Carbon nanotubes on partially depassivated n-doped Si(100)-(2x1):H substrates
aa r X i v : . [ c ond - m a t . m e s - h a ll ] J un Carbon nanotubes on partially depassivated n -doped Si(100)-(2 × Salvador Barraza-Lopez , ∗ Peter M. Albrecht , † and Joseph W. Lyding
1. School of Physics. Georgia Institute of Technology. Atlanta GA, 30332.2. Department of Electrical and Computer Engineering and Beckman Institutefor Advanced Science and Technology. University of Illinois. Urbana IL, 61801. (Dated: October 30, 2018)We present a study on the mechanical configuration and the electronic properties of semicon-ducting carbon nanotubes supported by partially depassivated silicon substrates, as inferred fromtopographic and spectroscopic data acquired with a room-temperature ultrahigh vacuum scanningtunneling microscope and density-functional theory calculations. A mechanical distortion and dop-ing for semiconducting carbon nanotubes on Si(100)-(2 × PACS numbers: 73.22.-f, 81.07.-b, 68.37.Ef, 68.43.-h
The modifications of the intrinsic electronic andthermal properties of single-walled carbon nanotubes(SWNTs) due to their interaction with the semiconduct-ing surface by which they are supported have been thefocal point of a sizeable number of experimental[1, 2,3, 4, 5, 6, 7, 8, 9] and theoretical[4, 10, 11, 12, 13]studies in recent years due to the technological inter-est in hybrid SWNT-semiconductor devices. Dry con-tact transfer (DCT)[2] allows for the in situ depositionof SWNTs from solid sources onto technologically rele-vant surfaces, such as Si(100)[2, 3, 4, 8, 9] and the (110)surfaces of GaAs and InAs[5], forming an atomically pris-tine interface. Comprehensive studies of semiconduct-ing SWNTs (s-SWNTs) on Si(100) and Si(100)-(2 × ∼ × ∗ Electronic address: [email protected] † Electronic address: [email protected]
Ag(100)[15]), unpassivated III-V compound semiconduc-tors (GaAs(110) and InAs(110)[5]) and an ultrathin insu-lating film (NaCl(100)/Ag(100)[15]). Faithful to exper-imental conditions, our computational studies includeddopants within the Si(100) slab. Ultrahigh vacuumscanning tunneling microscope (UHV-STM) based nano-lithography on hydrogen-passivated Si(100) enables thedefinition of patterns of reactive depassivated Si[16, 17]with possible consequences for the adhesion and elec-tronic properties of the adsorbed SWNTs[3, 8, 9]. Inthis Letter, we report on the properties of isolated s-SWNTs interfaced with nanoscale regions of selectivelydepassivated Si as determined from room-temperatureUHV-STM measurements and DFT calculations.Fig. 1 summarizes the experimental observations; re-producible results were obtained for several unique s-SWNTs on partially depassivated Si(100)-(2 × n -type doped Si(100) substrates (As, 10 cm − ) were employed, and subjected to UHV H-passivation[2]. Isolated HiPco SWNTs[18] were de-posited by DCT. The STM was operated at room temper-ature in constant-current mode with the bias voltage ( V )applied to the substrate and the electrochemically etchedW tip grounded through a current ( I ) preamplifier. Par-tial surface depassivation, as seen in the filled-states to-pograph of Fig. 1(a), was achieved with the methods de-scribed in Refs. 8 and 16. Fig. 1(b) depicts the relativeSTM height along the top of the SWNT, as indicated bythe blue line in Fig. 1(a). When the SWNT is on the H-passivated substrate[2] the height fluctuations are of theorder of 0.2 ˚A, and they are directly related to the under-lying honeycomb lattice of the SWNT. The dip in the ap-parent SWNT height stressed by the horizontal red line,beyond the 0.2 ˚A fluctuations, correlates with the loca-tion where the SWNT traverses the depassivated stripe(brighter region) in Fig. 1(a). Similar trends were re-ported before[8]. Given that the substrate is degenerately n -doped, in the absence of a mechanical deformation, onewould anticipate the negative charging of the Si surfacestates within the depassivated region[19] and a protru-sion, rather than a dip, in the height profile: to maintain FIG. 1: (color online) (a) UHV-STM image ( − × × n − type alignment of the substrate d I /d V is also evident. (e) Absolute tunneling currentplot along the axis of the SWNT (blue line in Fig. 1(c). Spatial resolution: 2.5 ˚A.). To the right of the vertical dashed whiteline the tube sits on the depassivated stripe. The white traces in the profile signal a current of 1 pA, (close to the edge of thevalence and conduction bands). Horizontal dotted lines serve as guide to the eye. The midgap energy (also shown) depicts aslight n -doping of the SWNT in the section on top of the depassivated substrate. constant current, the tip should retract due to the higherdensity of states of the Si dangling bonds. Hence thedata in Fig. 1(b) provides evidence for a slight conformaldeformation (of the order of 0.5 ˚A) of the SWNT alongthe depassivated region. In a subsequent STM scan, theabsolute current vs. bias was recorded ([ − , +2] V , ∆ V = 20 mV) along the blue line in Fig. 1(c). In Fig. 1(c), wenotice the apparent widening of the s-SWNT as the STMtip moves away from the depassivated region (the regionwithin the two dashed vertical lines). This was previ-ously observed[9] and is consistent with the fact that theSWNT on Si(100)-(2 × I /d V characteristics for theSWNT shown in Fig. 1(d) are consistent with those ofa s-SWNT, as determined in Ref. 4. In Fig. 1(e), theabsolute current vs bias, as a function of position alongthe SWNT, is shown[20]. The white traces on Fig. 1(e)highlight the onset of the gap (upper and lower curves,at 1pA), as well as the midgap bias, equidistant from theconduction (upper) and valence (lower) band edges. Theaverage onset biases are − . ± .
10 V and +0 . ± . − . ± . . ± .
06 V, for an average made from 150 to 250 ˚Ain Fig. 1(e) (standard deviations are also indicated). Theaverage values indicate a ∼ L =11.29 ˚A). The supercell hassix Si monolayers. The lowermost layer is passivatedwith H in the dihydride configuration[22]. The upper- TABLE I: Parameters of the structural deformation on theSWNT (˚A).Parameter Undoped n -doped φz max φy max φz min − − φy min − − z min z ′ max most Si layer is also H passivated, but in the monohy-dride configuration. The area spanned by the super-cell is 43.21 × . The supercell employed con-tains 1024 atoms when both Si surfaces are passivatedwith hydrogen, and 1012 atoms when a stripe of depas-sivated Si is formed. The SIESTA code[23] is employedin the local density approximation (LDA) for exchange-correlation as parametrized by Perdew and Zunger[24]from the Ceperley-Alder data[25]. Double- ζ plus polar-ization numerical atomic orbitals were used to expandthe electronic wavefunctions, and a mesh cutoff of 220Ry was employed to compute the overlap integrals. Sidimer rows form an angle of 45 o with respect to the x direction, as seen in Fig. 2. A section 10 ˚A wide (yellowrectangle in Fig. 2) is rendered chemically reactive by theremoval of H atoms. Afterwards, the SWNT is placed onthis substrate, crossing the depassivated section. A singlephosphorous atom in the slab provides an n -type dopingdensity of 10 cm − . Due to the lack of covalent bond-ing we find between s-SWNTs and Si(100), a better func-tional (i.e, that found in Ref. [26]) should in principle beused. We choose LDA as it well describes (by cancellationof errors) the spacing between the s-SWNT and Si(100) FIG. 2: (color online) Top: Ball-and-stick model of the(8,4) SWNT on a partially depassivated (10 ˚A wide) n -dopedSi(100)-(2 × o angle with re-spect to the SWNT axis. Only the lower half of the SWNT isshown for clarity. Side: The side view of the system, showingin red the location of the phosporous ( n − type) dopant. Hori-zontal dashed lines serve to indicate distortion in the SWNT.Maximum distortion in SWNT occurs at x and x . Inset:The (8,4) SWNT was contracted by 3.8% (blue vertical line)in order to be placed on top of the Si substrate. This implieda 30% reduction of its gap and a 0.75% increase in diameterto compensate longitudinal compression. better than GGA functionals[27]. No corrections for basisset superposition error were added either. More details ofthe calculations can be found in Ref. 12. Commensura-bility of the system required a non-negligible longitudinalcontraction of the SWNT by 3.8%. As seen in the insetin Fig. 2, this entails a reduction of 30% in the semi-conducting gap, and an increase in diameter by 0.75% tominimize the additional forces caused by the longitudinalcontraction[28]. The entire system shown in Fig. 2 wasrelaxed employing only the Γ point until individual forcesdid not exceed 0.04 eV/˚A. Because of periodic boundaryconditions, the hydrogen stripe appears along the SWNTaxis multiple times. This is to be contrasted with exper-iment, where a single stripe is fabricated. The SWNTdisplays a periodic distortion: it appears oblate with itsmaximum distortion occurring at x and x (Fig. 2). At x , the major axis is parallel to the y − direction; while at x it is the minor axis that is parallel to the y − direction.The reason for the distortion is that the SWNT bends to-wards surface depassivated Si atoms; to relieve the moststress, this vertical elongation is accompanied by a hor-izontal elongation at the edges of the unit cell. TheSi atoms in the depassivated section also protrude to-wards the SWNT. Specific values are in Table I. Althoughsmaller than experimental values in magnitude, the DFTresults are consistent with a mechanical distortion of the FIG. 3: (a) Band structures and PDOS of systems shown inFig. 2. Flat bands around the Fermi level arise from local-ized states in the uppermost, unpassivated Si atoms. Thehighlighted PDOS of C atoms, shift downwards in energy inthe n -doped plot, along with the bands in the substrate; com-pare to the C PDOS when no dopants are present. (b) Thedoping effect observed in Fig. 1(e) is independently confirmedfrom our calculations: Both C band edges go down by 0.11 eVonce the depassivated stripe is present in the substrate. (c)The band structure of a 2-unit-cell long (8,4) SWNT in theabsence of compression, and the corresponding band struc-ture of a SWNT with the parametric distortion as in Eq. (1).An ever slight reduction of the semiconducting gap is seen,as well as the breaking of the degeneracy in the points high-lighted by horizontal arrows, also present in (a) when dopingis present. (d) Schematic view of the parametric distortion(the distortion seen is larger than that in Eq. (1) for clarity). SWNT caused by the substrate (in simulations the de-passivated stripe is 10 ˚A wide; in experiment it is about100 ˚A wide). The resulting band structure, computedwith a 4 × × k − point mesh[29], withand without dopants is given in Fig. 3(a). Flat bandsare due to dangling bonds in Si atoms which pin theFermi level. The projected density of states (PDOS) ofC atoms is highlighted in Fig. 3(a). For an undoped sub-strate, electrons from the periphery of the SWNT escapeto the substrate, and as a result the SWNT becomes p -doped as the carbon HOMO level moves upward towardsthe Fermi energy (see also Ref. 12). Upon n -doping ofthe Si substrate, the location of the carbon band edgesin Fig. 3(a) moves downwards with respect to the sys-tem’s Fermi level, as the Coulomb repulsion caused byexcess electrons in the substrate suppress to some extentelectron transfer from the SWNT.In order to provide theoretical support to the loweringof the band edges when the substrate is locally depas-sivated, the PDOS for the SWNT on a n − doped sub-strate with full H-coverage on its upper surface was ob-tained. (In this case, no further relaxation to the fullypassivated H substrate was performed upon placementof the dopant atom.) The location of the SWNT con-duction and valence band edges are shown in Fig. 3(b).It can be seen that the band edges shift down by 0.11eV when the H-depassivated strip is present. The largervalue than the one found in experiment may be due to thefact that in calculations the depassivated strip repeats in-finitely along the nanotube’s length. Discrepancies mayalso be due to the approximations in the calculations.(The change in the nanotube band gap of about 10 meVlays within our precision in computing the PDOS). Asimilar calculation was performed for the case when thesubstrate was undoped. In that case the band edges re-mained in their original positions even when the depas-sivated strip was present: The band edges in this lattercase were at − .
69 ( − .
69) eV and − .
32 ( − .
33) eV onthe full H-passivated (partially depassivated) systems.The mechanical distortion in the SWNT and its rela-tion to the electronic band structure can be understoodby introducing a parametric distortion along the y and z directions to an uncompressed, isolated SWNT: y = y [1 + 0 .
04 cos( πx /L )] ,z = z [1 + 0 .
07 sin( πx /L )] . (1)( x , y , z ) are the coordinates of an undistorted, uncom-pressed SWNT. Eq. (1) implies a periodicity in the x direction over two SWNT unit cells, aimed to reduce thelocal distortion for C atoms, while keeping a relativelysmall supercell. The dissimilar amplitude of the modu-lation along the y and z directions is responsible for the lifting of the degeneracy at k − points, highlighted by hor-izontal arrows in Fig. 3(a), n-doping and Fig. 3(c). Thisparametric distortion results in a modest reduction ofthe semiconducting gap, also consistent with results fromfull-scale calculations (Fig. 3(a)). Fig. 3(d) schematicallydepicts the shape of the SWNT after a distortion as thatshown in Eq. (1) is applied. The distortion also resultsin a shift of the nanotube’s conduction and valence bandedges away from the Γ − point, as is the case in Fig. 3(a).In conclusion, it has been shown from STM data andDFT calculations that partial depassivation of degener-ately n − doped Si(100)-(2 × [1] T. Hertel, R. E. Walkup, and P. Avouris, Phys. Rev. B , 13870 (1998).[2] P. M. Albrecht and J. W. Lyding, Appl. Phys. Lett. ,5029 (2003).[3] P. M. Albrecht and J. W. Lyding, Small , 146 (2007).[4] P. M. Albrecht, S. Barraza-Lopez, and J. W. Lyding,Nanotechnology , 095204 (2007).[5] L. B. Ruppalt, P. M. Albrecht, and J. W. Lyding, J. Vac.Sci. Technol. B , 2005 (2004); L. B. Ruppalt and J. W.Lyding, Nanotechnology , 215202 (2007).[6] A. Jensen, J. R. Hauptmann, J. Nygard, J. Sadowski,and P. E. Lindelof, Nano Lett. , 349 (2004); S. Stobbe,P. E. Lindelof, and J. Nygard, Semicond. Sci. Technol. , S10 (2006); C.-W. Liang and S. Roth, Nano Lett. ,1809 (2008).[7] Y. M. You, T. Yu, J. Kasim, H. Song, X. F. Fan, Z. H.Ni, L. Z. Cao, H. Jiang, D. Z. Shen, J. L. Kuo, and Z. X.Shen, Appl. Phys. Lett. , 103111, (2008).[8] P. M. Albrecht and J. W. Lyding, Nanotechnology ,125302 (2007).[9] P. M. Albrecht, S. Barraza-Lopez, and J. W. Lyding,Small , 1402 (2007).[10] W. Orellana, R. H. Miwa, and A. Fazzio, Phys. Rev. Lett. , 166802 (2003); Y.-H. Kim, M. J. Heben, and S. B.Zhang, Phys. Rev. Lett. , 176102 (2004); S. Berber andA. Oshiyama, Phys. Rev. Lett. , 105505 (2006); J.-Y.Lee and J.-H. Cho, Appl. Phys. Lett. , 023124 (2006);G. W. Peng, A. C. H. Huan, R. Q. Wu, L. Liu, andY. P. Feng, Phys. Rev. B , 235416 (2006); W. Orellana,Appl. Phys. Lett. , 093109 (2008); L. Yan, Q. Sun, andY. Jia, J. Phys.: Condens. Matter , 225016 (2008). [11] R. H. Miwa, W. Orellana, and A. Fazzio, Appl. Phys.Lett. , 213111 (2005).[12] S. Barraza-Lopez, P. M. Albrecht, N. A. Romero, andK. Hess, J. Appl. Phys. , 124304 (2006).[13] D. Donadio and G. Galli, Phys. Rev. Lett. , 255502(2007). Results of this work apply to metalic SWNTs,which do form covalent bonds to Si(100).[14] J. W. G. Wildoer, L. C. Venema, A. G. Rinszler,R. E. Smalley and C. Dekker, Nature , 59 (1998);T. W. Odom et al. , Nature , 62 (1998).[15] H.-J. Shin, S. Clair, Y. Kim, and M. Kawai, Appl. Phys.Lett. , 233104 (2008).[16] J. W. Lyding, T.-C. Shen, J. S. Hubacek, J. R. Tucker,and G. C. Abeln, Appl. Phys. Lett. , 2010 (1994).[17] T.-C. Shen, C. Wang, G. C. Abeln, J. R. Tucker, J. W.Lyding, Ph. Avouris, and R. E. Walkup, Science ,1590 (1995).[18] Carbon Nanotechnologies, Inc., Houston, Texas.[19] M. Lastapis, M. Martin, D. Riedel, and G. Dujardin,Phys. Rev. B , 125316 (2008).[20] The data is filtered below 1 pA, which is about a factorof two above the noise floor resulting from the tunnelingpreamplifier gain setting of 10 V/A.[21] S. Lee, G. Kim, H. Kim, B.-Y. Choi, J. Lee, B. W. Jeong,J. Ihm, Y. Kuk, and S.-J. Kahng, Phys. Rev. Lett. ,166402 (2005).[22] J. E. Northrup, Phys. Rev. B , 1419 (1991).[23] J. M. Soler, E. Artacho, J. D. Gale, A. Garc´ıa, J. Jun-quera, P. Ordej´on, and D. S´anchez-Portal, J. Phys.: Con-dens. Matter , 2745 (2002).[24] J. P Perdew and A. Zunger, Phys. Rev. B , 5048 (1981).[25] D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. , 566(1980).[26] M. Dion, H. Rydberg, E. Schr¨oder, D. C. Langreth, andB. I. Lundqvist, Phys. Rev. Lett. , 246401 (2004).[27] R. Armiento and A. E. Mattsson, Phys. Rev. B ,085108 (2005).[28] The effect of axial strain σ on the electronic structure ofSWNTs has been addressed before[30, 31]. We placed a(8,4) SWNT on a unit cell of dimensions 20˚A × × (1 + σ ) L ( σ varying from −
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