HAL Id: jpa-00225701
https://hal.archives-ouvertes.fr/jpa-00225701
Submitted on 1 Jan 1986
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
GEOMETRICAL ANALYSIS OF FIELD - ION IMAGES
M. Chandrasekharaiah
To cite this version:
M. Chandrasekharaiah. GEOMETRICAL ANALYSIS OF FIELD - ION IMAGES. Journal de Physique Colloques, 1986, 47 (C2), pp.C2-437-C2-442. �10.1051/jphyscol:1986267�. �jpa-00225701�
J O U R N A L DE P H Y S I Q U E
C o l l o q u e C 2 , s u p p l h e n t au n 0 3 , Tome 47, m a r s 1986 page c z - 4 3 7
GEOMETRICAL ANALYSIS OF FIELD - ION IMAGES
M.N. C H A N D R A S E K H A R A I A H
Materials Science Section, Department of Mechanical Engineering, Twente University of Technology, N L 7500 AE Enschede,
The Netherlands
Abstract - Field - ion microscopy (FIM), transmission electron microscopy (TEM) and computer simulation techniques have been used to experimentally investigate the field - ion image geometry. Electron micrographs and electron diffraction patterns were obtained from tungsten specimens after controlled amounts of field evaporation. From a knowledge of the changes in the image dimensions as a function of the variation in the tip radius and the tip profile from the electron micrographs, an attempt has been made to define the projection point and the ion trajectory. The information has been used to obtain computer simulated patterns and the results are discussed.
I. INTRODUCTION
In field - ion microscopy, a knowledge of the exact profile of the field evaporated end form of the specimen and the projection geometry are extremely important for quantitative study of interface structures. Most of the earlier Qork was based on the assumption that the tip was hemispherical and that the projection was stereographic. These were soon realised to he approximations and several emperical equations and geometrical relations were developed (1-4). However, none of them considered the tip geometry and the image projection as a function of field evaporation sequence. This paper aims to show that TEM and FIM can be conveniently used to gain a better insight into the tipe profile and the projection geometry.
11. EXPERIMENTAL
Tungsten specimens (Nos. 1 and 2) were prepared and were first examined in the FIM.
When an observable image was formed on the screen, the specimens were removed and examined in the Philips EM - 300 TEM at the highest possible calibrated magnification of 202,000 X. The specimens were tilted to obtain the <001>
orientation normal to the tip axis and the images and diffraction patterns were recorded. Similar recordings were made by tilting the specimen to the maximum possible extent in the positive and negative directions to get a three dimensional profile of the tip. The specimens were then transferred to the FIM and careful field evaporation was carried out. After a certain number of layers of evaporation, they
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986267
C2-438 JOURNAL DE PHYSIQUE
were again transferred to the TEM and the procedure was repeated; once for Speci3en 1 and twice f o r specimen 2.
SPECIMEN - 1
[0011 orientation. +42'
a. F b. C.
Semi cone angles: 16.5' 22.25' 2 0'
F i g . 1. Electron and f i e l d - ion micrographs of specimen 1. Note the variation in the tip profiles and the ovality of the central (110) rings.
SPECIMEN - 1
After evaporation of 150 - (l 10) layers
[Ooll orientation, +42' tilt.
r
r-45r
a. b. C.
Semi cone angles: 13.25' 17.25" 15.5'
Fig. 2. Electron and field - ion micrographs of specimen 1 after field evaporation.
The tip profiles are becoming uniform.
11. RESULTS
Figure 1 shows the electron micrographs and the field - ion micrographs obtained before and after the initial TEM examination on specimen 1. Fig. 2 shows the electron micrographs and the field - ion image after the evaporation of 150 - (110)
layers. The results of field evaporation studies are represented in Fig. 3(a) for specgmen 1 and in Fig. 3(b) for specimen 2 respectively.
The tip height in the specimen holder was initially measured using an optical microscope and the tip to screen distance was noted. The positions of I2001 poles were noted after enlarging the negatives to the exact size of the screen. The pole positions on the electron micrographs were marked from an analysis of the electron diffraction patterns. This method was considered to be more accurate than the geometrical approach (5) or the relationship based on the measurement of distances on the field - ion micrographs (6). The projection points were determined by assuming straight line relationship from the observed {200} pole positions to those determined by electron diffraction on the tip profiles. Such an assumption has been shown to be valid both experimentally and theoretically (7,4).
It is apparent from Figs. 1 and 2 that the tip profile is far from spherical. The pole normals do not intersect at a point along the tip axis and hence, defining the tip centre is not exact. As an alternatiue, the cone half - width at the tip apex was represented as R and was evaluated to be 178 A for tl\e initial position at A and 346 A for the final position at B for specimen 1. The ratios of these widths with the projection distances are 4.15 and 4.86 for specimen 1 and 3.39 and 4.04 for specimen 2. The corresponding N values are 3.15, 3.86, 2.39 and 3.04 respectively.
(b)
Channel Plate
.- P d e posltlot. rvaporation of 1 2 0 - (110) lab I tip a t A.
S - Initial pole positions. ? = 3 2 0 A hi
R = 1 7 8 h N = 315.
e - Pole posltlons after evapr ,Ion I 5 0 - ( 110) layers.
ker evaport.
a y e r e from tip .
Fig. 3(a) Tracings oi i m - 2 pole positions
after field evapora- 9f 150 1
Fig. 3(b) Tracings of the t i p 'iles and the f i e A i - ir image pole positions after field evaporation of 'ayers for specimen 2
SOURNAL DE PHYSIQUE
The field evaporated tip shows a displacement of 6.78 m for specimen 1 and 13.5 mm for specimen 2 which agree exactly with the calculated values of 150 and 300 - (110)
interplanar spacings for tungsten at a magnification of 202,000. Similar detailed analysis could not be conducted in the region A-B for specimen 2 because of its extremely sharp and uneven tip surface.
IV. DISCUSSION
The uncertainties associated with unambiguous identification of the tip profile and the image projection stem from (a) the tip asymetry, (b) the deviation from a spherical surface, and (c) the shift in the point of projection.
Irrespective of the initial end forms, the specimens tend to achieve an equilibrium shape after certain amount of field evaporation. This is clear from the electron micrographs shown ing Fig. 4. Specimen 1 was examined after 150 layers of evaporation when the best image voltage was 20 kV and specimen 2 after 420 layers of evaporation at a best image voltage of 11.4 kV. Detailed analysis of the profiles revealed the two surfaces to be exactly parallel to each other inferring that at a constant best image voltage, the tip profiles of <loo> oriented tungsten specimens will be identical within the limited volume that contributes to the image (approx.
60-100 A normal to the tip apex). This equilibrium shape is not spherical and tends to have a flattened apex confirming the earlier observations (8). The corresponding (110) rings in the field - ion image tend to have an oval shape, the ovality depending on the asymmetry in the tip itself (cf. Figs. 1 and 2). This deviation from the circular shape can be used as a measure of the tip asymmetry.
The deviation from a spherical cap at the apex renders stereographic projection (N = 1) to be a rough approximation to the field - ion image. While Brandon (9) proposed a projection based on N = 2, Southworth and Walls (6) reported N to be varying from 0.5 to 5 and an experimentally observed value of 0.8. However, it is clear from Fig. 3 that the projection point shifts as the tip surface enlarges and
Specimen - 1
a. b.
Initial Final
Specimen - 2
C. d.
Initial Final
Fig. 4 . Electron micrographs of specimens 1 and 2 before and after field evaporation. Note that final profiles are parallel within the limited volume
contributing to the image.
Fig. 5. Field - ion images from three tungsten specimens with varying symmetry.
Fig. 6. Computer simulated patterns with varying projection points.
R = 150 a, P = 0,02 a.
JOURNAL DE PHYSIQUE
thus, N tends to decrease as the field evaporation continues. Thus, a quantitative estimation of the deviation from the stereographic projection is possible only through a linear measurement of distances between the poles on the field - ion
micrographs. Computer simulation can be used as a convenient tool realising, however, that the spherical shape is only an approximation.
Figure 5 shows three different field - ion micrographs with varying symmetry and Fig. 6 shows three computer simulated patterns with N = l (stereographic), N = 2 (Brandon) and N = 4. The linear distances for the various poles shown in the stereogram were measured and normalised with respect to the distance for the smallest angle of 26.57'. Such an approach is justified because all projections show a linear relationship upto about 25ee (2). The results are shown in Table 1. It is evident that at higher angles (45 and above) stereographic projection (N = 1) deviates considerably from the field - ion image while N = 4 shows a very good agreement. However, an exact fit is possible only when the linear distances and the ovality of the central (110) rings are taken into account to define the tip envelope.
I I l Computed Patterns I Field - Ion Micrographs I
ACKNOWLEDGEMENT
Poles
(1 10) - (130) ( 1 1 0 ) - ( 2 1 1 ) (110) - (121)
( l 10) - (222) ( l 10) - (020) ( l 10) - (112)
(1 10) - (101)
(110) - (011) ( 1 10) - (130)
Fig. d
The author wishes to thank Prof. B.H. Kolster for his encouragement. Part of the experimental work was done at the Department of Metallugy & Science of Materials, University of Oxford and the author is grateful to Dr. G.D.W. Smith and T.J. Godfrey for help and assistance.
. all distances in mm.
Angles
26.57*
30- 30- 35.17' 45O 54.73' 60"
60' 63.45
REFERENCES
Fortes, M.A., Surface S c i . 2 (1971) 95.
Wilkes, T.J., Smith, G.D.W. and Smith, D.A., Metallography, 7 (1974) 403.
Bolin, P.L., Ranganathan, B.N. and Bayzick, R.J., Phys. E: sci. Instr. 9 (1976) 363.
Smith, R. and Walls, J.M., J. Phys. D: Appl. Phys.g(l978) 409.
Barsotti, T., Bermond, J.M. and Drechsler, H., J. de Physique, z(1984) C9-43.
Southworth, H.N. and Walls, J.M., Surface Sci. 75 (1978) 129.
Lewis, R., Godfrey, T.J. and Smith, G.D.W., 20th Int. Field Emission Symp. 1975.
Loberg, B. and Nordsn, H., Ark. F y s . 2 (1969) 383.
Brandon, D.G., J. Sci. Instr. 5 (1964) 373.
N=2
18.3 20.55 20.55 24.28 33.81 37.31 40.86 40.86 42.94 N = l
Calculated 18.3 20.57 20.57 24.47 31,71 39.72 44.15 44.15 47.41
-
Computed 18.3 20.52 20.52 24.4 31.73 39.68 44.18 44.18 47.38
