J. Phys. Chem. 1995,99, 1896-1899
1896
Electronic Structures of Layered Polysilanest J. S . Tse* Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada KIA OR6
J. R. Dahn Department of Physics, Simon Fraser University, Bumaby, British Columbia, Canada V5A I S 6
F. Buda FORUM-INFM, Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy Received: August 17, 1994; In Final Form: November 22, 1994@
The electronic band structure of a newly characterized polysilane (Si6H6) sheet has been studied with HartreeFock and local density-functional calculations. A direct band gap was found with a calculated absorption edge at 3 eV. Layered structures (SGH6) with thicker Si sheet cores can be constructed by linking several layers followed by hydrogen termination of the exposed surfaces. The multiply linked materials are found to develop a weak indirect band gap approaching that of bulk silicon as the number of layers increases. The observed band-gap variation in hydrogen-passivated porous silicon (p-Si) may be related by recognizing that the p-Si is made of cross-linking Si sheet structures (Si6,&) whose Si core thickness (n) varies with preparation conditions.
The origin of efficient luminescence in porous Si (p-Si)'Z2 is still uncertain. There are two main proposals to account for this effect. The original proposal suggests that a quantum size confinement effect2 due to the small dimensionality of the p-Si is responsible for the interesting optical properties. Based on the similarity in the optical and vibrational properties of chemically synthesized siloxene to that of p-Si, the possibility of the presence of a trace of siloxene derivatives as luminescent agent has been Theoretical studies on model H-terminated Si and several hypothetical structures of siloxene1° have revealed that strong excitations in the visible region are possible in both systems. In a recent critical examination of siloxene prepared from the method described by Weiss et al.," no evidence of oxygen insertion into the Si layers was found.12 In fact, experimental evidence strongly suggests that siloxene prepared under controlled conditions has H-terminated Si[ll 11 layers stacked to form a disordered crystal called layered polysilane (Si&) (Figure 1). There is a large probability to find adjacent layers stacked with random rotations or shifts parallel to the layers,",'* a disordered (turbostratic) stacking commonly found in carbon. Perhaps, most significantly, similar to p-Si, the Si K-shell absorption edge for this compound is found to be blue shifted relative to crystalline silicon by 0.6 eV,13 which is consistent with the notion of quantum ~0nfinement.l~ The electronic band structure of a model compound, similar to the layered polysilane, constructed from corrugated Si[ 1111 layers terminated by H atoms, has been reported r e ~ e n t l y .A~ weak indirect band gap of 2.75 eV and a strong zone-center transition only 0.2 eV higher in energy were found.9 Now that there is experimental evidence for a van der Waals bonded layered polysilane, which is the silicon analogue to graphite, it is of considerable importance to further investigate the electronic properties of this compound and its modifications. This article focuses on the elucidation
* To whom correspondence should be addressed. Published as NRCC 37307. @Abstractpublished in Advance ACS Abstracts, February 1, 1995.
0022-365419512099-1896$09.00/0
Figure 1. Schematic representation of (a) a single polysilane layer viewed down the c axis, (b) packing of layered Si.& polysilane in the crystal, and (c) a single slab of doubly linked Si12H6 polysilane.
0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 7, 1995 1897
Electronic Structures of Layered Polysilanes
J a \
x
r
Y C
Portio1 Density of States
Figure 2. HF electronic band structure and projected partial density of states for crystalline Si,&
(solid line, Si 3s; dashed line, Si 3p; dot-dashed
line, H 1s). of the geometric and electronic structures of layered polysilanes. Based on the structural similarity, a common cause for the luminescence in layered polysilane, p-Si, and siloxene is proposed. The electronic band structures of crystalline layered Si& and several multiply linked layer derivatives are studied with the ab initio self-consistent-field all-electron periodic HartreeFock (HF) method.15 An atom-centered split-valence 6-21G Gaussian basis set16for H and a similar basis set for Si optimized for crystalline silicon15were employed in the calculations. To complement the HF study, first principles local densityfunctional (LDF) pseudopotentia18J7 calculations were performed on several selected structures. The Si electron-ion interactions were described in terms of the norm-conserving Bachelet-Hamann-Schluter pseudopotential18 retaining only s nonlocality and expressed in the Kleinman and Bylander’s form.lg A local potential was employed for the H atom.8 The r point (k = 0) was used for Brillouin-zone (BZ) sampling, and the Kohn-Sham orbitals were expanded in plane wave (PW) using an energy cutoff of 12 Ry. The calculations on crystalline Si6H6 assume a trigonal unit cell with a = 3.83 8, and c = 5.50 A as determined from X-ray diffraction.12 The atomic positions for Si and H were optimized by a series of HF calculations. The optimized Si-Si bond length of 2.34 A can be compared with the bulk value of 2.3517 A. The optimized Si-H bond length is 1.50 A. The band structure and projected density of states are shown in Figure 2. A direct band gap is found at the zone center. It is well-known that the HF method often overestimates the band gap;15 nevertheless, a qualitative value of 2.8 eV can be obtained by subtracting the same amount (about 5 eV) that was required to match the HF eigenvalues with the experimental band gap in bulk Si.2o The band dispersions in the direction perpendicular to the plane of the layers (r A and M L) are very small. The dispersion along the r A (located at the edge of the BZ perpendicular to the layers) and r M (halfway along one of the axes in the plane of layers) branches are in good agreement with that reported for the corrugated H-terminated S i [ l l l ] model, except that a weak indirect band gap between the conduction band M point and the valence band r point was found in the earlier calc~lation.~ The small discrepancy can be attributed to different interplanar separations used in the calculations. The lack of dispersion perpendicular to the plane is indicative of weak interlayer interactions. This is confirmed by a
-- - -
calculation of the electronic band structure of an isolated 2-D Si6H6[001] sheet which shows the dispersions in the electronic bands parallel to the plane of the isolated layer are indeed almost identical to that in the crystalline structure, only the direct band gap at r has widened slightly. Additional calculations varying the interplanar separation show that the interlayer interactions are indeed van der Waals type. The calculations give an optimal interplanar separation of about 6 A. This value is comparable to the experimental d u e l 2 of 5.5-5.9 A. In contrast, earlier LDF calculations on the Si[ 1111 layers yield a smaller interplanar distance of 4.78 A.g The partial density of states for crystalline S i a b is shown in Figure 2. The lower valence bands are primarily Si 3s. There is a small gap between Si 3s and 3p bands. The Si-H bonds are situated at the bottom of the 3p band, and the upper valence band is almost entirely Si-Si p-bonding. The lower conduction bands are rich in Si 3p and H Is, indicating strong antibonding Si-H character. First principles LDF calculations on S a gave essentially the same density of states profile as the I-IF results, with anticipated narrowing of the gap between the valence Si 3s and 3p bands. The optimized Si-Si and Si-H bond lengths are 2.33 and 1.55 A, respectively. The photoluminescence (PL) spectra for p-Si and siloxene are ~ i m i l a r .Unfortunately, ~ calculation of the PL spectrum is complicated by relaxation, impurity scattering, and excitonic interactions. We instead studied the dipole transitions which are directly related to the absorption and indirectly can provide information on the radiative PL processes. The dipole transition matrix elements can be computed readily from the PW wave functions obtained from LDF calculations.* The calculated absorption spectrum for layered Si6Hs is shown in Figure 3. The qualitative features of the spectrum are remarkably similar to that of H-terminated Si quantum wires.8 The excitations in layered polysilane are shifted to higher energies as compared with the quantum wire calculations.8 The threshold of the absorption is located at 3.0 eV. This value collaborates with the approximate value estimated from the HF calculation. However, it should be noted that LDF calculations often underestimate the band gap. In the visible and ultraviolet region below 4.5 eV, two weak shoulders at 3.3 and 3.6 eV and a strong peak at 4.2 eV can be identified. These excitations originate from valence-bonding Si-Si to antibonding Si-H transitions. This assignment is in full agreement with the previous corrugated S i [ l l l ] modelg and Si quantum wires calculations.8 The absorption spectrum calculated for a single
Tse et al.
1898 J. Phys. Chem., Vol. 99, No. 7, 1995
2
4
6
8
Energy / eV Figure 3. Calculated LDF absorption spectra (arbitraq units) for crystalline Si& (solid),[Ool] slab S a (dash), and crystalline Si,z&
(dot-dash). 3.02
0.0
’
Si,H,
SiizH6
Sil,He
Si2,H6
Si&
C-Si
Figure 4. Band gap trends for crystalline polysilanes. Open circles indicate indirect band gap, and the filled circles indicate direct band
gap at r.
isolated si6H6 layer is also shown in Figure 3. The low-energy absorptions are found to shift to higher energies as compared to crystalline Si6H6. The shift to higher energy is due to more diffuse antibonding Si-H orbitals in a more “molecule-like” environment. It is suggestive that the interplanar interactions, albeit weak, help to confine the wave functions of the filled and empty Si-H bonds perpendicular to the plane of the layer. The same effect is also observed in the HF calculations as discussed above. The similarity between the electronic structure of crystalline raises the speculation layered polysilane and Si quantum that layered polysilane and p-Si may be related. Anodic etched crystalline wafer Si in HF solution produces a porous random network of H-capped nanometer “wire” which might be considered as a connected, conducting network of fused crystalline.21 Inspection of the crystal structure reveals that nanostructure 2-D Si quantum slabs can be constructed by vertically linking several adjacent Si6 layers through the Si atoms and terminating the surfaces with H atoms to make SianH6(e.g., Figure I C shows Si1zH6). For example, if five such sheets (n = 5 ) are linked together, the thickness of the slab would be about 15 A, which falls within the size domain of the structure found in p-Si fabricated by electrochemical etching of Si wafers ,2 To investigate this possibility, the electronic band structures for multiply linked polysilanes (n = 2-5) were studied with HF calculations. A summary of the major band gap features is depicted in Figure 4. When the Si layers are linked, an indirect band gap develops between the r point in the valence band and the M point in the conduction band. The indirect band
energy gap decreases as the number of Si layers increases. The energy gap at the zone center also shows a small decrease with the number of Si layers. The magnitude for both zone center gap and indirect band gap approaches that of bulk silicon as the number of Si layers increases. This trend is not unexpected. The Si6 layers in the trigonal polysilane structure are the [ 1111 planes in bulk silicon. In bulk silicon, the S i [ l l l ] planes are cross-linked, but in polysilanes, the Si layers form 2-D slabs stacked in a parallel fashion. Consequently, as the number of Si layers within each slab increases, the polysilane becomes increasingly bulk Si-like. The absorption spectrum calculated for Si12H6 is shown in Figure 3. The main absorption peak has shifted to lower energy (3.7 eV), and the threshold of the absorption edge is now at 2.5 eV. The LDF results are in complete agreement with the HF calculations. Moreover, the theoretical results are also consistent with a narrowing of the band gaps observed in synthetic organopolysilanes with increasing dimensionality due to cross-linkages.22 Although indirect energy gaps are predicted for the multiply linked layered polysilanes, the PL efficiency for these materials does not necessarily have to be low. Provided the nonradiative decay rates for electron-hole pairs are lower than the radiative decay rates, efficient luminescence will be observed. In nanocrystals, the electron-hole pair decay rates are often dominated by radiative processes.23 This conjecture is recently confirmed by PL experiments on size-selected surface-oxidized silicon nanocrystals which show that these materials behave as indirect band gap substances in spite of their high luminescence yields.24 There is a controversy concerning the relationship between siloxene and p-Si. The strong resemblances in their vibrational3 and some optical ~ p e c t r a ~have - ~ led to the suggestion that the presence of a trace of siloxene may be responsible for the luminescence in p-Si. However, recent experiments show that p-Si which luminesce well can have no oxygen, while siloxene contains substantial oxygen, so that the strong luminescence in p-Si is not necessarily due to the presence of oxygen.25 It is now recognized that layered polysilane is the primary product of the reaction of CaSiz with HCl under controlled conditions.l2 Siloxene prepared by the same reaction is partially hydrolyzed layered polysilane due to exposure to air and excessive heating. Substitution of Si-H with Si-0-H will alter the position of the luminescence maximum. Previous LDF calculations showed that the band gap is dependent on the SiOH substituents and decreased from 2.75 to 1.7 eV when half of the Si-H bonds were r e p l a ~ e d . ~It is noteworthy that nanometer Si crystallites with an oxidized surface were also found to luminesce in the red.21,24,26 It is plausible that stacked polysilane layers may be connected to p-Si. The linking of polysilane layers (Si6,Ha) results in a distribution of band gaps from 1.2 eV for n = = to 2.8 eV for n = 1 which fall into the range for p-Si. There is other experimental evidence in favor of this proposal. It is recognized that the local structure of p-Si is essentially bulk crystallinelike.22327The Si K absorption spectrum for layered polysilane Si6H6 shows a characteristic blue shift indicative of quantum confinement as was observed in p-Si.13 The luminescence spectrum of electrochemically etched p-Si depends on the preparative conditions and the luminescence maximum shifts to higher energy as the porosity increase^.^^^^^^^ A more porous columnar structure indicates the thickness of Si may approach that of the multiply linked polysilanes. Thus, through extended etching, a series of single SGH6 sheets could be prepared, with n depending on the etching time and conditions. Since n = 1 is the limiting value, this suggests a terminal material, Si6H6 sheet, with a maximum band gap. In numerous attempts to
J. Phys. Chem., Vol. 99,No. 7, 1995 1899
Electronic Structures of Layered Polysilanes prepare p-Si with large band gap, only a maximum gap of 3.1 eV could be achieved?g in agreement with this hypothesis. In summary, we believe that the linked polysilane sheet compounds, Si6,&, possess interesting optical properties and may be related to p-Si. The limiting member in this series, S i & j , and multiply linked layered polysilane are indeed very similar to the hydrolyzed form commonly called siloxene.
Acknowledgment. We thank Drs. T. Tiedje, T. Van Buuren, and D. D. H u g for many useful discussions. References and Notes (1) Canham, L. T. Appl. Phys. Lett. 1987, 51, 1509. (2) Cullis, A. G.; Canham, L. T. Nature 1991, 353, 335. (3) Brandt, M. S.; Fuchs, H. D.; Stutzmann, M.; Weber, J.; Cardona, M. Solid State Commun. 1992, 81, 307. (4) Stutzmann, M.; Brandt, M. S.; Rosenbauer, M.; Weber, J.; Fuchs, H. D. Phys. Rev. 1993, 847,4806. (5) Stutzmann, M.; Weber, J.; Brandt, M. S.; Fuchs, H. D.; Rosenbauer, M.; Deak, P. D.; Hopner, A.; Breitschwerdt, A. Adv. Solid State Phys. 1992, 32, 179; Fuchs, H. D.; Stutzmann, M.; Brandt, M. S.; Rosenbauer, M.; Weber, J.; Breitschwerdt, A.; De&, P. Cardona, M. Phys. Rev. 1993,848, 8172. (6) McCord, P.; Yau, S.-L.; Bard, A. J. Science 1992, 257, 68. (7) Read, A. J.; Needs, R. J.; Nash, K. J.; Canham, L. T.; Callcott, P. D. J.; Qteish, A. Phys. Rev. Lett. 1992, 69, 1232. (8) Buda, F.; Kohanoff, J.; Paninello, M. Phys. Rev. Lett., 1992, 69, 1272. (9) Van de Walle, C. G.; Northrup, J. E. Phys. Rev. Lett. 1993, 70, 1116. (10) Deak, P.; Rosenbauer, M.; Stutzmann, W.; Weber, J.; Brandt, M. S.Phys. Rev. Lett. 1992, 69, 2531.
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