http://orcid.org/0000-0001-8089-9869
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ABSTRACT
The thermal conductance of isotopic-superlattice graphene nanoribbons randomly mixed with isotope defects is investigated by atomistic Green’s function method. The isotopic-superlattice structure reduces the thermal conductance, which changes non-monotonically as the superlattice period length decreases, and there exists a minimum thermal conductance at the critical period length. About 20% defects just further increase the reduction and shorten the critical period length. As the defect concentration in superlattice increases, the thermal conductance decreases monotonically in the zigzag nanoribbon, but in armchair nanoribbon the thermal conductance first decreases to its minimum value and then increases. The isotopic doping effect is particularly evident for large isotope mass, in armchair nanoribbons and for out-of-plane phonon modes. Isotope defects lead to additional phonon scattering in the superlattice structure, which is explained by analyzing the phonon transmittance.
Nomenclature
| a | = | bond length |
| f | = | Planck distribution |
| G | = | Green’s function matrix |
| I | = | identity matrix |
| i | = | unit of imaginary number |
| KS | = | harmonic matrix of scattering region |
| L | = | superlattice period length |
| LC | = | critical superlattice period length |
| Na | = | number of dimer lines |
| Nz | = | number of zigzag lines |
| n | = | number of isotope defects in one superlattice layer |
| n0 | = | number of atoms in one superlattice layer |
| T | = | temperature |
| 0+ | = | broadening constant, which is a positive infinitesimal number |
| = | broadening function, defined in Eq. (4) | |
| γ | = | thermal conductance ratio defined in Eq. (6) |
| η | = | defect concentration defined in Eq. (1) |
| Σ | = | self-energy matrix |
| σ | = | thermal conductance defined in Eq. (5) |
| σIS | = | thermal conductance of isotopic-superlattice |
| σ12 | = | thermal conductance of pristine 12C graphene nanoribbon |
| τ | = | phonon transmittance defined in Eq. (3) |
| ω | = | angular frequency of phonons |
| ℏ | = | reduced Planck constant |
| = | Subscripts | |
| I | = | in-plane modes |
| IS | = | isotopic-superlattice |
| LT | = | left terminal |
| O | = | out-of-plane modes |
| RT | = | right terminal |
| S | = | scattering region |
| = | Superscripts | |
| A | = | armchair edge type |
| Z | = | zigzag edge type |
| * | = | conjugate transpose of a matrix |
Nomenclature
| a | = | bond length |
| f | = | Planck distribution |
| G | = | Green’s function matrix |
| I | = | identity matrix |
| i | = | unit of imaginary number |
| KS | = | harmonic matrix of scattering region |
| L | = | superlattice period length |
| LC | = | critical superlattice period length |
| Na | = | number of dimer lines |
| Nz | = | number of zigzag lines |
| n | = | number of isotope defects in one superlattice layer |
| n0 | = | number of atoms in one superlattice layer |
| T | = | temperature |
| 0+ | = | broadening constant, which is a positive infinitesimal number |
| = | broadening function, defined in Eq. (4) | |
| γ | = | thermal conductance ratio defined in Eq. (6) |
| η | = | defect concentration defined in Eq. (1) |
| Σ | = | self-energy matrix |
| σ | = | thermal conductance defined in Eq. (5) |
| σIS | = | thermal conductance of isotopic-superlattice |
| σ12 | = | thermal conductance of pristine 12C graphene nanoribbon |
| τ | = | phonon transmittance defined in Eq. (3) |
| ω | = | angular frequency of phonons |
| ℏ | = | reduced Planck constant |
| = | Subscripts | |
| I | = | in-plane modes |
| IS | = | isotopic-superlattice |
| LT | = | left terminal |
| O | = | out-of-plane modes |
| RT | = | right terminal |
| S | = | scattering region |
| = | Superscripts | |
| A | = | armchair edge type |
| Z | = | zigzag edge type |
| * | = | conjugate transpose of a matrix |