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FIELD EMISSION FLUCTUATIONS INDUCED BY THE DIFFUSION OF ATOMS ON A CLEAN METAL
SURFACE
R. Bakhtizin, V. Valeyev, E. Shikhovtseva
To cite this version:
R. Bakhtizin, V. Valeyev, E. Shikhovtseva. FIELD EMISSION FLUCTUATIONS INDUCED BY THE DIFFUSION OF ATOMS ON A CLEAN METAL SURFACE. Journal de Physique Colloques, 1989, 50 (C8), pp.C8-117-C8-122. �10.1051/jphyscol:1989821�. �jpa-00229919�
COLLOQUE DE PHYSIQUE
Colloque C8, suppl6ment au n o 11, Tome 50, novembre 1989
FIELD EMISSION FLUCTUATIONS INDUCED S Y THE DIFFUSION OF ATOMS ON A CLEAN METAL SURFACE
R . Z . . BAKHTIZIN, V.G. VALEYEV and E.S. SHIKHOVTSEVA
Department of Physical Electronics, Bashkir State University, 450074.
Ufa, ul. Frunze, 32, USSR
Abstract
-
The present paper deals with t h e s t r u c t u r e and dpamfc pro- p e r t i e s o f a clean metal s u r f a c e , t h a t were s t u d i e d by meastwine; f l u c - t u a t i o n s of t h e f i e l d emission current noise. Such. noises can avpear a s a r e s u l t of generation of plasma and acouatic waves, a s well as of sur- f ace self-diffusion.The s u r f a c e dl.ffusion as a m s e i b l e mechanism of the f i e l d emission nois@ ge- n e r a t i o n w a s d i s e w s e d , f o r instance, i n [I, 21
.
The d i f f u s i o n nodels used in t h e s e papers a r e based on t h e theory a f fluckua%ion concentration develo- ped by Smolnchowski [3, 41.
A det&led descript;ion o f t h e charge c a r r i e rn o i s e conditioned by t h e low-frequency f l u c t u a t i o n s in t h e s o l i d s i s contai- ned, f o r instance, i n a review paper [5]. B e method which was o r i g i n a l l y de- veloped f o r t h e study o f noises induced by adatom d i f f u s i o n on t h e e m i t t e r smXace
b-4
might be well applied t o describe the noises o f a clean surfa- c e [IO].
It i s well known &hat fluctua%ions of t h e f i e l d emission c u r r e n t
%j
i n the case of metals a r e mainly determined by t h e elec-kron3.c work f u n c t i o n (jJ,
which i s connected with t h e e x p o n e n t i d dependence of
j
upon.
!iceor-din:;ly, f o r -&he autocorrela&ion function of f i e l d emission c u r r e n t , averaged over t h e e m i t t e r s u r f a c e , we shall! have
i s t h e average density of t h e f i e l d emission c u r r e n t ,
~ = ( F , z ) ,
whg=dlg
i s t h e element of tibe e m i t t e r s u r f a c e area andh
i s t h o coordi- nate normal t o t h e surface. I n accordance v i a,
t h e followin& r e l a t i o n - ship i s v a l i d f o r t h e i n s t m t a n e o u s value of t h e work function9
,% ) :where
p
(,
t) i s the l o c a l value of charge density. F r e m B$B. (I ) and (2), and takirig i n t o account t h e f l u c t u a t i o n - d i s s i p a t i o n theoremCI21
f o rArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989821
t h e s p e c t r a l f u n c t i o n o f &&ionciry f l u c t u a z i o s e o f fAeld m i s s L e n eercbnt 3
, in $ems of t h e P i v
?i
= Q ekt;libmtien,
vhere -A i s We vector po- t e n k i d , we obtadn :In 3@.(3) t h e first item describes t h e eqzilibriwn c u r r e n t ncise in t h e ays- tern and pzovides an information on t h e spectrum o f c o l l e c t i v e e x c i t a t i o n s of,
%he sarfaea:
&era !I! i s t h e temperatawe. ,:D
-
( z , P ) a component o f t h e r e t a r d b n g Green f u n c t i o n f o r t h e electromagnetic f i e l d . The second item Ln EU.(~) ena- b l e s one t o t a k e i n t o c o n s i d e r a t i o n t h e c o r ~ t r i b u & i o n o f noa-equUfbriupl pro- c e s s e s ~ it ha^^ t h e following form:Here
< 8p 8p' >,
i s t h e @enporal F o u r i e r component of t h e n o n - e q u i l f b ~ i m c o r x e l & i o n a l f u n c t i o n f o r charge d e n s i t y f l u c t u a t i o n s .Let us c o n s i d e r t h e c o n t ~ i b n t i . o n o f d i f f u s i o n p r o c e s s e s t o t h e spec-tral fun- c t i o n ,S o f f i e l d m i s s i o n c u r s e n t n o i s e f o r a one-dimensfonal ease. Self- d i f f u s i o n o f &oms t a k e s p l a c e i n a p e r i o d i c p o t e n t i a l d o n g t h e surface. In t h e g e n e r a l case, t h e corresponding item i n ( 3 ) i s d e s c r i b e d by Eq.(5). The d i p o l e moment assocltated with each near-sstrface atom i s denoted by
a
;p o l a r i z a b i l i t y , i,e. a change of jibe d i p o l e moment as a r e s u l t of i n t e r a t o - mic i n t e r a c t i o n s
rnw
be neglected.L e t t h e p o t e n t i a l o f the f i e l d acting upon an atom on t h e s u r f a c e be o f t h e
f o m :
where x i s t h e s p a c e c o o r d i n a t e along t h e e m i t t e r surfaee; a is t h e Us- t a n c e between t h e atoms o f the l a t t i c e , and Vo i s t h e a c t i v a t i o n energy.
The p o t a n t i d ( 6 ) r e p r e s e n t s an a r r a y of p o t e n t i d wells. Atom in such a po- tential m a y o m i l l & e at t h e bottom o f each p o t e n t i a l w e l l with a frequency
C
U"(X,,)/JTI]''~,
and it i s capable o f jumping, w i t h a c e r t a i n p r o b a b i l i t y , t o a d j a c e n t wells. Thus, d i f f u s i o n occurs, as a. rule, by jamps w i t h t h e i r minimum l e n g t h appmxim&ely equal. t o t h e i n t e r a t o m i c U&aace.The d i s t r i b u t i o n function of d i f f u s i n g p a r t i c l e s m a y b e g i v e n as f o l l o w s ( s e e , e.g., 021
>
:i s t h e solution of t h e Focker-Planck stationarity equation:
Let us denote by z t h e lifetime o f a diffusing atom i n each p o t e n t i a l w e l l (6). 'Phe l i f e k i m e i s defined by t h e Arrhenius formula:
Eere %in fs t h e c o o s d i n a t e f o r t h e minimum o f t h e poten-kial and m k s the
mass o f atom. 00
For t h e p a r t i c l e d e n s i t y defined as n(x, t) =
l f ( p , ~ , t ) d p
we s h a l l o b t a i n f o r t h e F o u r i e r component o f t h e d e n s i t i z d e n s i t ~ correlation :Thus, t h e c o n t r i b u t i o n o f +he item describing t h e s u r f a c e atom d i f f i ~ s i o n ta t h e speofm3 function
SS, of t h e f i e l d emission c u r r e n t n o i s e (5) may be expressed as follows:
Here IV i s t h e number of c e l l s of %he s u r f a c e l a t t i c e i n t h e region of t h e suxfaee under i n v e s t i g a t i o n , and I, i s t h e Ressel function.
~ ~ ~ i . k n d h g on t h e r e l a t i o n between t h e a,
1. ,
T, and Vo parameters, t h e$ S e t b e Z o f t h e atom in a well (see Eq. ( 1 2 ) ) m a y b e calculated, f o r some charactezliatic cases, by means of (10).
Fop instance, in t h e C1assiciil c a s e , w h e r e t h e atom c a n l e a v e t h e well only un- d e r i n f l a m c e o f fluctuations :
B e r e l a a i o n s h i p (13) i s did provided t h a t
In -view of khe quantum tmnspazl.ency of barriers ( L e o , when the followAng in- equality(
2 a 3 r ~ / z 3 ) - <<
1 i s s a t i s f i e d ) t h e expression f o r the Iffetiree of the atom in2 aY
(g~'12mud)
In the exCreme case o f t w a e l i n g
C8-121
&t low temperatures ( T / U0 « 1 ) Bq. (12) may be r e w r i t t e n i n a simpliear form:
( 16 )
Equations (12) and ( 1 6 ) , with t h e l i f e t i m e determined from Eq.a, (13) - (15) give a. frequency dependence of t h e diffusion p a r t of t h e s p e c t r a l density
~ x/(,cj1vz+\') f o r one-dimensional surface s e l f - d i f f u s i o n of atoms, p r o - vided t h a t t h e diffusion proceeds i n a periodic p o t e n t i a l r e p r e s e n t i n g an a r - ray of s i m i l a r l y shaped, p o t e n t i a l wells,' The obtained expression which desc- r i b e s t h e c o n t r i b u t i o n of diffusion processes t o S has t h e f oEiri of t h e Ue- bye -Lorentz spectrum, f h i s i s associated with t h e fact t h a t t h e d i s t r i b u t i o n
function of diffusing atoms can be described by a r e l a t i o n s h i p of t h e form ( 7 ) . She frequency dependence Sw agrees well with experimental data (see ( P i g . I ) , 5fhe p l o t shows experimental curve Sw f o r a clean IT , taken from
10 , and the curve described by ( 8 ) . Since expression (8) includes t h e qua- n t i t i e s 7Q, a , P and Y defining t h e s t r u c t u r e and dynamic p r o p e r t i e s by comparing t h e frequency dependence (8) with experimental curves S .
P i g . I . fhe frequency dependence of Sw for (a) clean W (see Pig.5 i n [1.0] ) and (b) function described by ( 8 ) .
Pn t h e framework af t h e present paper we confined o u r s e l v e ~ t o consideration Qf t h e diffusion mechanism o f t h e f i e l d emission noise generation. A study
69 t h e equilibzdglg component of S, may be of a c e r t a i n i n t e r e s t as well.
It f s believed t o be t h e subject of o m ftwbher work.
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