Temperature dependence of the band gap of semiconducting carbon nanotubes.

The temperature dependence of the band gap of semiconducting single-wall carbon nanotubes (SWNTs) is calculated by direct evaluation of electron-phonon couplings within a "frozen-phonon" scheme. An interesting diameter and chirality dependence of E(g)(T) is obtained, including nonmonotonic behavior for certain tubes and distinct "family" behavior. These results are traced to a strong and complex coupling between band-edge states and the lowest-energy optical phonon modes in SWNTs. The E(g)(T) curves are modeled by an analytic function with diameter- and chirality-dependent parameters; these provide a valuable guide for systematic estimates of E(g)(T) for any given SWNT. The magnitudes of the temperature shifts at 300 K are smaller than 12 meV and should not affect (n,m) assignments based on optical measurements.

[1]  J. Lefebvre,et al.  Bright band gap photoluminescence from unprocessed single-walled carbon nanotubes. , 2003, Physical review letters.

[2]  P. Keblinski,et al.  Thermal expansion of carbon structures , 2003 .

[3]  S. Iijima.  Helical microtubules of graphitic carbon , 1991, Nature.

[4]  S. Louie,et al.  Excitonic effects and optical spectra of single-walled carbon nanotubes. , 2003, Physical review letters.

[5]  E. Antončík.  On the theory of temperature shift of the absorption curve in non-polar crystals , 1955 .

[6]  H. J. Liu,et al.  Polarized absorption spectra of single-walled 4 A carbon nanotubes aligned in channels of an AlPO(4)-5 single crystal. , 2001, Physical review letters.

[7]  Manuel Cardona,et al.  Theory of the temperature dependence of the direct gap of germanium , 1981 .

[8]  D. Tománek,et al.  Thermal contraction of carbon fullerenes and nanotubes. , 2004, Physical review letters.

[9]  Charles M. Lieber,et al.  Structural ( n, m) determination of isolated single-wall carbon nanotubes by resonant Raman scattering. , 2001, Physical review letters.

[10]  Sawada,et al.  New one-dimensional conductors: Graphitic microtubules. , 1992, Physical review letters.

[11]  O. Madelung.  Semiconductors : group IV elements and III-V compounds , 1991 .

[12]  Ray H. Baughman,et al.  Mechanical and electromechanical coupling in carbon nanotube distortions , 2003 .

[13]  Riichiro Saito,et al.  Trigonal warping effect of carbon nanotubes , 2000 .

[14]  H. Y. Fan.  Temperature Dependence of the Energy Gap in Semiconductors , 1951 .

[15]  R. Smalley,et al.  Structure-Assigned Optical Spectra of Single-Walled Carbon Nanotubes , 2002, Science.

[16]  S. Okada,et al.  Electronic Structure of C78 and C78-Graphite Cointercalation Compound. , 1995 .

[17]  V. C. Moore,et al.  Band Gap Fluorescence from Individual Single-Walled Carbon Nanotubes , 2002, Science.

[18]  L. Novotný,et al.  Simultaneous Fluorescence and Raman Scattering from Single Carbon Nanotubes , 2003, Science.

[19]  Stergios Logothetidis,et al.  Temperature dependence of the dielectric function of germanium , 1984 .

[20]  S. Reich,et al.  Chirality dependence of the density-of-states singularities in carbon nanotubes , 2000 .

[21]  Philip B. Allen,et al.  Theory of the temperature dependence of electronic band structures , 1976 .

[22]  Manuel Cardona,et al.  Temperature dependence of the direct gap of Si and Ge , 1983 .

[23]  Linda S. Schadler,et al.  Temperature dependence of radial breathing mode Raman frequency of single-walled carbon nanotubes , 2002 .

[24]  J. Lefebvre,et al.  Temperature-dependent photoluminescence from single-walled carbon nanotubes , 2004 .

[25]  P. Lam,et al.  Ab initio calculation of phonon frequencies of Al , 1982 .

[26]  M. Thewalt,et al.  Temperature dependence of the energy gap of semiconductors in the low-temperature limit. , 2004, Physical Review Letters.

[27]  H. Y. Fan,et al.  Optical Properties of Semiconductors. III. Infra-Red Transmission of Silicon , 1949 .

[28]  Donald W. Brenner,et al.  A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons , 2002 .

[29]  R. Pässler.  Semi‐empirical descriptions of temperature dependences of band gaps in semiconductors , 2003 .