Lecture 1: Introduction to NEMS

Transcription

1 Lecture 1: Introduction to NEMS Horacio D. Espinosa Acknowledgments: NSF-NIT, NSF-NSEC

2 Int. Technology oadmap for Semiconductors Technology Tmi n(s) Tmax (s) CDmin (m) CDmax (m) Energy J/op Cost min $/gate Cost max $/gate NEMS 1E-7 1E-3 1E-8 1E-7 1E-1 1E-8 1E-5 Molecular 1E-8 1E-3 1E-9 5E-9 1E- 1E-1 1E-1

3 ecent Developments In Nanoelectronics First CNT Single-Electron-Transistor (SET) by depositing of a CNT on top of Au electrodes with SiO as the dielectric layer. Local barrier induced with atomic force microscope (AFM) Dekker, et al, Science, 1, 93, 76 Logic Circuit with Carbon Nanotube Transistor Adrian Bachtold, et al, Science, 1, 94, 1317

4 Nanodevices in the Life Sciences NW or CNT sensors Principle: Biologically gated transistors Nano size is needed to achieve high signal to noise ratios. Largest multiplexing capability. Micro/Nano Cantilevers Principle: Molecular binding deflects the cantilevers and introduces a frequency shift. Good multiplexing capability. Challenges Fabrication yield Need for covalent binding of biomolecules deconvolution of noise from signal, especially from nonspecific molecules. M. Ferrari, Nature, Vol. 5, 5

5 NanoElectroMechanical Systems ueckes, et al., Science, 89, U i W/Pt CNT or NW NANTEO Cantilever NEMS Si 3 N 4 Au Principle for bi- stability van der Waals Latching Electrostatic forces with feedback control SiO Gap < 1 nm ~ 1-1 nm Si AM type Non-Volatile Volatile Ke and Espinosa, App. Phys. Letts., 85(4), 681

6 Other NEMS Examples CNT nanorelay device Schematic diagrams of a CNT nanorelay device (A) (eprinted with permission from [13], J. Kinaret, et al., Appl. Phys. Lett. 8, 187 ()., American Institute of Physics) and SEM image of a fabricated nanorelay device (B) (eprinted with permission from [4], S. Lee, et al., Nano Lett. 4, 7 (4). 4, American Chemical Society). I-V sg characteristics of a nanotube relay initially suspended approximately 8 nm above the gate and drain electrodes. eprinted with permission from S. Lee, et al., Nano Lett. 4, 7 (4). 4, American Chemical Society.

7 Tunable oscillators Other NEMS Examples SEM image of a suspended device (top) and a schematic of device geometry (bottom). Scale bar, 3 nm. The sides of the trench, typically µm wide and 5 nm deep, are marked with dashed lines. A suspended nanotube can be seen bridging the trench. eprinted with permission from [3], V. Sazonova, et al., Nature 431, 84 (4). 4, Nature Publishing Group. Measurements of resonant response. (a) Detected current as a function of driving frequency; (b)- (c) Detected current as a function of gate voltage Vg and frequency for devices 1 and ; (d) Theoretical predictions for the dependence of vibration frequency on gate voltage for a representative device. eprinted with permission from V. Sazonova, et al., Nature 431, 84 (4). 4, Nature Publishing Group.

8 otational motors Other NEMS Examples Series of SEM images showing the actuator rotor plate at different angular displacements. The schematic diagrams located beneath each SEM image illustrate a cross-sectional view of the position of the nanotube/rotor-plate assembly. Scale bar, 3 nm. eprinted with permission from A. M. Fennimore, et al., Nature 44, 48 (3). 3, Nature Publishing Group.

9 Case Study: Nanocantilever Switch Si 3 N 4 W/Pt U i CNT or NW Au Operation Electrostatic force deflects the cantilever until pull-in leading to a lower stable equilibrium position, current in the circuit i>. When the cantilever is deflected in the upper stable equilibrium position, current in the circuit i= SiO Nano Device Features Si eliable ON and OFF states due to the feedback control mechanism U U i = i > OFF ON Operating frequency (1 to 1MHz) Critical Dimension (1-1 nm) C.-H. Ke, et al., App. Phys. Letts, 85(4), 681

10 van der Waals Forces A B ext SWNT int t MWNT graphene d n = 1 n = n = 3 graphene d n = 1 n = n = 3 n = N n = N van der Waals integration of a SWNT (A) and MWNT(B) over a graphite ground plane, M. Desquenes,, et al., Nanotechnology 13, 1 ()., Institute of Physics.

11 Continuum Approximation The Lennard-Jones potential between two atoms i and j is given by C C φ ij = (1) r r 1 1 ij 6 6 ij A Where r ij is the distance between atoms i and j and C 6 and C 1 are attractive and repulsive constants, respectively. For the carboncarbon interaction, C 6 = 15. evå 6, C 1 = 4.1 kevå 1, and the equilibrium spacing r = Å. SWNT A continuum model was established to compute the van der Waals energy by the double volume integral of the Lennard- Jones potential, that is, E vdw = ν1 ν n1n r 1 C 1 6 ( ν, ν ) r ( ν, ν ) 1 Let us consider a single walled carbon nanotube (SWNT) freestanding above a ground plane consisting of layers of graphite sheets, with interlayer distance d = 3.35 Å. The energy per unit length of the nanotube is given by C 1 6 dν1dν () graphene d n = 1 n = n = 3 n = N E vdw L = πσ N π π n= 1 1 C 1 [( n 1)d + r + + sinθ ] 4[ ( n 1)d + r + + sinθ ] init 1 C init 6 4 dθ (3) where, L is the length of the nanotube, is the radius of the nanotube, is the distance between the bottom of nanotube and the top graphene sheet, N is the number of graphene sheets and σ= 38 nm - is the graphene surface density.

12 Continuum Approximation When r init is much larger than the equilibrium spacing r, the repulsive component can be ignored and Eq. (3) can be simplified as E vdw L = C σ π 6 ( N 1) d + rinit ( + r)[ 3 + ( r + ) ] 7 / [ ( r + ) ] r= rinit (4) For a multi-walled carbon nanotube, as illustrated in the figure to the left, the energy per unit length can be obtained by summing up the interaction between all separate shells and layers. E C σ π + = ext ( N 1) d rinit vdw 6 L = int r= rinit ( + r)[ 3 + ( r + ) ] 7 / [( r + ) ] (5) B ext MWNT int t graphene d n = 1 n = n = 3 n = N Comparison of the continuum van der Waals energy given by Eq. (1) with the discrete pairwise summation given by Eq. (4).

13 x Electrostatic Force Charge Distribution along the Nanotube (I) L/ L/ The governing equations include: V y H z The Laplace s Equation: V V V V = + + x y z = The electric field strength is given by, Schematic of a biased nanotube with radius and length L above a grounded infinite plane. V is the biased voltage E = - V The charge density per unit length V = V V = Ω 1 Ω ρ L = ρ Ads = ρ Ads s s V = -V Ω The surface charge density is ρ A =ε E n Computational domain

14 BEM Electrostatic Analysis Electrostatic Force Charge Distribution along the Nanotube (II) ρ L [pc/μm ] ρ L Charge per unit length (pc/m) Position (μm) Q se Q se z -L/ L/ Through a parametric study, we found that if L>> L * Total Charge where ρ Q = ρ L = 1 cosh L L + Q c πε V ( 1+ H / ) Charge distribution for a biased armchair carbon nanotube. The parameters are ext = 9.15nm, H = 1nm and L = 1µm. Q c.85ρ L[ (H+) ] 1/3 L* is the minimum length beyond which the end charge distribution function does not change. It is related to and H, see Ke and Espinosa, JAM, Vol.7, 5.

15 q elec 1) Mechanical Equation Continuum theory 1 = V EI Electrostatic: dc( r) dr van der Waals: Time Independent Analysis 4 d w 4 dx ; = qelec ( r) + q C( r) = C d vdw ( r) ( r){1 +.85[( H Uniform charge Dequesnes et al., Nanotechnology, 13,, pp q n vdw 1 d = dr and n E L vdw are the density of ; E vdw + ext ) V ext ] 1/3 H δ ( x x Concentrated charge C1 = n1n 1 vv 1 r 1 atoms in volumes v x tip L )}; C 6 ( v, v ) r ( v, v ) 1 and v C 1 6 d dv q 1 = dv cosh r 1 πε (1 + w r ext ) E is the Young s Modulus; I is the moment of inertia; w is the deflection of the cantilever; r is the distance between the axis of the cantilever to the ground; H is the step height, C d is the capacitance for an infinite long cylinder, ext is the outer radius of the cylinder; L is the length; q vdw is the van der Waals distributed force, ε ο is the permittivity in vacuum.

16 Time Independent Analysis ) Electrical Equations Lumped Model x L q w A U Equivalent circuit V H r T V V U T = 1- V U Tunneling resistance T = exp( / λ) Tunneling current i = V exp(- / 1 λ ) ; λ = 1. φ(ev) o -1 A U is the total applied voltage; V is the voltage applied to the cantilever; is the contact resistance; is the feedback resistor; Δ is the gap between the cantilever and the ground; Φ is the work function( for MWNT Φ = 5eV)

17 Device Characteristics 1 (a) 1-6 (b) (nm) 1 1 Pull-out Pull-in i (A) Pull-out Pull-in U (volt) U (volt) The pull-in and pull-out processes plus the lower and upper stable equilibrium positions form the characteristic curve of the device with a hysteretic loop. E = 1. TPa, ext =9.15nm, int =6nm, L=5nm, H = 1nm, o =1KΩ and = 1GΩ.

18 Key Issues in the Device Design 1) van der Waal (vdw) force - If the length of cantilever is long enough, the vdw force may hold the cantilever down ( stiction ) ) Condition on the Feedback esistor 3) Thermal Vibration V V V PI exp( / λ) The CNT tip vibration amplitude is A = A = 1.86 T = 3 K A =. T = 4. K 3 L kt E( 4 ext int ) where k is Boltzmann constant (1.38x1-3 J/K) and T is the temperature in Kelvins Treacy et al, Nature, 381,

19 V H x s Finite Kinematics and Charge Concentration Effects L q Pull-in Analytical Model w c Energy Method: the total potential energy of the system is: W ( c) = E ( c) E ( c) E ( c) elast elec vdw E E elast = () c EI L dϑ ds L devdw ds ds ( w) ds E elec () c w( x) = L x L vdw V PI k 1+ k 1+ k FK TIP ; ; H ln L H ext deelec ds EI ε c ( w) ds k.85 Equilibrium: Instability: FK 8 H ; k ; 9 L d dw dc W dc ( c) ( c) = = ( ( H ) ) TIP 55 ext + k. L FK refers to finite kinematics; TIP refers to concentrated charge Ke et al., J. Mech. Phys. Solids, 53, 1314 (5) ext 1 3

20 Time Dependent Analysis - Device Dynamics Objective: examine the time response of pull-in and pull-out processes x L q elec C CNT C I ; CNT much smaller than I CNT U H r U A C V C CNT T Governing Equations (1) r r r ρa + c + EI = q elec + q 4 vdw t t x πaρω c where = Q (3) C ( x,t) 4 CNT () U = 1+ C CNT Equivalent circuit for short and small diameter nanotubes L T dc + dt CNT ( t) = C( r( x, t)) dx V + ( C + C ) CNT dv dt 1 / { 1+. ( ext ( ext + H ) ) ( x L) } 1 3 ( 1+ r( x,t) / ) = 85 δ 1 cosh ext

21 Pull-in esponse Applied voltage signal Tip Position vs. time Time esponse U U Fastest time response for minimized C and t Current vs. time V max = 63m/s U V max =8m/s U E = 1. TPa, ext =9.15 nm, int =6 nm, L= 5 nm, H = 1 nm, =1 KΩ and =1 GΩ, Q = 5, C =C CNT ()

22 Device Level In-Situ SEM Experiments Objective: experimentally identify pull-in, pull-out and I-V characteristic curve SEM Gun SEM chamber Flange i Probe Coaxial cable Triaxial cable U CNT SMU w/ PA Keithley SMU w/ PA 4 SCS BNC-TX adapter The resolution of current measurement is up to.1fa

23 Flange Nanomanipulation A customized SEM flange holding a 3-D nanomanipulator manufactured by Klocke Nanotechnik Inc. with two electric feedthroughs, a 3-axis PZT actuator, and a tungsten probe mounted to the manipulator s probe holder. probe PZT actuator Feedthroughs SEM images of the manipulation of carbon nanotubes using the 3D Klocke Nanotechnik nanomanipulator. (A) Manipulator probe is approaching a protruding nanotube. The sample is dried nanotube solution on top of a TEM copper grid. (B) Manipulator probe makes contact with the free end of the nanotube and the nanotube is welded to the probe by EBID of platinum. (C) A single nanotube mounted to the manipulator probe. (A) (B) (C)

24 In-Situ SEM Pull-in Experiments 93 o SEM Gun CNT Probe Gap (µm) V PI k 1+ k 1+ k FK TIP H ln L H ext EI ε E = 1. TPa, = 3.5 nm, L = 6.8 µm, H = 3 µm V PI =48 Volts Electrode 1.5 Experimental Data Analytical esult When finite kinematics is neglected, error is 7%. U Voltage (volt) When charge concentration is neglected, error is 15%. U = 1 Volt 5µm U = 3 Volts 5µm U = 46 Volts 5µm H

25 Pull-in/Pull in/pull-out Experiment and I-V I V curve U = U = 3 Volts U = 1 Volts 3 μm 3 μm 3 μm I (A ) 1.E-7 1.E-8 1.E-9 1.E-1 1.E-11 1.E-1 1.E-13 1.E-14 Experiment Measurement Theoretical Prediction U (volt) Parameter used in theoretical prediction Length of nanotube L = 9 µm (before pull-in) L = 7.9 µm (after pull-in) Outer diameter: 5 nm; inner diameter:15 nm E = 1TPa, Feedback resistor = 1 GΩ Contact resistance 5 Ω

26 L = 13. µm Failure Modes L = 11.3 µm 3 μm 3 μm Original L = 9. µm L = 7.9 µm After 1 st pull-in/pull-out 3 μm L = 7. µm 3 μm 3 μm 3 μm After nd pull-in/pull-out After 3 rd pull-in/pull-out After 4 th pull-in/pull-out

27 Failure Modes L = 9. µm U IN =3 V L = 7.9 µm L = 7. µm After nd P in -P out After 3 rd P in -P out 3 μm After 4 th P in -P out Possible Failure Modes - Fracture - Sublimation 3 µm 3 µm 3 nm Pull-in voltage: U=7 volts ; V max ~ 3 m/s

28 Failure Modes - Fracture (a) Before actuation (b) After second pull-in/pull in/pull-out (c) After lateral displacement of nanomanipulator

29 Failure Mode Dynamic Buckling? 4 r r r ρa + [ fc ( x, t) ] + EI = qelec + q 4 t x x x vdw Gladden et al, PL, Vol σ = fc fc.58µ N = = = 3. 64GPa A π d π *4nm*.335nm ext α CNT f c (x,t) Moment(N*m) 8.E-14 6.E-14 4.E-14.E-14.E+ -.E-14-4.E-14-6.E-14 t=.191ns t=.ns t=.5ns t=.7ns t=3.ns t=3.5ns f λ = πd c V T = π *8e 9 3e9 sqrt =.968µ m -8.E x(nm) Breaking points at n 4 λ λ = 1.484µ m ; ; 3λ 4 =.6µ m

30 Discussion Density-Functional Calculations of charge distribution reveal that there is a threshold Voltage beyond which Coulomb repulsion of concentrated charges lead to unstable CNT ends with C atom ejection. This voltage is a function of the tube end (open/close) and length. Capped SWNTs can withstand voltages as high as 1 Volts. However, thermal motion induced by charge transport and mechanical deformation can destabilize the tube at lower voltages. Observed failure is likely the result from both high current densities and mechanical impact effects. To decouple these effects AFM tunneling measurements should be pursued. Multiscale electro-mechanical modeling is also needed to gain insight into deformation and electronic states. Ultimately, dimensionless maps defining regions of robust device operation need to be developed. elaxed atomic positions and bonding for (5,5) arm chair SWNT; Keblinski et al., PL, Vol. 89,.

31 Nanofabrication of NEMS Arrays Si wafter with SiN 4 layer, patterned Au/Cr layer and PECVD SiO layer Au/Cr Si 3 N 4 SiO Si Surface functionalization using NFP Directed Self assembly of CNTs/NWs in solution E-beam evaporation of Au/Cr and pattern with e-beam lithography ao et al, Nature, Vol. 45, 3 elease the CNT by removing the SiO layer using wet etching (HF) or plasma etching Schematic of fabrication steps

32 1-D D Array of Nano Fountain Probes Microchannels eservoir Substrate a b LFM images of areas (15 µm x 15 µm) patterned with 16- mercaptohexadecanoic (MHA) and H-Perfluorododecane- 1-thiol (PFD)

33 SWCNT Assembly by DPN patterning MHA patterns with ODT passivation directs the self assembly of SWCNTs Preliminary NEMS devices fabricated by lithography and directed self assembly of SWCNTs SWCNTs

34 Direct CVD Growth Electric-field-directed growth of freestanding single-walled nanotubes. Y. Zhang, et al., Appl. Phys. Lett. 79, 3155 (1). 1, American Institute of Physics.

35 Conclusions We reviewed some advances and applications of Nanoelectronics and Nanoelectromechanical Systems We reviewed the in-situ SEM electromechanical testing of a NEMS bi-stable switch. The study revealed failure modes as a function of current density and mechanical deformation. Additional experiments and models are needed to define design maps and optimal operation conditions. Scaling up the nanofabrication of NEMS into arrays appears feasible. New tools such as the Nano Fountain Probe Array appears promising for the patterning of various inorganic and organic molecular inks that can be employed in the directed self-assembly of CNTs or NWs with a control of length, orientation and characteristic dimensions.

36 Acknowledgments: Y. Zhu, Northwestern University C-H. Ke, Northwestern University N. Moldovan, Northwestern University K-H. Kim, Northwestern University B. Peng, Northwestern University T. Belytschko, Northwestern University G. Schatz, Northwestern University C. Mirkin, Northwestern University Z. Bazant, Northwestern University N. Pugno, Politecnico di Torino P. Zapol, ANL O. Auciello, ANL I. Petrov, UIUC J. Mahon, UIUC M. Marshall, UIUC B. Prorok, Aurburn University National Science Foundation-NIT, J. Larsen-Basse, K. Chong Federal Aviation Administration, J. Newcomb NSF-NSEC at NU for Integrated Nanopatterning and Detection Technology Office of Naval esearch, L. Kabakoff