Nanoscale mechanical property measurements in AFM modes with direct force control Part I: PeakForce Tapping and Force Volume mechanical property mapping Bede Pittenger, Senior Applications Scientist

A brief review of AFM imaging technology • Mapping topography -> More information •

Contact mode (1986)

•

Tapping Mode (1992)

•

Force-Volume Mapping (~1992)

•

Contact Resonance (AFAM, UAFM~1996)

•

Peak Force Tapping/PeakForce QNM (2009) •

PeakForce TUNA (2011)

•

PeakForce KPFM (2012)

•

PeakForce IR (2014)

•

PeakForce XYZ (…)

7/16/2014

2

PeakForce QNM vs. Force Volume Mechanical property mapping modes

PeakForce Tapping (PF-QNM)

Force Volume (FV)

Z motion

Deflection

•

Sinusoidal ramping (not linear): no piezo resonance, no overshoot

•

Linear ramping: abrupt turn-around at high speed -> ringing, overshoot

•

Real feedback loop force control: benefits from prior curves

•

•

Fast ramping (~kHz): faster images, even with more pixels

Discrete force triggers at each ramp: attempts to turn around at trigger. At high speeds, it can’t reverse fast enough, so it overshoots.

•

Ramping rate is limited (1h) 3. Fast & good force control, but low resolution (few pixels)

4

PFT Provides Excellent Spatial Resolution & Force Control

7/16/2014

5

PF-QNM & FV calculate sample properties directly from force curves The complete force curve from every interaction between tip and sample is analyzed in real-time, allowing: •

Feedback based on the peak force, protecting the tip and sample.

•

Peak Force, Adhesion, Young’s Modulus, Deformation, Dissipation mapped simultaneously with topography.

•

Individual curves can be examined and analyzed offline (PeakForce Capture)

(ii)

7/16/2014

6

High resolution PF-QNM New information revealed

Barrier layer Nylon Strength & gas impermeability

Tie layer ULDPE Preserves layer adhesion

DMTModulus

Sealant layer Metallocene PE/LDPE blend Adheres to itself when heated

(a) (b)

Heat sealed bag: Barrier and Tie layers are incompatible, so we expect a relatively abrupt interphase. (c)

•

Single scan line has a clear step in modulus over a distance of ~75nm.

•

Lamella do not cross the interface, but grow epitaxially from the Barrier layer – can see in averaged profile.

•

Lamella are highly ordered and perpendicular to interface ~250nm into the Tie layer.

(a)

(b)

7/16/2014

7

High resolution PF-QNM New information revealed

Barrier layer Nylon Strength & gas impermeability

Tie layer ULDPE Preserves layer adhesion

DMTModulus Height

Sealant layer Metallocene PE/LDPE blend Adheres to itself when heated

(a)

(b)

Tie and Sealant layers are relatively compatible = wider interphase. (c)

•

Single scan line: the variation in modulus is dominated by individual lamella.

•

Collectively: modulus varies over a much wider range ~250nm to ~1um.

•

Lamella from Tie layer act as nucleation sites or penetrate into the Sealant: more ordered region to ~1um from the interface.

(a)

(b)

7/16/2014

8

Variation in viscoelastic response Visible in Dissipation map

Dissipation

• Dissipation in Barrier10x faster Bruker Nano Surfaces Division

14

PeakForce Tapping Mapping Breadth Stable, nondestructive imaging with simultaneous mechanical properties Height

Work function

Conductivity

PeakForce TUNA conductivity imaging, shown here on vertically standing carbon nanotubes. Impossible with contact mode. 1000nm image.

PeakForce KPFM work function imaging, here shown for reduced graphene oxide. Revealing > FV •

Allows high resolution mapping

•

Expands accessible range of frequency significantly

Time dependent mechanical properties can be investigated by observing modulus and dissipation at different ramp rates Tie-Sealant interface in heat •

DMT, Sneddon models do not include viscoelasticity

•

Further work required to make a quantitative connection between ramp observations and models

•

Contact Resonance may be able to help

sealed bag composite

PeakForce Tapping is a great candidate for integration with other AFM techniques 7/16/2014

16

contact me at: Bede Pittenger, PhD [email protected]

www.bruker.com/service/educationtraining/webinars/afm.html

Also check out Nanoscale world community and SPM Digest Forum: nanoscaleworld.bruker-axs.com/ 7/16/2014

17

Nanoscale mechanical property measurements in AFM modes with direct force control Part II: Force Control in Contact-Resonance Atomic Force Microscopy Gheorghe Stan

[email protected]

Contact resonance AFM: cantilever dynamics

Ultasonic Atomic force microscopy (UAFM)  

Atomic force acoustic microscopy (AFAM)  

Yamanaka et al., Japan. J. Appl. Phys. 35, 3787, 1996

Rabe et al., Rev. Sci. Instrum. 67, 3281, 1996

Mode 1

Mode 2 free

contact

Clamped‐spring‐coupled beam,  Rabe et al., Rev. Sci. Instrum. 67, 3281, 1996

2

Contact resonance AFM: contact mechanics Hertz model (sphere on flat) 

Tip 2r

M  E /(1  2 )

One reference

n n  1  k R  1  k R  1     1   M S  k S  M R  k S   M T 

test

Sample

n = 1 –flat punch n = 3/2 –spherical indenter

ES  ER (k S / k R ) n

reference

FN

F k N  N  2rE *  z 1/ E  1/ M S  1/ M T

uncertainty 20% U. Rabe et al., Ultrasonics 38, 430 (2000)

n

Two references

 k R*1   *   1  kR2  MS  n n  k R*1   1 1   k R*1  1 1  *      *     k S   M R 2 M R1   k R 2  M R1 M R 2

uncertainty 5% G. Stan and W. Price, Rev. Sci. Instrum. 77, 103707 (2006)

A. M. Jackob et al., Nanoscale, 6, 6898, (2014): “… in accordance to,20, 21 less effort in probe modeling is still sufficient for quantitative nano mechanical analysis of conventional materials as long as a multi‐ reference sample approach is used.  REFERENCE 11 REFERENCE

TEST TEST SAMPLE SAMPLE

REFERENCE 22 REFERENCE

3

Quasi‐static vs dynamic contact stiffness: measurement sensitivity AFM spectroscopy: Force‐distance curves S1 / S1(k*=0), CR-AFM first eigenmode S2 / S1(k*=0), CR-AFM second eigenmode Sfd / Sfd(k*=0), force-distance AFM

100

Sfd 

  k / kc

1 k t 1  kc  (   1) 2

CR‐AFM spectroscopy: Resonance spectra Sn 

1 f n  F (kn ,  ) f1 

Normalized sensitivity, S/S(k*=0) (%)

1 1 1   , k t kc k 



10

1

0.1

0.01

0

20

40

60

80

100

Normalized contact stiffness, k*/kc

4

F‐d versus CR‐AFM with a medium‐stiff cantilever, kc=35.5 N/m, on low‐k dielectric films

Samples from Sean King (Intel Corp.)

5

CR‐AFM imaging on Cu/low‐k dielectric interconnects On a Cu‐low‐k interconnection structure, CR‐AFM provided contrast in contact stiffness and damping between the Cu lines  and the surrounding dielectric material and the intervening Ta/TaN barrier layer. By varying the load applied to the probe,  clear differences in the decay of damping with depth beneath the surfaces of the Cu and the dielectric were revealed. 

Low‐k ILD

Ta/TaN

Cu

Si substrate

Stan et al., Nanotechnology 23, 215703 (2012)

6

CR‐AFM imaging on granular Au film Topography (STM)                  Contact resonance (CR‐AFM)

Both topography and contact stiffness maps were self‐consistently correlated to reveal nanoscale variations of the indentation modulus at the grain level as well as across the grains. Individual elastically‐deformed asperities make a non‐conforming contact with the spherical smooth end of the CR‐AFM probe.

20 10 0 10 20

20 10 0

100 nm

100 nm

10

20

30 30 10

20 10 0

20 nm

F = 350 nN

10

Stan and Cook, Nanotechnology 19, 235701 (2008)

30 30

20 nm

F = 250 nN 10 20

Indentation modulus

30 30 10

20 nm

F = 100 nN

10

10 20

30 30 10

20 nm

Single‐asperity contact

Multiple‐asperity contact

100 nm

7

Contact geometry: tip wear

Si tips, especially the sharp ones, wear when they are used in contact spectroscopy and scanning modes. Great care  is required to monitor the tip wear during use. This can be done from repeated contact stiffness measurements on  k  2rE the same material as the contact stiffness is in direct relationship with the change in contact area,                .  Consequently, reliable contact stiffness measurements required stable tip shapes, which, most likely, will be the  ones that are pre‐wear.

Fresh sharp tip (NanoSensors)

Tip used in contact AFM scanning mode Tip used in CR‐AFM spectroscopy

(Killgore, Geiss, and Hurley, Small 7, 1018 (2012))

(Stan and Price, Rev. Sci. Instrum. 77, 103707 (2006))

8

Flattened tip used in CR‐AFM measurements on low‐k dielectric thin films

Credit for SEM images: Kavuri Premsagar Purushotham (NIST) 9

Load‐dependent CR‐AFM measurements

Resonance frequency (kHz)

The measurements consist of recording simultaneously both the deflection and resonance frequency of an AFM cantilever as the probe is gradually brought in and out of contact. 710

Load-dependent CR-AFM on Si(100) Flattened-tip: RT=150 nm, r=32.5 nm

705 700 695 690 685 680

Applied force (nN)

1000 800 600 400 200 0

G. Stan et al., J. Mater. Res. 24, 2960 (2009)

0

10

20

30

40

50

Piezo displacement (nm) 10

Real‐time load‐dependent CR‐AFM on a 1.6 GPa low‐k dielectric Flat‐punch approximation:

k   2rc E  2rc (1/ MT 1/ MS )1

11

Intermittent Contact Resonance AFM (ICR‐AFM) The measurements consist of recording simultaneously the deflection, resonance frequency, and amplitude of the AFM cantilever as the probe is gradually brought in and out of contact at any point in the scan. Key points for quantitative nanoscale mechanical property characterization by 3D ICR‐AFM: ‐force control during intermittent contacts (Force Volume, Peak Force Tapping) ‐adhesive force measurement ‐force‐resonance frequency correlation during contacts ‐imaging at a non‐eigenmode frequency (lower than f 1 )

12

Intermittent Contact Resonance AFM (ICR‐AFM) in Force‐Volume AFM nm 80 60 40 20

ICR‐AFM on PS‐PP blend: 128x128 ramps over 2 µm x 2 µm area; 1 s per ramp.  

Approach

Retract

Resonance frequency Resonance amplitude 660 659 658

0.50 0.45 0.40

662 660 658

Resonance frequency Resonance amplitude 0.4 0.2

0.5 0.4 0.3

 = - 2.5 nm

670 665 660

0.4 0.2

665 660

0.3 0.2 0.1

 = - 1.0 nm

670 665 660

0.3 0.2 0.1

 = - 1.0 nm

665 660

0.20 0.15 0.10

 = - 0.5 nm

670 665 660

0.3 0.2 0.1

 = - 0.5 nm

670 665 660

0.20 0.15 0.10

 = 0.0 nm

680

0.2

680 670

0.20 0.15 0.10

 = 0.5 nm

680

690 680 670

0.20 0.15 0.10

 = 1.0 nm

690 680 670

0.20 0.15 0.10

 = 2.5 nm

690 680 670

0.20 0.15 0.10

out of contact

 = - 5.0 nm

670 665 660

in contact

660

660

680 660

680 660

 = 5.0 nm

680 660

 = - 5.0 nm

 = - 2.5 nm

0.1

 = 0.0 nm

0.2 0.1

 = 0.5 nm

0.2 0.1

 = 1.0 nm

0.2 0.1

 = 2.5 nm

0.2 0.1

 = 5.0 nm

f1air = 104.9 kHz, f2air = 657.6 kHz; kc = 9.5 ± 0.5 N/m 13

Tomographic ICR‐AFM x

Topography nm

y Frequency Approach

80 60 40 20

Frequency Retract

5 nm 0

-5

kHz

kHz

690 680 670 660

690 680 670 660

700 nm

2000 nm

Amplitude Approach

Amplitude Retract

z x

y

nm

nm

0.4

0.4

0.2

0.2

0.0

0.0

G. Stan, S. D. Solares, B. Pittenger, N. Erina, and C. Su, Nanoscale 6. 962 (2014) 14

Fast dynamic indentation on elastomers Approach; Retract Approach; Retract

4

With Schwarz contact model (U. D. Schwarz, J. Colloid Interface Sci., 2003, 261, 99),  a transition model between DMT and JKR models, the depth‐dependence of the  contact stiffness in the “ dynamic flat‐punch” limit is given by:

PP

3 PS

2

  k *2 / 4 RT E *2  

1 0

 1  0, DMT

-1 10

15

20

25

30

4 

2 1



2k * Fa / RT E *2



DMT ‐long‐range attractive force outside the contact area. JKR ‐short‐range attractive force inside the contact area.

 1, JKR

35

1

Contact stiffness, k* (N/m)

 / k *     k *3 / 2

1.0

PS

0.4 0.2

1 = 1.0

0.6

1 = 0.5

PP

0.8

1 = 0.0

5

1/2

0

 / k*

Indentation depth,  (nm)

PP:

5

In the case of a fast dynamic indentation of an elastomer (Wahl et al., J. Colloid  Interface Sci., 2006, 296, 178), due to viscoelastic effects, the contact area remains  approximately constant during oscillations and the contact geometry resembles  k * ~ rc that of a ”flat punch” configuration, with                  rather than                          .  k *  F / 

1 = 0.0 1 = 0.5 1 = 1.0

PS:

E*  1 / 4 RT 

 1  2  / 8Fa    2

0.0 -0.2 0

50

100

150 k*

200

250

3/2

15

Intermittent Contact Resonance AFM (ICR‐AFM)

0

2

4

6

GPa

Normalized measurements

Indentation modulus,  E * PP Approach Retract

PS

1

2 3 4 5 Indentation modulus (GPa)

6

Normalized measurements

Transition parameter,  1

-1

0

1

PS

Approach Retract

PP

-0.5

0.0

0.5

1.0

1.5

1

16

PS

Approach Retract Approach Retract

685 680

PP

675 670 665 660 -8

-4

0

4

b 0.5 0.4 0.3 0.2 0.1 -8

Indentation depth (nm)

Indentation depth (nm)

d -8

670

680

PS

-4

0

c

60

PP

40 20 0

4

-8

Resonance amplitude (nm)

690

PS

-4

0

4

Indentation depth,  (nm)

Resonance frequency (kHz) 660

Dissipated power (f W)

a

Resonance amplitude (nm)

Resonance frequency (kHz)

ICR‐AFM: Frequency, amplitude, and dissipated energy

0.1

e

PP

PS

0.2

0.3

Dissipated power (fW)

0.4

10

f

PP

20

30

PS

40

50

60

PP

-4 0 4

g

h

4

i

0 -4 -8 2000

1500

1000

500

0

2000

1500 1000 500 Distance (nm)

0

2000

1500

1000

500

0

17

Intermittent Contact Resonance AFM (ICR‐AFM) in Peak Force Tapping ‐force control during intermittent contacts (Force Volume, Peak Force Tapping) ‐adhesive force measurement ‐force‐resonance frequency correlation during contacts ‐imaging at a non‐eigenmode frequency (lower than f 1 )

Setpoint PI Controller

Peak Force Tapping @ 2 kHz

Force vs time and Displacement vs time

500 µs

Laser Photodiode diode Z Modulation Piezo detector shaker

PLL XYZ Piezo scanner

Frequency vs time and Amplitude vs time

f1air = 107.3 kHz, f2air = 670.5 kHz, f3air = 1,865.5 kHz; kc = 9.12 ± 0.07 N/m

Signal processor: Force, displacement, frequency, and amplitude vs time during individual oscillations.

G. Stan and R. Gates, Nanotechnology 25, 245702 (2014) 18

500 nm

(b)

20 0

nN 8 6 4 2

(c)

eV 400 300 200

(d)

GPa 4 3 2

(e)

kHz 2.2 2.0 1.8 1.6

(f)

kHz 6 5 4

Adhesion (nN)

40

Modulus (GPa) Dissipation (eV)

nm

Freq. shift (kHz) Freq. shift (kHz)

(a)

Height (nm)

ICR‐AFM as Amplitude Modulation – Frequency Modulation of Peak Force Tapping PS‐PMMA

(g) 40

Topography (PFT)

20 0

(h)

7 6 5 4

Adhesion (PFT) (i)

400

Dissipation (PFT)

300 200

(j)

4

DMT Elastic Modulus (PFT)

3 2

(k)

2.1

Resonance frequency shift f3 (ICR) slow  PLL ‐ 100 µs time constant

1.9 1.7

(l)

6 5 4 0

Resonance frequency shift f3 (ICR) fast  PLL ‐ 1 µs PLL time constant

1000 2000 3000 4000 5000

Distance (nm)

19

Applied force (nN)

30 15

15

20 10

10

105

5

00

0

-10 490

491

492

493

494

495

Time (ms)

Fast PLL detection

Applied force (nN)

40 15 30

15

10 20

10

105

5

00

0

-10 468

469

470

471

Time (ms)

472

473

Resonance frequency shift (kHz)

Slow PLL detection

40

Resonance frequency shift (kHz)

ICR‐AFM: Individual oscillations

With a slow detection, the changes in the contact resonance frequency are averaged over the entire period of an oscillation including out-ofcontact intervals.

With a fast detection, the averaging time is reduced, so the changes in the contact resonance frequency during individual oscillations are momentarily tracked.

20

PS-PMMA 50

nm 40

Approach on PS Retract on PS Approach on PMMA Retract on PMMA

40

20

PS

PMMA

k* (N/m)

0

500 nm

PS

30 20 EPS = 3.20 GPa, 1=0.27 EPS = 3.20 GPa, 1=0.72 EPMMA = 2.77 GPa, 1=0.08 EPMMA = 2.77 GPa, 1=0.66

10 0

40

Force (nN)

30 20

-10

10

-10

0

0

10

20

30

40

-10 780

800

820

840

Applied force, F (nN)

860

Frequency (kHz)

Time (ms)



12

k *  6 RT E *

8



2 1/ 3

4

  1   4   12

 3Fa  F  Fa  

2/3

0

780

800

820 Time (ms)

840

860

1/2

(nN )

6

EPMMA  2.83  0.09 GPa,  1  0.08  0.04 Negative  slope region : EPS  3.40  0.10 GPa,  1  0.72  0.01 EPS  2.83  0.09 GPa,  1  0.66  0.03

E*  1 / 6 RT  2

4

1/2

(F+Fa)

Positive  slope region : EPS  3.40  0.10 GPa,  1  0.27  0.04

F  Fa      k *3

PMMA retract data PMMA fit by eq. prediction band for PMMA fit PS retract data PS fit by eq. prediction band for PS fit

2

 1  2 / 3Fa   2 0 20

40

60

80 3/2

100

120

140

3/2

k* (N/m)

21

Conclusions

‐Depth‐dependence of contact stiffness in force‐controlled CR‐AFM. 

‐Load‐dependent CR‐AFM elastic modulus measurements with flattened tips.

‐ICR‐AFM (in force volume and peak‐force tapping) is a new 3D high‐speed nanomechanical property measurement AFM technique. 

‐Improved quantitative elastic modulus measurements were demonstrated by using ICR‐AFM  on PS/PP and PS/PMMA blends. 

‐Transition contact models (e.g. Schwarz model) provide a self‐adaptive analysis for the  heterogeneous mechanical properties of elastomeric surfaces at the nanoscale. 22

contact me at: Bede Pittenger, PhD [email protected]

www.bruker.com/service/educationtraining/webinars/afm.html

Also check out Nanoscale world community and SPM Digest Forum: nanoscaleworld.bruker-axs.com/ 7/16/2014

23