Principle of Electrostatic Force Microscopy and Applications. Thierry Mélin.

Transcription

1 Principle of Electrostatic Force Microscopy and Applications Thierry Mélin ANF-DFRT CEA Leti, Dec 1 st 2016

2 I Introduction II Electrostatic Force Microscopy (EFM) III Kelvin Probe Force Microscopy (KPFM)

3 I Introduction

4 A few motivations Source-drain current Source-drain current EX 1 : Imaging the operation of CNT-FETs as charge sensors [D. Brunel et al., ACS Nano 2010] Q < 10e EX 2 : coupled CNTFETs and nanocrystals 300K + CdSe nanocrystals Nanointegris tube + dots CdSe/CdS 5nm Back-gate voltage Back-gate voltage un(re)solved using AFM Nanoletters 2015

5 A few motivations EX 3 : photovoltaic materials light Change in local effective workfunctions upon illumination P3HT:PCBM blend molecular D/A junction cf Ł. Borowik / B. Grévin

6 EFM Electrostatic Force Microscopy Measurement of electrostatic force gradients Units : Hz or N/m KPFM Kelvin Probe Force Microscopy Compensation of electrostatic forces Units : V Charge detection Probing local surface potentials

7 Basics

8 Charge detection (tip probe charge) Q z C q?? V (sample charge) Q 0 Q charges in vacuum charges in a capacitor

9 Charge { capacitance} Q = C.V z lever V z C 2 Tip apex Cantilever 0 C 1 C 1 4pe 0 R apex C 2 e 0 S lever / z lever R apex =20nm S lever = 30µm 100µm z>>r apex z lever =15µm [V=1V] Q 1 20 e Q e

10 Energy stored in a capacitor ½ C V² Attractive force between capacitor plates F z = + ½ dc/dz V² (<0) <0 z F z z F z

11 Electrostatic Force { capacitance gradient} Energy stored in a capacitor ½ C V² z lever V Attractive force between capacitor plates F z = + ½ dc/dz V² (<0) z C 2 Tip apex Cantilever 0 C 1 dc 1 /dz 4pe 0 R² apex /z² dc 2 /dz e 0 S lever / z² lever R apex =20nm z=100nm S lever = 30µm 100µm z lever =15µm [V=1V] F 1 5 pn F pn

12 Force gradient detection F z = F z (z 0 ) + (z-z 0 ). F z (z 0 ) frequency shift : df= - f 0 /2k. F z (z 0 ) Here: long-range forces [ambient air / UHV] Short-range electrostatic forces disregarded here

13 Force gradient { capacitance 2 nd derivative} force gradient df z/ /dz = ½ d²c/dz² V² z lever V z 0 C 1 C 2 Tip apex Cantilever d²c 1 /dz² 8pe 0 R² apex /z 3 d²c 2 /dz² 2e 0 S lever / z 3 lever R apex =20nm S lever = 30µm 100µm z=100nm z lever =15µm [V=1V] df 1 /dz 10-4 N/m df 2 /dz N/m df 1 /dz (apex) exceeds df 2 /dz (cantilever)

14 We could almost stop the presentation now - due to tip apex size sensitivity to few or single charge events provided the signal to noise ratio is sufficient - typically sub-pn forces or 10-5 N/m force gradients (z=100nm) - force gradients at the tip apex can exceed force gradients at the cantilever Frequency Modulation (FM) modes already appear better than Amplitude Modulation (AM) modes with this respect

15 II - Electrostatic Force Microscopy

16 capacitive forces

17 Capacitive forces 1/2 Capacitive signals associated with topgraphic features Linear mode [constant height] z scale 50 nm V=-8V, freq. scale 40 Hz Topography image EFM (frequency shift) image

18 Capacitive forces 2/2 Capacitive signals associated with sub-surface nanostructures J. Nygard et al. Appl. Phys. Lett (2007)

19 charge manipulation

20 Charge manipulation Contact force : a few nn Charge retention time : of few 10 min (dry N 2 ) AFM Image 2500 x 2500 nm²

21 Imaging charged nanocrystals Appl. Phys. Lett., (2002)

22 electrostatic force analysis

23 Electrostatic forces Grounded surface Grounded tip Vacuum Isopotential map of a charged dielectric sphere with grounded substrate and tip 20 nm Electrostatic potential along z axis(v) 0,10 0,08 0,06 0,04 0,02 0,00 V=0,Q=0 V=0,Q=0 V=0,Q=0 E Q + E V E Q E V Distance (nm) substrate NC gap tip

24 Electrostatic forces electric field at the tip? [superposition theorem] E Q 0,V 0 = E Q=0,V 0 + E Q 0,V=0 E v + E Q a.v + b.q Electrostatic potential along z axis(v) 0,10 0,08 0,06 0,04 0,02 0,00 V=0,Q=0 V=0,Q=0 V=0,Q=0 E Q + E V E Q E V Distance (nm) substrate NC gap tip

25 Electrostatic forces electric field at the tip? [superposition theorem] E tip = E Q=0,V 0 + E Q 0,V=0 E v + E Q force applied to the tip? [electrostatic pressure] F tip =½ e 0 [E tip ]².dS proportional to [a.v + b.q]² a.v + b.q A.V² + B.Q.V + C.Q² capacitive force mixed term image force OK OK??

26 Charge screening +Q metal d +Q Q -Q d d charge in the vicinity of a conductive plane screened charge charge +Q + image charge -Q dipole prop. to Q

27 Two opposite situations +Q z d z<<2d insulators weak screening z>>2d conductors strong screening z the tip «feels» a charge (stronger forces) the tip «feels» a dipole (weaker forces) +Q d

28 Electrostatic forces without energy diagrams effective surface dipole Q h / e Q -Q charged nanoparticle (V=0) dipole-dipole interaction a Q²

29 Electrostatic forces without energy diagrams effective surface dipole Q h / e Q +Q c V -Q - Q c charged nanoparticle (V=0) dipole-dipole interaction a Q² charged nanoparticle (V 0V) dipole-charge interaction a Q.V uncharged nanoparticle (V 0) capacitive interaction a V²

30 Electrostatic forces without energy diagrams effective surface dipole Q h / e Q +Q c V -Q - Q c charged nanoparticle (V=0) dipole-dipole interaction a Q² charged nanoparticle (V 0V) dipole-charge interaction a Q.V uncharged nanoparticle (V 0) capacitive interaction a V²

31 Experimental spectroscopic analysis [here : screened charges above a conducting plane]

32 Spectroscopic analysis of charge signals Frequency shift (Hz) Surface potential e V inj = +5V -20 uncharged 0 Hz 4 Hz e V inj =-5V Cantilever bias Cantilever bias (V)

33 Dipole-dipole interaction frequency shift (Hz) dipole-dipole interactions Effective dipole moment (10 2 Debye) 0 repulsive attractive -1 numerical calculation Amount of injected charges (e)

34 Charges or dipoles?

35 Probing a charge or a dipole? - tip-substrate capacitance prop. to V EFM ² - nanoparticle capacitive effect prop. to V EFM ² - charge perturbation prop. to Q. V EFM (+Q² contribution)

36 Probing a charge or a dipole? Capacitive signal + - [polarization] Charge effect + - [surface dipole]

37 Probing a charge or a dipole? multiwalled carbon nanotube MWCNT (~20nm diameter) on 200nm thick SiO 2 - charge signal + - capacitive signal

38 Probing a charge or a dipole? After discharge + capacitive signal - + residual oxide charge Q ox [MWCNT with 18 nm diameter, V inj =-7V (3 min) detection V EFM =-3V]

39 image force contributions

40 Apparent topography due to image forces E. Boer et al. - APL (2002)

41 Apparent topography due to image forces AFM EFM phase image +2V 500nm -2V Charge injection in a 7nm thick SiO 2 layer R. Dianoux, PhD (2004)

42 Missing points - sensitivity - spatial resolution - time resolution - quantitative charge measurements?

43 Sensitivity Optical beam deflection EFM with soft cantilevers (k=3n/m;f 0 =60kHz) in air in vacuum, 300K limited by thermal noise F min ~10-5 N/m B=100Hz, Q=200 A=25nm a few 10-6 N/m B=50Hz, Q=20000 A=15nm F min = 4 k. k B T. B p f 0. A². Q <z> nm 10-20nm [ F. Giessibl et al., Phys. Rev. B references therein ]

44 Sensitivity Optical beam deflection EFM with soft cantilevers (k=3n/m;f 0 =60kHz) Qplus, LER in air in vacuum, 300K vacuum, 1-5 K limited by thermal noise deflection noise, thermal noise, F min ~10-5 N/m B=100Hz, Q=200 A=25nm a few 10-6 N/m B=50Hz, Q=20000 A=15nm ~ 10-3 N/m B=25Hz, Q=20000 A=200pm <z> nm 10-20nm < 1 nm Long-range (LR) LR + SR Short-range (SR)

45 single charge detection in air

46 w/2w EFM «modulated» EFM technique : - mechanical excitation - ac +dc bias at the tip - w << 2p f 0 (quasistatic) dc z-force gradient ½ d²c/dz² V² z 0 C (V s ) ~ ac (w) V(t) = V dc + V ac cos (wt) + surface potential V s (offset in tip bias) F z (t)= ½ d²c/dz² [(V dc -V s )+V ac cos wt]² three force components static F 0w = ½ d²c/dz² [(V dc -V s )²+V ac ²/2] w F w = d²c/dz² (V dc -V s ) V ac cos(wt) 2w F 2w = ¼ d²c/dz² V² ac cos(2wt) not desired here zero if V dc =V s capacitive interaction

47 w/2w EFM For V ds =V s, a surface charge Q will : z 0 C Q (V s ) ~ - interact with its image charges dc - interact with ac charges at the tip ac (w) Separation of charge and dielectric images three force components static F 0w = ½ d²c/dz² [(V dc -V s )²+V ac ²/2] + image force contributions w F w = d²c/dz² (V dc -V s ) V ac cos(wt) + K(z). Q. CV ac cos(wt) 2w F 2w = ¼ d²c/dz² V² ac cos(2wt) (no change)

48 Single charge detection in ambient air Topography Charge image Dielectric image CdSe nanocrystals ~5 nm HOPG Charge image Dielectric image +e neutral T. Krauss & L. Brus, PRL (1999)

49 Single-charge sensitivity with sub-nm resolution 1999 Columbia Univ., Phys. Rev. Lett IBM Zürich, Science [ac-modulated EFM in air] [4K AFM] Single charge fluctuations in CdSe nanocrystals resolution 25nm Single charge state of Au adatoms resolution < 1nm [UHV et 4K]

50 Time resolution - in general, limited by the phase demodulation of the cantilever oscillation - better resolution possible : - fast frequency shift demodulation, - oscillation transients (sub-µs see D. Ginger et al. Nanoletters 2012) - response under modulated illumination (see Ł. Borowik) Quantitative charge measurements? - in general, semi-quantitative models only - difficult due to the large variety of dielectric environments - numerical simulations in most situations - single charge events as calibration

51 III - Kelvin Probe Force Microscopy surface potential and charge detection

52 Principle Measuring surface potentials from forces - Lord Kelvin (1898) - Zisman (1932) : vibrating Kelvin probe (down to mm size) - Nonnenmacher (1991) : Kelvin probe force microscopy different metals e.g. f probe > f sample probe probe attractive force cancelled force V dc = (f probe f sample ) / e V s ++++ sample sample V s Work function measurement

53 Energy diagrams z sample vacuum probe Vacuum level energy of electrons - 0 f sample f probe E F,s E F,probe

54 electrons Energy diagrams sample z vacuum probe Vacuum level energy of electrons f probe f sample E F,s E F,probe

55 Energy diagrams Vacuum level sample z vacuum probe energy of electrons f sample f probe E F,s E F,probe V dc = (f probe f sample )/e

56 A few remarks The sign of V dc is user-dependent (V dc at the tip, or at the sample) V dc at the tip (and V s at the surface) electrostatics-friendly convention : a positive charge or dipole (e.g. adsorbate) is seen as a positive V s

57 A few remarks The sign of V dc is user-dependent (V dc at the tip, or at the sample) V dc at the tip (and V s at the surface) electrostatics-friendly convention : a positive charge or dipole (e.g. adsorbate) is seen as a positive V s Vacuum level energy of electrons f sample f probe E F,s E F,probe

58 A few remarks The sign of V dc is user-dependent (V dc at the tip, or at the sample) V dc at the tip (and V s at the surface) electrostatics-friendly convention : a positive charge or dipole (e.g. adsorbate) is seen as a positive V s Vacuum level energy of electrons f sample f probe E F,s E F,probe

59 A few remarks The sign of V dc is user-dependent (V dc at the tip, or at the sample) V dc at the tip (and V s at the surface) electrostatics-friendly convention : a positive charge or dipole (e.g. adsorbate) is seen as a positive V s Vacuum level E 0 energy of electrons f sample f probe E F,s E F,probe positive charge

60 A few remarks The sign of V dc is user-dependent (V dc at the tip, or at the sample) V dc at the tip (and V s at the surface) electrostatics-friendly convention : a positive charge or dipole (e.g. adsorbate) is seen as a positive V s Vacuum level E=0 energy of electrons f sample E F,s f probe positive charge E F,probe V dc >0

61 A few remarks The sign of V dc is user-dependent (V dc at the tip, or at the sample) V dc at the tip (and V s at the surface) electrostatics friendly convention a positive charge or dipole (e.g. adsorbate) is seen as a positive V s V dc at the sample work-function friendly convention : a material with a larger work-function will be imaged as «more positive» in KPFM images

62 Oscillating probe

63 Zisman method A B C(t) V s V dc C = C 0 + DC.sin wt i(t)= DC.w.[ V dc -V s ].cos(wt) Kelvin method Response of the electrometer deflection as a function of V dc to find the zero force to a loud speaker (!) (w in the audio range) : zero sound for V dc = V s

64 Frequency Modulation Kelvin Probe Force Microscopy (FM-KPFM)

65 FM-KPFM z 0 C Q (V s ) ~ dc ac (w) Principal similar to modulated EFM - mechanical excitation - ac +dc bias at the tip - w << 2p f 0 (quasistatic) + a feedback loop three force components static F 0w = ½ d²c/dz² [(V dc -V s )²+V ac ²/2] w F w = d²c/dz² (V dc -V s ) V ac cos(wt) + image force contributions + K(z) Q V ac cos wt 2w F 2w = ¼ d²c/dz² V² ac cos(2wt) regulating F w to zero (df w =0) gives : V dc = V s + V Q (z-dependent)

66 Imaging FM-KPFM Doped nanocrystals inducing charge transfers to the substrate nc-afm FM-KPFM FM-KPFM : f ac ~ 300Hz; V ac = 200 mv

67 Amplitude Modulation Kelvin Probe Force Microscopy (AM-KPFM)

68 AM-KPFM ac+dc force excitation z 0 C Q (V s ) ~ dc ac (w) - no mechanical excitation - ac +dc bias (here) at the tip - «free» w three force components static w 2w F 0w = ½ dc/dz [(V dc -V s )²+V ac ²/2] + image force contributions F w = dc/dz (V dc -V s ) V ac cos(wt) + K 1 (z).q.v ac cos (wt) F 2w = ¼ dc/dz V² ac cos(2wt) regulating F w to zero (i.e: A w =0) gives : V dc = V s + V Q (z-dependent)

69 Example of a single-pass (UHV) AM-KPFM mode 1/2 - first resonance f 0 - mechanical excitation - non-contact AFM Df = -5Hz oscillation amplitude 15 nm minimum tip-substrate distance ~5nm Amplitude (nm) f 0 = 67.6kHz Q~ Frequency (Hz) Phase (degrees) - second resonance f 1 ~6.2 f 0 - electrostatic excitation - KFM loop at f 1 Amplitude (nm) 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 f 1 = 422kHz Q~ Frequency (Hz) Phase (degrees)

70 Imaging AM-KPFM nc-afm AM-KPFM AM-KPFM : V ac = 200 mv; V dc = 2 V; t = 100 µs Similar image as FM-KPFM

71 AM-KPFM A [too] large variety of implementations w can be chosen freely : - close to the cantilever resonance (increases the sensitivity by Q 1/2 ) - at a cantilever higher eigenmode (e.g. f 1 =6.2 f 0 ) - at low frequency or high frequency, but out of resonance in conjunction or separately from topography imaging (single-pass versus lift/linear modes) with feedback loop on or off.

72 AM-KPFM versus FM-KPFM signal to noise resolution AM-KPFM + - FM-KPFM - + Side capacitance effects

73 Side-capacitance effects in AM- and FM-KPFM 1/5 Nullification of the w force component (AM-KPFM) C 1 C 2 C 3 dc 1 /dz V ac (V dc -V 1 ) + dc 2 /dz V ac (V dc -V 2 ) + dc 3 /dz V ac (V dc -V 3 ) = 0 V 1 V 2 V 3 V dc = dc 1 /dz. V 1 + dc 2 /dz.v 2 + dc 3 /dz.v 3 dc 1 /dz + dc 2 /dz + dc 3 /dz KPFM : averaging technique H. O. Jacobs et al. JAP (1998)

74 Side-capacitance effects in AM- and FM-KPFM - 2/5 gerenalization AM-KPFM FM-KPFM V dc = (S dc i /dz.v i ) / (S dci/dz) V dc = (S d²c i /dz².v i ) / (S d²ci/dz²) - intrinsic averaging effects in AM and FM modes - dc i /dz less peaked at the tip than d²c i /dz² : less resolution in AM modes EFM FM-KPFM AM-KPFM D. Brunel et al. ACS Nano (2010) ambient air imaging

75 Side-capacitance effects in AM- and FM-KPFM 3/5 Both FM- and AM- modes are sensitive to side-capacitance effects at small size Appl. Phys. Lett (2010)

76 Side-capacitance effects in AM- and FM-KPFM 4/5 sensitivity resolution AM-KPFM + - FM-KPFM less ac cross-talk - no need for a 2 nd resonance KCl islands on Au 111 (topo) KPFM accross KCl island boundaries U. Zerweck et al., Phys Rev B (2005)

77 Side-capacitance effects in AM- and FM-KPFM 5/5 KBr on InSb(001) FM-KPFM measurements convolution in FM mode for structures with smaller size than the tip apex F. Krok et al., Phys. Rev. B 77, (2008)

78 AM-KPFM versus FM-KPFM signal to noise resolution AM-KPFM + - FM-KPFM - + «usually reported» Justification, if AM and FM modes are performed on the same resonance (Q) : dc/dz. DV dcmin, AM. V ac, AM = F min (limited by thermal noise) d²c/dz². DV dcmin, FM. V ac, FM = F min (limited by thermal noise) for the same V ac : DV dcmin, FM / DV dcmin, AM = [ dc/dz / d²c/dz² ]. [F min / F min ] z / a-1 if d²c/dz² prop to z -a (in air a ~1.5)

79 AM-KPFM versus FM-KPFM signal to noise resolution AM-KPFM + - FM-KPFM - + «usually reported» Justification, if AM and FM modes are performed on the same resonance (Q) : dc/dz. DV dcmin, AM. V ac, AM = F min (limited by thermal noise) d²c/dz². DV dcmin, FM. V ac, FM = F min (limited by thermal noise) for the same V ac : DV dcmin, FM / DV dcmin, AM = > 1 >1 >1

80 AM-KPFM versus FM-KPFM signal to noise resolution AM-KPFM + - FM-KPFM less ac cross-talk - no need for a 2 nd resonance nc-afm AM-KPFM FM-KPFM AM-KPFM : V ac = 200 mv; V dc = 2 V; t = 100 µs FM-KPFM : f ac ~ 50Hz; V ac = 200 mv

81 Can we measure quantitatively a work function difference? (ac-crosstalk issues AM KPFM in air)

82 Phase j 1w (degrees) Practical operation principle Oscillation amplitude (a.u.) Y 0 1w cantilever oscillation amplitude [ proportional to V dc -V s ] j 1w X j Electrostatic excitation frequency (khz) projection angle necessary for the KFM feedback loop KFM "equation" : dc/dz. (V dc -V s ).V ac. cos(f 1w -f) = 0

83 Practical operation principle with ac cross-talks Y ac cross-talk (e.g. photodiode) KFM "equation" dc/dz. (V dc -V s ).V ac. cos(f 1w -f) + A ct.v ac. cos(f ct -f) =0 j ct j 1w X V dc =V s + A ct. cos(f ct -f) / dc/dz cos(f 1w -f) This term depends j - on f ("drive phase") - on f 1w (excitation frequency) - on z (via dc/dz) In practice (Brüker) : photodiode + mechanical ac-cross-talks

84 KFM loop KFM loop amplifier phase shifter 1.0 Cross-talk suppression/compensation 1.0 Measured surface potential V dc (V) 0.5 f exc =76.8 khz f exc =75.0 khz (a) -1.0 f exc KFM loop projection angle j ( ) Measured surface potential V dc (V) f exc =75.0 khz after suppression/compensation of ac cross-talks f exc f exc =76.8 khz (d) KFM loop projection angle j ( ) adder V dc V dc V ac (b) V ac (c)

85 Cross-talk suppression/compensation KFM loop KFM loop amplifier phase shifter 1,0 1 Measured surface potential V dc (V) 0,5 0,0-0,5 f exc = 75.0 khz f exc =76.8 khz f exc f exc -1, KFM loop projection angle j ( ) KFM projection angle j ( ) Measured surface potential V dc (V) 0 f exc =75.0 khz after suppression/compensation of ac cross-talks adder f exc =76.8 khz V dc V dc V ac V ac Rev. Sci. Inst. 2010

86 Conclusion This was an introduction lecture on Electrostatic Force Microscopy (EFM) - spectroscopy of electrostatic forces - sensitivity and limits Kelvin Probe Force Microscopy (KPFM) - basic implementations - AM-KPFM vs FM-KPFM - quantitative work function measurement issues

87 Questions?