THE MEASUREMENTS OF SURFACE MIGRATION ACTIVATION ENERGY FOR EDGE POSITIONED ATOMS OF TUNGSTEN (011) PLANE

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THE MEASUREMENTS OF SURFACE MIGRATION ACTIVATION ENERGY FOR EDGE POSITIONED

ATOMS OF TUNGSTEN (011) PLANE

Z. Stepien, J. Kukulka, W. Lenkow

To cite this version:

Z. Stepien, J. Kukulka, W. Lenkow. THE MEASUREMENTS OF SURFACE MIGRATION ACTI- VATION ENERGY FOR EDGE POSITIONED ATOMS OF TUNGSTEN (011) PLANE. Journal de Physique Colloques, 1986, 47 (C7), pp.C7-165-C7-168. �10.1051/jphyscol:1986730�. �jpa-00225923�

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THE MEASUREMENTS OF SURFACE MIGRATION ACTIVATION ENERGY FOR EDGE POSITIONED ATOMS OF TUNGSTEN (011) PLANE

Z.M. STEPIEN, J. KUKULKA and W. LENKOW

Institute of Physics, Surface Physics Laboratory, Pedagogical University of Czestochowa, Al. Zawadskiego 13/15,

PL 42-200 Czestochowa, Poland

En se basant sur le phdnomane des cycliques changements du courant de 1°Bmission Blectrique par champ dlectri ue sous & la constante pression qui extorque cette dmission, observ2 en train des succe- sives, incandescences

/

de courte durde

/

de 1°6metteur & la tempera- tuse de 1135

-

¹²⁹⁰^K,on a fix6 l'dnergie de l'activation pour le processus de l'dlimination et de la migration des atomes de bord for- mant le disque de sommet de l'dmetteur de tungst6ne & l'orientation

[011]. En partant du principe que les changements du courant de 1 '&mission sont provoquds par 1 'eff et "patch-f ieldt', accompagnant le changement du diamstre du disque de sommet, on a obtenu pour les dif- fdrents diametres du disque l'dnergie constante de l'activation

Qe = 1.3 2 0.2 eV. L'agent prd-exponentiel he & 1'Bquation

-

^d'Arrhe-

-

nius ddcrivant le processus Btudid avait la valeur de 10

'

^s-

' .

Summary

The activation energy on the removal and self-diffusion process of edge atoms of the top [~ll] oriented tungsten field emitter has been determined on the basis of the cyclic field emission current changes observed after the successive, short duration annealing of emitter, The consideration both the processes surface migration towards the base of emitter and so called "patch-fieldw effect permits to obtain the activation energy Qe = 1.3

2

0.2 eV and preexponential factor Ae of the order of

lo7

s" from measurements in the effective temperatures range 1135

-

¹²⁹⁰^K.

Apparatus

An all glass, seal-off valve more detaily described previously together with measuring sys tem [l

j

has been used. The geometrical aperture angle 0.17~ permits to investigate a very small areas limited only by FEM resolution. All experimental chamber was placed in liquid _- _- nitrogen to obtain low pressure not exceeding 5 x 10'~' hPa. The local field emission current was measured by usin of channel electron mul- tiplier KPE 7 operating in pulse mode. The f0111 oriented tungsten tip with final radius about 1200

1

was used. The deflection of probe hole was realized by precise electrostatic system, The emitter temperature was controlled with !: 5 K accuracy.

Experimental procedure and results

The local field emission current from the center of top disk,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986730

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C7-166 JOURNAL DE PHYSIQUE

Ffg.2. The standardieed FE cy- Fig.3. The geometrical model of cle

/

see text for co- apex part of [OI I ] oriented ordinates description

/,

tungsten enLtter tip.

structured as (011) plane was measured after the succesive, short duration overheating of emitter without field. At constant voltage conditions a characteristic periodical changes of the field emission current, described by authors previously, were observed [1,2]. On the

Fig.1 a typical dependence of field emission current, versus 5.0

2

0.1

. ,

sec pulse overheating number is presented for temperatures 1180 and 1245 K. The measurements were made

700 at effective temperatures 1135 K,

: :

No

... ... ...:- .

^-.* ¹¹⁸⁰K, 1225 K, 1245 K and 1290 K.

. . . ...

Although overall lenght of cycles decreases when temperature increa-

0 10 20 30 40 5 0 60 ses, they shape is retained, so

that standardized field emission current cycle

/

presented on the Fig.2 at eo-ordinates N/No versus x =

the

where No

-

counts for cycle beginning,

re -

mean cycle

. ..

. ... -

^lenght

^/

can be constructed.

..;.,... ."

Discussion

0 10 20 30 40 50 60

number of obsermtton The geometrical model of the

apex part of [011] oriented tungs- Fig.1, The typical results of ten emitter presents Fig.3. It may

PE current measurements be constructed from concentric vs overheating number for disks with thickness corresponding a/ 1245 K, b/ 1180 K. to interplanar space. For thermal-

ly smoothed emitter with tip radius ,- 1200

a,

the apex disk radius calculated from crystallographic relations is about 70

1,

the next one

-

about 1 3 0

8.

At high temperatures conditions, the edge atom migrate on the next step towards the emitter base. Since the mean diffusion lenght per second of se- parate surface tungsten atom on the

1'

k

1,30 1,25 1 3

-

- -

(01 1) plane, calculated after Cra- ham and Ehrlich [3] for the temq- rature 1200 K is the order of 10

x,

therefore all the edge atoms of apex disk removed in the course of heating pulse, are going tow- the

1J5-

IJO

-

>

[0111

Q 0;l

Q2

_q3

Qk 95 M ⁰¹¹ 8 09 x

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c ~ n n e c t e d w i t h "patch-field

F].

e f f e c t , described by Young and Clark f51, can e x p l a i n t h e observed c y c l i c f i e 1 mission c u r r e n t changes. A s suggested by P o l i z z o t t i and l h r l i c h ?6? t h e "patch-fieldn e f f e c t ap- pear t o be overestimated. Authors propose t o c a l c u l a t e t h e f i e l d s t r e n g t h Po caused by npatch-field" e f f e c t from r e l a t i o n :

= 4 Y

F. ^R ^. ^.

^{/ 1 /}

where :4p

-

work f u n c t i o n d i f f e r e n c e between (011) plane and n e x t w e l l developed plane, n

-

number of n e t r i n g s between this planes, R

-

d i s k r a d i u s , e

-

elementary charge.

If we assume t h e work f u n c t i o n of (01 1) plane 5.6 eV i n t o c o n s i d e r a t i o n (012) plane w i t h work f u n c t i o n 4.34 eV c a l c u l a t e , on t h e base of geometrical model

/

presented on

r a t i o . Its value f o r 1200

1

r a d i u s e m i t t e r was 0.048 V.

e n

The t o t a l f i e l d s t r e n t h on t h e apex d i s k i s t h e f u n c t i o n of R and can be denoted as P ' / R ~ = P

+

Po

,

^whereF is t h e a r a r a g e f i e l d

f o r smooth (01 1) plane f o r example from van Oostrom

.

For l a r g e d i s k s i z e ftpatch-fieldn e f f e c t i s n e g l i g i b l e

.

Considering a l l a b ~ v e r e l a t i o n s we can c a l c u l a t e from Pow- t h e j ( F ) / j ( ~ ) r a t i o as a f u n c t i o n of R. Now on

t h e base of above c a l c u l a t i o n s and l o c a l c u r r e n t measurements r e s u l t s

/

presented on Fig.2

/,

t h e r e l a t i o n between apex d i s k r a d i u s R and c y c l e phase x, sho- wed on t h e Fig.4 w a s c a l c u l a t e d . The apex d i s k r a d i u s shows l i n e a r

40 changes t o about 20

8 .

The i n i -

t i a l d i s k r a d i u s i s 70 1 what i s

30 i n e x c e l l e n t agreement w i t h geo-

m e t r i c a l considerations.

.

20 Assumed, t h a t t h e edge atoms

1 0 number i n d i s k i s proportional t o

f l ,

where N i s t h e t o t a l nuniber O;l

M ⁰³ a 05 46

07 08

09

of d i s k atoms, we can describe

t h e removing process of t h e edge atoms by expression :

Fig.4. The r e l a t i o n between apex

d i s k r a d i u s and cycle phase.

- + ⁼ ⁴ ^exp(- +) ^/

²

^/

where : Qe

-

an a c t i v a t i o n energy on t h e described process, A,

-

preexponential f a c t o r . If we have cor- r e l a t i o n between d i s k s i z e and c y c l e phase, as w e l l t . v a l u e a t f i v e constant temperatures, we can formulate t h e f i v e equations system ba- sed on formula /2/. Its s o l u t i o n , obtained by l e a s t squares method, gives a n a c t i v a t i o n energy and preexponential f a c t o r a s a f u n c t i o n of apex d i s k radius. Obtained values :

Qe 1.3 2 0.2 eV A,,

lo7

s -1 a r e independent on digk r a d i u s R.

Comments

a/ I n t h e papers of Barbour a t a l l [lo], B e t t l e r and Charbonnier [11] and B e t t l e r and Barnes [I23 t h e s u r f a c e migration a c t i v a t i o n energy of i n d i v i d u a l tungsten atom w a s measured by s o c a l l e d "disap- pearing r i n g s t t method using. On account of migration of t h e apprecia-

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C7-168 JOURNAL DE PHYSIQUE

ble part of emitter tip material, together with destruction of relati- vely large micromonocrystal volume, the obtained value of activation energy 2,7

-

3.14 eV per atom can not be recognized as a surface migration energy on the individual net plane. Barbour at all and Bettler and Charbonnier

[lo,

11

I

have suggested, that for the close packed

(011) plane, the surface migration activation energy can be signifi- cant smaller. The actual results obtained by FIM method [3,13,14] gives for activation energy on the self-diffusion process of tungsten atom on the (011) plane a value of 0.85 to 0.95 eV. The result obtained by authors for the remove of the outer atoms from the top disk for following diffusion on the next disk of

\

01 1) plane is the complement to previous results,

b/ The va iation in the course of disk radius for final cycle stage

/

R - 20

fi ^/

can be caused by low resolution of FEM or by fact, that the assumption about proportional of the edge atoms number to square root N is not true for small disk radii,

This work was supported by Central Project of the Basic Research under contract 01,12.3.3.2.

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-

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-

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/

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/

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^/

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^/

THE MEASUREMENTS OF SURFACE MIGRATION ACTIVATION ENERGY FOR EDGE POSITIONED ATOMS OF TUNGSTEN (011) PLANE

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