Tuning Carbon Nanotube Band Gaps with Strain Jo Sung Ph.D. Student, Dept. of Electrical Engineering & Computer Science Ken Loh Ph.D. Student, Dept. of Civil & Environmental Engineering EECS 598 Nanoelectronics Week 8 Presentation Ann Arbor, MI November 1, 2005

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Presentation Outline  Review of Carbon Nanotubes  Research Purpose and Motivation  Experimental Setup  Nanotube fabrication with CVD  Suspending the nanotube  AFM setup  Measurements  Experimental Results  Force-deflection relationship  Force/Conductance-deflection relationships  Conductance-voltage relationships  Evolution of energy-band diagram  Conclusion

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Carbon Nanotubes  Carbon nanotubes can be thought of as the rolling of a single graphene sheet  Depending on how the graphene sheet is rolled, nanotubes can be either metallic or semiconducting  n1 – n2 = 3q ~ metallic  n1 – n2 ≠ 3q ~ semiconducting

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Carbon Nanotubes  Left: Energy diagram of metallic carbon nanotubes  Right: Energy diagram of semiconducting carbon nanotubes

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  To demonstrate that strain modifies the band structure of nanotubes  Employ AFM tip to simultaneously vary the nanotube strain and to electrostatically gate the tube  Find, under strain, conductance of the nanotube can increase or decrease  Experimental setup  Measuring conductance with gold contacts  L 0 is the distance between anchoring points  z is the distance the center of the nanotube is displaced Research Purpose and Methodology

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Tombler, et al. (2000)  Pioneering experiment showed the conductance of a metallic nanotube could decrease orders of magnitude when strained by an AFM tip  Tombler, et al. (2000) ~ Hongjie Dai group  SWNT formed using CVD method  Large diameter tube (or small bundle), d = 3.1 ± 0.2 nm

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Tombler, et al. (2000)  Using t ~ 3.4 Å (van der Waals wall thickness), yields Y (Young’s Modulus) ~ 1.2 TPa  Corresponds with results from literature, where Y ~ 0.6 – 1.3 TPa  F(δ) α δ 3 relation indicates SWNT deflection can be modeled as elastic string under initial loading at its center  Assume deflected SWNT forms triangle with its original configuration, we can define  Global strain parameter  Angle between deflected nanotube and its original configuration

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Tombler, et al. (2000)  Cantilever deflection during cycle of pushing and releasing nanotube  Inset, F(δ) versus nanotube deflection curve  Fitted solid line  Arrow highlights deviation point from F(δ) α δ 3

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Tombler, et al. (2000)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Tombler, et al. (2000)  To understand results, authors performed order-N non-orthogonal tight-binding molecular-dynamics simulation of an AFM tip deflecting a (5, 5) SWNT  Electrical measurements indicated nanotube is metallic in nature, hence, MD simulation performed on a (5, 5) SWNT  Simulations carried out at 300 K  Calculated conductance evolution as nanotube is deflected  Found conductance decreased two-fold at θ = 7.0°  Conductance decreased more significantly at larger bending angles  Analysis indicated that local bonding deformation induced by AFM tip responsible for large conductance decrease  When pushed, region proximal to tip exhibits significant change in atomic bonding configuration  Nanotube responds elastically, but exhibits large bond distortion

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Tombler, et al. (2000)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Maiti, et al. (2002)  Argue that drop in conductance due to a band gap induced in the nanotube as it is axially stretched  Explore conductance change under tube bending and tip-induced deflection  Tip deflection accomplished with 15-atom Li tip  Main difference is there is an overall stretching in a tip-deformed tube  In bending, extra compressive strain on the bottom side is relieved through formation of a kink beyond a critical angle  Find that under bending and tip-deformation, carbon nanotubes essentially remain all hexagonal  Conductance drop distributed over the entire tube, rather than focused at the tip region

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Maiti, et al. (2002)  Conductance of uniformly stretched tube compared to that of a tip-deformed one.  Inset shows transmission for a uniform strain of 10% and a deformation angle of 25° as compared to an undeformed one.

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Experimental Setup  Samples consist of nanotubes suspended over a trench and clamped at both ends by electrical contacts Walters, et al. (1999) Nygard, et al. (2001)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Fabrication  Fabrication steps  Pattern catalytic islands on Si substrate  Electron-beam lithography  Deposition of Fe(NO 3 ) 3 ·9H 2 O, MoO 2 (acac) 2 and alumina nanoparticles in the liquid phase  Lift-off  Chemical vapor deposition (CVD) growth is utilized to grow nanotubes with diameters between 1 and 10 nm  Growth initiated at lithographically defined catalyst sites on Si substrate with a 500-nm oxide  Based on Kong, et al. (1998)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Kong, et al. (1998)   A: E-beam used to fabricate square holes on PMMA layer   B: 0.05-mmol Fe(NO 3 ) 3 ·9H 2 O, mmol of MoO 2, and 15-mg of alumina nanoparticles added to 15 mL methanol; drop of suspension deposited on substrate   C: Lift-off of PMMA in 1,2-dichloroethane leads to the final substrate containing catalyst islands   D: CVD of methane at 1,000 C produces SWNTs off islands

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Kong, et al. (1998)  A: SEM images show line-like substances (nanotubes) extend off island after CVD  B: High-magnification SEM image of same sample  C: Typical large-scale phase image recorded by tapping mode AFM

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Establish Electrical Contacts  Once nanotubes are grown using CVD, metal contacts are patterned using photolithography  Rosenblatt, et al. (2002)  5 nm Cr  50 – 80-nm Au  Spaced 1 – 3 μm between source and drain  Annealed at 600 C for 45 minutes in an argon environment to improve the contact resistance  Typically by an order of magnitude

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Fabrication Process  Ashing step removes photoresist residue and improves contact resistances  400 C for 10-min in Ar atmosphere  Suspend carbon nanotube  HF etch  6:1 BHF, etch rate 80-nm/min  Critical point drying  Device conductance not significantly changed by etching process

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Measurements  Dimension 3100, Digital Instruments AFM system used for simultaneous electrical measurements and AFM imaging/manipulation  Park, et al. (2002)  Sample stage modified to allow mechanical probes to make contact to the sample pads during imaging  Metallized AFM tips (Pt-Ir coated) is employed  Voltage can be applied using the AFM controller electronics  After identifying nanotube, tip brought down until it is very near or in contact with the nanotube Left: Perspective-view of a carbon nanotube on an oxide layer imaged in tapping-mode AFM

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Making Measurements  Following the process of Kong, et al. (2002), measurements can be made using AFM  In addition, Nanosensor EFM tips are utilized  Nominal radius of 20-nm  Coated with a Pt-Ir metal layer  To prove mechanical and electromechanical properties, the AFM tip is centered above a suspended nanotube using a tapping mode image for guidance  Tube moved in the z-direction while monitoring the static deflection of the cantilever and the conductance of the tube

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Force-Distance Measurements  Plot upward force on the cantilever F z as a function of tip height z while raising AFM tip  Force the tube exerts on the tip can be both positive (upward) and negative (downward)  Separated by region of near-zero force when tip is near the plane of the contacts  Curve A: d = 5.3 ± 0.5 nm, L 0 = 1.0 ± 0.1 μm  Curve B: d = 2.3 ± 0.5 nm, L 0 = 1.5 ± 0.1 μm  Curves show strong adhesion between AFM tip and nanotube  Inset shows a number of fitted YA values

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Slack  From distance between pushing and pulling onsets, ±z onset, the “slack” of a suspended nanotube can be determined  Slack defined as L tube – L 0  L tube = tube length and is greater than L 0, the separation between anchoring points  Nearly all nanotubes were slack, with typically 5 – 10-nm of slack for a 1-μm tube  Slack consistent with curved path nanotubes followed across oxide surface before etching

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Theoretical Analyses  Find force-distance curves ca nbe accurately fit by ignoring bending modulus of the tube  Assume linear proportionality between nanotube tension T and axial strain σ  Write proportionality constant as YA  Y = effective Young’s modulus  A = effective cross-sectional area  For |z| ≥ z onset and F z (z) = 0 for |z| ≤ z onset  For |z| ≥ z onset  Magnitude of YA values and linearity with diameter d suggests that a single shell is carrying the mechanical load, even for large diameter tubes likely having multiple walls

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Derivation of Force-Deflection Equation L/2 T θ T sinθ Since the structure is symmetric, the total resultant vertical component is From Hooke’s Law, we know that: where, σ = stress, ε = strain, and E = Young’s Modulus And, z L/2 x By Pythagorean’s Theorem, we can calculate x: Again, due to symmetry: Thus, strain =

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Salvetat, et al. (1999)  Magnitude of YA values are similar to what Salvetat, et al. (1999) have determined  To measure Young’s modulus, they first determine the location of a nanotube using an AFM tip  Determine its diameter, suspended length, and deflection midway along the suspended length  From a series of images taken at different loads  d, deflection, can be calculated as such (from small-deformation theory)  F is the applied force, I is the second moment-of-area, a = 192 for a clamped beam  For a hollow cylinder, I can be computed as such  R o = outer radius, R i = inner radius RoRo RiRi

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Mechanics of Materials  Calculating deflection of idealized-beam elements  Simply-supported beam  Fixed-fixed beam F L/2 F

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Salvetat, et al. (1999)  Reversibility of the tube deflection and the linearity of the d-F curve shows that the nanotube response is linearly elastic  Slope of the curve gives directly the Young’s modulus of the CNT  Found to be 810 ± 410 GPa (taken as a minimum value)

Tuning Carbon Nanotube Band Gaps with Strain (Part II) Ken Loh Ph.D. Student, Dept. of Civil & Environmental Engineering Sung Hyun Jo Ph.D. Student, Dept. of Electrical Engineering & Computer Science EECS 598 Nanoelectronics Week 8 Presentation Ann Arbor, MI November 1, 2005

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Deflection Force & Conductance  When cantilever is deflected, G is lowered  When Strained  Two s.c. tubes: increasing G,  One s.c. tube & two metallic tubes: decreasing G  Two metallic tubes: nearly same G  Why?

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  The gate voltage versus the conductance  The tube can be turned on by applying negative voltage, and turned off with a positive voltage. The device turns on at a negative voltages because holes are added to the tube.  Because the contact resistance is quite high, the conductance eventually stops increasing and becomes constant. Conductance of the S.C. CNTs

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Conductance of the S.C. CNTs  No surface state problem  Tubes are inherently two dimensional materials and the cylinder as no edges  The conductance is limited by any barriers that holes see as they traverse the tube  The resistance of the tube will be dominated by the highest barriers in the tube  Barriers – due to structural defects, atoms adsorbed on the tube or localized charges

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  The map of barriers to conduction to be produced  The tip of a scanning probe microscope can be used to map the barriers. The conductance of tubes is measured as the positively biased tip is scanned over the sample. The bright spots are where the tip decreased the conductance, with greater intensity corresponding to greater change in the conductance. Conductance of the S.C. CNTs

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Conductance of the Metallic CNTs  The conductance of the metallic carbon nano tubes is not noticeably affected by the addition of a carriers.  Many groups have made tubes with conductances that are between 25% and 50% of the value of 4e 2 /h that has been predicted for perfectly conducting ballistic nanotubes.  Very long mean free path (~um)  At low temperature, the tube acts like a long box (quantum dot).

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  Nanotube quantum dots reveal a great deal about the behaviour of carriers in nanotubes  Periodic oscillation: the electronic states are extended along the entire length of the tube – if there were many scattering, the oscillation would be less regular  Electrons can travel for long distance without being back scattered – fundamental difference between conventional metal (e.g. Cu) and nanotube Conductance of the Metallic CNTs

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  To understand the characteristic of strain versus conductance, we need to investigate the band structure of the NT  Tip is used as a gate Metallic CNT Semiconducting CNT Carrier depletion

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Deformed Carbon Nanotube  When deformed, we need to consider the change in k F relative to k lines  | k F – k | t L. Yang et al., Phys. Rev. Lett (2000)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 The Effect of Strain on the E g  The rate of change of band gap with respect to strain

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  Semiconducting NTs  p = 1  Strain causes G to decrease  p = -1  Strain causes G to increase  If G does not change L. Yang et al., Phys. Rev. Lett (2000) P = 1 P = -1

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 The Effect of Strain on Bandgap  Density of States (a) (17 0) p= -1 (b) (18 0) p= 0 (c) (19 0) p= 1 Strain (%) E (eV) DOS

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  Initially P-type contact S. J. Tans et al., Nature (1998) Work function: Pt(5.7 eV), CNT(~4.5eV) Fermi level pinning

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  Field effect doping  e.g. J. Park et al., APL (2001)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  Tip gate affects the center part of the tube & the sections near the contacts are held p-type P P P P P N Tunneling occurs Few electrons & large barrier

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  Potassium doping of individual SWNTs: n-type tubes C.Zhou et al., Science (2000)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Possible Reasons for Initially P-type  P-type  Oxygen increases the conductivity of the CNT  It is believed that the metal electrodes as well as chemical species absorbed on the tube “dope” the tube to p-type  Fermi-level pinning

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005  Two terminal conductance (Metallic CNTs)  Landauer’s equation  If no scattering inside the tube & contacts  As for semiconducting CNTs or when there are strains the band gap term must be included in the conductance modeling P. Avouris. MRS Bulletin/June (2004)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Modeling of the R( )  The low-bias resistance of the device  From the fitting model  From the = Junction resistance

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Results  From the measured value

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Selective Bandgap Engineering  Fullerenes or endohedral metallofullerenes such as Gd encapsulated inside C82 (GdMF) can be inserted into SWNTs  e.g. keeping GdMFs with SWNTs in a sealed glass ampoule at 500C for 3 days J. Lee. Nature (2002)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Unified Model  The band gap change under small strain L. Yang et al., Phys. Rev. Lett (2000)

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Conclusion  The 1D character of CNTs greatly reduces the phase space for scattering  The effective way for bandgap engineering of NTs: the strain  Applying selective strain on different sections: NT heterostructures  Estimating the chiral angle by measurement of the - useful for small-diameter tubes

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Appendix A: Poisson’s Ratio  Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Tensile deformation is considered positive and compressive deformation is considered negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio.

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Appendix B: Quantum of Conductance  The conductivity  For a 1-D conductor with one channel

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005 Appendix C: Tight Binding Model

Tuning Carbon Nanotube Band Gap With Strain EECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005