4) s t a t e s by i t s e l f aX8Fher Stefan boundary problem. The thermodynamical c o n d i t i o n on t h e surface f r o n t v a l o c i t y S i s given by one o f t h e f o l l o w i n g two r e l a t i o n s h i p s , s t a t e d i n terms o f t h e surface temperature Ts:

U exp ( - M H / k Ts),

i = U exp(-MH /k TS), VaP T~ < Teb

vap ( 5a ,b)

as given by eq. (41, T = T

p l u s eq. ( 1 ) d i s c r e t i z e d S eb Here M i s t h e mass o f t h e metal atoms, k t h e Bo tzmann constant and

3

(5b) as t o surface and b u l k evaporation r e s p e c t i v e l y . Case (5b) corresponds t o o r d i n a r y b o i l i n g . U l t r a s h o r t l a s e r induced evaporative t r a n s i e n t s may be discussed from t h e p o i n t o f view o f t h e so c a l l e d developed o r i n t e n s e evaporation regime.

Such a regime, when heat d i f f u s i o n may be assumed as unidimensional, corresponds t o a conversion of the absorbed energy i n t o heat o f v a p o r i z a t i o n o n l y and i s cha- r a c t e r i z e d by an evaporated thickness Sev >> J2Krp/pc ( r p i s t h e p u l s e d u r a t i o n ) . I n terms o f l a s e r pulse i n t e n s i t y t h e r e i s a t h r e s h o l d i n t e n s i t y value 25) f o r achieving t h e i n t e n s e evaporation regime, given by Ithr = (PH,,~/(I - R ) ) . J K / ~ C T ~ , ( R i s the r e f l e c t i v i t y ) . I n Fig. 4 (r.h.s.) we p l o t such a t h r e s h o l d i n t e n s i t y as a f u n c t i o n o f T f o r some metals (At,Ni and Sb): as i t may be seen the

P

Fig. 4 - (r.h.s.) Developed evaporation regime t h r e s h o l d as a f u n c t i o n od p u l s e d u r a t i o n f o r At, Ni, Sb t o g e t h e r w i t h t h e P L I region, ( 1 .h.s.)T@mperature o f t h e s t a t i o n a r y f r o n t (abscissa) as a f u n c t i o n o f i n c i d e n t l a s e r energy ( o r d i n a t e ) ; arrows r e f e r t o c r i t i c a l temperatures (see side t a b l e ) .

JOURNAL DE PHYSIQUE

PLI r e g i o n i s below t h r e s h o l d f o r AR and N i , b u t f o r Sb i t i s j u s t on t o p o f t h e t r a n s i t i o n r e g i o n f r o m a weak t o an i n t e n s e e v a p o r a t i v e regime. N o t i c e t h a t f o r a g i v e n T,, and f o r an i n t e n s i t y I above Ithr(rp), a s t a t l o n a r y regime i s reached w i t h c o n s t a n t v a p o r i z a t i o n f r o n t temperature To and f r o n t v e l o c i t y 5 ,

I n t h e 1.h.s. o f F i g . 4,T, i s p l o t t e d as a f u n c t i o n o f I , f o r t e same m e t a l s as a t r.h.s., up t o t h e i r c r i t i c a l temperature (%8600 ^{O K} f o r AR 26p and e s t i m a t e d t o be about 4 s 7 t i m e s Teb i n t h e o t h e r cases). Q u a l i t a t i v e l y i t i s t h e n p l a u s i b l e t h a t P L I may l e a d t o a h i g h s u r f a c e superheating, p r o v i d e d an adequate p r e s s u r e p r e v e n t s u r f a c e b o i l i n g : w h i l e i n t h i s r e s p e c t ambient p r e s s u r e seems n e g l i g i b l e , r a d i a t i o n and r e c o i l p r e s s u r e m i g h t p l a y a r o l e . Plasma f o r m a t i o n may a l s o be i m p o r t a n t . The s i t u a t i o n seems q u i t e open t o i n v e s t i g a t i o n . From t h e general s t r u g t u r e o f t h e h e a t f l o w e q u a t i o n s o l u t i o n , i t i s found t h a t t h e e v a p o r a t i v e / b o i l i n g t r a n s i e n t i s always n e s t e d i n t h e warmer s t a g e o f t h e h e a t t r a n s i e n t i t s e l f . A

parameter which assesses i t s importance i s t h e r a t i o between t h e energy used f o r i t and t h e t o t a l absorbed energy. As an example, i n t h e case o f s u r f a c e e v a p o r a t i o n ( 5 a ) , such a r a t i o i s 2% and 81% f o r Sb under P L I a t 0.41 and 2.1 ~ / c m ' r e s p e c t i - v e l y ( 7 ns Fwhm, R = 0.63). F o r AR under PLL a t 5 ~ / c m ' (15 ns Fwhm, R = 0.79) t h e same r a t i o i s 6%, c o r r e s p o n d i n g t o 100 A evaporated t h i c k n e s s . I f t h e surface temperature i s clamped a t Teb = 2740 :K ( b u l k e v a p o r a t i o n , see ( 5 b ) ) , t h e n t h e r a t i o r i s e s up t o 51%, and about 900 A b o i l o f f .

Experimental s t u d y of t h e s e t r a n s i e n t s may be c a r r i e d o u t by means o f a l a y e r e d s t r u c t u r e , e.g. Pb o v e r l a y e r s d e p o s i t e d on b u l k AR. The s t r u c t u r e o f t h e t r a n s i e n t , w i t h e v a p o r a t i o n / b o i l i n g l o c a t e d i n t h e e a r l y p a r t o f t h e g l o b a l t r a n s i e n t , i s w e l l i l l u s t r a t e d by experiments u s i n g two d i f f e r e n t energy sources, r u b y l a s e r which causes h e a t i n g up j u s t a t t h e ( e x t e r n a 1 ) s u r f a c e o f t h e Pb l a y e r , c h a r a c t e - r i z e d by a d e f i n i t e l y p o o r e r thermal c o n d u c t i v i t y w i t h r e s p e c t t o t h e AR s u b s t r a t e , and e-beam which on t h e c o n t r a r y may d e p o s i t energy o v e r s e v e r a l d i f f e r e n t ranges w e l l i n s i d e t h e A!?, substrate,thus o f f e r i n g d i f f e r e n t i a t e 2 h e a t i n g up o p p o r t u n i t i e s . I n F i g . 5, RBS s p e c t r a a r e shown as o b t a i n e d from a 500 A t h i c k Pb l a y e r vacuum evaporated over a p u r e AR m a t r i x , a f t e r t r e a t i n g by means o f a monochromatic (15 keV) e-beam pulse, 50 ns Fwhm, and a t energy d e n s i t i e s equal t o 0.11, 0.16, 0.43 J/cm2. I t i s seen t h a t a t t h e l o w e s t energy d e n s i t y AR and Pb mix t o g e t h e r and no Pb l o s s i s d e t e c t a b l e , a t 0.16 J/cm2 b o t h m i x i n g and Pb l o s s occur, w h i l e a t 0.43 J/cm2 o n l y Pb l o s s ( i .e. e v a p o r a t i o n o r b q i l i n g ) occurs. We suggest t h e f o l l o w i n g mechanism f o r a c o m p e t i t i o n between m i x i n g and e v a p o r a t i o n , on t h e b a s i s o f t h e general s t r u c t u r e o f t h e u l t r a s h o r t h e a t f l o w t r a n s i e n t . The h e a t o f s o l u - t i o n o f a Pb gram i n t o A!?, i s ( p o s i t i v e , i.e. absorbed and) equal t o 236 J / g r and has t o be compared w i t h 24 J / g r f o r t h e h e a t o f f u s i o n and 863 J / g r f o r t h e h e a t of evaporation. I n t h e a c t u a l t r a n s i e n t , e v a p o r a t i o n o r b o i l i n g , i f any, occurs e a r l y and once s t a r t e d consumes mudh o f t h e d e p o s i t e d energy which t h e n cannot be used f o r m i x i n g processes.

T h i s i s j u s t t h e case i n t h e h o t t e s t t r a n s i e n t . On t h e o t h e r hand " c o l d e r " t r a n - s i e n t s a l l o w m i x i n g t o o c c u r as soon as b o t h Pb and AX a r e molten. A c o r r e l a t e d mechanism may a l s o o f f e r a key t o t h e b e h a v i o u r o f t h e Pb l o s s e s under P L I vs.

Pb l a y e r t h i c k n e s s , a t a c o n s t a n t energy d e n s i t y ( F i g . 6). From t h e RBS Spectra ( n o t shown), i t nay be segn t h a t a t l o w e r t h i c k n e s s a l m o s t n o m i x i n g occurs, w h i l e a t t h i c k n e s s 2 750 A b o t h l o s s and m i x i n g occur: i n t h i s case t h e AR

m a t r i x , because o f i t s h i g h e r thermal c o n d u c t i v i t y , a c t s as a h e a t pump, which i s

C H A N N E L S

Fig. 5 - RBS s p e c t r a (1.8 MeV ~ e ' ) of Pb (500 ~ ) / A R system a s evaporated and a f t e r d i f f e r e n t e-beam induced t r a n s i e n t s (cooperation Padua-Lecce)

I " " " " ' " I

2 600 RUBY LASER

:O 1.5 ~/crn'

F

m P--- ^-0

0

Fig. 6 - Pb l o s s under PLI of a 500 A t h i c k Pb l a y e r over pure AR ( r e s u l t s from Padua GNSM-CNR group)

more e f f e c t i v e a t lower Pb t h i c k n e s s , t h u s preventing mixicg. In Fig. 6 we c l e a r l y see a s a t u r a t i o n of t h e l o s s mechanism, roughly above 500 A l a y e r thickness. A p o s s i b l e explanation i s t h a t , when mixing has occurred up t o t h e sample s u r f a c e , Pb evaporation becomes more d i f f i c u l t . Me a r e then faced with t h e problemof evaporation of a s i n g l e atom, which has neighbours d i f f e r e n t from i t s e l f . In t h e

JOURNAL DE PHYSIQUE

l i m i t o f a v e r y d i l u e a l l o y t h i s problem may be t a c k l e d by means o f t h e macro- s c o p i c atom model 27f. P r e l i m i n a r y r e s u l t s , t o be p r e s e n t e d i n a l a t e r paper, show t h a t t h e r a t i o o f t h e i m p u r i t y ( A ) . t o m a t r i x (B) e v a p o r a t i n g f l u x i s

@A/@B = cA %/a; exp

[

- vap vap -

where CA i s t h e i m p u r i t y c o n c e n t r a t i o n , t h e d o t t e d f l u x e s r e f e r t o p u r e m e t a l s A and B, w h i l e

~ l ~ ; ~

3. Conclusions

As a c o n c l u s i o n , i n t h e p r e s e n t work we have d i s c u s s e d t h e p y h y s i c a l processes which a l l o w d e t e c t i n g o f a s t r u c t u r e i n t h e h e a t f l o w t r a n s i e n t induced i n metal samples by u l t r a r a p i d p u l s e d energy beams. Many o f t h e s e processes a r e c l e a r l y r e l a t e d t o t h e temporal e v o l u t i o n o f t h e h e a t f l o w t r a n s i e n t ; t h e s i t u a t i o n i s q u i t e complex o f f e r i n g i n t e r p l a y o f d i f f e r e n t mechanisms i n t h e two e x p e r i m e n t a l regimes which may be r e f e r r e d t o as l o w e r and h i g h e r absorbed e n e r g i e s . I n t h e former, t r a s p o r t p r o p e r t i e s o f i m p l a n t e d i m p u r i t i e s have by now been s t u d i e d i n many cases: perhaps what i s c a l l e d f o r now i s an a t t e m p t t o s y s t e m a t i z e and g i v e a macroscopic f o u n d a t i o n t o many d i f f e r e n t f a c t s . The l a t t e r regime, b ~ h i c h seems more d i f f i c u l t t o d e s c r i b e i n a d e t a i l e d q u a n t i t a t i v e manner, n a t u r a l l y o f f e r s t h e o p p o r t u n i t y f o r a d i r e c t comparison between d i f f e r e n t d i r e c t e d energy sources: t h i s v e r y f a c t may be o f g r e a t value,mainly f o r s t u d y i n g t h e r e f l e c t i v i t y problem under P L I a t h i g h energy d e n s i t i e s .

Acknowledgements

I would l i k e t o thank a l l t h e s t a f f o f GNSM-CNR groups i n Padua and Lecce U n i - v e r s i t i e s f o r t h e i r a s s i s t a n c e w h i l e w r i t i n g t h i s paper up and f o r p r o v i d i n g u s e f u l e x p e r i m e n t a l m a t e r i a l , t o be p u b l i s h e d i n coming works. A p a r t i c u l a r t h a n k t o V.N. K u l k a r n i , A. M i o t e l l o and D. G u i d o l i n f o r u s e f u l d i s c u s s i o n s , t o P. Meneghello f o r c o o p e r a t i o n i n e v a p o r a t i v e t r a n s i e n t c a l c u l a t i o n s and t o P. Troncon f o r a i d i n t h e problem o f p r e f e r e n t i a l e v a p o r a t i o n . A warm thank t o A. Rampazzo f o r h i s drawings .

References

1) See MRS Boston M e e t i n g Proceedings o v e r l a s t f i v e y e a r s .

2) JAIN A.K., KULKARNI V.N., SOOD D.K. and UPPAL J.S., 3. Appl . Phys. 52 (1981)4882.

3 ) L a s e r and Electron-Beam I n t e r a c t i o n s w i t h S o l i d s , 1981, ed. B.R. ~ ~ F e t o n , G.K.

Cel l e r , ( N o r t h - H o l l and, New York, 1982).

4 ) PEERCY P.S., FOLLSTAEDT O.M., PICRAUX S.T. and WAMPLER W.R., i n r e f . 31, pag.401.

5 ) BATTAGLIN G., CARNERA A., DELLA MEA G., MAZZOLDI P., JANNITTI E., JAIN A.K.

and SOOD D.K., J. Appl. Phys. 3 (1982) 3224.

6 ) FOLLSTAEDT D.M., PICRAUX S.T., PEERCY P.S. and WAMPLER W.R., Appl . Phys. L e t t . 39 (1981) 327.

7) E s e r and E l e c t r o n Beam S o l i d i n t e r a c t i o n and ) ( l a t e r i a l s Processing, 1980, eds.

J.F. Gibbson, L.D. Hess, T.W. Sigmon (North-Hol l a n d , New York, Oxford, 198 1 ) .

8 ) WAMPLER W.R., FOLLSTAEDT D.M. and PEERCY P.S., i n r e f . 7 , page 567.

9 ) JAIN A. K., KULKARNI V .N. , NAMBIAR K. B. , SOOD D. K. , SHARMA S.C.L. and MAZZOLDI P., Rad. E f f . 63 (1982) 175.

1 0 ) BATTAGLIN

c,

1 1 ) EDWARDS J.B., HUCKE E.E. and MARTIN J.J., M e t a l l u r g i c a l Rev. 13 (1968) 1 . 1 2 ) JAIN A.K., KULKARNI V.N. and SOOD D.K., N.I.M. 191 (1981) 151.

1 3 ) MIOTELLO A., DONA' DALLE ROSE L.F., Rad. E f f . 5-1981) 235.

1 4 ) POSSIN G.E., PARKS H.G. and CHIANG S.W., i n r e f - 7 , page 73.

1 5 ) DONA' DALLE ROSE L. F. , MIOTELLO A., Rad. E f f . - 53 (1980) 7 and r e f e r e n c e s t h e r e i n .

1 6 ) TURNBULL D., p r i v a t e communication.

1 7 ) DONA' DALLE ROSE L.F., MIOTELLO A,, BROTTO R., Rad. E f f . 69 (1983) 1.

1 8 ) MIOTELLO A., DONA' DALLE ROSE L.F., DESALVO A., Appl

.

19) WAMPLER W.R., FOLLSTAEDT D.M. and PICRAUX S.T., Appl. Phys. L e t t . 36 (1980) 366.

2 0 ) DRAPER C.W., KAUFMANN E.N. and BUENE L., S u r f a c e and I n t e r f a c e A n a l y s i s 4

(1982) 8 .

21) TILLER W.A., JACKSON K.A., RUTTER J.W. and CHALMERS B., A c t a M e t a l l u r g i c a 1 (1953) 428.

2 2 ) PICRAUX S.T., FOLLSTAEDT D.M., KNAPP J.A., WAMPLER W.R. and RIMINI E., i n r e f . 7, page 575.

23) MULLINS W.W., SEKERKA R.F., J. Appl. Phys. 35 (1964) 444.

2 4 ) BUNKIN F.V., TRIBEL'SKII M.J., Sov. Phys. Uspekhi 23 (1980) 105.

2 5 ) BATANOV V.A., BUNKIN F.V., PROKHOROV A.M. and FEDOE V.B., Sov. Phys. JETP, 3 6 (1973) 311.

26) Thermophysical P r o p e r t i e s o f M a t t e r , Vol . 10, Thermal D i f f u s i v i t y , Y .S.

Touloukian, R.W. Powell, C.Y. Ho and M.C. N i c o l a o v eds. IFI-Plenum, New York, 1973.

2 7 ) MIEDEMA A.R., DE CHATEL ^P.F., de BOER F.R., Physica 1008 (1980) 1.