Electronic signature of the pentagonal rings in silicon clathrate phases: Comparison with cluster-assembled films

Article abstract of DOI:10.1103/PhysRevB.58.12590

The valence-band spectrum of the silicon Si-34 clathrate phase has been measured by photoemission spectroscopy. In contrast with tetrahedral Si (diamond phase), the clathrate structure presents mainly five-member rings. From the comparison between the tetrahedral Si and the clathrate spectra, we show that the presence of odd-member rings induces the merging between s-like and sp-like bands and a strong reduction of the valence-band width. These results are corroborated by first-principles calculations within an accurate quasiparticle approach.

Full text of DOI:10.1103/PhysRevB.58.12590

PHYSICAL REVIEW B
VOLUME 58, NUMBER 19
15 NOVEMBER 1998-I
Electronic signature of the pentagonal rings in silicon clathrate phases:
Comparison with cluster-assembled films
P. M e´ linon, P. K e´ gh e´ lian, X. Blase, J. Le Brusc, and A. Perez
D e´ partement de Physique des Mat e´ riaux (UMR CNRS 5586), Universit e´ Claude Bernard-Lyon 1, B aˆ timent 203,
4
3 Boulevard du 11 Novembre 1918, 69622 Villeurbanne C e´ dex, France
E. Reny, C. Cros, and M. Pouchard
Institut de Chimie de la Mati e` re Condens e´ e de Bordeaux, UPR/CNRS 9048 and Universit e´ Bordeaux I, F33608 Pessac, France
͑Received 27 March 1998͒
The valence-band spectrum of the silicon Si-34 clathrate phase has been measured by photoemission spec-
troscopy. In contrast with tetrahedral Si ͑diamond phase͒, the clathrate structure presents mainly five-member
rings. From the comparison between the tetrahedral Si and the clathrate spectra, we show that the presence of
odd-member rings induces the merging between s-like and sp-like bands and a strong reduction of the valence-
band width. These results are corroborated by first-principles calculations within an accurate quasiparticle
approach. ͓S0163-1829͑98͒05240-0͔
3
During the last three decades, a considerable effort has
been devoted to the understanding of the polymorphism of
a sp -like configuration. The samples used for this study
were obtained by thermal decomposition of NaSi under
vacuum (10 Torr͒ in the temperature range 670–710 K.
3
Ϫ6
silicon ͑Si͒ with particular attention to the sp -hybridized
1
–5
networks.
defects, as compared to the ‘‘ideal’’ sp diamond structure
c-Si͒, is of much importance since it is expected to greatly
For example, the presence of topological
They are in the form of a powder with a mean grain size of
the order of a few micrometers. The crystalline phase purity
was deduced from the x-ray diffraction pattern. A small so-
dium component remains within the cages. In order to check
its influence, we have studied two stoichiometric compounds
3
͑
influence the structural, dynamical, and electronic properties
of various Si-based materials such as ͑e.g.͒ amorphous sili-
con ͑a-Si͒, cluster-assembled films, reconstructed surfaces or
Na Si-34 with respectively xϭ7 ͑labeled clat1͒ and xϭ1
x
6
interfaces, and c-Si core dislocations. Since the early work
͑labeled clat 2͒. A careful analysis of the x-ray powder dif-
fraction pattern reveals that the alkali atoms occupy prefer-
entially the Si28 cages. Therefore, in the clat1 phase, all the
Si28 cages are endohedrally doped. We find that the VB of
both the clat 1 and clat 2 samples are very similar, yielding
DOS peaks at the same energies.
Clathrates samples are introduced in a dual XPS/Auger
camera Nanoscan-100 type microprobe operating at a base
pressure Ͻ4ϫ10
K␣ x-rays ͑1486.6 eV͒. The clathrate samples were com-
pared to a nearly intrinsic Si͑100͒ crystal (␳Ͻ400 ⍀ cm,
n-type, at room temperature, labeled tetrahedral Si͒. The
most accurate VB is obtained by in situ crystal cleaving be-
fore analysis. In our case, such a procedure is of course pos-
sible for the reference sample but unsuitable for the clathrate
powders, which are therefore previously pasted on another Si
substrate. Both samples are cleaned by chemical way ͑HF
1
1–4
by Joannopoulos and Cohen, it has been suggested
on
theoretical grounds that the presence of pentagons signifi-
cantly affects the valence-band ͑VB͒ density of states ͑DOS͒
and the fundamental band gap. However, on the experimen-
tal side, measurements conducted on the various phases
quoted above average over both the even- and odd-member
rings and it is difficult to resolve each contribution specifi-
cally.
Ϫ10
Torr. The XPS is performed using Al
7
13
New crystalline phases named clathrates, which are built
from the regular arrangement of a combination of Si20 (Ih)
and Si24 (D ) or Si (T ) cages, have been synthesized.
6d
28
d
Both the crystalline order and the very large predominance
of fivefold rings (87%) in such materials should allow one in
principle to specifically study the signature of the odd-
member rings and much theoretical effort has been recently
8,9
devoted to the study of the electronic properties and pho-
1
0–12
non modes
of such materials. In this work, we report on
solution͒ and dried by a N gas just before introducing them
2
a measurement of the VB DOS of a clathrate on the basis of
photoemission spectroscopy ͑XPS͒. Our results clearly show
that the presence of pentagons induces a contraction of the
VB width and the merging of the s and s-p occupied sub-
bands with respect to tetrahedral Si. These results are cor-
roborated by ab initio calculations within an accurate quasi-
particle approach.
Our clathrate samples ͑labeled Si-34͒ can be described as
being composed of Si28 face-sharing polyhedra, with a Si
atom in the vertices ͑space group Fd3m aϭ1.462 nm͒. The
space between the Si28 forms Si20 cages and each atom is in
into the XPS apparatus. To check the influence of the
‘‘glue,’’ we have compared the spectra obtained for the
clathrate powders pasted or directly deposited on a gallium
or indium substrate. The differential charging was estimated
to be ϳ0.2 eV ͑because of the insulating character of the
glue͒. This value sets the accuracy of our data.
Figure 1 shows the XPS near the Fermi level observed for
the reference ͑a͒ and the clat 1 ͑b͒ samples. These spectra are
corrected for the inelastic scattering tail. The Si2p core line is
taken as a reference to align the ͑a͒ and ͑b͒ spectra.14 We
observe in both cases three ‘‘subbands,’’ well known in the
0
163-1829/98/58͑19͒/12590͑4͒/$15.00
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©1998 The American Physical Society

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FIG. 2. Theoretical DOS for tetrahedral Si and Si-34 ͑solid
lines͒. The s- and p-resolved contributions are shown with dotted
and dashed lines, respectively. The angular momentum decomposi-
tion of the DOS is obtained by projecting the wave functions on a
spherical harmonics basis centered on each Si atom. The DOS have
been aligned at the VB top edge. A 0.1-eV Gaussian broadening has
been used.
FIG. 1. VB DOS for tetrahedral Si ͑a͒ and clathrate ͑b͒. The
dotted and continuous lines are, respectively, the theoretical and
experimental spectra. The theoretical spectra are calculated from
the DOS ͑Fig. 2͒ after several corrections indicated in the text.
Theoretical and experimental spectra have been aligned through
matching of the intrinsic Fermi level.
clathrate and c-Si phases opens up to 1.9 and 1.2 eV, respec-
tively. As for the VB, the effect of the quasiparticle correc-
tion as compared to DFT-LDA results merely in a slight
‘‘stretching’’ of the VB width, which increases by ϳ0.25 eV
in both cases. The resulting DOS are represented in Fig. 2
and compared to the experimental data in Fig. 1. In this latter
case, the effect of cross-section modulation for 3s and 3p
states and a broadening taking into account the experimental
dispersion have been applied for better comparison with the
experimental results.20
We further plot in Fig. 2 the s-resolved ͑dotted line͒ and
p-resolved ͑dashed line͒ DOS. The calculated DOS repro-
duce quite well the experimental observations, namely, the
shift of the s and sp bands and the reduction of the VB width
in the clat1 phase as compared to tetrahedral Si. We do not
observe a clear reduction of the s-DOS band width but rather
a loss of structure. On the contrary, the band width of the
p-DOS decreases by ϳ2 eV from the tetrahedral Si to the
clathrate phase. This strong reduction, which affects the top
of the VB, can clearly explain both the ϳ0.7-eV opening of
the band gap and the ϳ1-eV shift towards the Fermi level of
the sp peak in the Si-34 phase as compared to the tetrahedral
Si reference. As another consequence, we observe a strong
‘‘steepening’’ of the DOS just below the top of the VB edge
in the clathrate phase as compared to tetrahedral Si. This is
very similar to what happens in a-Si for which one would
expect the introduction of random disorder to broaden the
bands.
case of tetrahedral Si, and that we label respectively s, sp,
and p with respect to their angular momentum character.1
We find, however, significant differences in the position and
width of these subbands when comparing both phases. In
particular, the clat1 total VB width (W ϭ11.5 eV͒ is smaller
cl
than the tetrahedral Si one (W ϭ13.5 eV͒. Further, the clat 1
d
s subband maximum lends at roughly the same energy as the
‘‘valley’’ between the s and sp subbands of tetrahedral Si.
These measurements confirm therefore on an experimental
basis that the presence of pentagonal rings significantly af-
fect the VB electronic DOS and the corresponding modifica-
tions are clearly identified.
Further insight into the properties of the pentagonal rings
may be obtained by conducting a first-principles study of the
electronic DOS of Si-34. The present calculations are first
15
performed within the local density approximation ͑LDA͒
16
to the density functional theory ͑DFT͒. A standard
1
7
pseudopotential is used for Si and the wave functions are
expanded on a plane-wave basis with kinetic energy up to 20
Ry. We first relax the system with respect to both cell size
and atomic positions and find a lattice constant of 27.55 a.u.
We then calculate the band structure of Si-34. The VB width
and fundamental band gap are, respectively, 10.84 and 1.25
eV. This can be compared to 11.92 and 0.51 eV for bulk Si
within the same theoretical framework. Therefore, the band
gap opens by 0.7 eV from the tetrahedral Si to the clathrate
phase, in good agreement with the results of Refs. 8 and 9,
while on the contrary the valence-band width decreases by
Now, we can use the clathrate sample as a reference to
1
8
21
1.1 eV.
study other Si phases such as cluster-films. Figure 3͑a͒
We recall now that the DFT usually underestimates by as
shows the ‘‘addition’’ of both the tetrahedral Si and clathrate
sample’s XPS spectra. This is compared in Fig. 3͑b͒ to the
XPS of a film obtained by the deposition of free Si ͑size
range 20–50 atoms͒.21 Such small clusters present a combi-
nation of fivefold and sixfold rings. The straightforward ad-
dition of both the tetrahedral Si and clathrate sample’s XPS
much as 50% the band gap of semiconductors and insulators.
In order to provide an accurate value for the band gap
of Si-34, we perform further a quasiparticle energy
1
9
calculation for both the tetrahedral Si and clathrate phases.
We find that within this formalism, the band gap of both the

12 592
BRIEF REPORTS
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FIG. 3. Addition ͑1/1 ratio͒ of both the experimental VB of the
clathrate and Si-diamond samples ͑a͒ compared to the VB observed
for cluster-assembled films ͑b͒ ͑see Ref. 21͒. The corresponding
FIG. 4. Valence band for Si diamond ͑a͒, and clathrate ͑b͒ after
ϩ
Ar etching. The addition of the clathrate and Si-diamond theoret-
ical DOS in a 1/1 ratio is shown in ͑c͒. In this latter case, the
intrinsic Fermi levels have been aligned and the s and p cross-
section corrections have been applied as in Fig. 1.
‘
‘ring configurations’’ are given at the top of the figure.
spectra is certainly a rather crude approximation that should
not be used to describe the fine details of Fig. 3͑b͒. However,
one observe in both cases a large merging of the s and the sp
bands as mentioned for other structures such as a-Si ͑Ref.
tures are ‘‘dual’’ if we consider the nature of the defects
selectively created during the etching process. The similar-
25
ity between both spectra and their stability under further
bombardment suggests that in both cases the number of odd-
2
2͒ or porous silicon.23 As emphasized above ͑see Fig. 1͒,
26
and even-membered rings is comparable. Such dual defects
this feature originates in the shift of the s-pentagon-related
band as compared to the bulk diamond structure. It appears
therefore that the s- and sp-like bands merging is the signa-
ture of the fivefold rings, as originally proposed by Joan-
yield electronic levels in the valley between the s and sp
bands, leading again to their merging. This is another experi-
mental confirmation that the merging between the s and sp
subbands originates in the coexistence of odd- and even-
membered rings in a close to 1/1 ratio.
1
nopoulos and Cohen on the basis of calculations performed
on the hypothetical ST-12 Si phase. The present experimen-
tal results clearly confirm these early predictions. Let us em-
phasize that the filling of the valley between both s- and
sp-like bands is achieved with a large proportion of five-
member rings ͓43% in Fig. 3͑a͔͒. This is a confirmation of
the so-called memory effect in cluster-assembled films,
In conclusion, we have studied both theoretically and ex-
perimentally the valence band spectrum of a pure Si crystal-
line clathrate phase having mainly pentagonal rings. The po-
sition of the subbands attributed to such odd-membered rings
has been measured. By comparison with the valence-band
spectrum of tetrahedral Si, we have shown that the introduc-
tion of pentagons in the diamond lattice leads to a merging of
the s- and sp-like bands, the contraction of the VB width and
to a steepening of the DOS below the VB edge. The avail-
ability of precise and specific data for pentagonal rings
should prove very useful to further study various Si struc-
tures such as ͑e.g.͒ a-Si, cluster-assembled films, recon-
structed surfaces, and interfaces or core dislocations in sol-
ids.
namely, that such materials ‘‘remember’’ the structural prop-
erties of the corresponding free clusters.24
Finally, we report on the XPS spectra obtained after in
ϩ
situ bombardment by Ar ions. Figure 4 gives the resulting
VB DOS for the tetrahedral Si reference ͑a͒ and the clat1 ͑b͒
samples. The spectra, which both show a strong modification
as compared to Figs. 1͑a͒ and 1͑b͒, are now remarkably simi-
lar, indicating that both samples have transformed into a
similar structure under bombardment. This suggests that the
defects in clathrate are formed by even-membered rings such
X.B. acknowledges use of the supercomputer facilities
͑Cray-C94͒ at the French Commissariat a` l’Energie Atom-
as Si while those in diamond phase are constituted by odd-
ique ͑CEA-CENG͒ in Grenoble, France. The authors would
6
membered rings such as Si . In this respect, the two struc-
like to thank Professor M. Broyer for fruitful discussions.
5
1
6
J.D. Joannopoulos and M.L. Cohen, Phys. Rev. B 7, 2644 ͑1973͒;
Examples for the role of odd-member rings in the stability and
8
, 2733 ͑1973͒; M.L. Cohen and J.R. Chelikowsky, Electronic
mobility of core dislocations in Si-diamond may be found in J.
Bennetto, R.W. Nunes, and D. Vanderbilt, Phys. Rev. Lett. 79,
245 ͑1997͒, and references therein.
Structure and Optical Properties of Semiconductors, Springer
Series in Solid-State Sciences Vol. 75 ͑Springer Verlag, Berlin,
7
1989͒, pp. 199–203, and references therein.
J. Kasper, P. Hagenmuller, M. Pouchard, and C. Cros, Science
2
3
S.L. Clark, Phys. Rev. B 49, 5341 ͑1993͒.
A. Demkov, W. Windl, and O.F. Sankey, Phys. Rev. B 53, 11 288
150, 1713 ͑1965͒.
S. Saito and A. Oshiyama, Phys. Rev. B 51, 2628 ͑1995͒.
A.A. Demkov, O.F. Sankey, K.E. Schmidt, G.B. Adams, and M.
O’Keeffe, Phys. Rev. B 50, 17 001 ͑1994͒.
D. Kahn and J.P. Lu, Phys. Rev. B 56, 13 898 ͑1997͒.
M. Menon et al., Phys. Rev. B 56, 12 290 ͑1997͒.
Y. Guyot et al., Phys. Rev. B 57, R9475 ͑1998͒.
8
9
͑
1996͒.
4
5
J. Singh, Phys. Rev. B 23, 4156 ͑1981͒.
10
R. Grigorovici and R. Manaila, Thin Solid Films 1, 343 ͑1968͒;
see also N.F. Mott and E.A. Davis, Electronic Processes in Non-
Crystalline Materials ͑Clarendon Press, Oxford, 1971͒, p. 276;
J.F. Sadoc and R. Mosseri, Philos. Mag. 45, 467 ͑1982͒.
1
1
1
1
2
3
The resolution was measured at 1.2 eV on Ag 3d3/2 line for the

PRB 58
BRIEF REPORTS
12 593
core levels. For the VB measurements the energy pass was fixed
bottom of the conduction bands, leaving the VB unchanged, in
good agreement with previous theoretical work ͑Refs. 8 and 9͒
and with the present conclusions drawn from the comparison of
the clat1 and clat2 spectra.
We use the so-called ‘‘GW’’ approximation for the self-energy as
originally introduced by Hedin ͓L. Hedin, Phys. Rev. 139, A796
at 0.8 eV. For depth profile, we use an argon ion operating at
Ϫ8
low flux (Ͻ10 Torr͒ and medium energy ͑3 keV͒. The etch-
ing rate is less than a few monolayers per hour.
1
4
1
9
This procedure of alignment through calculation of the Si2p core
lines is necessary in the present case since the position of the
Fermi level is unknown for the clat1 sample. For both the tetra-
hedral Si- and clat1 samples, the Si2p core level were measured
to be equal within the 0.2 eV accuracy of our measurements.
This indicates that the possible core-level shift between both
phases is rather small. We note that the position of the Si2p line
with respect to the intrinsic Si-diamond Fermi level is equal to
͑1965͔͒. This approach has been shown to yield band gap of
bulk and surfaces semiconductors accurate to within 0.1 eV as
compared to experiment. Technical details can be found in M.
Hybertsen and S.G. Louie, Phys. Rev. B 34, 5390 ͑1986͒; X.
Blase, X. Zhu, and S.G. Louie, ibid. 49, 4973 ͑1993͒. More
detailed results will be given in a subsequent paper.
W.B. Jackson et al., Phys. Rev. B 31, 5187 ͑1985͒.
P. M e´ linon et al., J. Chem. Phys. 107, 10 278 ͑1997͒.
R.P. Vasquez, A. Madhukar, and A.R. Tanguay Jr., J. Appl. Phys.
99.3 eV.
2
2
2
0
1
2
1
1
1
5
6
7
D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45, 566 ͑1980͒;
J.P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 ͑1981͒.
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 ͑1964͒; W.
Kohn and L.J. Sham, Phys. Rev. 140, A1133 ͑1965͒.
K. Kleinman and D.M. Bylander, Phys. Rev. B 48, 1425 ͑1982͒;
N. Troullier and J.L. Martins, Solid State Commun. 74, 613
58, 2337 ͑1985͒.
2
2
3
4
R.P. Vasquez et al., Appl. Phys. Lett. 60, 1004 ͑1992͒.
V. Paillard et al., Phys. Rev. Lett. 71, 4170 ͑1993͒; A. Canning,
G. Galli, and J. Kim, ibid. 78, 4442 ͑1997͒.
P. Morgen and F. Ryborg, J. Vac. Sci. Technol. 17, 578 ͑1980͒.
Indeed, it is only in this case that further defects creation should
turn as many odd- into even-member rings and vice versa.
͑
1990͒.
2
2
5
6
1
8
Similar calculations have been performed for the Na-doped clat1
phase. Upon doping, hardly any structural relaxation is ob-
served. The introduction of the Na3s orbitals affects mainly the