Materials Theory and Computation

1. Materials Theory and Computation • S. V. Khare • Department of Physics and Astronomy • University of Toledo, Ohio • 2. Department of Electrical Engineering and Computer Science • University of Toledo, Ohio • http://astro1.panet.utoledo.edu/~khare/ • Funding: DARPA, Air Force, NSF, DoE, State of Ohio

2. General theme of research My research involves the application of appropriate theoretical and computational techniques to understand condensed matter systems of significant experimental interest. This work involves predictions for new phenomena, explanation of existing data, and collaborations with experimentalists on their current experiments. It has involved a variety of thin film and bulk materials from metals to semiconductors, crystalline to disordered materials, and nano- to micro- length scales. Varied theoretical techniques utilized are density functional theory based computations, classical molecular dynamics, Monte Carlo simulations, and continuum analytical equations.

3. Papers with students I • Effect of structure, surface passivation, and doping on the electronic and optical properties of GaAs nanowires: A first principles study • V. Gade, N. Shi, D. Medaboina, S. V. Khare, R. Ramprasad (Submitted to journal) • Structural and Electronic properties of β-In2X3 (X = O, S, Se, Te) using ab initio calculations • S. Marsillac, N. S. Mangale, V. Gade, S. V. Khare (Submitted to journal) • Super Hard Cubic Phases of Period VI Transition Metal Nitrides: A First Principles Investigation S. K. R. Patil, N. S. Mangale, S. V. Khare, and S. Marsillac Accepted in Thin Solid Films 2008. • Effect of structure, surface passivation, and doping on the electronic properties of Ge nanowires: A first-principles study D. Medaboina, V. Gade, S. K. R. Patil, and S. V. Khare Phys. Rev. B 76, 205327 (2007). • Impact of Structure Relaxation on the Ultimate Performance of a Small Diameter, n-Type <110> Si-Nanowire MOSFET G. Liang, D. Kienle, S. K. R. Patil, J. Wang, A. W. Ghosh, and S. V. Khare IEEE Trans. Nano. Tech.6, 225 (2007).

4. Papers with students II • Mechanical stability of possible structures of PtN investigated using first-principles calculations S. K. R. Patil, S. V. Khare, B. R. Tuttle, J. K. Bording, and S. Kodambaka Phys. Rev. B 73, 104118 (2006). • Ab Initio calculations for Properties of MAX phases Ti2TlC, Zr2TlC, and Hf2TlC J. A. Warner, S. K. R. Patil, S. V. Khare, and R. S. Masiuliniec Appl. Phys. Lett. 88, 101911 (2006).

5. Ab initio computations of structural and electronic properties of doped and undoped Ge nanowires • S. V. Khare1, D. Medaboina2, V. Gade2, and S. K. R. Patil3 • Department of Physics and Astronomy • University of Toledo, Ohio • 2. Department of Electrical Engineering and Computer Science • University of Toledo, Ohio • 3. Department of Mechanical and Industrial Engineering • University of Toledo, Ohio • http://www.physics.utoledo.edu/~khare/

6. Outline • Experimental motivation • Ab initio methods • Structural properties • Band structures of doped and undoped nanowires • Band gaps of Si and Ge nanowires • Conclusions

7. Introduction Diameter (d) of NWs range from 1 nm – 100 nm. Length (ℓ) varies from 10nm – 1µm Different names to NWs in literature: Nanowires: Wires with large aspect ratios (ℓ/d > 20) Nanorods: Wires with small aspect ratios (ℓ/d) Nanocontacts: Short wires bridged between two larger electrodes. ℓ

8. Experimental methods for preparing Ge nanowires • Laser ablation • Vapor transport • Low-temperature CVD • Supercritical fluid–liquid–solid synthesis : In this method thermal evaporation of Ge powder at 950C onto silicon wafer and ceramic (alumina) substrate using Au catalyst via a vapour–liquid–solid (VLS) process. Diameters up to 30 nm and length tens of micro meters. Preferred growth direction for the nanowires is [111]. Nanowires developed by Nguyen et al*., grown along [110] on heavily doped Si. Nanowires developed by Kamanev et al†.,of 40 nm diameter along [111] growth direction grown on silicon substrate. * Nguyen, P.; Ng, H. T.; Meyyappan, M. Adv. Mater.2005, 17, 5. †Kamanev, B. V.; Sharma, V.; Tsybeskov, L.; Kamins, T. I. Phys. Stat. Sol. (a) 2005, 202, 2753.

9. [211] [110] [111] [111] Orientation of Ge nanowires generated using SLFS method Tip of nanowires generated using supercritical fluid–liquid–solid (SLFS) method by Hanrath et al*., * Hanrath, T.; Korgel, B. A. Small2005, 1, 7.

10. Faceting of Ge nanowires Fourier transform of image representing the [110] pole axis of the wire [110] Tapered end of nanowire showing the facets HRTEM image of nanowire along [110] growth direction showing the length of nanowire. Crystallographic model of nanowire showing the facets of nanowire. HRTEM image of [110] growth direction developed by Hanrath et al*., representing the faceted cap structure of nanowire. *Hanrath, T.; Korgel, B. A. Small2005, 1, 7.

11. A SEM image of a p-n diode. Diode obtained by simply crossing p- and n-type NW.* Diode made of NWs n p-n p 1 μm FET made of NWs Schematics illustrating the crossed NW-FET concept.Ŧ * Duan et al., Nature 2001, 409, 66, Harvard University, Cambridge. ŦHuang et al., Pure Appl. Chem. 2004, 76, 2051, Harvard University, Cambridge.

12. Ab initio method Powerful predictive tool to calculate properties of materials Fully first principles  (1) no fitting parameters, use only fundamental constants (e, h, me, c) as input (2) Fully quantum mechanical for electrons Thousands of materials properties calculated to date Used by biochemists, drug designers, geologists, materials scientists, and even astrophysicists! Evolved into different varieties for ease of applications Awarded chemistry Nobel Prize to W. Kohn and H. Pople 1998

13. Pros and Cons of ab initio method • Pros: • Very good at predicting structural properties: • (1) Lattice constant good to 0-3%. • (2) Bulk modulus good to 1-10%. • (3) Very robust relative energy ordering between structures. • (4) Good pressure induced phase changes. • Good band structures, electronic properties. • Used to study the properties of materials at unstable conditions. • Cons: • Computationally intensive. • Excited electronic states: difficult to compute. • Band gaps are under estimated by 50%.

14. Ab initio method details • LDA, Ceperley-Alder exchange-correlation functional as parameterized by Perdew and Zunger • Generalized ultra-soft Vanderbilt pseudo-potentials and plane wave basis set • Supercell approach with periodic boundary conditions in all three dimensions • Wires are infinite along their axis

15. Theoretical and experimental comparison of lattice constant and bulk modulus of Ge * Kittel, C. Introduction to Solid State Physics, 2nd ed., (John Wiley & Sons, Inc., New York, 1976), p. 40.

16. Nomenclature used for describing a nanowire Number of Ge atoms in the nanowire Diameter of the nanowire in nm Number of H atoms in the nanowire ( ) 2 . 03 [ 001 ] Nanowire Orientationof the nanowire - - ( , 44 ) Ge H 89 NW

17. [001] [110] [111] [001] [110] [111] Structural Properties of Ge nanowires All results in this talk are with DFT-LDA, VASP.

18. [001] [110] [111] [001] [110] [111] Electronic Properties: Band Structures of Ge nanowires

19. Band Structures of doped and undoped Ge nanowires n-doped undoped p-doped [100] [110] [111]

20. Plot of Energy gap (eV) versus Diameter (nm)

21. Dia (nm) Axis Comparison of band gap of Ge and Si nanowires along different diameter and axes Ge nanowires Si nanowires* Dia (nm) D = Direct band gap, I = Indirect band gap * Zhao, X.; Wei, C. M.; Yang, L.; Chou, M.Y. PRL2004, 92, 23.

22. Conclusions of work on Ge nanowires • Study of structural, energetic, and electronic properties of hydrogen-passivated doped and undoped germanium nanowires along [001], [110], and [111] directions with diameter d up to 3 nm, using ab initio methods. • The electronic band structure shows a significant response to changes in surface passivation with hydrogen. • Doping of wires with n and p type atoms produced a response in the band structure similar to that in a doped bulk crystal. • Quantum confinement has a substantial effect on the electronic band structure and hence the band gap, which increases with decreasing diameter. • Wires oriented along [110] are found to have a direct band gap while the wires along [111] are found to have an indirect band gap. Wires along [001] show a crossover from a direct to an indirect band gap as diameter increases above the critical diameter for the transition being 1.3 nm.

23. Institutional Support • University of Toledo Parallel Computing Cluster • Ohio Supercomputer Cluster • National Center for Supercomputing Applications (NCSA)

24. Thank you!

25. Ab initio method details • LDA, Ceperley-Alder exchange-correlation functional as parameterized by Perdew and Zunger • Used the VASP code with generalized ultra-soft Vanderbilt pseudo-potentials and plane wave basis set • Supercell approach with periodic boundary conditions in all three dimensions • Energy cut-offs of 150.00 eV for H-terminated Ge nanowires, dense k-point meshes • Forces converged till < 0.01 eV/ Å • Used supercomputers of NCSA and OSC

28. Structural and Electronic Properties of Doped and Undoped GaN Nanowires: A First Principles Investigation Shandeep Voggu (MS Thesis Candidate) Department of EECS University of Toledo

29. Acknowledgements • People • Prof. Sanjay V. Khare (Thesis advisor) • Prof. Daniel Georgiev (Committee member) • Prof. Vijay Devabhaktuni (Committee member) • Varun Gade, Dayasagar Medaboina, Sunil K. R. Patil, Nikhil Mangale, Ashok Kolagatla, Kausthuba Ippagunta, Abbas Naseem, Krishnakanth Ganguri (Prof. Khare’s group) • Institutional support • Ohio Supercomputer Center (OSC) • National Center for Supercomputing Applications (NCSA)

30. Outline Introduction Experimental motivation and applications Crystal structures Generation of nanowires Ab initio methods Properties: Doped and undoped nanowires 1) Structural 2) Electronic Conclusions Future work

31. Outline Introduction Experimental motivation and applications Crystal structures Generation of nanowires Ab initio methods Properties: Doped and undoped nanowires 1) Structural 2) Electronic Conclusions Future work

32. Introduction Diameter (d) of NWs range from 1 nm – 100 nm. Length (ℓ) varies from 10nm – 1µm Different names to NWs in literature: Nanowires: Wires with large aspect ratios (ℓ/d > 20) Nanorods: Wires with small aspect ratios (ℓ/d) Nanocontacts: Short wires bridged between two larger electrodes. ℓ

33. Outline Introduction Experimental motivation and applications Crystal structures Generation of nanowires Ab initio methods Properties: Doped and undoped nanowires 1) Structural 2) Electronic Conclusions Future work

34. Growth of GaN NWs using the Metalorganic Chemical Vapour Deposition (MOCVD) Electron microscopy images of synthesized GaN nanowires. (a)Scanning electron microscopy (SEM) images of GaN nanowires grown on sapphire substrate. Scale bar, 3μm. (b)High-resolution transmission electron microscopy image of GaN nanowire.Scale bar, 1 nm. (c)SEM image of single GaN wire after dispersing onto sapphire substrate. Scale bar, 5μm. 5 nm 50 nm * J. C. Johnson et al., Nature Materials 1, 106–110 (2002), University of California, Berkeley.

35. Growth of GaN NWs using the Metalorganic Chemical Vapour Deposition (MOCVD) TEM images of the GaN nanowires. a–c,Wires grown on (100) γ-LiAlO2.The inset in a is an electron-diffraction pattern recorded along [001] axis. d–f,Wires grown on (111) MgO substrates.The insets in d show the hexagonal cross-section of the wire and an electron-diffraction pattern recorded along the [100] axis. c and f show space-filling structural models for the nanowires with triangular and hexagonal cross-sections. * Kuykendall et al., Nature Materials 3, 524–528 (2004), University of California, Berkeley.

36. Advantages of NWs NW devices can be assembled in a rational and predictable way because: NWs can be precisely controlled for structure and chemical composition during synthesis. NW building blocks can be combined in ways not possible in conventional electronics. Series of electronic devices are being assembled using semiconductor NWs: Crossed NW p-n diodes, Crossed NW-FETs, Nanoscale logic gates, Optoelectronic devices

37. A SEM image of a p-n diode. Diode obtained by simply crossing p- and n-type NW.* Diode made of NWs n p-n p 1 μm FET made of NWs Schematics illustrating the crossed NW-FET concept.Ŧ * Duan et al., Nature 2001, 409, 66, Harvard University, Cambridge. ŦHuang et al., Pure Appl. Chem. 2004, 76, 2051, Harvard University, Cambridge.

38. Far-field image of a single GaN nanolaser* GaN nanowire laser 1 μm GaN Nanowire Transistor: n-type • SEM image of a GaN nanowire connected with twoelectrodes for the transport study. The inset is an illustration of the GaN transistor layout. • Current-voltage measurement at different gating voltages for the GaN nanowire. Ŧ *J. C. Johnson et al., Nature Materials 1, 106–110 (2002). Ŧ Kuykendall et al., Nano. Lett. 3, 1063, 2003. University of California, Berkeley.

39. Outline Introduction Experimental motivation and applications Crystal structures Generation of nanowires Ab initio methods Properties: Doped and undoped nanowires 1) Structural 2) Electronic Conclusions Future work

40. Definition of a crystal a y y z z x x • Crystal atomic position = Bravais lattice position + Basis vector • Bravais lattice is regular arrangement of points. • Vectors determining the position of the atom from every Bravais lattice point are called basis vectors. • Basis vector = 1 – basis atom4 – basis atoms Bases atomic positions: (0.0, 0.0, 0.0) (0.0, 0.5, 0.5) (0.5, 0.0, 0.5) (0.5, 0.5, 0.0) Basis atomic position: (0.0, 0.0, 0.0)

41. Hexagonal Bravais lattice structures Hexagonal Bravais lattice structure The wurtzite lattice. Wurtzite unit cell Basis Vectors Lattice Vectors

42. Wurtzite structure Ga atoms N atoms Structure representing the wurtzite lattice.

43. Outline Introduction Experimental motivation and applications Crystal structures Generation of nanowires Ab initio methods Properties: Doped and undoped nanowires 1) Structural 2) Electronic Conclusions Future work

44. Objective of making NW structures Periodically repeating unit along arbitrary direction (m n o) in a crystal. - For example consider a [001] axis wire • -  Indicate Ga atoms •  Indicate N atoms y x z

45. Objective of making NW structures Periodically repeating unit along arbitrary direction (m n o) in a crystal. - For example consider a [001] axis wire • -  Indicate Ga atoms •  Indicate N atoms y x z

46. Objective of making NW structures Periodically repeating unit along arbitrary direction (m n o) in a crystal. - For example consider a [001] axis wire • -  Indicate Ga atoms •  Indicate N atoms y z x • Surfaces should be passivated

47. Generation of nanowires Three major steps in generation of nanowires: Generate a large cube of bulk material using lattice and basis vectors of wurtzite lattice. Cut a wire of given length and diameter from the bulk material using a separate algorithm. Identify the missing neighbors and passivate the dangling bonds with hydrogen atoms.

48. Generation of Bulk material ai • -  Indicate Ga atoms •  Indicate N atoms • Position vector of any atom in bulk material is given by = ´ + n å å R b a ( ) j i i • represents the lattice vectors for i = 1, 2, and 3; represent the basis atoms. • The generated bulk material has square cross-section. bj

49. Extracting the nanowire Axis of the NW • For each atom in the bulk material: • Cross product of its position vector with the normal along the axis of wire < radius of the wire. • Dot product of the position vector of atom and normal along the axis of wire lies in the range  -(wire-length)/2 to +(wire-length)/2 3. Wire-length determined from the crystal * Goldstein. H, Poole. C, Safko. J, Classical Mechanics, 3rd Edition, Addison Wesley.

50. Generated nanowire • -  Indicate Ga atoms •  Indicate N atoms • The generated nanowires will have dangling bonds left on the surface of wire due to the cutting. • These dangling bonds create states in bandstructure. d ℓ Nanowire cut from bulk material.