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ELECTRON EMISSION FROM SMALL MICROTIPS
J. Sáenz, N. García, H. de Raedt, Vu Binh
To cite this version:
J. Sáenz, N. García, H. de Raedt, Vu Binh. ELECTRON EMISSION FROM SMALL MICROTIPS.
Journal de Physique Colloques, 1989, 50 (C8), pp.C8-73-C8-78. �10.1051/jphyscol:1989813�. �jpa-
00229911�
COLLOQUE DE PHYSIQUE
Colloque C8, supplement au n o 11, Tome 50, novembre 1989
ELECTRON EMISSION FROM SMALL MICROTIPS
J. J. S~ENZ* , , N. GARC~A* , , H. DE RAEDT* * * and W THIEN BINH* * * *
*IBM Zurich Research Laboratories, CH-8803 Riischlikon, Switzerland
.
* Dept. Materia Condensada, Univ. ~ut6noma de Madrid, Cantoblanco,$Tf;28049 Madrid, Spain
Physics Dept., Univ. of Antwerp, Universiteitsplein 1, B-2610
y;;f
i jk, BelgiumDepartement de Physique des Materiaux (UA CNRS). Universite Claude Bernard
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Lyon 1, F-69622 Villeurbanne, FranceABSTRACT- Electron field emission calculations on atomic-size microtips are presented. Models inorporating the atomic size and the particular geometrical shape of the tip are proposed. Theoretical analysis explain the remarkable properties observed experimentally:
strong electron beam focusing and anomalous I-V characteristics. We present a first series of experiments and quantum mechanical calculations that suggest the possibility of atomic resolution in Electron Field Emission.
I
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INTRODUCTIONSmall microtips producing bright and very collimated electron-beams would be very valuable for electron microscopy, holography and interferometry /1,2/.
Three techniques are now available to produce such microtips: the deposition technique (ultra sharp tips) introduced by Fink / 3 / , the " b ~ i l d - u p ~ ~ technique and the pseudo-stationary profile (teton tips) introduced by Vu Thien Binh 4 The experiments with atomic-size tips have shown that the properties of the field-emitted electron beam differ markedly from those of beams emitted by conventional sources. The angular spread of the emitted beam is only of a few degrees (smaller than 6 O ) for total emitted currents & PA, both for ultra sharp tips /3/ and build-up and teton tips (Vu Thien Binh, to be published). However, there is a remarkable difference in the experimental I-V characteristics obtained with different techniques. While the buid-up tips show a normal Fowler-Nordheim behavior, the measured I-V characteristics of a teton tip show a clear deviation from the standard behavior 4 Both semiclassical /2/ and full quantum mechanical calculations (Garcia, Sdenz and De Raedt, to be published) have shown that the emisson from smooth tips having atomic-size radius of curvature can not account for the observed experimental results. Only if the electron source has a plane emitting surface (i.e. a plane triangular metal-vacuum tunnel barrier) it is possible to obtain a collimation of the electron beam consistent with the experimental results (Garcia, Sdenz and De Raedt, to be published).
The present study introduces a simple method to obtain the local field and equipotential lines around a small protuberance placed on top of a support tip. The local tunneling barrier associated to a teton-like tip geometry can explain the electron beam focalization and the anomalous I-V characteristics.
New results of full quantum mechanical sLmulations demostrate the possibility to achieve electron field emission with atomic resolution. New experiments, still to be confirmed by field ion microscopy, indicate that this is indeed the case.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989813
2
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LOCAL FIELD AND TUNNELING BARRIER CALCULATION. BEAM FOCUSINGDifferent fabrication methods yields tips having a different geometry and consequently the electron emission patterns will be different. In the case of tttetontt tips the experimental stationary profile consist on a small microtip erected on top of a support tip / 4 / . On the other hand, the "build uptt tips show a more or less smooth surface except very near the tip appex, where the atomic-size corrugation can be considered as an atomic size bump
4 In both cases, the presence of these protuberances would distort and compress the equipotential lines in the vicinity of the apex, causing a local field enhancement and an increase of localized emission / 5 / . For simplicity, we will consider in our calculations a hyperbolic shape for the macroscopic support tip (the main results do not depend on the exact shape of the support tip) In order to simulate a protuberance at the tip apex we can use the following trick, based on the superposition principle. Let us superpose the potential of the hyperboloid-screen system and the potential of a point charge placed near the tip apex. This new potential lead to a set of equipotential lines which, near the tip apex, resembles a teat-like geometry.
Provide the tip-screen distance is large enough, the new potential is still a solution of the Laplace equation and fulfit our boundary conditions, i.e., the equipotential which defines the screen is flat and, far from the tip apex, the tip equipotential has a hyperbolic shape. In fig. la we show schematically the basic arrangement of the model. The position and strength of the point charge can be adjusted to match an equipotential line to the protrusion/support-tip geometry. Figure lb illustrate the equipotential lines corresponding to the superposition of the potentials of fig. la. The influence of the image force on the equipotential lines is shown in figure lc. We have calculated the image force correction in an approximated way.
At eveky point we calculate the shortest distance, d, to the tip. Then, the image potential at this point is calculated as if it were at a distance d from a flat surface. The dashed lines define the limit of the tunneling region, i.e. the tip surface and the equipotential line at which the potential has drop the work function of the tip.
FIGURE 1. (a) Equipotential lines for a hiperbolic tip (50 radius of curvature, 2 cm tip-screen distance and applied voltage V=200V) and a point charge (dashed lines). ( b ) Equipotential lines corresponding to the superposition of the potentials given in (a). (c) The same as (b) including the image force correction. Dashed lines define the tunneling region.
The field contribution of the protrusion itself falls off very fast with the distance from the tip surface. At a distance of the order of the protrusion size, 6 2 , the equipotential lines are almost those of the support tip which, on a microscopic scale, has a large radius. Then, if the size of the protuberance is in the nanometer range, the equipotential line, defining the classical turning point of the tunneling barrier outside the tip, is almost flat (see fig. 1). Assuming a flat barrier, it can been shown (Gar~ia, sdenz and De Raedt, to be published) that for typical fields between 1 V/A and .25
v/&
the angular spread of the emitted current goes from 25O to 10' justoutside the tip. After the emission there is another focusing effect associated with the field in the free region between tip and screen /2,5/.
For typical applied voltages of several hundred volts the reduction factor can be of the order of 5 /2/. This angular spreading of less than 5O is in full agreement with the experiments / 3 / .
3
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I-V CHARACTERISTICS: EXPERIMENTS AND THEORYWe have carried out a new set of experiments employing both build-up and teton tips. The three-atom build-up tip is obtained by the standard procedure /4/ i.e. heating a clean (111)-W tlp under ultra-high vacuum in the presence of an applied electric field. A teat-like geometry (single-atom teton tip) is obtained by further sharping of the tip in a pure oxygen atmosphere 4 A three-atom apex can be obtained by taking off the outermost atom located at the centre of the three-atom layer of the protrusion. In this case we have the same apex configuration as for the build-up tip but with different geometrical arrangement of the supporting layers. For buid-up tips the I-V curve follows the standard Fowler-Nordheim (F-N) law. However, for the teton tips, deviations from this behavior are found, as exemplified in fig. 2a. In some cases / 4 / , teton tips can show a crossover in the I-V curve similar to that associated to the space charge effect /6/. However, as we will see, it can be intrerpreted as a result of the particular geometry of the teton tip.
FIGURE 2. Current-voltage characteristics of a teton-tip. (a) Experimental data (stars) deviate from the linear Fowler-Nordheim law (dashed line). Solid lice: theoretical results for a support tip having a radius of 400 A and a protrusion of heigh 20
h .
(bTheoretical I-V curves for a support tip of a radius of 400 and different protusion sizes.
We have we calculated the current density on the tip surface for different protrusion/support-tip geometries by means of a semi-classical approximation
/ 2 , 6 / . In all the cases analyzed, we have taken a fermi energy of 8 eV and a
work function of 4.5 eV which corresponds to a typical tungsten tip. In fig.
2b we show the results obtained for a support tip of a radius of 400
A,
with three different protusion sizes d z . As it can be seen, for small S z (which would correspond to the atomic corrugation of a build up tip) the I-V plot is almost a straight line. However, as 52 increases the deviation from the F-N behavior ks clear. Moreover, for some particular 5 z we obtain the crossover behavior observed in the experiments. In the case of a protruded tip and for low fields, the main contribution to the total current comes from the protrusion at the tip apex. As the field increases the emitted intensity begin to saturate mainly because of the image force.
At the same time, there is an increasing contribution comming from the support tip (with a lower field but larger emitting area). Eventually the support tip contribution dominates and there is a crossover in the F-N plot (fig. 2b).4
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IS IT POSSIBLE TO OBTAIN ATOMIC RESOLUTION ?FIGURE 3. Field Electron patterns of 111)-W : a Buid up tip with a three-atom apex. The applied voltage V = 1350V and emission current I = 5 lo-* A ; b) Teton tip with a Three-atom apex. The applied voltage V = 2100V and emission current I = 1.6 10-9 A ; c) Same as bg but now the applied voltage V = 2470V and I = 5 10- A
.
Aditional signalsoriginate from the atoms supporting the three top atoms; d) same as b) but in addition an adsorbed atom, indicated by the arrow, is present. The applied voltage V=2100V and emission current I
= 1.8 A.
In fig. 3 we present the experimental field emission patterns obtained for a three-atom apex buid-up (Fig.3a) and teton tip (Fig.3b) respectively. In the former case one, nearly triangular, spot resulting from overlapping signals of the three atoms is observed. The corresponding experiment for the teton tip clearly shows three circular, well-separated spots, the size of which increases with the applied field (for a one-atom teton tip only one spot is observed). Increasing the applied voltage more and more, the three-fold symmetry of the (111) direction, characteristic for electron emission of the atoms of the shank underneath the three top atoms becomes visible (Fig.3~).
In combination with the experimental observation of the deviation of the I-V characteristic of this three-atom teton tip from the Fowler-Nordheim law, this strongly suggests that each of the three main spots is an image of an
atom and not of some small facets. An additional test is to heat the teton tip to destroy the protrusion by surface diffus.ion and to monitor the field emission. Our experiments indeed show the expected clean (111) pattern of the support tip. Assuming the distance between the atoms at the apex is the same as in the bulk, the magnifaction factor is found to be 6 106
.
Foreach spot the angular spread is below 5.6O. The resolution achieved in this way can be employed to monitor the adsorption of an atom at the apex. This is illustrated in Fig.3d where we show a field emission diagram of atom (most likely oxygen) absorbed on the same three-atom teton tip. It is worth to point out that the current of the three-atom teton tip was constant over a period of five hours, occasionally interrupted by small reversible jumps caused by atoms adsorbed on the apex.
The conditions under which a 3-atom teton tip, such as the one described above, emits three separated waves are not known. Within the context of classical electrgdynamics, it was shown that under favorable conditions a resolution of 3 A can bg achieved /7/ In view of the small distance between the atoms ( s A F z 4.4 A for W ) and the small emitting areas ($AF) it is remarkable indeed the emitted wave packe'ts do not seem to merge. To investigate this problem theoretically it is sufficient to work in two spatial dimensions and to examine the conditions under wich the top atoms (two instead of three in this case) emit well-separated electron waves. To this end the time-dependent Schroedinger equation (TDSE) is solved by numerical integration 8 Analysis of the time development of the wave packets should then reveal which physical mechanism(s) control the resolution and other properties. As precise information about the electrostatic potential surrounding the teton tip is lacking, the calculations outlined above are used as a guidance to construct a potential which is both simple and has the main ingredients. The curvature of the electrostatic potential seem to be such that each atom sees a potential which has a minimum along a certain direction, depending on the position of the atom. Moving in a direction perpendicular to this preferential path, the potential increases rapidly (see fig. 1). This can be modelled by a constriction which has a size of the atom. This effectively limits the emission area. Each ons strict ion is titled by a certain angle to take into account the curvature of the equipotential lines at the tip apex. The distance between
Constrictions I
FIGURE 4. (a) Geometry of the 2D model of the teton tip used in TDSE simulations. (b) Real space probability distribution of the transmitted electron wave for an angle 8 = 30°. (c) the same as
(b) but without tunnel barrier.
constrictions is taken to be slightly larger than the atom separation (in the bulk) as the emission is not originated from the center of the atoms. The metal-vacuum tunnel barrier is assumed to have a plane triangular shape, properly tilted by the angle @ (see fig. 4a). In our simulations the slits are ~"&/2 wide and ~=&/2 long, their separation D=1.5
hF
and the slope of the tunneling barrier corresponds to a field of 0.33 v/I.Figure 4b shows a snap-shot of the transmitted electron probability distribution for a tilting angle of 8 = 30°. Two well-separated wave packets are observed. This is associated to the focusing properties of the plane triangular barrier. Without tunnel barrier the transmitted wave looks as one big packet with a lot of structure (see fig. 4b). On a screen placed at a macroscopic distance, such a wave packet would be seen as one big spot.
Simulations with other conditions have been carried out and lead to the same conclusion: The slit angle 8 necessary to observe two well separated electron beams is in the range of 20" and 30°. From the geometry of the teton tips these are very reasonable values. However, in the case of build-up tips ( 6 6
l o 0 ) ,
the spots should merge. The TDSE simulations suggest that theteton-tip geometry has all the features required to produce field-emitted electron beams with atomic resolution.
ACKNOWLEDGEMENT
We deeply appreciate extensive interactions with Dr. H. Rohrer. We are grateful to L. Escapa for helpful discussions. Work of N.G. and J.J.S. is partially supported by a joint agreement between the Univ. Auton. de Madrid and IBM Research Lab. Zurich. H.D.R would like to thank Control Data Corporation (The Netherlands) for a generous grant of computer time on the CYBER 205, the University of Leuven for providing unrestricted access to their IBM 3090-300/VF, and the Belgian National Science Foundation for financial support.
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