Imaging the atomic orbitals of carbon atomic …

1 Imaging the atomic orbitals of carbon atomic chains with field-emission electron microscopyI. M. Mikhailovskij,*E. V. Sadanov, T. I. Mazilova, V. A. Ksenofontov, and O. A. VelicodnajaDepartment of Low Temperatures and Condensed State, National Scientific Center, Kharkov Institute for Physics and Technology,Academicheskaja, 1, Kharkov 61108, Ukraine Received 17 July 2009; revised manuscript received 2 September 2009; published 7 October 2009 A recently developed high-field technique of atomic chains preparation has made it possible to attain theultrahigh resolution of field-emission electron microscopy FEEM , which can be used to direct Imaging theintra- atomic electronic structure. By applying cryogenic FEEM, we are able to resolve the spatial configurationof atomic orbitals , which correspond to quantized states of the end atom in free-standing carbon atomic of the intra- atomic structure will make it possible to visualize generic aspects of quantum mechan-ics and also lead to approaches for a wide range of nanotechnological number s : a, , INTRODUCTIONC arbon atomic chains have remarkably high stability andfailure-current density, and are therefore especially promis-ing in all- carbon molecular electronics.

2 In all reported ap-proaches to realize free-standing carbon atomic chains, high-resolution microscopy has been exploited in process controlsand structural 4 Field-emission electronmicroscopy5and scanning tunneling microscopy STM ,6,7inparticular, have been used to direct probe the local density ofstates LDOS of single atoms, but the symmetry of the elec-tronic states could be inferred only indirectly and the intra- atomic electronic structure or the shapes of atomic orbitalsare only known from theoretical investigations. At present,there are several kinds of microscopes that are characterizedby atomic resolution in routine operating regimes. They arethe field-ion microscope FIM , the scanning tunneling mi-croscope in its various instrumental forms, and the high-resolution electron microscopy . Scanning tunneling spectros-copy and field-emission electron microscopy provides adirect method to probe the discrete electronic structure 10 Low-temperature ultrahigh-vacuum STM and FEEM can be used to perform atomi-cally localized spectroscopic measurements of a single enables the observation single quantum dots mol-ecules and atomic clusters.

3 The organic molecules are rep-resented on the phosphor screen by bright multiplets or someirregularly shaped FEEM images, known as 13 The visibility of atoms in the FEEM wasstrongly evidenced in the few special ,14 However,FIM, STM, and FEEM images of the single atoms look likerelatively wide structureless spots. These images of singleatoms can be approximated by a simple Gaussian distribu-tion, and hence it is more argued to consider such a situationin recent atomic -resolution microscopy as detecting a singleatom rather than obtaining its real image. To date, there havebeen no reported experimental observations of the spatialform of the atomic of these atomic -resolution microscopes requiresspecimens with different configurations. The resolution of anFEEM decisively depends on the geometry of sample, whichdetermines the field-enhancement factor above its tip. Thereis general trend toward enhancement of the FEEM resolutionwith the miniaturization of pointed ,15 The re-cent progress in the carbon atomic chain preparation,2hasmade it possible to attain the extremely large field-enhancement factors corresponding to subangstrom reso-lution of a field-ion ,17 The finite one-dimensional atomic chains, nanotubes, and graphenenanoribbons exhibit peculiar electronic end states localizedat their termini,10,18which hold significant promise for futurenanoelectronic device applications.

4 Scanning tunneling spec-troscopy measurements revealed the formation of quantizedelectronic end states, which transform the energy levels andthe LDOS within the surface-supported finite the space configuration of wave functionsof end states has not been characterized METHODSE xperiments were performed with the FEEM operating K in ultrahigh vacuum. An individual image spot on themicroscope screen is formed by beam of electrons originat-ing at the end atom of the chain a . Experimentalprocedures includedin situfabrication of atomic chains sup-ported by the parabolic carbon tip of less than 1 m radiusare described before in ,17 The controlled formationof carbon atomic chains on the apex of mesoscopic tips hasbeen obtained by the high-field unraveling chains were fabricated at low temperatures underhigh-vacuum conditions by the application of positive elec-tric field in a voltage range 1 15 kV. During this treatmentthe electric field was maintained constant at a level of1011V/m.

5 All FEM experiments were performed inultrahigh-vacuum chamber with a 1 10 7Pa base ultrahigh-vacuum conditions prevented the residual gasatoms from striking the surface under study. The migrationof residual gases adsorbed on the surface of the chain andsupporting carbon tip was strongly suppressed by deep freez-ing. A microchannel plate with a phosphor screen was usedas an anode. The effective diameter of the screen was 60mm. Local current characteristics of the field- electron emis-sion were determined through digital microphotometry in or-der to avoid the uncertainties connected with secondaryemission at high voltages in the complex conditions of aPHYSICAL REVIEW B80, 165404 2009 1098-0121/2009/80 16 /165404 7 2009 The American Physical Society165404-1field-emission microscope. Image-intensity variations on thescreen reflect the transverse field-emission density variationsat the chain terminus. To get statistically relevant informationon peculiarities of FEEM images of the atoms of atomicchains and to prove reliability of the method, we investigated41 different carbon atomic chains produced during high-fieldtreatment.

6 The distribution of the atomic chain length di-rectly calculated from the compression factor has a meanvalue of nm, with a variance of examine the atomic chain formation in high electricfields, we carried out calculations of the graphene unravel-ing. The numerical simulations were carried out using theclassical molecular-dynamics MD method, employing theshort-range Tersoff-Brenner bond order elec-tric force producing an axial tension is localized at the top ofthe chain. In our molecular dynamics modeling the electricforce was nN. The time unit is 10 14s andthe time step is 10 16s. The nonbonded interactionsbetween the graphite monolayers graphenes determined byweak van der Waals forces were neglected in our graphene sheet model used in the computations contains33 interacting and 30 boundary atoms arranged in the samemanner as in the zigzag nanotube. Computer modeling em-ployed rigid boundary conditions on the lateral grapheneedges.

7 Boundary atoms were kept on lattice sites. The modelis stable with respect to both homogeneous strain and RESULTS AND DISCUSSIONSFree-standing carbon atomic chains attached to the sharp-ened carbon fibers are characterized by a high mechanicalstrength and may provide the ultimately dense atomic -scalefield- electron emission. The subangstrom FIM image reso-lution of anchored carbon atomic chains made it possible todemonstrate the feasibility of quantum motion Imaging ofatomic chains and to visualize in real space their atomicwave functions near the ground quantum field-emission current can be calculated by multiplying the im-pingement rate of free electrons at the surface by appropriatepenetration coefficient. As only the states lying near theFermi level of chains contribute to the field-emission pro-cess, the supply of tunneling electrons in a FEEM is to agood approximation proportional to the density of electronicstates,15,21and a two-dimensional Imaging of the LDOS cor-responds to a spatial mapping of wave function probabilitydensities 2 The FEEM pattern on the screen is not exactly sharp,because electrons emitted from any point at the specimenhave a transverse velocity, which results in a scattering diskon the phosphor screen.

8 The resolution of the FEEM can beexpressed in terms of a parameter , which is defined as theminimal diameter of the image disk, divided by the magni-fication of the imageM. There are at least three factors,which limit the resolution of the FEEM, namely, the velocityof an electron near the Fermi level, the momentum uncer-tainty, and the geometric magnification factor depending onthe specimen end form. The resolution of FEEM images ofnanoobjects characterized byM 106is dominated by themomentum uncertainty this approximation, theresolution is given by = 2 /meM 1/2, wheremeis themass of the electron and is the time of flight from tip toscreen. The time is almost exactly equal to the flight timeof electrons at full energyeV, wereeis the charge of theelectron andVis the applied potential. A carbon atomic chaincan perfectly screen the applied electric field, resulting insharp enhancement of the electric field at the end atom. Tocalculate the resolution of FEEM images of the carbonatomic chain on the needle-shaped electrode we used the post on a paraboloid model17 a , in which thechain stands normally on the parabolic electrode with theradius of curvaturer0, having a cylindrical shape of heightland closed with a hemispherical cap with radius 0= the carbon atomic chain is conductingand hence an equipotential surface, line of force, and an ini-tial part of trajectory are orthogonal to the effective elec-tronic surface a.

9 The lines of the force emergingfrom a chain are compressed after traveling normal to itssurface for a short distance. The parabolic compression ofthe force line reduces the actual magnification. The imagemagnification of FEEM is proportional to the ratio of thespecimen-to-screen distanceRto the apex radius of thespecimen 0, that is:M=R/ 0, where is the image com-pression factor. In conventional FEEM of specimens de-scribed by a paraboloid, is about , however, for one-dimensional chains on the tips this value is the framework of this approximation, the compres-sion factor is given by = r0/L 1/2, 1 whereLis the total distance of the apex of the hemispherefrom the paraboloid surface L=l+ 0 and is a numericalFIG. 1. Color online Characterization of high-resolution field-emission electron microscopy . a A schematic drawing of electronemission from a self-standing atomic chain anchored at the graphiteparabolic tip, mounted opposite a luminescent screen.

10 B The de-pendence of theoretical resolution of FEEM on the radius of thesupporting parabolic electrode for carbon atomic chains, closed car-bon nanotubes with fullerene end caps and conventional parabolicemitters. c The calculated resolution of FEEM as a function of thelength of carbon atomic chains and REVIEW B80, 165404 2009 165404-2constant which is almost independent of configurations ofchains and supporting tips and has an approximate value apex field-enhancement factor for the chain on aparaboloid model is given by = 2+L/ 0 The fieldFat the end of the chain anchored at the apex of a parabo-loidal tip can be shown to beF=2 V/r0ln 2R/r0 . Usingthese expressions, the calculation yielded the following ex-pression for the minimal diameter of resolved emission spotsin FEEM images of free-standing linear nanoobjects: = 2 0 1/2 eme LFln 2R/r0 1/4. 2 The field strengthFin FEEM examinations of carbon atomicchains is usually varied in a narrow range about 109 resolution is determined by the uncertainty principle andthe image magnification factor mostly depending on the ra-dius 0and lengthLof the chain nanotube.