Band Structure and Optical Absorption Properties of Polysilane Chains

29 Band Structure and Optical Absorption Properties of Polysilane Chains Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0224.ch029

J. W. Mintmire1 and J. V. Ortiz2 Chemistry Division, Naval Research Laboratory, Washington, DC 20375 Department of Chemistry, University of New Mexico, Albuquerque, NM 87131

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An LCAO (linear combination of atomic orbitals) local-density func tional approach was used to calculate the band structures of a series of polymer chain conformations: unsubstituted polysilane in the all -trans conformation and in a 4/1 helical conformation, and all-trans poly(dimethylsilane). Calculated absorption spectra predict a highly anisotropic absorption for the all-trans conformation of polysilane, with the threshold absorption peak arising strictly from polarizations parallel to the chain axis. The absorption spectrum for the helical conformation is much more isotropic. Results for the dimethyl-sub stituted polysilane chain suggest that the states immediately sur rounding the Fermi level retain their silicon-backbone σ character upon alkyl-group substitution, although the band gap decreases by ~1 eV because of contributions from alkyl substituent states both below the valence band and above the conduction band to the frontier states.

^EXPERIMENTAL AND THEORETC IAL

interest in organosilane polymer sys tems (I) has increased in recent years largely because of the potential tech nological applications of these materials as silicon carbide precursors, as photoresists in photolithography, as photoinitiators in radical-assisted polymerization, and as photoconductors in photocopying processes. Many of the technological applications for the organosilane polymers depend in timately on the electronic structure and resulting optical properties of these materials. The absorption threshold in the ultraviolet (UV) of a range of substituted polysilanes decreases in energy with both increasing molecular 0065-2393/90/0224-0543$06.00/0 © 1990 American Chemical Society

Zeigler and Fearon; Silicon-Based Polymer Science Advances in Chemistry; American Chemical Society: Washington, DC, 1989.

Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0224.ch029

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SILICON-BASED POLYMER SCIENCE: A COMPREHENSIVE RESOURCE

weight and increasing substituent size (2, 3). The absorption and emission spectra suggest that photoexcitation may produce a localized triplet-defect state that leads to silicon-silicon bond scission and silylene production (3, 4). Several dialkyl-substituted polysilanes, in particular poly(di-n-hexylsilane), exhibit a red shift of the absorption peak of up to 40 nm (corresponding to an energy shift of 0.4-0.5 eV) and a concomitant narrowing of the absorption line shape with decreasing temperature (5-8). These bathochromic shifts have been attributed to an order-disorder transition of the silicon backbone from a highly ordered system with nearly all-trans (or planar zigzag) conformations of the backbone to a disordered system with an entropie mix of trans and gauche conformers along the silicon backbone. A variety of theoretical methods (9-17) have been used to investigate the electronic structure of both polymeric chain systems (9-12) and model molecular species (13-17). Theoretical studies of the polymeric chains have consisted of semiempirical calculations of the band structure and of the effects of substituents and conformation on the band structure (10-12) and ab initio calculations of the electronic structure and minimum energy conformations of the unsubstituted polysilane chain (9). As part of a broader theoretical study of the electronic structure and properties of organopolysilanes, we have begun a study of these systems by using our previously developed linear-combination-of-atomic-orbitals local-density functional (LCAO-LDF) method for chain polymers (18, 19). This method calculates both the band structure and total energy of a polymer chain possessing translational periodicity in one dimension; an equilibrium geometry can thus be obtained by a search for the minimum energy conformation. Absorption spectra can be estimated from interband transition cross-sections evaluated by using the one-electron wave functions and energy levels.

Experimental Procedures In this study, we investigated a set of model polysilane chain systems that illustrate the basic physics and chemistry of some optical properties of these materials. In particular, we looked at the band structure for unsubstituted polysilane in an alltrans conformation, as well as in a 4/1 helical conformation with four silicon atoms contained in one translational repeat unit. In addition, we compared results for the dimethyl-substituted polysilane in an all-trans conformation with the results for the unsubstituted polysilane. The bond lengths and band angles for these calculations were chosenfromab initio Hartree-Fock geometric optimizations for tetrasilane and other model molecular systems (17). The bond lengths used were 2.35 Â for the Si-Si bonds, 1.48 Â for the Si-Η bonds, 1.89 Â for the Si-C bonds, and 1.08 Â for the C-H bonds. The Si-Si-Si bond angle was chosen to be 111.6°, the same as that obtained in our earlier geometric optimization of tetrasilane. For consistency with the tetrasilane results, the H-Si-H bond angle was chosen to be 108°, and the C-Si-C bond angle was also set to this value. All bond angles centered on the carbon nuclei were set to tetrahedral bond angles of 109.47°, with the hydrogens staggered relative to the bonds on the nearest silicon. The version of the LCAO-LDF method we used re-


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Band Structure and Optical Absorption Properties

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quired translational symmetry; therefore the Si-Si-Si-Si dihedral angle for the hel ical conformation was set to 62.56° to generate a translational unit cell containing four silicons while being close to an all-gauche backbone conformation. These cal culations were performed with a moderate-size orbital basis set: 10s 6p Id for silicon, Is 3p for carbon, and 3s for hydrogen.


Results and Discussion Figures 1 and 2 depict our calculated band structures for the all-trans con formations of unsubstituted polysilane and poly(dimethylsilane). Because the reflection plane containing the silicon nuclei in the all-trans conformations commutes with the operations of the one-dimensional translation group, all one-electron wave functions will be either symmetric (σ-like) or antisym metric (ττ-like) with respect to this reflection operation. Thus the bands in Figures 1 and 2 are labeled with solid lines or dashed lines, which indicate that the corresponding one-electron wave functions are σ-like or ττ-like, respectively. As noted by other workers (II), the highest occupied band (valence 5

,

,

,

r

k value ( π / a ) Figure 1. Band structure for all-tram conformation of unsubstituted polysilane calculated by using the LCAO-LDF method, σ-like bands are denoted with solid lines, ττ-like bands are denoted with dashed lines. The Fermi level is de noted as € F . k represents the wave vector, and a is the length of the unit cell.



546


>

0.0

0.2

0.4

0.6

k value ( π / a ) Figure 2. Band structure for all-trans conformation of poly(dimethylsilane) calculated by using the LCAO-LDF method, σ-like bands are denoted with solid lines, ir-like bands are denoted with dashed lines. The Fermi level is de noted as €F- k represents the wave vector, and a is the length of the unit cell.

band) and the lowest unoccupied band (conduction band) are predominantly silicon-backbone bonding and antibonding states, respectively. Indeed, the highest state in the valence band at the edge of the Brillouin zone is a σlike state that is antisymmetric with respect to the reflection planes per pendicular to the chain axis containing the silicon nuclei. This state is thus not only predominantly composed of a bonding combination of silicon p states (where the chain axis defines the ζ axis) but also has a small contribution from symmetric combinations of the carbon p orbitals in the dimethylsubstituted system. The lowest state in the conduction band, also at the edge of the Brillouin zone, is a σ-like state symmetric with respect to the reflection plane normal to the chain axis and is predominantly a siliconbackbone antibonding state that is slightly bonding to almost nonbonding with respect to the substituents. The band gap decreases on going from the unsubstituted polysilane to the dimethyl-substituted polysilane from 3.52 to 2.64 eV, in line with pre vious semiempirical studies (11, 12). Local-density functional methods typ ically underestimate the band gap in insulators and semiconductors by 30-50% (20). For poly(dimethylsilane), with an experimentally indicated gap z

z



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of 4.22 eV (21), that underestimation is 37%. Most of the decrease in gap on methyl substitution is attributable to an upward shift of the valence band edge, which is largely caused by mixing with lower lying bands, C - H bond ing bands introduced from the methyl substituent. These states can be seen lying in the vicinity of -10 eV in Figure 2. Other than this shift in gap, no major changes occur in states immediately about the Fermi level in the valence and conduction bands of the polysilanes; the frontier states re main largely silicon-backbone bonding states immediately below the Fermi level and largely silicon-backbone antibonding states immediately above the Fermi level. Our calculations using a smaller basis set for the dimethyl-, diethyl-, and dipropyl-substituted polysilanes also indicate the same behavior. This similarity of states immediately around the Fermi level manifests itself in the similarity of predicted extinction coefficients for polysilane and dimethyl-substituted polysilane (Figure 3). The optical conductivity σ/ω) is directly calculated for the three polarization directions by using oscillator strengths calculated for direct interband transitions and by neglecting localfield effects (18). This approach yields excellent results for ττ-conjugated polymers such as polyacetylene. The three curves in each diagram for the all-trans conformations correspond to the polarization parallel to the chain axis (solid lines), the polarization perpendicular to the plane of the siliconbackbone nuclei (dash-dotted lines), and the polarization in the plane of the silicon backbone (dashed lines); for the helical conformation, of course, the results for the two perpendicular polarizations are equivalent to within the numerical accuracy of our evaluation procedure. The extinction coefficient used in Figure 3 is thus a measure of the optical conductivity and is actually OjO/c, in which σ is the calculated optical conductivity, Ω is the volume per silicon nucleus, and c is the speed of light in vacuum. Although the absolute magnitudes of the predicted extinction coefficients are not in par ticularly good agreement with experimental results, this approach allows us to analyze the expected line shape and to compare differences between similar polymeric systems. The dominant low-energy feature of the absorption spectra for the alltrans conformations is the strong absorption peak for polarizations parallel to the chain (Figure 3). This peak arises from the excitation between the top of the valence band and the bottom of the conduction band. Because these two states differ in parity with respect to the reflection planes per pendicular to the chain axis and containing the silicon nuclei, large on-site matrix elements occur for the interband transition oscillator strengths for polarizations parallel to the chain axis and lead to a strong absorption peak. This strong threshold absorption for polarizations parallel to the chain axis is similar to that observed in ττ-conjugated polymers, but the large on-site matrix elements should lead to extinction coefficients larger than that ob served in the ττ-conjugated systems, which have no contribution from onsite terms in the threshold absorption. ί

American Chemical Society Library

Zeigler and Fearon; 1155Silicon-Based 16th St., Polymer N.W. Science Advances in Chemistry; American ChemicalDC Society: Washington, DC, 1989. Washington, 20036



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Figure 3. Calculated absorption spectra for all-trans unsubstituted polysilane (a), all-trans poly(dimethylsilane) (b), and helical unsubstituted polysilane (c). Solid lines denote absorption for polarizations parallel to chain axis, dashedand-dotted lines denote absorption for polarizations perpendicular to the plane of the silicon backbone (for the all-trans conformations), and dashed lines denote the remaining polarization. All curves have been broadened with a 0.7eV full width at half-maximum Gaussian.



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This dominant feature is essentially the same for both the unsubstituted and dimethyl-substituted all-trans polysilane chains, and an equivalent feature is found when a smaller basis set is used for the dimethyl-, diethyl-, and dipropyl-substituted polysilanes. For the helical conformation, however, along with the larger band gap in this conformation (Figure 3c), a pronounced shift of the direct-gap absorption peak to higher energy is observed, with a trend toward a less anisotropic absorption. These results support current interpretations of the bathochromic shifts observed in dialkyl-substituted polysilane. Experimental results for poly(din-hexylsilane) indicate that as the temperature is cooled below a transition temperature of roughly -35 °C, the major absorption peak shifts from a broad peak at about 310-320 nm (3.9-4.0 eV) to a narrower peak at about 350-370 nm (3.3-3.5 eV), with the red shift being attributed to a transition from a disordered system with a large population of gauche bond twists in the silicon backbone and in the alkyl substituent to a planar all-trans backbone conformation (5-8, 15). Results from polarized absorption spectra of stretchoriented samples for the cooled samples exhibit absorbance only for polarizations parallel to the stretch (and presumably the chain axis) direction (22).

Summary The local-density functional approach was used to compare the band structures of the all-trans conformation of unsubstituted polysilane with a 4/1 helical conformation and with an all-trans conformation of dimethyl-substituted polysilane. In line with previous theoretical studies, the electronic wave functions in the vicinity of the Fermi level are primarily silicon-backbone states, with the major effect of methyl substitution being a decrease in the gap. The predicted absorption spectra for the all-trans conformations of unsubstituted and dimethyl-substituted polysilane are similar for nearthreshold absorption. Given this similarity, we believe that the shift in energy and strong anisotropy of threshold absorption that we predict for the two extremes of the all-trans conformation and the all-gauche model will also occur in alkyl-substituted systems, which are currently under investigation.

Acknowledgments We thank J. Zeigler and G. Fearon for their part in organizing the workshop on which this volume is based. J. V. O. acknowledges partial support of this work, which was performed during the summer of 1987 under the auspices of the American Society for Engineering Education Summer Faculty Program at the Naval Research Laboratory.



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19. Mintmire, J. W.; White, C . T. Phys. Rev. B: Condens. Matter 1983, 27, 1447. 20. Trickey, S. B.; Ray, A. K. ; Worth, J. P. Phys. Status Solidi Β 1981, 106, 631.

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RECEIVED for review May 27, 1988. ACCEPTED revised manuscript November 16, 1988.


Band Structure and Optical Absorption Properties of Polysilane Chains

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