Surface energies and surface structure of small crystals studied by use of a stem instrument

587

Surface Science 114 (1982) 587-606 North-Holland Publishing Company

SURFACE ENERGIES AND SURFACE STRUCI’URE OF SMALL CRYSTALS STUDIED BY USE OF A STEM INSTRUMENTJ.M. COWLEY Depurtment O/Ph.vsics, Armmu Received

14 August

St&e Unioersr(s. Temp.

198 I : accepted

for publication

Anzom~ M-787. USA

5 October

I98

1

The surfaces of small regularly-shaped crystals of MgO and NiO have been examined by use of a scanning transmission electron microscopy (STEM) instrument. Images of the surfaces obtained with diffracted electron beams show surface detail with high resolution. Microdiffraction patterns obtained with beams of 15 A diameter from small crystals having one flat face parallel to the beam show the effects of the interactions of the electrons with the potential field of the crystal and of diffraction and channelling at the surface. Electron energy loss spectroscopy (ELS) of beams which have traversed flat surfaces of the crystals show energy losses due to the excitation of surface states and also energy losses associated with the generation of radiation as the electron beam enters and leaves the crystal potential field and as it is channelled along the surface by diffraction and refraction effects.

1. Introduction

Scanning transmission electron microscopy (STEM) instruments offer important new means for the study of the surface structures of crystals. Particularly when adapted to allow easy observation and recording of diffraction data [l] they offer the combination of high resolution imaging, microdiffraction from extremely small specimen areas and microanalysis using electron energy loss spectroscopy (ELS). These techniques can be applied to the investigation of the structure and energetics of crystal surfaces using either the transmission mode for very thin films or the reflection mode for the surfaces of large crystals or bulk specimens. Here we will consider applications of a STEM instrument, used in the reflection mode, to studies on small crystals of MgO and NiO. The imaging of surfaces by the use of diffracted electron beams formed at crystal surfaces with the grazing-incidence RHEED (reflection high energy electron diffraction) geometry was explored in this laboratory a number of years ago using a fixed-beam transmission electron microscopy (TEM) instrument [2]. Difficulties of the standard TEM instruments include the relatively poor vacuum, the high specimen contamination rates and the lack of means for specimen heating, cooling or other treatment. With a special ultra-high vacuum 0039-6028/82/0000-0000/$02.75

0 1982 North-Holland

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TEM instrument, special equipped for surface treatment, the group at Tokyo Institute of Technology have made spectacular progress in studies of semiconductors surfaces [3]. The HB5 high resolution STEM instrument from VG Microscopes Ltd. was seen as potentially an ideal instrument for surface studies. The vacuum in the specimen chamber is of the order of lop9 Torr. There is sufficient access to the specimen to allow heating and other specimen treatments to be arranged, although this has not yet been done in our case. The high resolution’imaging by the scanning method can readily be combined with microdiffraction from regions of the surface 10 A or less in width and with ELS from areas of the same size. In practice images of surfaces of MgO smoke particles and of bulk MgO crystals have been obtained with a lateral resoluton of 10 A or better although, because of the small glancing angle of incidence (usually much less than 10 - ’ rad) the image is heavily fore-shortened in the beam direction [4]. Surface steps which appear to be no more than 2-3 A high are clearly seen. The geometry and diffraction conditions necessary for the imaging are established by observation of microdiffraction patterns which are observed and recorded by means of an optical analysis system attached to the STEM instrument [5] and involving an image intensifier for the diffraction pattern formed on. a fluorescent screen followed by a low-light-level TV camera with video-tape recorder. Alternatively, any part of the diffraction pattern can be chosen for energy analysis by use of the ELS spectrometer. Spectra from chosen diffracted beams have been obtained and have shown evidence for surface states [4]. However, the quality of these spectra has not yet been vety satisfactory because the requirement is that electron beams of diameter 20A or less be held stationary on crystal surfaces over the extended periods of time required to organize and record the ELS spectra with low beam currents. Under these conditions the requirements on specimen stability and cleanliness are extreme. Greater success has been possible when the ELS spectrum is recorded in the selected-area diffraction mode in which a large area of the specimen is irradiated [6]. Recently, it has been shown that much greater sensitivity to surface states

Fig. I. Diagram suggesting the ray paths for an electron traversing the face of a small crystal either being deflected by the external potential field or being channelled along the surface. reverse arrows (right to left) indicate the equivalent configuration used in practice.

and The

may be achieved in microdiffraction [7] and ELS [8] if the surface is aligned exactly parallel to the incident beam so that the beam runs along the surface with a minimum of penetration into the crystal (see fig. 1). In the microdiffraction patterns, as the distance betwen the axis of the incident beam and the crystal face is decreased, there is initially a deflection of the central spot of the pattern by the extemaf potential field. Then, as the beam is deflected enough to strike the crystal face at, or near, the Bragg angle for reflection from the

surface planes, extra spots appear in the pattern [7]. In the O-50 eV energy loss range the ELS spectrum from a beam which has traversed the crystal surface shows features quite different from those observed in transmission through a thin crystal Some of the maxima correspond to the excitation of surface states. Others have been associated with the generation of radiation which is emitted when, the incident electrons interact with the potential field of the crystal [8]. Additional information can be obtained by combining dark field imaging with the microdiffraction or ELS observations. Images may be recorded with a detector placed at the position in the microdiffraction pattern corresponding to either the displaced central spot or one of the extra spots generated at the surface [7]. The dark field images formed in this way can show the width of the region at the edge of the crystal giving rise to these spots and the variation of the intensity in each spot as a function of crystal thickness. Images recorded with different energy losses are dark field images which show the localization of the energy-loss processes at the crystal surface and the variation of the intensity of energy loss electrons with crystal thickness or other parameters.

2. Experimental methods

The magnesium oxide crystals used were formed by burning magnesium in air and collecting the smoke on bare copper grids. The use of carbon supporting film and carbon micromesh supports was avoided, because these appear to be sources of conta~nation. Specimens formed under conditions of normal atmospheric humidity (5-20s) showed mostly weIl formed cubic crystals with smooth flat (100) faces although for the larger crystals (1 pm or more in diameter) the edges were often rounded off with the formation of steps, bounded by (100) type faces and having widths of the order of lOOA 141.For relative humidities greater than about 20% the crystals were often less perfect cubes and the surfaces showed etch pits having dimensions of the order of 20 A PI. The nickel oxide samples used were kindly supplied by Dr. P.S. Turner of Griffith University, and were formed by vapor phase recrystalhzation of Ni0 in the presence of silica. The crystals are octahedral in shape with smooth (I I 1) faces and have dimensions up to about I pm. [lo]. Spectroscopic evidence

shows an average silicon content of 200 ppm. It has been suggested that a relatively high content of silicon at the surface is responsible for stabilizing the (111) faces and producing the octahedral shape. All the observations of these materials reported here were made with the HB5 STEM instrument. Most of the images were obtained using a small mirror in the optical system to reflect light from a selected part of the diffraction pattern into a photomultiplier. Energy loss images were obtained using the conventional bright field STEM detector, which follows the energy analyser, after the crystals had been aligned by observation of the diffraction pattern by use of the optical system. Usually, for the imaging of surface structure an objective aperture size of 60 ym was used giving a beam convergence angle of 2 X lo-* rad and a beam diameter of about 5 A at the specimen. The diffraction pattern was then a convergent beam (CBED) pattern in which strong reflections appeared as short bright lines [4]. With the incident beams close to the edge of a crystal two parallel lines often appeared corresponding to the surface reflection and the transmitted diffracted beam which was less deflected by refraction at the surface and so appeared further away from the incident beam position. The detector mirror in the optical system could then be set to collect the light from the surface reflection only. Microdiffraction patterns obtained with the incident beam parallel to a crystal face were observed by use of the low-light-level TV camera associated with the optical system and were recorded by use of a video-tape recorder. For most diffraction patterns (e.g. fig. 3) a 10 pm objective aperture was used to give a convergence angle of about 3 X 10e3 rad *and an incident beam cross-over diameter at the specimen of about 15 A. Series of diffraction patterns were recorded on videotape as the incident beam was moved from the vacuum on to the crystal. The total movement of the beam, in a period of a few seconds, was of the order of 50 A. Playing back the patterns from the video tape allowed the changes in the diffraction pattern for beam movements of 1 A or less to be followed. For the recording of ELS spectra, the crystal was first aligned by observation of the diffraction pattern, using the optical system so that the incident beam was exactly parallel to a crystal face and, usually, parallel to a principal crystallographic axis. The entrance aperture for the spectrometer was then inserted and positioned to receive the appropriate part of the diffraction pattern and the spectrometer magnet was energized. It would, in principle, be preferable to record the ELS spectrum from each part of the microdiffraction pattern since the different spots represent electrons which have followed different paths along the surface. This is marginally feasible because the signal strengths are small, requiring long recording times, and the requirements for specimen stability and cleanliness are extreme. The only apparent source of contamination in our microscope is that from organic material, introduced with the specimen, which migrates over the specimen

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surface to the electron-irradiated area. Devices designed to clean the specimen in situ have not yet been installed and specimen contamination is often a problem for critical experiments of this type. For initial experiments therefore an alternative system was used. If the whole of the diffraction pattern given for any particular incident beam position were to be collected and fed into the ELS spectrometer the signal strength would be much greater. However the use of such a large entrance aperture for the spectrometer would seriously degrade the energy resolution. Hence an arrangement was used which is equivalent to this, as seen by the reciprocity relationship [ ii]. No objective aperture was used, so that the angle of convergence of the incident beam was very large and a very small aperture (10 -3 rad) was used for the input to the spectrometer. This is equivalent to reversing the ray-paths of fig. 1 so that electrons converge from a large range of angles from the right and a small aperture selects a very small range of outgoing beam positions on the left. Then, when the axis of the incident beam is positioned with respect to the crystal face and the ELS spectrum is recorded with. the small entrance aperture, the result is identical with that when a narrow incident beam is used and the energy analysis is made of the whole diffraction pattern. An important benefit of this scheme is that a large specimen area is flooded with electrons because of the effects of spherical aberration of the objective lens on off-axis beams and contamination of the specimen by migration of organic materials along the surfaces is very effectively eliminated.

3. Observations on MgO Images of the surfaces of MgO smoke crystals, such as fig. 2~ show the faces to be smooth and flat with surface steps no more than a few A in height. This picture was obtained by detecting the (600) diffracted beam. If the crystal is aligned so that one (100) face is exactly parallel to the incident beam, a bright field image such as fig. 2b is recorded. The incident beam here is close to the [ 1IO] direction so that the crystal acts as 90” wedge with the beam making an angle of 45O with the incidence surface. The corresponding thickness fringes are visible at the thin end of the wedge. The small bright rectangle is the marker used to indicate the position of the beam when the scan is stopped. From the known geometry of the crystal, the thickness of he crystal at the beam position can be calculated readily. For crystals in the [ lOO]orientation, no wedge shaped regions are visible in the images since the beam is parallel or perpendicular to all faces. The crystal thickness can then be inferred if it is assumed that the crystal approximates to a perfect cube with all dimensions equal. The series of microdiffraction patterns of fig. 3 was recorded with an objective aperture size of 10 pm and a beam diameter at the specimen of about

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Fig. 2. Images of MgO smoke crystals. (a) A reflection image obtained with the (600) dlffracted beam of one face of a crystal showing a few surface steps. (b) Bright field STEM image of a crystal aligned in the [1 IO] orientation. The small white rectangle indicates the position of the mcident beam when the scan is stopped.

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Fig. 3. Series of microdiffraction patterns obtained as a beam of diameter about I5 i and parallel to the [ IOO]direction and the (100) face of a crystal of MgO smoke. Total beam movement, about 30 A. For (a) the beam is just missing the crystal and for (f) it is Just inside the crystal.

15 A. The incident beam is almost parallel to a [loo] axis and the crystal thickness is estimated to be 3OOOi. The patterns were obtained as the beam was moved progressively from the vacuum into the crystal with a total translation of about 30 A. They were recorded on video-tape and played back, one frame at a time. Most of the graininess of the back-ground results from noise generated in the recording system. The black flares associated with high intensity spots result from overloading of the TV system. For fig. 3a the incident beam does not hit the crystal but is deflected by the potential field of the crystal to give a strong displaced central spot. The beam path may be as represented by the upper path line of fig_ 1. For figs. 3b to 3e the incident beam is bent to strike the crystal at the Bragg angle for the (200) reflection. Diffracted beams leaving the crystal can not escape because the (200) Bragg angle is less than the critical angle for total internal reflection [ 121. The electrons are therefore reflected back by the potential field to strike the surface again at the Bragg angle. The electrons are thus channelled along the surface with alternate diffraction in the crystal and reflection from the potential barrier in the vacuum. When they eventually reach the rear face of the crystal they meet the potential barrier at right angles and so can surmount it readily.’ Diffraction in the crystal gives rise to a deflected incident beam, now in the (TOO)position, and diffracted electron beams with the (200) reflection

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b

c

Fig. 4. Series of ELS spectra obtained as the electron beam is moved progressively closer to the (100) face of a MgO smoke crystal. The numbers on the curves in (b) indicate the sequence in which the curves were obtained. The path length of the beam across the crystal face was 3500 A for (a), 4900 A for (b) and 6800 A for (c).

displaced to the (100) position. Other fine detail appears in the intensity distribution of the patterns as a result of coherent edge interferenceqeffects [ 131. Finally, with the incident beam travelling more than about 10 A inside the crystal. the usual transmission diffraction pattern (fig. 3f) is seen. The intensities of the extra spots in the diffraction patterns, the flare on the central spot and the spots at the (100) and (iO0) positions, vary with the crystal thickness in a way which may be predicted by use of a simple geometric optics theory with an assumed form for the variation of the potential perpendicular to the crystal surface 171.The thickness variation may best be seen, for orientations other than [IOO], by observing the dark field images recorded with the detector placed at the extra spot positions [7]. The ELS spectra of fig. 4 were obtained with much the same geometry as the microdiffraction patterns of fig. 3. Each set of curves represents the series of ELS spectra obtained as the beam was moved, in steps of a few A, from the vacuum into the crystal. As explained previously, no objective aperture was used but the entrance aperture for the spectrometer was small. Each spectrum

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therefore is equivalent to the energy analysis for the whole of one of the diffraction patterns of fig. 3. The energy resolution of the spectrometer was roughly 1 eV and each curve was recorded in 10 s. The exact spatial position at which each curve was recorded could not be determined with sufficient accuracy for meaningful comparison with theory, since it was evident that large changes in the ELS curve could result from beam movements of l-2 A. Because of this sensitivity to beam position and also because the signal levels were low, the curves were often noisy. If slower recording had been used to obtain smooth curves, the total recording time would have been excessive in view of possible specimen drift and the limited, although good, mechanical and electrical stability of the instrument. The ELS spectra obtained in this way show marked differences from those obtained in transmission through thin crystals, Spectra which we obtained in transmission were in agreement with those of Venghaus [14] in showing one strong peak at 20.5 eV and weak maxima at about 8.5, 11.8, 15.8, 22.3, 24.8 and 33 eV. From his energy loss curve, Venghaus calculated the imaginary part of the dielectric constant, Ed, which had maxima at 8.5, 10.5 and 13.0 eV. Cohen et al. [ 151 have shown that these maxima correspond to interband transitions of the MgO bulk structure. From the many spectra obtained from the surfaces, the predominant maxima were found to occur at 6.7, 11.6, 16.6, 20.5, 24, 29.5 and 35 eV. In addition, individual curves showed many smaller maxima. Some of these were undoubtedly due to noise. Others appeared at positions dependent on the distance traversed by the beam across the crystal surface, as discussed below (section 5). In order to determine whether these small peaks occurred consistently and so could be considered as characteristic of the MgO surface, the histogram of fig. 5 was plotted, showing the number of observations of peaks at particular energy losses. The number of observations is sufficient to decrease the effects of random noise and the number of thicknesses involved is sufficient to smooth out any thickness dependent effects. It is probable that in addition-to the main peaks listed above and indicated in fig. 5 there are energy loss maxima at about 3.7, 4.9, 9.3, 13.2, 15.2, 19.4, 21.5, 27.3, 36.5 and 40 eV.

Fig. 5. Histogram showing the numbers of observations made of small peaks in the ELS spectra of MgO surfaces having the particular energy losses in the range O-40 eV, superimposed on a curve representing the positions and approximate relative intensities of the main, broad peaks of the spectrum. The upper diagram represents the positions and approximate relative intensities of peaks in the ELS spectrum obtamed by transmission.

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Of the main peaks, that at 20.5 eV is usually quite weak and may be attributed to the bulk plasmon loss. That at 11.6 eV may correspond to the bulk interband transition, but because of its much greater strength relative to the small peak in-the transmission spectrum, this may also be due to a surface

Fig. 6. A series of images of a crystal of MgO smoke aligned with the incident beam in the [ IOO] direction, obtained with electrons which had lost the amounts of energy, in eV, indicated. The transmitted intensity is seen to be greatest for energy losses around the bulk plasmon peak at 20.5 eV. The itensity from the crystal face parallel to the beam is a maximum (for thickness > 1000 A) for losses of IO- 12 eV and 14- 17 eV.

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plasmon. The 6.7 eV peak lies below the bulk band gap and so may be attributed to a surface state or an exciton. The most prominent of the unexplained peaks is that at 16.6 eV. This broad maximum which dominates many of the spectra has been attributed to the generation of radiation associated with the oscillating motion of electrons being channelled along the surface, as suggested in fig. 1 and discussed further in section 5, below. The order in which the various ELS spectra appear has been indicated in fig. 4b. As the beam approaches the crystal, the first curves recorded show a relatively smooth decrease with energy loss; then the maxima in the lo-20 eV loss range appear and become stronger. Finally, with the beam striking the crystal, the zero loss peak falls rapidly in intensity and the spectrum begins to resemble that for transmission. For several crystals, aligned with one (100) face parallel to the axis of the incident beam, series of images were obtained using electrons which had lost particular amounts of energy in the range0 to 30 eV. Such a series is shown in fig. 6. The bright line along the edge of the crystal in each case shows the variation of the probability of the corresponding energy loss with thickness. For the bulk plasmon energy loss of about 20 eV, the electrons transmitted through relatively thin parts of the crystal show a maximum of intensity, and the thickness fringes show a maximum of contrast, as expected from the non-localized nature of the volume plasmon excitation. The overall intensity of the line along the crystal edge shows a maximum at about 12 eV, as would be expected for the generation of a surface plasmon, and also at 16-17 eV.

4. Observations for NiO The small NiO crystals appeared to be predominantly octahedral with well formed (111) faces, although for most crystals the corners of the octahedra were flattened off, and in many cases clear deviations from the octahedral shape occurred with other bounding planes (fig. 7a). Care had to be exercised in the selection of crystal faces of well defined geometry which were sufficiently flat. In some cases, crystals which appeared to be near perfect octahedra when seen in silhouette in bright field images, were shown by reflection dark field imaging to have faces parallel to the beam which deviated strongly from the ideal shapes. Also the faces were frequently broken up by quite large ridges and hollows (fig. 7b). However, in a number of cases it was possible to find faces which appeared to be flat within a few A (fig. 7c) with outlines sufficiently clear to allow reasonably accurate estimates of the lengths of the beam paths across the face. With one crystal face aligned to be exactly parallel to the incident beam axis, the sets of microdiffraction patterns, recorded as the beam was moved

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from the Fig. 7. Images of NiO octahedral crystals obtained using electron bean ns diffracted surfaces. For the low-magnification image (a) the transmitted diffracted bes km was also detectes d so that the thinner parts are bright. For (b) there are bumps and dips on the surface but for (c) the surface steps are no more than a few A in height.

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a

20eV

b

C

Fig. 8. Series of ELS spectra,

all on the same energy loss scale. obtained with a beam parallel to a as the beam is moved towards the face is indicated by the numbers in (a). The path kngth of the beam across the face is estimated to be 1600 A for (a), 3800 A for (b) and 9600 A for (c).

(1II) face of a NiO crystal. The sequence of curves obtained

from the vacuum on to the crystal, showed much the same behavior as those of fig. 3 for MgO. The energy loss spectra recorded with the beam axis parallel to a crystal face were similar in general form to those recorded for MgO, but quite different in detail (fig. 8). Also, they differed strongly from the ELS spectra obtained in transmission through thin crystals, which showed strong maxima at 5.5, 21.2 and 3 1.6 eV and weaker maxima at 7.9, 11.9, 26.4, 29, 39.5 and 47.2 eV. Peaks at these positions appeared weakly in some of the spectra from the surfaces, but with the beam parallel to the (111) surfaces the predominant energy loss peaks appeared at 3.1, 4.3, 10.7, 12.4, 14.2 and 20.4 eV, with weaker peaks at 6.7, 7.9, 16.5, 25.2, 27 and 30 eV.

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Balabonova and Stepin [ 161have identified a bulk plasmon peak at 22.3 eV, corresponding to our observation of a peak at 21.2 eV, and peaks due to interband transitions at 7.5 and 36 eV. It is not known to what extent the surface spectra are affected by the possible presence of silicon at the surface. Silicon is known to have well-defined bulk and surface plasmon peaks at 16.6 and 10.8 eV [ 171,respectively. Peaks at both of these locations appear in the spectra, but even if the silicon, which is known to be present in the NiO, is concentrated at the surface it would presumably have a local environment sufficiently different from that in bulk silicon to ensure large deviations from the energy loss spectra of pure silicon.

5. Energy losses by electrons at surfaces For an electron traversing a crystal face along the paths of fig. 1, the interaction with the crystal may be divided into two components. Firstly, the electron enters and leaves the potential field of the crystal at the incident and exit edges of the crystal face. Secondly, those electrons which are deflected so that they strike the crystal face at the Bragg angle for reflection from the lattice planes parallel to the surface will be channelled along the surface, being alternately Bragg-reflected within the crystal and reflected by the potential barrier outside the crystal. Each of these components of the interaction involves acceleration of the electrons and therefore the emission of electromagnetic radiation, analogous to synchrotron radiation. The production of such radiation in relation to the transmission electron microscopy of crystals has been discussed by Humphreys [ 181 and radiation of this sort has been observed by Alguard et al. [ 191. However, a much stronger source of radiation is present as a result of the modification of the electromagnetic field of the electron by the polarization of the crystal. This is the transition radiation, usually discussed in relation to Cerenkov radiation.[20], which has been explored in detail for the case of an electron transmitted through a thin film [21,22]. Much of the discussion of this type of radiation has referred to high energy (MeV) particles. Recent references in relation to electrons of electron microscope energies (20-100 keV) are mostly confined to discussions of the radiative or non-radiative modes of surface plasmon excitation [23]. The strength of this transition radiation for the transmission case, relative to that due to acceleration by the average inner potential of the crystal, may be assessed from the simplified picture involving the destruction and creation of the dipole made up of the incident electron and its image in the crystal surface [20]. Because, in effect, a charge is accelerated from rest by the full energy of 100 keV rather than by the inner potential of about 10 eV, the transition radiation should be about lo4 times stronger. Because the calculation of the transition radiation for electron paths along the surface of a crystal, as in fig. 1, is a complicated and, as yet, untreated

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problem, we consider instead the much simpler problem of the synchrotron type of radiation and the consequent energy losses. Since the time variation and spatial variations will be much the same in the two cases, the resulting predictions as to the magnitudes of the energy losses and forms of the energy loss peaks will be very closely similar and only the relative scattering probabilities will be greatly different. For an accelerated electron, the intensity of the emitted radiation of frequency o per unit solid angle is given by Jackson [24] as -=-

[ iw ( t- *)]

nX(nXfi)exp

dt[,

where n is the unit vector in the direction of the detector and /I is the velocity vector of magnitude u/c. For the first of the two components of the acceleration, the double pulse at the crystal edges, we may write B(t)

=&-z+y(t)e,

where ‘(‘I I _1

for for

t
or

t 0
t>tO+T,

+T

9

(2)

where x is a unit vector in the beam direction, /IO is the initial velocity, T = L/j?,c, with L the length of the electron path across the crystal, and A, = (~,/2Eo)Po, with V, the average value of the potential field due to the crystal. It has been shown [8] that with reasonable approximations the corresponding contribution to the energy loss spectrum can be written Z(AE)

resin*

(O.,;;AE). (3)

Thus the energy loss spectrum should show sinusoidal variations of intensity having a periodicity inversely proportional to L. For 100 keV electrons this periodicity is 12,400/L for L in A. Oscillations of this sort are clearly visible in some of the curves for MgO (fig. 3) and for NiO (Fig. 8). The observed periodicities are, plotted against the measured crystal thickness in fig. 9 and are compared with the theoretical curve deduced from eq. (3). The maximum values of the periodicities observed agree well with the theoretical curve except that they tend to be consistently about 10% too high. This could be a result of the approximations made in the theoretical treatment or could possibly arise from a consistent overestimate of L which could occur if the edges of the crystals were not sharp but rounded off with a series of fine steps such as have been observed on MgO crystals. [4]. A number of measured periodicities showed lower values. These appear to cluster around the curve drawn for half the theoretical value. The reason for these observations is not

Fig. 9. Periodicities in eV measured in ELS spectra for MgO (0) and NiO (0) crystals plotted against the path length for the beam traversing the crystal face. The upper curve is given by eq. (3) and the lower. dashed curve indicates half this value.

clear. The effective value of L may possibly be reduced by the occurrence of steps or other features on the surface but there seems to be no means by which it can effectively be increased. The oscillatory motion of the electrons being channelled along the surface, assumed to be sinusoidal, may be represented by putting r(t)=c~*t~~+(Acosw,t)‘J?,

(4)

and finding /3(t) by differentiation. The frequency of the emitted radiation, w, and hence the contribution to the energy loss spectrum, will depend on the direction of the detector. It has been shown [8] that the intensity emitted at an angle (Yto the in&dent beam is I(0)

= ~~~~~[~~+(BoWsin2a-o,cosa)‘]S(o(l-~~COsff)-~~).

(5)

The dependence on o4 ensures that there is a sharp maximum at around (Y= 0 or w = 0,(1 - /3,)-‘, or, for 100 keV electrons, E = 2.21tio ,. In terms of the spatial perodicity P of the channelling oscillations, E = 1.52 X 104/P eV for P in A. In order to estimate ‘the periodicityp with any accuracy it would be necessary to make a full many-beam dynamical calculation using the method of periodic continuation to represent the non-periodic potential field [25] with an accurate expression for the form of the potential field. Since very few data are available concerning the form of the potential field, such extensive calculations would not be profitable. Instead, we may make approximate estimates of P from reasonable assumptions concerning the form of the potential field and estimates of the path length of the electrons in the crystal, equated to half the

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extinction distance in the bulk crystal for electrons incident with similar orientations. The potential field outside of the crystal should be proportional to y - ’ for large distances from the surface, but for the smaller distances involved in the channelling it may be more appropriate to assume the form C#J( y) = A( y + b) -2 previously used [7], for reasons of convenience in integration, in estimating the effects on the diffraction pattern. For the MgO (200) Bragg angle of 8.5 X 10 -’ rad with Ab* = - 14 and b = 3 A, the length of the path outside the crystal is 710 A. For transmission through MgO crystals the extinction distance has been measured as 407 A for the case of (200) systematic reflections only, 175 A for the incident beam in the [ 1001 direction [26] and 36OA for the beam in the [ 1lo] direction [27]. Assuming a spatial periodicity P = 900 A gives the peak in the energy loss spectrum at 17 eV for MgO. A range of energy loss values for this peak varying by 20-30% could be obtained by making equally valid assumptions for either component of P. However, it appears that the agreement with the observation of the strong peak at 16.6 eV is as good as can be expected with the present incomplete theory. Measurements made on MgO crystals in [ 1001 and [ 1lo] orientations gave values of 16.8 and 16.3 eV, respectively, for this peak position. The difference between these values is in the right direction but may not be significant because the accuracy of the measurements is probably no better than about 0.5 eV. For NiO less is known about the values for the inner potential or the extinction distances for dynamical diffraction. It is reasonable to expect that the path length in vacuum may be shorter than for MgO because the inner potential is greater and the Bragg angle for NiO (111) planes is less than that for MgO (200) planes. On the other hand the extinction length for the (111) reflection of NiO may well be greater than the extinction length assumed for MgO. Hence it is not unreasonable to suppose that the periodicityp may be comparable for the two cases. The strong broad peak at 14.2 eV for NiO has much the same shape and appears in much the same way in the series of ELS spectra as the 16.6 eV peak for MgO and so may well be the corresponding energy loss due to radiation associated with surface channelling. It is to be anticipated that the energy loss peak due to channelling will be relatively weak for small crystal thicknesses, because only a very small part of the incident beam will be bent by the potential field strongly enough to meet. the surface at the Bragg angle and the periodicity of the channelling motion will not be well established for thicknesses less than one repeat distance. This expectation is consistent with the evidence of the energy loss images of fig. 6. For the energy loss of 17 eV the intensity along the crystal edge is seen to be less than for the bulk plasmon loss at 20 eV for small thicknesses but much greater for large thicknesses, above about 1OOOA. It may be noted that dark field images obtained with no energy filtering

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from the (100)~type spots of MgO, which are produced by the channelling process, were also reported to show intensity maxima for thicknesses of the order of 1OOOA171. This analysis has been made in terms of energy losses associated with the radiation emitted due to the acceleration of electrons, analogous to synchrotron radiation. As stated earlier such radiation is expected to be similar in form, and in energy loss values, to the very much stronger transition radiation associated with the modification of the electromagnetic field in the dielectric material of the crystal, Because of the relative theoretical simplicity, we have treated the former rather than the latter case. The formulas (3) and (5) suggest itensities for the energy loss components of the order of 10 -6 of the incident beam intensity. Measurements of the observed intensities for MgO suggest this ratio to be 10e3 to low2 for the 17 eV loss peak and a factor of 10 smaller for the oscillatory component. Estimates of the strength of transition radiation for the simple case of transmission through a thin foil suggest intensities up to 10 -* of the incident beam intensity [20]. For an electron passing along a crystal surface the relative strength should be within a factor of 10 of these values. The observation of an oscillatory component of the energy loss spectrum appears to be new, but is undoubtedly related to the prediction of the oscillatory dependence of the intensity of emitted radiation on the thickness of thin films predicted by Heitmann [28]. It thus appears that the explanation of our observations is satisfactory in terms of both the forms and the intensities of the energy loss features within the broad limitations set by the incomplete nature of the theoretical treatments and by the probable errors in the experimental m~surements. Energy loss features similar to those which we have observed should be present in spectra obtained in transmission through thin crystals as a result of the radiation from the crystal surfaces and from the channelling of the electrons between planes of atoms [ 181. However, for the specimen thicknesses which we have used, and for most transmission spectra, the bulk inelastic scattering processes are very much stronger, giving energy loss peaks comparable with the zero-loss peak, so that the surface-loss peaks are not normally detectable.

6. ConeIusIons The combination of techniques made available by use of the suitably modified STEM instrument have proved valuable in making possible the series of measurements on surfaces which we have described. Further refinements of the techniques may allow the extension of the methods to supply more accurate and complete data than those reported here which must be considered exploratory in nature.

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The bright field STEM imaging combined with the observation of diffraction patterns by use of the optical system, allows suitable crystals to be chosen and aligned with respect to the axis of the microscope. The imaging of the surfaces in dark field using reflected diffracted beams provides clear evidence on the dimensions, smoothness and imperfections of the crystal faces. Observations of the series of microdiffraction patterns obtained with a beam aligned parallel to a crystal face, moved by small steps perpendicular to the face, provide a wealth of detail which has not yet been fully interpreted or analysed. The main features of the patterns have been explained in terms of rough geometric-optic models for the electron beam paths across the crystal face, with reasonable assumptions for the form of the potential field. It seems probable that more accurate calculations, made in conjunction with quantitative measurements of diffraction pattern intensities, will allow more complete analysis of the data and provide direct experimental measurements of the form of the potential field at crystal surfaces. The amount of information contained in the energy loss spectra, obtained with the electron beam traversing a crystal face, is considerable and may be made much greater if techniques are applied to make the measurements more quantitative. It should be possible to make quite accurate correlation of the energy loss spectra with the distance of the electron beam from the crystal face if a very slow lateral scan of the incident beam is made and the ELS spectra are recorded at carefully timed intervals. The beginning and end points of the scan may be recorded as the positions of the marker on high magnification STEM images. The prominent ELS peak appearing in many of these surface spectra and also the smaller thickness-dependent oscillations on the curves have been attributed to energy losses associated with the excitation of radiative modes. Other peaks appear to be identifiable as those occurring in transmission ELS spectra and due to plasmon, interband excitation or exciton losses. Many of the peaks observed, however, have no immediate explanation and are presumably due to the excitation of electronic states associated with the surfaces of the crystals. More complete interpretations of these ELS maxima may well follow from more complete studies of the conditions under which they are produced, observations of the dependence of their intensities on various physical and chemical surface treatments and more complete theoretical studies of the surface excitations of the oxide crystals. Acknowledgements The author is indebted to Dr. P.S. Turner for supplying the specimens of NiO. The work was supported by US Department of Energy Contract DEAC02-76ER02995 and made use of the resources of the Facility for High Resolution Electron Microscopy which is supported by NSF Regional Instrumentation Facilities Program, Grant CHE-7916098.

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Refereces [I] J.M. Cowley, in: Scanning Electron Microscopy/l980, Vol. I, Ed. 0. Johati (SEM Inc., AMF O’Hare, Illinois, 1980) p. 61. [2] P.E. H@md Nielsen and J.M. Cowley, Surface Sci. 54 (1976) 340. [3] N. Osakabe, Y. Tanishiro, K.Yagi and G. Honjo, Surface Sci. 97 (1980) 393. [4] J.M. Cowley, in: Microbeam Analysis-1980, Ed. D.B. Wittry (San Francisco Press, San Francisco, 1980) p. 33. [S] J.M. Cowley and J.C.H. Spence, Ultramicroscopy 3 (1979) 433. [6] J.M. Cowley, in: Proc. 39th Annual Meeting EMSA, Ed. G.W. Bailey (Claitor’s, Baton Rouge, Louisiana, 1981) p. 212. [7] J.M. Cowley, Ultramicroscopy 7 (1981) 181. [8] J.M. Cowley, Phys. Rev. B, in press. [9] R.R. Cowley, R.L. Segall, R.St.C. Smart and P.S. Turner, Phil. Mag. A39 (1979) 163. [IO] W.R. Pease, R.L. Segall, R.St.C. Smart and P.S. Turner, J. Chem. Sot. Faraday I. 76 ( 1980) 1510. [I I] J.M. Cowley, Appl. Phys. Letters 15 (1969)58. [ 121 P.S. Turner and J.M. Cowley. Ultramicroscopy 6 (1981) 125. [13] J.M. Cowley and J.C.H. Spence, Ultramicroscopy 6 (1981) 359. [14] H. Venghaus, Opt. Commun. 2 (1971) 447. [ 151 M.L. Cohen, P.J. Lin, D.M. Rocssler and W.C. Walker, Phys. Rev. I55 ( 1967) 992. [ 161 L.A. Balabonova and E.V. Stepin, Soviet Phya-Solid State 19 (1977) 1766 [translated from Fiz. Tverd. Tela 19 (1977) 30181. [ 171 H. Raether, Excitation of Plasmons and Interband Transitions by Electrons (Springer, Berlin, 1980). [ 181 C.J. Humphreys, in: Electron Microscopy 1980, Vol. 4. High Voltage, Eds. R. Brederoo and J. van Landuyt, 7th European Congr. in Electron Microscopy Foundation, Leiden, 1980, p. 68. [ 191 M.J. Alguard, R.L. Swent, R.H Pantell, B.L. Berman, SD. Bloom and S. Datz. Phys. Rev. Letters 42 (1979) 1148. [20] K.V. Jelley, Cerenkov Radiation and its Applications (Pergamon, New York, 1958) p 57. [21] E. Kroger, 2. Physik 216 (1968) 115. [22] E. Kroger, 2. Physik 235 (1970) 403. [23] R. Vincent and J. Silcox, Phys. Rev. Letters 31 (1973) 1487. [24] J.D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975) p. 671. [25] J.C.H. Spence, Acta Cryst. A34 (1978) I 12. [26] P. Goodman, Acta Cryst. A27 (1971) 140. [27] G. Lehmpfuhl; Z. Naturforsch. 27a (1972) 425. (281 D. Heitmann, Z. Physik 245 (1971) 154.