The formation of Self-Assembled Nanowire Arrays on Ge(001): a DFT study of Pt Induced Nanowire Arrays

Authors: Danny E. P. Vanpoucke and Geert Brocks
Book title: Symposium Z–Computational Nanoscience–How to Exploit Synergy between Predictive Simulations and Experiment
proceeding: Mater. Res. Soc. Symp. Proc. 1177, 1177-Z03-09 (2009)
doi: 10.1557/PROC-1177-Z03-09
export: bibtex
pdf: <MRS Proceeding> <arXiv>

Abstract

Nanowire (NW) arrays form spontaneously after high temperature annealing of a sub monolayer deposition of Pt on a Ge(001) surface. These NWs are a single atom wide, with a length limited only by the underlying beta-terrace to which they are uniquely connected. Using ab-initio density functional theory (DFT) calculations we study possible geometries of the NWs and substrate. Direct comparison to experiment is made via calculated scanning tunneling microscope (STM) images. Based on these images, geometries for the beta-terrace and the NWs are identified, and a formation path for the nanowires as function of increasing local Pt density is presented. We show the beta-terrace to be a dimer row surface reconstruction with a checkerboard pattern of Ge-Ge and Pt-Ge dimers. Most remarkably, comparison of calculated to experimental STM images shows the NWs to consist of germanium atoms embedded in the Pt-lined troughs of the underlying surface, contrary to what was assumed previously in experiments.

Formation of Pt-induced Ge atomic nanowires on Pt/Ge(001): A density functional theory study

Authors: Danny E. P. Vanpoucke and Geert Brocks
Journal: Phys. Rev. B 77, 241308 (2008)
doi: 10.1103/PhysRevB.77.241308
IF(2008): 3.322
export: bibtex
pdf: <Phys.Rev.B> <arXiv> <UTwentePublications>

Abstract

Pt deposited onto a Ge(001) surface gives rise to the spontaneous formation of atomic nanowires on a mixed Pt-Ge surface after high-temperature annealing. We study possible structures of the mixed surface and the nanowires by total energy density functional theory calculations. Experimental scanning-tunneling microscopy images are compared to the calculated local densities of states. On the basis of this comparison and the stability of the structures, we conclude that the formation of nanowires is driven by an increased concentration of Pt atoms in the Ge surface layers. Surprisingly, the atomic nanowires consist of Ge instead of Pt atoms.

f-orbitals

3D f-Orbitals

3D gnuplot-gif-animations of the f-orbitals S03(θ,φ), S23(θ,φ) and
S33(θ,φ). In the images presented, the blue part represents the positive phase, and the red part the negative phase. Note that in gnuplot, the spherical coordinate θ is defined as π/2 – θ. Other than that the definitions of φ and θ coincide with those used in Griffiths’ Introduction to Quantum Mechanics.

For those interested: animations in gnuplot are only available for gnuplot versions > 4.0 (which at the moment of making these animations, was still in beta version).

S03(θ,φ)


Animated f-orbitals (gnuplot) of the S03 function. Different phases indicated in red and blue.

S23(θ,φ)


Animated f-orbitals (gnuplot) of the S23 function. Different phases indicated in red and blue.

S33(θ,φ)


Animated f-orbitals (gnuplot) of the S33 function. Different phases indicated in red and blue.

d-orbitals

3D d-Orbitals

3D Maple-images of the d-orbitals S02(θ,φ), S12(θ,φ) en S22(θ,φ). Note that the spherical coordinates (θ and φ) used by Maple are reversed compared to the definitions used in Griffiths’ Introduction to Quantum Mechanics (the latter being the more standard definition in physics and mathematics courses).

S02(θ,φ)

>  plot3d(abs(3*cos(phi)*cos(phi)-1),theta=0..Pi,phi=0..2*Pi,
grid=[60,60],coords=spherical,axes=frame,labels=[x,y,z]);

Maple 3D representation of atomic d-orbitals defined by the S02 function.

S12(θ,φ)

>  plot3d(abs(sin(phi)*cos(phi)*cos(theta)),theta=0..2*Pi,phi=0..Pi,
grid=[60,60],coords=spherical,axes=frame,labels=[x,y,z]);

Maple 3D representation of atomic d-orbitals defined by the S12 function.

S22(θ,φ)

>  plot3d(abs(sin(phi)*sin(phi)*cos(2*theta)),theta=0..2*Pi,phi=0..Pi,
grid=[60,60],coords=spherical,axes=frame,labels=[x,y,z]);

Maple 3D representation of atomic d-orbitals defined by the S22 function.

Effect of exchanging θ and φ

Maple assumes the first angle given is the angle in the xy-plane; the second angle is with regard to the z-axis. This makes that you have to be very careful when giving Maple the θ and φ angles, and make sure that their definitions are the same. If the definitions
are reversed: I.e. if we use the variable θ as the variable φ and vice versa, the resulting plots become something quite different. This goes for all available plotting programs (Maple, gnuplot…); make sure you certain that what you think you enter is also what the program thinks you have entered. If not you could end up with surprising results. The same images as above, but now with θ and φ exchanged:


Wrong Maple 3D representation of atomic d-orbitals defined by the S02 function. The theta and phi angles are exchanged.
Wrong Maple 3D representation of atomic d-orbitals defined by the S12 function. The theta and phi angles are exchanged.

Wrong Maple 3D representation of atomic d-orbitals defined by the S22 function. The theta and phi angles are exchanged.