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M. Drechsler, B. Blackford, A. Putnam, M. Jericho

To cite this version:

M. Drechsler, B. Blackford, A. Putnam, M. Jericho. A MEASUREMENT OF A SURFACE SELF-


Colloques, 1989, 50 (C8), pp.C8-223-C8-228. �10.1051/jphyscol:1989838�. �jpa-00229936�



Colloque C8, Supplkment au n o l l , Tome 50, novembre 1989



$.RMC2-CNRS, Campus de Luminy, F-13288 Marseille, France

Physics Department, Dalhouse University, Halifax, Nova Scotia, Canada


A technique is described to measure a surface self-diffusion coefficient (D) of a metal (gold) by scanning tunneling microscopy. Micro-hills formed on a gold face show a shape evolution by a diffusion transport of kink site atoms.

D is determined via a measurement of the hill apex radius as a function of time and includes corrections of image errors. The technique shows that STM can be used to study diffusion and it opens the possibility of measuring diffusion at lower temperatures where D could not be measured previously.

1. I n t r o d u a

In scanning tunneling microscopy (STM), changes of the shape of surface structures with time have often been interpreted in terms of rnatter transport by surface self-diffusion /1//2//3//4/. It may be interesting to improve this type of observation in order to develop a technique to determine surface self-diffusion coefficients. Such a technique is described in this paper. As a test example the diffusion coefficient of gold is determined.


9 . .

f' i

2.1. Basis of the method

To determine a surface self-diffusion coefficient by mass transport, two conditions have to be fulfilled : (1) The initial surface shape should be simple in order to facilitate the mathematics of the shape evolution and (2) the driving force should be capillarity, because this force can be determined from measurable geometrical data. Both conditions are fulfilled only in a few cases, specifically, sinusoidal profile decay /5N6/ and the tip blunting technique /7//8//9//15//16/. The STM technique which we will describe can be considered as a new version of the tip blunting technique.

The microscope we used is a high stability bimorph



The phenomenon of the growth of micro-hills takes place on STM specimens. A hill or tip grows when the horizontal sweep is stopped and the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989838



--. .--p--

l : Shape evolution of a gold tip (hill) with time (300 K). STM micrograp hs.

(a) t = 0 (shape 95 minutes after hill formation). (b) t = 174 minutes.

voltage is varied in a special manner (details to be described elsewhere, see also /10/). The radius of curvature at the hill apex (summit) increases with time and temperature. In the case of gold tip growth occurs even at 300 K.

This increase in tip radius with time can be interpreted as a classical blunting of a conical tip /11//7//9/. The numerical value of the cone angle a, which is between 0 and 10" in classical experiments, is about 45" in the case of the STM hill blunting (Fig.4) (although the apparent angle is only about 15' (Fig.1)). Nevertheless, both shape evolutions are describable by the same equation for the surface diffusion coefficient D /11//7//8//9/ :

A, is a known constant which varies with the measurable cone angle a / I l l , y is the mean surface free energy of the solid, R is the atomic volume and v is the number of diffusing atoms per cm2 ( v = R - ~ / ~ ) . RI and R2 are the measured tip radii at times t l and t2, respectively.

2.2. lmaae errors and its correction

In order to determine hill apex radii (equ.1) three types of corrections are made which concern :

(1) profile irregularities, (2) a slope error and (3) the image distortion error.

Profile irreaularitie~

Hill profiles as in fig.1 show many small irregularities. The tip apex radii in equation 1 are mean radii and should not be confounded with the radii of such irregularities. Consequently the profile irregularities can simply be ignored here in a graphical manner (see fig.3 a and b) without a discussion of its origin (probably irregularities of the emitting regions of the STM tip).


tip positions to visualize A and B

Fia. 2 : Scheme the STM image.

1 1xP-l

-apparent distance AB

/ \

'\.--apparent hillprofile real distance \

I '\

of -the STM slope eiror. A distance as AB appears too large in

Fia. 3 : Examples of image corrections :

a) Profile with irregularities (see fig. 1) (which are probably artefacts).

b) The smoothed profile of (a) has an apex radius which is the basis to determine R for equation 1.

c) This profile has a typical slope error (see also fig. 1 and 2) : There are two minimum radii somewhat outside the hill apex and the apex radius appears as a maximum. Three arbitrary hill diameters are indicated by e l , e2 and e3.

d) Corrected hill of (c) : All hill diameters (el , e2,

. . . .

) are multiplied by A=0.8


Thus a profile is obtained which corresponds reasonably to a real profile (/7//13/, fig. 2 and 4). In particular the minimum radii are shifted to the hill apex.

The slope error

An error called "slope error" exist on sloped or rough surface regions of an STM specimen (illustrated in fig. 2). A strong change of the slope within a specimen must usually include a change of the emitting tip region. In such a case, the distance between two image points (as AB in Fig. 2) represents only the enlarged apparent distance, and not the real distance. A consequence of the slope error is a change of the hill apex radius in which we are interested. In the STM image the hill apex radius appears often


erroneous (fig. 1, 2 and 3c), i.e. as a maximum radius, while results on profiles of annealed hills indicate, that the apex radius is always a minimum /7//8//9/. This error ( a consequence of the slope error ) is here corrected in a graphical manner by reducing all hill diameters ( e l , e2,

. . . .

) by a factor A. A reasonable value of A is found by reducing systematically A until a profile is obtained (fig. 3d) which agrees approximately with the theoretical profile /7//8//9/. The value found in the example of fig. 3d is Az0.8. After (or before) the slope error correction it may be necessary to correct also the image distortion error as described in the following.

The imaae distortion error :

This error exists because the STM magnification is usually different in the two directions of the image plane (see coordinates in fig. l b and 4).


As an image distortion changes the apparent tip apex radius considerably, a correction is necessary. Fig. 4 shows examples.




Fia. 4 : Image distortion correction and apex radius determination : (a) Hill of Fig. l a after slope correction.

(b) Hill of Fig. l b after slope correction.

(c) and (d) Hills of (a) and (b), respectively, after distortion correction.

Dotted lines are circular arcs having apex radii as indicated.

By using the described corrections, the error in the determination of D (equ.1) can be considerably reduced. Nevertheless, the remaining error in D may be at present still


30 Oh , or even somewhat more. Such an error is tolerable since D is a quantity which varies over more than a factor of 10lO.

2.3. Test of a diffusion coefficient determination

With the radius of curvature obtained after making the two corrections



1200' 800' 600' 400' 300' K


I l l l

Q = 8 k cal /m01




8 - e

test result of this paper is compared to data obtained by sinusoidal profile decay (SPD) 151 and by the transmission electron microscope technique (TEMT) 1141.


(Fig. 4), the diffusion coefficient of gold is then determined by equation 1.

The data used for this determination are : T = 300 K, k = 1.38 X 1 0 - l ergldegree, y(Au) = 1400 erg/cm2 1131, A, = 37 / l l/ , C l = 11.8 x 10-24, v

- T~ (AU) ='1336'K this paper

1 I I I

= R - h'/, R1 ~ ~ = ~155 X 1 0 cm, R2 ~ ~ = 270 X 1 0 - ~ cm (Fig. 4) and t2


t l =

10.4 x103 seconds. The surface self-diffusion coefficient of gold thus obtained is D = 8.4 X 10-I !li cm2/sec, with an estimated error of


2.5 X

1 0 - A cm2/sec. This D value is compared in Fig. 5 with D values of gold determined by other methods. The fact that our STM value of D lies on the straight line extrapolation of the TEMT values indicates that the diffusion mechanism does not change between these two regions. Consequently the prefactor DO and the activation energy Q must be valid in both regions.

1 2 3 4 5

Trne~t / T



: The surface self-diffusion coefficient (D = Do exp(Q/kT) of gold. The

3. Discussion

The STM technique typically studies matter transport on surfaces having radii of curvature which are much smaller than those used in classical techniques to measure D (such as sinusoidal profile decay /5//6/

and tip blunting techniques / l 5/11 6//7//8//9/).

The important consequence is that the driving force for matter transport (capillarity) is much stronger in the STM experiments. The'refore, D values becomes measurable at temperatures which are lower than those usually used. In fact, D values become measurable which are more than

l o 5

times smaller than those measured by classical techniques (SPD, fig. 5). But


intermediate D values are measurable by rarely used techniques like the field electron microscope protrusion technique / 1 7 / 8 / and the transmission electron microscope technique (TEMT) 1141 (see Fig. 5).

In order to avoid misinterpretation, we point out that the studied diffusion concerns the crystal shape changing transport of atoms from kink sites across steps to other kink sites. This diffusion process is very different from the diffusion of atoms which impinge on a close-packed terrace and diffuse into neighbored terrace sites, as studied by field ion microscopy.

In any case, our measured value of D (8.4 X 10-15 cm2/s) seems to be the smallest mass transport surface self-diffusion coefficient measured so far, and even smaller coefficients may be measurable by the described technique. In this manner, it was possible (perhaps for the first time) to measure the D value of a metal at a relative temperature as low as :

TITm = 0.22 (Tmelt(Au) = 1336 K).

Finally, it is remarkable that the surface of gold at 300 K is already in a state of self-diffusion. Consequently, a piece of gold at room temperature should change its shape continuously towards a shape of lower free energy.

In practice, however, the driving forces (and therefore the matter fluxes, see Nernst-Einstein equation) are so small that macroscopically visible shape changes would require very long times, on the order of centuries or longer. But shape changes in the order of 102


occur on the time scale of minutes and thus can be visualized and measured by STM, as described here.


/ 1 I R.J. Behm in M. Grunze, H.J. Kreuzer and J.J. Weiner (eds) : Diffusion at Interfaces, Springer Verlag, Berlin 1987, p. 92-101.

I 2 l T.S. Lin and Y.-W. Chung : Surface Science 2pZ (1989) 539.

1 3 I J. Schneir, R. Sonnenfeld, 0. Marti, P.K. Hansma, J.E. Demuth and R.J. Harners : J. Appl.

Phys. (1988) 717.

1 4 l R.C. Jaklevic and L. Elie : Phys. Rev. Letters 6Q (1988) 120.

1 5 l N.A. Gjostein in "Surfaces and Interfaces " (eds : Burke, Reed and Weiss), Syracuse University Press, Syracuse, N.Y. 1321 0 (1 967) p. 271 -304.

1 6 l H.P. Bonzel in "Surface Physics of Materials" Vol. II (ed. Blakely), Academic Press 1975, p.


1 7 1 Vu Thien Binh, A. Piquet, H. Roux, R. Uzan and M. Drechsler : Surface Science 25. (1971) 348.

1 8 l M. Drechsler : Jap. Journ. Appl. Physics, Suppl. 2, Pt. 2 (1974) 25.

1 9 1 H. Roux, A. Piquet, R. Uzan, M. Drechsler : Surface Science (1976) 97-114.

11 0 1 A. Putrnann, B.L. Blackford, M.H. Jericho and M.O. Watanabe : Research Report, Dalhousie University, Halifax (unpublished).

I1lIF.A. Nichols and W.W. Mullins : J. Appl. Physics (1965) 1826.

11 2 1 B.L. Blackford, D.C. Hahn and M.H. Jericho : Rev. Scient. Instr.


(1987) 1 3 4 3 - 1 348.

11 3 l N. Eustathopoulos : J. Chim. Phys. 1 (1973) 43.

I 1 4 1 M. Drechsler, J.J. MBtois and J.C. Heyraud : Surface Science LQH (1981) 549.

11 5 l W.P. Dyke and W.W. Dolan : Advances in Electronics Vlll (1 956) 89-1 85.

l 1 6 l P.C. Bettler and G. Barnes : Surface Science LQ (1 968) 165.

l 1 7 1 A.J. Melrned : J. Appl. Physics (1967) 1885.

I 1 8 1 J. Bardon and M. Drechsler : Rev. de Physique Appl. 2 (1974) 989.


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