THERMAL DISSOLUTION OF FACE SPECIFIC Al-OXIDE LAYERS IN THE PRESENCE OF ELECTRIC FIELDS - OBSERVATION OF COMPENSATION EFFECTS

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THERMAL DISSOLUTION OF FACE SPECIFIC Al-OXIDE LAYERS IN THE PRESENCE OF

ELECTRIC FIELDS - OBSERVATION OF COMPENSATION EFFECTS

R. Vanselow

To cite this version:

R. Vanselow. THERMAL DISSOLUTION OF FACE SPECIFIC Al-OXIDE LAYERS IN THE PRES- ENCE OF ELECTRIC FIELDS - OBSERVATION OF COMPENSATION EFFECTS. Journal de Physique Colloques, 1984, 45 (C9), pp.C9-53-C9-57. �10.1051/jphyscol:1984910�. �jpa-00224388�

JOURNAL DE PHYSIQUE

Colloque C9, suppl6ment au n012, Tome 45, d k e m b r e 1984 page c9-53

THERMAL DISSOLUTION OF FACE SPECIFIC A1-OXIDE LAYERS IN THE PRESENCE OF ELECTRIC FIELDS - OBSERVATION OF COMPENSATION EFFECTS

R. Vanselow

Department of Chemistry and Laboratory for Surface Studies, University of Wisconsin -Milwaukee, Milwaukee, Wisconsin 53201, U . S.A.

Resume - La d i s s o l u t i o n thermique de monocouches d'oxyde de A1 sur W 11101 e t dedoublescouches deposees sur Wdlb e t Mo d l t a &t& e t u d i e e e n t r e 700 e t 1200K dans une gamme de champs F a l l a n t de -45 a +I05 MV/cm. La dependance en champs de l ' e n e r g i e d ' a c t i v a t i o n EF e t du f a c t e u r preexponentiel, A , a pu P t r e mesuree e t l ' e x i s t e n c e d ' e f f e t s de compensation a pu P t r e e t a b l i e . F ~ h a c u n des deux mecanismes de d i s s o l u t i o n ( d i f f u s i o n ?I f a i b l e F, desorption ionique ?I f o r t F) r e v e l e son propre p o i n t i s o c i n e t i q u e c a r a c t e r i s t i q u e . Les v a l e u r s ex- perimentales de EE e t E, a i n s i que l e s temperatures i s o c i n e t i q u e s c a r a c t e r i s - t i q u e s , + T , permettent l e c a l c u l des changements d ' e n t r o p i e ArS , p o u r 1 e s changements de phases : couche s o l i d e - couche d i f f u s a n t e t couche s o l i d e

-

Abstract. - The thermal d i s s o l u t i o n of Al-oxide monolayers on W {110} and of d e p o s i t double l a y e r s on W < I l l > and Mo < I l l > has been s t u d i e d between 700 and 1200K i n a f i e l d s t r e n g t h range of -45 t o +I05 MV/cm. The f i e l d s t r e n g t h dependence of t h e a c t i v a t i o n energy, E F , and of t h e pre-exponential f a c t o r , AF, could be measured and t h e e x i s t e n c e of compensation e f f e c t s could be e s t a b l i s h e d . Each of t h e two d i s s o l u t i o n mechanisms ( d i f f u s i o n a t low F ' s ; ion desorption a t high F i s ) shows i t s own c h a r a c t e r i s t i c i s o - k i n e t i c point. The experimental values of E g and

E t

A comparison with corresponding t h e o r e t i c a l entropy values shows good agreement.

1 . Introduction. - Numerous homologous s e r i e s of r e a c t i o n s which can be described by Arrhenius or Arrhenius-Frenkel type equations

T=A exp (E/kT) (1

show a c h a r a c t e r i s t i c l i n e a r compensation between t h e logarithm of t h e pre- exponential f a c t o r , A , and t h e corresponding a c t i v a t i o n energy, E , (e.g. /1-41)

(where *A : c o n s t a n t , k : Boltzmann c o n s t a n t , and *T

-

Linear r e l a t i o n s have a l s o been found between a c t i v a t i o n e n t h a l p i e s , A H + , and t h e corresponding a c t i v a t i o n e n t r o p i e s , AS+, /3/

AH+ = *TAS+ ( 3 )

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984910

C9-54 JOURNAL DE _PHYSIQUE

Various names have been used f o r these r e l a t i o n s : compensation law or o-rule ( c a t a l y s i s ) and isokinetic relationship. A relationship between equilibrium q u a n t i t i e s , corresponding t o eq. 3, i s called isoequil ibrium relationship /3/. The i s o k i n e t i c temperature, *T, i s the temperature a t which a l l differences in r a t e ( o r the equilibrium constants) will vanish / 3 / ,

n ~ t a t T;*i = O ( 4 )

The f i r s t compensation r e l a t i o n s have been observed by Wilson /5/ and by Richardson /6/ who studied the e f f e c t of adsorption on electron emission. Their description i s based on the original Richardson equation

Richardson recognized t h a t "there i s a correspondence between the values of AR and b [=@/k], so t h a t large values of AR correspond t o large values of b, and

conversely." Usually, Constable i s credited f o r reporting the f i r s t compensation behavior ( f o r a c a t a l y t i c reaction) in 1925 (e.g. / 3 / ) .

In the present paper compensation e f f e c t s will be described which have been observed during the thermal dissolution of face s p e c i f i c a l l y grown Al-oxide layers (on W and Mo) i n the presence of e l e c t r i c f i e l d s /7,8/.

2. Experimental Procedure.

-

.

According t o mass spectrometer measurements [e.g./9/] the main oxide in the vapor beam i s A10. When t h e emitters a r e kept a t room temperature during the deposition, the oxide deposit layer remains coherent u p t o two monolayers. Higher layers break up and form c l u s t e r s . When the emitter i s heated, a t f i r s t the c l u s t e r s disappear and then the coherent deposit layer dissolves - the layer boundary recedes. The detached molecules - i t i s assumed t h a t the suboxide A10 i s the major species in- volved in the dissolution process - move i n t o a diffusion layer. Depending on the supersaturation, various face-specific oxide layers can be formed (they are l i s t e d according t o increasing supersaturation required f o r t h e i r growth) : {loo} double layer / l o / , C1101 monolayer /11/ and C1121 monolayer /12/. The most s u i t a b l e layer f o r dissolution studies i s the W {110} l a y e r , which i s a perfect layer without steps. Very reproducible r e s u l t s have a l s o been obtained with the deposit (double) layer i n the areas of W < I l l > and Mo < I l l > . Therefore, W {110} layers and deposit layers in the areas W < I l l > and Mo < I l l > have been used f o r the dissolution experi- ments described here. Electric f i e l d s were s e t by means of a special high voltage square wave generator. For a detailed description of the experimental set-up, see reference /7/.

3. Experimental Results. - The time, T, required t o dissolve a given f r a c t i o n of an oxide layer was measured as a function of the temperature, T , with the e l e c t r i c f i e l d strength, F , kept constant. The temperature was varied between 700 and 1200 K. Using the Arrhenius-Frenkel type equation ( I ) , pre-exponential f a c t o r s

and corresponding a c t i v a t i o n e n e r g i e s could be determined i n a f i e l d s t r e n g t h range of -45 t o +I05 MV/cm ( n e g a t i v e s i g n i n d i c a t e s cathodic e m i t t e r ) . P l o t s of t h e a c t i v a t i o n energy, E F , and t h e logarithm of t h e pre-exponential f a c t o r , In A F , a s a f u n c t i o n of F reveal two d i s s o l u t i o n mechanisms.

In t h e low f i e l d s t r e n g t h range (F: -45 t o +55 MV/cm) t h e d i s s o l u t i o n can be described b e s t by

and

In AF i In A; = In A: -auF/k*T

(where E:, A: z zero f i e l d s t r e n g t h values; A u = u d i f f e a - u s o l . a ; u d i f f .a ⁱ d i p o l e moment of molecule i n d i f f u s i o n l a y e r ;

u s o l . a ^: formal d i p o l e moment of molecule i n sol i d l a y e r kink s i t e ) , in t h e high f i e l d s t r e n g t h range (F>+55 M~/cm) by

and

In A~ = In A: = In A$ + n 3/2 ,3/2 F1/2/k*T

(where E:, A: z zero f i e l d s t r e n g t h values; ne

-

I t appears t h a t t h e l a y e r d i s s o l u t i o n i n t h e low f i e l d s t r e n g t h range can be a t t r i b u t e d t o s u r f a c e d i f f u s i o n and i n t h e high f i e l d s t r e n g t h range t o ion de- s o r p t i o n . In g e n e r a l , t h e d i s s o l u t i o n process can be described by

T~ = *Ao exp (-EF/k*T) exp (EF/kT) ( 9 )

(where *Ao z i s o k i n e t i c o r d i n a t e belonging t o t h e corresponding i s o k i n e t i c temperature, *T).

4. Discussion and Conclusions. - In t h e Arrhenius-Frenkel p l o t ( I n -cF versus 1/T, according t o eq. 9) a l l constant f i e l d 1 ines belonging t o one type of d i s s o l u t i o n mechanism i n t e r c e p t i n one point ( i s o k i n e t i c p o i n t ) which i s c h a r a c t e r i z e d by t h e corresponding i s o k i n e t i c coordinates In *Ao and l/*T. Since two mechanisms a r e p r e s e n t , such a p l o t shows two i s o k i n e t i c p o i n t s . They have t h e following average values: l o g *A: = 2.5 and *T = 920K f o r d i f f u s i o n (W<111> and Mo<lll> l a y e r s ) ; log *A: = -1 and *T = 1240 K f o r ion desorption (W{110} and W<111>). The influence of t h e l a y e r type and t h e support metal appears t o be small i n t h e s e cases.

A comparison of eq. 9 with eq. 1 shows t h a t

which i s of t h e form of t h e c l a s s i c a l compensation equation (eq. 2 ) . Therefore, a p l o t of In AF versus E F should y i e l d s t r a i g h t l i n e s f o r which t h e s l o p e s a r e determined by.l/*T. This, indeed, i s t h e case. In accordance with t h e above find-

ings one observes two s t r a i g h t l i n e s with t h e e a r l i e r mentioned average i s o k i n e t i c

C9-56 JOURNAL D E PHYSIQUE

temperatures *Tdiff= 920 K and *Tion des. = 1240 K. The corresponding c o r r e l a t i o n f a c t o r s are rz0.998 and t h e standard d e v i a t i o n s are about c3%.

If eq. 9 i s r e w r i t t e n so t h a t one o b t a i n s t h e i o n c u r r e n t d e n s i t y a t zero f i e 1 d s t r e n g t h , j:,

j+ - -

*jz

* .+ - X A - l J O - o~ie

(where pi-molecular packing d e n s i t y i n oxide l a y e r ; e-elementary charge;

s i n g l y charged i o n s assumed)

then eq. 11 can be compared w i t h t h e corresponding unabridged equation f o r thermionic e l e c t r o n emission (Richardson-Laue-Dushman equation) /13/

3/2(kT)5/2

j; = e ( l - ~ ) ( ~ ~ m , k ~ ) - ~ / ~ [ ~ ( ~ ' ~ e ) l e x p (-+/kT)

h (13)

(Where G E f a c t o r c o n s i d e r i n g degeneracy caused by e l e c t r o n s p i n (G=2); h

-

Planck constant; me = e l e c t r o n r e s t mass; F E average r e f l e c t i o n c o e f f i c i e n t ;

+

e l e c t r o n work f u n c t i o n ) .

I n t r o d u c i n g ex5/' (ex base o f t h e n a t u r a l l o g a r i t h m s ) i n t o t h e bracketed term, one o b t a i n s

One e a s i l y recognizes t h a t t h i s bracketed term i s now equal t o the exponential o f t h e Sackur-Tetrode entropy f o r an e l e c t r o n i n an i d e a l gas s t a t e ( o u t s i d e o f t h e metal) a t u n i t pressure ( p =*p=l dyn/cm 2 ) , d i v i d e d by t h e Boltzmann constant

Also r e f e r r i n g t o T=*T ( a t F=O), one obtains f o r eq. 1 4

j i = * j i exp (n*so/k) exp (-+/kT) (16)

A comparison w i t h eq. 11 suggests t h a t

which i s i n agreement w i t h eq. 3. The corresponding entropy change f o r t h e case of d i f f u s i o n i s

Using t h e e x p e r i m e n t a l l y determined values f o r EZ, E:, *Tdiff., and *Tion des. /7,8/, one can c a l c u l a t e t h e entropy changes f o r t h e phase changes s o l i d l a y e r -+ d i f f u s i o n l a y e r and s o l i d l a y e r -+ i o n gas ( a t u n i t pressure, T=*T, and F=O):

A * S ~ = 31 eu (average f o r W<111> and M o < l l l > )

and

A * S ~ = 94 eu (average f o r W{110} and W<111>)

I n t h e f o l l o w i n g c a l c u l a t i o n o f t h e o r e t i c a l entropy values, which s h a l l be used f o r comparative purpo$es, t h e c o n t r i b u t i o n o f v i b r a t i o n a l changes has been neglected f o r b o t h phase changes. I t a l s o i s assumed t h a t i n t h e d i f f u s i o n l a y e r t h e A10 d i p o l e a x i s i s o r i e n t e d perpendicular t o t h e s u b s t r a t e surface.

To o b t a i n t h e entropy f o r two dimensional t r a n s l a t i o n , t h e Kemball equation /14/ i s combined w i t h t h e i d e a l surface s t a t e - e q u a t i o n ( a t T=*T and p = 1 dyn/cm)

2 t r a n s

*s

(where M = molecular weight; R = gas constant) 2 t r a n s *s = B-EL

The l a t t e r i s about 10% s m a l l e r than t h e experimental A*':.

I n t h e case o f i o n desorption i t i s assumed t h a t T=*T, p=*p=l dyn/cm2, and

a*St(theor.) = *Strans(ion gas) + *Srot(ion gas) (20)

(where m = molecular mass o f A10; I E moment o f i n e r t i a o f A10) A * S ~ ( t h e o r . ) =

The l a t t e r i s about 7% s m a l l e r than t h e experimental A*s:.

The agreement between t h e o r e t i c a l and experimental values appears t o be good.

I t has t o be p o i n t e d o u t t h a t t h e d e v i a t i o n s l i e w i t h i n t h e e r r o r l i m i t s o f A*S, o f about 10%. However, because o f t h e omission o f v i b r a t i o n a l c o n t r i b u t i o n s t o AXSO ( t h e o r . ) , one would expect t h a t a*S, ( t h e o r . ) < a*So (exp. )

.