Skip to main content
SpringerLink
Log in

Recent developments in tight-binding approaches for nanowires

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

Full-band nanowire simulations pose significant computational challenges. Nanowires and nanostructures in general have many interfaces, may be composed of alloys, and feature confinement on a scale of a few tens of nanometers. The empirical tight-binding approach is well-suited for modeling these devices: Its basis consists of atomic-like orbitals with limited-range interactions and reasonably-sized basis sets can accurately reproduce the bands of a wide range of semiconductors. The method easily accommodates strain and electromagnetic fields. Over the years the application of the tight-binding approach to nanodevices such as superlattices and resonant-tunneling diodes has led to the development of many useful computational techniques. Recently, its application to random-alloy nanowire calculations has led to the development of approximate bandstructure methods superior to the Virtual-Crystal Approximation for these nanostructures, and its use in nanowire transmission calculations has led to a highly efficient method for transmission calculations. I discuss tight-binding models generally and then give a more in-depth discussion of the recent developments in tight-binding models as applied to nanowires.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Slater, J.C., Koster, G.F.: Simplified LCAO method for the periodic potential problem. Phys. Rev. 94, 1498 (1954)

    Article  MATH  Google Scholar 

  2. Vogl, P., Hjalmarson, H.P., Dow, J.D.: A semi-empirical tight-binding theory of the electronic structure of semiconductors. J. Phys. Chem. Solids 44, 365 (1983)

    Article  Google Scholar 

  3. Jancu, J.-M., Scholz, R., Beltram, F., Bassani, F.: Empirical sp3 d 5 s * tight-binding calculation for cubic semiconductors: General method and material parameters. Phys. Rev. B 57, 6493 (1998)

    Article  Google Scholar 

  4. Harrison, W.A.: Elementary Electronic Structure. World Scientific, New Jersey (1999)

    Google Scholar 

  5. Lowdin, P.O.: On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals. J. Chem. Phys. 18, 365 (1950)

    Article  Google Scholar 

  6. Boykin, T.B., Klimeck, G., Bowen, R.C., Oyafuso, F.: Diagonal parameter shifts due to nearest-neighbor displacements in empirical tight-binding theory. Phys. Rev. B 66, 125207 (2002)

    Article  Google Scholar 

  7. Boykin, T.B., Klimeck, G., Bowen, R.C., Lake, R.: Effective mass reproducibility of the nearest-neighbor models sp3 s *: Analytic results. Phys. Rev. B 56, 4102 (1997)

    Article  Google Scholar 

  8. Boykin, T.B.: Improved fits of the effective masses at Γ in the spin-orbit, second-near neighbor sp3 s * model: Results from analytic expressions. Phys. Rev. B 56, 9613 (1997)

    Article  Google Scholar 

  9. Boykin, T.B., Klimeck, G., Oyafuso, F.: Valence-band effective mass expressions in the sp3 d 5 s * empirical tight-binding model applied to a Si and Ge parameterization. Phys. Rev. B 69, 115201 (2004)

    Article  Google Scholar 

  10. Klimeck, G., Bowen, R.C., Boykin, T.B., Salazar-Lazaro, C., Cwik, T., Stoica, A.: Si tight-binding parameters from genetic algorithm fitting. Superlattices Microstruct. 27, 77 (2000)

    Article  Google Scholar 

  11. Graf, M., Vogl, P.: Electromagnetic fields and dielectric response in empirical tight-binding theory. Phys. Rev. B 51, 4940 (1995)

    Article  Google Scholar 

  12. Boykin, T.B.: Incorporation of incompleteness in the kp perturbation theory. Phys. Rev. B 52, 16317 (1995)

    Article  Google Scholar 

  13. Shishidou, T., Oguchi, T.: kp formula for use with augmented plane wave calculations. Phys. Rev. B 78, 244510 (2008)

    Article  Google Scholar 

  14. Boykin, T.B., Bowen, R.C., Klimeck, G.: Electromagnetic coupling and gauge invariance in the empirical tight-binding method. Phys. Rev. 63, 245314 (2001)

    Google Scholar 

  15. Boykin, T.B., Vogl, P.: Dielectric response of molecules in empirical tight-binding theory. Phys. Rev. B 65, 035202 (2002)

    Article  Google Scholar 

  16. Foreman, B.A.: Consequences of local gauge symmetry in empirical tight-binding theory. Phys. Rev. 66, 165212 (2002)

    Article  Google Scholar 

  17. Sandu, T.: Optical matrix elements in tight-binding models with overlap. Phys. Rev. B 72, 125105 (2005)

    Article  Google Scholar 

  18. Boykin, T.B.: Tight-binding-like expressions for the continuous-space electromagnetic coupling Hamiltonian. Am. J. Phys. 69, 793 (2001)

    Article  Google Scholar 

  19. Virgilio, M., Grosso, G.: Quantum-confined Stark effect in Ge/SiGe quantum wells: A tight-binding description. Phys. Rev. B 77, 165315 (2008)

    Article  Google Scholar 

  20. Virgilio, M., Grosso, G.: Valley splitting and optical intersubband transitions at parallel and normal incidence in [001] Ge-Si/Ge quantum wells. Phys. Rev. B 79, 165310 (2009)

    Article  Google Scholar 

  21. Kharche, N., Prada, M., Boykin, T.B., Klimeck, G.: Valley splitting in strained silicon quantum wells modeled with 2° miscuts, step disorder, and alloy disorder. Appl. Phys. Lett. 90, 092109 (2007)

    Article  Google Scholar 

  22. Rahman, R., Park, S.H., Boykin, T.B., Klimeck, G., Rogge, S., Hollenberg, L.C.L.: Gate induced g-factor control and dimensional transition for donors in multi-valley semiconductors. Submitted Xarchive arXiv:0905.3200 (2009)

  23. Dou, Y., Lei, Y., Wen, Z., Wang, Y., Lo, G.V., Allen, R.E.: Effect of C-C-C bond bending vibration on the photodissociation of cyclobutane. Appl. Surf. Sci. 253, 6400 (2007)

    Article  Google Scholar 

  24. Klimeck, G., Oyafuso, F., Boykin, T.B., Bowen, R.C., von Allmen, P.: Development of a nanoelectronic 3-D (NEMO 3-D) simulator for multimillion atom simulations and its application to alloyed quantum dots. J. Comp. Mod. Eng. Sci. 3, 601 (2002)

    MATH  Google Scholar 

  25. Klimeck, G., Ahmed, S., Bae, H., Kharche, N., Rahman, R., Clark, S., Haley, B., Lee, S., Naumov, M., Ryu, H., Saied, F., Prada, M., Korkusinski, M., Boykin, T.B.: Atomistic simulation of realistically sized nanodevices using NEMO 3-D: Part I—Models and benchmarks. IEEE Trans. Electron. Dev. 54, 2079 (2007)

    Article  Google Scholar 

  26. Klimeck, G., Ahmed, S., Kharche, N., Korkusinski, M., Usman, M., Prada, M., Boykin, T.B.: Atomistic simulation of realistically sized nanodevices using NEMO 3-D: Part II—Applications. IEEE Trans. Electron. Dev. 54, 2090 (2007)

    Article  Google Scholar 

  27. Boykin, T.B., Klimeck, G.: Practical application of zone-folding concepts in tight-binding. Phys. Rev. B 71, 115215 (2005)

    Article  Google Scholar 

  28. Boykin, T.B., Kharche, N., Klimeck, G., Korkusinski, M.: Approximate bandstructures of semiconductor alloys from tight-binding supercell calculations. J. Phys.: Condens. Matter. 19, 036203 (2007)

    Article  Google Scholar 

  29. Boykin, T.B., Kharche, N., Klimeck, G.: Allowed wavevectors under the application of incommensurate periodic boundary conditions. Eur. J. Phys. 27, 5 (2006)

    Article  MATH  Google Scholar 

  30. Boykin, T.B., Kharche, N., Klimeck, G.: Non-primitive rectangular supercells for tight-binding electronic structure calculations. Physica E 41, 490 (2009)

    Article  Google Scholar 

  31. Madelung, O. (ed.): Semiconductors: Group IV Elements and III–V Compounds. Springer, New York (1991)

    Google Scholar 

  32. Lee, J.H., Juravel, L.Y., Wooley, J.C., Spring Thorpe, A.J.: Electron transport and band structure of Ga1−x Al x As alloys. Phys. Rev. B 21, 659 (1980)

    Article  Google Scholar 

  33. Boykin, T.B., Luisier, Schenk, A., Kharche, N., Klimeck, G.: The electronic structure and transmission characteristics of disordered AlGaAs nanowires. IEEE Trans. Nanotechnol. 6, 43 (2007)

    Article  Google Scholar 

  34. Luisier, M., Schenk, A., Fichtner, W., Klimeck, G.: Atomistic simulation of nanowires in the sp3 d 5 s * tight-binding formalism: From boundary conditions to strain calculations. Phys. Rev. B 74, 205323 (2006)

    Article  Google Scholar 

  35. Kharche, N., Luisier, M., Boykin, T.B., Klimeck, G.: Electronic structure and transmission characteristics of SiGe Nanowires. J. Comput. Electron. 7, 350 (2008)

    Article  Google Scholar 

  36. Boykin, T.B.: Generalized eigenproblem method for surface and interface states: the complex bands of GaAs and AlAs. Phys. Rev. B 54, 8107 (1996)

    Article  Google Scholar 

  37. Boykin, T.B.: Tunneling calculations for systems with singular coupling matrices: results for a simple model. Phys. Rev. B 54, 7670 (1996)

    Article  Google Scholar 

  38. Lee, D.H., Joannopoulos, J.: Simple scheme for surface band calculations. I. Phys. Rev. B 23, 4988 (1981)

    Article  Google Scholar 

  39. Grosso, G., Moroni, S., Parravicini, G.P.: Electronic structure of the InAs-GaSb superlattice studied by the renormalization method. Phys. Rev. B 40, 12328 (1989)

    Article  Google Scholar 

  40. Boykin, T.B., van der Wagt, J.P.A., Harris, J.S. Jr.: Tight-binding model for GaAs/AlAs resonant-tunneling diodes. Phys. Rev. B 43, 4777 (1991)

    Article  Google Scholar 

  41. Boykin, T.B., Harris, J.S. Jr.: X-valley tunneling in single AlAs barriers. J. Appl. Phys. 72, 988 (1992)

    Article  Google Scholar 

  42. Ting, D.Z.-Y., Yu, E.T., McGill, T.C.: Multiband treatment of quantum transport in interband tunnel devices. Phys. Rev. B 45, 3583 (1992)

    Article  Google Scholar 

  43. Lake, R., Klimeck, G., Bowen, R.C., Jovanovic, D.: Single and multiband modeling of quantum electron transport through layered semiconductor devices. J. Appl. Phys. 81, 7845 (1997)

    Article  Google Scholar 

  44. Boykin, T.B., Luisier, M., Klimeck, G.: Multi-band transmission calculations for nanowires using an optimized renormalization method. Phys. Rev. B 77, 165318 (2008)

    Article  Google Scholar 

  45. Luisier, M., Klimeck, G., Schenk, A., Fichtner, W., Boykin, T.B.: A parallel sparse linear solver for nearest-neighbor tight-binding problems. In: Lunque, E., Maragalef, T., Benitez, D. (eds.) Euro-Par 2008. Lecture Notes in Computer Science, vol. 5168, pp. 790–800 (2008)

  46. Chadi, D.J.: Spin–orbit splitting in crystalline and compositionally disordered semiconductors. Phys. Rev. B 16, 790 (1977)

    Article  Google Scholar 

  47. Amestoy, P.R., Duff, I.S., L’Excellent, J.Y.: Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput. Methods Appl. Mech. Eng. 184, 501 (2000)

    Article  MATH  Google Scholar 

  48. Schenk, O., Gärtner, K.: Solving unsymmetric sparse systems of linear equations with PARDISO. J. Future Gener. Comput. Syst. 20, 475 (2004)

    Article  Google Scholar 

  49. Bowen, R.C., Klimeck, G., Lake, R., Frensley, W.R., Moise, T.: Quantitative simulation of a resonant tunneling diode. J. Appl. Phys. 81, 3207 (1997)

    Article  Google Scholar 

  50. Klimeck, G., Boykin, T.B., Bowen, R.C., Lake, R., Blanks, D., Moise, T., Kao, Y.C., Frensley, W.R.: Quantitative simulation of strained and unstrained InP-based resonant tunneling diodes. In: Proc. 55th IEEE Device Res. Conf. Dig., pp. 92–93 (1997)

  51. Bowen, R.C., Fernando, C., Klimeck, G., Chatterjee, A., Blanks, D., Lake, R., Hu, J., Davis, J., Kularni, M., Hattangady, S., Chen, I.C.: Physical oxide thickness extraction and verification using quantum mechanical simulation. In: IEDM Tech. Dig., pp. 869–872 (1997)

  52. Ma, D.D.D., Lee, C.S., Au, F.C.K., Tong, S.Y., Lee, S.T., et al.: Small-diameter silicon nanowire surfaces. Science 299, 1874 (2003)

    Article  Google Scholar 

  53. Wang, J.: Device physics and simulation of silicon nanowire transistors. Ph.D. dissertation, DAI-B 66/08, Purdue Univ., West Lafayette, IN, p. 4414 (2006)

  54. Rahman, R., Wellard, C.J., Bradbury, F.R., Prada, M., Cole, J.H., Klimeck, G., Hollenberg, L.C.L.: High precision quantum control of single donor spins in silicon. Phys. Rev. Lett. 99, 036403 (2007)

    Article  Google Scholar 

  55. Liang, G., Xiang, J., Kharche, N., Klimeck, G., Lieber, C.M., Lundstrom, M.: Performance analysis of a Ge/Si core/shell nanowire field effect transistor. Nano Lett. 7, 642 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Alabama in Huntsville, Huntsville, AL, 35899, USA

    Timothy B. Boykin

Authors
  1. Timothy B. Boykin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Timothy B. Boykin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boykin, T.B. Recent developments in tight-binding approaches for nanowires. J Comput Electron 8, 142–152 (2009). https://doi.org/10.1007/s10825-009-0287-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-009-0287-x

Keywords

Search

Navigation