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Slow electron scattering from metals
SURFACE
SCIENCE 17 (1969) 132-160 0 North-Holland
SLOW ELECTRON I. THE EMISSION
SCATTERING
Publishing
Co., Amsterdam
FROM METALS
OF TRUE SECONDARY
ELECTRONS
M. P. SEAH School of Physics,
University
of Warwick,
Received 11 November
Coventry,
England
1968
The energies and angular distributions of electrons inelastically scattered and emitted from polycrystalline evaporated films of copper and silver and epitaxially grown silver single crystal films have been measured for primary electron energies between 5 and 300 eV. The results of these experiments on the secondary electron emission are presented in this series of papers under the three headings, “I, The emission of true secondary electrons”; “II, The inelastically scattered primary electrons” and “III, The coherently elastically scattered primary electrons”. The true secondary electrons are shown to have a “cascade” form of energy spectrum following the relation (Es + 4.5)-*r, where X = 2.0 for silver and 1.6 for copper, inside the metal. This spectrum is of the same form as that predicted by Wolff and also by Streitwolf. The surface threshold function for slow electrons emitted from copper and silver rises much more rapidly than predicted by the Sommerfield model and is attributed to a free-electron-like electron band starting approximately 0.4 eV below the vacuum level in both copper and silver. For silver, two emission peaks are superimposed on the true secondary electron cascade spectrum at 12.8 and 17.3 eV with intensity halfwidths of 0.75 and 4.0 eV respectively. Both of these emission peaks are most intense along the surface normal and are strongest for a well ordered surface. They are interpreted as due to the decay of hitherto unpredicted surface related excited states. The emissions at 14.1 and 11.7 eV in copper and gold are thought to have an origin similar to that of the 12.8 eV emission in silver.
1. Introduction Because of their very low penetration, electrons in the 5-500 eV energy range have been extensively used in the investigations of surfaces and thin films. In recent years interest in the elastic and inelastic scattering of low Studies of the energy electrons from surfaces, has grown considerably. coherent elastic scattering or low energy electron diffraction (LEED) has been very fruitful and has been the major interest in electron scattering at low energies. However, with the availability of new equipment and techniques the inelastic scattering of low energy electrons is now being given considerable attention. Fig. I depicts the well known secondary electron energy spectrum from solids. For convenience we consider the three distinct groups of electrons 132
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separately.
The electrons
ELECTRON
SCATTERING
in region
FROM METALS.
III are the elastically
electrons or primary electrons that have undergone which energies of only a few hundredths of an electron
133
I
scattered
primary
phonon scattering in volt are lost. Electrons
that have lost more energy are shown in region II. The peaks in region II are known as the characteristic losses, and in general lie between 2 eV and 50 eV below the elastically scattered peak. These peaks are fixed in relation to the primary energy and are attributed to the excitation of interband transitions and collective oscillations of the lattice electrons. The true
J 100
80 Emission Energy (eV)
0
Fig. 1. Secondary electron energy spectrum emitted to the surface of polycrystalline silver under bombardment by 100 eV electrons incident at 70” from the normal. Electrons in region I are true secondary electrons whereas those in II and III are, respectively, inelastically and elastically scattered primary electrons.
secondary electrons which are mainly of low energy and are thought to be emitted as the result of a cascade process in the solid appear in region I. Superimposed on the cascade background spectrum are some peaks at fixed emission energies generally known as the Auger emission peaks. Of course, after two electrons have interacted, it is impossible to say which was originally the primary electron, hence rigorously speaking, the titles of regions I, II and III are meaningless. However, the titles are those in current use and at the present level of knowledge are useful as a basis for discussing the inelastic scattering of electrons. Despite the lack of adequate theoretical treatments concerning regions I, II and especially III, much useful work has been completed in the fields of surface chemistry, epitaxy etc. by utilising, on an empirical basis, the sensitivity of low energy electron scattering and diffraction to changes in the surface state. Good reviews of the use of LEED are given by Maya) and Landers). In some simple cases, results from low energy electron scattering
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M. P. SEAH
allow unambiguous interpretations to be made for certain aspects of surface reactions. In general, however, much of the information available in low energy electron scattering experiments cannot be adequately interpreted. Analysis of LEED patterns allows simple deductions of the symmetry and size of the surface unit cell to be made, but it is not yet possible to carry the analysis further. By treating nominally clean and well ordered single crystal surfaces of a number of materials in many different ways and by following the changes in symmetry or beam intensities in the LEED pattern, certain empirical rules have been developed by which the quality and state of a surface may be assessed. Similarly as each element under electron bombardment emits a characteristic Auger “line” spectrum4), the presence of elements on a given surface can be detected with great sensitivity by determination of the Auger emission. Unfortunately the relative number of atoms of a given element and their distribution in depth cannot be accurately determined, as yet, from the Auger analysis. Positions of the Auger emission peaks can be predicted from X-ray spectral data, but as X-ray and Auger emissions are competing processes, one cannot even predict the relative intensities of different Auger emissions from the same element. Under ideal experimental conditions simultaneous use of the LEED and Auger emission techniques allows a determination to be made of the surface unit cell and the atomic nature of the contents of the cell. The determination of the positions of the atoms in the surface unit cell must await the full development of a dynamical theory of LEED. The characteristic energy losses, like the Auger emissions, may be used to calibrate the atomic nature of the surface. These losses are not as sensitive as LEED and Auger analysis to surface conditions and have, therefore, not been much used for surface analysis. The mechanisms causing the losses are thought to be mainly interband transitions and collective excitations of the lattice electrons, however, the detailed interpretation for particular elements is still, in general, obscure. In this and the two other papers in this series, some of the fundamental processes involved in electron scattering will be considered in relation to the results of detailed experimental observations. As has been pointed out above most of the investigations concerned with the three regions of electron scattering study the effect of changes in the electron scattering properties with change in surface state or consider the identification of the atomic nature of elements present at the surface. The majority of the information available in these experiments cannot be used until there is adequate knowledge of the fundamental processes involved. In order to obtain a complete experimental description of the electron scattering processes a new instrument has been constructed, full details of which will be published elsewhere.
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ELECTRON
SCATTERING
FROM
METALS.
I
135
As was pointed out by Scheibner and Tharps), if electron spin is ignored, a complete experimental description of the secondary electrons requires the measurement of their distributions in angle and energy as a function of sample surface condition and incident beam energy and direction. An instrument was built bearing this in mind and the initial results of investigations in regions I, II and III will be presented in these papers. This work is mainly concerned with silver in both single crystal and polycrystalline form and copper in polycrystalline form only. Primary electron energies from 5 to 300 eV are used. This paper (I) is concerned with region I of the secondary electron emission spectrum and papers II and III of this series with regions II and III respectively. 2. The apparatus Details of the construction of the apparatus are the subject of a separate paper and so will only be dealt with briefly here. In general the system is similar to the commercial stainless steel UHV LEED apparatus. System pressures of 5 x lo-l1 Torr are routine after a 24 hour bake in the normal manner. As in the LEED apparatus a low energy electron gun is arranged to direct a well collimated monochromatic beam of electrons of variable energy onto the target at T as shown in fig. 2. The electron optical system was designed so that by simply altering the potential of the target with respect to everything else, the energy of the electron beam at the target could be varied without significantly altering the beam current and the focussing. In the work described in these papers the beam current was maintained within 1% of 0.8 /LA. The target is mounted on a special goniometer which has its main axis of rotation coincident with the electron gun axis. The rotation shaft has six insulated slip rings which provide six separate electrical connections to the target through brushes and standard feedthroughs whilst still allowing continuous rotation of the shaft. The goniometer has a further axis of rotation at right angles to the main axis, allowing the target to be inclined at any angle between +70” to the main axis. The single crystal film of silver was grown on a special holder, described later. The special holder clips onto the target so that the crystal film may be rotated about its surface normal or be removed altogether by means of a manipulative finger. The single crystal film may thus be set in any desired orientation. A “tilt and translate” crystal manipulator of the type described by DickerG) mounted horizontally allows the target to be translated up to 1 cm in any direction at right angles to the electron beam. Because of the enclosed nature of the measurement
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M. P. SEAH
area, the target surface preparation services are housed well to the right in fig. 2 and the target manipulator accommodates the necessary movement. Electrons backscattered from the target move in an effectively field free space to the inner sphere S. Space charge inside S is reduced by keeping S 1.5 V more positive
than the target.
S is coated
T
:
with woolly soot and so
R
H
Fig. 2. Diagram of the electron optics for studying the energy and angular distributions of electrons emitted from a sample at T whilst monitoring the LEED pattern visually. A Circular aperture covered with coarse (64 mesh) tungsten gauze B Slot shaped aperture covered with fine (100 mesh) tungsten gauze C 6” x 6” collector D Fine gauze E Coarse gauze at cathode potential F Collector “guard ring” spherical surface G Highly collimated electron gun
H Cleaning and crystal service area J Viewingdirection through Pyrex vacuum window at 60” to the electron beam P LEED display phosphor screen on tin oxide coated glass. R Full rotation main axis shaft S Inner sphere at target potential + 1.5 V T Target position for measurements
absorbs nearly all the electrons falling on it. Two apertures A and B are cut in S and are covered with a fine tungsten mesh formed to the same radius as S. Aperture A is circular and subtends an angle of 130” at T. B, on the other hand, is rectangular, with width I cm and with its length, being in the plane of the figure, subtending an angle of 130” at T. Beyond and concentric with A and B are two more fine meshes D and E which subtend rather larger angles at T than B and A respectively. The meshes A and E together with the phosphor screen P form a normal LEED camera. This can also be used in the manner of Scheibner and Tharp”) to give the energy spectrum of secondary electrons emitted from the target and passing through A. The
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phosphor
screen
ELECTRON
is deposited
SCATTERING
FROM METALS.
on glass coated
I
with tin oxide and
137
so the
phosphor is viewed in transmission. A typical diffraction pattern from a single crystal film of silver in (111) orientation is shown in fig. 3. A similar electron optical system operates behind the aperture B except that the meshes are finer and F is covered with woolly soot instead of a phosphor. A collector C, skimming 0.5 mm inside F and fixed to a rotary drive whose axis passes
Fig. 3. Diffraction pattern produced by 126 eV electrons incident at 52” to the normal, in the [lo] azimuth, of a (111) clean silver single crystal. Also shown is part of the experimental arrangement. The electron gun is mounted on the vacuum prot to the left of the photograph.
through T perpendicular to the plane of the drawing, measures the current reaching it through B and D. The collector fitted for these experiments had a square section subtending 6” at T, and was covered with woolly soot. With the collector at the same potential as F and with both held 30 V more positive than D, C collects all electrons which move in its direction radially from T and surmount the potential barrier presented by D. In this mode C is a perfectly satisfactory Faraday cup without the experimental drawbacks normally shown by Faraday cups. By keeping D at cathode potential, and by varying the incident electron energy, the position of C or the crystal geometry, the electron elastic scattering properties of the surface may be
138
M.P.SEAH
investigated. Alternatively, if everything else is kept fixed and the potential of D is swept from target to cathode potential, in the usual manner, the inelastically scattered electron spectrum may be obtained. For the correct operation of this system in measuring the energy and angular distributions of low energy electrons, the electrons emitted from the target must move in perfectly radial paths. Magnetic fields in the target region were therefore reduced to a few millioersteds by enclosing the whole experimental chamber in a double-walled magnetic screening box of high permeability material. The energy resolution in the spectrum for inelastic scattering was 0.3 eV for low energy secondary electrons; whereas for elastically scattered 100 eV electrons the measured halfwidth was 0.8 eV. The resolution for low energy secondaries depends on patch fields on the target and can be reduced below 0.2 eV for single crystal targets. The figure for the elastically scattered primary electrons, however, depends on the energy spread and the actual energy of the electrons in the primary beam; lowering of the filament temperature reduces the figure for 100 eV electrons to below 0.45 eV. Energy resolution as used here is defined as the measured width at half the peak value of the energy spectrum of monochromatic electrons. Unlike deflection electron energy analysers, this type of analyser has an effective aperture that is independent of energy. For the particular collector used in these experiments the aperture was 12 millisteradians. 3. Sample preparation Polycrystalline surfaces of copper and silver were formed in the usual way by evaporating previously outgassed pure (originally 6 N purity) metal from beads on clean tungsten wire filaments onto the substrates at room temperature. Evaporation rates of a few monolayers per minute were used to build up films more than 50 A thick. The ambient pressure rose to I .5 x lo-” Torr whilst evaporating but fell to 5 x 10-r’ Torr immediately on cooling the evaporation filaments. Two polycrystal electropolished molybdenum substrates were used, one being outgassed by prolonged heating to 1500°C and the other being untreated. Subsequent evaporations of copper and silver were not removed from the target before adding a fresh layer of metal. The only target heating that occurred in the experiments on these polycrystalline copper and silver films was in the initial preparation of the first molybdenum substrate. The single crystal film of silver used for these experiments was epitaxially grown on mica after the method of Jaeger7) and others. In actual fact, the crystal referred to in this and the other papers in this series as a single crystal, was not single, but due to double positioning of the silver atoms on
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ELECTRON
SCATTERINO
FROM METALS.
f
139
the micas), was heavily twinned. The region of crystal exposed to the electron beam was expected to have as much material in one orientation as in the other. A clean square mica target was prepared in the manner of Allpress and Sandersa). A crack was started from one edge of the square so that a small piece of mica coufd be bent away from the rest exposing part of a fresh cleavage face. This is shown in fig. 4. By inserting a knife edge into the angle so formed, the mica could be cleaved inside the UHV chamber exactly at a predetermined plane. Pure silver was evaporated onto the
Fig. 4. The mica target ready for UHV cleaving and for epitaxial growth of the (111) silver film. (1) Lifting hooks for the manipulative finger. (2) Precleaved part of the mica surface covered with silver. (3) Spring clips to retain the mica target on the goniometer. These clips allow full rotation about the surface normal and provide eiectrical contact to the silver film grown later on the mica. (4) Uncleaved part of the mica surface.
exposed part of the cleavage face before assembly of the target, as shown in fig. 4, so that electrical contact would be made with the epitaxial film grown later over the rest of the face exposed by cleavage in UHV. The mica was then cleaved in UHV in the work area and transferred to the goniometer for examination by LEED through the aperture A as described earlier. Very sharp LEED patterns of the type aIready published for micaQ) were observed. The mica target was then returned to the work area and heated on a special heating stage to approximately 3OO’C. Silver was deposited on the cteaved face at a rate of a few monolayers per minute to a final thickness of 200 A. As mica is a poor heat conductor, no attempt was made to heat it uniformly. The target was then returned to the LEED display area, and as expected from the non-uniform heating during deposition, certain regions of the film gave a very good strong sharp LEED pattern whilst other regions only gave a poor pattern and some regions none at all. Despite the very liberal covering of all the mica surfaces with silver before introduction of the target to the apparatus, some electrical charging still occurred at the film edges. The vacuum system contained a titanium sublimation pump which was used very extensively in the initial stages of the pumping procedure. LEED
140
M.P.SEAH
studies of the single crystal film during subsequent exposure to the argon and carbon monoxide ambient atmosphere showed that, for silver under the normal UHV conditions used, the monolayer adsorption time was in excess of 10 years. The results presented below were reproducible in absolute intensities to within 0.3% for the polycrystalline films. For the single crystal films, however, reproducibility was not so good, but by choosing the same area of the crystal, absolute intensities could be reproduced within 5% and relative intensities within 1% during the period of the experiments.
4. Theory for the true secondary electron cascade process Generally, theories of secondary electron emission consider the action of a fast moving primary electron on a slow moving lattice electron and attempt to evaluate the transition rate for the transfer of different amounts of energy or wave vector from the primary electron to the lattice electron. The literature on this topic is not inconsiderable and a review is given by Hachenberg and Brauerlo). Many of the primary electrons which suffer an inelastic scattering event are subsequently elastically scattered out of the target and so reflect fairly faithfully the original scattering event. We shall deal with these electrons and their properties in paper II of this series. The slow secondary electrons, having been produced by inelastic scattering of the primary electrons, then undergo some sort of diffusion process through the target, multiplying and losing energy en route, until they reach the surface with sufficient energy to escape or till they fall back into the “sea” of conduction electrons. These electrons have, in general, undergone so many scattering events since the initial one that the energy and angular distribution of the true secondary electron cascade retains little information about the initial event. This fact is born out by the observation that the energy and angular distribution of the secondary electrons in region I is fairly independent of the incident electron energy and direction. As will be seen later the cascade contains some information concerning the metal itself. Most of the theories simply describe the diffusion process by an exponential absorption term and a mean depth of creation for the secondary electrons. The work of Wolff 1) is one of the few attempts to describe the cascade accurately. Wolff uses a Sommerfeld model of a metal and assumes that the secondaries lose energy by scattering with the conduction electrons and not by phonon scattering. It is well known that, in general, the energy lost in a phonon scattering event is negligible (e.g. see p. 1034 of ref. 11). Wolff shows that for electrons in the solid with energies below 50 eV scattering from a lattice electron which may be effectively described by a short range screened potential, is predominantly s-wave in character. The
SLOW
scattering
is spherically
ELECTRON
SCATTERING
symmetric
FROM
METALS.
in the c-system
141
I
and,
on average,
an
electron loses half its energy per collision. The results of Wolff’s analysis are that in the cascade produced by an incident electron of energy E,, the number of secondary electrons with energy Es per unit energy internal is: X
n (E,) = A
( )
E2JT , s
(1)
I
isotropically in the metal. A is approximately constant, Es is the secondary electron energy in the vacuum surrounding the metal and E, is the inner potential of the metal. Xis a function that is just greater than 2 for electrons with sufficient energy to escape from the metal. A number of other theories, amongst which are those of Streitwolf 12) and van der Ziells) give a predicted spectrum of the form: 1
for the secondary electrons produced directly as a result of the interaction of the primary electron with the lattice electrons. E, is a constant whose value depends on the theory chosen. On Wolff’s theory E, is the inner potential, whereas on Streitwolf’s it is the work function and on van der Ziel’s it is the inner potential plus h2A2/2m, where 2 is the screening length for the energetic primary electron interacting with the lattice electron via a screened Coulomb field. Since A depends quite markedly on the incident electron energy, van der Ziel’s theory predicts that the true secondary electron spectrum should also be markedly dependant on the incident electron energy. No such dependence has been observed in the present experiments and therefore it is not thought that van der Ziel’s theory is relevant here. If the secondary electrons undergo a number of inelastic scattering events before emission, the number of low energy secondary electrons is enhanced at the expense of the higher energy ones. In this manner Stolz 14) has developed the work of Streitwolf further by considering the transport of the secondary electrons through the metal and their subsequent escape from the surface. The final result is rather complicated but is significantly different from the inverse square form represented by relation (2), even if E, is allowed any value. Thus, if the secondary electron spectrum is of the form of eq. (2), the only current theories which can be assumed valid are Streitwolf’s theory if the secondary electrons are mainly emitted without inelastic scattering after their initial production, or Wolff’s theory if the energies of the secondary electrons can be measured from the Fermi level and not the bottom of the conduction band. Wolff multiplies eq. (1) by a surface escape probability to convert the
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M.P. SEAH
internal secondary electron energy spectrum into the externally measured spectrum. The function that he uses, the total escape probability, is not the correct one to use for comparison with energy analysers only accepting a small solid angle of emission. To evaluate the correct function, we proceed as follows and determine the angular dispersion that the electron flux occupying a small solid angle, would undergo. If an electron crosses a surface barrier as shown in fig. 5 the component
Fig. 5.
Wave vector diagram for a plane wave electron crossing the flat surface barrier of a Sommerfield model metal.
of the electron
wave vector parallel
to the surface is conserved,
hence
ki sin Oi = k, sin 0,. If we define the refractive
index as
p (E,) = Eif,
I
then
p (E,) = ii . 0
Clearly, a beam of electrons occupying a small element inside the metal, will occupy dQ, outside in the usual external
secondary
electron
energy spectrum,
of solid angle dRi manner. Thus the
from eq. (1) is
n (E,) = A T (Oi, E,) (3) iz (E,) = A T (Qi, E,) where T(O,, ES) is the transmission coefficient for electrons incident on the inner surface at an angle Oi with energy Es +E,. T is quantum mechanical in origin and, for the electron energies considered here, will probably be near unity15). The ratio dQJdS2, is defined as the surface threshold function. Thus, if eq. (1) is correct for the simple case of the spectrum emitted normal to the surface, the spectrum shape is given by 1 n(E,) ac -*--~~ P (ES + EJX.
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For a Sommerfeld
ELECTRON
SCATTERING
FROM METALS.
143
I
model of the metal,
p2= (EI + EJIEs+ and the spectrum
then shows a single peak at Et/X or if X= 2, at +E, as in
fig. 6.
Fig. 6. (----) internal cascade secondary electron energy spectrum following a (ES + ED) -z law (---) external secondary electron energy spectrum deduced from the internal spectrum and the surface threshold function fora Sommerfeldmetal.
5. Results and discussion 5.1. THE SLOW ELECTRON CASCADE SPECTRUM FROM POLYCRYSTALLINE TARGETS
The results for emission along the surface normal from the with incident primary electrons inclined at 70” from the surface shown in fig. 7. The curves have been normalised for the low in the spectrum. Similar results were obtained for clean silver.
copper film normal are energy peak The curves
can be conveniently split into two parts; one due to the cascade process which is common to all curves and the other due to the inelastically scattered primary electrons. Some numerical results are summarised in table 1. E+ is the full width of the low energy peak at half the peak height. The free electron model of a metal predicted the peak in the emission spectrum along the surface normal to be at JE, which should be at about 7 eV for copper and silver. Thus, if expression (2) is valid for the internal secondary electron energy spectrum, the surface threshold function must rise much more rapidly than the Sommerfeld model predicts in order to give the experimental peak around 0.7 eV. To find the power law controlling the emission, plots of log n(E,) versus log(E,+E,) were made, E, being chosen each time to produce a straight line plot over as wide an energy range as possible.
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M.
P. SEAH
Fig. 7. Energy spectra of the secondary electrons emitted along the surface normal from a polycrystalline copper target under bombardment by primary electrons, of 61,76,91 and 300 eV energy, incident at 70” to the surface normal. The curves have been normalised for the intensity of the slow electron cascade peak. TABLEI Data for the slow electron cascade Target
CU
cu Ag Ag
Incident energy CeV)
Peak WI
30 300 30 300
0.7 0.6 0.8 0.8
5.6 5.5 3.4 3.4
The gradient of this line gives X directly. The departure from a straight line at low energies gives the surface threshold function. It will be assumed that this function may be described by the expression (E,/(E,+E,)) along the surface normaI, in analogy with the Sommerfeld model. The results are summarised in table 2. The value of E, chosen gave a straight line plot for electrons with emission energies between 3 and 60 eV, as shown in fig. 8. The value of E, is really only accurate for low energy secondary electrons. The cascade energy spectrum cannot be evaluated with any greater accuracy to determine whether E, varies from 4.5 eV as the secondary electron emission energy is increased, since Auger transitions and inelastically scattered primary electrons contribute significantly to the spectrum and the background cannot therefore be estimated with sufhcient accuracy. The results
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shown
in table
2 verify
ELECTRON
SCATTERING
the correctness
FROM METALS.
145
I
of eq. (1) for the secondary
electron
cascade energy spectrum. In silver it is found that X=2.0 and in copper X = 1.6. For silver, the result may be interpreted to show either that the prediction of Streitwolf l2) is correct and also that the secondary internal
TABLE
2
Analvsis of the slow electron cascade Target material cu Ag Error
(e?) 4.5 4.5 k1.0
0
Fig. 8. Plot of loglo (intensity) against log10 (ES) and log10 (ES + &) to determine the power law governing the emission in the slow electron cascade. These results are for emission along the surface normal from polycrystalline silver under bombardment by 300 eV primary electrons incident at 70” to the normal. (1) Experimental results. (2) Adjusted results E, = 4.5 eV.
I46
M.P.SEAH
electrons are not appreciably scattered after creation, or that the prediction of Wolffl) is correct provided that energies are measured from the Fermi level and not the bottom of the conduction band. A simple experiment was performed to show that the small half width and low energy of the cascade peak in table 1 was not spurious and not, for example, due to patch fields causing local pockets of space charge on the target surface or due to tertiary electrons from the grids. The potential of the inner sphere S was increased to 50 V positive with respect t.o the target without significantly broadening or shifting the low energy peak. From the surface threshold functions shown in fig. 9 the average Ei (ki)
@$M
Emission Enegy (eVl
Fig. 9. Deducedsurfacetheshofd fu~c~i~~s for low energy secondary electrons. (I) Clean copper polycrystailine surface. (2) Clean silver polycrystalline surface. (3) After Berglund and Spicer’sift) results for silver averaged over all emission directions.
relation may be obtained. The surface threshold function obtained by Berglund and SpicerIG) is also shown for comparison. Since for normal emission and since k, = ,uk,,, then
The approximate wave vector of the electron before emission can therefore be deduced, Note that eq. (5) does not depend on the free electron assumption : E = Fz2k2/2m
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ELECTRON
SCATTERING
FROM METALS.
I
14-l
but it does assume that the Bloch wave describing an electron in the solid is just a single plane wave. If the threshold functions are assumed to be near unity where they level off, the results shown in fig. 10 are obtained. Noncancellation of the magnetic fields in the experiments carried out by Berglund and SpicerIG) may account for the difference between curves 2 and 3. Comparison is not made with any other work as the low energy part of the spectrum in other experiments has usually been influenced by poor resolution. Curve 4 is obtained by assuming that the threshold function is not near unity as shown in fig. 9 but is 0.574 at 3 eV in accordance with the result obtained by Appelti7) for a (110) copper surface; p= 1.32 at 3 eV.
Fig. 10. Deduced values of internal wave vector of the electrons emitted as a function of their emission energy and assuming the validity of fig. 5. (1) Free electrons. (2) Results for silver, those for copper are nearly identical. (3) Berglund and Spicer’srs) threshold function similarly treated. (4) The result of fitting the threshold function for copper to Appelt’sr7) result point “A”.
These results may be interpreted as showing that inside the metal the electrons behave as if they were in a free-electron-like band starting 0.35 eV (E, of table 2) below the vacuum level; hence /L’ = 1 + 0.35/E, instead
of the prediction
of /Lz = 1 + 14/E,
which is based on the Sommerfeld model of a metal. The calculations of Segall18) and Burdicklg) show that the bottom of a free-electron-like band starts just below the vacuum levels of copper and silver. The results obtained by Appelt17) also show that, in copper, low energy electrons appear to come from a free-electron like band starting just below the vacuum level.
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M. P. SEAH
All the spectra measured for the true secondary electron emission normal to the target surface, were within 2% of the shape
(6) where X=2.0 for silver and 1.6 for copper. Spectra were also recorded for emissions along directions other than the normal to the surface. As predicted by eq. (3) for the values used above, a shift in the peak value for silver from 0.8 to I .2 eV is observed for the spectra of electrons emitted at 65” to the surface normal. As the angle of observation of the emission was varied, the peak emission intensity followed the usual cos 0, distribution, as expected, but there was some enhancement close to the incident electron direction. The true secondary emission, in general, was found to follow a similar cos 0, distribution with no marked angular structure. If the true secondary electrons are emitted directly as a result of the inelastic scattering of the primary electrons by Streitwolf’sre) free electron scattering process, without subsequent inelastic scattering, then for an electron beam incident along the surface normal, the majority of the secondary electrons would be produced moving in a direction unsuitable for emission. Streitwolf12) shows that most of the secondary electrons are initially produced moving in a cone of semivertical angte slightly less than a right angle, about the primary electron beam direction. Thus most of the secondary electrons are produced moving more deeply into the target and only the small number of backscattered primary electrons can give rise to emitted secondary electrons. Since, for 100 eV electrons, the penetrating unscattered eIectron beam is probably ten times as strong as the backscattered primary current near the surface, as soon as the incident electron beam is inclined away from the surface normal, the penetrating electron beam should begin to contribute strongly to the emitted secondary electron current in the manner noted above. Experiments showed that the emitted secondary electron current did not increase as rapidly as Streitwolf’s free electron scattering theory would predict when the angle of incidence of the primary electron beam is increased. For non-normal incidence of the primary electron beam, the angular distribution of the emitted true secondary electrons was observed not to be of the form predicted by the direct application of Streitwolf’s result or of the form predicted by Stolzr”). It will be shown in Paper II of this series, that, in silver the dominant mode of scattering of the primary electrons is by plasmon excitation. The primary electrons are observed to lose energy without being significantly scattered from their original direction. Thus the plasmons excited are of very long wavelength. Free electron scattering of the form used by Streitwolf
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ELECTRON
SCAlTERING FROM METALS. 1
149
in his H=O process predicts an angular scattering of the primary electrons with loss of energy which was not observed. Thus a spectral distribution for the true secondary electrons based on a free electron single particle excitation process, such as that of Streitwolf, may not be relevant in this study. The experimental results therefore, demonstrate the validity of Wolff’s approach only. 5.2.
AUGEREMISSIONPEAKSSUPERIMPOSEDONTHECASCADEBACKGROUND
Superimposed on the background distribution of cascade emission the spectra show peaks at fixed emission energies which are characteristic of the target material (see fig. I>. The peaks also give rise to deviations from iinearity in fig. 8. These peaks in general are due to Auger electrons. A summary of references concerning Auger electrons will be found in ref. 4. Auger electrons are ejected from the bulk target by means of radiationless transitions occurring in the target atoms. In the Auger process the primary electron ejects another electron from one of the inner atomic levels. This, in itself, does not give rise to a peak in any of the electron distributions as the two electrons can share the initial energy after scattering in any way that conserves the total energy of the system. However, when an electron from a higher energy level, E, falls into the lower vacant level, E,, a fixed amount of energy, E.-El is available to eject an electron from a third level, Es. The latter electron can appear outside the target with an energy EA=EZ--El-(&--Es),
where E4 is the value of the vacuum level. The shape of the emission peak will depend on the densities of states in energy of the levels E,, E2 and E3. A threshold energy, E,, exists for the primary electron, below which the initial electron in E, cannot be excited. Using the Pauli exclusion principle, clearIy (algebraically) ET = 2E, - E, (7) where EF is the Fermi energy, ET, of course, is always less than the emission energy of the finally ejected electron. In general, because of the diminishing densities of final states for both eiectrons in the initial excitation process, the intensity of the Auger peak declines long before ET is reached and the experimental threshold is then a function of the instrumental sensitivity. However, determination of the threshold energy does allow one to deduce which initial levels are not being excited and also whether the peak is due to an Auger process at ail. The minimum difference between ET and EA for any Auger process can be seen to be zero; however, in practice the limit will be at least 2 (EF - E,) where Ev is the highest energy peak in the density of
1.50
M. P. SEAH
states in the conduction
band.
In the cases of copper
and
silver this limit
will be about 8 eV because of the very low density of states towards the top of the conduction band. The minimum observed value of ET- EA, if the final electron is ejected from the conduction band is 2E,- E,-- Ea. The Auger peaks can be thought of as simply superimposed on the cascade background and not, in any way, interacting with it. The Auger emission peaks shown in table 3 have been observed in the present experiments in agreement with the results of Scheibner and Tharp5) and also Palmberg and Rhodin 20). TABLE3 Fixed emission peaks in the secondary electron energy spectra Target material
Peak energy W) ..““.____....-~
-cu Ag
Au
61.0 14.2 40.4 26.0 12.8 60.5 43.0 II.7
Theoretical energy%‘) feV) ~._ 63.6 see later 41.8 28.7 see later 57.6 46.8 see later
Lowest primary electron energy at which the peak is visible E3 f% tevt .~.~~____ __..
Transitions -‘I) Er! ..__.__ Mr\-,v
MIII
Mrv,v
NIV,~ NIII
NIH Nr
Niv,v Nrr,v
OIV, v 011 OItr, v 01v.v 0111 OlV,V
90 below 50 below below 90 7s below
20 40 20
20
To determine the theoretical Auger emission energies in table 3, it was assumed that the peak in the conduction band (ES) giving the emitted electron was 9 eV below the vacuum level. Other fixed emission energy peaks (e.g. the large peak in fig. 1 I) were observed besides the Auger emission peaks, and are discussed later. If the experimentally determined cascade background is subtracted from the total emission spectrum, the true shape and actual intensity of the Auger peaks can be determined. Fig. 11 is typical of the result so obtained for the 61.0 eV Auger emission peak in copper and is confirmed by results taken under conditions when the large peak is absent. From fig. I I the probability of ionisation of the RIICI level in copper by 120 eV electrons can be deduced. The primary electron beam was used at near grazing incidence in this experiment so that the majority of excited atoms would be near the surface and so all the Auger electrons moving along the surface normal in the metal would be emitted. The 61 .O eV Auger peak in fig. 1 I contains approximately 1O-61, electrons where I, is the primary electron beam intensity. If it is assumed that the Auger electrons are excited isotropically in the target and that all Auger electrons moving along the surface normal are emitted, then
SLOW
ELECTRON
SCAlTERINF
FROM
METALS.
I
151
Fig. 11. Emission spectrum along the surface normal in excess of the cascade background for copper in the energy region 20-70 eV, due to bombardment by 120 eV primary electrons at 70” to the surface normal. The emission intensity is given by the scale on the left or by the small box whose area is equal to 10 -B of the incident beam current.
the total number of Auger electrons produced near 61 .O eV is approximately 10m31, and the probability of ionising the Mm level in copper by 120 eV electrons is 0.1%. It is assumed that the Auger process is the only mode of de-ionising the M,,, level. The large peak in fig. 11 does not appear for all specimens and varies in an unusual way with angle of incidence of the primary electrons and angle of emergence of the secondaries. For a fixed geometry this type of peak remains at a fixed emission energy independant of the primary electron energy. The behaviour of these peaks as a function of angle of incidence and energy of the primary electrons and angle of emission of the secondary electrons was found to be identical to that of the elastic scattering of primary electrons at the energy of the peak. Some of the primary electrons are thus thought to lose energy without appreciable angular scattering, and then are elastically backscattered out of the target. Thus any peak in the elastic scattering current as a function of primary electron energy, angle of incidence or angle of emission will create a similar peak in the inelastically scattered current. It should be noted that if the elastic scattering is a maximum at an energy E,, then the inelastic scattering is a maximum at the emission energy E,, and not when the primary energy is E,,. We will term these peaks in the inelastic scattering as “diffracted inelastic” peaks. For fixed geometry these peaks are easily distinguished from Auger peaks, as the intensity of the latter decreases as the primary electron energy decreases, whereas the intensity of the former increases, rising very rapidly indeed as the primary and emission
152
M. P. SEAH
peak energies approach. Observation of the 61 .O eV Auger peak from copper showed that it increased roughly proportional to the primary energy between 100 and 300 eV whereas the background only increased as the square root of the primary energy. Scheibner and Tharp5) report a 13 eV emission peak in copper whereas Palmberg and Rhodin20) find peaks at 7 eV in copper and 12 eV in gold. The latter offer no explanation whereas the former relate the emission to the strong characteristic energy loss at 20.5 eV observed in their experiment. The first results obtained of the emission peaks around 12 eV, as shown in table 3 for copper, silver and gold showed intensities of the order of the peak in Scheibner and Tharp’s resultss). The elastic scattering properties of the surfaces used showed that they were probably composed of very small randomly oriented crystallites. Later experiments with a silver film, characterised by broad diffraction rings and which was therefore thought to be mainly composed of small crystallites predominantly oriented with their [l 111 axes along the surface normal, gave a much stronger emission peak at 12.8 eV as shown in fig. 12. In this case the emission current was concentrated along the surface normal. For all these metals, the emission intensities of the peaks near 12 eV were fairly independent of primary electron energy down to about 22 eV. These peaks are thus thought to be neither Auger emission nor diffracted inelastic peaks.
Fig. 12. Energy spectrum of electrons emitted along the surface normal from silver in the IO-22 eV energy range due to bombardment by 60 eV primary electrons incident at 50” to the normal. The dotted line shows the estimated cascade background, the very strong emission curve is that due to the (I 11) single crystal surface and the two intermediate curves are those of the polycrystalline surfaces.
SLOW
ELECTRON
SCATTERING
FROiU METALS.
I
Studies were now made of the single crystal film. The film was thought
153
to
be well ordered but extensively twinned. Some comments concerning the crystallography of the film are given in Paper III of this series. The energy and angular distributions of the inelastically scattered electrons showed the 12.8 eV emission peak to be very sharp in energy and primarily oriented along the foil normal. The experimental results are summarised in figs. 13 and 14. The intensity of the peak was highest for regions of the surface giving the best quality LEED patterns, and also highest for the highest angle of incidence of the primary beam.
Fig. 13. Secondary electron emission spectrum in excess of the background cascade taken from the result of the (11 I) surface of the silver single crystal as shown in fig. 12. The peaks occur at 12.8 eV and 17.3 eV.
Fig. 14. Intensity of the 12.8 eV (upper curve) and the 17.3 eV (lower curve) secondary electron emissions as a function of emission angle measured from the surface normal of the (111) surface of the silver single crystal film due to bombardment by 60 eV primary electrons incident at 50” from the surface normal.
A careful investigation of the emission peak energy as a function of emergence angle showed that, to within 0.05 eV and 0.15 eV respectively, the peaks at 12.8 eV and 17.3 eV remained constant in energy. In all respects the 17.3 eV peak behaved identically to the 12.8 eV peak. It was first thought that this was the sort of result predicted by the Urnkiupp theory embodied in the papers of Burnsz2) and Appeltr7). However, closer inspection of the theory leads one to suspect that this result should not be predicted unless the
154
M. P. SEAH
theory is extensively modified. the target with energy near
Burns expected
E,,, = 2”,:, (h2 -t- k2 + 1’) + E,
to see electrons
ejected from
(algebraically)
primarily oriented parallel to the [Ml] reciprocal lattice direction. E, is the inner potential of the metal for silver; LEED measurements imply E,= - 14 eV, whereas the calculations of Segallm) give E,= - 12 eV and the sum of the work function and Fermi energy generally used given E,= - 10 eV. Thus for the [I 1I] direction we find E r,i = 27.1 - 14to
IOeV,
thus E 111 = 13.1 to 17.1 eV, and either peak could fit Burn’ss2) or Appelt’si7) predictions. To check whether another, unknown, mechanism was producing the process described by eq. (8) the emissions associated with the [220] and [222] reciprocal lattice directions were looked for. The 12201 emission should occur at 58-62 eV and at 40” from the normal in the [lo] azimuth and the 12221 at 94-98 eV along the surface normal. The intensities for these effects would be expected to be less than for the [I 1 I] as they are of higher order. No such peaks were found. Within the limits of the experimental technique, if emission occurred at these energies and directions it was less than 1% of the 12.8 eV emission intensity. Palmberg and Rhodinas) with a more sensitive technique did not observe these peaks. It is therefore assumed that the process described by eq. (8) does not occur and that the correlation along the [I 1 I] reciprocal lattice direction is coincidental. An alternative interpretation is that, by the time electrons in the primary beam have lost energy down to 30 eV in the solid, they will be travelling in all directions. Those directed along the surface normal into the crystal lose a little more energy until they are on the upper edge of the free-electron-like band gap at around 27 eV, they are then Bragg reflected along the surface normal and emitted, However, for a nearly free electron model of the band structure of silver, this process predicts that, for electrons emitted at an angle 8 to the surface normal, the peak, although weaker, should show a shift of 27 (tan2 0) eV towards higher emission energies. For 0 = 8” and 12” this gives a shift of 0.5 and 1.2 eV respectively for the 12.8 eV emission. Since the observed shifts of the 12.8 eV and 17.3 eV emissions were less than 0.05 eV and 0.15 eV respectively over this range, these emission peaks are not thought to be due to diffraction phenomena.
SLOW
Before
the results
ELECTRON
were
SCATTERING
obtained
FROM METALS.
it was considered
155
I
that
for a single
crystal, minima should occur in the emission spectra taken along a given direction due to the band gaps existing along that direction. The calculations of Burdicklg) on the band structure of copper give the only available data in the required energy range. The relevant part of the band structure in the [ 11I] direction is shown in fig. 15a. The band structure of silver was deduced approximately from this by reducing the energy scale by a factor equal to are the lattice constants, as shown on the right (%/aAg)2, where acu and aAg (000)
02hb)
15..
_._____._. _._. _I0
IO. &j
Fermi Enwgy
__! _ I
z8
r Ag
C”L (4
. Demify of Stder
hfe&tyofExclar Emhim
(b)
Fig. 15. (a) The energy bands for copper in the [ill] direction after Burdicklg). (b) Schematic density of unoccupied stated deduced from the energy bands for copper compared with the excess emission peaks of fig. 13.
of fig. 15. The density of unoccupied states relevant to fig. 15a is shown schematically in fig. 15b, together with the excess emission peaks. It seems as though good correlation does exist if the inner potential is assumed to be - 14 eV as amply demonstrated from LEED studies. The constancy of the emission energies as a function of emission angle of the 12.8 and 17.3 eV peaks is hard to explain on this model. From these experiments it is not possible to determine whether the decay is occurring primarily along the [l 1 I] direction or perpendicular to the surface as these are coincident in the specimen used in this study. If the decay is perpendicular to the surface, a system like that used by Scheibner and Tharps) should show the same emissions diminished by a factor of 30. This
156
M. P. SEAH
is approximately their result for copper. If the decay is parallel to the [1 I l] axis which is at 54” to the surface normal in their experiment, the electrons will be totally internally reflected and the peaks not seen. Thus the 12.8 and 17.3 eV emissions in silver are thought to be related to the surface and not to the band structure. The sharpness of the 12.8 eV emission peak in energy and its preferred direction might indicate that it is due to the decay of a surface-related excited state in the crystalea). It is likely that the 14 eV and 11 eV emissions in copper and gold have a similar origin. If the excited state decays by emitting a conduction electron, there will be an associated spectrum of emission energies with peaks due to the peaks in the conduction band density of states. As there are two sharp d-band peaks in the conduction bands of these metals it must be postulated that only one can participate in this process. Thus the emission energy minus (algebraically) the d-band peak energy should equal one of the characteristic loss energies. If the excited state is due to a collective effect of electrons near the Fermi surface, the ejected electron could have been one of these electrons. Thus the characteristic loss should then be equal to the emission energy minus the Fermi energy. The intensities of the characteristic losses are of the correct order of magnitude for correlation with this emission. Correlations are shown in table 4. The d band peaks of copper and silver are taken from Berglund and Spicer’sis) work and for gold by estimation from the American Institute of Physics handbookal). The observed losses A and B are those measured in this apparatus and are seen to be at least 0.5 eV lower than other published data. The correlation between the peak emission energies if the electron is originally one of those near the Fermi surface and the characteristic losses, B, is clearly quite good. The 18.4, 24.4 and 22.2 eV energy losses in copper, silver and gold respectively are generally called the plasmon losses as they are more intense than the other losses. It may be that correlation with the emission peaks should be sought for these. The justification for their description as plasmon losses is not obvious, whereas the justification for labelling the 4 eV loss in silver as a plasmon lossa4) seems well founded. The other losses shown in table 4 are generally the 27.5 eV loss in copper being strong and the others labelled “unknown”; weak. If the emission is due to an excited state and not due to a band structure effect, which seems quite reasonable, it is surprising that the appropriate characteristic loss is not sharper. In order to investigate the emission further, the intensity of the 12.8 eV emission peak along the surface normal was measured as a function of the incident electron energy. Reproducibility was not excellent, due to nonuniformity in the specimen, but was adequate for a qualitative discussion. The curve is shown in fig. 16. The result is much like that for total emission
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ELFCTRON
SCATTERING
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METALS.
I
158
M. P. SEAH
Fig. 16. (1) Intensity of the 12.8 eV emission peak above the background as a function of incident electron energy scaled up by a factor of 8. (2) Intensity of the background emission near 12.8 eV as a function of incident electron energy. These results are taken for emission along the surface normal of the (111) silver surface for primary electrons incident at 50” from the surface normal.
except that the maximum occurs at a much lower energy. The maximum in the total emission is due to the fact that as the primary electron energy rises more energy is available to excite secondaries and thus the emission rises. However, as the primary energy rises the secondary electrons are created deeper and deeper in the target and are Iess likely to escape. The product of the two functions, one rising and one falling, produces a peak in the region of l-2 keV. In the case of the excited state mentioned above, the peak occurs at 80 eV so the decreasing function must be characterised by a length much shorter than the mean free path of the low energy secondaries. If, as proposed, the excited state is related to the surface, the excitation would only occur in a narrow surface zone whose depth would indeed be much shorter than the accepted mean free path of the secondaries lo). Thus the proposition that the emission peak at 12.8 eV in silver is due to the decay of a surfacerelated excited state corresponds with all the experimental observations. The experimental results on the other hand are contrary to the density of states and band structure explanation, or indeed, any explanation associated with the crystal rather than the surface. It is not understood why the influence of the density states and band structure is not observed whereas in the photoemission work of Berglund and SpiceriG) they are clearly evident. 6. Conciusio~ The energy polycrystalline
spectrum of the cascade of true secondary electrons from copper and silver follows a well defined law of the form
where
for silver and
X=2.0
1.6 for copper
and
where
S is the surface
SLOW
threshold
function,
ELECTRON
SCATTERING
FROM METALS.
and 4 is the work function.
I
This type of spectrum
159
is
predicted by Streitwolf 12) if the secondary electrons undergo little inelastic scattering after creation. However, for non-normal incidence of the primary electron beam, lack of agreement between the measured angular distribution of the secondary electron current and that predicted using Streitwolf’sra) result, implies that direct application of Streitwolf’s result may not be adequate here. The above type of spectrum is also predicted by Wolff 1) if a diffusion cascade of the true secondary electrons occurs and if energies are measured from the Fermi surface and not the bottom of the conduction band. The threshold function 5’ is not of the form expected on the Sommerfeld model of a metal, but for silver and copper has been shown to be approximately S = E,/(E, + 0.35)) from which it is deduced that secondary electrons escaping from these metals behave as if they occupied a free-electron-like band starting 0.35 eV below the vacuum level in both metals. Auger peaks have been observed in the spectrum as generally reported by other workers. Care must be taken in identifying Auger peaks, especially when using energy analysers accepting only a small solid angle of the emission current, as confusion can arise with “diffracted inelastic” peaks. The occurrence of the “diffracted inelastic” peaks shows that some of the primary electrons can lose large amounts of energy without appreciable angular scattering and then undergo diffraction in the same way as primary electrons at that energy would. The emission peak at 12.8 eV in silver is interpreted as an emission due to the decay of a surface-related excited state with the emission occurring primarily along the surface normal. The correlation with the characteristic losses in silver implies that the emitted electrons in the 12.8 eV emission peaks were originally very near the Fermi surface. The emissions at 14.1 eV and 11.7 eV in copper and gold are thought 12.8 eV emission from silver.
to have the same origin as the
Acknowledgements The author wishes to express his sincere thanks to Professor C. F. Powell for the facilities provided in the H. H. Wills Physical Laboratories of the University of Bristol where preliminary experiments on secondary electron emission were performed, to Professor A. J. Forty for his encouragement and interest in the work and to Dr. B. W. Holland for stimulating and useful discussions. A grant from the Science Research Council for the construction of the apparatus is gratefully acknowledged.
160
M. P. SEAH
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24)
P. A. Wolff, Phys. Rev. 95 (1954) 56. J. W. May, Ind. Eng. Chem. 57 (1965) 18. J. J. Lander, Progr. Solid State Chem. 2 (1965) 26. L. A. Harris, J. Appl. Phys. 39 (1968) 1419, 1428. E. J. Scheibner and L. N. Tharp, Surface Sci. 8 (1967) 247. B. E. Dicker, J. Sci. Instr. 42 (1965) 887. H. Jaeger, P. D. Mercer and R. G. Sherwood, Surface Sci. 6 (1967) 309. J. G. Allpress and J. V. Sanders, Surface Sci. 7 (1967) 1. K. Mtiller, Z. Physik 195 (1966) 105. 0. Hachenberg and W. Brauer, Advan. Electronics and Electron Phys. ll(1959) 413. C. N. Berglund and W. Spicer, Phys. Rev. 136 (1964) 1030. H. W. Streitwolf, Ann. Physik 3 (1959) 183. A. Van der Ziel, Phys. Rev. 92 (1953) 35. H. Stolz, Ann. Physik 3 (1959) 197. P. H. Cutler and J. C. Davis, Surface Sci. 1 (1964) 194. C. N. Berglund and W. Spicer, Phys. Rev. 136 (1964) 1045. C. Appelt, Phys. Status Solidi 27 (1968) 657; see also a “comment” on this paper, M. P. Seah, Phys. Status Solidi 31 (1969) K 123. B. Segall, Phys. Rev. 125 (1962) 109. G. A. Burdick, Phys. Rev. 129 (1963) 138. P. W. Palmberg and T. N. Rhodin, J. Appl. Phys. 39 (1698) 2425. American Institute of Physics. Handbook 7-138, 2nd ed (McGraw-Hill, New York, 1963). J. Burns, Phys. Rev. 119 (1960) 102. An idea originally proposed by B.W. Holland, private communication. H. Raether, Surface Sci. 8 (1967) 233.
SCIENCE 17 (1969) 132-160 0 North-Holland
SLOW ELECTRON I. THE EMISSION
SCATTERING
Publishing
Co., Amsterdam
FROM METALS
OF TRUE SECONDARY
ELECTRONS
M. P. SEAH School of Physics,
University
of Warwick,
Received 11 November
Coventry,
England
1968
The energies and angular distributions of electrons inelastically scattered and emitted from polycrystalline evaporated films of copper and silver and epitaxially grown silver single crystal films have been measured for primary electron energies between 5 and 300 eV. The results of these experiments on the secondary electron emission are presented in this series of papers under the three headings, “I, The emission of true secondary electrons”; “II, The inelastically scattered primary electrons” and “III, The coherently elastically scattered primary electrons”. The true secondary electrons are shown to have a “cascade” form of energy spectrum following the relation (Es + 4.5)-*r, where X = 2.0 for silver and 1.6 for copper, inside the metal. This spectrum is of the same form as that predicted by Wolff and also by Streitwolf. The surface threshold function for slow electrons emitted from copper and silver rises much more rapidly than predicted by the Sommerfield model and is attributed to a free-electron-like electron band starting approximately 0.4 eV below the vacuum level in both copper and silver. For silver, two emission peaks are superimposed on the true secondary electron cascade spectrum at 12.8 and 17.3 eV with intensity halfwidths of 0.75 and 4.0 eV respectively. Both of these emission peaks are most intense along the surface normal and are strongest for a well ordered surface. They are interpreted as due to the decay of hitherto unpredicted surface related excited states. The emissions at 14.1 and 11.7 eV in copper and gold are thought to have an origin similar to that of the 12.8 eV emission in silver.
1. Introduction Because of their very low penetration, electrons in the 5-500 eV energy range have been extensively used in the investigations of surfaces and thin films. In recent years interest in the elastic and inelastic scattering of low Studies of the energy electrons from surfaces, has grown considerably. coherent elastic scattering or low energy electron diffraction (LEED) has been very fruitful and has been the major interest in electron scattering at low energies. However, with the availability of new equipment and techniques the inelastic scattering of low energy electrons is now being given considerable attention. Fig. I depicts the well known secondary electron energy spectrum from solids. For convenience we consider the three distinct groups of electrons 132
SLOW
separately.
The electrons
ELECTRON
SCATTERING
in region
FROM METALS.
III are the elastically
electrons or primary electrons that have undergone which energies of only a few hundredths of an electron
133
I
scattered
primary
phonon scattering in volt are lost. Electrons
that have lost more energy are shown in region II. The peaks in region II are known as the characteristic losses, and in general lie between 2 eV and 50 eV below the elastically scattered peak. These peaks are fixed in relation to the primary energy and are attributed to the excitation of interband transitions and collective oscillations of the lattice electrons. The true
J 100
80 Emission Energy (eV)
0
Fig. 1. Secondary electron energy spectrum emitted to the surface of polycrystalline silver under bombardment by 100 eV electrons incident at 70” from the normal. Electrons in region I are true secondary electrons whereas those in II and III are, respectively, inelastically and elastically scattered primary electrons.
secondary electrons which are mainly of low energy and are thought to be emitted as the result of a cascade process in the solid appear in region I. Superimposed on the cascade background spectrum are some peaks at fixed emission energies generally known as the Auger emission peaks. Of course, after two electrons have interacted, it is impossible to say which was originally the primary electron, hence rigorously speaking, the titles of regions I, II and III are meaningless. However, the titles are those in current use and at the present level of knowledge are useful as a basis for discussing the inelastic scattering of electrons. Despite the lack of adequate theoretical treatments concerning regions I, II and especially III, much useful work has been completed in the fields of surface chemistry, epitaxy etc. by utilising, on an empirical basis, the sensitivity of low energy electron scattering and diffraction to changes in the surface state. Good reviews of the use of LEED are given by Maya) and Landers). In some simple cases, results from low energy electron scattering
134
M. P. SEAH
allow unambiguous interpretations to be made for certain aspects of surface reactions. In general, however, much of the information available in low energy electron scattering experiments cannot be adequately interpreted. Analysis of LEED patterns allows simple deductions of the symmetry and size of the surface unit cell to be made, but it is not yet possible to carry the analysis further. By treating nominally clean and well ordered single crystal surfaces of a number of materials in many different ways and by following the changes in symmetry or beam intensities in the LEED pattern, certain empirical rules have been developed by which the quality and state of a surface may be assessed. Similarly as each element under electron bombardment emits a characteristic Auger “line” spectrum4), the presence of elements on a given surface can be detected with great sensitivity by determination of the Auger emission. Unfortunately the relative number of atoms of a given element and their distribution in depth cannot be accurately determined, as yet, from the Auger analysis. Positions of the Auger emission peaks can be predicted from X-ray spectral data, but as X-ray and Auger emissions are competing processes, one cannot even predict the relative intensities of different Auger emissions from the same element. Under ideal experimental conditions simultaneous use of the LEED and Auger emission techniques allows a determination to be made of the surface unit cell and the atomic nature of the contents of the cell. The determination of the positions of the atoms in the surface unit cell must await the full development of a dynamical theory of LEED. The characteristic energy losses, like the Auger emissions, may be used to calibrate the atomic nature of the surface. These losses are not as sensitive as LEED and Auger analysis to surface conditions and have, therefore, not been much used for surface analysis. The mechanisms causing the losses are thought to be mainly interband transitions and collective excitations of the lattice electrons, however, the detailed interpretation for particular elements is still, in general, obscure. In this and the two other papers in this series, some of the fundamental processes involved in electron scattering will be considered in relation to the results of detailed experimental observations. As has been pointed out above most of the investigations concerned with the three regions of electron scattering study the effect of changes in the electron scattering properties with change in surface state or consider the identification of the atomic nature of elements present at the surface. The majority of the information available in these experiments cannot be used until there is adequate knowledge of the fundamental processes involved. In order to obtain a complete experimental description of the electron scattering processes a new instrument has been constructed, full details of which will be published elsewhere.
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ELECTRON
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FROM
METALS.
I
135
As was pointed out by Scheibner and Tharps), if electron spin is ignored, a complete experimental description of the secondary electrons requires the measurement of their distributions in angle and energy as a function of sample surface condition and incident beam energy and direction. An instrument was built bearing this in mind and the initial results of investigations in regions I, II and III will be presented in these papers. This work is mainly concerned with silver in both single crystal and polycrystalline form and copper in polycrystalline form only. Primary electron energies from 5 to 300 eV are used. This paper (I) is concerned with region I of the secondary electron emission spectrum and papers II and III of this series with regions II and III respectively. 2. The apparatus Details of the construction of the apparatus are the subject of a separate paper and so will only be dealt with briefly here. In general the system is similar to the commercial stainless steel UHV LEED apparatus. System pressures of 5 x lo-l1 Torr are routine after a 24 hour bake in the normal manner. As in the LEED apparatus a low energy electron gun is arranged to direct a well collimated monochromatic beam of electrons of variable energy onto the target at T as shown in fig. 2. The electron optical system was designed so that by simply altering the potential of the target with respect to everything else, the energy of the electron beam at the target could be varied without significantly altering the beam current and the focussing. In the work described in these papers the beam current was maintained within 1% of 0.8 /LA. The target is mounted on a special goniometer which has its main axis of rotation coincident with the electron gun axis. The rotation shaft has six insulated slip rings which provide six separate electrical connections to the target through brushes and standard feedthroughs whilst still allowing continuous rotation of the shaft. The goniometer has a further axis of rotation at right angles to the main axis, allowing the target to be inclined at any angle between +70” to the main axis. The single crystal film of silver was grown on a special holder, described later. The special holder clips onto the target so that the crystal film may be rotated about its surface normal or be removed altogether by means of a manipulative finger. The single crystal film may thus be set in any desired orientation. A “tilt and translate” crystal manipulator of the type described by DickerG) mounted horizontally allows the target to be translated up to 1 cm in any direction at right angles to the electron beam. Because of the enclosed nature of the measurement
136
M. P. SEAH
area, the target surface preparation services are housed well to the right in fig. 2 and the target manipulator accommodates the necessary movement. Electrons backscattered from the target move in an effectively field free space to the inner sphere S. Space charge inside S is reduced by keeping S 1.5 V more positive
than the target.
S is coated
T
:
with woolly soot and so
R
H
Fig. 2. Diagram of the electron optics for studying the energy and angular distributions of electrons emitted from a sample at T whilst monitoring the LEED pattern visually. A Circular aperture covered with coarse (64 mesh) tungsten gauze B Slot shaped aperture covered with fine (100 mesh) tungsten gauze C 6” x 6” collector D Fine gauze E Coarse gauze at cathode potential F Collector “guard ring” spherical surface G Highly collimated electron gun
H Cleaning and crystal service area J Viewingdirection through Pyrex vacuum window at 60” to the electron beam P LEED display phosphor screen on tin oxide coated glass. R Full rotation main axis shaft S Inner sphere at target potential + 1.5 V T Target position for measurements
absorbs nearly all the electrons falling on it. Two apertures A and B are cut in S and are covered with a fine tungsten mesh formed to the same radius as S. Aperture A is circular and subtends an angle of 130” at T. B, on the other hand, is rectangular, with width I cm and with its length, being in the plane of the figure, subtending an angle of 130” at T. Beyond and concentric with A and B are two more fine meshes D and E which subtend rather larger angles at T than B and A respectively. The meshes A and E together with the phosphor screen P form a normal LEED camera. This can also be used in the manner of Scheibner and Tharp”) to give the energy spectrum of secondary electrons emitted from the target and passing through A. The
SLOW
phosphor
screen
ELECTRON
is deposited
SCATTERING
FROM METALS.
on glass coated
I
with tin oxide and
137
so the
phosphor is viewed in transmission. A typical diffraction pattern from a single crystal film of silver in (111) orientation is shown in fig. 3. A similar electron optical system operates behind the aperture B except that the meshes are finer and F is covered with woolly soot instead of a phosphor. A collector C, skimming 0.5 mm inside F and fixed to a rotary drive whose axis passes
Fig. 3. Diffraction pattern produced by 126 eV electrons incident at 52” to the normal, in the [lo] azimuth, of a (111) clean silver single crystal. Also shown is part of the experimental arrangement. The electron gun is mounted on the vacuum prot to the left of the photograph.
through T perpendicular to the plane of the drawing, measures the current reaching it through B and D. The collector fitted for these experiments had a square section subtending 6” at T, and was covered with woolly soot. With the collector at the same potential as F and with both held 30 V more positive than D, C collects all electrons which move in its direction radially from T and surmount the potential barrier presented by D. In this mode C is a perfectly satisfactory Faraday cup without the experimental drawbacks normally shown by Faraday cups. By keeping D at cathode potential, and by varying the incident electron energy, the position of C or the crystal geometry, the electron elastic scattering properties of the surface may be
138
M.P.SEAH
investigated. Alternatively, if everything else is kept fixed and the potential of D is swept from target to cathode potential, in the usual manner, the inelastically scattered electron spectrum may be obtained. For the correct operation of this system in measuring the energy and angular distributions of low energy electrons, the electrons emitted from the target must move in perfectly radial paths. Magnetic fields in the target region were therefore reduced to a few millioersteds by enclosing the whole experimental chamber in a double-walled magnetic screening box of high permeability material. The energy resolution in the spectrum for inelastic scattering was 0.3 eV for low energy secondary electrons; whereas for elastically scattered 100 eV electrons the measured halfwidth was 0.8 eV. The resolution for low energy secondaries depends on patch fields on the target and can be reduced below 0.2 eV for single crystal targets. The figure for the elastically scattered primary electrons, however, depends on the energy spread and the actual energy of the electrons in the primary beam; lowering of the filament temperature reduces the figure for 100 eV electrons to below 0.45 eV. Energy resolution as used here is defined as the measured width at half the peak value of the energy spectrum of monochromatic electrons. Unlike deflection electron energy analysers, this type of analyser has an effective aperture that is independent of energy. For the particular collector used in these experiments the aperture was 12 millisteradians. 3. Sample preparation Polycrystalline surfaces of copper and silver were formed in the usual way by evaporating previously outgassed pure (originally 6 N purity) metal from beads on clean tungsten wire filaments onto the substrates at room temperature. Evaporation rates of a few monolayers per minute were used to build up films more than 50 A thick. The ambient pressure rose to I .5 x lo-” Torr whilst evaporating but fell to 5 x 10-r’ Torr immediately on cooling the evaporation filaments. Two polycrystal electropolished molybdenum substrates were used, one being outgassed by prolonged heating to 1500°C and the other being untreated. Subsequent evaporations of copper and silver were not removed from the target before adding a fresh layer of metal. The only target heating that occurred in the experiments on these polycrystalline copper and silver films was in the initial preparation of the first molybdenum substrate. The single crystal film of silver used for these experiments was epitaxially grown on mica after the method of Jaeger7) and others. In actual fact, the crystal referred to in this and the other papers in this series as a single crystal, was not single, but due to double positioning of the silver atoms on
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ELECTRON
SCATTERINO
FROM METALS.
f
139
the micas), was heavily twinned. The region of crystal exposed to the electron beam was expected to have as much material in one orientation as in the other. A clean square mica target was prepared in the manner of Allpress and Sandersa). A crack was started from one edge of the square so that a small piece of mica coufd be bent away from the rest exposing part of a fresh cleavage face. This is shown in fig. 4. By inserting a knife edge into the angle so formed, the mica could be cleaved inside the UHV chamber exactly at a predetermined plane. Pure silver was evaporated onto the
Fig. 4. The mica target ready for UHV cleaving and for epitaxial growth of the (111) silver film. (1) Lifting hooks for the manipulative finger. (2) Precleaved part of the mica surface covered with silver. (3) Spring clips to retain the mica target on the goniometer. These clips allow full rotation about the surface normal and provide eiectrical contact to the silver film grown later on the mica. (4) Uncleaved part of the mica surface.
exposed part of the cleavage face before assembly of the target, as shown in fig. 4, so that electrical contact would be made with the epitaxial film grown later over the rest of the face exposed by cleavage in UHV. The mica was then cleaved in UHV in the work area and transferred to the goniometer for examination by LEED through the aperture A as described earlier. Very sharp LEED patterns of the type aIready published for micaQ) were observed. The mica target was then returned to the work area and heated on a special heating stage to approximately 3OO’C. Silver was deposited on the cteaved face at a rate of a few monolayers per minute to a final thickness of 200 A. As mica is a poor heat conductor, no attempt was made to heat it uniformly. The target was then returned to the LEED display area, and as expected from the non-uniform heating during deposition, certain regions of the film gave a very good strong sharp LEED pattern whilst other regions only gave a poor pattern and some regions none at all. Despite the very liberal covering of all the mica surfaces with silver before introduction of the target to the apparatus, some electrical charging still occurred at the film edges. The vacuum system contained a titanium sublimation pump which was used very extensively in the initial stages of the pumping procedure. LEED
140
M.P.SEAH
studies of the single crystal film during subsequent exposure to the argon and carbon monoxide ambient atmosphere showed that, for silver under the normal UHV conditions used, the monolayer adsorption time was in excess of 10 years. The results presented below were reproducible in absolute intensities to within 0.3% for the polycrystalline films. For the single crystal films, however, reproducibility was not so good, but by choosing the same area of the crystal, absolute intensities could be reproduced within 5% and relative intensities within 1% during the period of the experiments.
4. Theory for the true secondary electron cascade process Generally, theories of secondary electron emission consider the action of a fast moving primary electron on a slow moving lattice electron and attempt to evaluate the transition rate for the transfer of different amounts of energy or wave vector from the primary electron to the lattice electron. The literature on this topic is not inconsiderable and a review is given by Hachenberg and Brauerlo). Many of the primary electrons which suffer an inelastic scattering event are subsequently elastically scattered out of the target and so reflect fairly faithfully the original scattering event. We shall deal with these electrons and their properties in paper II of this series. The slow secondary electrons, having been produced by inelastic scattering of the primary electrons, then undergo some sort of diffusion process through the target, multiplying and losing energy en route, until they reach the surface with sufficient energy to escape or till they fall back into the “sea” of conduction electrons. These electrons have, in general, undergone so many scattering events since the initial one that the energy and angular distribution of the true secondary electron cascade retains little information about the initial event. This fact is born out by the observation that the energy and angular distribution of the secondary electrons in region I is fairly independent of the incident electron energy and direction. As will be seen later the cascade contains some information concerning the metal itself. Most of the theories simply describe the diffusion process by an exponential absorption term and a mean depth of creation for the secondary electrons. The work of Wolff 1) is one of the few attempts to describe the cascade accurately. Wolff uses a Sommerfeld model of a metal and assumes that the secondaries lose energy by scattering with the conduction electrons and not by phonon scattering. It is well known that, in general, the energy lost in a phonon scattering event is negligible (e.g. see p. 1034 of ref. 11). Wolff shows that for electrons in the solid with energies below 50 eV scattering from a lattice electron which may be effectively described by a short range screened potential, is predominantly s-wave in character. The
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scattering
is spherically
ELECTRON
SCATTERING
symmetric
FROM
METALS.
in the c-system
141
I
and,
on average,
an
electron loses half its energy per collision. The results of Wolff’s analysis are that in the cascade produced by an incident electron of energy E,, the number of secondary electrons with energy Es per unit energy internal is: X
n (E,) = A
( )
E2JT , s
(1)
I
isotropically in the metal. A is approximately constant, Es is the secondary electron energy in the vacuum surrounding the metal and E, is the inner potential of the metal. Xis a function that is just greater than 2 for electrons with sufficient energy to escape from the metal. A number of other theories, amongst which are those of Streitwolf 12) and van der Ziells) give a predicted spectrum of the form: 1
for the secondary electrons produced directly as a result of the interaction of the primary electron with the lattice electrons. E, is a constant whose value depends on the theory chosen. On Wolff’s theory E, is the inner potential, whereas on Streitwolf’s it is the work function and on van der Ziel’s it is the inner potential plus h2A2/2m, where 2 is the screening length for the energetic primary electron interacting with the lattice electron via a screened Coulomb field. Since A depends quite markedly on the incident electron energy, van der Ziel’s theory predicts that the true secondary electron spectrum should also be markedly dependant on the incident electron energy. No such dependence has been observed in the present experiments and therefore it is not thought that van der Ziel’s theory is relevant here. If the secondary electrons undergo a number of inelastic scattering events before emission, the number of low energy secondary electrons is enhanced at the expense of the higher energy ones. In this manner Stolz 14) has developed the work of Streitwolf further by considering the transport of the secondary electrons through the metal and their subsequent escape from the surface. The final result is rather complicated but is significantly different from the inverse square form represented by relation (2), even if E, is allowed any value. Thus, if the secondary electron spectrum is of the form of eq. (2), the only current theories which can be assumed valid are Streitwolf’s theory if the secondary electrons are mainly emitted without inelastic scattering after their initial production, or Wolff’s theory if the energies of the secondary electrons can be measured from the Fermi level and not the bottom of the conduction band. Wolff multiplies eq. (1) by a surface escape probability to convert the
142
M.P. SEAH
internal secondary electron energy spectrum into the externally measured spectrum. The function that he uses, the total escape probability, is not the correct one to use for comparison with energy analysers only accepting a small solid angle of emission. To evaluate the correct function, we proceed as follows and determine the angular dispersion that the electron flux occupying a small solid angle, would undergo. If an electron crosses a surface barrier as shown in fig. 5 the component
Fig. 5.
Wave vector diagram for a plane wave electron crossing the flat surface barrier of a Sommerfield model metal.
of the electron
wave vector parallel
to the surface is conserved,
hence
ki sin Oi = k, sin 0,. If we define the refractive
index as
p (E,) = Eif,
I
then
p (E,) = ii . 0
Clearly, a beam of electrons occupying a small element inside the metal, will occupy dQ, outside in the usual external
secondary
electron
energy spectrum,
of solid angle dRi manner. Thus the
from eq. (1) is
n (E,) = A T (Oi, E,) (3) iz (E,) = A T (Qi, E,) where T(O,, ES) is the transmission coefficient for electrons incident on the inner surface at an angle Oi with energy Es +E,. T is quantum mechanical in origin and, for the electron energies considered here, will probably be near unity15). The ratio dQJdS2, is defined as the surface threshold function. Thus, if eq. (1) is correct for the simple case of the spectrum emitted normal to the surface, the spectrum shape is given by 1 n(E,) ac -*--~~ P (ES + EJX.
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For a Sommerfeld
ELECTRON
SCATTERING
FROM METALS.
143
I
model of the metal,
p2= (EI + EJIEs+ and the spectrum
then shows a single peak at Et/X or if X= 2, at +E, as in
fig. 6.
Fig. 6. (----) internal cascade secondary electron energy spectrum following a (ES + ED) -z law (---) external secondary electron energy spectrum deduced from the internal spectrum and the surface threshold function fora Sommerfeldmetal.
5. Results and discussion 5.1. THE SLOW ELECTRON CASCADE SPECTRUM FROM POLYCRYSTALLINE TARGETS
The results for emission along the surface normal from the with incident primary electrons inclined at 70” from the surface shown in fig. 7. The curves have been normalised for the low in the spectrum. Similar results were obtained for clean silver.
copper film normal are energy peak The curves
can be conveniently split into two parts; one due to the cascade process which is common to all curves and the other due to the inelastically scattered primary electrons. Some numerical results are summarised in table 1. E+ is the full width of the low energy peak at half the peak height. The free electron model of a metal predicted the peak in the emission spectrum along the surface normal to be at JE, which should be at about 7 eV for copper and silver. Thus, if expression (2) is valid for the internal secondary electron energy spectrum, the surface threshold function must rise much more rapidly than the Sommerfeld model predicts in order to give the experimental peak around 0.7 eV. To find the power law controlling the emission, plots of log n(E,) versus log(E,+E,) were made, E, being chosen each time to produce a straight line plot over as wide an energy range as possible.
144
M.
P. SEAH
Fig. 7. Energy spectra of the secondary electrons emitted along the surface normal from a polycrystalline copper target under bombardment by primary electrons, of 61,76,91 and 300 eV energy, incident at 70” to the surface normal. The curves have been normalised for the intensity of the slow electron cascade peak. TABLEI Data for the slow electron cascade Target
CU
cu Ag Ag
Incident energy CeV)
Peak WI
30 300 30 300
0.7 0.6 0.8 0.8
5.6 5.5 3.4 3.4
The gradient of this line gives X directly. The departure from a straight line at low energies gives the surface threshold function. It will be assumed that this function may be described by the expression (E,/(E,+E,)) along the surface normaI, in analogy with the Sommerfeld model. The results are summarised in table 2. The value of E, chosen gave a straight line plot for electrons with emission energies between 3 and 60 eV, as shown in fig. 8. The value of E, is really only accurate for low energy secondary electrons. The cascade energy spectrum cannot be evaluated with any greater accuracy to determine whether E, varies from 4.5 eV as the secondary electron emission energy is increased, since Auger transitions and inelastically scattered primary electrons contribute significantly to the spectrum and the background cannot therefore be estimated with sufhcient accuracy. The results
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shown
in table
2 verify
ELECTRON
SCATTERING
the correctness
FROM METALS.
145
I
of eq. (1) for the secondary
electron
cascade energy spectrum. In silver it is found that X=2.0 and in copper X = 1.6. For silver, the result may be interpreted to show either that the prediction of Streitwolf l2) is correct and also that the secondary internal
TABLE
2
Analvsis of the slow electron cascade Target material cu Ag Error
(e?) 4.5 4.5 k1.0
0
Fig. 8. Plot of loglo (intensity) against log10 (ES) and log10 (ES + &) to determine the power law governing the emission in the slow electron cascade. These results are for emission along the surface normal from polycrystalline silver under bombardment by 300 eV primary electrons incident at 70” to the normal. (1) Experimental results. (2) Adjusted results E, = 4.5 eV.
I46
M.P.SEAH
electrons are not appreciably scattered after creation, or that the prediction of Wolffl) is correct provided that energies are measured from the Fermi level and not the bottom of the conduction band. A simple experiment was performed to show that the small half width and low energy of the cascade peak in table 1 was not spurious and not, for example, due to patch fields causing local pockets of space charge on the target surface or due to tertiary electrons from the grids. The potential of the inner sphere S was increased to 50 V positive with respect t.o the target without significantly broadening or shifting the low energy peak. From the surface threshold functions shown in fig. 9 the average Ei (ki)
@$M
Emission Enegy (eVl
Fig. 9. Deducedsurfacetheshofd fu~c~i~~s for low energy secondary electrons. (I) Clean copper polycrystailine surface. (2) Clean silver polycrystalline surface. (3) After Berglund and Spicer’sift) results for silver averaged over all emission directions.
relation may be obtained. The surface threshold function obtained by Berglund and SpicerIG) is also shown for comparison. Since for normal emission and since k, = ,uk,,, then
The approximate wave vector of the electron before emission can therefore be deduced, Note that eq. (5) does not depend on the free electron assumption : E = Fz2k2/2m
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ELECTRON
SCATTERING
FROM METALS.
I
14-l
but it does assume that the Bloch wave describing an electron in the solid is just a single plane wave. If the threshold functions are assumed to be near unity where they level off, the results shown in fig. 10 are obtained. Noncancellation of the magnetic fields in the experiments carried out by Berglund and SpicerIG) may account for the difference between curves 2 and 3. Comparison is not made with any other work as the low energy part of the spectrum in other experiments has usually been influenced by poor resolution. Curve 4 is obtained by assuming that the threshold function is not near unity as shown in fig. 9 but is 0.574 at 3 eV in accordance with the result obtained by Appelti7) for a (110) copper surface; p= 1.32 at 3 eV.
Fig. 10. Deduced values of internal wave vector of the electrons emitted as a function of their emission energy and assuming the validity of fig. 5. (1) Free electrons. (2) Results for silver, those for copper are nearly identical. (3) Berglund and Spicer’srs) threshold function similarly treated. (4) The result of fitting the threshold function for copper to Appelt’sr7) result point “A”.
These results may be interpreted as showing that inside the metal the electrons behave as if they were in a free-electron-like band starting 0.35 eV (E, of table 2) below the vacuum level; hence /L’ = 1 + 0.35/E, instead
of the prediction
of /Lz = 1 + 14/E,
which is based on the Sommerfeld model of a metal. The calculations of Segall18) and Burdicklg) show that the bottom of a free-electron-like band starts just below the vacuum levels of copper and silver. The results obtained by Appelt17) also show that, in copper, low energy electrons appear to come from a free-electron like band starting just below the vacuum level.
148
M. P. SEAH
All the spectra measured for the true secondary electron emission normal to the target surface, were within 2% of the shape
(6) where X=2.0 for silver and 1.6 for copper. Spectra were also recorded for emissions along directions other than the normal to the surface. As predicted by eq. (3) for the values used above, a shift in the peak value for silver from 0.8 to I .2 eV is observed for the spectra of electrons emitted at 65” to the surface normal. As the angle of observation of the emission was varied, the peak emission intensity followed the usual cos 0, distribution, as expected, but there was some enhancement close to the incident electron direction. The true secondary emission, in general, was found to follow a similar cos 0, distribution with no marked angular structure. If the true secondary electrons are emitted directly as a result of the inelastic scattering of the primary electrons by Streitwolf’sre) free electron scattering process, without subsequent inelastic scattering, then for an electron beam incident along the surface normal, the majority of the secondary electrons would be produced moving in a direction unsuitable for emission. Streitwolf12) shows that most of the secondary electrons are initially produced moving in a cone of semivertical angte slightly less than a right angle, about the primary electron beam direction. Thus most of the secondary electrons are produced moving more deeply into the target and only the small number of backscattered primary electrons can give rise to emitted secondary electrons. Since, for 100 eV electrons, the penetrating unscattered eIectron beam is probably ten times as strong as the backscattered primary current near the surface, as soon as the incident electron beam is inclined away from the surface normal, the penetrating electron beam should begin to contribute strongly to the emitted secondary electron current in the manner noted above. Experiments showed that the emitted secondary electron current did not increase as rapidly as Streitwolf’s free electron scattering theory would predict when the angle of incidence of the primary electron beam is increased. For non-normal incidence of the primary electron beam, the angular distribution of the emitted true secondary electrons was observed not to be of the form predicted by the direct application of Streitwolf’s result or of the form predicted by Stolzr”). It will be shown in Paper II of this series, that, in silver the dominant mode of scattering of the primary electrons is by plasmon excitation. The primary electrons are observed to lose energy without being significantly scattered from their original direction. Thus the plasmons excited are of very long wavelength. Free electron scattering of the form used by Streitwolf
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ELECTRON
SCAlTERING FROM METALS. 1
149
in his H=O process predicts an angular scattering of the primary electrons with loss of energy which was not observed. Thus a spectral distribution for the true secondary electrons based on a free electron single particle excitation process, such as that of Streitwolf, may not be relevant in this study. The experimental results therefore, demonstrate the validity of Wolff’s approach only. 5.2.
AUGEREMISSIONPEAKSSUPERIMPOSEDONTHECASCADEBACKGROUND
Superimposed on the background distribution of cascade emission the spectra show peaks at fixed emission energies which are characteristic of the target material (see fig. I>. The peaks also give rise to deviations from iinearity in fig. 8. These peaks in general are due to Auger electrons. A summary of references concerning Auger electrons will be found in ref. 4. Auger electrons are ejected from the bulk target by means of radiationless transitions occurring in the target atoms. In the Auger process the primary electron ejects another electron from one of the inner atomic levels. This, in itself, does not give rise to a peak in any of the electron distributions as the two electrons can share the initial energy after scattering in any way that conserves the total energy of the system. However, when an electron from a higher energy level, E, falls into the lower vacant level, E,, a fixed amount of energy, E.-El is available to eject an electron from a third level, Es. The latter electron can appear outside the target with an energy EA=EZ--El-(&--Es),
where E4 is the value of the vacuum level. The shape of the emission peak will depend on the densities of states in energy of the levels E,, E2 and E3. A threshold energy, E,, exists for the primary electron, below which the initial electron in E, cannot be excited. Using the Pauli exclusion principle, clearIy (algebraically) ET = 2E, - E, (7) where EF is the Fermi energy, ET, of course, is always less than the emission energy of the finally ejected electron. In general, because of the diminishing densities of final states for both eiectrons in the initial excitation process, the intensity of the Auger peak declines long before ET is reached and the experimental threshold is then a function of the instrumental sensitivity. However, determination of the threshold energy does allow one to deduce which initial levels are not being excited and also whether the peak is due to an Auger process at ail. The minimum difference between ET and EA for any Auger process can be seen to be zero; however, in practice the limit will be at least 2 (EF - E,) where Ev is the highest energy peak in the density of
1.50
M. P. SEAH
states in the conduction
band.
In the cases of copper
and
silver this limit
will be about 8 eV because of the very low density of states towards the top of the conduction band. The minimum observed value of ET- EA, if the final electron is ejected from the conduction band is 2E,- E,-- Ea. The Auger peaks can be thought of as simply superimposed on the cascade background and not, in any way, interacting with it. The Auger emission peaks shown in table 3 have been observed in the present experiments in agreement with the results of Scheibner and Tharp5) and also Palmberg and Rhodin 20). TABLE3 Fixed emission peaks in the secondary electron energy spectra Target material
Peak energy W) ..““.____....-~
-cu Ag
Au
61.0 14.2 40.4 26.0 12.8 60.5 43.0 II.7
Theoretical energy%‘) feV) ~._ 63.6 see later 41.8 28.7 see later 57.6 46.8 see later
Lowest primary electron energy at which the peak is visible E3 f% tevt .~.~~____ __..
Transitions -‘I) Er! ..__.__ Mr\-,v
MIII
Mrv,v
NIV,~ NIII
NIH Nr
Niv,v Nrr,v
OIV, v 011 OItr, v 01v.v 0111 OlV,V
90 below 50 below below 90 7s below
20 40 20
20
To determine the theoretical Auger emission energies in table 3, it was assumed that the peak in the conduction band (ES) giving the emitted electron was 9 eV below the vacuum level. Other fixed emission energy peaks (e.g. the large peak in fig. 1 I) were observed besides the Auger emission peaks, and are discussed later. If the experimentally determined cascade background is subtracted from the total emission spectrum, the true shape and actual intensity of the Auger peaks can be determined. Fig. 11 is typical of the result so obtained for the 61.0 eV Auger emission peak in copper and is confirmed by results taken under conditions when the large peak is absent. From fig. I I the probability of ionisation of the RIICI level in copper by 120 eV electrons can be deduced. The primary electron beam was used at near grazing incidence in this experiment so that the majority of excited atoms would be near the surface and so all the Auger electrons moving along the surface normal in the metal would be emitted. The 61 .O eV Auger peak in fig. 1 I contains approximately 1O-61, electrons where I, is the primary electron beam intensity. If it is assumed that the Auger electrons are excited isotropically in the target and that all Auger electrons moving along the surface normal are emitted, then
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ELECTRON
SCAlTERINF
FROM
METALS.
I
151
Fig. 11. Emission spectrum along the surface normal in excess of the cascade background for copper in the energy region 20-70 eV, due to bombardment by 120 eV primary electrons at 70” to the surface normal. The emission intensity is given by the scale on the left or by the small box whose area is equal to 10 -B of the incident beam current.
the total number of Auger electrons produced near 61 .O eV is approximately 10m31, and the probability of ionising the Mm level in copper by 120 eV electrons is 0.1%. It is assumed that the Auger process is the only mode of de-ionising the M,,, level. The large peak in fig. 11 does not appear for all specimens and varies in an unusual way with angle of incidence of the primary electrons and angle of emergence of the secondaries. For a fixed geometry this type of peak remains at a fixed emission energy independant of the primary electron energy. The behaviour of these peaks as a function of angle of incidence and energy of the primary electrons and angle of emission of the secondary electrons was found to be identical to that of the elastic scattering of primary electrons at the energy of the peak. Some of the primary electrons are thus thought to lose energy without appreciable angular scattering, and then are elastically backscattered out of the target. Thus any peak in the elastic scattering current as a function of primary electron energy, angle of incidence or angle of emission will create a similar peak in the inelastically scattered current. It should be noted that if the elastic scattering is a maximum at an energy E,, then the inelastic scattering is a maximum at the emission energy E,, and not when the primary energy is E,,. We will term these peaks in the inelastic scattering as “diffracted inelastic” peaks. For fixed geometry these peaks are easily distinguished from Auger peaks, as the intensity of the latter decreases as the primary electron energy decreases, whereas the intensity of the former increases, rising very rapidly indeed as the primary and emission
152
M. P. SEAH
peak energies approach. Observation of the 61 .O eV Auger peak from copper showed that it increased roughly proportional to the primary energy between 100 and 300 eV whereas the background only increased as the square root of the primary energy. Scheibner and Tharp5) report a 13 eV emission peak in copper whereas Palmberg and Rhodin20) find peaks at 7 eV in copper and 12 eV in gold. The latter offer no explanation whereas the former relate the emission to the strong characteristic energy loss at 20.5 eV observed in their experiment. The first results obtained of the emission peaks around 12 eV, as shown in table 3 for copper, silver and gold showed intensities of the order of the peak in Scheibner and Tharp’s resultss). The elastic scattering properties of the surfaces used showed that they were probably composed of very small randomly oriented crystallites. Later experiments with a silver film, characterised by broad diffraction rings and which was therefore thought to be mainly composed of small crystallites predominantly oriented with their [l 111 axes along the surface normal, gave a much stronger emission peak at 12.8 eV as shown in fig. 12. In this case the emission current was concentrated along the surface normal. For all these metals, the emission intensities of the peaks near 12 eV were fairly independent of primary electron energy down to about 22 eV. These peaks are thus thought to be neither Auger emission nor diffracted inelastic peaks.
Fig. 12. Energy spectrum of electrons emitted along the surface normal from silver in the IO-22 eV energy range due to bombardment by 60 eV primary electrons incident at 50” to the normal. The dotted line shows the estimated cascade background, the very strong emission curve is that due to the (I 11) single crystal surface and the two intermediate curves are those of the polycrystalline surfaces.
SLOW
ELECTRON
SCATTERING
FROiU METALS.
I
Studies were now made of the single crystal film. The film was thought
153
to
be well ordered but extensively twinned. Some comments concerning the crystallography of the film are given in Paper III of this series. The energy and angular distributions of the inelastically scattered electrons showed the 12.8 eV emission peak to be very sharp in energy and primarily oriented along the foil normal. The experimental results are summarised in figs. 13 and 14. The intensity of the peak was highest for regions of the surface giving the best quality LEED patterns, and also highest for the highest angle of incidence of the primary beam.
Fig. 13. Secondary electron emission spectrum in excess of the background cascade taken from the result of the (11 I) surface of the silver single crystal as shown in fig. 12. The peaks occur at 12.8 eV and 17.3 eV.
Fig. 14. Intensity of the 12.8 eV (upper curve) and the 17.3 eV (lower curve) secondary electron emissions as a function of emission angle measured from the surface normal of the (111) surface of the silver single crystal film due to bombardment by 60 eV primary electrons incident at 50” from the surface normal.
A careful investigation of the emission peak energy as a function of emergence angle showed that, to within 0.05 eV and 0.15 eV respectively, the peaks at 12.8 eV and 17.3 eV remained constant in energy. In all respects the 17.3 eV peak behaved identically to the 12.8 eV peak. It was first thought that this was the sort of result predicted by the Urnkiupp theory embodied in the papers of Burnsz2) and Appeltr7). However, closer inspection of the theory leads one to suspect that this result should not be predicted unless the
154
M. P. SEAH
theory is extensively modified. the target with energy near
Burns expected
E,,, = 2”,:, (h2 -t- k2 + 1’) + E,
to see electrons
ejected from
(algebraically)
primarily oriented parallel to the [Ml] reciprocal lattice direction. E, is the inner potential of the metal for silver; LEED measurements imply E,= - 14 eV, whereas the calculations of Segallm) give E,= - 12 eV and the sum of the work function and Fermi energy generally used given E,= - 10 eV. Thus for the [I 1I] direction we find E r,i = 27.1 - 14to
IOeV,
thus E 111 = 13.1 to 17.1 eV, and either peak could fit Burn’ss2) or Appelt’si7) predictions. To check whether another, unknown, mechanism was producing the process described by eq. (8) the emissions associated with the [220] and [222] reciprocal lattice directions were looked for. The 12201 emission should occur at 58-62 eV and at 40” from the normal in the [lo] azimuth and the 12221 at 94-98 eV along the surface normal. The intensities for these effects would be expected to be less than for the [I 1 I] as they are of higher order. No such peaks were found. Within the limits of the experimental technique, if emission occurred at these energies and directions it was less than 1% of the 12.8 eV emission intensity. Palmberg and Rhodinas) with a more sensitive technique did not observe these peaks. It is therefore assumed that the process described by eq. (8) does not occur and that the correlation along the [I 1 I] reciprocal lattice direction is coincidental. An alternative interpretation is that, by the time electrons in the primary beam have lost energy down to 30 eV in the solid, they will be travelling in all directions. Those directed along the surface normal into the crystal lose a little more energy until they are on the upper edge of the free-electron-like band gap at around 27 eV, they are then Bragg reflected along the surface normal and emitted, However, for a nearly free electron model of the band structure of silver, this process predicts that, for electrons emitted at an angle 8 to the surface normal, the peak, although weaker, should show a shift of 27 (tan2 0) eV towards higher emission energies. For 0 = 8” and 12” this gives a shift of 0.5 and 1.2 eV respectively for the 12.8 eV emission. Since the observed shifts of the 12.8 eV and 17.3 eV emissions were less than 0.05 eV and 0.15 eV respectively over this range, these emission peaks are not thought to be due to diffraction phenomena.
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Before
the results
ELECTRON
were
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it was considered
155
I
that
for a single
crystal, minima should occur in the emission spectra taken along a given direction due to the band gaps existing along that direction. The calculations of Burdicklg) on the band structure of copper give the only available data in the required energy range. The relevant part of the band structure in the [ 11I] direction is shown in fig. 15a. The band structure of silver was deduced approximately from this by reducing the energy scale by a factor equal to are the lattice constants, as shown on the right (%/aAg)2, where acu and aAg (000)
02hb)
15..
_._____._. _._. _I0
IO. &j
Fermi Enwgy
__! _ I
z8
r Ag
C”L (4
. Demify of Stder
hfe&tyofExclar Emhim
(b)
Fig. 15. (a) The energy bands for copper in the [ill] direction after Burdicklg). (b) Schematic density of unoccupied stated deduced from the energy bands for copper compared with the excess emission peaks of fig. 13.
of fig. 15. The density of unoccupied states relevant to fig. 15a is shown schematically in fig. 15b, together with the excess emission peaks. It seems as though good correlation does exist if the inner potential is assumed to be - 14 eV as amply demonstrated from LEED studies. The constancy of the emission energies as a function of emission angle of the 12.8 and 17.3 eV peaks is hard to explain on this model. From these experiments it is not possible to determine whether the decay is occurring primarily along the [l 1 I] direction or perpendicular to the surface as these are coincident in the specimen used in this study. If the decay is perpendicular to the surface, a system like that used by Scheibner and Tharps) should show the same emissions diminished by a factor of 30. This
156
M. P. SEAH
is approximately their result for copper. If the decay is parallel to the [1 I l] axis which is at 54” to the surface normal in their experiment, the electrons will be totally internally reflected and the peaks not seen. Thus the 12.8 and 17.3 eV emissions in silver are thought to be related to the surface and not to the band structure. The sharpness of the 12.8 eV emission peak in energy and its preferred direction might indicate that it is due to the decay of a surface-related excited state in the crystalea). It is likely that the 14 eV and 11 eV emissions in copper and gold have a similar origin. If the excited state decays by emitting a conduction electron, there will be an associated spectrum of emission energies with peaks due to the peaks in the conduction band density of states. As there are two sharp d-band peaks in the conduction bands of these metals it must be postulated that only one can participate in this process. Thus the emission energy minus (algebraically) the d-band peak energy should equal one of the characteristic loss energies. If the excited state is due to a collective effect of electrons near the Fermi surface, the ejected electron could have been one of these electrons. Thus the characteristic loss should then be equal to the emission energy minus the Fermi energy. The intensities of the characteristic losses are of the correct order of magnitude for correlation with this emission. Correlations are shown in table 4. The d band peaks of copper and silver are taken from Berglund and Spicer’sis) work and for gold by estimation from the American Institute of Physics handbookal). The observed losses A and B are those measured in this apparatus and are seen to be at least 0.5 eV lower than other published data. The correlation between the peak emission energies if the electron is originally one of those near the Fermi surface and the characteristic losses, B, is clearly quite good. The 18.4, 24.4 and 22.2 eV energy losses in copper, silver and gold respectively are generally called the plasmon losses as they are more intense than the other losses. It may be that correlation with the emission peaks should be sought for these. The justification for their description as plasmon losses is not obvious, whereas the justification for labelling the 4 eV loss in silver as a plasmon lossa4) seems well founded. The other losses shown in table 4 are generally the 27.5 eV loss in copper being strong and the others labelled “unknown”; weak. If the emission is due to an excited state and not due to a band structure effect, which seems quite reasonable, it is surprising that the appropriate characteristic loss is not sharper. In order to investigate the emission further, the intensity of the 12.8 eV emission peak along the surface normal was measured as a function of the incident electron energy. Reproducibility was not excellent, due to nonuniformity in the specimen, but was adequate for a qualitative discussion. The curve is shown in fig. 16. The result is much like that for total emission
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158
M. P. SEAH
Fig. 16. (1) Intensity of the 12.8 eV emission peak above the background as a function of incident electron energy scaled up by a factor of 8. (2) Intensity of the background emission near 12.8 eV as a function of incident electron energy. These results are taken for emission along the surface normal of the (111) silver surface for primary electrons incident at 50” from the surface normal.
except that the maximum occurs at a much lower energy. The maximum in the total emission is due to the fact that as the primary electron energy rises more energy is available to excite secondaries and thus the emission rises. However, as the primary energy rises the secondary electrons are created deeper and deeper in the target and are Iess likely to escape. The product of the two functions, one rising and one falling, produces a peak in the region of l-2 keV. In the case of the excited state mentioned above, the peak occurs at 80 eV so the decreasing function must be characterised by a length much shorter than the mean free path of the low energy secondaries. If, as proposed, the excited state is related to the surface, the excitation would only occur in a narrow surface zone whose depth would indeed be much shorter than the accepted mean free path of the secondaries lo). Thus the proposition that the emission peak at 12.8 eV in silver is due to the decay of a surfacerelated excited state corresponds with all the experimental observations. The experimental results on the other hand are contrary to the density of states and band structure explanation, or indeed, any explanation associated with the crystal rather than the surface. It is not understood why the influence of the density states and band structure is not observed whereas in the photoemission work of Berglund and SpiceriG) they are clearly evident. 6. Conciusio~ The energy polycrystalline
spectrum of the cascade of true secondary electrons from copper and silver follows a well defined law of the form
where
for silver and
X=2.0
1.6 for copper
and
where
S is the surface
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threshold
function,
ELECTRON
SCATTERING
FROM METALS.
and 4 is the work function.
I
This type of spectrum
159
is
predicted by Streitwolf 12) if the secondary electrons undergo little inelastic scattering after creation. However, for non-normal incidence of the primary electron beam, lack of agreement between the measured angular distribution of the secondary electron current and that predicted using Streitwolf’sra) result, implies that direct application of Streitwolf’s result may not be adequate here. The above type of spectrum is also predicted by Wolff 1) if a diffusion cascade of the true secondary electrons occurs and if energies are measured from the Fermi surface and not the bottom of the conduction band. The threshold function 5’ is not of the form expected on the Sommerfeld model of a metal, but for silver and copper has been shown to be approximately S = E,/(E, + 0.35)) from which it is deduced that secondary electrons escaping from these metals behave as if they occupied a free-electron-like band starting 0.35 eV below the vacuum level in both metals. Auger peaks have been observed in the spectrum as generally reported by other workers. Care must be taken in identifying Auger peaks, especially when using energy analysers accepting only a small solid angle of the emission current, as confusion can arise with “diffracted inelastic” peaks. The occurrence of the “diffracted inelastic” peaks shows that some of the primary electrons can lose large amounts of energy without appreciable angular scattering and then undergo diffraction in the same way as primary electrons at that energy would. The emission peak at 12.8 eV in silver is interpreted as an emission due to the decay of a surface-related excited state with the emission occurring primarily along the surface normal. The correlation with the characteristic losses in silver implies that the emitted electrons in the 12.8 eV emission peaks were originally very near the Fermi surface. The emissions at 14.1 eV and 11.7 eV in copper and gold are thought 12.8 eV emission from silver.
to have the same origin as the
Acknowledgements The author wishes to express his sincere thanks to Professor C. F. Powell for the facilities provided in the H. H. Wills Physical Laboratories of the University of Bristol where preliminary experiments on secondary electron emission were performed, to Professor A. J. Forty for his encouragement and interest in the work and to Dr. B. W. Holland for stimulating and useful discussions. A grant from the Science Research Council for the construction of the apparatus is gratefully acknowledged.
160
M. P. SEAH
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24)
P. A. Wolff, Phys. Rev. 95 (1954) 56. J. W. May, Ind. Eng. Chem. 57 (1965) 18. J. J. Lander, Progr. Solid State Chem. 2 (1965) 26. L. A. Harris, J. Appl. Phys. 39 (1968) 1419, 1428. E. J. Scheibner and L. N. Tharp, Surface Sci. 8 (1967) 247. B. E. Dicker, J. Sci. Instr. 42 (1965) 887. H. Jaeger, P. D. Mercer and R. G. Sherwood, Surface Sci. 6 (1967) 309. J. G. Allpress and J. V. Sanders, Surface Sci. 7 (1967) 1. K. Mtiller, Z. Physik 195 (1966) 105. 0. Hachenberg and W. Brauer, Advan. Electronics and Electron Phys. ll(1959) 413. C. N. Berglund and W. Spicer, Phys. Rev. 136 (1964) 1030. H. W. Streitwolf, Ann. Physik 3 (1959) 183. A. Van der Ziel, Phys. Rev. 92 (1953) 35. H. Stolz, Ann. Physik 3 (1959) 197. P. H. Cutler and J. C. Davis, Surface Sci. 1 (1964) 194. C. N. Berglund and W. Spicer, Phys. Rev. 136 (1964) 1045. C. Appelt, Phys. Status Solidi 27 (1968) 657; see also a “comment” on this paper, M. P. Seah, Phys. Status Solidi 31 (1969) K 123. B. Segall, Phys. Rev. 125 (1962) 109. G. A. Burdick, Phys. Rev. 129 (1963) 138. P. W. Palmberg and T. N. Rhodin, J. Appl. Phys. 39 (1698) 2425. American Institute of Physics. Handbook 7-138, 2nd ed (McGraw-Hill, New York, 1963). J. Burns, Phys. Rev. 119 (1960) 102. An idea originally proposed by B.W. Holland, private communication. H. Raether, Surface Sci. 8 (1967) 233.