Polysilanes band structure

Figure 7. Schematic view of polysilane band structure. The abbreviations and symbols are defined as follows me, effective mass of electrons mh effective mass of holes lumi., luminescence abs., absorption T, k = 0 point and k,...

As the number of silicon atoms in the delocalized backbone cr-electron system increases, the number of HOMO and LUMO states increases, resulting in a band structure for high molecular weight polymers. Electronic absorptions from the HOMO (cr) to LUMO (essentially a ) are responsible for the characteristic UV absorption of polysilanes observed between 300 and 400 nm, the transition moment for which is in the direction of the Si chain.198 Polysilanes are... 

FIGURE 5. Band structure correlation for linear peralkylated polysilanes (a) (He I) PE spectra of hexamethyldisilane and octamethyltrisilane, (b) ab initio calculated band-structure dispersion (DIS) and (c) state density (DOS) for poly-dimethylsilane R(SiR2)R32... 

The next question is how side-chain substitutions and skeleton conformations affect the band structures of polysilanes. Side chains provide two interesting effects (7) band gap reduction caused by substitution of larger alkyl side chains and skeleton-side chain interaction (i.e., (j-tt mixing) in aryl poly silanes. This interaction was confirmed by UV photo spectroscopy (UPS) (8-9) and photoabsorption and luminescence measurements (iO, 11). Skeleton conformations are related to thermochromism (12-17). The ab initio... 

Substitution of aryl side chains results in a different band structure. A perspective end view of poly(diphenylsilane) is shown in Figure 11a. Electrons conduct along the red region under the influence of a potential barrier of phenyl groups. This electrical analogue of an optical fiber consists of an electrical core and an electrical clad. A perspective end view of poly-(methylphenylsilane) is shown in Figure 11b. In these aryl polysilanes, two important points should be considered the existence of states localized at phenyl side chains and the a-7T interaction between delocalized skeleton ct bands and localized tt states. 

Figure 9. Calculated band structures of parent and alkyl-side-chain-substituted polysilanes. The abbreviations and symbols are defined as follows CB, conduction band VB, valence band F, k = 0 point and X, Brillouin zone edge. Bsu, Bu, B2g, Bg, and Ag denote orbital symmetries.

EflFect of Conformation on Band Structure. The trans and gauche parent polysilanes are shown in Figure 15. Thermochromism is one of the most controversial subjects in polysilanes. However, the following basic questions have not been answered yet Which conformation is more stable, trans or gauche What is the essential difference in their band structures ... 

Band Structure and Optical Absorption Properties of Polysilane Chains... 

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. 

Figure 31 Band structures for polysilanes, polygermanes, and polystannanes (top, frans-planar conformation below, gauche-helical conformation). (Adapted with permission of Elsevier Ltd. from Takeda, K. and Shikaishi K., Chem. Phys. Lett 1992,195,121.)...

Band structure calculations have also been reported for hypothetical polystannanes 6.4 (R=R =H), and the results have been compared with those for analogous polysilanes and polygermanes [15]. The band gap (Eg) was calculated to decrease in the... 

Fig. 6.5 Band structures for polysilanes (PSi), polygermanes (PGe), and polystannanes (PSn) (top, trans-planar conformation below, gaucfie-helical conformation). (Adapted from [15])...

Theoretical predictions of the optical properties of polysilanes have been recently published. From his LDA band structure calculations, Mintmire has calculated the extinction coefficient expected for various orientations of planar-zigzag poly(di-methylsilane) [14]. His results for a randomly oriented film are shown in figure 4, along with the extinction coefficient for poly(di-n-hexylsilane) from our experiment. With the assignment of the one-dimensional direct gap of the band structure calculation to the second UV absorption peak at 3.91 eV, the band structure calculations predict both the... 

Figure 1. Summery of calculated results on the band structures of polysilanes. a and a means valence and conduction band formed by a-conjugation along a chain, respectively.

Trans to Gauche, Helical angle dependence of the band structures of parent polysilanes was calculated by the ab initio crystal orbital method . When the screw axis is taken to be coincident with the Cartesian z axis, the pxi and pyJ basis functimis belonging to the j i cell from the reference cell can be obtained by the relationships of the Cartesian Px-) and pyj orbitals... 

Figure 2. Calculated band structures of trans and gauche parent polysilane. ...

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