Atomic basis sets for first-principle studies of Si nanowires Dimpy Sharma, Hadi Hassanian Arefi, Lida Ansari, Giorgos Fagas Electronics Theory group Tyndall National Institute, University College Cork
Outline Motivation - Experimental - Links to atomic-scale simulations Background - DFT Methodology - Previous studies Workplan - Electronic structure - Transport properties Concluding remarks
Motivation Silicon Nanowires (SiNW): promising nanomaterials for a wide range of applications Nanowire-FET(MOSFET, FinFET) Electrostatic control Nano Lett., 2011, 11 (12), p. 5465 Sensors Selectivity and sensitivity Photovoltaic Improved absorption of light IEEE Trans. Nanotech. 2011, 10 (6), p.
Why atomic-scale simulations? Experimental results on Si nanowire devices are becoming increasingly available BUT challenging, time consuming and expensive Atomic-scale modelling and simulations can provide design guidelines and be used for optimisation Current methods offer the possibility of developing such a methodology with acceptable accuracy and reasonable computational cost
Background: DFT Methodology Aim: Electronic and electrical properties of small-diameter oxidised SiNWs use a first-principles method (Density Functional Theory) Common DFT implementations use plane wave or atomic basis sets Plane waves (PW): - extremely accurate but computationally expensive - very cumbersome (and prohibitively expensive) to apply in transport studies! Numerical atomic orbitals (NAOs): very efficient but less accurate their performance needs to be tested their transferability between different systems has to be checked
Previous studies: benchmarking atomic orbitals for transport M. Strange et al. [J. Chem. Phys. 128, 114714 (2008)] studied f ive representative single-molecule junctions convergence of NAO-basis set with Wannier (from PW) basis calculations J. A. Driscoll and K. Varga [Phys. Rev. B 81, 115412 (2010)] studied two similar junctions transmission most sensitive to self-consistent potential (i.e., electron density)
Investigated structures Ideal periodic NWs Hydogenated SiNWs (SiNW:H) W=1.15nm Hydroxylated SiNWs (SiNW:OH) Ga-doped SiNWs
Total energy calculations Use of a minimal basis set for Si (SZ, DZ, TZ) yields a stretched Si-H bond with length 1.68Å, much longer than the typical Si-H bond length Optimised orbitals proved to be computationally efficient compared to higher contractions
Band gap benchmarking If d-orbitals are not included the band gap is indirect which disagrees with our plane wave results and zone-folding arguments (recall, stretched Si-H bond) The s,p,d set on Si yields reasonable band structure both for valence and conduction bands
Benchmarking of numerical atomic orbitals Conduction Plane waves: red solid lines Valence NAOs: purple dotted lines (double-zeta polarized) black dashed lines (optimized double-zeta polarized)
Transferability of NAOs [100] [111] orientation Conduction Valence Bands of [100]-oriented SiNW:H calculated using optimised orbitals from [100]-oriented SiNW: H (black solid lines) and using optimised orbitals from [110]-oriented SiNW:H (red dashed lines). applied also in SiNW:OH Optimised NAOs are transferable
Similar observations for SiNW:OH and Ga doped SiNW SiNW:OH Valence
Similar observations for SiNW:OH and Ga doped SiNW Ga doped SiNW Total energy
Sub-bands analysis: 1 st valence band effective mass group velocity
Sub-bands analysis: 1 st conduction band effective mass group velocity
Sub-bands analysis NAOs with respect to PW: - overestimate effective mass - underestimate group velocity Conductivity Mean free path
Transport studies Systems investigated SiNWs with impurities locally oxidised Highly-doped Ga Computational method Use optimised structures with OpenMX code and extract Hamiltonian in specified basis set Input Hamiltonian to TIMES simulator and calculate transmission of charge carriers
transmission Transport results on SiNW Scattering due to impurities
Mean Free Path Valence l imp =(G s /G c )*d Gc: ideal conductance Gs: conductance due to scattering from a single defect d: mean distance between impurities Confirms that mean free path estimates from various basis sets do not vary significantly
Concluding Remarks Optimised double zeta polarised basis set offers results with good compromise between accuracy and efficiency Inclusion of d-polarization functions is crucial for correct results Transferable optimised NAOs can be used in realistic device simulations Conductivity is more sensitive to the basis sets than mean-free-path
Acknowledgement Supervisor Dr. Giorgos Fagas Computational resources ICHEC (Irish Centre for High-End Computing Science Foundation Ireland.