Improving the accuracy of Atomic Force Microscope based nanomechanical measurements. Bede Pittenger Bruker Nano Surfaces, Santa Barbara, CA, USA

Transcription

1 Improving the accuracy of Atomic Force Microscope based nanomechanical measurements Bede Pittenger Bruker Nano Surfaces, Santa Barbara, CA, USA

2 How can we improve accuracy in our nanomechanical measurements? 1. Choose the right tool for the job 2. Understand and minimize error sources 3. Improve modeling of contact mechanics and cantilever dynamics 2

3 AFM mode time and modulus ranges Force Volume and PeakForce Tapping 3

4 PeakForce QNM and Force Volume Non-resonant mechanical property mapping modes ~1994: Force Volume (FV) ~2010: PeakForce Tapping Z motion Deflection Linear ramping: abrupt turn-around at high speed -> ringing, overshoot 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 (~.1kHz) Sinusoidal ramping (not linear): no piezo resonance, no overshoot Real feedback loop force control: benefits from prior curves Fast ramping (~khz): faster images, even with more pixels Low force, high stability PeakForce QNM & FV both collect the complete force curve from every interaction between tip and sample, directly calculating and mapping sample properties 4

5 Resolution & Force Control at high ramp rate with PeakForce Tapping 2000Hz 5

6 Improved Force Volume & Ramping High Speed, Wide Ramp Range & Quantitative Data High Speed, Quantitative Force Maps From <1Hz to >200Hz linear ramping Overlaps PeakForce Tapping rates 156Hz 1Hz High Resolution Force Maps in X, Y, Z >512x512 pixel images practical Multiple property maps calculated Multiple ramp data channels acquired Collect up to 12 data cubes at once Improved offline analysis allowing direct comparison with PFC data sets Surface hold functionality 6

7 Load F (nn) Deflection (nm) Analyzing Force Curves From Deflection and Z to modulus Deflection (V) Z Position (V) time time 1. Eliminate time 2. Apply Deflection sensitivity 3. Apply Z sensitivity Load vs. Displacement F = 4 3 E Rd 3/2 Indentation d (nm) Elastic Unloading curve 4. Calculate indentation 5. Apply Spring constant 6. Fit data with contact mechanics model Force Curve Z Position (nm) 7

8 Force Volume Error Analysis Consider Hertzian (DMT) contact model Force F = 4 3 E Rd 3/2 = K c D If Z is piezo extension, d ~ Z Z 0 D Where D and d are deflection and indentation relative to pull-off. Deflection D = S D V where V is the deflection voltage d Potential sources of error include: tip radius (R), spring constant (Kc), Z position, deflection voltage (V), and deflection sensitivity (Sd) Variance formula allows estimation of error in E = 3K c δe E 2 = 1 4 δr R 2 + δkc Kc D d 2 δz Z Substitute indentation Ratio : d D = K c F and E* if desired D 3 4E RF 2d 2 δs D S D 4 R D d δv V 2 3 to put in terms of 8 2

9 Estimated error in modulus for force volume dr~15%, dkc~6-16%, dsd~5%, dv~1%, dz~1% Constant Force Constant Force: low modulus limit is dominated by error in R and Kc Not always practical to go to very low modulus with stiff probes since deformation gets huge (may need nonlinear elasticity, plastic deformation) High modulus limit dominated by error in Z and Deflection Sensitivity Constant deformation: error increases for soft samples due to baseline deflection noise For PeakForce Tapping, Z error will be higher: typically adds ~5% to FV error 9

10 How to improve accuracy in FV & PFT New probes for cells LDV calibrated spring constants Controlled tip radius=65nm New probes for materials LDV calibrated spring constants Controlled tip radius =33nm Selection of spring constants to cover range of moduli 0.25, 5, 40, 200 N/m Guided calibration software Better contact modeling 10

11 Accuracy of PF-QNM (vs. DMA) Ternary polymer blend DMT Modulus PE PP PS PP PE PS PE:PP PS:PP DMA avg AFM stdev stdev/avg 8% 18% 13% 12% 8% DMA-AFM 10% 45% 10% 36% 1% 11

12 Practical issues with nanomechanical measurements Special modeling Time-dependent deformation: include viscoelasticity Non-ideal sample geometry: sample not homogeneous! Tip contamination Must detect and clean or replace tip Elastic limit Avoid exceeding elastic limit: results in increased contamination & needs inelastic modeling Surface layer? Compare properties at different deformation depths (and ideally with Hysitron nanoindenter) [1] M. Chyasnavichyus, S. L. Young, and V. V Tsukruk, Langmuir, [2] Y. M. Efremov, W.-H. Wang, S. D. Hardy, R. L. Geahlen, and A. Raman, Sci. Rep.,

13 AFM mode time and modulus ranges Contact Resonance 13

14 Contact Resonance for stiff materials (also E, E, loss tangent) Challenges: Preserving the tip (repeatability) Modeling tip-sample behavior (CR freq & Q -> moduli) Calibrating all of the parameters (accuracy) 14

15 Bruker Contact Resonance Key Features Bruker CR is based on FASTForce Volume Provides standard force curve for comparison for each pixel in map Approach Hold Force and sweep frequency Retract More repeatable: lateral force on tip is minimized, reducing tip wear More information: allows measurement of Adhesion force for each pixel better contact mechanics modeling Whole sweep is saved, allowing detection of artifact peaks and multiple modes 15

16 Real-time Contact Resonance Sweeping Force Volume for mapping, Ramp for single points Single point Ramp with sweep Real-time Force Volume maps Height frequency Q Amplitude Real-time Force Volume mapping: f, Q, A, k*/kc, E, E, loss tangent, etc. 16

17 Consistent measurement of modulus Minimal tip wear over many engages Al Si Cr 327,680 curves, 80 frames, 40 hours later Si: 165±11 GPa Al: 123±27 GPa Cr: 203±22 GPa Si: 165±8 GPa Al: 141±24 GPa Cr: 209±25 GPa 17

18 Consistent measurement of modulus Stiff materials over a range of loads 200nN 500nN 1000nN Al Si Cr 18

19 Measuring Loss Modulus E in addition to storage modulus E Loss tangent or loss modulus can be calculated from CR f & Q Research into the best way to calculate the loss modulus is ongoing, so we implemented three popular algorithms YHT 2008 and Rabe 2006 require a reference sample with known loss modulus, while PKAS 2016 does not tan δ = E E P. A. Yuya, D. C. Hurley, and J. A. Turner, J. Appl. Phys., U. Rabe, Atomic Force Acoustic Microscopy, in Applied Scanning Probe Methods II, Springer-Verlag, M. Kalyan Phani, A. Kumar, W. Arnold, and K. Samwer, J. Alloys Compd., PS-PMMA topography with false coloring by loss modulus 19

20 Modulus maps from 2 nd and 3 rd modes Choose mode for optimal sensitivity Second mode E E PS PCL Third mode E E Data acquired in collaboration with Philippe Leclere, U. Mons 20

21 Storage and loss modulus mapping FFV-CR on a ternary polymer blend PE PP PS PE PP PS 21

22 Summary Combined, non-resonant and resonant AFM modes cover a huge range of properties FV force curves for soft samples at low frequencies CR for stiff samples at higher frequencies CR provides direct access to viscoelastic parameters Understanding the various error sources allows us to prioritize improvements to address them Spring constant and tip shape are key for all methods FV can be fairly accurate even without a reference sample PFT is not as accurate, better for resolution and speed Contact resonance has a lot of parameters to calibrate, making relative measurements (with a reference material) more practical Room for improvement still exists Better modeling and operator guidance, etc. 22

23 Copyright Bruker Corporation. All rights reserved.