p r e s s u r e can be found f o r th e r a r e - g a s w here th e q u en ch in g l o s s and sp o n tan eo u s l o s s o f th e excim er a r e e q u a l. As b e fo r e , t h i s p r e s s u r e c o u ld be re g a rd e d as a u s e f u l maximum and v a lu e s f o r c a se s w ith r a t e c o n s ta n ts i n T able 2 .4 a r e g iv e n i n T able 2 .5 ( b ) . I f , how ever, th e 3-body quenching i s due to two r a r e - g a s e s , a maximum v a lu e can o n ly be found f o r th e p ro d u ct o f th e p a r t i a l p r e s s u r e s o f th e two g a s e s . Such v a lu e s a r e a ls o shown i n T ab le 2 .5 ( b ) alo n g w ith v a lu e s f o r th e p ro d u c t o f th e maximum p r e s s u r e s o f th e two g a se s from th e 2-body quenching d a ta f o r co m parison.
Some d a ta i s a v a il a b l e on th e q u enching o f m e ta s ta b le p r e c u r s o rs i n 2-body and 3-body r e a c ti o n s . I n th e ab sence o f o th e r e f f e c t s th e r a t e o f change o f th e m e ta s ta b le d e n s ity i s g iv e n by
dU g/dt = M - k^ngUg - k^ngC^n^ , (10)
w here th e sym bols r e t a i n t h e i r p re v io u s m eaning and w here kj^ i s th e 3-body m e ta s ta b le q u en ch in g r a t e c o n s ta n t and M i s th e m e ta s ta b le p ro d u c tio n r a t e . S in ce i t i s d e s ir a b le t h a t q u en ch in g sh o u ld n o t com pete w ith excim er fo rm a tio n , maximum q u en ch an t and th ird -b o d y p a r t i a l p r e s s u r e s a r e ta k e n as th o se r e q u ir e d to make th e q u en ch in g l o s s r a t e e q u al to th e excim er fo rm a tio n r a t e u s in g
= V 5 “6 • (11)
V alues o f maximum q u en ch an t and th ird -b o d y p a r t i a l p r e s s u r e s can be o b ta in e d i f a v a lu e f o r n^ i s assum ed. Minimum v a lu e s f o r n^ , th e donor d e n s ity , w ere c a lc u la te d above ( i n term s o f p a r t i a l p r e s s u r e ) .
Chapter 2 33
By u sin g th e s e and m e ta s ta b le q u en ch in g r a t e c o n s ta n ts from T able 2 .4 we g e t th e v a lu e s shown i n T able 2 .5 ( c ) . As b e fo r e , th e c a se s o f a s in g le r a r e - g a s and two r a r e -g a s e s a r e dea].t w ith .
Quenching o f io n ic r a r e - g a s p r e c u rs o rs w i l l be an alo g o u s to m e ta s ta b le q u en ch in g . However, th e co m p lex ity o f th e io n ic fo rm a tio n r a t e c o e f f i c i e n t and la c k o f know ledge o f io n d e n s i t i e s mean t h a t th e s im p lif ie d a n a ly s is o f quen ch in g p re s e n te d above can n o t be a p p lie d and no o th e r a n a ly s is w i l l be a tte m p te d h e re .
2 .2 .3 H alid e, K in e tic s
The r o le s o f th e h a lo g e n donor and i t s p ro d u c ts i n d is c h a rg e s i n r a r e - g a s h a lid e gas m ix tu re s a r e v a r ie d and c r u c i a l in. d e te rm in in g th e f lu o r e s c e n t e f f i c i e n c y . The e l e c t r o - n e g a t i v i t y o f th e h a lid e s r e s u l t i n t h e i r h av in g a la r g e in f lu e n c e on d is c h a rg e s t a b i l i t y ; th ey a ls o have f a s t r e a c ti o n r a t e s i n b o th fo rm a tio n and q u en ch in g r e a c ti o n s . Of s p e c ia l im p o rtan ce i n th e p r e s e n t stu d y i s th e r e a c ti v e n a tu re o f th e h a lo g e n s w hich r e s u l t i n th e e v e n tu a l l o s s o f u s a b le donor m o le c u le s. As t h i s h ap p en s, th e s t a b i l i s i n g e f f e c t o f th e e le c tr o n a tta c h in g h a lo g e n s i s l o s t , r e s u l t i n g i n a runaw ay d isc h a rg e c u r r e n t i n DC d is c h a rg e s o r la r g e r e f l e c t i o n s i n m icrow ave d is c h a r g e s . The h a lo g e n s a r e l o s t by th e fo rm a tio n o f h ig h ly s t a b l e compounds form ed from th e o r ig i n a l donor c o n s ti tu e n t atom s o r , more im p o r ta n tly , by r e a c ti o n w ith w a ll m a te r ia ls . I n th e p r e s e n t s tu d y , d is c h a rg e tu b e s o f sm a ll d ia m e te r w ere used so t h a t th e l o s s o f h a lo g e n s i n w a ll r e a c ti o n s was f a s t ; c o n se q u e n tly , e f f e c t i v e g as l i f e
m easurem ents c o n s ti tu t e d a la r g e p ro p o rtio n o f th e e x p e rim e n ta l w ork. In a c tiv e l a s e r s th e h a lo g e n donor and i t s p ro d u c ts may red u ce th e l a s e r perform ance by a b so rb in g a t th e l a s e r w a v e len g th . T h is and o th e r c o n s id e r a tio n s r e s u l t i n th e r e b ein g v e ry few h a lo g e n compounds w hich a re s u i t a b l e d o n o rs. The m ost f r e q u e n tly used do n o rs a r e th e d ia to m ic h a lo g e n s, NF^, and HCl, I n th e p r e s e n t work SF^ was used e x te n s iv e ly b ecau se i t i s ch eap , s t a b l e , and r e l a t i v e l y u n s tu d ie d i n an excim er c o n te x t. I n a few c a se s NF^ was used f o r com parison w ith SFg. The donor u sed f o r XeCl and KrCl was HCl. In th e fo llo w in g d is c u s s io n , F^ i s in c lu d e d b ecau se o f i t s w id e sp re a d u se and b ecau se i t w i l l be form ed when th e o th e r f lu o r in e d o n o rs, NF^ and SF^ d i s s o c i a t e in th e d is c h a r g e .
F lu o rin e M o lecu lar f lu o r in e i s p ro b ab ly th e b e s t donor f o r KrF and ArF l a s e r s though s l i g h t l y i n f e r i o r to NF^ f o r u se i n XeF l a s e r s . I t g iv e s r a p id fo rm a tio n r a t e s b oth by th e m e ta s ta b le ch an n el ( r e a c t i o n 8 , T able 2 .1 ) and th e io n ic ch an n el ( r e a c ti o n 12, T able 2 . 1 ) . The io n ic ch an n el fo rm a tio n r a t e i s a c tu a ll y d e te rm in e d by th e slo w er e le c tr o n d i s s o c i a t i v e a tta c h m e n t r a t e which i s a b o u t 7x10™^^ cm^s ^ f o r 5 eV th erm al e le c tr o n s . The r a p id fo rm a tio n r a t e s w ith as donor a r e m atched by r a p id q u en ch in g o f th e excim er by F^ as shown i n T ab le 2 .4 , I f donor c o n c e n tr a tio n s a r e h ig h enough f o r e q u a tio n (6) o f S e c tio n 2 .2 .2 to a p p ly , th e r a t i o o f th e excim er d e n s ity to th e m e ta s ta b le d e n s ity i s lim ite d to 2,1 : 1 f o r XeF, 1 .2 ; 1 f o r E rF, and 0 .4 : 1 f o r ArF.
Chapter 2 35
F or each r a r e - g a s f lu o r id e m o le c u le , two f lu o r in e atom s a r e g e n e ra te d w ith th e r e s u l t t h a t th e d e n s ity o f f r e e f lu o r in e i s h ig h e s t when i s used as th e d o n o r. S in ce f lu o r i n e , and th e o th e r h a lo g e n s, a re e f f e c t i v e l y l o s t v i a r e a c tio n s in v o lv in g th e f r e e atom s, th e gas l i f e w ith F^ as donor i s l i k e l y to be p o o r. The m ajor c o n s id e r a tio n c o n c ern in g gas l i f e i s th e com parison o f th e w a ll c o l l i s i o n r a t e w ith th e F -r F re c o m b in a tio n r a t e . The re c o m b in a tio n r a t e i s q u ite slow . For exam ple, Johnson and H u n ter (1980) g iv e an e s tim a te d v a lu e o f 10 orn^s"^ f o r th e r e a c ti o n
F 4 F M — Fg + M ,
w here M i s a th ir d -b o d y . The f lu o r in e lo s s r a t e w i l l be tw ice th e re c o m b in a tio n r a t e o f fo rm a tio n o f F^ and i s t h e r e f o r e g iv e n by
d n ^ /d t = 2kg(n^)^ng , (1)
w here n^(cm ^) i s th e f lu o r in e number d e n s ity , n ^ ( cm"^) i s th e b u f f e r g as d e n s ity , and k^ i s th e r a t e c o n s ta n t. S u b s t it u ti o n o f th e above v a lu e f o r k^ g iv e s
d n ^ /d t = 2x10”^^(n ^ )^ n g cm^^s"^ . (2)
I f i t i s assum ed t h a t each f lu o r in e atom t h a t c o ll id e s w ith th e c o n ta in e r w a ll i s l o s t th e r e , th e d if f u s io n l o s s r a t e i s g iv e n by
w here (om °^s” ‘ ) i s th e d i f f u s io n l o s s r a t e , D th e d if f u s io n c o e f f i c i e n t and A th e c h a r a c t e r i s t i c d i f f u s io n le n g th . F or a c y li n d r ic a l volume w ith n e g lig ib le end a re a s (a lo n g t h in tu b e f o r