Modified valence force field approach for phonon dispersion: from zinc-blende bulk to nanowires

The correct estimation of the thermal properties of ultra-scaled CMOS and thermoelectric semiconductor devices demands for accurate phonon modeling in such structures. This work provides a detailed description of the modified valence force field (MVFF) method to obtain the phonon dispersion in zinc-blende semiconductors. The model is extended from bulk to nanowires after incorporating proper boundary conditions. The computational demands by the phonon calculation increase rapidly as the wire cross-section size increases. It is shown that nanowire phonon spectra differ considerably from the bulk dispersions. This manifests itself in the form of different physical and thermal properties in these wires. We believe that this model and approach will prove beneficial in the understanding of the lattice dynamics in the next generation ultra-scaled semiconductor devices.

[1]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[2]  A. S. Kronrod,et al.  Nodes and weights of quadrature formulas : sixteen-place tables , 1965 .

[3]  Bowen,et al.  Transmission resonances and zeros in multiband models. , 1995, Physical review. B, Condensed matter.

[4]  Gerhard Klimeck,et al.  Resolution of Resonances in a General Purpose Quantum Device Simulator (NEMO) , 1998, VLSI Design.

[5]  R. Landauer.  Spatial variation of currents and fields due to localized scatterers in metallic conduction , 1988 .

[6]  Y. Xiao,et al.  Phonon spectrum and specific heat of silicon nanowires , 2007 .

[7]  Gerhard Klimeck,et al.  An atomistic model for the simulation of acoustic phonons, strain distribution, and Grüneisen coefficients in zinc-blende semiconductors , 2003 .

[8]  A. Zacarias,et al.  Quantum Transport , 2008 .

[9]  N. Aluru,et al.  Quasiharmonic models for the calculation of thermodynamic properties of crystalline silicon under strain , 2006 .

[10]  Gerhard Klimeck,et al.  Effect of anharmonicity of the strain energy on band offsets in semiconductor nanostructures , 2004, cond-mat/0405627.

[11]  A. Zunger,et al.  Phonons in GaP quantum dots , 1999 .

[12]  Heat conductance is strongly anisotropic for pristine silicon nanowires. , 2008, Nano letters.

[13]  G. Nilsson,et al.  Study of the Homology between Silicon and Germanium by Thermal-Neutron Spectrometry , 1972 .

[14]  A. Stroud,et al.  Nodes and Weights of Quadrature Formulas , 1965 .

[15]  Gerhard Klimeck,et al.  Quantum device simulation with a generalized tunneling formula , 1995 .

[16]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[17]  Gerhard Klimeck,et al.  Band Structure Lab , 2006 .

[18]  W. Gander,et al.  Adaptive Quadrature—Revisited , 2000 .

[19]  Sui,et al.  Effect of strain on phonons in Si, Ge, and Si/Ge heterostructures. , 1993, Physical review. B, Condensed matter.

[20]  Dimensional crossover of thermal conductance in nanowires , 2007, 0704.0702.

[21]  H. McMurry,et al.  The use of valence force potentials in calculating crystal vibrations , 1967 .

[22]  D. Wallace,et al.  Thermodynamics of Crystals , 1972 .

[23]  W. Weber,et al.  Adiabatic bond charge model for the phonons in diamond, Si, Ge, and α-Sn , 1977 .

[24]  W. M. McKeeman,et al.  Algorithm 145: Adaptive numerical integration by Simpson's rule , 1962, Communications of the ACM.

[25]  de Gironcoli S.  Phonons in Si-Ge systems: An ab initio interatomic-force-constant approach. , 1992, Physical review. B, Condensed matter.

[26]  O. Madelung.  Semiconductors: Data Handbook , 2003 .

[27]  A. Majumdar,et al.  Predicting the thermal conductivity of Si and Ge nanowires , 2003 .

[28]  K. Rustagi,et al.  Adiabatic bond charge model for the phonons in A3B5 semiconductors , 1976 .

[29]  Natalio Mingo,et al.  Phonon transport in nanowires coated with an amorphous material: An atomistic Green’s function approach , 2003 .

[30]  Jack Dongarra,et al.  ScaLAPACK Users' Guide , 1987 .

[31]  Herman,et al.  Lattice properties of strained GaAs, Si, and Ge using a modified bond-charge model. , 1996, Physical Review B (Condensed Matter).

[32]  M. Anantram,et al.  Significant enhancement of hole mobility in [110] silicon nanowires compared to electrons and bulk silicon. , 2008, Nano letters.

[33]  Gerhard Klimeck,et al.  Development of a Nanoelectronic 3-D (NEMO 3-D ) Simulator for Multimillion Atom Simulations and Its Application to Alloyed Quantum Dots , 2002 .

[34]  Z. Hendrikse,et al.  Computation of the independent elements of the dynamical matrix , 1995 .

[35]  Kurt Maute,et al.  Strain effects on the thermal conductivity of nanostructures , 2010 .

[36]  F. Peeters,et al.  Phonon band structure of si nanowires: a stability analysis. , 2009, Nano letters.

[37]  P. N. Keating,et al.  Effect of Invariance Requirements on the Elastic Strain Energy of Crystals with Application to the Diamond Structure , 1966 .

[38]  G. Mahan,et al.  Phonon modes in Si [111] nanowires , 2004 .

[39]  Alexander A. Balandin,et al.  Phonon heat conduction in a semiconductor nanowire , 2001 .

[40]  Carrier-phonon interaction in small cross-sectional silicon nanowires , 2008 .

[41]  B. Weinstein,et al.  Raman scattering and phonon dispersion in Si and GaP at very high pressure , 1975 .