Band structure unsubstituted polysilane

An LCAO (linear combination of atomic orbitals) local-density functional 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 411 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-substituted polysilane chain suggest that the states immediately surrounding the Fermi level retain their silicon-backbone a character upon alkyl-group substitution, although the band gap decreases by I eV because of contributions from alkyl substituent states both below the valence band and above the conduction band to the frontier states. 

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 all-trans 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 dl -trans conformation with the results for the unsubstituted poly silane. 

Figures 1 and 2 depict our calculated band structures for the all- rans conformations of unsubstituted polysilane and poly(dimethylsilane). Because the reflection plane containing the silicon nuclei in the all- rans conformations commutes with the operations of the one-dimensional translation group, all one-electron wave functions will be either symmetric (a-like) or antisymmetric (7T-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 a-like or 7T-like, respectively.

Figure 1. Band structure for all-trans conformation of unsubstituted polysilane calculated by using the LCAO-LDF method, cr-like bands are denoted with solid lines, u-like bands are denoted with dashed lines. The Fermi level is denoted as f. k represents the wave vector, and a is the length of the unit cell.

The local-density functional approach was used to compare the band structures of the sW-trans conformation of unsubstituted polysilane with a 4/1 helical conformation and with an dll-trans conformation of dimethyl-substituted poly silane. In line with previous theoretical studies, the electronic wave functions in the vicinity of the Fermi level are primarily silicon-back-bone states, with the major effect of methyl substitution being a decrease in the gap. The predicted absorption spectra for the dll-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 dll-trans conformation and the dll-gauche model will also occur in alkyl-substituted systems, which are currently under investigation. 

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