CROSS-CORRELATION FUNCTIONS OF THE FIELD EMISSION FLUCTUATIONS WITH SLIT PROBED REGIONS

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CROSS-CORRELATION FUNCTIONS OF THE FIELD EMISSION FLUCTUATIONS WITH SLIT

PROBED REGIONS

J. Beben, Ch. Kleint, R. Meclewski

To cite this version:

J. Beben, Ch. Kleint, R. Meclewski. CROSS-CORRELATION FUNCTIONS OF THE FIELD EMIS-

SION FLUCTUATIONS WITH SLIT PROBED REGIONS. Journal de Physique Colloques, 1989, 50

(C8), pp.C8-97-C8-102. �10.1051/jphyscol:1989817�. �jpa-00229915�

COLLOQUE DE PHYSIQUE

Colloque C8, suppl6ment au no 11, Tome 50, novembre 1989

CROSS-CORRELATION FUNCTIONS OF THE FIELD EMISSION FLUCTUATIONS WITH SLIT PROBED REGIONS

J. BFBEN, CH. KLEINT' and R. MFCLEWSKI

Institute of Experimental Physics, WrocYaw University, PL-50-205 YrocYaw, Poland

Sektion Physik, Karl-Marx-UniversitSt Leipzig, DDR 7010 Leipzig, D.R.G.

bbstract

-

Using a two-dimensional isotropic adparticle diffusion law the cross-correlation function of the field emission f 1 uctuations is calculated. The i nf 1 uence of the different geometrical parameters including the distance between probe regions is investigated. The results are compared with measurements of the adsorption system WI112)K for a chosen coverage. Some conclusions are drawn referring to the experimental arrangement and the explanation of cross-carrel ation functions.

The cross-correlation technique of the field emission fluctuations was introduced by Dabrowski and Kleint C1.21 as an extension of the time autocorrelation measurements t31. Originall y the cross-correlation function ICCF) was evaluated C21 and determined experimentally C2,4,5,53 for two spherical probed regions with constant distance A between them.

More recently E7,8,93 CCFs were measured for slit-shaped probe regions.

This shape was suggested, C 1 0 , l i I for investigation of the s~rrface dif f crsion anisotrnpy. It seems to be preferable for the determination of diffusion parameters for chosen crystallagraphic directions.

In the present paper CCFs for the slit-shape probed regions are evaluated at various geometric parameters as slit length, a, and distance A between the slits. The curves obtained are compared with experimental results +or the potassium-tungsten adsorption system.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989817

2

-

T h e o r e t i c a l c r o s s - - c o r r e l a t i o n f ~ t n c t i ons

Using Gomer" s expression f o r t h e a u t o c o r r e l a t i o n f u n c t i o n and extending i t t o t h e s l i t c r o s s - c o r r e l a t i o n geometry by i n t e g r a t ~ o n upon two separate probe r e g i o n s C12,21 we o b t a i n f o r t h e probe area dependent f a c t o r (cf.C31)

where 7 i s t h e t i m e delay. A and F ) a r e t h e areas o f t h e probed regions, a, b and A a r e s i d e s and d i s t a n c e between t h e areas, r e s p e c t i v e 1 y , D i s t h e d i f f u s i o n c o e f f i c i e n t . As an argument o f t h e CCF t h e product DT was chosen.

The f o r m u l a (11 is v a l i d o n l y under t h e c o n d i t i o n s assumed i n Refs. f3.21.

By ser i es expansion of t h e exponenti a1 and i n t e g r a t i on t h e i n f l uenre of t h e s l i t geometry on t h e c r o s s - c o r r e l a t i o n f u n c t i o n s i s c a l c u l a t e d .

The s o l i d curves shown i n F i g . % r e p r e s e n t CCFs corresponding t o a s h o r t s l i t i.e. square-shape probed regions. The d i s t a n c e between t h e i r c e n t r e s i s A = 300

8.

The dashed curve carresponds t o t h e l i m i t of p o i n t probe regions. The l a t t e r curve was obtained u s i n g t h e formula

w i t h A = 300

8,

i n s t e a d o f e l . ( 1 ) .

Fig.2 p r e s e n t s CCFs c a i c u l a t e d f o r a constant s l i t prnbe wrsth o f 50

8,

v a r i a b l e l e n g t h and a constant d i s t a n c e between t h e s l i t c e n t r e s o f A = 300

8.

Fig.3 shows CCFs corresponding t o 50

8

x 300

8

s l i t s w i t h v a r y i n g d i s t a n c e A between t h e s l i t probe centres.

Fig.4 g i v e s a comparison o f a CCF obtained by a p p l i c a t i o n o f t h e new approximation i.e. f o r m u l a ( 1 ) ( s o l i d c u r v e ) , w i t h t h e CCF c a l c u l a t e d by eq. ( 2 ) (dashed c u r v e ) as used b e f o r e C4-61. The geometry o f t h e s l i t s i s t h e same.

3 - Experiment and experimental r e s t t l t s

The d i s t a n c e dependence o f t h e c r o s s - c o r r e l a t i o n was determined f o r t h e a d s o r p f i o n system W ( 1 1 2 ) K f o r an average potassium coverage o f 8 = 0.3. The experimental arrangement and o t h e r d e t a i l s a r e described e l sewhere C 1-2.7-97. Selected r e s u l t s a r e presented i n Fig.5 i t r i a n g l e s , c i r c l e s and squares )

.

The same f i g u r e c o n t a i n s a l s o a comparison o+ t h e t h e o r e t i c a l CCFs ( s o l i d curves obtained by u s i n g t h e new approximation e q 1 j w i t h t h e measured values. The curves correspond t o t h e S l i t probe s i d e s 50

8

^x

300

8.

The c u r v e f i t t i n g procedure was done by s h ~ f t ~ n g a correspanding s e t o f CCFs IFig.3) t o an estimated optimum p o s i t i o n .

F i g . 1 . The s o l i d curves r e p r e s e n t t h e CCFs f o r t w o s q u a r e p r o b e r e g i o n s w i t h c o n s t a n t d i s t a n c e (300

8 )

b e t w e e n t h e i r c e n t r e s . The s i d e l e n g t h

i n d i c a t e d i s a p a r a m e t e r . F o r t h e d a s h e d c u r v e see t e x t .

F i g . 2. CCFs f o r t w o s l i t p r o b e r e g l o n s o f 50

8

w i d t h and a c o n s t a n t p r n b e d i s t a n c e ot 300

8.

T h e s l i t l e n g t h i n d i c a t e d i s a p a r a m e t e r .

F i g . 3. CCFs f o r s l i t r e g i o n s o f 50

8

x 300

x

and t h e i n d i c a t e d probe d i s t a n c e s .

F i g . 4 . CCFs f o r probe d i s t a n c e of 300

8:

c a l c u l a t e d b y eq. 1 f o r s l i t r e g i o n s of

50 x

^{x 300}

x

C s o l i d l i n e > , and c a l c u l a t e d by e q . 2 Cdashed l i n e > .

Fig. 5 . Comparison of theoreticai CCFs calculated by eq. i (solid lines) with experimental points for the W ( 1 I Z ) K (8 = 0 . 3 ) at different probe distances indicated in the figure.

4 - Short disc~tssion

The goal of the above calculation is an insight into the result of the geometry as well a s the optimization of the probe arrangements. W e arrive at the following conclusions which refer to isotropic 2D-dif fusion owing to the diffusion law supposed. The square probes are similar to point or circular probes if their dimensions are small, otherwise they imply a worse r~solution. M i th increasing slit length the resolution decreases slightly (because of a stronger averaging by the bigger areas). For an anisotropic diffusion, however. the slit geometry has a much better ang~tlar resslcrtion than the square slit arrangement E10,ll I. (We neglect the ineluence of the FEW resolution caused by the finite transverse electron momentum which was considered lor autacorrelation measurements recently E153). Fig.3 shows the strong decrease of the cross-correlation with increasing distance and also the increase in the delay time of the CCF maximum. Both features were observed experimentally C7,8,9.133. A negative part of the CCF appearing sometimes clearly, is beyond the scope of this model and other explanations are required C12.4,141.

The cnmparison of the approximate (point probe) formula and the integral eepression (eq. 1 ) for a n , of ten used geometry shows a small deviation in the diffusion coe+ficient which can be determined from the CCF. An estimation o+ the error leads to a difference af about 12 per cent. This might be a tolerable deviation in view of a much faster evaluation of D in a first approximation. Finally Fig.5 reveals that the experiments are described reasonably we1 1 by the integral cross-correlation curves. Because a critical behaviour might appear near phase transitions of the adlayer, a

general judgment of t h e simulation of t h e adparticle induced noise bv t h e above equations must await a. more extensive comparison especially at various coverages and temperatures.

Acknowledgements

Work supported by t h e Polish Ministry of Education within t h e Central Project of Basic Research CPBP 01.08. A. Technical assistance of Mr. S - S u r m a i s acknowledged.

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