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Optical functions of epitaxial β-FeSi2 on Si(001) and Si(111)
aI!@
Solid State Communications,
Pergamon
0038-1098(95)00546-3
Vol. 96, No. 10, pp. 751-756, 1995 Elsevier Science Ltd Printed in Great Britain 0038-1098/95 $9.50+.00
Optical functions of epitaxial p-FeSi, on Si(OO1) and Si(ll1)
INFM-Dipartimento
V. Bellani’, G. Guizzetti, F. Marahelli and M. Patrini di Fisica “A. Volta”, Uniuersitci degli Studi di Pauia, Via Bassi
6, I-&‘YlOO Pauia,
Italy
S. Lagomarsino lstituto di Elettronica
dello Stato Solido,
Consiglio
delle Ricerche,
Nazionale
Via Cineto
Roman0
42,
I-00156
Roma,
iI. von Kane1 Laboratorium
fir
Festkiirperphysik,
(Received
Eidgen&sische
Technische
18 July 1995; accepted
Hochschule,
CH-8099
Ziirich,
Switzerland
10 August 1995 by P. Wachter)
We accurately measured the complex refractive index and dielectric functions from 0.2 to 5 eV of high-quality p-FeSi2 epitaxial films, with thicknesses ranging from 100 A to 8000 A, grown on Si(OO1) and Si( I 11) using two different techniques. Reflectance, transmittance and spectroscopic ellipsometry were used and the spectra were analyzed within a multilayer model, by checking the Kramers-Kronig consistency of the derived optical functions. These functions, compared with previous results for polycrystalline samples, showed a very good agreement with those obtained for bulk samples and a significant difference to films. The nature (direct or indirect) of the lowest optical gap and the effects of the film thickness and the substrate orientation on the optical response were also investigated.
Keywords:
A. semiconductors
B. epitaxy
D. optical properties
* Present address: Departamento de Fisica de Materiales, Cantoblanco, E-28049 Madrid, Spain.
Universidad
Autonoma,
1 INTRODUCTION
Among the semiconducting silicides, FeSiz has received renewed interest in the last few years, both from applied and fundamental points of view, for different reasons. In the orthorhombic p-phase it exhibits a direct energy gap of _ 0.85 eV at room temperature,‘-” matching the transmission window of SiOz optical fibers at 1.55 pm quite well. This feature, added to the possibility of growing d-FeSiz films epitaxially on both (111) and (001) Si substrates,‘*‘-‘7 opens interesting perspectives for application in optoelectronic devices compatible with silicon technology. Moreover, recent transport measurements” on high-quality p and n-type &FeSiz single-crystals showed a significant increase in mobility (up to 50 times). so that the common assumption of limited applicability in electronics, due to the earlier observed and estimated low mobility, no longer holds. From the fundamental point of view the iron disilicide, depending on growth conditions, displays several epitaxial phases on silicon,‘g~20 some of which are bulk stable (a- and d-phase), while some others (y- and d4-phase) just exist as thin films. The stable semiconducting #-FeSiz can be obtained by a Jahn-Teller-like
structural transition of the met&able metallic y-phase (CaFz-like). and the nature of itsgap (indirect or direct) is strongly dependent on the first-neighbours distance.‘l Thin polycrystalline films of p-FeSiz on Si have been optically characterized by different authors on spectral intervals from far-infrared (FIR) to vacuumultraviolet (VUV).‘-4~6*22-2g Discrepancies among the results have been attributed to different growth conditions. measurement methods and surface contamination. Epitaxial &FeSiz films have been extensively subjected to structural characterization while their electronic and vibrational properties have been studied mainly by electron and photoelectron spectroscopies.7-10~30~31 Optical measurements have been performed only within a narrow spectral interval around the gap5~8-‘0 and in FIR.‘7,25 The nature of the /?-FeSiz band-gap is still an open question. Electronic structure calculations,21~32~33 optical absorption6 and photothermal deflection spectroscopy (PDS)*-*’ support the presence of an indirect gap of few tens of meV narrower than the direct 751
Italy
OPTICAL
752
FUNCTIONS
ES, while other experimental works ‘a425 have attributed the absorption tail or subgap absorption band to defect states in the gap. Because of the importance of the optical functions, from both the fundamental and technological points of view, the aim of this work was the accurate determination of the complex refractive index ii = n + ik and the complex dielectric function E‘ = ci + it2 = n2 in a wide spectral range (from 0.2 to 5 eV) of high-quality $-FeSis epitaxial films. The effects of different growth techniques, thicknesses d and substrat.e orientation (Si (001) and Si( Ill)) were analyzed to check if their influence on the electronic transitions is as strong as that on phonon spectra.17 Reflectance (R), transmittance (T), and spectroscopic ellipsometry (SE) measurements were performed at room temperature; T was also measured at low temperatures in a narrow interval around the absorption edge in order to investigate the nature (direct or indirect) of the lowest optical gap. All the spectra were analysed using a multilayer model, in order to account for interface and substrate effects in the transparency region. A comparison with previous results, relative to both bulk and film samples. was also performed.
2 EXPERIMENT Two sets of B-FeSi2 films were epitaxially grown with two different techniques. In the first the samples were prepared in a CHV system consisting of a load-lock and two separate chambers (see details in ref. 13). The Si(ll1) substrate was pre-cleaned following the Shiraki procedure.34 A sharp 7x 7 reconstruction and the absence of contaminants was checked by low energy electron diffraction (LEED) and Auger spectroscopy. Iron was then evaporated from a resistively heated high-purity Fe wire onto the substrate maintained at room temperature. Fe thickness was measured with a quartz microbalance, calibrated by Rutherford backscattering spectrometry (RBS). Then the sample was annealed at about 500 “C for 20 min. resulting in the formation of ,!-FeSis. Film composition and thickness were determined by RBS, yielding the correct Fe/Si ratio of 1:2 and a thickness of about 200 A. X-ray double crystal diffrartometry evidenced a good crystalline quality of the $FeSiz layer, with well-oriented domains whose (101) planes were parallel to the Si(ll1) surface. However, due to the different symmetry of Si and @-FeSis, three distinguished areas with relative rotation of 120” were formed.13 The second set of samples consisted of films with
OF EPITAXIAL different machine
p-FeSi,
thicknesses on Si(ll1)
Vol. 96, No. 10
grown in a commercial 3-in. MBE and Si(OO1) substrates. Typical
deposition rates were 0.8+1 A/s for Si and 0.3 A/s for Fe. After thermal pre-cleaning of the wafer and desorption of the oxide. a Si buffer layer was grown in order to provide clean reconstructed surfaces. In the first step a thin crystalline template of some Angst,rom was grown by depositing moderately Fe-rich silicide on the substrate maintained at temperature below 200 “C. Ihe templates were successively annealed at higher temperatures, up to a maximum of 600 “C. In the second step the desired thickness was reached by stoichiometric coevaporation of Fe and Si at different temperatures. Hence a variety of growth conditions (and crystalline orientation of the samples) were obtained. The films were characterized in situ by reflection highenergy electron diffraction (RHEED), ultraviolet and x-ray photoemission spectroscopy (UPS/XPS), and scanning tunnel microscopy. Transmission electron microscopy (TEM) was used for plan view investigation in the bright field- and in the selected area electron diffraction-modes. The relevant parameters of the samples for optical investigation are listed in Table I.
R and T measurements at near-normal incidence and at room temperature were performed in the 0.4~0.5 eV photon energy range using a Cary 5E automatic spectrophotometer, with a photometric accuracy of 0.5 Yo. An Al mirror covered with MgFs film, whose absolute reflectivity was directly measured, was used as reference for R. R and T were also measured at low temperatures. down to 3 K. using a homemade spectrometer equipped with a Spex 1402 double monochro mator between 0.5 and 1.3 eV, where the system FeSisSi was transparent. In t.he 0.2~0.6 eV range R and T were measured by a Fourier transform spectrometer Bruker IFS 113~~ using an Au mirror as reference. The spectra from different instruments merge one into the other. The FIR spectra of the same samples from 0.2 eV down to 6 meV displayin the IR-active phonons have been already published.’ g 125 The
ellipsometric
functions
tan$
Thickness (A)
#lOOO #2508 #2504 #2503 #2506
220 8000 3000 250 180
and cosA
(with
j=tanJ1 eiA, where p is the complex ratio of the parallel to perpendicular polarization reflection coefficients) were measured between 1.4 and 5 eV using a spectroscopic ellipsometer Sopra mod. MOSS ES4G. The argle of incidence was 75”, close to the Brewster angle for optimum sensitivity. Spectral resolution was better than 4 meV over the whole range. From tan+ and cosA we derived E and fi using the structural model and the data analysis procedure described below.
Table I. Relevant structural parameters of the P-FeSi2 epitaxial layers.
Sample
selected
Si substrate
orientation
( l l 1)
~~lol,~~~~~irj
(661) (661) (661) LOOl)
Fe-(lOO)//Si(OOl)
Fe( lOO)//Si(OO1) A
mainly Fe( lOO)//Si(OOl) Fe( lOO)//Si(Oa
Vol. 96, No. 10
OPTICAL
3 RESULTS
AND
FUNCTIONS
1-P
+ sin’q5 tan 2 Q ( -) 1 + p
sin20
k. probably due to the occurrence in the real system of roughness and non-ideal (plane and abrupt) interfaces. Moreover, small errors in R and T strongly affect the values of n and k in this high-dispersion region. These considerations should be kept in mind when evaluating the confidence in the optical functions derived from R and T measurements, both on thick and thin films.‘.5,6 above all if the tail of the absorption coefficient o = 4ak/X is used to determine the nature (direct or indirect) of the gap. In Figs. 2 and 3 the room-temperature spectra of ii and i respectively for the same sample as in Fig. 1 are reported. The spectra of polycrystalline films (d=
2
where 4 is the angle of incidence. This bulk-like behaviour was confirmed by the independence of Z from Q (besides 75”, two other d values. 65” and 70”, were proved). Moreover no differences in i were evidenced using a four-phase model (vacuum-film-Si-vacuum), with the optical functions of Si from literature and the nominal value of d. The same behaviour and the same 2 were displayed by the sample #2504. We note that the near-normal reflectivity calculated from g was generally 0.04 higher than R directly This discrepmeasured by the spectrophotometer. ancy has very likely ascribable to light scattering by macroscopic surface roughnesses, affecting photometric but not eilipsometric measurements. To account for this difference, the reflectance spectrum was scaled to match the SE results. Below 1.4 eV. strong interference fringes appear in R (as well as in T), due to coherent multireflection effects in the layered structure air-film-Si-air. Then Z and ?z for photon energy less then 1.4 eV were obtained by fitting the expression of R and T for a multilayer to the experimental spectra. 35 At each step of the fit procedure the consistency of n and k was checked through the Kramers-Kronig (KK) causality relations. TO prr-
I
753
@-FeSi,
form the KK transforms we extrapolated R spectrum beyond the highest experimental energy with a tail constructed to make the calculated n and k coincident with those measured directly by SE in the 1.4 to 5 eV range. Below 0.7 eV, where k z 0 and the amplitude of the interference fringes is quasi-constant, n and d were obtained directly from the spacing and amplitude of the fringes in R and T for both thick samples (#2508 and #2504). We note that the numerical inversion of R and T expressions around the absorption edge gives numerically instable or non-physical solutions for n and
DISCUSSION
Figure 1 shows the reflectance spectrum (dashed line) at room temperature of the thickest FeSiz-Si sample (#2508), and the corresponding reflectivity of FeSiz, determined by R and SE in the following way. .4bove 1.4 eV the FeSiz film is totally absorbing, i.e. it behaves as a semi-infinite bulk, so that i can be derived in a two-phase model (air-film) from the direct inversion of the ellipsometric jj spectrum through the well-known relationship: P =
OF EPITAXIAL
6300
Aand 4800 .&. respectively)2s4
and bulk4 samples.
-Film - -
epi (#2508) Bulk poly (Ref. 4)
------~~-Film poly (Ref. 4) o
Film poly (Ref. 2)
# 2508 i,,$
3
~~~~~~~~~ Reflectance
; :I :;2.,: : 1:! ::Ijy
-Reflectivity
0.6 p! 0.5
‘0
I
2
3
4
5
Photon energy (eV)
Fig. 1. Reflectance and reflectivity at room t.emperature of the p-FeSi:, epitaxial film (# 2508. d=SOOO A).
0
0
1
2 3 Photon energy (eV)
4
5
Fig. 2. Refractive index (n) and extinction coefficient (k) of the &FeSiz epitaxial film (# 2508), compared with those of polycrystalline bulk and films from literature.
754
OPTICAL
FUNCTIONS
-2
30 w--
20
the other hand. for states lying farther apart, the character gradually switches to Si 3s.3~ (bonding and antibonding states) and the momentum matrix elements become appreciable. These features are common to many transition-metal silicides and determine the close resemblance to the interband er and ez spectra of the semiconducting silicides, 27 despite their different crystalline structure. In particular. the strong and composite band in ez just above the direct gap in all these silicides determines the strong dispersion in cl and high values of e, (e.g. c, -32.5 and n CI 5.7 for both /3FeSiz and CrSiz 37). In CrSiz this band is split into two main peaks separated by -0.5 eV and attributed to different polarization dependent interband transitions, along the same symmetry directions of the Brillouin zone (BZ).3’ As regards d-FeSiz, a peak in R at -1.05 eV has been observed in polycrystalline films ” and related to additional direct-transitions, due to the spin-orbit splitting (estimated -0.2 e\‘) of the direct gap Eg at I point. This attribution appears plausible, but we do not think that the strength of this transition can be inferred from R spectra. because interference can induce artifacts just near 1 eV (cfr. Fig. l), where the absorption rises abruptly. In our and in other P and ri spectra only a shoulder was observed at -1 eV.
epi (#X508)
- - -Bulk poly (Ref. 4) -------.-Film poly (Ref. 4)
10
Concerning the optical gap, R and T measurements around the absorption edge, on both thick and thin samples, gave a room-temperature absorption coefficient o which rises abruptly up to a value of N 1.2 x lo5 cm-’ at 1 eV and then slopes less steeply at higher energies. A plot of o2 versus photon energy showed a linear variation. yielding a direct optical gap E, of -0.85 e\‘, which falls within the interval from 0.83 to 0.90 eV reported in literature. E, shows anomalous behaviour with decreasing temperature: it increases for the thickest samples (up to 0.89 eV, for T = 3 K), and reduces for the thinnest ones. Other than experimental uncentainty, this thickness dependence may be a misfit-strain effect, which is expected to be stronger in thin films.
0
20 WN 10
0
Vol. 96, No. 10
The assignement of the peaks in ez to specific interband transitions requires the knowledge of the joint density of states and the momentum matrix elements. due to the flatness of the valence bands of &FeSiz near the Fermi leve1.32 Moreover, the states in conduction and valence bands around the energy gap have primarily the d character of Fe (non-bonding states) so that the across-gap oscillator strengths are very small. On
50 -Film
p-FeSi,
EELS spectrum. measured on epitaxial films3’ displayed two peaks at _ 2.5 and -5 eV. but their absolute intensities were lower and their relative strengths inverted with respect to the optical findings.
measured on a narrower range, are also report.ed for comparison. The dielectric functions for thick epitaxial samples (#2508 and #2504) agree very well with those of bulk polycrystalline samples, measured with SE by Dimitriadis et al..* which differ by only 10% in the amphtude of the composite ez structure peaked at -1.8 eV. On the contrary, the er and ez spectra of polycrystalline filmsj,26 generally present similar shapes, but the structures are broadened and energy-shifted. and their intensity can be significantly lower, as in the case of Fig. 3. A remarkable exception is represented by the n and k: values around the absorption edge reported from Ref. 2: their k spectrum is quasi-coincident with our, while their R peak at -0.9 eV is slightly different (and not KK consistent with k). The disagreement between optical functions of polycrystalline bulk and films has been attributed4 to void fractions and surface roughness in the films, depending on growth conditions and thermal annealing: in this respect, the interband optical response, as well as the sharp vibrational structures,‘6~25 of our epitaxial films confirms their good crystalline quality. Lastly, e:, obtained from the KK analysis of the
40
OF EPITAXIAL
0
I
2
3
4
5
Photon energy (eV)
Fig. 3. Real (~1) and imaginary (sz) part of the complex dielectric function of the p-FeSiz epitaxial film (# 2508), compared with those of polycrystalline bulk and film from literature.
\Z;e also obtained an absorption tail below E, which cannot be unambigously ascribed to the indirectgap transitions because of the aforementioned uncertainty in R and T data and analysis in this spectral However, complementary PL measurements region. on our high-quality samples didn’t evidence any signal around the direct gap, supporting the absence of impurities and thr presence of an indirect gap, just below E, (in agreement with findings of Ref. 10 on buried @-FeSi:!). We think that, in addition to the theoretical results2’.“2*33 which agree on the existence of an indirect gap at L point of the BZ, the experimental evi-
Vol. 96, No. 10
OPTICAL
FUNCTIONS
dence. more than from R and T measurements on thin films, comes from PDS measurements. These give an indirect gap value of O.i6-0.8 eV and a dirert one at 0.83+--0.85 eV at room temperature,s-I0 and of -0.86 and -0.875, respectively. at 77 K.” However. because of PDS signal saturation at high a values, these measurements have to be normalized beyond the absorption edge to accurate values of Ic, as for example those extracted from SE. Optical measurements on bulk single-crystals, recently grown by chemical vapor transport using iodine as a transport agent, ” should overcome the problems connected with thin films and, in particular, the mismatch strain which can critically affect the nature of the gap. 21 However the as-grown samples are n-type, so that doping compensation can be requested to avoid free-carrier screening of the gap, as with CrSiz singlecrystals.37 Fig. 4 displays n and k spectra, derived from SE measurements. of all the samples reported in Table I (except for the sample #2504, because its optical response is quasi-coincident with that of sample #2508). Beyond the overall agreement among the spectra, two features should be underlined: a) in the thin films (#lOOO, #2503. #2506) the valley at m 3.3 eV and the two adjacent broad peaks appear enhanced with respect to the thick film (#2508). This is a partial artifact due to the d value used in the multilayer model. In fact, in absence of interference fringes useful to optically determine d in thin films, we assumed the nominal value of d, derived from RBS or RHEED. If d is underestimated. the numerical inversion of SE spectra produces spurious structures. reflecting in negative the structures of Si substrate (in particular the strong peak around 3.5 eV). This effect increases with decreasing d; however we cannot exclude a contribution from mixed interface regions. b) In sample #lOOO, the energy position of the peak at _ 1.8 eV is slightly red-shifted: this effect can be attributed to the optical anisotropy of the orthorhombic structure. In fact, sample #lOOO was grown on Si( 111) with the orientation FeSis( lOl)llSi( ill), while all the other samples were grown on Si(OO1). with FeSisllSi(OO1).
4 CONCLUSIONS We accurately measured the complex refractive index and the dielectric functions of P-FeSiz epitaxial films in the 0.2t5 eV photon energy interval. The thickest films displayed an optical response very similar to that of bulk polycrystalline samples. The direct gap was clearly determined, while interference effects in thick films, non-ideal conditions of thin films, and the strong dispersion of i7. at the absorption edge prevented a clear determination of the lower-energS indirect-gap:
OF EPITAXIAL
p-FeSi, I
755 I
I
I
_______#,0()0
2
3
----..-_._
#2503 #25O(j
-
#2508
4
5
Photon energy (eV)
Fig. 4. Refractive index (n) and extinction coeficient (k) derived from SE spectra of &FeSis epitaxial films, with different thicknesses and orientations (see Table I).
however its existence was confirmed by complementary luminescence measurements. The crystalline orientation of the films with respect to the silicon substrate mainly affects the first optical structure around 1.8 eV.
ACKNOWLEDGMENTS This work has been partially supported by the European Project Nr.CHRX-CT93-0318, “Physical properties of bulk single crystals and thin films of metal silicides” within the Program “Human capital and mobility”.
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J.H. Werner, S. Logothetidis, M. 4. C.A. Dimitriadis, Stutzmann, J. Weber, and R. Nesper, J. Appl. Phys. 68, 1726 (1990). 5. K. Lefki, P. Muret, N. Cherief, and R.C. Cinti, J. Appl. Phys. 69, 352 (1991).
756
OPTICAL
FUNCTIONS
F. Scarinci, and P. 6. C. Giannini. S. Lagomarsino, Castrucci, Phys. Rev. B 45. 8822 (1992). Sci. 7. A. Rizzi, H. Moritz, and H. Liith, J. Vat. Technol. A9, 912 (1991). 8. B.N.E. R&en, D. Freundt, Ch. Dieker, D. Gerthsen. -4. Rizzi, R. Carius and H. Liith, Mater. Res. Sot. Symp. Proc. 320. 139 (1994). in “Formation of semiconductor inter9. A.Rizzi. faces” edited by B.Lengeler. H.Luet.h. W.Moench. J.Pollmann (World Scientific 1994). p. 439. R. Carius and S. Mantl, Nucl. 10. K. Radermacher. Instr. and Meth. B 84. 163 (1994). 11. K. Radermacher, 0. Skeide. R. Carins. J.Klomfab and S. Hantl, Mat. Res. Sot. Symp. Proc. 320, 115 (1994). 12. N. Cherief. C. d.Anterroches, R.C. Cinti, T..4. Nguyen, and J. Derrien. Appl. Phys. Lett. 55, 1671 (1989). 13. J.E. Mahan, K.M. Geib, G.Y. Robinson. R.G. Long. Y. Xinghua, G. Bai, M.A. Nicolet. and 21. Nathan, Appl. Phys. Lett. 56, 2126 (1990). 14. S. Lagomarsino. F. Scarinci, G. Savelli, C. Giannini, P. Castrucci, and M.G. Grimaldi, J. Appl. Phys. 71, 1224 (1992). 15. J. Derrien, J. Chevrier. V. Le Thanh and J.E. Mahan, Appl. Surf. Sci. 56-58, 382 (1992). 16. H.Ch. Shafer, B. R&en, H. Moritz, A. Rizzi, B. Lengeler, and H. Liith, .4ppl. Phys. Lett. 62, 2271 (1993). 17. G. Guizzetti. F. Marabelli, M. Patrini, Y. MO, N. Onda and H. von K%.nel. Mater. Res. Sot. Symp. Proc. 320, 127 (1994). 18. E. Arushanov, Ch. Kloc, H. Hohl, and E. Bucher, J. Appl. Phys. 75, 5106 (1994); Phys. Rev. B 50, 2653 (1994). 19. J. Chevrier, V. Le Thanh, S. Nitsche, and J. Derrien, Appl. Surf. Sci. 56-58, 438 (1992). 20. H. Sirringhaus, N. Onda. E. hItiller-Gubler, P. Miiller, R. Staider. and H. von Kinel. Phys. Rev. B 47, 10567 (1993). 21. L. Miglio and G. Malegori. Phys Rev B 52. 15 July 1995.
OF EPITAXIAL
P-FeSi,
Vol. 96, No. 10
22. A. Borghesi, A. Piaggi, A. Stella, G. Guizzetti, F. Nava, and G. Santoro, Proc. 20th ICPS, ed. by E.M. Anastassakis and J.D. Joaunopouios (World Sci.. Singapore, 1991) p. 2001. ‘3. S. Kotini, D.I. Siapkas. and C.A. Dimitriadis, Proc. 20th ICPS, ed. by E.M. hnastassakis and J.D. Joannopoulos (World Sci.. Singapore, 1991) p. 316. 24. K. Lefki, P. Muret, E. Bustarret, N. Boutarek, R. Madar, J. Chevrier, J. Derrien, and M. Brunel, Sol. State Commun. 80. 791 (1991). 2.5. F. Marabelli, M. Amiotti. V. Bellani, G. Guizzetti, A. Borghesi, S. Lagomarsino. and F. Scarinci, Proc. 21st ICPS, ed. by P. Jiang and H.Z. Zheng (World Sci.. Singapore. 1992) p. 209. ‘6. W. Henrion, H. Lange, E. Jahne and M. Giehler. Appi. Surf. Sci. 70/71, 569 (1993). 2i. H. Lange. W. Henrion. E. Jahne, M. Giehler, 0. Giinther. and J. Schumann, Mater. Res. Sot. Symp. Proc. 320, 479 (1994). 2s. M. Powalla and K. Herz. Appl. Surf. Sci. 65/66, 482 (1993). 29. L. Wang, L. &in, Y. Zheng, W. Shen, X. Chen, X. Lin. C. Lin, and S. Zou, .4ppl. Phys. Lett. 65, 3105 (1994). 30. M. De Crescenzi, G. Gaggiotti, N. Motta, F. Patella, A. Balzarotti, G. Mattogno, and J. Derrien. Surf. Sci. 251/52, 175 (1991). 31. C. Stuhlmann, J. Schmidt, and H. Ibach, .J. Appl. Phys. 72,5905 (1992). 32. N.E. Cristensen, Phys. Rev. B 42, 7148 (1990). 33. R. Eppenga, J. Appl. Phys. 68. 3027 (1990). 34. .4. Ishizaka, N. Nakagawa and Y. Shiraki, Proc. 2nd Int. Symp. on MBE and Related Clean Surface Techniques, Tokyo, 1982, p. 183. 33. O.S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965). 36. K.Lefki and P.Muret, J. Appl. Phys. 74, 1138 (1993). 3i. V. Bellani, G. Guizzetti, F. Marabelli, A. Piaggi, .4. Borghesi, F. Nava, V.N. Antonov, 0. Jepsen, O.K. Andersen and V.V. Nemoshkalenko, Phys. Rev. B 46, 9380 (1992).
Solid State Communications,
Pergamon
0038-1098(95)00546-3
Vol. 96, No. 10, pp. 751-756, 1995 Elsevier Science Ltd Printed in Great Britain 0038-1098/95 $9.50+.00
Optical functions of epitaxial p-FeSi, on Si(OO1) and Si(ll1)
INFM-Dipartimento
V. Bellani’, G. Guizzetti, F. Marahelli and M. Patrini di Fisica “A. Volta”, Uniuersitci degli Studi di Pauia, Via Bassi
6, I-&‘YlOO Pauia,
Italy
S. Lagomarsino lstituto di Elettronica
dello Stato Solido,
Consiglio
delle Ricerche,
Nazionale
Via Cineto
Roman0
42,
I-00156
Roma,
iI. von Kane1 Laboratorium
fir
Festkiirperphysik,
(Received
Eidgen&sische
Technische
18 July 1995; accepted
Hochschule,
CH-8099
Ziirich,
Switzerland
10 August 1995 by P. Wachter)
We accurately measured the complex refractive index and dielectric functions from 0.2 to 5 eV of high-quality p-FeSi2 epitaxial films, with thicknesses ranging from 100 A to 8000 A, grown on Si(OO1) and Si( I 11) using two different techniques. Reflectance, transmittance and spectroscopic ellipsometry were used and the spectra were analyzed within a multilayer model, by checking the Kramers-Kronig consistency of the derived optical functions. These functions, compared with previous results for polycrystalline samples, showed a very good agreement with those obtained for bulk samples and a significant difference to films. The nature (direct or indirect) of the lowest optical gap and the effects of the film thickness and the substrate orientation on the optical response were also investigated.
Keywords:
A. semiconductors
B. epitaxy
D. optical properties
* Present address: Departamento de Fisica de Materiales, Cantoblanco, E-28049 Madrid, Spain.
Universidad
Autonoma,
1 INTRODUCTION
Among the semiconducting silicides, FeSiz has received renewed interest in the last few years, both from applied and fundamental points of view, for different reasons. In the orthorhombic p-phase it exhibits a direct energy gap of _ 0.85 eV at room temperature,‘-” matching the transmission window of SiOz optical fibers at 1.55 pm quite well. This feature, added to the possibility of growing d-FeSiz films epitaxially on both (111) and (001) Si substrates,‘*‘-‘7 opens interesting perspectives for application in optoelectronic devices compatible with silicon technology. Moreover, recent transport measurements” on high-quality p and n-type &FeSiz single-crystals showed a significant increase in mobility (up to 50 times). so that the common assumption of limited applicability in electronics, due to the earlier observed and estimated low mobility, no longer holds. From the fundamental point of view the iron disilicide, depending on growth conditions, displays several epitaxial phases on silicon,‘g~20 some of which are bulk stable (a- and d-phase), while some others (y- and d4-phase) just exist as thin films. The stable semiconducting #-FeSiz can be obtained by a Jahn-Teller-like
structural transition of the met&able metallic y-phase (CaFz-like). and the nature of itsgap (indirect or direct) is strongly dependent on the first-neighbours distance.‘l Thin polycrystalline films of p-FeSiz on Si have been optically characterized by different authors on spectral intervals from far-infrared (FIR) to vacuumultraviolet (VUV).‘-4~6*22-2g Discrepancies among the results have been attributed to different growth conditions. measurement methods and surface contamination. Epitaxial &FeSiz films have been extensively subjected to structural characterization while their electronic and vibrational properties have been studied mainly by electron and photoelectron spectroscopies.7-10~30~31 Optical measurements have been performed only within a narrow spectral interval around the gap5~8-‘0 and in FIR.‘7,25 The nature of the /?-FeSiz band-gap is still an open question. Electronic structure calculations,21~32~33 optical absorption6 and photothermal deflection spectroscopy (PDS)*-*’ support the presence of an indirect gap of few tens of meV narrower than the direct 751
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OPTICAL
752
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ES, while other experimental works ‘a425 have attributed the absorption tail or subgap absorption band to defect states in the gap. Because of the importance of the optical functions, from both the fundamental and technological points of view, the aim of this work was the accurate determination of the complex refractive index ii = n + ik and the complex dielectric function E‘ = ci + it2 = n2 in a wide spectral range (from 0.2 to 5 eV) of high-quality $-FeSis epitaxial films. The effects of different growth techniques, thicknesses d and substrat.e orientation (Si (001) and Si( Ill)) were analyzed to check if their influence on the electronic transitions is as strong as that on phonon spectra.17 Reflectance (R), transmittance (T), and spectroscopic ellipsometry (SE) measurements were performed at room temperature; T was also measured at low temperatures in a narrow interval around the absorption edge in order to investigate the nature (direct or indirect) of the lowest optical gap. All the spectra were analysed using a multilayer model, in order to account for interface and substrate effects in the transparency region. A comparison with previous results, relative to both bulk and film samples. was also performed.
2 EXPERIMENT Two sets of B-FeSi2 films were epitaxially grown with two different techniques. In the first the samples were prepared in a CHV system consisting of a load-lock and two separate chambers (see details in ref. 13). The Si(ll1) substrate was pre-cleaned following the Shiraki procedure.34 A sharp 7x 7 reconstruction and the absence of contaminants was checked by low energy electron diffraction (LEED) and Auger spectroscopy. Iron was then evaporated from a resistively heated high-purity Fe wire onto the substrate maintained at room temperature. Fe thickness was measured with a quartz microbalance, calibrated by Rutherford backscattering spectrometry (RBS). Then the sample was annealed at about 500 “C for 20 min. resulting in the formation of ,!-FeSis. Film composition and thickness were determined by RBS, yielding the correct Fe/Si ratio of 1:2 and a thickness of about 200 A. X-ray double crystal diffrartometry evidenced a good crystalline quality of the $FeSiz layer, with well-oriented domains whose (101) planes were parallel to the Si(ll1) surface. However, due to the different symmetry of Si and @-FeSis, three distinguished areas with relative rotation of 120” were formed.13 The second set of samples consisted of films with
OF EPITAXIAL different machine
p-FeSi,
thicknesses on Si(ll1)
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grown in a commercial 3-in. MBE and Si(OO1) substrates. Typical
deposition rates were 0.8+1 A/s for Si and 0.3 A/s for Fe. After thermal pre-cleaning of the wafer and desorption of the oxide. a Si buffer layer was grown in order to provide clean reconstructed surfaces. In the first step a thin crystalline template of some Angst,rom was grown by depositing moderately Fe-rich silicide on the substrate maintained at temperature below 200 “C. Ihe templates were successively annealed at higher temperatures, up to a maximum of 600 “C. In the second step the desired thickness was reached by stoichiometric coevaporation of Fe and Si at different temperatures. Hence a variety of growth conditions (and crystalline orientation of the samples) were obtained. The films were characterized in situ by reflection highenergy electron diffraction (RHEED), ultraviolet and x-ray photoemission spectroscopy (UPS/XPS), and scanning tunnel microscopy. Transmission electron microscopy (TEM) was used for plan view investigation in the bright field- and in the selected area electron diffraction-modes. The relevant parameters of the samples for optical investigation are listed in Table I.
R and T measurements at near-normal incidence and at room temperature were performed in the 0.4~0.5 eV photon energy range using a Cary 5E automatic spectrophotometer, with a photometric accuracy of 0.5 Yo. An Al mirror covered with MgFs film, whose absolute reflectivity was directly measured, was used as reference for R. R and T were also measured at low temperatures. down to 3 K. using a homemade spectrometer equipped with a Spex 1402 double monochro mator between 0.5 and 1.3 eV, where the system FeSisSi was transparent. In t.he 0.2~0.6 eV range R and T were measured by a Fourier transform spectrometer Bruker IFS 113~~ using an Au mirror as reference. The spectra from different instruments merge one into the other. The FIR spectra of the same samples from 0.2 eV down to 6 meV displayin the IR-active phonons have been already published.’ g 125 The
ellipsometric
functions
tan$
Thickness (A)
#lOOO #2508 #2504 #2503 #2506
220 8000 3000 250 180
and cosA
(with
j=tanJ1 eiA, where p is the complex ratio of the parallel to perpendicular polarization reflection coefficients) were measured between 1.4 and 5 eV using a spectroscopic ellipsometer Sopra mod. MOSS ES4G. The argle of incidence was 75”, close to the Brewster angle for optimum sensitivity. Spectral resolution was better than 4 meV over the whole range. From tan+ and cosA we derived E and fi using the structural model and the data analysis procedure described below.
Table I. Relevant structural parameters of the P-FeSi2 epitaxial layers.
Sample
selected
Si substrate
orientation
( l l 1)
~~lol,~~~~~irj
(661) (661) (661) LOOl)
Fe-(lOO)//Si(OOl)
Fe( lOO)//Si(OO1) A
mainly Fe( lOO)//Si(OOl) Fe( lOO)//Si(Oa
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3 RESULTS
AND
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1-P
+ sin’q5 tan 2 Q ( -) 1 + p
sin20
k. probably due to the occurrence in the real system of roughness and non-ideal (plane and abrupt) interfaces. Moreover, small errors in R and T strongly affect the values of n and k in this high-dispersion region. These considerations should be kept in mind when evaluating the confidence in the optical functions derived from R and T measurements, both on thick and thin films.‘.5,6 above all if the tail of the absorption coefficient o = 4ak/X is used to determine the nature (direct or indirect) of the gap. In Figs. 2 and 3 the room-temperature spectra of ii and i respectively for the same sample as in Fig. 1 are reported. The spectra of polycrystalline films (d=
2
where 4 is the angle of incidence. This bulk-like behaviour was confirmed by the independence of Z from Q (besides 75”, two other d values. 65” and 70”, were proved). Moreover no differences in i were evidenced using a four-phase model (vacuum-film-Si-vacuum), with the optical functions of Si from literature and the nominal value of d. The same behaviour and the same 2 were displayed by the sample #2504. We note that the near-normal reflectivity calculated from g was generally 0.04 higher than R directly This discrepmeasured by the spectrophotometer. ancy has very likely ascribable to light scattering by macroscopic surface roughnesses, affecting photometric but not eilipsometric measurements. To account for this difference, the reflectance spectrum was scaled to match the SE results. Below 1.4 eV. strong interference fringes appear in R (as well as in T), due to coherent multireflection effects in the layered structure air-film-Si-air. Then Z and ?z for photon energy less then 1.4 eV were obtained by fitting the expression of R and T for a multilayer to the experimental spectra. 35 At each step of the fit procedure the consistency of n and k was checked through the Kramers-Kronig (KK) causality relations. TO prr-
I
753
@-FeSi,
form the KK transforms we extrapolated R spectrum beyond the highest experimental energy with a tail constructed to make the calculated n and k coincident with those measured directly by SE in the 1.4 to 5 eV range. Below 0.7 eV, where k z 0 and the amplitude of the interference fringes is quasi-constant, n and d were obtained directly from the spacing and amplitude of the fringes in R and T for both thick samples (#2508 and #2504). We note that the numerical inversion of R and T expressions around the absorption edge gives numerically instable or non-physical solutions for n and
DISCUSSION
Figure 1 shows the reflectance spectrum (dashed line) at room temperature of the thickest FeSiz-Si sample (#2508), and the corresponding reflectivity of FeSiz, determined by R and SE in the following way. .4bove 1.4 eV the FeSiz film is totally absorbing, i.e. it behaves as a semi-infinite bulk, so that i can be derived in a two-phase model (air-film) from the direct inversion of the ellipsometric jj spectrum through the well-known relationship: P =
OF EPITAXIAL
6300
Aand 4800 .&. respectively)2s4
and bulk4 samples.
-Film - -
epi (#2508) Bulk poly (Ref. 4)
------~~-Film poly (Ref. 4) o
Film poly (Ref. 2)
# 2508 i,,$
3
~~~~~~~~~ Reflectance
; :I :;2.,: : 1:! ::Ijy
-Reflectivity
0.6 p! 0.5
‘0
I
2
3
4
5
Photon energy (eV)
Fig. 1. Reflectance and reflectivity at room t.emperature of the p-FeSi:, epitaxial film (# 2508. d=SOOO A).
0
0
1
2 3 Photon energy (eV)
4
5
Fig. 2. Refractive index (n) and extinction coefficient (k) of the &FeSiz epitaxial film (# 2508), compared with those of polycrystalline bulk and films from literature.
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OPTICAL
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-2
30 w--
20
the other hand. for states lying farther apart, the character gradually switches to Si 3s.3~ (bonding and antibonding states) and the momentum matrix elements become appreciable. These features are common to many transition-metal silicides and determine the close resemblance to the interband er and ez spectra of the semiconducting silicides, 27 despite their different crystalline structure. In particular. the strong and composite band in ez just above the direct gap in all these silicides determines the strong dispersion in cl and high values of e, (e.g. c, -32.5 and n CI 5.7 for both /3FeSiz and CrSiz 37). In CrSiz this band is split into two main peaks separated by -0.5 eV and attributed to different polarization dependent interband transitions, along the same symmetry directions of the Brillouin zone (BZ).3’ As regards d-FeSiz, a peak in R at -1.05 eV has been observed in polycrystalline films ” and related to additional direct-transitions, due to the spin-orbit splitting (estimated -0.2 e\‘) of the direct gap Eg at I point. This attribution appears plausible, but we do not think that the strength of this transition can be inferred from R spectra. because interference can induce artifacts just near 1 eV (cfr. Fig. l), where the absorption rises abruptly. In our and in other P and ri spectra only a shoulder was observed at -1 eV.
epi (#X508)
- - -Bulk poly (Ref. 4) -------.-Film poly (Ref. 4)
10
Concerning the optical gap, R and T measurements around the absorption edge, on both thick and thin samples, gave a room-temperature absorption coefficient o which rises abruptly up to a value of N 1.2 x lo5 cm-’ at 1 eV and then slopes less steeply at higher energies. A plot of o2 versus photon energy showed a linear variation. yielding a direct optical gap E, of -0.85 e\‘, which falls within the interval from 0.83 to 0.90 eV reported in literature. E, shows anomalous behaviour with decreasing temperature: it increases for the thickest samples (up to 0.89 eV, for T = 3 K), and reduces for the thinnest ones. Other than experimental uncentainty, this thickness dependence may be a misfit-strain effect, which is expected to be stronger in thin films.
0
20 WN 10
0
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The assignement of the peaks in ez to specific interband transitions requires the knowledge of the joint density of states and the momentum matrix elements. due to the flatness of the valence bands of &FeSiz near the Fermi leve1.32 Moreover, the states in conduction and valence bands around the energy gap have primarily the d character of Fe (non-bonding states) so that the across-gap oscillator strengths are very small. On
50 -Film
p-FeSi,
EELS spectrum. measured on epitaxial films3’ displayed two peaks at _ 2.5 and -5 eV. but their absolute intensities were lower and their relative strengths inverted with respect to the optical findings.
measured on a narrower range, are also report.ed for comparison. The dielectric functions for thick epitaxial samples (#2508 and #2504) agree very well with those of bulk polycrystalline samples, measured with SE by Dimitriadis et al..* which differ by only 10% in the amphtude of the composite ez structure peaked at -1.8 eV. On the contrary, the er and ez spectra of polycrystalline filmsj,26 generally present similar shapes, but the structures are broadened and energy-shifted. and their intensity can be significantly lower, as in the case of Fig. 3. A remarkable exception is represented by the n and k: values around the absorption edge reported from Ref. 2: their k spectrum is quasi-coincident with our, while their R peak at -0.9 eV is slightly different (and not KK consistent with k). The disagreement between optical functions of polycrystalline bulk and films has been attributed4 to void fractions and surface roughness in the films, depending on growth conditions and thermal annealing: in this respect, the interband optical response, as well as the sharp vibrational structures,‘6~25 of our epitaxial films confirms their good crystalline quality. Lastly, e:, obtained from the KK analysis of the
40
OF EPITAXIAL
0
I
2
3
4
5
Photon energy (eV)
Fig. 3. Real (~1) and imaginary (sz) part of the complex dielectric function of the p-FeSiz epitaxial film (# 2508), compared with those of polycrystalline bulk and film from literature.
\Z;e also obtained an absorption tail below E, which cannot be unambigously ascribed to the indirectgap transitions because of the aforementioned uncertainty in R and T data and analysis in this spectral However, complementary PL measurements region. on our high-quality samples didn’t evidence any signal around the direct gap, supporting the absence of impurities and thr presence of an indirect gap, just below E, (in agreement with findings of Ref. 10 on buried @-FeSi:!). We think that, in addition to the theoretical results2’.“2*33 which agree on the existence of an indirect gap at L point of the BZ, the experimental evi-
Vol. 96, No. 10
OPTICAL
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dence. more than from R and T measurements on thin films, comes from PDS measurements. These give an indirect gap value of O.i6-0.8 eV and a dirert one at 0.83+--0.85 eV at room temperature,s-I0 and of -0.86 and -0.875, respectively. at 77 K.” However. because of PDS signal saturation at high a values, these measurements have to be normalized beyond the absorption edge to accurate values of Ic, as for example those extracted from SE. Optical measurements on bulk single-crystals, recently grown by chemical vapor transport using iodine as a transport agent, ” should overcome the problems connected with thin films and, in particular, the mismatch strain which can critically affect the nature of the gap. 21 However the as-grown samples are n-type, so that doping compensation can be requested to avoid free-carrier screening of the gap, as with CrSiz singlecrystals.37 Fig. 4 displays n and k spectra, derived from SE measurements. of all the samples reported in Table I (except for the sample #2504, because its optical response is quasi-coincident with that of sample #2508). Beyond the overall agreement among the spectra, two features should be underlined: a) in the thin films (#lOOO, #2503. #2506) the valley at m 3.3 eV and the two adjacent broad peaks appear enhanced with respect to the thick film (#2508). This is a partial artifact due to the d value used in the multilayer model. In fact, in absence of interference fringes useful to optically determine d in thin films, we assumed the nominal value of d, derived from RBS or RHEED. If d is underestimated. the numerical inversion of SE spectra produces spurious structures. reflecting in negative the structures of Si substrate (in particular the strong peak around 3.5 eV). This effect increases with decreasing d; however we cannot exclude a contribution from mixed interface regions. b) In sample #lOOO, the energy position of the peak at _ 1.8 eV is slightly red-shifted: this effect can be attributed to the optical anisotropy of the orthorhombic structure. In fact, sample #lOOO was grown on Si( 111) with the orientation FeSis( lOl)llSi( ill), while all the other samples were grown on Si(OO1). with FeSisllSi(OO1).
4 CONCLUSIONS We accurately measured the complex refractive index and the dielectric functions of P-FeSiz epitaxial films in the 0.2t5 eV photon energy interval. The thickest films displayed an optical response very similar to that of bulk polycrystalline samples. The direct gap was clearly determined, while interference effects in thick films, non-ideal conditions of thin films, and the strong dispersion of i7. at the absorption edge prevented a clear determination of the lower-energS indirect-gap:
OF EPITAXIAL
p-FeSi, I
755 I
I
I
_______#,0()0
2
3
----..-_._
#2503 #25O(j
-
#2508
4
5
Photon energy (eV)
Fig. 4. Refractive index (n) and extinction coeficient (k) derived from SE spectra of &FeSis epitaxial films, with different thicknesses and orientations (see Table I).
however its existence was confirmed by complementary luminescence measurements. The crystalline orientation of the films with respect to the silicon substrate mainly affects the first optical structure around 1.8 eV.
ACKNOWLEDGMENTS This work has been partially supported by the European Project Nr.CHRX-CT93-0318, “Physical properties of bulk single crystals and thin films of metal silicides” within the Program “Human capital and mobility”.
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OF EPITAXIAL
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