THE SCATTERING DISTRIBUTION FROM SEMICONDUCTORS AS A FUNCTION OF ANGLE AND ENERGY LOSS IN THE ELECTRON MICROSCOPE

C. B. BOOTHROYD, R. E. DUNIN-BORKOWSKI AND T. WALTHER

Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QZ, UK

ABSTRACT

We examine the scattering distribution from thin C, Ge and thick Si specimens as a function of scattering angle and energy loss, in order to gain insight into the relative contributions to both low and high angle annular dark field images from elastically and inelastically scattered electrons.

INTRODUCTION

Annular dark field imaging in the electron microscope is increasingly being used as a means for measuring compositions in systems where only a few known elements are present. It is usually assumed that if the scattering angles of the electrons collected (determined by the inner angle of the detector) are large enough, then the majority of the electrons collected can be modelled using Rutherford scattering (ie high angle elastic scattering), whose intensity is proportional to the atomic number Z² for constant specimen thickness. High angle annular dark field images are normally obtained either at high resolution, in order to image atomic columns, or at low resolution in order to obtain chemical information. High resolution imaging requires the use of an electron beam smaller than the inter-atomic column distance and produces contrast incoherently, thus avoiding the contrast reversals found in conventional high resolution imaging as a function of thickness and defocus. The images can then be interpreted qualitatively in terms of projections of the atomic columns [1, 2]. At lower resolutions, the Z² dependence of the image intensity is used to measure compositions, notably in semiconductor layers [3, 4] and doping distributions [5]. However, Perovic et al. [5] have shown that for B doping in Si the contrast does not in fact depend on Z² because of strain effects, while Spence, Zuo and Lynch [6] have shown that high order Laue zones can make a significant contribution to the contrast.

In general, all the possible mechanisms by which electrons can be scattered into a high angle image must be considered. Thermal diffuse or phonon scattering has been considered theoretically [7, 8]. Wang and Cowley [9] found that phonon scattering has an atomic number dependence that is not simply proportional to Z², and that high angle contrast is also affected by high order Laue zones. Much of the work on phonon scattering has concentrated on its effect on high resolution images, owing to the fact that phonon scattering is localised at atomic sites and can thus affect the form of the lattice image. Higher energy loss contributions have been considered in less detail. Eaglesham and Berger [10] found large contributions to "thermal diffuse" scattering from higher losses using energy loss spectra, and showed that Compton scattering was comparable to phonon scattering for low atomic number materials.

In this paper, we are concerned with the quantification of low resolution annular dark field contrast and are therefore interested in all of the contributions to the image intensity. Such information will allow the origin of the background to high resolution high angle dark field images to be explained more quantitatively. We have measured each of the contributions experimentally, and will describe our results both for thin C and Ge films and for the effect of specimen thickness on the contrast for a thicker Si specimen.

SCATTERING AS A FUNCTION OF ANGLE AND ENERGY LOSS IN THIN FILMS

We begin by examining the scattering distributions from films of C and Ge that are thin enough for little multiple scattering to occur. The C film examined was a commercially available continuous carbon film containing graphite particles while the Ge film of nominal 15 nm thickness was made by evaporation onto NaCl and then floating off onto a holy carbon coated grid. Both specimens were examined at 100kV in a VG HB501 scanning transmission electron microscope equipped with a Gatan imaging filter.

For the C film, energy filtered diffraction patterns were collected using an energy selecting slit of width 7 eV. Parallel illumination over a large area was used, with a high objective excitation to reduce the camera length and thus increase the maximum scattering angle that could be collected. Each diffraction pattern was averaged radially, and figure 1 shows the resulting intensity plotted as a function of angle on a logarithmic scale for energy losses of up to 1000 eV. For zero energy loss the expected [theta]^-4 dependence in intensity is seen, with broad amorphous rings and sharp diffraction rings from the graphite superimposed. At a loss of 25 eV, corresponding to the energy of the plasmon peak, the curve is similar to that for the zero loss at larger scattering angles because the cutoff angle for plasmon scattering for C is about 20 mrad. Below this angle plasmon scattering depends on [theta]^-2. Thus, all the plasmon scattering at higher angles seen here arises from multiple elastic or phonon and plasmon scattering. At higher losses the [theta]^-4 dependence remains but the diffraction rings are blurred by the angular scattering distributions of the plasmons and the higher losses. At an energy loss of 100 eV, the Compton scattering peak is first seen. This peak arises as a result of electrons scattering from electrons in the valence band, and forms a broad ridge with an energy loss dependence of E = [theta]²[gamma]²T, where T is the incident energy and [gamma] a relativistic correction. Below 284 eV the intensity rises due to the C K edge.

Figure 1 Intensity as a function of scattering angle for different energy losses for C. Each graph is plotted on the correct absoute scale relative to all the others.

For the Ge film, in order to record higher scattering angles than was possible from filtered diffraction patterns, energy loss spectra were collected as a function of scattering angle. Figure 2 shows such spectra plotted as a function of angle, again on a logarithmic scale. The presence of C and O edges indicates that the film was not as pure as it could have been. The spectra at zero scattering angle and at 13 mrad look similar, apart from the presence of a Compton peak in the 13 mrad spectrum. At high scattering angles, the shape of the low loss peak remains very similar to that at zero scattering angle, suggesting that the plasmon peak arises from multiple scattering at high scattering angles as was the case for C. The overall scattering distribution can be seen more clearly in figure 3, which shows a plot of the intensity as a function of both energy loss and scattering angle.

Figure 2 Intensity as a function of energy loss for 12 different scattering angles from 0 to 165 mrad for amorphous Ge. Each graph is plotted on a scale where the incident intensity is 1.

Figure 3 Scattering intensity as a function of both energy loss and scattering angle for Ge, represented as brightness from black to white on a logarithmic scale and with two contours drawn for every order of magnitude.

In order to determine the proportion of electrons that have been scattered to high angles in a single scattering event, the effects of the angular elastic and phonon scattering must be deconvoluted from the scattering distribution as a function of energy loss. To a good approximation, this can be done by scaling each spectrum so that the zero loss peaks have the same area, as shown in figure 4 and then subtracting the zero scattering angle spectrum from each of the spectra collected for finite scattering angles, as shown in figure 5. The strongest feature remaining in figure 5 is the broad Compton profile, which increases in intensity for low losses and low scattering angles.

Figure 4 Intensity as a function of energy loss for 6 different scattering angles from 0 to 75 mrad for Ge. Each graph has been scaled so the zero loss peak has an area of 1.

Figure 5 Single scattering intensity as a function of both energy loss and scattering angle for Ge with a linear intensity scale. Two contours are drawn for every order of magnitude.

The scattered electrons can now be divided into three groups, elastic or phonon scattering (with virtually no energy loss) which appear as the zero loss peak for all scattering angles in figures 3 and 4, multiple elastic or phonon plus inelastic losses which we assume are the same for all scattering angles and thus are represented by the loss part of the zero scattering angle spectrum, and single scattering events, as shown in figure 5. Each of the contributions has been determined as a function of scattering angle from figures 4 and 5, and is plotted in figure 6. For high scattering angles in the thin specimen examined here, about 60 to 65% of the electrons are pure elastically or phonon scattered while about 35% of the electrons are multiply scattered to high angles. Surprisingly, for small scattering angles about 25% of the intensity arises from Compton scattering, which is not inconsistent with the results of Eaglesham and Berger [10]. This intensity falls off rapidly with angle to reach a constant level of about 5% up to scattering angles of 75 mrad. Above 75 mrad, the Compton peak lies beyond the end of our energy loss spectra, and so the recorded single scattering intensity drops to zero. Although the single scattering contribution is only a relatively small contribution to the total high angle dark field intensity, Ge has a relatively high atomic number (32) and for lower atomic numbers the fraction of electrons that have been Compton-scattered will be higher [10] and will provide a component of a high angle dark field image that does not depend on Z².

Figure 6 Fractions of different scattering mechanisms as a function of scattering angle for amorphous Ge.

SCATTERING FROM THICK FILMS

Although high resolution images are usually obtained from the thinnest possible specimens, for lower resolution work it is often useful to examine higher specimen thicknesses, particularly when surface damage layers are present from the specimen preparation. Energy loss spectra were obtained as a function of specimen thickness for Si and we consider here only electrons scattered to the rather high angle of about 200 mrad as shown in figure 7. For a thick specimen, the ratio of plasmon loss to zero loss scattering increases with increasing thickness owing to multiple scattering, and this contribution has been plotted separately. The Si L loss at 99 eV also forms a significant contribution, which can be separated out to a first approximation. For low losses it can be seen that only about 55% of the intensity is elastic or phonon scattering, which is a lower proportion than for Ge as expected. With increasing thickness, the proportion of inelastic and multiply scattered electrons increases dramatically, with plasmon, Si L and multiple scattering each contributing comparable intensities. Despite the inelastic and multiple scattering present in such high angle dark field images, the image intensity still increases linearly with thickness (figure 8). This is in contrast to the intensity in a dark field image with an inner cut-off angle of 50 mrad, which is also shown in figure 8, and which is in agreement with the calculations of Treacy and Gibson [11].

Figure 7 Fractions of different scattering mechanisms for an annular dark field image with an inner radius of about 200 mrad as a function of specimen thickness for Si.

Figure 8 Intensity as a fraction of the incident beam intensity as a function of specimen thickness for two high angle annular dark field detectors.

CONCLUSIONS

Our experimental examination of the scattering behaviour as a function of angle and energy loss has shown that even for very thin specimens of Ge and at scattering angles as large as 75 mrad about 5% of the image intensity arises from Compton scattering. For thicker specimens, most of the intensity is associated with electrons that have been inelastically scattered. For thick Si, a large proportion of the scattering is associated with the Si L edge. This edge will naturally be absent for other elements and will thus cause Si to have an artificially high intensity when comparing its atomic number contrast with that from other elements.

ACKNOWLEDGEMENTS

We are grateful to Paul Brown and Angus Kirkland for provision of specimens and the EPSRC for financial support.

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