THERMAL FIELD DESORPTION

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THERMAL FIELD DESORPTION

H. Kreuser, L. Wang

To cite this version:

H. Kreuser, L. Wang. THERMAL FIELD DESORPTION. Journal de Physique Colloques, 1989, 50

(C8), pp.C8-9-C8-14. �10.1051/jphyscol:1989802�. �jpa-00229900�

COLLOQUE DE PHYSIQUE

Colloque C8, suppl6ment au n o 11, Tome 50, novembre 1989

THERMAL FIELD DESORPTION

H.J. KREUSER and L.C. WANG

Department of P h y s i c s , D a l h o u s i e U n i v e r s i , t y H a l i f a x , N.S. B3H 3 5 5 . Canada

Abstract

-

Adiabatic p o t e n t i a l energy curves have been calculated a s a function of e l e c t r i c f i e l d s t r e n g t h f o r t h e ground s t a t e and an excited s t a t e of helium adsorbed on tungsten. Using a unitary transformation we construct t h e diabatic energy curves f o r n e u t r a l helium and its singly charged ion. We a l s o obtained the coupling term between t h e s e s t a t e s from which we c a l c u l a t e the temperature dependent ionisation probability of an adsorbed atom and t h e r e s u l t i n g ion yield.

1

-

Introduction

Thermal f i e l d desorption is the removal of field-adsorbed species from the surface of a f i e l d ion t i p which can be achieved by raising the temperature of t h e metal tip. Being an activated process, one could argue t h a t its r a t e constant should follow an Arrhenius param- e t r i z a t i o n

where Ed is the activation energy, obtained from adiabatic energy curves, and t h e prefactor v r e f l e c t s the ionization probability of the adsorbed molecule. This simple-minded approach, however, ignores a number of i n t e r e s t i n g questions, e.g. whether the desorbing species emerge a s ions or n e u t r a l s , whether postionization occurs, and what the energy d i s - t r i b u t i o n of t h e desorbing species is. To ansver such questions one has t o s e t up a kinetic theory t h a t accounts f o r energy and charge t r a n s f e r by formulating the appropriate master equation f o r t h e problem and c a l c u l a t e a l l t r a n s i t i o n probabilities from f i r s t principles.

T h i s theory was formulated r e c e n t l y / l / . In t h i s paper we w i l l present detailed c a l c u l a - tions of the kinetics of thermal f i e l d desorption of helium. In following papers we w i l l study t h e kinetics of f i e l d ionization, necessary f o r a microscopic theory of image forma- tion in the f i e l d ion microscope, and f i e l d evaporation, including the e f f e c t s of postionlza- tion.

We s t a r t our discussion of f i e l d desorption by considering a helium atom adsorbed on a f i e l d ion t i p . A s temperature is raised, it w i l l eventually g e t t h e chance t o escape from its binding potential. If i t s escape from the s u r f a c e is slow enough it w i l l g e t ionized a t the hump of the ground s t a t e energy curve and reach the d e t e c t o r a s an ion. However, i f ioniza- tion, 1.e. tunneling of an e l e c t r o n from the adatom t o the metal, is too slow, the adpartl- c l e w i l l escape a s a n e u t r a l atom with a kinetic energy t h a t has no r e l a t i o n t o the ground s t a t e energy curve. Indeed, a n e u t r a l atom i n a f i e l d past a c r i t i c a l distance no longer corresponds t o t h e ground s t a t e of t h e system but t o some excited s t a t e . I t s p o t e n t i a l energy s u r f a c e is c a l l e d diabatic.

From t h i s s h o r t discussion it should be obvious t h a t adiabatic s t a t e s a r e not the most intu- i t i v e basis t o s e t up a kinetic theoriy of f i e l d desorption and f i e l d ionization. Rather a new basis must .be constructed in which t h e motion of the gas species is e x p l i c i t l y taken i n t o account; they a r e known a s diabatic s t a t e s . Their construction from adiabatic s t a t e s

w i l l be reviewed i n t h e next section including the ldentificatlon of the coupling terms

between them. The l a t t e r then form t h e s t a r t i n g point f o r t h e c a l c u l a t i o n of t r a n s i t i o n probabilities f o r ionization which in t u r n w i l l e n t e r a master equation from which observ- a b l e s l i k e energy dependent ion yields, t h e probability f o r post-ionization e t c . can be com- puted.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989802

Fig.1: Adiabatic (V) and d i a b a t i c (W) energy curves f o r He on W in a f i e l d of 5

v/l

(upper s e t and enlarged version In c e n t e r ) and i n 6 ~ / i (lower s e t ) .

In Fig.1 we present adiabatic and diabatic p o t e n t i a l energy curves f o r several f i e l d s t r e n g t h s . Such curves have been drawn q u a l i t a t i v e l y t o serve a s a basis of Muller's image hump mode1/6,7/, Comer's charge exchange rnode1/8,9/, and f o r discussions of charge hopping and charge draining mechanisms./lO/ According t o t h e discussion above, the difference between the adiabatic potential energy curves reaches a minimum a t the apex and is of the order of the i n t e r a c t i o n energy between the highest occupied and the lowest unoccupied orbl- t a l s . With increasing f i e l d , t h e apex w i l l move towards t h e metal surface, r e s u l t i n g in an increase in t h e i n t e r a c t i o n energy and thus i n an increase in t h e energy difference between the adiabatic energy curves. We note t h a t 8 v a r i e s rapidly from 0' t o 90' over a very s h o r t distance, 1.e. l e s s than 0.1A around t h e apex of t h e adiabatic ground s t a t e energy curve, ln- dicative of t h e narrowness of t h e ionization zone.

2

-

Adiabatic and diabatic s t a t e s

We consider an atom i n f r o n t o f a metal a distance R away from t h e topmost ion core. The hzmiltonian o f t h e s y s t e m can be w r i t t e n a s

where

T N =

-c

az/aR2

2M

i s t h e k i n e t i c energy o f t h e atomic nucleus and

i s t h e hamiltonian o f t h e e l e c t r o n s a t positions r , , r z , . . . V e includes t h e Coulomb i n t e r a c - t i o n s between t h e e l e c t r o n s , between t h e e l e c t r o n s and t h e n u c l e i , and between a l l n u c l e i ( m e t a l l i c and a t o m i c ) .

Let us f i x t h e position o f t h e adatom, t h u s s e t t i n g i t s k i n e t i c energy (3) equal t o zero.

Physically t h i s i m p l i e s t h a t t h e e l e c t r o n i c degrees o f freedom f o l l o w t h e nuclear motion i n s t a n t l y . We can t h e n diagonalize He ( i n practice, a f t e r approximating i t , e.g., by a t i g h t binding hamiltonian or using d e n s i t y f u n c t i o n a l t h e o r y ) t o obtain

where t h e c i are adiabatic many e l e c t r o n wavefunctions. The l o w e s t eigenvalue o f ( 5 ) , V o ( R ) r e p r e s e n t s t h e ground s t a t e o f t h e system and corresponds t o t h e adiabatic binding energy curve. L i f t i n g an e l e c t r o n from t h e h i g h e s t occupied l e v e l ( i n t h e ground s t a t e ) t o t h e l o w e s t unoccupied one, generates t h e energy ourve ( o r r a t h e r s u r f a c e , because R i s a t h r e e - dimensional space coordinate) o f t h e f i r s t e x c i t e d s t a t e e t c .

To t a k e t h e nuclear motion o f t h e adqtom i n t o account we now proceed t o c o n s t r u c t diabatic s t a t e s . There d e f i n i t i o n i s not unique but must be adopted t o t h e s p e c i f i c process t o be studied. In t h i s paper we r e s t r i c t o u r s e l v e s t o f i e l d desorption o f helium f o r which two diabatic s t a t e s are r e l e v a n t , namely t h o s e f o r a n e u t r a l atom and f o r a s i n g l y charged ion.

They are obtained from t h e adiabatic p o t e n t i a l energy c u r v e s , V i ( R ) i n ( 5 ) , by a unitary t r a n s f o r m a t i o n which reads e x p l i c i t l y / l /

Here W o o i s t h e potential curve f o r a n e u t r a l atom, and W++ t h a t o f an ion. The o f f - d i a g o - nal t e r m s Wo+-W+, couple t h e s e s t a t e s t o g e t h e r and a r e responsible f o r ionization or neu- t r a l i z a t i o n .

We have c a l c u l a t e d t h e t r a n s f o r m a t i o n angle 0 assuming t h a t t h e many-electron wavefunctions E i are given a s S l a t e r determinants w i t h t h e c o n s t i t u e n t s i n g l e e l e c t r o n wavefunctions, H r ; R ) , obtained from t h e ASED-MO programme (including e l e c t r i c f i e l d e f f e c t s ) / 2 - 5 1 . The r e l e v a n t excited s t a t e i s s e l e c t e d as belonging t o t h e same symmetry representation as t h e ground s t a t e , e.g. i f we model t h e gas-metal system by a t e t r a h e d r a l c l u s t e r o f metal atoms w i t h helium adsorbed on i t s apex, it has C2, symmetry. Wlth He i n

i t s

1s ground s t a t e , t h e t o t a l ground s t a t e wave f u n c t i o n ,

$,

belongs t o t h e A , representation. Because W,+ preserves t h i s symmetry, t h e r e l e v a n t excited s t a t e has a wave f u n c t i o n ,

ee,

w i t h t h i s symmetry. Because t h e atom or ion w i l l desorb along t h e s t e e p e s t f i e l d gradient, i.e. per- pendicular t o t h e s u r f a c e , we can n e g l e c t any l a t e r a l v a r i a t i o n , s o t h a t , by assumption, O=B(z) depends on t h e d i s t a n c e , z , from t h e m e t a l o n l y , and i s given by

3

-

Kinetics

To c a l c u l a t e t h e k i n e t i c s of f i e l d desorption and ..field ionization a master equation has been derived which r e a d s f o r our present problem/ll/

Here i = O , + r e f e r s t o t h e n e u t r a l and ionic s t a t e of helium. v and

u

l a b e l t h e s t a t e s i n t h e diabatic p o t e n t i a l s , Woo(z) and W++(z), among which phonon-induced t r a n s i t i o n s take place with r a t e s Ri(v,p). The tunneling r a t e s connecting n e u t r a l and ionic s t a t e s a r e given by

To+(u. v) = ?=A4

1

^h~ n0,'(R) Wo+(R) n+,,(R)

1'

A(E+v-Eop, To$ (1 1) with

In (11)

row

is t h e h a l f width of t h e ( d i s c r e t e ) l e v e l p in Woo due t o phonon t r a n s i t i o n s and is given a s

To determine t h e nuclear wave functions, nOv and r ~ + ~ , i n t h e diabatic p o t e n t i a l s we have f i t t e d a Morse p o t e n t i a l t o Woo(z) adjusting its parameters a s a function of f i e l d s t r e n g t h . Likewise, we s e t W++(z) = Wc -eF(z-zc) f o r t h e d i a b a t i c curve of t h e ion. For both poten- t i a l s t h e wave functions can be given a n a l y t i c a l l y .

The ion yield can be c a l c u l a t e d from (10-13) and is given approximately by

Fig.2: Time of f l i g h t curves f o r He f i e l d desorbed from W a t 4.5V/A0.

Left curve: experiment /12/;

r i g h t curve from (14) with

200-

(83

-

'2.06 k V

U)

C 160-

He'

-

^{1 ns : 0.33 eV}

140-

: 0.075

A

\ 120- t,

=

13559 ns

c n .

2 103-

0

peak position and height FL CnT I ME <ns, adjusted f o r comparison.

In Fig.2 we show t h e ion yield a s a time of f l i g h t curve adjusted i n position and height t o allow d i r e c t comparison with experimental d a t a by Tsong /12/. We note t h a t t h e t h e o r e t i c a l curve has an energy width of about 0.6 eV a s compared t o about 1 eV i n t h e experiment.

Considering a number of t h e o r e t i c a l approximations, discussed i n e a r l i e r papers /1-5/ and a l s o t h a t t h e experiment y i e l d s an upper l i m i t , t h e s e two e s t i m a t e s compare r a t h e r favor- ably. Thermal f i e l d desorption being an a c t i v a t e d process, we have evaluated t h e yield (14) according t o an Arrhenius parametrization (1). The r e s u l t s are presented in Fig.3 (together with t h e position of adsorption) a s a function of f i e l d s t r e n g t h . A s explained i n e a r l i e r papers /I-5/ we t a k e t h e s e l f c o n s i s t e n t f i e l d from density f u n c t i o n a l c a l c u l a t i o n s /13/

performed a t f l a t surfaces. This introduces some u n c e r t a i n t i e s i n t o t h e theory because we have t o r e p r e s e n t W, a t r a n s i t i o n metal, by an approximate rs value. To e s t i m a t e t h e r e l i a - b i l i t y of t h i s procedure we p r e s e n t t h e r e s u l t s i n Fig.3 f o r two values rs=1.5 and 2.0. The theory is d e f i n i t e l y not more a c c u r a t e than t h e spread i n d a t a points; t h i s is t h e b e s t we can do with our present, r a t h e r crude, c l u s t e r programme (based on t h e ASED-MO method). We a r e a t present writing a b e t t e r code.

Fig.3: Position of f i e l d - adsorbed He, zad. a c t i v a t i o n energy, Ed, and p r e f a c t o r , v, a s a funciton of f i e l d s t r e n g t h . Local f i e l d s from density func- t i o n a l c a l c u l a t i o n s with rs=l .5 (squares) and 2.0 ( t r i a n g l e s ) .

The lower panel i n Fig.3 i n d i c a t e s an i n t e r e s t i n g q u a l i t a t i v e f e a t u r e , and t h a t is, t h e dra- matic increase i n t h e p r e f a c t o r a s a function of f i e l d , more ?r l e s s i n an exponential fash- ion. We r e c a l l t h a t i n ordinary, i.e. f i e l d f r e e , thermal desorption, t h e e f f e c t i v e prefac- t o r is a product of a s t i c k i n g c o e f f i c i e n t and an a t t e m p t frequency t o desorb. In thermal f i e l d desorption, t h e r o l e of t h e s t i c k i n g c o e f f i c i e n t is replaced by t h e ionization proba- b i l i t y a t the apex of t h e adiabatic ground s t a t e energy curve. It v a r i e s from zero i n F=O t o a s a t u r a t i o n l i m i t in high f i e l d s , a s borne out by our c a l c u l a t i o n s . For He t h i s s t r o n g f i e l d dependence of t h e p r e f a c t o r has an i n t e r e s t i n g consequence. We note t h a t f o r He t h e a c t i v a t i o n energy f o r f i e l d desorption is roughly equal t o t h e depth of the d i a b a t i c curve f o r t h e n e u t r a l species. Thus thermal desorption of n e u t r a l and ionic He i n a f i e l d have t h e same desorption energy, implying t h a t t h e r a t i o of ions t o n e u t r a l s is proportional t o t h e r a t i o of t h e p r e f a c t o r s . Because t h e p r e f a c t o r f o r t h e desorption of n e u t r a l He is not a s t r o n g function of f i e l d s t r e n g t h , we predict t h a t t h e r a t i o of ion t o n e u t r a l y i e l d is an

exponential function of f i e l d s t r e n g t h . In p a r t i c u l a r , w e l l below t h e b e s t image voltage, thermal desorption w i l l only yield n e u t r a l He. To t e s t t h i s idea, an experiment should s t a r t from a w e l l defined, constant coverage of He t h a t is t o t a l l y removed by a f a s t tem- p e r a t u r e r i s e s o t h a t t h e t o t a l number of desorbed species remains constant. I f t h e detec- t o r only r e g i s t e r s ions, one should s e e t h e exponential increase i n ion yield d i r e c t l y .

References

/1/ Kreuzer, H.J., and Watanabe, K., J. de Physique

3

(1988) C6-7.

/2/ Tomanek, D., Kreuzer, H.J., and Block, J.H., Surf. Sci.

157

(1985) L315.

/3/ Nath, K., Kreuzer, H.J., and Anderson, A.B.,. Surf. Sci.

176

(1 986) 261.

/4/ Ernst, N., Drachsel, W., L i , Y., Block, J.H., and Kreuzer, H.J., Phys. Rev. L e t t .

57

(1986) 2686.

/5/ Kreuzer, H.J., and Nath, K., Surf. Sci.

183

(1987) 591.

/ 6 / ~ u l l e r , E.W., Naturwissenschaf t e n

29

(1 941 ) 533.

/7/ ~ i i l l e r , E.W., Phys. Rev.

102

(1959) 618.

/8/ Gomer, R., J. Chem. Phys.

2

(1959) 341.

/9/ Comer, R., and Swanson, L.W., J. Chem. Phys.

2

(1963) 161 3.

/ l o / Forbes, R.G., Surf. Sci.

102

(1981) 255.

/11/ Tsukada, M., and Gortel, Z.W., Phys. Rev. B

2

(1 988) 3892.

/12/ Tsong, T.T.. Surf. Sci.

177

(1986) 593.

/13/ Gies, P., and Gerhardts, R.R., Phys. Rev. B B 11986) 982.