Copolymers as one-dimensional superlattices

Current research focuses mainly on polymers with band gaps smaller than our forecasts for BN polymers. However, it is desirable to have polymers with band gaps spanning the whole spectral range, from infrared to ultraviolet, thus expanding the possibilities for nanotechnology applications. By combining carbon and BN monomers in the same chain, one-dimensional superlattices or copolymers can be created. By analogy with conventional semiconductor superlattices and quantum wells, we expect to be able to tune the gap by varying the lengths of the BN and carbon segments. Copolymers derived from borazine and silazane have been successfully synthesized [52] as precursors to SiNCB ceramics. Our study focuses on the electronic properties of carbon and BN copolymers, and allows us to investigate the performance of polymers made up of a mixture of organic and inorganic monomers. Indeed, it is also possible to tune the band gaps using conjugated oligomers of different lengths [53] or polymers where the conjugation is broken by adding different components. The systems we propose here are characterized by essentially the same polymer structure over their entire length. Given the difference in band gap between the carbon and BN systems, the range of band gap tuning will be fairly large, thus covering a large region of the spectrum and being of interest for a wide range of applications.

Figure 6: Band gaps for copolymers with different numbers of BN monomers between the carbon regions and for carbon oligomers.

The variation of the band gap is shown in Fig. 6, where the calculated energy gaps for copolymers of PPP and PBZ are shown as a function of the number of PPP monomers. There are three sets of data differing in the number of BN monomers in between the carbon regions, and one set of data for the carbon oligomers. As expected, all the energy gaps of these copolymers lie in between the pure PPP and PBZ values (1.81 and 4.66 eV respectively, if calculated within DFT-LDA). Although these results suffer from the LDA-DFT underestimation of the band gap and the neglection of the electron-hole interaction, they clearly show a tuning trend.

Figure 7: LUMO (top) and HOMO (bottom) wavefunctions for the 3-1 copolymer.

Figure 8: LUMO (top) and HOMO (bottom) wavefunctions for the 3-2 copolymer.

Fig. 7 shows the HOMO and LUMO states for the 3-1 copolymer, i.e. made of three monomers of carbon separated by one monomer of BN. Fig. 8 shows the same states but for the case of the 3-2 copolymer. Because of the large difference in the BN and C gaps, we expect that the HOMO and LUMO states should be confined mainly within the carbon segment. Of course, the larger the BN segments are, the more definite the confinement is and the less tunnelling which occurs. This is evident for the structures shown: in the case of the 3-1 copolymer, there is significant spilling of the otherwise confined wavefunctions into the BN segment, resulting in a continuous wavefunction along the entire copolymer. When the length of the BN segment becomes significant, the band gap essentially depends on the length of the carbon segments. The characters of the HOMO and LUMO states in these copolymers, except for the confinement, are essentially the same as the ones shown for the PPP polymer in Fig. 4. The energy cost for the formation of the copolymers was calculated to be about 1 eV per unit cell, independent of the carbon polymer length. This suggests that the dominant cost is related to the formation of the C-B and C-N bonds at the interfaces between segments of the different copolymers. Since the BN monomer lacks inversion symmetry, the two interfaces that each BN region makes in a copolymer are different, being either a C-N or a B-C bond. This results in a different charge distribution at the two interfaces. In Fig. 8, the HOMO state resides mostly in the carbon region, but is weighted towards the end bonded to the nitrogen atom with significant weight on the nitrogen itself. On the other hand, the LUMO state is weighted towards the opposite end of the region close to the boron atom.

Figure 9: LUMO (top), HOMO (center) and HOMO-1 (bottom) wavefunctions for the 2-1 copolymer with opposite orientation of the BN monomers.

By alternating the orientation of consecutive BN regions, thus doubling the unit cell, it is possible to create inequivalent carbon regions, one terminated by a boron atom at each end and the other by nitrogen atoms. Fig. 9 shows such model for the 2-1 copolymer. For this arrangement, all wavefunctions are completely symmetric with respect to the center of the carbon region as expected. The last two occupied states (HOMO and HOMO-1) have wavefunctions with essentially the same character, similar to the HOMO of PPP, but localized in the two inequivalent carbon regions. The HOMO-1 (with energy -1.2 eV) is localized in the carbon region interfaced by the boron atoms, whereas the HOMO (0 eV) is localized in the carbon region interfaced by nitrogen atoms. An interesting fact is that the HOMO and LUMO states are confined within different carbon regions as shown in Fig. 9. This will certainly affect the excited state behaviour, since there is practically no overlap between the electrons and the holes which make the exciton state. The energy gap of 2.0 eV for this 2-1 copolymer is significantly smaller that band gap (2.6 eV) for the 2-1 copolymer with BN region oriented in the same direction, which we report in Fig. 6. Following a similar idea, DFT calculations have recently been performed to investigate the properties of BN/C nanotube superlattices, which could be used for band-offset nanodevice engineering, polarization-based devices and robust field emitters [54].