No Access
Published Online: 21 July 2020
Accepted: June 2020
Journal of Applied Physics 128, 034306 (2020); https://doi.org/10.1063/5.0009838
Empirical pseudopotentials (EPs) allow for accurate and efficient modeling of atomistic electron transport. Unfortunately, EPs are available only for a few materials and atomic configurations. Furthermore, EPs for nanostructures have historically been described using a variety of different parameterized forms. To compete with more general first-principles methods, we propose an automated workflow to generate EPs of a general form for any material and atomistic configuration. In particular, we focus on the generation of EPs for electron transport calculations, i.e., we provide an EP that accurately reproduces a reference band structure. To demonstrate the applicability of the proposed method, we generate the EPs to reproduce the band structure for bulk Si, Ge, 3C–SiC (zinc-blende polytype), 4H–SiC (hexagonal polytype), diamond, and hydrogen terminated 100 oriented Si and Ge thin films, calculated using first principles. In addition, using the generated EPs, along with the virtual crystal approximation, we demonstrate that our method reproduces accurately the band structure related properties of Si 1 x Ge x alloy as a function of Ge mole fraction, x. As an application of our generated EPs, we perform ballistic quantum transport simulations of extremely scaled ( 0.6 nm wide), hydrogen terminated, 100 oriented Ge and Si gate-all-around nanowire field-effect transistors and compare their transfer characteristics.
This material is based upon work supported by the National Science Foundation (NSF) under Grant No. 1710066.
  1. 1. D. J. Frank, R. H. Dennard, E. Nowak, P. M. Solomon, Y. Taur, and H.-S. Philip Wong, “Device scaling limits of Si MOSFETS and their application dependencies,” Proc. IEEE 89, 259–288 (2001). https://doi.org/10.1109/5.915374, Google ScholarCrossref
  2. 2. N. Collaert, Device Architectures for the 5 nm Technology Node and Beyond (Semicon, Taiwan, 2016). Google Scholar
  3. 3. G. Le Lay, “2d materials: Silicene transistors,” Nat. Nanotechnol. 10, 202 (2015). https://doi.org/10.1038/nnano.2015.10, Google ScholarCrossref
  4. 4. J. Hu, T. W. Odom, and C. M. Lieber, “Chemistry and physics in one dimension: Synthesis and properties of nanowires and nanotubes,” Acc. Chem. Res. 32, 435–445 (1999). https://doi.org/10.1021/ar9700365, Google ScholarCrossref
  5. 5. Y. Liu, N. O. Weiss, X. Duan, H.-C. Cheng, Y. Huang, and X. Duan, “Van der waals heterostructures and devices,” Nat. Rev. Mater. 1, 16042 (2016). https://doi.org/10.1038/natrevmats.2016.42, Google ScholarCrossref
  6. 6. J. Maassen, M. Harb, V. Michaud-Rioux, Y. Zhu, and H. Guo, “Quantum transport modeling from first principles,” Proc. IEEE 101, 518–530 (2013). https://doi.org/10.1109/JPROC.2012.2197810, Google ScholarCrossref
  7. 7. J. Muscat, A. Wander, and N. Harrison, “On the prediction of band gaps from hybrid functional theory,” Chem. Phys. Lett. 342 397–401 (2001). https://doi.org/10.1016/S0009-2614(01)00616-9, Google ScholarCrossref
  8. 8. A. D. Becke, “A new mixing of Hartree–Fock and local density-functional theories,” J. Chem. Phys. 98, 1372–1377 (1993). https://doi.org/10.1063/1.464304, Google ScholarScitation, ISI
  9. 9. G. Bester, “Electronic excitations in nanostructures: An empirical pseudopotential based approach,” J. Phys. Condens. Matter 21, 023202 (2008). https://doi.org/10.1088/0953-8984/21/2/023202, Google ScholarCrossref
  10. 10. P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50, 17953–17979 (1994). https://doi.org/10.1103/PhysRevB.50.17953, Google ScholarCrossref
  11. 11. M. L. Cohen and T. K. Bergstresser, “Band structures and pseudopotential form factors for fourteen semiconductors of the diamond and zinc-blende structures,” Phys. Rev. 141, 789–796 (1966). https://doi.org/10.1103/PhysRev.141.789, Google ScholarCrossref
  12. 12. M. M. Rieger and P. Vogl, “Electronic-band parameters in strained Si 1 x Ge x alloys on Si 1 y Ge y substrates,” Phys. Rev. B 48, 14276–14287 (1993). https://doi.org/10.1103/PhysRevB.48.14276, Google ScholarCrossref
  13. 13. S. B. Zhang, C.-Y. Yeh, and A. Zunger, “Electronic structure of semiconductor quantum films,” Phys. Rev. B 48, 11204–11219 (1993). https://doi.org/10.1103/PhysRevB.48.11204, Google ScholarCrossref
  14. 14. P. Friedel, M. S. Hybertsen, and M. Schlüter, “Local empirical pseudopotential approach to the optical properties of Si/Ge superlattices,” Phys. Rev. B 39, 7974–7977 (1989). https://doi.org/10.1103/PhysRevB.39.7974, Google ScholarCrossref
  15. 15. T. T. Y. Kurokawa, S. Nomura, and Y. Aoyagi, “Large-scale calculation of optical dielectric functions of diamond nanocrystallites,” Phys. Rev. B 61, 12616–12619 (2000). https://doi.org/10.1103/PhysRevB.61.12616, Google ScholarCrossref
  16. 16. K. A. Mäder and A. Zunger, “Empirical atomic pseudopotentials for AlAs/GaAs superlattices, alloys, and nanostructures,” Phys. Rev. B 50, 17393–17405 (1994). https://doi.org/10.1103/PhysRevB.50.17393, Google ScholarCrossref
  17. 17. S. Pugh, D. Dugdale, S. Brand, and R. Abram, “Electronic structure calculations on nitride semiconductors,” Semicond. Sci. Technol. 14, 23 (1999). https://doi.org/10.1088/0268-1242/14/1/003, Google ScholarCrossref
  18. 18. D. Fritsch, H. Schmidt, and M. Grundmann, “Band-structure pseudopotential calculation of zinc-blende and wurtzite AlN, GaN, and InN,” Phys. Rev. B 67, 235205 (2003). https://doi.org/10.1103/PhysRevB.67.235205, Google ScholarCrossref
  19. 19. M. L. Van de Put, M. V. Fischetti, and W. G. Vandenberghe, “Scalable atomistic simulations of quantum electron transport using empirical pseudopotentials,” Comput. Phys. Commun. 244, 156–169 (2019). https://doi.org/10.1016/j.cpc.2019.06.009, Google ScholarCrossref
  20. 20. J. R. Chelikowsky and M. L. Cohen, “Nonlocal pseudopotential calculations for the electronic structure of eleven diamond and zinc-blende semiconductors,” Phys. Rev. B 14, 556–582 (1976). https://doi.org/10.1103/PhysRevB.14.556, Google ScholarCrossref
  21. 21. L. Bellaiche, S. H. Wei, and A. Zunger, “Localization and percolation in semiconductor alloys: GaAsN vs GaAsP,” Phys. Rev. B 54, 17568–17576 (1996). https://doi.org/10.1103/PhysRevB.54.17568, Google ScholarCrossref
  22. 22. G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6, 15–50 (1996). https://doi.org/10.1016/0927-0256(96)00008-0, Google ScholarCrossref
  23. 23. M. L. Van de Put, W. G. Vandenberghe, B. Sorée, W. Magnus, and M. V. Fischetti, “Inter-ribbon tunneling in graphene: An atomistic Bardeen approach,” J. Appl. Phys. 119, 214306 (2016). https://doi.org/10.1063/1.4953148, Google ScholarScitation, ISI
  24. 24. G. Ng, D. Vasileska, and D. K. Schroder, “Empirical pseudopotential band structure parameters of 4h-sic using a genetic algorithm fitting routine,” Superlattices Microstruct. 49, 109 (2011). https://doi.org/10.1016/j.spmi.2010.11.009, Google ScholarCrossref
  25. 25. J. Nocedal and S. J. Wright, Numerical Optimization (Springer, New York, 2006). Google ScholarCrossref
  26. 26. E. Jones, T. Oliphant, P. Peterson et al., “SciPy: Open Source Scientific Tools for Python,” (2001). http://www.scipy.org/ Google Scholar
  27. 27. H. Holloway, K. C. Hass, M. A. Tamor, T. R. Anthony, and W. F. Banholzer, “Isotopic dependence of the lattice constant of diamond,” Phys. Rev. B 44, 7123–7126 (1991). https://doi.org/10.1103/PhysRevB.44.7123, Google ScholarCrossref
  28. 28. Semiconductors, Group IV Elements and III-V Compounds, edited by O. Madelung (Springer-Verlag, Berlin, 1991). Google Scholar
  29. 29. S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (John Wiley & Sons, 2006). Google ScholarCrossref
  30. 30. O. Madelung, U. Rössler, and M. Schulz, “Silicon carbide (SiC), lattice parameters, thermal expansion,” in Group IV Elements, IV-IV and III-V Compounds. Part b - Electronic, Transport, Optical and Other Properties (Springer, Berlin, 2002), pp. 1–11. Google Scholar
  31. 31. S. T. Picraux, S. A. Dayeh, P. Manandhar, D. E. Perea, and S. G. Choi, “Silicon and germanium nanowires: Growth, properties, and integration,” J. Mater. 62, 35–43 (2010). https://doi.org/10.1007/s11837-010-0057-z, Google ScholarCrossref
  32. 32. K. J. Sankaran, Y.-F. Lin, W.-B. Jian, H.-C. Chen, K. Panda, B. Sundaravel, C.-L. Dong, N.-H. Tai, and I.-N. Lin, “Structural and electrical properties of conducting diamond nanowires,” ACS Appl. Mater. Interfaces 5, 1294–1301 (2013). https://doi.org/10.1021/am302430p, Google ScholarCrossref
  33. 33. J. Casady and R. Johnson, “Status of silicon carbide (SiC) as a wide-bandgap semiconductor for high-temperature applications: A review,” Solid State Electron. 39, 1409–1422 (1996). https://doi.org/10.1016/0038-1101(96)00045-7, Google ScholarCrossref
  34. 34. M. W. Geis, N. N. Efremow, and D. D. Rathman, “Summary abstract: Device applications of diamonds,” J. Vac. Sci. Technol. A 6, 1953–1954 (1988). https://doi.org/10.1116/1.575213, Google ScholarCrossref, ISI
  35. 35. T. L. Cottrell, The Strengths of Chemical Bonds (Academic Press, 1958). Google Scholar
  36. 36. J. Fang, W. G. Vandenberghe, B. Fu, and M. V. Fischetti, “Pseudopotential-based electron quantum transport: Theoretical formulation and application to nanometer-scale silicon nanowire transistors,” J. Appl. Phys. 119, 035701 (2016). https://doi.org/10.1063/1.4939963, Google ScholarScitation, ISI
  37. 37. L. D. Laude, F. H. Pollak, and M. Cardona, “Effects of uniaxial stress on the indirect exciton spectrum of silicon,” Phys. Rev. B 3, 2623–2636 (1971). https://doi.org/10.1103/PhysRevB.3.2623, Google ScholarCrossref
  38. 38. L. E. Vorobyev, “Germanium (Ge),” in Handbook Series on Semiconductor Parameters (World Scientific, London, 1996), pp. 33–57. Google Scholar
  39. 39. I. Balslev, “Influence of uniaxial stress on the indirect absorption edge in silicon and germanium,” Phys. Rev. 143, 636–647 (1966). https://doi.org/10.1103/PhysRev.143.636, Google ScholarCrossref
  40. 40. D. Takeuchi, S. Koizumi, T. Makino, H. Kato, M. Ogura, H. Ohashi, H. Okushi, and S. Yamasaki, “Negative electron affinity of diamond and its application to high voltage vacuum power switches,” Phys. Status Solidi A 210, 1961–1975 (2013). https://doi.org/10.1002/pssa.201300385, Google ScholarCrossref
  41. 41. S. Y. Davydov, “On the electron affinity of silicon carbide polytypes,” Semiconductors 41, 696–698 (2007). https://doi.org/10.1134/S1063782607060152, Google ScholarCrossref
  42. 42. K. C. Pandey and J. C. Phillips, “Nonlocal pseudopotentials for Ge and GaAs,” Phys. Rev. B 9, 1552–1559 (1974). https://doi.org/10.1103/PhysRevB.9.1552, Google ScholarCrossref
  43. 43. C. Codreanu, M. Avram, E. Carbunescu, and E. Iliescu, “Comparison of 3C–SiC, 6H–SiC and 4H–SiC MESFETS performances,” Mater. Sci. Semicond. Process. 3, 137–142 (2000). https://doi.org/10.1016/S1369-8001(00)00022-6, Google ScholarCrossref
  44. 44. X. Huang, E. Lindgren, and J. R. Chelikowsky, “Surface passivation method for semiconductor nanostructures,” Phys. Rev. B 71, 165328 (2005). https://doi.org/10.1103/PhysRevB.71.165328, Google ScholarCrossref
  45. 45. L. W. Wang and A. Zunger, “Electronic structure pseudopotential calculations of large (.apprx. 1000 atoms) Si quantum dots,” J. Phys. Chem. 98, 2158–2165 (1994). https://doi.org/10.1021/j100059a032, Google ScholarCrossref
  46. 46. E. S. M. Goh, T. P. Chen, C. Q. Sun, and Y. C. Liu, “Thickness effect on the band gap and optical properties of germanium thin films,” J. Appl. Phys. 107, 024305 (2010). https://doi.org/10.1063/1.3291103, Google ScholarScitation, ISI
  47. 47. H.-G. Junginger and W. van Haeringen, “Energy band structures of four polytypes of silicon carbide calculated with the empirical pseudopotential method,” Phys. Status Solidi B 37, 709–719 (1970). https://doi.org/10.1002/pssb.19700370222, Google ScholarCrossref
  48. 48. L.-W. Wang and A. Zunger, “Local-density-derived semiempirical pseudopotentials,” Phys. Rev. B 51, 17398–17416 (1995). https://doi.org/10.1103/PhysRevB.51.17398, Google ScholarCrossref
  49. 49. L. Wang and A. Zunger, “Solving Schrödinger’s equation around a desired energy: Application to silicon quantum dots,” J. Chem. Phys. 100, 2394–2397 (1994). https://doi.org/10.1063/1.466486, Google ScholarScitation, ISI
  50. 50. L. Nordheim, “Zur elektronentheorie der metalle. I,” Ann. Phys. 401, 607–640 (1931). https://doi.org/10.1002/andp.19314010507, Google ScholarCrossref
  51. 51. J. P. Dismukes, L. Ekstrom, and R. J. Paff, “Lattice parameter and density in germanium-silicon alloys,” J. Phys. Chem. 68, 3021–3027 (1964). https://doi.org/10.1021/j100792a049, Google ScholarCrossref
  52. 52. J. Weber and M. I. Alonso, “Near-band-gap photoluminescence of Si-Ge alloys,” Phys. Rev. B 40, 5683–5693 (1989). https://doi.org/10.1103/PhysRevB.40.5683, Google ScholarCrossref
  53. 53. M. V. Fischetti and S. E. Laux, “Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys,” J. Appl. Phys. 80, 2234–2252 (1996). https://doi.org/10.1063/1.363052, Google ScholarScitation, ISI
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