Secondary Electron Emission

Scanning Electron Microscopy

Volume 1982 Number 1 1982 Article 3

1982

Secondary Electron Emission

Hellmut Seiler University Hohenheim

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SECONDARY ELECTRON EMISSION

Hellmut Seiler

University Hohenheim, lnstitut fUr Phy sik Garbenstr. 30, D-7000 Stuttgart 70 West Germany Phone: 0711 / 4501/2150

ABSTRACT INTRODUCTION

The paper surveys experimental and theoretical work on Secondary electron emission (SEE) discovered in 1902 by secondary electrons released by primary electrons with ener Austin and Starke, is the proces s by which electrons are emit gies greater than 100 eV with regard to electron microscopy ted from the surface of a solid as a result of its bombardment and microanalysis. The secondary electron emission is a by fast primary electrons (PE) . rather complex phenomenon: I) The interaction of energetic Fig. I shows schematically the energy distribution of these primary electrons with material and the excitation of elec electrons released by fast PE with energies EpE> 100 eV. trons of the solid into higher energetic states, 2) The tran s According to their energy the electrons can be divided in two port of the electrons to the solid-vacuum interface, 3) The groups: emission of secondary electrons over the surface barrier into I) Electrons with energies E ~ 50 eV : Secondary Electrons the vacuum. (SE); 2) Electrons with energies 50 eV < E ~ EPE: Inelastical For the interpretation of scanning electron micrographs ly or elastically back sca ttered electrons or reflected electrons especially the secondary electron yield is important, the es (RE). cape depth of the secondary electrons and the contribution According to the two groups we can define of the backscattered electrons to the yield. The yield depends I) SE-yield o = number of SE / number of PE on the material of the surface and on the angle of incidence . 2) Back sca ttering coefficient r, = number of RE/ num The investigation of the fine structure in the energy distribu ber of PE and also a total yield a = o + r,. tion of the secondary electrons released on clean surfaces is Using PE with EPE = 2 keV we get on metal surfaces necessary for the theories, e.g. the production of secondary o = 0.3 , Auger yield = number of Auger electrons per electrons by plasmon decay . PE = 10 - 4 _ ...... 10- 5, 'YIERE= number of elastically reflected electrons per PE = 0.03. Fig. lb shows the energy distri bution of electrons released from a Ta- surface by electron impact of 1000 eV. The peak of the ERE is also to be seen if EPE = 25 keV (Bauer, 1979). SEE is a complex phenomenon involving interactions be tween energetic electrons and a solid, electron transport and surface physics. The PE may be scattered elastically. These ERE are used for the investigation of crystal structure in LEED and HEED (Low resp. High Energy Electron Diffrac tion). The PE may be scattered inelastically and undergo characteristic energy losses. These can be divided into 4 cate gories (Ertl and Kuppers, 1974): I) Excitation of core electrons, if the energy of the PE is Keywords: Secondary electron em1ss1on by primary elec suffic ient to ionize the atom by exciting one core electron to trons, secondary electron yield of metals and insulators, an unfilled state above the Fermi level. escape depth of the secondary electron s, contribution of 2) One electron excitations of valence electrons. An elec backscattered electrons to the yield, recent theoretical work tron in the valence band may be excited to a higher level of on secondary electron emission, retarding field analyzer the same band (intraband transition) or into another energy (RFA), angle resolved secondary electron spectrometer band (interband transition) . The energy losses of the PE are (ARSES), cylindrical mirror analyzer (CMA). typically of the order 3 - 20 e V. 3) Collective excitation of valence electrons (Plasmon Losses). The theory of plasmon excitation has been devel oped by Bohm and Pines (1952, 1953). The frequency wP of

33 H. Seiler

n(E) N(E) 14--SE _,, ______RE ______SE / Fig. lb

~ Auge\E J l-__:~===i=====:::t:===·u.1__ E 1+-S0eV-t0 IEpe ERE ---E--- 14--l!.E~ Fig. la Schematic energy distribution of electrons emitted from a surface as a result of its bombardment by fast electrons.

Fig. lb The energy distribution of electrons emitted from a Ta-surface. EPE = 1 keV. 0 500 1000 eV

the volume plasma oscillation of an electron gas is given by

LIST OF SYMBOLS

SE Secondary electron w = ~ = p SEE = Secondary electron emission -v--;;;--;; PE = Primary electron ne = density of the electrons E = Energy m = mass of the electron RE = Reflected or backscattered electron e = charge of the electron ERE = Elastically RE t = permittivity of vacuum 0 = Secondary electron yield 0 Backscattering coefficient 7/ = The theory of surface plasmons was developed by Ritchie a = Total yield = o + r, (1957). WP = Volume plasmon frequency ws = Surface plasmon frequency w 5 = WP / ✓ 1 + to ne = Electron density m,e = Mass, charge of electron to = dielectric constant of the medium outside to = Permittivity of vacuum the solid to = Dielectric constant = Mean escape depth of SE The excitation of surface plasmons depends strongly on " = Most probable energy of SE thin adsorbed layers on the surface . Without adsorbed layers = Half width of energy distribution of SE Ws =WP / ._fI = Maximum of SE-yield EfE = Energy of PE where o reaches its maximum The energy losses of the PE are between 5 and 60 eV. J = Ionization energy 4) Excitation of surface vibrations (Phonons). These T = Maximal escape depth of SE "" 5>. energy losses are very small, in the range of some 100 meV IMFP = Inelastic mean free path of monoenergetic elec- and cannot be detected with normal spectrometers in reflec trons tion (Froitzheim 1977). In transmission they were detected by {} = Angle of incidence of PE against surface normal Boersch et al. 1969. oPE = Number of SE released per PE The electrons which have suffered characteristic energy oRE = Number of SE released per RE losses can be distinguished from the other features in the energy distribution curve (Fig. la) by changing the energy of (3 = ORE/OP E D = Information depth in SEM the PE . They have a constant energy difference with respect to EPE· Auger electrons and SE have fixed energies and only t = Energy to produce one SE B = Constant < 1 the shapes and the heights of the various peaks may change e = Density on variation of EPE· E, = EPE/ Ef E In the elementary theory of SEE developed by Salow = Work function (1940) and Bruining (1954) and others, the SE-yield o as a

34 Secondary Electron Emission

function of primary energy EPE can be written in th e fol lowing form: 0-.... ' o = l n (x, Epti) f(x) dx (I) SE+RE' \ n (x, Epti) is the number of SE produced at a dista nce x from the surfac e by a PE with the energy EPE· f(x) = B e -x /"is the probability that a SE originating from ~PE the depth x reaches the surface and is emitt ed into the vacuum. B is a coefficient which takes into acco unt that only a frac RFA tion of the excited electrons migrates towards the surfac e, ARSES reaches the surface and passes over the sur face barrier into the vac uum . >--is the mean escape depth of the SE. PE The SEE has been reviewed by severa l aut hors: Bruining (1954), Kollath (1956), Dekker (1958), Hachenberg and PE Brauer (1959),Streitwolf (1959),Wh etten (1961), Puff (1964), Bronst ein an d Fryma n (1969). But recently there has been a 11:~ lot of new experiment al or theore tical work in this field: Kanter (1961), Jahrrei ss (1965), Wittry (1965), Mayer and ~ E!Y --y Holz! (1966), Seiler (1967, 1968), Appe lt (1968), Simo n and ~ William (1968), Seah (1969), Drescher et al. (1970), Shimizu and Murata (1971), Kanaya and Kawakatsu (1972), Murata SEM EEM (1973), Shimizu (1974), Fitting (1974, 1976, 1980), Willis and Feue rba ch (1975), Voreades (1976), Pillon et al. (1976), Chung and Ever hart (1977), Reimer and Drescher (1977), y Kanaya and Ono (1978), Alig and Bloom (1978), Ono and Kana ya (1979), Ga nachaud and Ca iller ( 1979), Chase et al. (1980), Rosier and Brauer ( 198 1), Ca iller et al. (198 1). ~y ! EX PERIM ENTAL METHODS FOR MEASU RING SEE

Fig. 2 show s different ana lyzers and electron microscope s CMA for measuring SEE .

1. Retarding Field Analyzer (RF A) Fig. 2 Various analyzers and electron microscopes for mea ---s uring SEE. This ana lyzer is normally used for determining the crysta l struct ur e of the outermost layer of single crysta ls by Low Energy Electron Diffra ction (LEED) an d for mat erial analy sis by Auger Electron Spectroscopy (AES) . By sweep ing suited for exac t measurements of SE-yie ld. The take-off the potential of the retarding grid the energy distribution of ang le is on ly 42 ± 6° and the electrons are mostly registered the emitted electrons can be measured indepen dent of their by a multipl ier, the characteris tics of which may influ ence emission dire ction. With the co llector , a and r, can be deter the number of measured SE. mined and hen ce the yield o = a - r,. This RF A can be very simply built into ultra high vac uum system s so that SEE can 4. Scanning Electron Microsco pe (SEM) be measured on clean surfa ces. The number of SE which reach the detector per object 2. Angle Resolved-SE-Spectrometer (ARSES) point gives the SE-signal. This signal is influenced by SE released by RE at the wall of the micro scope. Furthermore With a revolving Faraday cup, combined with a retarding most SEM's do not use ultra high vacuum , so that the surfa ce field, it is po ssible to measure the energy-angle-distribution of the objects are contaminated. Henc e it is sometime s diffi of SE. cult to use result s of SEE for the interpretation of image contrast in a SEM. 3. Cylindrical Mirror Analyzer (CMA) 5. Emission Electron Microscope (EEM) By sweeping the potential of the outer cylinder, electrons of a certain energy are focu sed on the detector. This CMA is Normally in EEM the electrons are released by photo emis mostly used for AES because of its high SI N-ratio . In the sion or ion impact , but it is also possible to use a PE-be am to energy spectrum the SE can be seen, but the CMA is not well release SE. The se SE are acce lerated by an electric field , fo-

35 H. Seiler

Fig. 3 Energy distribution E-N(E) of SE and of RE (near SE (Fig, 3a) ERE -- -ERE) of an oxidized Al-surface (-a-) and of a clean Al surface (-b-) (Bauer and Seiler, 1982). On the clean Al surface the volume plasma (6E = 15 eV) and the sur face plasma loss (6E = 10.6 eV) are to be seen. EPE = 0.5 keV. cussed by a cathode lens and the object is imaged on a screen. By using an aperture in the focal plane of the cathode lens it is possible to separate the SE from the RE. In an ultra high vacuum EEM it is possible to use the information on SEE for the interpretation of the image contrast. EEM's are rather rare, because they allow only imaging of plane surfaces.

EXPERIMENT AL DAT A ON SEE

I. Energy distribution of SE The energy distribution of SE, released by fast PE (EpE > 100 eV) is nearly independent of the energy of the PE, and is characterized by the most probable energy E 5E and the half 10 eV 50 eV width (HW). ElfE is difficult to measure . Generally O eV is I I I chosen at the intersection of the steep linear increase with the energy axes. In a correct description the energy Esk should be measured above the Fermi energy. E5E and HW both SE (Fig, 3b) ERE depend on the material of the surface. HW is sma ller for in sulator s than for metals and especially the HW depend s strong ly on very thin layers on the surface (Dietrich and Seiler, 1960). According to Kollath (1956), for metals 1.3 eY :SEsE :S 2.5 eV and 4 eV :S HW :S 7 eV. New mea sure ments on clean metal surfaces show 1 :S Esk :S 5 eY and 3 :S HW :S 15 eY (Schafer and Holz!, 1972). Fig. 3 shows the energy distr ibution of an oxidized Al-surface and an Al-sur face cleaned by ion spu ttering (Bauer and Seiler, 1982). Superimposed on the energy distributions of clean surface s there are often so me maxima. Only some of these can be in terpreted as Auger-maxima. This SE-spectroscopy will be discussed later.

2. Angle distribution of SE The angle distribution of SE from polycrystalline surfaces is a cosine-distribution, nearly independent of the angle of incidence of the PE (Jonker, 1957). The angle distribution of 10 eV SOeV SE of a single crystal face shows an anisotropy (Burns, 1960), I I and the energy-angle-distribution shows a sharp fine struc ture (Appelt, 1968). The angle distribution of the SE is not important for image B contrast in SEM because the extraction field of the SE-detec (Fig, 4) tor is generally strong enough to collect the SE.

3. SE-yield I ----t------Fig. 4 shows schematically the SE-yield o as a function of 1 I primary energy EPE· The general shape is the same for all I materials: o increases with EPE• reaches a maximum value omat E~E and then decreases with increasing EPE· Values for omand E~E can be seen in many publication s (Seiler (1967, 1968); Kanaya and Kawakatsu (1972); Kanaya and Ono (1978); Ono and Kanaya (1979)) . Fig. 4 The SE-yield o as a function of primary energy.

36 Secondary Electron Em ission

However some care mu st be taken because often in older the SE and we can assume that T == 5 • A (Seiler, 1967), 01 01 The escape depths of the SE from metals are very small papers a is cited instead of 6 • For metals we have values (>-==0.5 - 1.5 nm; T ==5 nm) compared with that of insula 0.35 s 601 s 1.6 at 100 eV s ErE s 800 eV, for insulators tors (>-== 10 - 20 nm; T == 75 nm) . Mean escape depths of 1.0 s 601 s 10for300eV s ErE s 2000eV . High values for metallic oxides as AliO 3 and MgO and alkali halides as BaF 2, c5are found on single crystals of insulator s such as MgO : NaCl and KCI are shown by Kanaya and Ono (I 978) . The c5rn== 20 - 25. Very high values c5 > 100 are found for sur high yields of insulators may be caused by the large escape faces with negative-electron affinity (see 5). 601 reaches high depths . According to ca lculations of Ono and Kanaya ( 1979) 01 the escape depths of the SE show regularities within the values if ErE is also high, so that for metal s 6 / ErE == elements of the periodic table. 3 2. 10 - e V - t (Ono and Kana ya, 1979). This mean escape depth of SE is different from the inela s An interesting example of the simultaneous increase of tic mean free path (IMFP) of monoenergetic Auger electrons 601 and ErE is shown by Beisswenger and Gruner (1974) mea (AE) in the material. The IMFP of AE is also the mean suring the yield of reactive evaporated BeO-layers. escape depth of AE. If an AE has lost energy it is no longer There exists no monotonic relation between c5 and the detectable as an AE, whereas a SE, which has lost energy atomic number Z of the surface atoms. So a material analysis may still have sufficient energy to leave the surface. Thu s the by mea suring the SE-yield is not possible. Many authors tried mean escape depth of SE of a particular energy should be not to show regularities of the dependence of c5rnwithin the ele smaller than the IMFP. An estimate of the escape depth for ments of the periodi c table (e.g., Seiler (1967), Ono and an electron can be obtained / Simon a nd Williams ( 1968) / Kanaya (1979), Makarov and Petrov (1981)). Atoms with a by use of the following three-dimensional random walk for 112 large diameter have small c5rn(Seiler, 1967). According to mula: escape depth>.== (N/ 3) -IMFP. N is the number of collisions in which the electron can participate and still be Ono and Kanaya (1979) 601 and ErE depend both on the 415 emitted. Amongst the values of IMFP's for slow electrons ionization energy J of the surface atoms: c5rn- J , ErE - reported by Kanter (1970), Quinn (1962), Voreades (1976), j4 15_ the curve of Seah and Dench (1979) is the mo st powerful, In SEM the energies of the PE are normally higher than cove rin g mea surement s in different materi als and with differ ErE· For ErE ~ ErE c5i s proportional to ErE - o.s (Reimer ent energies . Thi s curve show s a minimum IMFP of 0.5 nm and Pfefferkorn, 1977). For Al c5decrease s from c5 == 0.3 for electrons with energies of about 40 eV. (Er E = 10 keV) to c5 == 0.03 (Er E = 100 keV) . The yield Hence the >-(SE) seems to be rather sma ll compared with depend s stro ngly on thin surfa ce layers and in particular the the IMFP's. However it must be taken into consideration, contaminatio n layer at the impa ct point of the electron beam that I) th e energies of the SE must be ca lculated above the in normal vacuum changes the yield (Wittry (1965), and Fermi level, and 2) the mean escape depth of the SE is mea Seiler and Stark (1965a)). sured by the decrease in the SE-current with increasing thick The measurement of c5on the surface of insulators is dif ness of layers with smaller SE-yield . A large contribution to ficu lt beca use of charg ing effects. If a = o + .,, > I, the the SE-current stems from SE with energ ies above the most charging of the surface becomes positive, but the positive probable energy which are thus nearer the minimum on the potential of the surface can only reach values of the potential curve of IMFP's. of the collector. If a = o + .,,< I for E PE > E PE• the charg ing of the surface becomes negative. The incoming PE are 5. The yield c5as a function of the angle of incidence. decelerated and the potential of the surface changes until c5increases with increa sing angle of incidence (} against the a = I is reached. The potential of the surface may reach surface normal according to values near the potential of the cathode of the PE beam. Thin insulating layers can be investiga ted on co nductin g o((}) = o /cos (}; (2) bulk material. The charging can be limited by field emission 0 through the layer or by electron-induced conductivity. Using this relation is valid for objects with a mean atomic number highly insulating material such as KCI or BaF 2, especially and not to close to 90°. The increase of c5 with increa sing when evaporate d under rather high pressure to give a layer of angle of incidence (} is greater for objects with low atomic low density, field enhanced SEE may arise (Goetze et al. number and smaller for specimen with high atomic number (1964), Goetze (1968) , Seiler and Stark (1965b)). as shown by Reimer and Pfefferkorn (1977). This increase of c5is due to the small escape depth of the SE. The longer the 4. Escape depth of the SE pathway of the PE within the escape depth of the SE, the The escape depth of the SE is very small. Only SE excited higher the yield . With increasing (} c5mand ErE increase / near the surface have a certain possibility to reach and to Reimer and Pfefferkorn (1977), Sa lehi and Flinn (1981) /. leave the surface . The escape probability for SE produced at Using single crystals superimposed on the monotonic in a distance x from the surface, decreases with e - xi\ where >. crease, there is a fine structure (Palmberg (1967), Seiler and is the mean escape depth, which can be measured by various Kuhnle (1970)) as shown in Fig. 5 which causes the electron methods (Seiler, I 967). Layer s of increasing thickness were channelling pattern (ECP) and the different brightnes s of usually evaporated onto bulk material. Beyond a particular di fferent crystal faces (the orientation contrast) in SEM and thickne ss T of the layer, c5no longer depends on the bulk EEM (Carle and Seiler, I 966). material. If 'f/bulk = 'f/Jayer ' T gives a maximal escape depth of

37 H. Seiler

(1 {3 ==4; for EPE~ 10 keV, {3 ==2; Dre scher et al. (1970): {3 > I, because firstly the mean energy of the RE is less 0,425 than EPE and so o is nearer to om, and secondly the angle of 6,5 kV distribution of the RE causes that (at normal incidence of the PE) the pathways of the RE are usually longer than tho se of 0,400 the PE. With increasing angle of incidence of the PE, {3 decreases (Seiler, 1968). This contribution of RE to o is very important for the ob servations in SEM. There is often a contamination layer on 0,375 the object surface so that the image contrast is caused by the difference in !J rather than in o.For an Al surface with a con tamination layer we get a yield o ==0.10 at E PE = 20 ke V. With {3 = 4 we can calculate that oPE = 0.07 and oRE = 0.28 . 0,350 The spatial distribution of SE released by RE at an angle of incidence of 50° was determined by Ha sselbach and Rieke (1978, 1982) in a combination of SEM and EEM . Only the SE-Image is focussed by the cathode lens on the photograph 0,3 25 '------.------.---.....---,----r---..,,.----,-- ic plate. The spatial distribution of the SE relea sed by the RE +300 +20° +10° oo -10° -20° -30°d.. from a fine electron probe increases with increasing energy of the PE and is much greater for Si than for Au.

6,5 kV 7. Information Depth 0,100 The Information Depth D in SEM is defined as the depth below the surface of the object contributing to the SEM pic ture. Object details in a depth d, with d ~ D, can be recog nized. D depends on the minimal contrast which is detectable 0,080 in the SEM, on the maximum exit depth of the RE which is about R/2 (R = range of the PE), even if secondary elec trons or Auger electrons are used, and on the difference tl.!J in the backscattering coefficients between the object detail and the adjacent material (Seiler, 1976). 0,060L...... ---r-----r-----r-----r-----r-----r-----r-- Assuming a minimal contrast of 0.01 in the SEM, the in +300 +20° +10° 0° -10° -20° -30° c1 formation depth is D = R/ 8,ln (100 tl.!J). With the energy range relationship the information depth becomes D = 1.4 • Fig. 5 Dependence of the total yield a and !J on the angle of In (100 tl.!J) ,E '-35 (Din µg/ cm 2 for E in keV) . The calculated --- incidence for a Si-(111)-face (Seiler and Kuhnle, values are in rather good agreement with experimental 1970). results. In a SEM with 8 keV primary electrons, gold can be detected within compact aluminium in a depth less than D = 30 nm. 6. Contribution of RE to SE-yield SE are not only released by PE but also by RE. This con tribution by RE to the SE-yield has been investigated by SEMIEMPIRICAL THEORY OF SEE several authors (Kanter (1961), Bronstein and Frayman ( 1969), Seiler ( 1967, 1968), Drescher et al. ( 1970), Kana ya The elementary theory developed by Sal ow ( 1940) and and Kawakatsu (1972), Fitting (1974, 1976), Reimer and Bruining (1954) has been reviewed by Dekker (1958) and Pfefferkorn (1977)). Kollath (1956). Kanter (1961) showed that the SE-yield of thin foils is less The SE-yield can be written in the following form : than that of bulk material because most PE can penetrate thin foils, !J is very small and hence the SE are released almost o = l n (x, Ep0 f(x) dx (I) exclusively by PE. n(x, Ep0 is the number of SE produced at a distance x The SE-yield is given by two parts: from the surface by a PE of the energy EPE ' · f(x) is the probability that a SE produced at x reaches the o = 0PE + !JORE (3) surface and is emitted into vacuum. oPE is the number of SE released per PE Assuming that n(x, Ep0 is proportional to the average oRE is the number of SE released per RE energy loss per unit path length

For EPE > E~E is oRE/ oPE = {3 > l. The measurements of dE (4) Bronstein reviewed by Seiler (I 967) result for EPE < 5 keV, E dx

38 Secondary Electron Emission

E is the energy required to produce a SE. It is generally as value corresponds well with the experimental data . sumed that With (7) and (10) we get

(5) ==0.4 (12) were 8 is a constant < I, and takes into account that only a fraction of the excited electrons migrates towards the surface and the probability of these electrons reaching the surface Using the experimental values for different metals / Ono and pass over the surface barrier into vacuum . and Kanaya ( 1979) I According to Young (1956, 1957) the energy dissipation of 8 m 3 PE within the material is approximately constant and hence 2 • 10- E ==----,we get - ==200 eV (13) eV 8

-dE For insulators a relation exists (Alig and Bloom, 1978) be (6) tween E, the electron hole-pair creation energy and the band dx R gap Eg : E = 2.8 • E g. From this 8 can be estimated. (Si: where R is the range of the PE B = 0.034, Ge: 8 = 0.013, KC!: 8 = 0.32). From equations (I, 4-6) we get an expression for 8 (EPE) From (9) and (11) the mean escape depth >-.thof the SE can be estimated from experimental values for EPE• and then R 8 EPE compared with experimental values for >--exp· 8 = - - - e - xi >-dx JO E R (7) Al : Ath = 3.7 nm, >--exp== 0.5 - 1.5 nm Pt : Ath = 1.5 nm, >--exp = 0.5 - 1.5 nm MgO: Ath 18 nm , >--exp 10 - 20 nm (8) = = MISCELLANEOUS PROPERTIES OF SEE Using the ener gy range relation 1. Influence of work function on SEE 5 R I. 15 • I 0 E PE 1.35 Contrary to photo, thermionic - and field-electric emission , (9) the work function ¢ of the surface is not as much important nm e I (kg/ m 3) ( keV ) for SE yield. Metals with high ¢ often show also high o.Both ¢ and 8 are small if the diameter of the surface atoms is large, we get 8 = 8 (Ep[) or 8 = 8 (R) as for Li, Na, K, Rb , Cs . Of the three proce sses which con 8 (Ep[) is a function which increa ses with EP E up to a tribute to SEE, I) SE production, 2) migration of the elec maximum 8m at EP E and then decrease s. tron s to the surface and 3) escape of the SE over the surface For EP E ~ Ep E: 8 - EPE - 0-35, wherea s experimentally / potential barrier, the first two processes strongly depend on Reimer and Pfefferkorn (1977) / 8 - EP E - o.swas measured . the bulk properties, while the third process should cause an increase in 8 with decreasing ¢ . Palmberg (1967), Schafer and The reduced yield 8 I 8m as a function of Ep E/ EP E is in Holz! (1972) tried to reduce¢ by evaporating Na on Ge or Pt surfaces . Reduction of ¢ from 4. 79 to 2.3 eV increased 8m dependent of the constants 8, E, Q, which are characteristic for the material under con sideration. Thu s according to this from 1.2 to 3.6, while EPE increased from 700 to 2000 eV. theory the reduced yield curves should all follow a single uni Haas and Thomas (1977) investigated the SE-yield of differ versal curve . ent single crystal face s of Cu . The increase of 8m from 1.2 to 1.5 with decreasing ¢ from 4.65 to 4.35 eV wa s found to be determined primarily by ¢ of the different crystal faces and not so much by the bulk lattice orientation .

2. Fine structure of the energy distribution of SE with Er = EpE/ EPE· Heinrich's (1973) measurements on polycrystalline Al Calculating the maximum of the yield curve 8 = 8 (R) we showed that for very clean surfaces, the peak of the energy get the maximum for distribution of SE is broadened and a structure appears. Sub sequently many measurements (Everhart et al. (I 976), Chase R = 2.3 • >-. et al. (1980), Massignon et al. ( 1980), Bauer and Seiler (1982)) of the SE region and of the characteristic loss region According to several authors (Seiler (1967); Simon and near the elastic electron spectrum have been made in order to Williams (1968); Buchholz (1969)) the maximum of the yield explain the structure. Everhart et al. (I 976) and Chung and curve is reached if the range of the PE is approximately the Everhart (1977) concluded that an appreciable contribution escape depth of the SE. Using the maximal escape depth to the total number of SE emitted from nearly free electron R == T and the mean escape depth R ==>-., the theoretical metals under keV electron bombardment may come from the

39 H. Seiler decay of surface and volume plasmons into single electron Monte- Ca rlo calculations of SEE from metal s and from Al excitations . were published by Ganachaud and Ca iller (1979). The various types of collisions suffered by an electron travelling in the 3. Excitation of SE with slow PE so lid are analyzed. Th e different damping mechanism s for pla smon s are reviewed and their influence on SEE is empha Using PE with high energies EPE > 100 eV ther e are many sized. The elastic and ionizing collisions with the ionic core possibilities for excitation of electrons, which can migrate to are described by a random model and the relative importance the surface and leave the surface as SE. With slow PE we of each of the above proce sses for SEE is discus sed. Cailler et have fewer excitation possibilities. So it should be possible to al. (1981) de scribed the interaction of an energetic electron separa te between Auger processes and interband excitation beam with a metallic target and the fundamentals of SEE and (Holz!, 1965). calculated the mean free path of an electron in Cu between Very interesting is the Total C urrent Spectroscopy (TCS) two inelastic collisions. of Komolov and Chadderton (1979) : A beam of low energy Rosier and Brauer ( 198 I) developed a theor y on SEE for electrons (0 - 15 eV) is directed to the surface and the emis nearly-free electron metals and applied it to Al. The creation sion of electrons is investigated by monitoring the target cur of SE by PE collisions with metal electrons in core states and rent. A TCS-signal is the derivative of the target current with in the Fermi sphere is co nsidered . In particular a calculation respect to the incident energy of PE. TCS gives information is given of SE production by pla smo n decay on the base of a on the interaction processes which alter the electron emission general model potential. Both elastic and inelastic collisions especially on the energy dependence of the elastic reflection o f internal secon dari es are taken int o account. EPE is limited coefficient . to I to 2 keV. General formulas are derived for the excitation functions , mean free path scattering functions and for o. 4. Angular resolved SE-spectroscopy (ARSES) A simple calculation of the energy distribution of SE from Usually the angle integrated energy distr ibution of SE is metal s was given by Chung and Everhart (I 974). A model for measured. In ARSES the energy dist ribution of SE released the calculation of the energ y di stribution of SE from semi by slow PE from monocrystalline sam ples in a particular conductors was presented by Bouchard and Carette (I 980). direction is measured. The experiments of Willis and Feuer bach (I 975), Willis and Christiansen (1978), Schafer et al. ACKNOWLEDGEMENTS (1981), Hol z! and Schafer (1981) show a fine structure which can be partially correlated with the one-dimensional densit y The author thank s Dip!. Phys . H .E . Bau er for many help of final states along symmetry lines co rresponding to each ful discussions. face . A theory of ARSES was developed by Feder and Pen dry (1978). REFERENCES

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40 Secondary Electron Emission

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