Nanoelectromechanical Systems Continuum Solid: Equations of Motion

PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

NEMS: multiterminal mechanical devices

introduction to nano- ELECTRICAL ELECTRICAL input output INPUT mechanical OUTPUT transducer mechanical transducer nanoelectromechanical systems SIGNAL mechanical SIGNAL stimulus system response

mechanical perturbation

ELECTRICAL control CONTROL transducer SIGNAL

mechanical domain Michael Roukes -signal processing Kavli Nanoscience Institute Physics, Applied Physics, & -measurement / sensing Bioengineering -computation California Institute of Technology

Continuum Solid: Equations of Motion Isotropic solid with local displacement u(r,t) ∂2u ρ = ()()λ + μ ∇ ∇ ⋅u + μ∇2u μ(3λ + 2μ) ∂t 2 Young’s modulus E = Fundamentals: important concepts λ + μ λ, μ are the Lamé constants: λ – beam mechanics (review) λ = c μ = c = (c −c )/2 Poisson ratio ν = 12 44 11 12 2λ + 2μ – responsivity sensitivity –noise – dynamic range Boundary conditions define stress or strain: – nonlinear response Fixed boundary: u(rb ,t)= 0 for rb on boundary Stress-free boundary: T (rb ,t)⋅nˆ = 0 for rb on boundary, n ˆ unit normal Tii = (λ + 2μ)∇ ⋅u nˆ

1 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Flexural Beams: Equations of Motion Flexural Beams: Solutions

Yn (x,t)= an (cosβn x − coshβn x)+ bn (sin βn x − sinh βn x)

Doubly-clamped beam Cantilevered beam Doubly-clamped beam Y(x,t) an ≈ bn (a1 = 1.018b1,a2 = 0.9992b2 ,a3 = 1.000b3 …) Euler-Bernoulli theory: length >> width, thickness … βn L = 4.730, 7.853,10.996 x • Neutral axis displacement Y ωn = E 12ρ βnt • Width w, thickness t (along y)

• Density ρ, modulus E = (3λ+2μ)/(λ+μ) Y(x,t) 1234

∂2Y wt3 ∂4Y x ρwt + E = 0 ∂t 2 12 ∂x4

Boundaries: Clamped end: Y = 0, Y’ = 0 Free end: Y’’ = 0, Y’’’ = 0

See Timoshenko, Vibration Problems in Engineering (1974) © M.L. Roukes 2005 Ph/EE 118c, Ch227 — Micro- and Nanoscale Sensors © M.L. Roukes 2005 Ph/EE 118c, Ch227 — Micro- and Nanoscale Sensors

Flexural Beams: Solutions Flexural Beams: Damped Harmonic Motion

undamped oscillator Yn (x,t)= an (cosβn x − coshβn x)+ bn (sin βn x − sinh βn x)

amplitude

Cantilevered beam time an ≈ −bn ()a1 = −1.362b1,a2 = −0.982b2,a3 = −1.008b3 … Y(x,t) damped decay

βnL = 1.875,4.694,7.855… ωn = E 12ρ βnt exp(-ω t/2Q) x amplitude 0

1 2 3 frequency response

ω0/Q Q resonance frequency:

amplitude 1/2 ω0~ (Eeff / ρ) ω0 quality factor: frequency Q ~ 1/Δ © M.L. Roukes 2005 Ph/EE 118c, Ch227 — Micro- and Nanoscale Sensors © M.L. Roukes 2005 Ph/EE 118c, Ch227 — Micro- and Nanoscale Sensors

2 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Single Mode Model: Damped SHO Single Mode Model: Damped SHO A damped, simple harmonic oscillator model describes the flexural motion of a A damped, simple harmonic oscillator model describes the flexural motion of a beam in the vicinity of the fundamental resonance with an accuracy to within beam in the vicinity of the fundamental resonance with an accuracy to within 1% for Q>10. 1% for Q>10. displacement applied force displacement applied force

F ()ω F ()ω complex displacement complex displacement x()ω = 2 x()ω = 2 response function: []()KMi−−ω effω γ eff ω response function: []()KMi−−ω effω γ eff ω

Q>>1 ⇒ resonant mechanical response

comments: 106 10000 force constant Q =100 force constant 5 Q =1000 100 • this is a “dynamical version” of 10 =300

=100 1 4 Hooke’s law x = F /k 2 applied Parameters: 10 =30 0.01 Parameters: )| =10

ω 3 • the complex AC mechanical responsivity effective mass, M ( 10 0.0001 effective mass, M eff A 0.1 1 10 eff | 2 is defined as xF () ω =ℜ ()() ωω , dynamic stiffness (for point 10 dynamic stiffness (for point 1 loading at beam’s center), K 101 loading at beam’s center), K i.e. ℜ=()ω eff eff 2 0 10 []()KMi−−ω effω γ eff ω quality factor, Q 0.8 0.9 1.0 1.1 1.2 1.3 quality factor, Q Normalized Frequency, ω /ω © M.L. Roukes 2005 Ph/EE 118c, Ch227 — Micro- and Nanoscale Sensors © M.L. Roukes 2005 Ph/EE 118c, Ch227 0— Micro- and Nanoscale Sensors

Single Mode Model: Damped SHO Single Mode Model: Cantilever DSHO A damped, simple harmonic oscillator model describes the flexural motion of a ω0 Eeff t beam in the vicinity of the fundamental resonance with an accuracy to within Resonance frequency (cantilever): = 0.159 2π ρ L2 1% for Q>10. 3 ⎛⎞t eff. force constant (cantilever): K = (0.2575) Ew F ()ω eff ⎜⎟ displacement x ()ω = ⎝⎠L 2 -1 response function: [()]()KM−−ω effωω iγ eff ω Dissipation: Q 2 Effective mass: Meff = keff / ω0 For the fundamental-mode response of a simple doubly-clamped beam, DC Response: ΔY = F/ Keff (constant force)

effective mass: M eff = 0.735ltwρ N.B. For this simple treatment of beam 3 3 Resonant response: ΔY = Q F / Keff (at ω0) dynamic stiffness: κ eff = 32Et w / l elasticity, all of these factors apply only 2 to the specific mode considered. resonance frequency: ω0 = 2π (1.05) E / ρ (t / l ) ΔY eiωt Here, l × t × w are the beam’s dimensions, E is Young’s modulus and ρ is the mass density of the F/K QF/Keff beam. The above assumes the material is isotropic; for single-crystal devices anisotropy in the eff amplitude elastic constants yields resonance frequency dependence upon crystallographic orientation. iωt F e frequency ω © M.L. Roukes 2005 Ph/EE 118c, Ch227 — Micro- and Nanoscale Sensors © M.L. Roukes 2005 Ph/EE 118c, Ch227 — Micro- and Nanoscale Sensors

3 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Fluctuation-Dissipation Theorem: Displacement and Force Noise Thermomechanical Noise x()ω = ℜ(ω)F(ω) ω0/Q Thermal force spectral density associated with finite Q: Q/k 1/k keff Response SF ()ν = 4kBTN TN = noise temperature ω0Q force spectral density

1/2 Displacement spectral density S (ω) for force density S (ω) (4kkBT/ω0Q) x F

2 ω 4kT Force Noise 0 BN SSxF()ωω=ℜ() = 2 ωω 2 QM eff ωω22−+0 ()0 ()Q displacement spectral density 1/2

(4ω Qk T) This yields thermal equilibrium of the average total energy: 0 B Displacement E = T +U = k T B N Frequency

The two key attributes for sensing: Displacement and Force Noise • responsivity x()ω = ℜ ω ()()F ω metric quantifying transduction (conversion between signal domains; generalization of “gain”) ω0/Q Q/k 1/k Response

force spectral density • noise

1/2 imposes minimum detectable signal level; each element of a (4kkBT/ω0Q) system degrades the overall SNR (signal-to-noise ratio). Force Noise

displacement spectral density Integrated energy 1 1/2

k T (4ω Qk T) 2 B 0 B Displacement

Frequency

4 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

generalized measurement analysis: transduction generalized measurement analysis: responsivity

SIGNAL ELECTRICAL SIGNAL ELECTRICAL DOMAIN, DOMAIN, DOMAIN, DOMAIN, “X ” “V ”or “I ” LOW NOISE “X ” “V ”or “I ” LOW NOISE input input SYSTEM ELECTRONIC SYSTEM ELECTRONIC transducer data transducer data UNDER MEASUREMENT UNDER MEASUREMENT (sensor) storage (sensor) storage STUDY signal electrical SYSTEM STUDY signal electrical SYSTEM input input

X V, I

Responsivity R = ∂∂VX/ a generalized representation of “gain” (here we’ve ignored I/O phase relationship and have assumed transducer linearity) Small signal analysis: δ VX=R ⋅δ

example: magnetic force microscope NEMS attributes: power level for operation

“ganged responsivities” fiber optic interferometer Signal Ceiling

VBzkRm=∂[ /(1/) ∂ − ] ) int z microcantilever

1. miniature magnet dB ( provides coupling dynamic to magnetic sample ) range ∂B FmBm=⋅∇=() zz∂z m a “magnetization-to-force” Noise Floor

transducer Input level ( Sample (e.g. magnetic dots)

2. mechanical force detector ( compliant mechanical element) 3. displacement readout x =−Fk/ ( e.g. fiber-optic interferometer ) a “force-to-displacement” VRx= int transducer a “position-to-voltage” transducer

5 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

NEMS attributes: power level for operation “thermomechanical” noise floor

• fundamental thermodynamic Signal Ceiling noise limit 4kTQB ) Sx = “displacement noise spectral density” kω0 dB units: [ (nm)2/Hz ] dynamic on resonance range Q>>1 ⇒ resonant mechanical response

106 10000 Q =100 5 Q =1000 100 Noise Floor 10 =300 Input level (

=100 1 is routinely determined by 4 2 10 =30 0.01 )| =10

ω 3 • thermomechanical noise ( 10 0.0001

A 0.1 1 10 | 102

but, in certain systems (at millikelvin 101 temperatures) is now approaching: 100 • quantum displacement fluctuations 0.8 0.9 1.0 1.1 1.2 1.3 Normalized Frequency, ω /ω (lecture 2) 0

“thermomechanical” noise floor NEMS attributes: power level for operation

• fundamental thermodynamic noise limit 4kTQB Sx = nm-Scale “displacement noise spectral density” kω0 units: [ (nm)2/Hz ] Mechanical on resonance Mo Li, H.X Tang, M.L. Roukes Resonators Nature Nanotechnology (2007) Doubly-clamped beam Q>>1 ⇒ resonant mechanical response Thermomechanical noise spectrum

and Lorentzian fit6 (blue trace) for a 10 10000 ultralow operating power required (T=300K) 123 MHz nanocantilever measured at Q =100 1μm room temp. & atmospheric5 pressure.Q =1000 100 10 =300

=100 1 6 4 f0 Q Pmin 10 ·Pmin 1.68 2 10 =30 P = E / τ* Hz ] 0.01 min min )| 72 electrical =10 √ 100 MHz 10,000 40 aW 40 pW ω 3 m ( 0.0001 = (k T) / (Q/ω ) readout10 -15 B 0 1.66 A 0.1 1 10 " 100,000 4 aW 4 pW | 2 71 10 [10 1 GHz 10,000 0.4 fW 0.4 nW [nV/rtHz]

1 1.64 10 70 " 100,000 40 aW 40 pW

100 1.62 0.8 0.969 1.0 1.1 1.2 1.3 • even 10 6 (10 6 ·P ) ~ μwatts << watts (digital electronics) Voltage Noise Voltage Normalized Frequency, ω /ω min 0

6 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

NEMS attributes: signal ceiling and dynamic range intrinsic mechanical nonlinearity / bistability • easily attainable & useful mechanical nonlinearity cf. onset of lattice anharmonicity (few percent strain = huge! ) Signal Ceiling ) Is typically determined by, e.g.: • two classic examples:

dB •onset of nonlinearity (linear applications) dynamic (e.g., 1dB gain compression point - amplifiers) Duffing Instability Euler Instability range •spurious product generation (nonlinear apps) (frequency stiffening) (beam buckling)

δ) 1.0

0.8 Noise Floor γ=0 Input level ( is routinely determined by: 0.6 γ=1 • thermomechanical noise 0.4 ( . . .ultimately quantum limited ) 0.2 γ=1.3

0.0 χ=0.2 Normalized Amplitude Normalized -0.2 -2.0 -1.0 0.0 1.0

Normalized Frequency, Q(f-f0)/f0 U( Energy, Potential Normalized Normalized Displacement, δ

Equation of motion Typical Duffing oscillator response

Time-dependent tension z (x) ω increase 0 Boundary conditions : RF det x L drive amp

0 displacement

B displacement increase Galerkin discretization procedure : drive freq

ω0 drive frequency drive amplitude

yields time-dependent Duffing equation : hysteresis in frequency hysteresis in amplitude

resp amp resp amp

drive freq drive amp

7 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Nanowire NEMS dynamic range “issues”…

Duffing model :

apeak

1 ac signal driven Pt nanowire response

T0 ~ 0.56 μN dynamic range L = 2.15 μm 0.1 d = 39 nm N.B. Available

Gap = 66 nm (a.u.) Response linear dynamic noise undrivenrange can be 0.01 responseminimal (i.e. zero)! -6 -3 0 3 6 (H. Ch. Postma et al., APL 2005) f = 45.45 MHz, Q = 18,000 Detuning frequency/Resonance width (-)

Onset of nonlinearity depends on beam parameters intrinsic mechanical nonlinearity / bistability beam length • easily attainable & useful mechanical nonlinearity cf. onset of lattice anharmonicity (few percent strain = huge! ) • two classic examples: In next lecture

critical amplitude where resonance Duffing Instability Euler Instability beam diameter curve starts to lean over (frequency stiffening) (beam buckling)

δ) 1.0

0.8 Small ac = large nonlinearity γ=0 0.6 γ=1 0.4 • Smaller diameter beams are more nonlinear 0.2 γ=1.3 • Shorter and fatter beams are more nonlinear 0.0 χ=0.2 • Systems with low dissipation (high Q) exhibit stronger nonlinear behavior Amplitude Normalized -0.2 -2.0 -1.0 0.0 1.0 • Higher initial tension delays the onset of nonlinearity Normalized Frequency, Q(f-f0)/f0 U( Energy, Potential Normalized Normalized Displacement, δ

8 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

parametric control Induced electrostaticelectrostatic nonlinearity mechanical signal processing Coulomb’s “Electrical Balance” (1785)

nano- ELECTRICAL Signal output mechanical OUTPUT transducer Forces mechanical system mechanical SIGNAL stimulus response

mechanical perturbation Parametric control can ELECTRICAL control CONTROL be based upon: transducer SIGNAL - intrinsic mechanical nonlinearity - additional terms, beyond Charles-Augustin those from elasticity, in de Coulomb potential (e.g. electrostatic, (1736-1806) magnetic,…

NEMS attributes: induced mechanical bistability nanomechanical electrometer

• example: electrostatic pull-in gate mechanical charge detector electrode inner torsional 1.0 resonator Schematic View Coupling Parameter inner 0.8 z = 0.00 torsional z = 0.01 resonator

U(y) 0.6 z = 0.05 z = 0.10

z = 0.148 Charge Noise 0.4 Charge Noise Phase Detection T = 4.2 K S

1/f Q

0.2 1/2 00 1010 (e/Hz

0.0 1/2 (e/ ) (SSB) √ Potential Energy Energy Potential z-SSB) Hz - -0.2 w. bound 1010-1-1 white -0.4 unbound 10101 1 101022 101033 101044 0.0 0.5 1.0 1.5 2.0 q2 Frequencyν (H z) (Hz) Coupling Parameter: z∝ 3 Position y = δ/δ0 ksδ0 A.N. Cleland and M.L. Roukes, Nature 392, 160 (1998) A.N. Cleland and M.L. Roukes (‘95)

9 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Transduction, Noise, and Information Flow nanosensor responsivity

Force responsivity Q>>1 ⇒ resonant mechanical response

force domain displacement domain 106 10000 xF ()ω = ()ω ℜ()ω Q =100 5 Q =1000 100 10 =300

NEMS resonator =100 1 4 1 22 10 =30 0.01 force displ. )|)| =10

= F (ω ) ω 3 (( 2 10 0.0001

signal signal AA 0.1 1 10 R [](KMi−−ω effωγ eff ω) || mech + + 102 noise noise 101 3 100 Size KwtL~(/) d 0.80.91.01.11.21.3 2 Normalized Frequency, ω /ω scaling: 0 ω0 ~/tL 1/d mechanical responsivity (force-to-displacement) nm 1 Mass responsivity (areal) ⎡⎤ A R mech == ⎢⎥aN ⎡⎤222 2 δωω/ δ0 = Smm Sauerbrey Equation ⎣⎦ MQ00⎣⎦()(/)ωω−+ ωω 0 (Areal )Mass Sensitivity Accreted Mass/unit area

AAAeffδω ℜ eff eff Sm ==−=− δωmM00 ω 2 eff Size scaling: 1/ t

Two examples of responsivity – there are many others…

Transduction, Noise, and Information Flow nanosensor noise mechanisms dissipation ↔ fluctuations force domain displacement domain

NEMS resonator Surrounding Gas force displ. External Thermal Bulk Defects signal signal R mech Phonons (e.g. Two Level Systems) + + (Clamping Losses) noise noise thermomech. noise Internal Thermal Surface Defects Phonons and Adsorbates mechanical responsivity (force-to-displacement) (other Resonator Modes) ⎡⎤nm 1 Resonator Mode R == mech ⎢⎥ 222 2 ⎣⎦aN MQ00⎡⎤()(/)ωω−+ ωω 0 ⎣⎦ External Electrons External Photons (e.g. in electrodes) (Black Body) thermomechanical noise Thermomechanical 2 ⎡⎤N 4kTkBeff Noise SF ()ω ==⎢⎥ ⎣⎦Hzω0 Q one resonator mode, many external energy reservoirs

10 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Transduction, Noise, and Information Flow Why Nano ?

Pin Pin • Unprecedented performance, through scaling . . . force domain displacement domain electrical domain of Frequency NEMS resonator displacement transducer readout amplifier VHF cantilevers, UHF/Microwave beams (fundamental-mode) force displ. electr. signal signal signal R mech R trans A v of Compliance (Force Responsivity) + + + μN/m force constants straightforward noise noise noise thermomech. transducer amplifier noise noise noise of Mass Responsivity greater than 1Hz/zeptogram attained so far mechanical responsivity (force-to-displacement) of Areal Mass Responsivity ⎡⎤nm 1 2 R == better than 10pg/cm /Hz attained so far mech ⎢⎥aN ⎡⎤222 2 ⎣⎦ MQ00⎣⎦()(/)ωω−+ ωω 0 of Fluctuations -8 thermomechanical noise low frequency fluctuations: Allan deviation σA~10 ⎡⎤N2 4kTk transducer responsivity (displacement-to-voltage) S ()ω ==Beff • Minimal device footprint ⇒ ultrahigh packing density F ⎢⎥Hzω Q ⎣⎦ 0 ⎡nV ⎤ v. strongly • Ultralow power consumption ()P dependent R trans in = ⎢ ⎥ = ⎣nm⎦ on “process”

Frequency, Compliance Scaling Nanodevice Motion at Microwave Frequencies

Under uniform scaling of all dimensions: wa= ,, tb== Lc 15

HP 8720C 8T Network Analyzer •Scaling of frequency 10 7T Port 1 Port 2 6T t 1 5T Drive Detection (nV) 4T with decreasing 5 180° fE0 ≈∝αρ/ 3T power L splitter 0 48dB •Scaling of compliance (force responsivity) -5 Signal Amplitude 3

⎛⎞t -10 kEweff ≈∝β ⎜⎟ with decreasing IIIIII ⎝⎠L 1.00 1.01 1.02 1.03 1.04 Frequency (GHz)

X. M. Henry Huang •Scaling of thermomechanical noise C. Zorman*, M. Mehregany* 1/ 2 and M.L. Roukes 1/2 Caltech, *Case with decreasing SkTkQFBeff=∝()4/()ω0 Nature 421, 496 (2003)

11 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Self-sensing Nanomechanical Force Sensors (2005-06) Noise Floor & Dynamic Range

62 63 64 65 66 67 68 69 70 14 Cantilever a) a) 12 1st Mode

V) V) 10 μ

( 8

4 5μm b) c) d) 2.0 2nd mode

1.5 Noise Spectrum Density [nV/rt Hz] Density [nV/rt Spectrum Noise Amplitude 1.0 H.X. Tang, M. Li, M. Roukes, US patent pending 524 525 526 527 528 529 530 531 532 533 f [kHz] Frequency (Hz) M. Li, H. Tang, M. Roukes, to be published (2006) 10

f0 ≅11.3MHz 0 k = 2.64 N/m -10 -20 -30 -40 DR > 80dB -50

Amplitude [dBm] -60 2.5μm -70 -80 -90 11.0 11.1 11.2 11.3 11.4 11.5 11.6 Frequency [MHz]

VHF/UHF NEMS Applications Future proteomics • Mass sensing: toward 1yg resolution – single-molecule mass spectrometry Toward single-molecule mass spectrometry

• Gas phase sensing toward ultrafast ~ppt-concentration sensing Roukes Group: Dr. Wayne Hiebert (NINT), Selim Hanay, at ambient temperature & pressure Caltech Dr. Philip Feng, Mo Li, Ben Gudlewski, Dr. Akshay Naik (11/1/06) • Force sensing in vacuo: toward 100zN resolution next-gen scanning probe microscopy single-nucleus magnetic resonance imaging Prof. Kamil Ekinci Boston U. • Force sensing in fluid: toward fN-scale resolution High BW / high sensitivity biological force sensing Prof. Milan Mrksich U. Chicago • Energy sensing: toward μeV resolution measurements at the level of single mechanical quanta

Prof. Stephen Quake Stanford U.

12 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

mass spectrometry and proteomics mass spec: the state-of-the-art

“At present there is no other technology visible that can rival the speed, sensitivity, 8 and exact molecular characterization of MS methods of protein characterization”. 10 Perspectives for Mass Spectrometry and Functional Proteomics, J. Godovac-Zimmermann, and from G. Siuzdak, L. R. Brown, Mass Spectrometry Reviews, 20, 1-57 (2001). Mass Spectrometry For Biotechnology "Realistically, we probably need (sensitivity) to be down to the level of about 10 9 (Academic Press, 2003) copies per cell on the assumption that if you have 10 copies in a cell, they're 10 actually doing something of note.“ (# of molecules) (moles) Brian T. Chait, Director, Mass Spectrometry and Gaseous Ion Chemistry Lab, Rockefeller University (2001) 1010 “MS-based proteomics is still an emerging technology where revolutionary change is possible. … Recent successes illustrate the role of mass spectrometry-based

proteomics as an indispensable tool for molecular and cellular biology and for Sensitivity the emerging field of systems biology… The ability of mass spectrometry to Mass Range identify and, increasingly, to precisely quantify thousands of proteins from 1011 complex samples can be expected to impact broadly on biology and medicine… “ Mass Spectrometry-Based Proteomics, Ruedi Aebersold and Matthias Mann, Mass Range Nature 422, 198-207 (2003). (Daltons)

Inertial Mass Sensing Mass Resolution: Ingredients

two-port, T≈300 K ∂M eff -1 HF NEMS resonator δδM ≈ ω0 ~ R σ A ()τ F mass ∂ω mass Allan Sh 13.3 cm 0 TT resolution resp. deviation QCM

P D1 R D2 182.2 cm large mass responsivity frequency resolution 0° C T≈17 K RB 0° Ø LLO PS 0° D1 TT RO D2 z 180° NEMS RF M IIF VCO noise RF DC LPF x y SC A D1 R D2 processes

NEMS (f) low noise, phase locked a So loop detection 0° C

B 0° S log Ø LLO PS 0° D1 RO D2 180° NEMS RF M IIF VCO Kamil Ekinci, Caltech ‘99 RF DC LPF UHV microwave cryostat A

13 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Maximizing Mass Resolution State-of-the-art: Real-Time Zeptogram Sensitivity (1zg = 10-21-21g)

∂M 0 SiC doubly clamped beam NEMS δδM ≈ eff ω ~ R-1 σ ()τ UHF bridge configuration 0 A -200 ( f0 ~ 133 and 190 MHz ) ∂ω0 mass Allan Ultralow noise PLL readout resp. deviation -400 ~100 zg

-600 NEMS shutter large mass responsivity -800 100 frequency-shift resolution 0 Frequency Shift (Hz) Frequency Shift For any complex mechanical -1000 nozzle 10 ~7 zg

Two fundamental noise classes: -500 (zg) mode, modeled as a damped m

SHO: 0 50 100 150 200 250 300 350 δ 1 Extrinsic frequency-fluctuation processes: -1000 transducer losses, Time (sec) 0.1 ω0 0 2000 4000 read-out amplifiers, etc. R ≈− -1500 2M Time (s) eff Intrinsic frequency-fluctuation processes: -2000 1 huge benefit thermomechanical noise, Ya-Tang Yang, Carlo Callegari, ∝ in scaling Xiaoli Feng, Kamil Ekinci, MLR 133 MHz

4 1/f noise (Hz) Shift Frequency Nano Lett. 6, 583 (2006) downward ! temperature fluctuations -2500 190 MHz adsorption-diffusion-desorption noise ~1Hz/zg -3000 0 1000200030004000 Mass (zeptograms) © 2006 © 2006

State-of-the-art: Real-Time Zeptogram Sensitivity (1zg = 10-21-21g) Ultimate Limits of Inertial Mass Sensing

0 SiC doubly clamped beam NEMS UHF bridge configuration -200 ( f0 ~ 133 and 190 MHz ) Ultralow noise PLL readout -400 ~100 zg

-600 NEMS shutter -800 100 Experimental Resolution vs. Theory 0 Frequency Shift (Hz) FrequencyShift -1000 nozzle 10 ~7 zg

-500 (zg) mass sensitivity β M −(/20)DR

m tot

0 50 100 150 200 250 300 350 δ 1 of a NEMS resonator δ M ~10 -1000 2 Time (sec) Ekinci, Yang, & MLR (JAP, Mar 2004) α Q 0.1 0 2000 4000

-1500 Time (s) Equivalent to single (4 kDa) Ya-Tang Yang, Carlo Callegari, -2000 Xiaoli Feng, Kamilmacromolecular Ekinci, MLR sensitivity 133 MHz Frequency Shift (Hz) Shift Frequency Nano Lett. 6, 583...or (2006) about 30 Xe atoms.-2500 190 MHz ~1Hz/zg -3000 0 1000200030004000 Mass (zeptograms) © 2006 © 2006

14 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

toward next-gen NEMS mass responsivities Why 1 yg?

Achieved (top-down SiC NEMS), and coupled to low-noise PLL readout

f0 NEMS Device Dimensions Q Meff DR σA δm -8 295 MHz 2.66μm × 170nm × 80nm 3000 118 fg 80 dB 4.7×10 15 zg -7 420 MHz 1.8μm × 150nm × 100nm 1200 82 fg 90 dB 3.1×10 67 zg -8 411 MHz 1.7μm × 120nm × 80nm 2600 53 fg 85 dB 6.6×10 10 zg -8 428 MHz 1.65μm × 120nm × 80nm 2500 55 fg 90 dB 2.5×10 4 zg -8 482 MHz 1.6μm × 120nm × 80nm 2000 52 fg 98 dB 2.1×10 3 zg Toward Single-Dalton Resolution -16 Science 312, 683 (5 May 2006) • Next-generation NEMS resonators is a ~0.85 GHz resonator (with Mtot~2×10 1 kDa = 1.66 zg g). Expected advances should yield Q~104 and DR~80dB at this frequency, to yield a resolution δM ~1.6 × 10-24 g , i.e. 1Da.

• This will yield atomic resolution, with sufficient sensitivity to detect a single adsorbed hydrogen atom. • N.B.: (a) the species need not be charged to be detected. (b) no mass preselection is required (each molecule is weighed )

Current Efforts: real-time, electrospray injection to NEMS Microfluidics + Nanoelectrospray

Chip-based separation plus nanoelectrospray injection

( Tai Group, Caltech ) electrospray injection hexapole ion guide

Wayne Hiebert, Selim Hanay,

15 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech ... Vision: Single-Molecule NEMS ... Vision: Single-Molecule NEMS Mass-Spec-on-a-chip Vision: Single-Molecule NEMS Mass-Spec-on-a-chip Mass-Spec-on-a-chip

NEMS 1000’s of single-molecule channels per desktop system… NEMS ~ NEMS

NEMS V(ω )

NEMS

B two-port ... ext ... NEMS resonator (magnetomotive actuation & transduction)

6th US-Japan Joint Symposium on NanoSystems © Caltech 2005-2006 July 2005 Tokyo – 10 October 2006

Self-sensing Nanomechanical Force Sensors (2005-06)

Nanoelectromechanical “Nose” a) V) V) μ

Toward early-stage disease diagnosis via breath analysis (

Roukes Group: Dr. Ed Myers, Dr. Sequoyah Aldridge, b) c) d) Dr. Philip Feng, Mo Li, Ben Gudlewski Caltech Amplitude Lewis Group: Prof. Nathan Lewis, Heather McCaig Frequency (Hz)

1.68 72 Hz ] √

Dr. R.J. (Joe) Simonson m

(right) Thermomechanical -15 Dr. Josh Whiting 1.66 noise spectrum and Lorentzian 71

Sandia [10

Dr. David Wheeler fit (blue trace) for a 123 MHz Hz] [nV/rt Dr. Shawn Dirk nanocantilever (above right) 1.64 70 measured at room temperature and atmospheric pressure. 1.62 69

Prof. Hong Tang Yale U. Voltage Noise

1.60 68 Displacement Noise 122 123 124 Frequency [MHz]

16 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Q vs. Pressure : smaller is better !! Chemisorptive Nanocantilever Vapor-Phase Mass Sensing

25 25 Real time chemisorption (a) 0 0 20 measurements with two V] μ V] 20 15 High quality factors of

μ PMMA-coated NEMS [ 10 15 nanoscale resonators -100 resonators. Displayed 5

Amplitude [ Amplitude 10 ag

20 are frequency shift steps 0 persists at much 10 0 100 200 300 400 500 600 17 ag upon of adsorption of Drive Voltage [mV] higher pressures. -200 Amplitude

difluoroethane gas 5 molecules onto device 8 MHz 35 ag 40 0 -300 50 ag surface. 1000 (b) 0 0 These measurements In vacuo In Air (1 Atm) are carried out at atmospheric pressure 126 127 128 126 127 128 -1000 Frequency Shift [Hz] Shift Frequency 2 & room temperature. Mass [attogram] Frequency [MHz] Frequency [MHz] 0.4μm 1ag 100 -2000 2 ag 10000

The top and bottom 0.8μm 4 traces are measured with 1000 -3000 2μm 8 MHz and 128 MHz 128 MHz Quality factor Quality 100 5 ag nanocantilever devices, 5 m 500 nm μ 2.5μm -4000 respectively. 10 [Torr] Pressure 6 10 0 2000 4000 6000 Mo Li, Hongxing Tang, MLR – Caltech 2006 0.1 1 Cantilever width [μm] Time [seconds] 0.01 0.1 1 10 100 1000 TheThe minimumminimum resolvableresolvable Pressure [Torr] massmass isis ~~100100 zg.zg. © 2006 © 2006

The “electronic nose” paradigm: a chemical sensor array Chemical fingerprint analysis

Analyte Sensor a good algorithm maximizes separation Gas Array and minimizes spread for clear identification

Chemical “fingerprint” Signal analysis algorithm maps sensor signals to concentration data Sensor signal space analyte concentration space signal

sensor Signal processing algorithms: • principal component analysis • k-nearest neighbor analysis • neural networks: self-organizing maps, Kohonen maps • visual-empirical region-of-influence method (VERI)

17 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Electromechanical nose for clinical medicine? VOCs in human breath

Four independent studies have recently shown that vapor- phase screening technology can reveal volatile organic compounds (VOCs) on patients’ breath that are biomarkers for lung cancer. For lung cancer, as Recent study: (50 individuals) 12 well as for other - Approximately 3500 unique VOCs found; diseases, specific 10 ~200 per person VOCs can thus be - 27 common VOCs—almost all are alkanes or correlated with, and 8 methylated alkanes are indicative of, disease conditions not 6 Origin of common VOCs : present in healthy -Reactive oxygen species are byproducts of 4 patient controls. normal metabolic processes Number of subjects subjects of of Number Number 2 - These species then oxidize cellular material Table 1. Summary of - Normal oxidation thought to be important in the main volatile organic 140 150 160 170 180 190 200 210 220 230 240 250 aging process (antioxidants supposedly compounds (VOCs) associated with different Number of VOCs in breath counteract this behavior) disease types, as analyzed as chromatography (GC) or GC-linked with mass -- Byproduct Byproduct of of oxygen oxygen breakdownbreakdown ofof cellscells isis mostmost oftenoften alkanes, alkanes, which which are are spectrometry (GC-MS). thenthen releasedreleased intointo breathbreath © 2006

Array signal processing yields biomarker identification Caltech-Sandia Project: μGC + NEMS Sensor

species species … species • Processing algorithms of NEMS Nose : group A group B group M

sensor array response 0.5 A new paradigm based Microscale 0.4 (Sandia) (e.g., principal component 0.3 on microfluidic sample column 0.2 analysis) maps data into 0.1 preconditioning and 0 PC 3 “analyte identification space”. tetradecane -0.1 multiplexed arrays -0.2 -0.3 of ultrasensitive • Severin, Lewis et al.: 0 NEMS mass detectors (differentially functionalized) - An array of 20 chemiresistor dodecane 0.5 sensors were used to resolve a pentane 1.0 generic, homologous series of hexane PC 1 VOCs, into individual species decane heptane 1.5 nonane octane and binary mixtures. 2.0

-0.8 - Individual analytes can be -0.6 2.5 -0.4 -0.2 0.0 distinguished using principal 0.2 0.4 3.0 0.6 component analysis (PCA). PC 2 0.8 Polymer-Coated NEMS Resonator Arrays Severin, Lewis et al., 2000 (Caltech)

18 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Elements that determine concentration performance (in ppb): Microscale GC Front End: Sandia National Labs Chemisorptive coatings and ultrasensitive devices are key

Sandia National Laboratory Caltech

Integrated Device Die NEMS ~1ppt ~10ppb sensor size 12 mm x 9.5 mm CWA Preconcentrator GC column CWA array DRIE GC input pulse column Ingredients: Caltech Chemisorptive NEMS Sensor Element Sampling Valves (a) chemisorptive coating (c) control-loop readout

GC pulse (b) NEMS Resonator 1ppt CWA to MGA yields a pulse from NEMS sensors GC that is ~10ppb for Preconcentrator 10ms (typ.)

Frequency Resolution: 1×10-7 Areal responsivity: 8 pg cm-2 Hz-1

Concentration performance: Concentration performance: Analyte sticking probability determines sensitivity (in ppb) Analyte sticking probability determines sensitivity (in ppb)

Note: For concentration sensing, the appropriate metric for cross- Note: For concentration sensing, the appropriate metric for cross- comparison between bare (uncoated) sensing devices is their “areal” comparison between bare (uncoated) sensing devices is their “areal” mass sensitivity, with typical units pg/cm2. Conversion of this mass sensitivity, with typical units pg/cm2. Conversion of this areal mass sensitivity into a concentration sensitivity (e.g.,in “ppb”) areal mass sensitivity into a concentration sensitivity (e.g.,in “ppb”) is possible only by defining both the specific analyte to be measured is possible only by defining both the specific analyte to be measured and the specific polymer layer for its chemisorption onto the sensor. and the specific polymer layer for its chemisorption onto the sensor.

Analysis: Caltech Chemisorptive NEMS Sensor Element Analysis: Caltech Chemisorptive NEMS Sensor Element

Descriptive Analysis:* Areal Mass Accumulation (a) chemisorptive coating (a) chemisorptive coating • Physics determines the collision rate of a rare δ m Units: pg/cm2 CWA pulse analyte (e.g. CWA) with the sensor’s surface. CWA pulse δ mA = from GC is from GC is A eff ~ 10ppb for • The analyte’s sticking probability, s’ , ~ 10ppb for analyte flux sticking probability 10ms (typ.) determines whether or not it chemisorbs. 10ms (typ.) φ P Areal Mass integration ~ sm′ ′ τ int • The current class of optimal polymer coatings Accumulation time mk′ B T employed yield s’~1 for CWAs. analyte = operating pressure (1atm) P mass φ = analyte concentration (10ppb) ~ rmsm′ ′′τ int τ int = accumulation time (10ms) 2 m′ = analyte mass (DMMP=124amu) ≈ 10,000 pg/cm Legend ( for a 10ms, 10ppb DMMP pulse, s’=1 ) s′ = sticking probability (assume ~1) © 2006 © 2006

19 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Sensor surface area determines net mass accumulated Chemisorptive Concentration Sensing (Vapor-Phase)

Sandia National Laboratory Caltech 0 Concentration Demo Setup Calibrated Gas Generator NEMS -100 20 ppb Vici Metronics ~1ppt ~10ppb sensor noise floor [Hz] Dynacalibrator® Model 190 CWA Preconcentrator GC column CWA array is ~ 2 ppb input pulse -200

50 ppb -300

Ingredients: Caltech Chemisorptive NEMS Sensor Element Microchamber Frequency Shift Frequency -400 100 ppb (Sandia-compatible) 200 ppb 4.3 MHz (a) chemisorptive coating (b) NEMS mass sensor integrated -500 DKAP-coated 05000 500 10000 500 1000 0 500 1000 NEMS sensor gas sensor 3 um CWA pulse Time [s] Measurement setup for NEMS- from GC is Reversible chemisorptive response to based detection of calibrated ~ 10ppb for ppb-scale pulses of DMMP. These are concentrations of CWAs. 10ms (typ.) applied to a nanocantilever coated with A polymer-coated ~4.3 MHz nanocantilever resonator DKAP polymer & read out out by a fast is housed in a microchamber fixture. Calibrated ppb- + = scale concentrations of DMMP analyte in nitrogen areal mass accumulation ~100 zg sens. low-noise PLL. carrier gas are delivered to the fixture inlet. The DMMP Net Mass Accumulation analyte is generated by a calibrated industry-standard 2 at 1 Atm (10ms/10ppb pulse of DMMP) (For 1.2μm capture area) gas permeation chamber, and is mixed with a N carrier Exposures at calibrated concentrations 2 10,000 pg/cm2 for s’~ 1 ~120 ag for s’ ~ 1 ⇒ 8 pg/cm2 gas stream delivered by an electronic flow controller. as small as 20 ppb are detected; the 1,000 pg/cm2 for s’ ~ 0.1 over the 1.2μm2 ~12 ag for s’ ~ 0.1 background frequency fluctuations yield 100 pg/cm2 for s’ ~ 0.01 ~1.2 ag for s’~ 0.01 capture area a 2 ppb concentration noise floor. ⇒ Standard polymer coatings used to sensitize devices to CWAs (e.g. DMMP/BSP-1) yield s’~1

NEMS vs. Competing Microscale Gas Sensors Current gas flow chamber limits sensitivity

Detection Demonstrated detected • Gas concentration in 50-μL chamber not uniform during pulse Group MDL Reference Method DMMP concentration (noise floor) • Large volume and irregular flow spreads GC peaks and reduces

Nanotube E. S. Snow Science effective concentration at sensor 0.5 ppb chemicapacitor Naval Research Lab 320 ppb 307, 1942 (2005) Location of Jay W. Grate Surface Acoustic Chem. Mater. Pacific Northwest 1 ppb NEMS chip Wave (SAW) 1~2 ppm 9, 1201 (1997) National Lab in chamber

N. S. Lewis Chemiresistor 6~30 ppb Anal Chem Caltech 1 ppm 73, 884 (2001)

Z. Wang Tin Dioxide Nanobelt N/A Appl. Phys. Lett 86, Ga. Tech 53 ppb 063101 (2005)

DNA decorated A. T. Johnson Nano Letter 1 ppm Nanotube U. Penn 25 ppm 5, 1774 (2005)

M. Zaghloul CMOS Cantilever 20 ppb IEEE Sensors Journal GWU 720 ppb 5,641 (2005)

MEMS RF Ion Mobility R. Miller 90 ppb N/A 2000 Hilton Head Spectrometer Draper Lab Island 1 cm M. L. Roukes NEMS Cantilever 2 ppb Achieved in MGA Y1 Caltech 20 ppb NEMS gas sensors Finite-element simulation of flow stream are now the

20 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

In progress: nanoliter-scale chamber Value of NEMS-Enabled MGAs • NEMS are an enabler for next-generation, portable • Microchannel chamber with 15 nanoliter volume vapor-phase sensing: (developed by Sandia) mounts directly onto NEMS chip currently provide sensitivity that matches/exceeds state-of-the-art • We expect 2-3 orders of magnitude improvement in sensitivity operate at power levels ~X100 lower than SAW/FPW sensors sensor footprint is a million times smaller. Finite-element simulation of flow stream Ultracompact, multiple-element averaging (to improve sensitivity) Small-footprint, highly-multiplexed sensor systems

Channel dimensions: 2 mm length x Robust, validated, multilevel top-down fabrication en masse 300 μm width x 20 μm height • Still significant further opportunity for improvement NEMS sensor technology is in its infancy NEMS Advances are being made rapidly chip Significant further improvements possible: ganged sensors (for X3-X4 concentration sensitivity increase) sensor location thinner sensors (for X3 concentration sensitivity increase) 1 improved frequency-shift readout (X10 sensitivity increase possible) cm

routes to fluidic biosensing

Force sensing in fluid: fundamental physical process toward fN-scale resolution analyte molecular – high bandwidth / high sensitivity + recognition force resolution in liquid receptor

21 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

routes to fluidic biosensing routes to fluidic biosensing

electrically-based assays electrically-based assays

fundamental physical process fundamental physical process analyte analyte molecular molecular + + recognition recognition receptor receptor surface-mediated surface-mediated conductivity change conductivity change electrical electrical readout additional readout physics - A - - A - - - R charge carried by the R analyte is not generic

routes to fluidic biosensing BioNEMS inspiration: single-molecule biophysics

“force assay” Optical Tweezers e.g. Chu, Block, Bustamante, … Nature of Interaction Interaction Force fundamental physical process Receptor/Ligand Interaction 50−250pN analyte Avidin-Biotin 90−260 pN molecular Antibody-Antigen 50−300pN + recognition Cadherin-Cadherin 35−55pN receptor DNA Hybridization 65pN−1.5nN Chemical Bond 1−10nN direct readout Covalent(C-C, C-O, C-N) 4.0−4.5nN of binding forces Covalent (Au-S, Si-C) 1−3nN H-bond 10pN A Unfolding Forces 100−300pN Protein (Titin) unfolding 150−300pN R Dextran bond twists 100−300pN AFM-based (Force Spectroscopy) e.g. Hansma, Gaub, Fernandez, …

22 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

nanocantilever response in fluid nanocantilever response in fluid 3 3

22 1 22 1 c c Kx|| a Kx|| a n n t t R(/ωω0 )≡ c i R(/ωω0 )≡ c i 2 a le 2 a le ) ) Q>>1 ⇒ resonant mechanical response in vacuo n v n v

||F 0 t ||F 0 t i e i e c l r c l r e e ω a v 1 ω a v 1 n n 6 / e / e 10 10000 t r t r i i ω l 2 ω l 2

physics: Q =100 e physics: e v v

5 Q =1000 ( 0.1100 e ( 0.1 e 10 r r

=300 R R 3 3

ℜ << 1, yields =100 1 ℜ << 1, yields 4 2 10 =30 0.01 heavily)| damped =10 heavily damped ω 3 ( 10 0.0001

response,A Q ~ 1 0.1 1 10 response, Q ~ 1 | 102 0.01 0.01 0.002 0.01 0.1 1 0.002 0.01 0.1 1 101 Normalized Frequency, / Normalized Frequency, / ω ω0 ω ω0 100 0.8 0.9 1.0 1.1 1.2 1.3 # t w 1 b ω0 /2π K ℜ T # t w 1 b ω0 /2π K ℜ T Normalized Frequency, ω /ω 1 130nm 2.5μm 15μm 2.5μm 0.6μm 0.51MHz 0 34mN/m 5.0 8.22 1 130nm 2.5μm 15μm 2.5μm 0.6μm 0.51MHz 34mN/m 5.0 8.22 2 130nm 300nm 10μm 2.0μm 100nm 1.3MHz 20mN/m 0.19 0.986 2 130nm 300nm 10μm 2.0μm 100nm 1.3MHz 20mN/m 0.19 0.986 3 30nm 100nm 3μm 0.6μm 33nm 3.4MHz 3.0mN/m 0.054 1.42 3 30nm 100nm 3μm 0.6μm 33nm 3.4MHz 3.0mN/m 0.054 1.42

Fluidic response of NEMS: fluid loading determines effective mass and damping Ultrathin cantilevers for optimal force sensitivity in fluid x 1 H ()ω == Effective damping: Recently fabricated Caltech Small cantilever response (Viani et al.) devices ( 30nm thick ) FKM−+eff()ω iωγ ω eff () γαωeff ≅ ( Im{L })

Effective mass: M. Paul and M.C. Cross, PRL, 2005 2 ⎛⎞ 4iK1 ()−ℜ i i πρ L w L()ω =+⎜⎟1 2 4 ⎜⎟iKℜ−ℜ ii t=30nm, K=0.94mN/m ⎝⎠o ()1 t=50nm, K=1.6mN/m t=85nm, K=2.7mN/m M eff≅+αρ( CVL c Re{ }) t=140nm, K=4.4mN/m

J. E. Sader, J. Appl. Phys. 84, 64-76 (1998). t=300nm, K=9.4mN/m 0.1

Device dimensions (top curve): Silicon nitride cantilevers with gold pads ===10μm, wt2μm, 30nm (K~60mN/m, thickness 86nm)

leg==1.5μm, w leg 0.4μm 0.01 M.B. Viani, T.E. Schäffer, A. Chand, M. Rief,

All dimensions are (m/mN) function of Response Magnitude scaled uniformly for the 10m 100m 1 10 100 1k 10k 100k 1M H.E. Gaub, and P.K. Hansma, JAP 86 (1999) larger devices frequency (Hz)

23 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

Recently fabricated Caltech Small cantilever response (Viani et al.) devices ( 30nm thick ) concept: NEMS bioarray with microfluidic analyte delivery

Sub-Piconewton-Scale, High Bandwidth Force Response is Attainable 10 microfluidic flow channel

Silicon nitride cantilevers with gold pads (K~60mN/m, thickness 86nm) individual BW=f Integrated Noise (pN) M.B. Viani, T.E. Schäffer, A.3dB Chand, M. Rief, biofunctionalized 0.1 H.E. Gaub, and P.K. Hansma, time constant=1msec JAP 86 (1999) NEMS element 0.07 5 10 100 1000 Thickness (nm)

wafer-scale fab of BioNEMS sensors Realizing and deploying nanobiotechnology technology fusion BioNEMS wafer Microfluidics gen 1 Surface Nanoscale Signal Biochemistry Biosensors Processing

Large scale systems integration … nanofab at the wafer scale (ultimately 1000’s of nanobiosensors per system) is essential to provide chips in sufficient numbers to pursue there’s no “MOSIS” medical & biological discovery (foundry) for Production, en masse this kind of stuff! (100’s of systems)

24 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

there are no foundries most of this… progressive magnification: BioNEMS sensors

Foundry-basedIndividual BioNEMS device chip Foundry-based device preproduction, Local Nanofab preproduction: BioNEMS wafer Foundry: 4” or 6” wafers Caltech current format = 4” wafers • 36 chips per wafer piezo MEMS micro- • 32 contacts per chip SOI LSI epilayer DRIE electronics • 2 fluidic vias per chip wafers growth (membranes) fabrication nanofab

Foundry process flow summary: single-crystal Si special single-crystal deep backside etch frontside microfab BioNEMS structural layer doped Si epilayer prepares fluidic vias & for electronics fabrication on sacrificial layer for transducers membranes for nanofab and interconnects processes • 4” wafers (will scale to 6”) •Includesnanocantilever microelectronics: array Close up of active area: ~70μm fluidic vias • nanoscale transducers/actuators to external connections • ultrathin piezoresistive epilayer • Fluidic vias (to mate w/mfluidics) • Heavily passivated to insure biocompatibility, reliability • Fifty process steps ( before CAD layout motivation: microfluidics drives us to large chips commencement of nanofabrication !! )

microfluidics-embedded nanobiosensors picoliter-scale fluidic delivery & control BioNEMS = fluidic nanomechanics + soft microfluidics + surface biochemistry

top fluidic layer fluidic I/O (16 ports) microfluidic BioNEMS channels chip

front side back side

Side view, schematictop view glassbottom top layerview polymer for seal & BioNEMS bottom fluidic layer channel definition chip BioNEMS chip (w/ 2 vias) backside flow layer (PDMS) fluidic path Back side pumps / analyte inlets backside valve layer (PDMS)

25 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

first BioNEMS application: single-pathogen sensing BioNEMS pathogen detector (current gen)

all-electronic detection of individual, passivation unlabelled bacterial/viral pathogens k Pathogen-Specific fluidic via Antibodies steady & pulsatory microfluidic flow Au permits continuous Au 100 nm readout active cantilever pathogen binding k’ → perturbation of dock mechanical response “dummy” cantilever Reference Biospecifically immobilized pathogen Electrode “bridges” dual cantilever devices 20μm

BioNEMS pathogen detector (current gen) Current Experiments: Force-Correlation Sensing

passivation

fluidic via Au Au active cantilever

dock

anthrax“dummy” spore cantilever Reference (to scale) Cross-correlation sensors “Lock-in” force-transmission Electrode Cross-correlation sensors “Lock-in” force-transmission 1μm 20μm multiple-cantilever assays

26 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

realizing NEMS: mesoscopic mechanics

macroscopic mechanical resonator defects Ultimate Limits: fundamental noise processes

mesoscopic resonator

recall: Resistance switching in a small MOSFET. K.S. Ralls, et al., Phys. Rev. Lett. 52, 228 (1984).

realizing NEMS: Q, and its scaling with size realizing NEMS: acoustic loss processes at the nanoscale

slope ~ 1/3 MacGuigan ‘78 one resonator mode* – 109

8 10 Duffy ‘90

Kleiman ‘87 Agnolet ‘84 apparent 107 Klitsner ‘87 linear scaling 6 10 Buser & de Rooij‘90 of Q with Greywall & Yurke ‘94 dimension 5 10 Mihailovich & Parpia ‘95 ( ~ volume/surface ratio )

Q-factor for resonance for Q-factor Resonator Mode 4 10 Caltech Group ‘96-’99

-10 -5 0 5 10 log (resonator volume/mm3) * used for the measurement, computation, signal processing, etc . . .

27 PASI 2006 - Bariloche, Argentina Lectures M.L. Roukes, Caltech

realizing NEMS: acoustic loss processes at the nanoscale (some) references

(NOTE: many of the references on this page can be found on-line at: http://nano.caltech.edu/publicat.html )

one resonator mode – • Fundamentals, beam theory, etc. A. N. Cleland, Fundamentals of Nanomechanics (Springer-Verlag, Heidelberg, Germany, 2002). many energy reservoirs • Introductory Reviews M.L. Roukes, “Nanoelectromechanical Systems”, Opening Lecture, 2000 Solid State Sensor and Actuator Workshop, Hilton Head, SC 6/4/2000, published in "Technical Digest of the 2000 Solid State Sensor and Actuator Workshop" (Transducers Research Foundation, Cleveland, OH; 2000) ISBN 0-9640024-3-4; on-line at: External Thermal Surrounding Gas http://www.arxiv.org/pdf/cond-mat/0008187 Phonons Bulk Defects Ekinci KL, Roukes ML, “Nanoelectromechanical systems”, Review of Scientific Instruments 76 061101 JUN 2005 (Clamping Losses) (e.g. Two Level Systems) Roukes ML, “Plenty of Room Indeed”, SCIENTIFIC AMERICAN 285: (3) 48-57 SEP 2001 Roukes M, “Nanoelectromechanical systems face the future”, PHYSICS WORLD 14: (2) 25-31 FEB 2001 • Noise in NEMS Cleland AN, Roukes ML, “Noise processes in nanomechanical resonators”, J APPL PHYS 92 (5): 2758-2769 SEP 1 2002 Surface Defects Internal Thermal Ekinci KL, Yang YT, Roukes ML, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems”, Phonons and Adsorbates J. Appl. Phys. 95 2682 MAR2004 (other Resonator Modes) Resonator Mode • NEMS Transduction/Actuation K.L. Ekinci, “Electromechanical Transducers at the Nanoscale: Actuation and Sensing of Motion in Nanoelectromechanical Systems (NEMS)”, Small 2005, 1, No. 8-9, 786 –797; on-line at External Photons http://nanoscience.bu.edu/papers/Ekinci%20review.pdf External Electrons (Black Body) • Quantum Limits (in over-layer) Schwab KC, Roukes ML, “Putting Mechanics into Quantum Mechanics”, Physics Today JULY 2005 Other… on-line at: http://nano.caltech.edu/papers/Schwab-Roukes-PT-July05.pdf