Electron reflection measurements on W(001) and W(110) between 0 and 40 eV

234

Surface Scaence 166 (1986) 234-248 North-Holland, Amsterdam

E L E C T R O N R E F L E C T I O N M E A S U R E M E N T S ON W(001) AND W(I10) B E T W E E N 0 AND 40 eV J.M. B A R I B E A U * and D. ROY Departernent de Phvttque et Centre de Recherche tur let Atornes et let Mol&ule~ (('RAM), Unwersttl, Laval. Quebec, PQ G I K 7p4, Canada

Received 9 July 1985, accepted for publication 5 September 1985

High resolution low energy electron reflection measurements from W(001) and W(110) m the range 0 40 eV are reported Spectra recorded for a variety of angles of Incidence m several different azimuths are presented In parhcular, some fine structure features associated V,lth beam thresholds are observed for all incidence conditions However, it is found that other threshold effects are either absent or very weak It is shown that this phenomenon is probably a consequence of the hm~ted azimuthal resolution of the spectrometer used Because of the variety of incidence conditions m~estlgated, the measurements comprise a statable data base for testing LEED calculation schemes in the very low energy range

1. Introduction

In recent years, the measurement of the electron reflectlv~ty at crystal surfaces in the very low energy range has attracted considerable interest. This interest stems from the fact that spectra of the reflected intensity as a function of the electron energy often show very narrow intensity fluctuations. These so-called L E E D fine structures or threshold effects occur at energies just below the emergence of new diffracted beams and arise from multiple scattering of electrons between the substrate and the surface potential energy barrier [1] This particular phenomenon has proven to be very useful m the determination of the surface barrier on metals. Because of its prominent role in very low energy electron scattering ( E < 40 eV), a lack of knowledge of the surface barrier has hindered the extension of LEED analysis to the low energy V L E E D range From a fundamental point of wew such an extension would be of great interest because tt would provide information about the electronic potential and wavefunctlons needed for a proper description of phenomena such as surface wbrat~ons, secondary emission and inverse photoemlsslon. In recent * Present address Division of Mlcrostructural Sctences, National Research Council Canada, Ottawa. K1A 0R6. Canada

0039-6028/86/$03.50 © Elsevier Science Publishers B V. (North-Holland Physics Publishing Dlws~on)

J M Barlbeau, D Roy / Electron reflection on W(O01) and W(llO)

235

years, considerable improvements m the barrier model have been obtained from LEED fine structure studies [2-6], and it is now conceivable that rehable L E E D analyses could be undertaken m the very low energy range. Because of the computational simplification involved, V L E E D measurements could allow for the analysis of complicated systems such as large unit-mesh adsorbates and reconstructed surfaces, and therefore is of considerable practical interest. Fine structures in the reflected intensity are associated wxth interferences between a preemergent beam which undergoes a backreflection at the surface barrier and a wave directly reflected by the atomic planes or by the barrier [1,7]. Due to the 1/z dependence of the surface barrier (z xs the coordmate normal to the surface), such a process causes fine structure fringes in the reflected current which obey a Rydberg-like dispersion law converging towards the beam threshold into vacuum [8,9]. Intensity oscillations will be significant m the energy range where the reflection coefficient of the preemergent beam at the barrier is large. This will be the case in the energy range in which the preemergent beam is non-evanescent m the crystal, i.e. having a kinetic energy perpendicular to the surface eg ± (in Rydbergs) eg±

=

E -[k,, +g[ 2

(1)

xn the range V0 < eg ± < 0, where V0 is the crystal inner potential The observation of L E E D fine structures requires measurements w~th a high energy and angular resolution. Furthermore, for a given set of experimental conditions, the ability to resolve fine structures will strongly depend on the propagation direction of the preemergent beam relative to the plane of incidence. This question has been investigated m detail by Gaubert et al. [10]. These authors have introduced the concept of "emergence speed" which corresponds to the derivatives ere, ct0 and a , of % ± with respect to the incidence energy E, the polar angle of incidence 0 and the azimuth q~, respectively. General expressions and universal charts of these derivatives are given in their paper. As Gaubert et al. have pointed out, eg ± is the appropriate energy variable for characterizing L E E D fine structures. Threshold effects will be easier to observe for beams which emerge "slowly" for given incidence angles. Assuming a Gaussian distribution for the dispersion of E, 0 and q~, it is possible to define an equivalent resolution eg ± given by

Aeg± = [aEAE 2 + aoAO 2 + o¢~Aq~2]1/2,

(2)

where AE, AO and Aq~ are full-width at half-maximum values. Production and analysis of well collimated low energy electron beams is a challenging problem and conventional L E E D optics are not well stated for V L E E D measurements. There is only a small amount of experimental data of thas sort available at the moment on tungsten [9,11-17]. In this paper we present reflectivlty curves recorded for W(001) and W ( l l 0 ) for several angles

236

J M Bartheau. D Rot / Electron reflectton of W(O01) and W(IIO)

of incidence and various azimuths m the energy range extending from 0 to 40 eV. These new data provide for the first time an extenswe high resolutmn data base statable for the testing of LEED calculation schemes in the very low energy range. The spectra presented could also help to clarify specific questions concerning the magnitude of the variations of the inner potential and melastm scattering as a function of energy. Difficulties connected with the detection of fine structure features are also discussed. It is shown that with our spectrometer, a limited azimuthal resolution is responsible for the dampmg of several threshold effects

2. Experiment The experimental setup is the same as was used in a previous set of experiments [18,19]. Monoenergetlc electrons were produced and analyzed using two identical 127 ° cylindrical electron selectors. Both are equipped with a three-element electrostatic lens, designed accordmg to the theory presented by Read [20], which is followed or preceded by a colhmating slit. A schematic of the apparatus can be found elsewhere [21]. Experiments have been performed with an energy resolution of 15 meV (FWHM) and a polar angular resolution better than 0.5 ° Since cyhndrical spectrometers provide no focussing perpendmular to the plane of incidence, the azimuth angular resoluhon is determined by the dimensions of the different slits of the instrument. Entrance and exit slits of the selectors have a width of 0.254 mm and a height of 10 mm. Th,s defines an acceptance azimuthal angle of about 2.3 ° for our instrument. Reflected electron current versus incident energy curves were obtained by tuning the spectrometer to a fixed energy while sweeping the voltage applied to the crystal, its support, and the collimating slits. This method is analogous to the one used by Adnot [9,22] and by Edwards [16,17] in similar experiments. It provides a uniform current on the sample for energies above 2 eV and a good overall transmission in the energy and angular ranges investigated. The drop m current below 2 eV is believed to be caused by the spreading of the electron beam due to stray electromagnetic fields and other lnhomogenelties. Measurements of the current flowing through the analyzer collimation slit were carried out The absolute elastic reflectivitles were estimated to be between 5 and 10%. Current inside the analyzer is too low to be detected, and because of this it was impossible to measure the analyzer transmission function directly. Measurements of the reflected current on samples exposed to air showed httle fluctuation m intensity as a function of energy. This result suggests, on the assumption that such a highly contaminated substrate does not present marked structures in its reflectlvity profile, that there are no serious anomalies in the analyzer transmissmn funcUon.

J M Bartbeau, D Roy / Electron reflecnon on W(O01)and W(llO)

237

The tungsten crystals were cut and polished, following standard procedures, along the (001) and the (110) plane. Both samples had a cylindrical shape (7 m m diameter and 1 m m thickness) and were fixed to a molybdenum support by three 0.5 m m tungsten screws. This system allowed a precise angular alignment of the target and permitted heating treatments with no significant buckling. The microscopic surface of both samples was found to be slightly off their nominal orientation by about 1.5 ° for both crystals. Prior to any experimental work, the crystals were purified by annealing in 02 at 1600 K and 2 × 10 -8 Torr 02 pressure in a preparation chamber until sharp (1 × 1) L E E D patterns could be observed on both surfaces. The crystals were then removed, their azimuth was aligned to any accurhcy of 0.5 ° by the Laue technique and the angle of incidence adjusted in situ to within 1 ° by laser alignment. The angle of incidence 0 could be varied by a rotating feedthrough to any value in the range 42 ° to 90 °. However, a change in azimuth required the dismounting of the sample. Experiments were carried out in U H V at a base pressure below 5 × 10 - n Tort. Prior to each run the samples were cleaned by electron b o m b a r d m e n t to 2400 K for a few seconds. Subsequent high resolution energy loss measurements showed no contamination loss peaks. No conventional L E E D or Auger electron spectroscopy measurements were made during the course of these experiments.

3. Results 3.1. Methodology

All measurements presented here were obtained for clean surfaces. Experimental results have been grouped in series of curves corresponding to profile measured for different angles of incidence in a given azimuth. The detected signal in the specular direction was typically in the range 104-105 counts/s, enabling us to measure all curves of a series during the same experimental run. This guaranteed the same spectrometer settings, constant emission current and similar surface conditions for all curves in a series. The comparison of the absolute intensity from one azimuth to the other is probably not reliable due to possible changes in the operating conditions produced by the temporary removal of the sample from the chamber. For all the profiles, origin of the energy scale has been adjusted in order that beam threshold oscillations converge to their respective theoretical beam emergence energies. 3.2 Results on W(O01)

Current versus energy curves have been measured for several angles of incidence along the azimuths ~ = 0 °, 22.5 ° and 45 ° (with respect to the [010]

J M Bartbeau, D Roy / Electron reflection of 14"(001) and 14(110)

238

c r y s t a l l o g r a p h i c direction). These results are p r e s e n t e d in figs. 1 3 As a c o m p a r i s o n we have p l o t t e d the profiles o b t a i n e d b y E d w a r d s [16,17] at 0 = 53 ° a l o n g the same three azimuths. T h e a g r e e m e n t between the curves o b t a i n e d b y E d w a r d s a n d those m e a s u r e d b y us for similar incidence c o n d i tions IS very good. Curves m e a s u r e d at 0 = 45 ° a n d ~ = 0 ° are also m excellent a g r e e m e n t with the results of A d n o t a n d C a r e t t e [9]. T h e reflected current d i s p l a y m a r k e d v a r i a t i o n s as a function of energy, angle of incidence, a n d

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20

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10

20

30

I 10

I 20

I 30

Incident energy (eV) F i g ] R e f l e c t e d c u r r e n t o n W ( 0 0 l ) a l o n g the a z a m u t h ,~ = 0 ° for v a r i o u s angles of i n c i d e n c e In d a s h e d line results of E d w a r d s [16]

239

J M Banbeau, D Roy / Electron reflecnon on W(O01) and W(llO)

azimuth. The strong intensity peak observed below 5 eV may be related to the existence of an energy gap in the surface-projected tungsten band structure [23]. We have indicated with vertical marks the emergence threshold of the non-specular diffracted beams. All profiles show intensity oscillations related to the emergence of new beams into the vacuum. Along ~ = 0 °, the well known 10 beam threshold effect [9] is observed at all angles of incidence. This fine

'~ =

W(O01)

22.5 °

,~o 0 : ~5 °

ll I

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L

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° I

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10 5 H z

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20

30

Incident energy

I0

20

30

(eV)

Fig. 2 Reflectedcurrent on W(001) along the azimuth @= 22 5° for various angles of incidence. In dashed hne. results of Edwards [16]

J M Barlbeau. D Roy / Electron reflectton oJ 14/(001) and W(IlO)

240

structure r e m a i n s sharp along q~ = 22.5 ° b u t is absent along ¢ = 45 ° where new free structures associated with the 11 b e a m start to appear

3 3 Results on W(llO) Figs. 4 - 7 show intensity curves measured for W ( l l 0 ) along the azimuths = 0 ° ([11]), 90 ° ([11]), 54 7 ° ([01]) a n d 35.2 °. Here we a d o p t the crystallo-

~

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10

20

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10

20

30

Incident energy (eV) F~g 3 R e f l e c t e d c u r r e n t o n W ( 0 0 1 ) a l o n g the a z i m u t h q~ = 45 ° for ,~anous angles of i n c i d e n c e In d a s h e d h n e results of E d w a r d s [16]

J M Bartbeau, D Roy / Electron reflectton on W(O01) and W(110)

W(110)

241

~ = <1 1>

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50

Incident energy (eV) F~g 4 Reflected current on W ( l l 0 ) along the a z i m u t h ,/, = 0 ° for various angles of incidence

graphic convention described by Le Boss6 et al. [5]. To our knowledge these spectra represent the first low energy electron reflectivity measurements obtained for W ( l l 0 ) out of normal incidence in the range 0-40 eV. Besides the well studied 11 beam fine structures along ~ = 0 ° [19] and the 11 beam along q~ = 90 ° [18], sharp oscillations related to the 01 threshold are also observed for the azimuth ~ = 54.7 °. As these oscillations could be useful for surface barrier

242

J M Barlbeau. D Ro)' / Electron reflection of W(O01) and W(I IO)

W(llO)

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20

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Inc=dent energy (eV) F~g 5 Reflected current on W(] ]0) along the azimuth (~ = 90 ° for varlou~ angles of incidence

calculations, we present in fig. 8 an e x p a n d e d wew of these free structures recorded at different angles of incidence. U p to four fine structure fringes are well resolved with our i n s t r u m e n t .

J M Bartbea~ D Roy / Electron reflectton on W(O01) and 14I(110)

W (110)

243

~= <01>

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Tncident energy ( e V ) Fig 6. Reflected current on W(ll0) along the ammuth ~ = 54 7° for various angles of incidence

4. Discussion T h e e x p e r i m e n t a l results s u m m a r i z e d in figs. 1 to 8 represent, d u e to the high r e s o l u t i o n a n d the diversity of the incidence c o n d i t i o n s , a u n i q u e d a t a base from which L E E D theory can be tested in the very low-energy range. S o m e p r e l i m i n a r y i n f o r m a t i o n m a y b e o b t a i n e d from a visual i n s p e c t i o n of the

244

J M Bartbeau, D Roy / Electron reflection of W(O01) and W(l lO)

W(110)

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0

=60 ° : 352

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5

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15

Incident energy (eV) F~g 7 Reflected current on W ( l l 0 ) along the azimuth ~ = 35 2 ° f o r 0 = 6 0 °

different series of profiles. For a given azimuth, varmtlons of the spectrum as a function of the angle of incidence are more pronounced in the low angle range. This is accounted for by the fact that near grazing incidence the parallel part of the electron wave vector varies very slowly. Another interesting observanon is that in several cases the reflected current falls with increasing energy This behavlour could be explained m terms of an increasing number of nonevanescent diffracted beams or alternatively it could be an ind~canon of an increase m the absorpnon potentml as a function of energy. However, the hm~ted accuracy of the crystal-cut along the nominal crystallographic orientan o n may have caused the surfaces to be rather rough on the atomtc scale leading to significant diffuse scattering and a resultant intensity drop close to the specular direction. A L E E D intensity analysis could clarify this quesnon. It is interesting to note that not all of the beam thresholds gwe nse to fine structure oscdlanons. In fact, only beams emerging m or close to the direction

J M. Bartbeau, D. Roy / Electron reflectzon on W(O01) and W(llO)

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Incldenl energy (eV) F~g, 8 F m e structures o s c d l a t t o n s a s s o c m t e d w i t h the 01 t h r e s h o l d m e a s u r e d o n W ( l l 0 ) a z a m u t h ~ = 54 7 ° ([01]) for several a n g l e s o f i n c i d e n c e

a l o n g the

of the plane of incidence display significant fine structure. Although this could be a consequence of small reflection coefficients or small coupling with the specular beam, it certainly also has an instrumental origin. As mentioned earlier, the detection of fine structures depends on the direction of propagation of the preemergent beam relative to the plane of incidence. We have calculated the derivatives a E, a o , a~, and the equivalent energy resolution Ae~± for all

J M Bartbeau, D Roy / Electron reflection of 14/(001) and W( I I O)

246

Table 1 Beam thresholds ( E 1 ), denvauves aL-, %, % (absolute values), and eqmvalent resoluUon /leg ± (calculated at ET) for emerging beams on W(001) at 0 = 60 ° along the various azimuths studied Beams

E r (eV)

%

a 0 (eV/rad)

% (eV/rad)

Aeg z (eV)

0°

431 15 26 17 25 26 08

1 87 1 11 1 87 1 56

431 1 92 17 25 16 98

0 26 22 0 34 27

015 0 62 0 21 0 83

]0 11 01 ~-0 21 12

22 5 °

4 94 988 17 31 19 76 21 65 34 38

1 65 1 65 0 56 1 65 l 86 1 28

3 68 735 8 83 14 72 21 48 8 60

5 71 1142 25 79 22 84 4 94 57 62

0 19 031 0 61 0 57 0 27 1 36

01,10 11 12,21 20,02 22

45 °

773 8 62 23 61 30 51 34 50

1 11 l 87 I 72 1 11 1 87

097 8.62 19 50 3 84 34 50

1328 0 23 04 52 42 0

033 0 17 0 59 1 24 0 34

]0 11,11 20 21,21

fl~

emerging b e a m s along the various azimuths studied for both W(001) a n d W ( l l 0 ) . The values hsted in tables 1 a n d 2 have been o b t a i n e d for 0 = 60 ° using resolution values A E = 0.08 eV, A0 = 0.5 ° a n d Afl~= 1.36 ° The latter value ~s the half-width of the G a u s s l a n d i s t r i b u t i o n for which the spectrometer acceptance a z i m u t h angle is equal to four times the s t a n d a r d deviation. The Table 2 Beam thresholds (ET), derivatives ¢~E, ~0, c% (absolute value), and equivalent resolution ~eg (calculated at E v ) for emerging beams on W ( l l 0 ) at 0 = 60 ° along the various azimuths studied Beams

4'

E r (eV)

cq

a 0 (eV/rad)

a , (eV/rad)

J e g i (eV)

10, O] 11

90 °

9 10 17 25

1 36 1 87

3 80 17 24

14 32 0

0 35 0 21

]1 0],10 2i,12 22

0°

862 15 46 28 15 34 50

187 0 85 1 59 1 87

862 2 63 19 25 34 50

0 26 37 35 58 0

017 0 63 0 86 0 34

01 1i il 0:2 12

54 7 °

6 47 20.61 2427 25 87 30 03

1 87 1 44 0.78 1 87 1 09

6 47 10 39 621 2~ 87 3 30

0 30 83 4062 0 51 71

0 16 0 74 096 0 27 1 22

01 i1

35 2 °

7 18 12 13

1 70 0 85

5 79 2.06

7 37 20 72

0 23 0 49

J M Bartbea~ D Roy / Electron reflectwn on W(O01) and W(110)

247

energy resolution value used is poorer than the experimental resolution since it takes into account the width of the acquisition channel (typically 75-80 mV) used for wide energy range measurements. It is clear from tables 1 and 2 that only a limited number of beam threshold effects can actually be resolved with our instrument. Only beams for which the equivalent resolution is smaller than about 0.2 eV show typical fine structure fringes. The performance of our apparatus is limited by its azimuthal resolution and, to a lesser extent, by its polar angle resolution. The sharpness of threshold effects from beams emerging antiparallel to the plane of incidence is explained by the fact that in this particular direction, the derivative a~ is strictly equal to zero. For these singularities, reducing the acquisition channel width below A E allows the detection of several oscillation fringes as may be seen from fig. 8. For antiparallel emerging beams, the decrease of a 0 with 0 allows for a better fringe separation at large angles of incidence. This phenomenon is clearly in evidence in spectra recorded along ~ = 45 ° on W(001) and = 0 ° on W(ll0). Only in such incidence conditions is the energy resolution the limiting factor.

5. Conclusion In this paper we have presented novel electron reflection data recorded for W(001) and W(ll0). Our measurements have clearly shown that fine structures m VLEED is a very general phenomenon. Observation of sharp threshold effects requires not only high resolution but also appropriate incidence conditions. For a spectrometer having a cylindrical symmetry and equipped with narrow shts, the limited azimuthal resolution hinders the detection of fine structures for beams emerging far from the plane of incidence. Depending on the application, the azimuthal orientation of the crystal could thus be selected in order to facilitate observation of fine structures or to reduce their importance. These measurements, which were obtained at high resolution and over a wide range of incidence angles, provide a unique data base for a VLEED analysis of these substrates. The various incidence conditions investigated could help to study problems related to dynarmcal effects and the angular dependence of scattering parameters (especially the surface barrier) entering in VLEED calculations. Similarly the data provides a means of studying the variation of the inner potential as a function of energy. The fact that data have been collected for two faces of the same metal allows for an analysis of the influence of surface structure and ion-core potential on scattering intensities.

Acknowledgements The authors thank Dr. P. McBreen for a critical reading of the manuscript. This work is supported by NSERC of Canada and by le Fonds FCAR du Qu6bec.

J M Barlbeau, D Roy / Electron reflectton of W(O01) and W(IlO)

248

References [1] [2] [3] [4]

[5] [6] [7] [8] [9] [10] [11]

[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

E.G McRae, Rev Mod Phys. 51 (1979)541 R E Dletz, E G. McRae and R L Campbell, Phys Rev Letters 45 (1980) 1280 P J. Jennlngs and R O Jones, Solid State Commun. 44 (1982) 17 R O Jones, P J Jennmgs and O Jepsen, Phys Rev B29 (1984) 6474 J C Le Boss6, J Lopez, J M Barabeau and J.D Carette, Surface Scl 137 (1984) 361 J M Barabeau, J Lopez and J.C Le Boss6, J. Phys C 18 (1985) 3083 J C Le Boss6, J Lopez, C Gaubert, Y Gauth,er and R Baudolng, J Phys C15 (1982) 6087 J Rundgren and G Malmstrom, J Phys C10 (1977) 4671 A. Adnot and J.D Carette, Phys Rev Letters 38 (1977) 1084. C Gaubert, R Baudomg, Y Gauth,er and J Rundgren, Surface Scl 147 (1985) 162 Early low resolution electron reflection measurements on tungsten include I H Khan, J P Hobson and R A Armstrong, Phys Rev 129 (1963) 1513, R J Zollweg, Surface Scl 2 (1964) 409, R A. Armstrong, Surface Scl 47 (1975) 666 E G McRae and G H Wheatley, Surface Sci 29 (1972) 342 H J Herlt, R Feder, G Melster and E G Bauer, Sohd State Commun 38 (1981) 973 M A Stevens and G J Russell, Solid State Commun 34 (1980) 785 D T Pierce, R J Celotta and G C Wang, m Proc 4th Intern Conf on Sohd Surfaces and 3rd European Conf. on Surface Science, Eds D A Degras and M Costa, Pans, 1980 D Edwards, PhD Thesis, University of Illinois at Urbana-Champalgn (1970) D Edwards and F M Propst, J Chem Phys 56 (1972) 3124 J M Banbeau and J D Carette, Phys. Rev B23 (1981) 6201 J.M Barlbeau and J D. Carette, Phys Rev B25 (1982) 2962 F H Read, J Phys E3 (1970)127 D Roy and J D Carette, in Topics m Current Phys,cs, Vol 4. Ed H Ibach (Springer, Berhn. 1978) A Adnot PhD Thesis, Umverslt6 Laval. Qu6bec (1977) R F Wdhs, B Feuerbacher and N E Chrlstensen, Phys Rev Letters 38 (1977) 1087