BDS2016 Tutorials: Local Dielectric Spectroscopy by Scanning Probes

Transcription

1 BDS2016 Tutorials: Local Dielectric Spectroscopy by Scanning Probes Massimiliano Labardi CNR Institute for Physico-Chemical Processes (IPCF) Pisa (Italy)

2 OUTLINE Broadband Dielectric Spectroscopy (BDS): Information on relaxation dynamics through electric polariation. Local Dielectric Spectroscopy (LDS or nanods): the same kind of information on a nanometer-sie volume of material. How Local Dielectric Spectroscopy can be realied by resorting to scanning probe techniques like the Atomic Force Microscope.

3 ORIENTATIONAL DIELECTRIC RESPONSE E 0 cos(wt)

4 BROADBAND DIELECTRIC SPECTROSCOPY V(t)=V 0 cos(wt) I(t)=I 0 cos(wt - d) r (w) Zˆ( w) Vˆ( w) Iˆ( w) Zˆ 0 ( w) 1 iwc 0 C 0A 0 D Void parallel plate capacitor 1 1 Zˆ( w) Cˆ ( w) ˆ r( w) C0 iwcˆ( w) iwzˆ( w) Filled by dielectric Cˆ ( w ) Zˆ ( w ) w w w 0 ˆ r ( ) '( ) i "( ) C0 Zˆ( w )

5 DIELECTRIC RELAXATION SPECTRUM " / ' Material: Polymer (PVAc)

6 MOTIVATION FOR LOCAL MEASUREMENTS BDS provides the average behavior of a macroscopic sample volume. Behavior of nanometer-sie volume: - Single macromolecules - Heterogeneity - Interface

7 DIELECTRIC PROPERTIES ON A LOCAL SCALE A conductive tip acts as a nanometer-sie electrode. Applying electric potential to the tip a localied electric field is generated. A current is produced like in BDS. Current measurement noise prevents sensitivity to capacitance < 1 af.

8 ATOMIC FORCE MICROSCOPE (AFM) Also a force is produced that depends on polariation charge that can be measured accurately if the tip is the one of an ATOMIC FORCE MICROSCOPE. Microscope setup Cantilever force sensor Capacitance > F. Y. Martin et al Appl. Phys. Lett (1988).

9 ELECTROSTATIC FORCE MICROSCOPE conductive probe E V ~ conductive substrate tens of nm Y. Martin et al Appl. Phys. Lett (1988).

10 SOURCES OF ELECTRIC FORCE Coulomb force: F C q S qt ( qs V ) (Static charges) Capacitive force: F 1 2 dc dz V 2 (Induced charges) V surf V a ( V ) V cos( w t) surf surf surface potential difference V a external applied potential dc ac (v dc ) w m modulation frequency m

11 DIELECTRIC PROPERTIES BY FORCE MEAS. 1 C ( s) 1 C ( w ( )) Fdc v V dc 0 C ( w ( )) Fw ( t) vdcv0 cos( wt) Local dielectric spectroscopy (LDS) P.S. Crider et al. Appl. Phys. Lett (2007).

12 CAPACITANCE MEAS. BY FORCE MICROSCOPY r (w) V(t)=V 0 cos(wt) (air gap) h (dielectric thickness) Cˆ( w) 1 iwzˆ( w) Zˆ( w) 0A C0 ( ) Series capacitor 1 iwc ( ) 1 iwcˆ ( 0 1 w) C ˆ ˆ r ( w)a ( ) 0 1 w h Capacitance is no longer a linear function of r! Simple modeling for this geometry is needed to carry out r

13 CAPACITANCE MEAS. BY FORCE MICROSCOPY tip V(t)=V 0 cos(wt) r (w) (air gap) h (dielectric thickness) Series capacitor + tip (not plane) Capacitance is no longer a linear function of r! Modeling for this geometry is needed to carry out r

14 TIP/SAMPLE MODELING el V = 1V Tip radius R= 20 nm Tip Total Cantilever Cone [nm] Apex contribution to total force is dominant at small distance only (few nm) J. Colchero A. Gil A.M. Barò Phys. Rev. B (2001)

15 SPATIAL RESOLUTION: FORCE vs. GRADIENT F el ( ) Tip apex Cone Cantilever Total distance [nm] Force gradient allows to increase resolution. AFM is capable to measure -gradient.

16 AFM OPERATION: TAPPING and LIFT MODE 2 h lift 0 Topography is detected (1) by a dynamic AFM mode named TAPPING MODE (cantilever oscillates at its resonant frequency) V a is applied only during Lift scan (3) (to avoid charge transfer to sample)

17 FORCE and GRADIENT DETECTION... ) ( ) ( ) ( ) ( 0 0 V F V F V F el el el ) ( ) cos( w V F t F k m el d d ) ( ) ( ) cos( ) ( V F V F t F V F m m el el d d el w w Static deflection Cantilever: forced harmonic oscillator (F d ) in a force field (F el ) sensitive mainly to F el F el t d df k el res res 2 w w Resonant frequency shift

18 THE FREQUENCY SHIFT 1 2 FM: Chase resonance frequency by a self-oscillator.

19 EXAMPLE OF SPATIAL RESOLUTION IMPROVEMENT AM (Amplitude Modulation): Force mode () FM (Frequency Modulation): Chasing mode (force gradient) Improvement of spatial resolution with FM mode. U. Zerweck Ch. Loppacher T. Otto S. Grafstrom L.M. Eng Phys. Rev. B (2005)

20 2 C" 2 / 2 C' 2 LDS FREQUENCY MODULATION K K K K K K K K fitting N avg = 10 tan d v FM mode limit: Chasing speed Frequency [H]

21 PHASE MODULATION (PM) 1 2 Constant frequency: phase is proportional to frequency shift

22 BANDWIDTH EXTENSION WITH PHASE MOD. 2 C" 2 / 2 C' 2 Material: PVAc N avg = 4 PM data FM data PM mode limit:

23 LDS BANDWIDTH EXTENSION Frequency bandwidth of LDS can be extended up to MH range and more. SEE TALK O-71 on Thursday 15 th by M. Labardi et al.

24 APPLICATION OF LDS TO INTERFACE STUDY Cantilever Cone Apex (probe) Sample Interface region is probed : in section (phase separations emerging to free surface) or in depth (nanostructures near to free surface).

25 Mo 6 S 2 I 8 NANOWIRES IN PVP FILM Polymer: poly (vinyl pyrrolidone) T g 145 C. A C A C A C B Topography B Electric amplitude B Electric phase T = C f = 226 H M. Labardi et al J. Non-Cryst. Solids (2013)

26 MMT CLAY IN PVAc FILM Dielectric loss at 130 H 323 K T = 333 K Frequency shift M. Labardi et al JVST B 28 C4D11 (2010)

27 CONCLUSIONS Scanning Force Microscopy gives access to electrical properties on a nanometer scale. Local Dielectric Spectroscopy can be operated on frequency and temperature regimes comparable to the ones of BDS allowing comparison of average properties with local ones even of single macromolecules. Interfaces in nanocomposite materials can be studied by this technique when they are placed near to the free surface of the sample.