Si Tight-Binding Parameters from Genetic Algorithm Fitting

Abstract Quantum mechanical simulations of carrier transport in Si require an accurate model of the complicated Si bandstructure. Tight-binding models are an attractive method of choice since they bear the full electronic structure symmetry within them and can discretize a realistic device on an atomic scale. However, tight-binding models are not simple to parameterize and characterize. This work addresses two issues: (1) the need for an automated fitting procedure that maps tight-binding orbital interaction energies to physical observables such as effective masses and band edges, and (2) the capabilities and accuracy of the nearest and second-nearest neighbor tight-binding sp3s* models with respect to carrier transport in indirect bandgap materials. A genetic algorithm approach is used to fit orbital interaction energies of these tight-binding models in a nine- and 20-dimensional global optimization problem for Si. A second-nearest neighbor sp3s* parameter set that fits all relevant conduction and valence band properties with a high degree of accuracy is presented. No such global fit was found for the nearest neighbor sp3s* model and two sets, one heavily weighed for electron properties and the other for hole properties, are presented. Bandstructure properties relevant for electron and hole transport in Si derived from these three sets are compared with the seminal Vogl et al. [Journal of the Physics and Chemistry of Solids 44, 365 (1983)] parameters.

[1]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[2]  Yia-Chung Chang,et al.  Complex band structures of crystalline solids: An eigenvalue method , 1982 .

[3]  P. Vogl,et al.  A Semi-empirical tight-binding theory of the electronic structure of semiconductors†☆ , 1983 .

[4]  Chang,et al.  Band mixing in semiconductor superlattices. , 1985, Physical review. B, Condensed matter.

[5]  J. Schulman.  Ga1−xAlxAs‐Ga1−yAlyAs‐GaAs double‐barrier structures , 1986 .

[6]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[7]  Boykin,et al.  Tight-binding model for GaAs/AlAs resonant-tunneling diodes. , 1991, Physical review. B, Condensed matter.

[8]  Yu,et al.  Multiband treatment of quantum transport in interband tunnel devices. , 1992, Physical review. B, Condensed matter.

[9]  Raj Mittra,et al.  Optimal multilayer filter design using real coded genetic algorithms , 1992 .

[10]  William L. Goffe,et al.  SIMANN: FORTRAN module to perform Global Optimization of Statistical Functions with Simulated Annealing , 1992 .

[11]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[12]  W. Schattke,et al.  Band-structure parameters by genetic algorithm. , 1996, Physical review. B, Condensed matter.

[13]  K. B. Whaley,et al.  Electron-hole interactions in silicon nanocrystals , 1997 .

[14]  Eric Michielssen,et al.  Genetic algorithm optimization applied to electromagnetics: a review , 1997 .

[15]  V. Rahmat-Samii,et al.  Genetic algorithms in engineering electromagnetics , 1997 .

[16]  Timothy B. Boykin,et al.  Improved fits of the effective masses at Γ in the spin-orbit, second-nearest-neighbor sp 3 s * model: Results from analytic expressions , 1997 .

[17]  Gerhard Klimeck,et al.  Quantitative simulation of a resonant tunneling diode , 1997, Journal of Applied Physics.

[18]  Gerhard Klimeck,et al.  Effective-mass reproducibility of the nearest-neighbor sp 3 s * models: Analytic results , 1997 .

[19]  T. Cwik,et al.  Synthesis of novel all-dielectric grating filters using genetic algorithms , 1998 .

[20]  T. Boykin,et al.  VALENCE-BAND WARPING IN TIGHT-BINDING MODELS , 1999 .