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Schottky barriers in carbon nanotube-metal contacts
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Image of FIG. 1.

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FIG. 1.

(Color online) (a) Two dimensional hexagonal lattice with basis vectors indicated by and . A chiral CNT is conceptually formed by cutting the lattice along the vectors OT and OA and connecting points O and A by rolling it into a cylinder. The vector defines the circumference of the CNT and θ its chiral angle. The solid lines indicate the circumferences of a zigzag and an armchair CNT. The grey rhombus depicts a unit cell. (b) Examples of the three different types of CNTs. Adapted from X. Zhou, “Carbon nanotube transistors, sensors, and beyond,” p 26, Ph.D. dissertation (Cornell University, 2008). Copyright © 2008, Cornell University Press.

Image of FIG. 2.

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FIG. 2.

(Color online) (a) The band dispersion of graphene. k x and k y are the wave vectors in the plane and E is the energy. The bands meet at the K points around which the dispersion is conical.20 (b) The conical band structure of graphene with a slice of allowed wave vectors that pass through the point where the two bands meet at the Fermi level. This gives the 1D band structure of a metallic CNT. (c) Slice of allowed not passing through the point where the bands meet which gives the band structure of a semiconducting CNT. (d) DOS for a (5, 5) metallic CNT with a finite DOS at the Fermi energy and a (4, 2) semiconducting CNT with zero DOS around the Fermi energy. The peaks are van Hove singularities positioned at the edges of the subbands.21 Image adapted from E. Minot, “Tuning the band structure of carbon nanotubes,” Ph.D. dissertation (Cornell University, 2004). Copyright © 2004, Cornell University Press.

Image of FIG. 3.

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FIG. 3.

(a) Energy band diagram before contact is made between a metal and a n-type semiconductor. (b) When contact is made, the Fermi levels equilibrate and a Schottky barrier arise. The image depicts a case without interface states. (c) Energy band diagram of a contact between a metal and a n-type semiconductor with interface states in the band gap at the semiconductor surface. The charge Qss in the interface states creates a dipole over a distance δ that lowers the barrier height by Δ0. The notations used are defined in the main text.54 Adapted from J. Piscator, “Influence of electron charge states in nanoelectronic building blocks,” Ph.D. dissertation, (Chalmers University of Technology, 2009). Copyright © 2009, Johan Piscator.

Image of FIG. 4.

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FIG. 4.

(Color online) A (5, 5) CNT contacted to a (111) metal surface with an end bonded (a) and a side bonded (b) configuration.66 Reprinted with permission from J. J. Palacios, A. J. Pérez-Jiménez, E. Louis, E. SanFabián, and J. A. Vergés, Phys. Rev. Lett. 90, 106801 (2003). Copyright © 2003, American Physical Society.

Image of FIG. 5.

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FIG. 5.

Conduction band minimum as a function of distance from an end bonded CNT-metal junction for different densities of interface states. Dotted, dash-dotted, dashed, and solid lines are for 0, 0.01, 0.1, and 1 states/(atom-eV), respectively. The potential barrier induced by interface states decays within a few nm into the CNT. The inset shows the corresponding result for a planar junction where the interface states shift the bands far into the CNT. Reprinted with permission from F. Léonard and J. Tersoff, Phys. Rev. Lett. 84, 4693 (2000). Copyright © 2000, American Physical Society.

Image of FIG. 6.

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FIG. 6.

(Color online) Ratio of the Schottky barrier height (Δ) and a Schottky barrier height when the Fermi level is pinned to the middle of the band gap (Δpin = Eg/2) as a function of the density of gap states for several CNTs of different diameter. Reprinted with permission from F. Léonard and A. A. Talin, Phys. Rev. Lett. 97, 026804 (2006). Copyright © 2006, American Physical Society.

Image of FIG. 7.

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FIG. 7.

Schematic band diagrams of the contacts between metals and p-doped CNTs in the absence of Fermi-level pinning. The arrows indicate the Schottky barrier heights for holes. To simplify, the same distance is used between the top of the valence band in the bulk of the CNT and the Fermi level for all CNTs. (a) Contacts to CNTs with large (solid line), intermediate (dashed line) and small (dotted line) diameters. The CNT with the largest diameter has the smallest band gap, and thus, the lowest Schottky barrier. (b) Contacts using metals with high (solid line), intermediate (dotted line), and low (dashed line) work functions. The metal with the highest work function gives the lowest Schottky barrier for holes. Adapted from Z. Chen, J. Appenzeller, J. Knoch, Y. Lin, and P. Avouris, Nano Lett. 5, 1497 (2005). Copyright © 2005, American Chemical Society.

Image of FIG. 8.

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FIG. 8.

(Color online) Self-consistent electrostatic potential for a Pd-covered (8, 0) nanotube: (a) contours of constant potential plotted in a cross section, indicated by the red line in the inset. In (b) and (c), the potential contours on two different cross sections are shown, which are indicated by lines in the inset of d), with corresponding labels. The electrostatic potential is negative close to the nuclei and positive inbetween with respect to the Fermi level. (d) The electrostatic potential along five directions passing through C and Pd atoms near the contact region, and extending from the center of the nanotube (x = −3 Å) to well within the metal region (x = 3 Å); the colors of the curves correspond to the colors of the dashed lines indicating those directions in panels b and c; the red dashed line indicates the Fermi level. Reprinted with permission from W. Zhu and E. Kaxiras, Nano Lett. 6, 1415 (2006). Copyright © 2006, American Chemical Society.

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FIG. 9.

(a) DOS of an isolated (10,0) CNT. (b) DOS of an isolated (10, 0) CNT with the same atomic structure as a CNT adsorbed on a Ti(0001) surface. For (a) and (b), the Fermi level is set to be zero. (c) Projected DOS on C for the Ti-SWCNT system. The vertical line denotes the Fermi level of the Ti- SWCNT system. For this contact, there is a finite DOS at the Fermi level and no band gap. (d) Projected DOS on C for the Al-SWCNT system. The vertical line denotes the Fermi level of the Al-SWCNT system. Reprinted with permission from T. Meng, C. Wang, and S. Wang, J. Appl. Phys. 102, 013709 (2007). Copyright © 2007, American Institute of Physics.

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FIG. 10.

(Color online) The Bader charge distribution for different CNT-metal contacts along the CNT axis. The arrows show the dipole direction. Reprinted with permission from Y. He, J. Zhang, S. Hou, Y. Wang, and Z. Yu, Appl. Phys. Lett. 94, 093107 (2009). Copyright © 2009, American Institute of Physics.

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FIG. 11.

(Color online) (a) Transfer characteristics of a CNTFET at 10 different temperatures. Schematic band diagrams show hole transport dominated by tunneling for negative Vg, thermionic emission of holes for intermediate Vg and electron transport via tunneling at high Vg. (b) Arrhenius plot with linear fits for five different gate voltages calculated from the transfer characteristics in (a). The dashed lines show the theoretical result for thermionic emission over a barrier with a height of 106, 116, and 126 meV. (c) Activation energy as a function of Vg calculated from the linear fits for T = 300–450 K in (b). The maximum of 116 meV gives an estimate of the Schottky barrier height. At high and low Vg the activation energy is reduced due to tunneling. Reprinted with permission from J. Svensson, A. A. Sourab, Y. Tarakanov, D. S. Lee, S. J. Park, S. J. Baek, Y. W. Park, and E. E. B. Campbell, Nanotechnol. 20, 175204 (2009). Copyright © 2009, Institute of Physics.

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FIG. 12.

(Color online) (a) On-current as a function of nanotube diameter for CNTFETs with Pd, Ti, and Al metal contacts. The right axis is the Schottky barrier height extracted from the on-current using theoretical modeling. The inset includes three data points for Pd contacted CNFETs from other publications. Reprinted with permission from Z. Chen, J. Appenzeller, J. Knoch, Y. Lin, and P. Avouris, Nano Lett. 5, 1497 (2005). Copyright © 2005, American Chemical Society. (b) Schottky barrier heights for holes as a function of CNT diameter in Pd-CNT contacts from activation energy measurements,81 extracted from on-state currents67 and theoretical calculations.58 The solid line corresponds to the dependence expected from the Schottky-Mott relationship (Eq. (3)).

Image of FIG. 13.

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FIG. 13.

(a) IVg characteristics at different temperatures for a CNTFET with tox = 5 nm taken at Vd = 0.5 V. The inset displays Arrhenius plots for Vg values of − 0.5, −0.3, −0.1, and +0.1 V (from the top to bottom). (b) Schottky barrier height for the same device as a function of Vg. Reprinted with permission from J. Appenzeller, M. Radosaveljević, J. Knoch, and P. Avouris, Phys. Rev. Lett. 92, 048301 (2004). Copyright © 2004, American Physical Society.

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FIG. 14.

(Color online) (a) Schottky barriers extracted using activation energy measurements: Ti (square) and Pd (circle) barrier heights as a function of gate voltage. Inset: Optical image of the device layout. The solid line denotes the location of the single CNT used for all the measurements with four different metal electrodes. (b) Schottky barrier heights for low-work-function metals Cr (square) and Hf (circle). The solid lines are least-squares fits to the data. Reprinted with permission from D. J. Perello, S. ChuLim, S. J. Chae, I. Lee, M. J. Kim, Y. H. Lee, and M. Yun, ACS Nano 4, 3103 (2010). Copyright © 2010, American Chemical Society.

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FIG. 15.

(Color online) (a) Top panels show the charge transfer between CNT and Hf (low-work-function metal) with exposure to oxygen. The bottom panels show a comparison of a typical band diagram of a surface dipole layer model and a surface inversion channel (SIC) model. In the surface dipole layer model, band bending occurs due to the formation of a dipole layer and holes tunnel through the regular Schottky barrier. In the SIC model, three distinct CNT regions are formed: metal-covered CNT, CNT inversion layer, and intrinsic channel. (b) Band diagram of electron conducting on-state at Vg = 15 V. An electron barrier between the metal-covered section of the CNT and the inversion region dominates conduction. (c) Band diagram of hole conducting on-state at Vg = −15 V. Tunneling dominates and transport is governed by direct injection of holes from the metal. (d) The band diagram at intermediate gate bias shows negative transconductance due to band-to-band tunneling resulting from a large band offset at the interface. Reprinted with permission from D. J. Perello, S. ChuLim, S. J. Chae, I. Lee, M. J. Kim, Y. H. Lee, and M. Yun, ACS Nano 4, 3103 (2010). Copyright © 2010, American Chemical Society.

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FIG. 16.

(Color online) Schottky barrier height as a function of metal work function for CNTs of different diameter. The closed and open symbols correspond to electron and hole barriers, respectively, and the half filled symbols correspond to measurements where the barrier type is unknown. The corresponding reference number is in the legend. The dashed line illustrates the expected hole Schottky barrier height for a CNT-metal contact which is unaffected by Fermi level pinning assuming a CNT work function of 4.58 eV and a diameter of 1 nm.99 (a) Experimental results. All data except those from Chen et al. 67 have been obtained using the activation energy method. The CNT diameters have been measured using AFM except for Chen et al. 67 and Appenzeller et al. 34 where only the diameters of other CNTs from the same production source were measured. (b) Theoretical results. The metal work functions for the crystal orientations used in the calculation have been used if available, otherwise work functions for polycrystalline surfaces have been used.

Image of FIG. 17.

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FIG. 17.

(Color online) Open-circuit photovoltage microscopy of the contact region in a Pd-CNT contact. (a) Open circuit voltage images of the Schottky-barrier region at different gate voltages during the transition from p-type to n-type conduction in the transistor off state. The first panel is a schematic of the device. (b) Integrated open circuit voltage signal along the length of the CNT. The metal contact is located at the origin of the position scale, and the potential was fixed there for all gate voltages. (c) Schematic of the band bending for the two threshold voltages for hole and electron conduction at Vg = 1.6 and 3.4 V. The Schottky barrier heights for electrons and holes (Φel and Φho) and the depletion width at the threshold for electron conduction (Wd) are indicated. Reprinted with permission from M. Freitag, J. C. Tsang, A. Bol, D. Yuan, J. Liu, and P. Avouris, Nano Lett. 7, 2037 (2007). Copyright © 2007, American Chemical Society.

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/content/aip/journal/jap/110/11/10.1063/1.3664139
2011-12-08
2014-04-18

Abstract

Semiconducting carbon nanotubes(CNTs) have several properties that are advantageous for field effect transistors such as high mobility, good electrostatics due to their small diameter allowing for aggressive gate length scaling and capability to withstand high current densities. However, in spite of the exceptional performance of single transistors only a few simple circuits and logic gates using CNTs have been demonstrated so far. One of the major obstacles for large scale integration of CNTs is to reliably fabricate p-type and n-type ohmic contacts. To achieve this, the nature of Schottky barriers that often form between metals and small diameter CNTs has to be fully understood. However, since experimental techniques commonly used to study contacts to bulk materials cannot be exploited and studies often have been performed on only single or a few devices there is a large discrepancy in the Schottky barrier heights reported and also several contradicting conclusions. This paper presents a comprehensive review of both theoretical and experimental results on CNT-metal contacts. The main focus is on comparisons between theoretical predictions and experimental results and identifying what needs to be done to gain further understanding of Schottky barriers in CNT-metal contacts.

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Scitation: Schottky barriers in carbon nanotube-metal contacts
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/11/10.1063/1.3664139
10.1063/1.3664139
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