Atomic scale Design of Nanostructures

1. Atomic scale Design of Nanostructures Jerzy Bernholc North Carolina State Univ., Raleigh, NC 27695-8202 and Oak Ridge National Laboratories, TN 37831-6359 • Nanotube-cluster-based molecular sensors • Piezo- and ferroelectric materials • Boron nitride nanotubes • Ferroelectric polymers and prediction of new ones with 100% improved piezo- and ferroelectric properties • Optical signatures of surface structures • Feedback control during growth possible (with monolayer resolution) • Reconstruction patterns, nanowires on surfaces • Summary Collaborators: M. Buongiorno Nardelli, W. Lu, V. Meunier, S. Nakhmanson, W. G. Schmidt, S. Wang and Q. Zhao NC STATE UNIVERSITY

2. Properties (l,m) relation Geometric radius chiral angle Electronic metal semi-conductor chiral armchair zigzag Introduction to nanotubes o nanotube “rope” Thess, Smalley, et. al., Science 96

3. Carbon nanotubes as chemical sensors Adsorption of chemical species on single wall nanotubes can induce changes in the electrical characteristics(Kong et al., Science 2000) Semiconducting SW-CNT before and after exposure to NO2 and NH3: NO2 binds to the SWNT NH3 does not bind directly: - gating effect through substrate - binding to adsorbed species

4. Nanotube/metal-cluster sensors ?? • Understand the interactions amongcarbon nanotubes, metal clusters and molecules. • How does gas adsorption on metal clusters modify the atomic and electronic structures of NT/cluster assemblies? • Is this a good way to functionalize carbon nanotubes for sensor applications? • Clusters-decorated NT have been made (Au, Pt, Pd, Ti, Ni).

5. (5,5) nanotube Fermi level - - - - - - - - R lead L lead conductor reflection transmission Introduction to quantum conductance Conductance = 1 / Resistance • In general, the quantum conductance measures the number of electron channels extending through the conductor and the leads, each contributing 2e2/h. • For a perfect metallic nanotube and perfect contacts, both bands at the Fermi level contribute equally. • For a disordered nanotube or for poor contacts, the conductance is much less. • Conductance computed using a new, very efficient method Two bands cross at the Fermi levelConductance  T(EF) = 2 Units of2e2/h  (12.9 k)-1

6. Quantum transport in semiconducting NT-Al13 system I (mA) V (Volt) One cluster per 8 C double layers. (8,0)tube-metal cluster assembly becomes conducting after NH3 adsorption. Band gap is decreased and Fermi energy is shifted to the conduction band. Can function as a molecular sensor. The gap shrinks even more with the adsorption of a second cluster and NH3.

7. Selectivity of Gas adsorption (8,0)tube+Al13 + B2H6 Metal cluster’s structure is significantly changed. C-Al bond is weakened, lengthens from 2.15 Å to2.22 Å. No charge transfer between the (8,0)tube and the metal cluster with 2(BH3) adsorption. The tube-cluster assembly remains semiconducting.

8. Electronic Transport in Metallic NT-Al13 System I (mA) Current is zeroed upon adsorption of one or more NH3 molecules V (Volt) Conductance is reduced in regions with cluster electronic states Small gap in conductance from the CNT-metal interaction The gap is widened by the NH3 adsorption; conductance is much reduced

9. Armchair NT ─ non-polar (centrosymmetric) Zigzag NT ─ polar? BN NT as possible pyro/piezoelectric materials Excellent mechanical properties:light and flexible, almost as strong as carbon nanotubes(Zhang and Crespi, PRB 2000) Chemically inert:proposed to be used as coatings All insulatorswith no regard to chirality and constant band-gap of around 5 eV Intrinsically polardue to the polar nature of B-N bond Most of the BN nanotubes are non-centrosymmetric (i.e. do not have center of inversion), which is required for the existence of non-zero spontaneous polarization Possible applications in nano-electro-mechanical devices: actuators, transducers, strain and temperature sensors hexagonal BN

10. Carbon c c Boron-Nitride Boron-Nitride nanotubes: quasi-1D nano-piezoelectrics Zigzag nanotube index Electronic polarization looks especially simple when using orthogonal localized (Wannier) functions. Sum over centers of Wannier functions • All wide BN nanotubes are not pyroelectric due to screw symmetry! • Breaking the symmetry by bundling leads to • BN nanotubes are excellent nanoscale piezoelectrics: e33 0.25-0.4 C/m2 Nakhmanson, Meunier, Bernholc, Buongiorno Nardelli, PRB 67, 235406 (2003).

11. β-PVDF Ferroelectric polymers PVDF structural unit Representatives: polyvinylidene fluoride (PVDF), PVDF copolymers, nylons, etc. Spontaneous polarization: Piezoelectric const (stress): up to Mechanical/Environmental properties: Light, flexible, non-toxic Applications: sensors, transducers, hydrophone probes, sonar

12. Polarization and piezoelectricity in β-PVDF and copolymers Model (100% crystalline) 0.178 -0.268 -0.270 -0.332 No sensible comparison to experiment. Real β-PVDF is only 50% crystalline! β-PVDF Can be grown ~100% crystalline! 0.128 (0.123) -0.183 -0.192 -0.211 (Tajitsu et al. Jpn. J. Appl. Phys. 1987) (Furukawa, IEEE Trans. 1989) P(VDF/TrFE) (75/25) 0.104 (0.118) -0.135 -0.145 -0.150 (Tasaka and Miyata, JAP 1985) P(VDF/TeFE) (75/25)

13. Backbone substitution in PVDF – ? + polyaminodifluoroborane (PADFB) β-PVDF ? How large will be the improvement in polarization? Increasing polarization through charge transfer: ++ Carbon Nitrogen Carbon Boron – – BTW: polyaminoborane (PAB), [-BH2-NH2-]n, should also be polar

14. Polarization in BN-based polymers Rotation angle Additional bonus: improved thermal stability PbTiO3 data from G. Saghi-Szabo et. al. PRL 1998, PRB 1999. Heavy, brittle, toxic PADFB: polar properties improve by approximately 100% PADFB and PAB have already been synthesized, but only as precursors for other materials. Nakhmanson, Buongiorno Nardelli, Bernholc, PRL 92, 115504 (2004)

15. Dipole moment per monomer and packing of β-PVDF chains Interaction between chains is important! noninteracting chains weakly interacting chains crystal

16. “Dipole summation” models for polarization in PVDF β-PVDF crystal Most models fit to this point and then use this value in calculations for β-PVDF crystal noninteracting chains Empirical models (100% crystalline)Polarization (C/m2) Rigid dipoles (no dipole-dipole interaction): 0.131 Mopsik and Broadhurst, JAP, 1975; Kakutani, J Polym Sci, 1970:0.22 Tashiro et al. Macromolecules 1980: 0.140 Purvis and Taylor, PRB 1982, JAP 1983:0.086 Al-Jishi and Taylor, JAP 1985:0.127 Carbeck, Lacks and Rutledge, J Chem Phys, 1995:0.182

17. Reflectance Difference Spectroscopy (RDS/RAS) • Miniaturization of electronic devices requires in situ monitoringand feedback control of crystal growth • “Standard” techniques to monitor surfaces use electron scattering and are restricted to ultrahigh vacuum • Difference in reflectance between two polarizationsbulk contribution cancels out • Very sensitive to atomic structure at the surface • Can unambiguously determine surface structure, even when other techniques fail • Optical probe: can be used for feedback control during growth in gaseous environments Interpretation of spectra requires accurate calculations.We studied many complex surfaces, incl. steps, complex reconstructions and organics.

18. 110 layer stack schematic 100 HBT-structure emitter 90 cooling down InGaAs n++ 80 cooling GaAs n+ D |Re{ r/r}| 70 GaAs n 60 5 InGaP n GaAs p++ growth time (min) cooling 50 base collector 4 GaAs n- 40 3 heating 30 subcollector GaAs n 2 InGaP n+ 20 GaAs n+ 1 10 GaAs-substrate 0 0 2.0 2.5 3.0 3.5 4.0 4.5 photon energy (eV) Reflectance anisotropy for industrial applications Example: real-time monitoring of GaAs/InGaP HBT epitaxial growth Zettler et al., J. Crystal Growth 195, 151 (1998) Commercial RAS/RDS sensors: www.laytec.de www.aixtron.com/products/epiras.htm Early RDS work: Aspnes & Studna PRL 54, 1956 (1985); Jonsson, Samuelson et al., APL 56, 2414 (1990); Kamiya, Aspnes et al. PRL 68, 627 (1992); PRB 46, 15894 (1992). Zettler et al., J. Crystal Growth 195, 151 (1998)

19. r/r D 2 10 -1 -1 2 4 3 2 0 -2 RHEED (2x4) 4 5 3 2 Energy [eV] InP(001)(2x4): surface structure & RDS calculated reflectance anisotropy calculated reflectance anisotropy a InP(001) 2(2x4) Schmidt et al . PRB 59 , 2234 (1999) 1 0 measured RAS, KB Ozanyan et al. (2x4) mixed-dimer model J. Appl. Phys. 82 , 474 (1997) r/r D 3 10 • Reflectance asaa ... aa component of slab polarizability eb ... bulk dielectric function DFT-LDA qualitative agreement

20. Theory: E' E DFT-LDA 0 1 E 1 E' 0 S1/2 GWA S3 r/r 0.01 D Experiment: 300K E 1 S1 25K E' 0 2 3 4 5 6 Energy [eV] In-rich InP(001)(2x4):self-energy effects on optical anisotropy • non-uniform shift of bulk and surface related peaks with GW corrections • line shape changes • k-space resolution insufficient to resolve S1/S2 S1/2 S3 S3 Schmidt, N Esser, et al S2 PRB 61, R16335 (2000)

21. Optical signature of Si(111)-In nanowires Zigzag model p-bonded-chain- stacking-fault (7656)model In atoms on Si(111) self-organize into nanowires. Undergo a phase transition from (4x1) to (8x2) as temperature is lowered. Several models of (4x1) and (8x2) structures exist strongly anisotropic conductivity observed in experiments Calculated zigzag Calculated (7656) Experiment

22. Si/organics surface structures Organics on Si can lead to novel sensors and detectors Cyclopentene monolayer can be used to passivate the Si surface It is a starting point for DNA attachment DNA electrophoresis on a Si surface. N. Pernodet et al, PRL85, 5651(2000). A new opportunity for silicon-based microelectronics J. T. Yates Jr., Science 279, 335 (1998). Ordered array of organic molecules (cyclopentene) shows a strong optical anisotropy T.Strother, R. J. Hamers and L.M. Smith, Nucleic Acids Research, 28, 3535 (2000)

23. Organic molecule adsorption: C5H8 on Si(001) Dimerized model Dimer-cleaved model Hydrogen co-adsorption A: molecular C5H8 B: dimer-related C: dangling bond D: bulk-related Comparison to exp. (Esser et al, 2004) indicates that dimer is not cleaved Calculated RAS Energy barrier Lu, Schmidt and Bernholc, Phys. Rev. B 68, 115327 (2003)

24. Summary • Nanotube-cluster structures as ultrasensitive chemical sensors • Potential for detection of specific molecules • Piezo- and ferroelectric materials • Boron nitride nanotubes are excellent piezoelectrics, but are non-polar • Prediction of new, BN-based polymers with 100% improved properties • Building novel materials one layer at a time • Real-time optical monitoring and feedback control of growth • Nanowires on surfaces • Semiconductor/organic interfaces for nano/bio structures

26. Determination of surface structure of Si-rich SiC(001)(3x2) Results for the two-adlayer asymmetric dimer model (TAADM)are the only ones that agree with experiments Lu, Schmidt, Briggs, Bernholc, PRL 85, 4381 (2000)] Various models for Si-rich SiC(001)(3x2) are very close in energy, but comparisons between calculated and measured RAS/RDS allows for unambiguous determination of surface structure

27. Surface and bulk states contributing to RAS features of TAADM A C B Both intradimer and interdimer have to be taken into account to explain the RAS. The asymmetric dimer in top adlayer is responsible for Peak A and B. The dimers in second adlayer is responsible for the dip at 4.2 eV.

28. TAADM for SiC(001) 3x2: Further Confirmation by Recent X-ray study d1 ours exp. (Soukiassian PCSI ‘03) PRL 85, 4381 (2000) 2002 d1 = 2.24 2.42 d2 = 2.37 2.24 d3 = 2.38 2.55 Dz = 0.5 0.15 d2 d3

29. Investigate most common steps on Si(001) [Chadi, PRL 59, 1691 (1987)]

30. S A S r/r B D D B 0.002 (001)-1 O -2 O -4 O r/r D -6 O 0.001 E E 1 2 1 2 3 4 5 Energy [eV] Step contributions to RAS theory S , S and D steps • 3 eV feature (S) in spectra of vicinal Si(001) step related • DB steps dominate for miscuts larger than 40 • good agreement between experiment and theory A B B 63, 045322 (2001) Schmidt, Bechstedt, Bernholc, PRB S experiment: difference between flat & stepped surface Jaloviar et al. PRL 82 , 791 (1999) S

31. Ab initio O(N)-like quantum transport calculations • Expansion of the DFT total energy in localized, variationally optimized orbitals - – very few orbitals needed, e.g., 3-4 orbitals per carbon atom • Same computational cost as in tight-binding models for computing conductances • All operations performed on real-space grid with multigrid acceleration – fast convergence rate • Main parts scale linearly with the number of atoms • Unoccupied orbitals are essential (small O(N3)part) • Fully parallel on IBM SP and Cray T3E tested on > 1000 atoms • Forces, geometry optimization Multigrids Basis Briggs, Sullivan, Bernholc PRB 54, 14362 (1996). Fattebert, Bernholc, PRB 62, 1713 (2000). Buongiorno Nardelli, Fattebert, Bernholc, PRB 64, 245423 (2001). Shape of an optimized orbital: valence bond function

32. Macroscopic solid sample: and includes all boundary charges. Polarization is well defined but this definition cannot be used in realistic calculations. Periodic solid: Ionic part: Localized charges, easy to compute Electronic part Charges usually delocalized Polarization is ill-defined (except for Clausius-Mossotti limit) Charges are delocalized No surface charges A simple view on polarization

33. Piezoelectric polarization: Spontaneous polarization: Computing polarization of a periodic solid Modern theory of polarization R. D. King-Smith & D. Vanderbilt, PRB 1993 R. Resta, RMP 1994 1) Polarization is a multivalued quantity and its absolute value cannot be computed. 2) Polarization derivatives are well defined and can be computed. Modern approaches to compute polarization use Berry phase or Wannier function formalisms.