Charge injection and detection in semiconducting nanostructures studied by Atomic Force Microscopy

Transcription

1 Raphaëlle Dianoux injection in semiconducting nanostructures studied by Atomic Force Microscopy CEA Grenoble / DRFMC / SP2M / SiNaPS ESRF / Surface Science Laboratory

2 2XWOLQH Electrostatic Force Microscopy in dry atmosphere ¾ Principles of charge injection ¾ Minimum detectable in a Brownian motion ¾ Electrostatic tip-sample : the plane-plane approximation ¾ Method of charge ¾ of this model: numerical evidence of a repulsive force Non-linear dynamic ¾ Coupling with the higher oscillating modes of the cantilever ¾ of the cantilever motion ¾ Adding of the electrostatic on semiconducting nanostructures ¾ the oxide layer ¾ Si nanocrystals embedded ¾ Si nanostructures made by e-beam lithography 2

3 What is Electrostatic Force Microscopy? The idea: use the AFM probe to: Inject charges locally AND Detect charges Conditions: ¾ the tip must be metal-coated: W 2 C, PtIr Radius of curvature of the tip: ~35 nm ¾ the system must be electrically connected nanostructure SiO 2 9 ()0 Si Si-- nanostruc ¾ the tip must not touch the surface after injection oscillating mode 3

4 injection with the tip 1 4 V Si-- nanostruc 4 AFM in dynamic oscillating mode 2 Decrease of the amplitude setpoint to near 0: contact with the surface 3 V Application of a voltage (-12 to 12 V) for 1ms to 10s The setpoint is returned to its original value 5 Resumes scanning > Permanent N 2 flux

5 Si-- nanostruc 5 z0 3 Detection of the injected charges 1 st pass: topography Localized electric charges 2 nd pass: EFM signal EFM signal V EFM The double-pass method &2: Topography scan Feedback on the amplitude of oscillation 3: Raising of the AFM probe at a lift height z 0 of 30 to 100 nm The feedback is cut off 4&5: EFM scan: recording of the phase of oscillation The tip is brought to potential V EFM The EFM signal is sensitive to electrostatic s

6 of charges Example of charge injection on 7 nm of SiO 2 on Si Topography 1 x 2 µm 2 EFM signal EFM can distinguish the sign of the deposited charges Conditions: -10V/ 10s V EFM = +2 V V EFM = -2 V Si-- nanostruc BUT the tip-sample force is always attractive! EFM signal - (potential difference) 2 6

7 Mechanics of the cantilever µm Tip µm ] Single clamped beam x Si-- nanostruc Euler-Bernouilly equation of movement: w ] (, U w[ Fundamental mode w ] ww [ W $ [ W E : Young modulus I : moment of inertia ρ : density A : section 7

8 z 0 Detection of a A 1 (ω) I & ( A (ω) V EFM A 0 A(ω) ϕ ω ϕ(ω) -90 Si-- nanostruc 8 I q Point-mass model: ] ] Z Static deflection N P I ] Attractive force = phase lag I c] ] W ω 0 I ] P ω 0 : angular resonance frequency k: spring constant of the cantilever m: effective massshift of the resonance frequency β 0 : friction coefficient /m ' Z Z Z Z N wi w] ω ] ] ¹

9 Functioning point in amplitude feedback: G $ GZ Z Vr Z r 4 ¹ 4: quality factor of the oscillator = ω s± ω 0! G$ GZ Z Vr r $ P 4 Z A m : maximum amplitude of oscillation Si-- nanostruc ' G$ GZ Z ' Z $ ] $ V P 4 N wi w]

10 Minimum detectable in a brownian motion Thermal noise = white-spectrum noise R(ω) ^ Langevin equation in Fourier space: Z LE Z Z The generalized susceptibility is defined as (Landau-Lifschitz): D = Ö 5Ö = Ö 5Ö P Z DcZ LD cc Z Si-- nanostruc Spectral density of the fluctuations The dissipation-fluctuation theorem provides: Z N 7 SZ Z Ö % % = Dcc N 74 SNZ 4 Z Z ¹ Z Z

11 Minimum detectable in a brownian motion The standard deviation of movement N is: 1 S % = Ö where B is the bandwidth of the system (in Hz) Z Simplifications: Near the resonance 1 % N 74% NZ Away from resonance N 7% NZ 4 1 % Si-- nanostruc The minimum detectable is given when: amplitude variation = standard deviation of movement '$ 1

12 Si-- nanostruc Minimum detectable in a Brownian motion One-dimensional, simple harmonic oscillator Dissipation-fluctuation theorem: Finite Q -1 = dissipative system = source of noise White spectral density of the noise force f : Z N 7N 4Z 6 % Standard deviation of the force: I Units: N 2 /Hz Z 1 v %6 B= bandwidth of system I wi 1 N w] HII ] v $ where: P w w] $ WKHUPDO I % WKHUPDO v P N 7N% 4Z 9

13 Minimum detectable in a Brownian motion wi N% 7%N w] $ Z 4 PLQ At the resonance: P Si-- nanostruc In our conditions: A m = nm k B T = 26 mev ambient temperature Q = ambient pressure k = 01-1 N/m ω 0 = khz B = 500 Hz wi w] PLQ 1P Relation to min detectable charge? Plane-plane approximation 10

14 Si-- nanostruc of the electrostatic tip-sample The electrostatic force is capacitive: Capacitance C, C =?? Area A I wi w] Different capacitor geometries: 2R ] ] w& w] ] 9 w & w] ] 9 H θ 0 θ 0 z z z z Plane-plane Sphere-plane Cone-plane Truncated cone -plane R 11

15 Si-- nanostruc 12 of the electrostatic tip-sample Plot of the 2nd derivative of capacitance vs tip-sample distance &])P ( ( ( ]QP 3ODQHSODQH 6SKHUHSODQH &RQHSODQH 7UXQFDWHGFRQHSODQH &DQWLOHYHU ¾ Contribution of cantilever is negligible ¾ Area of plane capacitor is adapted to fit C (z) of truncated cone-plane at a lift height of 100 nm The simplest geometry is chosen: plane-plane capacitor & cc ] H H U $ ]

16 of the electrostatic tip-sample The system is modelled as 2 plane capacitors in series Tip area A Tip V EFM z~100nm V EFM q Sample C dt C ts Si-- nanostruc charge q SiO 2 Si d I c ] H ] H $ G 6L2 ¹ 9 ()0 H TG H 6L2 $ ¹ 13

17 Minimum detectable charge at V EFM =0 T PLQ I c PLQ ] H G 6L2 G ¹ H H 6L2 $ q min dependent on: z : lift height d : oxide thickness A : effective plane area Si-- nanostruc f min = 3 x 10-5 Nm -1 z= 100 nm, A= nm 2 (disc of 140 nm in diameter) GQP TPLQH z= 50 nm, A= 6260 nm 2 (disc of 90 nm in diameter) GQP TPLQH 14

18 Si-- nanostruc Method of charge Imaging and relating the recorded phase to a charge We established: Moreover: T ' Z GI G GI N ] H 4G 6L2 Z wi N w] 4 Z ¹ 'HWHFWHGFKDUJHH ' Z H H 6L2 ] on 7 nm SiO 2 (injection time: 10 s) $ 1RUP$PSOLWXGH )UHTXHQF\N+],QMHFWLRQYROWDJH9ROWV 3KDVHGHJUHHV 15

19 Method of charge Relate the minimum of EFM signal vs voltage to a charge Before and after injection, voltage V EFM applied on tip is scanned Minimum corresponds to V EFM = V surface ()0VLJQDO V min = 137 V 1RQFKDUJHGDUHD &KDUJHGDUHD Conditions: -10V/10s d = 25 nm Lift height: 300 nm A= 13 x m 2 (disc 400 nm in diam) Si-- nanostruc ' 9 PLQ 7LSYROWDJHYROWV H TG H 6L2 $ Here q = 1500 charges

20 of the capacitor model Capacitive force: always attractive Numerical evidence of a repulsive (JP Julien, CNRS) ¾ Distribution of equivalent charge q on the tip in rings ¾ Trapped charge q 0 is modelled above the symmetry plane ¾ s are adjusted to have a constant potential on the tip s surface ¾ Screening charges are taken into account Domain of repulsive force! Si-- nanostruc 16 electrons! =barely measurable 16

21 Non-linear dynamic What is a force curve: ¾ Scanning is stopped ¾ Feedback on amplitude is cut off ¾ Cantilever is mechanically excited near resonance frequency ¾ Tip is approached then retracted from the surface (height ~ 200 nm) ¾ Amplitude and phase of oscillation are recorded Si-- nanostruc Is the movement of the cantilever still that of a harmonic oscillator? $PSOLWXGHG% higher oscillating modes of the cantilever NO! Strong excitation f 1 f 2 f 3 f 4 )UHTXHQF\N+] f exc $PSOLWXGHG% YES! Normal excitation f 1 f 2 f 3 f 4 )UHTXHQF\N+] f exc 17

22 Non-linear tip-sample Deformation of the resonance curve with increasing tip-surface Amplitude Si-- nanostruc Amplitude and phase of oscillation undergo hysteresis Tip-sample distance 18

23 Amplitude Non-linear tip-sample Deformation of the resonance curve with increasing tip-surface Amplitude Si-- nanostruc f 0 f exc Frequency Amplitude and phase of oscillation undergo hysteresis Tip-sample distance 18

24 Si-- nanostruc of the movement of cantilever Non-perturbative (JP Aimé, CPMOH Bordeaux) G $ r I $ r ¾ Interaction is van der Waals : (attractive force) ¾ Amplitude and distance are normalized to free amplitude at resonance: a=a/a 0, d= z/a 0 D X DUFWDQ 4X N YG: # 4 X 4 D G $ r X N YG: D ¹ ¹ HR d 2 ¾ u= ω / ω 0 ¾ k vdw : dimensionless parameter related with strength of van der Waals forces 19

25 of the movement of cantilever These analytical curves explain the hysteresis observed experimentally curves Experimental curves Si-- nanostruc 20 Experimental parameters used in the analytical curves: Q = 80 k = 23 N/m ω 0 = 5785 khz u = A 0 =135 nm

26 Adding the electrostatic Capacitive tip-sample coupling taken into account G $ r I $ r D X DUFWDQ 4X N YG: N # 4 HOHFW X N 4 9 D X N ¹ YG: HOHFW G D $ r 9 ¹ where 9 N HOHF H $ 9 N$ Si-- nanostruc We take advantage of the fact that the capacitive force for a plane capacitor has the same distance-dependence d -2 as the van der Waals force 21

27 Si-- nanostruc Adding the electrostatic 1RUPDOL]HGDPSOLWXGH $PSOLWXGH curves Normalized distance A 0 = 14 nm Experimental curves ¾ For V=0, hysteretical behavior ¾ For V> 0, progressive return to linear behavior Potential curvature / potential gradient is in 1/d Non-linear terms fade with increasing distance 3KDVHGHJUHHV 3KDVHGHJUHHV 22

28 Quantitative charge measurement with Application to carbon nanotubes (M Paillet, Uni Montpellier) Before charging After charging Si-- nanostruc ¾ Fitting the data before injection provides all parameters (A 0, u, U vdw ) ¾ After injection, the fit provides q=10 electrons 23

29 on semiconducting nanostructures Objective: not quantify charges but investigate charging behaviors ¾ charging of individual structures ¾ charging of collection of nanostructures Si-- nanostruc Tunnel oxide SiO 2 (2,5 nm) Source Si gate SiO 2 p-si channel Si-nc non-volatile memory Si nanocrystals Drain 24

30 on semiconducting nanostructures 3 types of samples: SiO 2 Si 7-25 nm ¾ Reference SiO 2 layer on Si 9charging behavior of an insulator 5 nm SiO 2 Si 3 nm ¾ Si-nanocrystals embedded 9very small ~5 nm in diameter 9collective behavior Si-- nanostruc nm Si SiO 2 Si Si 20 nm ¾ Si-nanostructures made by e-beam lithography 9well-defined, ~100 nm in dimension 9individual behavior 25

31 insulators: the case of SiO 2 Time Large electric field (~10 8 Vm -1 ) necessary to deposit only a few 100 charges of 25 nm of thermal oxide, conditions: -10 V/ 10s Recording of the EFM signal Characteristic retention time: 94 seconds = Low retention time Si-- nanostruc 26

32 insulators: the case of SiO 2 of 25 nm of thermal oxide, conditions: -10 V/ 10s Recording of the EFM signal EFM signal Normalized EFM signal Si-- nanostruc Absence of lateral spreading of the charges 27

33 Silicon nanocrystals embedded Elaboration: (CEA Grenoble/LETI) ¾ deposition of a SiO x layer (x < 2) by LP-CVD ¾ annealing at 1000 C, 10 minutes = precipitation of Si nanocrystals matrix 3 nm 25 nm SiO 2 Si TEM pictures Cross-section Plane-view Typical dimension: 3 nm Si-nanocrystals Si-- nanostruc Density depends on x, varies from 3 x to cm -2 28

34 Silicon nanocrystals embedded First behavior: very low Si-nc density 'M PD[ Circular shape of injected charges that does not evolve in time Time retention: several hours Estimation of one electron per nanocrystal Si-nanocrystals Si-- nanostruc Any difference from reference SiO 2 sample? 29

35 Si-nanocrystals Si-- nanostruc Low-density Si-nanocrystals embedded 'LVF VGLDPHWHU'QP Same charging conditions: -10 V / 3 s Si-nanocrystals SiO 2 reference sample Disc diameter,qmhfwlrqqxpehu Si-nanocrystals: D ~200 nm φ max ~65 'I PD[ GHJUHHV SiO 2 reference: D ~350 nm φ max ~3 Smaller electron cloud Higher surface density of electrons,qmhfwlrqqxpehu e- density 30

36 Si-nanocrystals Si-- nanostruc 31 ):+0'QP Evolution of the disc with the injection time Reference SiO 2,QMHFWLRQWLPHV Larger disc s diameters= easier spreading of the charges Inhomogeneous distribution of slopes: due to flawed tip-sample contact? Reproducible experiment with homogeneous distribution of slopes The disc s diameter evolves as log (injection time) ):+0'QP Si-nanocrystals Infinitely slow saturation,qmhfwlrqwlphv

37 Low-density Si-nanocrystals vs SiO 2 reference sample ¾ Same circular shape of the electron cloud for both samples BUT in the same charging conditions: ¾ the electron cloud is smaller and denser for the Si-nanocrystal sample ¾ and it remains much longer (hours vs minutes) ¾ Same logarithmic injection-time dependence BUT Si-nanocrystals shows homogeneous distribution of slopes whereas SiO 2 shows an inhomogeneous one Si-nanocrystals Si-- nanostruc ¾ Tip-sample contact resistance is dominant sample ¾ Intercrystal-resistance is dominant in Si-nanocrystal sample 32

38 Energy Tentative illustration of charge localization Energetic diagrams Conduction band Valence band Traps Position SiO 2 gap ~8 ev Energy Conduction band Valence band Si nanocrystals Si gap ~1 ev Position Si-nanocrystals Si-- nanostruc SiO 2 layer Si nanocrystals layer 33

39 Si-nanocrystals Si-- nanostruc Silicon nanocrystals embedded 3 nm 25 nm SiO 2 Si TEM pictures Cross-section Plane-view Typical dimension: 3 nm Density depends on x, varies from 3 x to cm -2 3 kinds of sample prepared, with varying densities Fitting of the ellipsometric measurements provides: 6DPSOH 6L 6L2 )UDFWLRQ[ ( ( ( High Si-nc density Low Si-nc density Very low Si-nc density 34

40 Silicon nanocrystals embedded Sample E1: metallic behavior Si = 40 % SiO 2 = 60 % EFM signal ¾ s spread away on a time scale of seconds Si-nanocrystals Si-- nanostruc Si-nc touch one another, no confinement possible 35

41 Silicon nanocrystals embedded Sample E3: strongly confining behavior Si = 6 % SiO 2 = 94 % Very low Si-nc density Circular shape of injected charges that does not evolve in time Estimation of one electron per nanocrystal Si-nanocrystals Si-- nanostruc 36

42 Silicon nanocrystals embedded Sample E2: partially confining behavior Si = 8 % SiO 2 = 92 % conditions -10 V / 10 s Low Si-nc density Si-nanocrystals Si-- nanostruc 37 ¾ Rough bordeline ¾ Inhomogeneous distribution of charges inside the electron cloud Reflects disorder in the distribution of Si-nc at nanoscale metallic intermediate confining Si content

43 Sample E2: time evolution of the electron cloud EFM images Profiles of EFM signal Normalized profiles Si-nanocrystals Si-- nanostruc 38 Irregular spreading of the charges, on a time scale of hours = kinetic roughening

44 Sample E2: mechanism of charge spreading Si-nc section: S Intercrystal spacing: d Quenched disorder Zone of charged Si-nc V~01 V Zone of non-charged Si-nc: V=0 Si-nanocrystals Si-- nanostruc 39 Electron transport is explained with the orthodox model of the Single Electron Transistor (SET) with V gate =0 Passage from one Si-nc to another occurs through tunneling Percolation threshold related to intercrystal distances (=density)

45 Sample E2: mechanism of charge spreading 6 π U with U 3 nm ρ 6L2 to Ω cm d 1 nm Tunneling of the electrons in the frame of orthodox model Transition rate Γ= τ 1 is: * ') H[S & ε ε 6L2 6 G ad) where: ¾ F = f( V, C) energy associated with the passage of one e - from one Si-nc to its neighbor ~-80 mev H ') 5 N 7 7 % 5 7 ρ 6L2 G 6 a Ω Si-nanocrystals Si-- nanostruc 40 Γ = 5 x 10-2 s -1 or τ = 20 s Progression of the borderline : 1 µm/hour 1 electron tunnels through ~200 Si-nc /hour = 1Si-nc / 20s! Paper accepted in Phys Rev B (Dec 2004)

46 Silicon nanostructures made by e-beam e lithography ¾ Dots are polycrystalline Si deposited by LP-CVD ¾ 2 nm of SiO 2 is grown on top to protect the dots d1= 20nm Si nm Si SiO 2 (5-7 nm) Si d1= 15nm Si nm Si ¾ Dots are monocrystalline Si made from SOI ¾ 2 nm of SiO 2 is grown on top to protect the dots SiO 2 (400nm) Si- nanostruc Si 41

47 AFM characterization P =>QP@ ;> P@ Most Si nanostructures are well-defined 100 nm in diameter dots but some are more extravagant P =>QP@ ;> P@ Si- nanostruc 50 nm in diameter dots P =>QP@ ;> P@

48 Influence of the oxide thickness conditions: -8V / 5s Thin oxide (7 nm) Height EFM signal 2 o Si- nanostruc Thick oxide (400 nm) Considering the expression of charge vs phase shift: T GM N ] G H G 4 H 6L2 6L2 6L G H 6L ¹ G H H ¹ $ For the same recorded phase shift, there are 7x less charges on thick oxide 2 o 42

49 Existence of a voltage threshold for injection of charges On thin-oxide sample: Height EFM signal V=-5 V t=10 s V=-6 V t=10 s Si- nanostruc Minimum electric field of ~3 x 10 8 Vm -1 is required 43

50 Propagation of the charges inside a ramified structure Thin-oxide sample conditions: -10 V / 10 s Amplitude EFM signal Si- nanostruc is point-like s extend immediately over several microns V tip = 1 V 44

51 +HLJKW Trapping of charges in the top oxide conditions: -7 V/ 10 S ()0VLJQDO point Si- nanostruc Good quality oxide ( Rapid Thermal Oxide ) traps charges for more than 30 minutes 45

52 De-charging of the ramified structures Thin oxide (7 nm) conditions: -10 V/ 10 s +HLJKW ()0VLJQDO Homogeneous de-charging of the structure, although 7 nm of oxide prevent direct tunneling De-charging mechanisms? Si- nanostruc Strong repulsion between the electrons (electronic density is high: ~10 17 cm -3 ) Existence of a Wigner crystal = ordering of the electrons on a regular lattice?

53 Silicon nanocrystals embedded Sample E3: strongly confining behavior AFM image Si = 6 % SiO 2 = 94 % EFM images t=0 t=4 hours -6 V +6 V Very long retention time Si- nanostruc Circular shape of injected charges that does not evolve in time Estimation of one electron per nanocrystal

54 &RQFOXVLRQ Electrostastic Force Microscopy in dry atmosphere: 9 Powerful method to characterize electrical properties at the nanoscale 9 resolution: a few tens elementary charges 9Analysis of the non-linear tip-sample Semiconducting nanostructures: 9 Reference SiO 2 sample shows low charge retention and low charge density 9 Collective behavior of Si-nanocrystals show 3 regimes: ƒ metallic ƒ intermediate: observable spreading ƒ confining 9 Individual behavior of Si-nanostructures Perspectives: Need for better resolution (charge, drift) future under vacuum, low temperatures = single electron detection 46

55 $FNQRZOHGJHPHQWV For the Henk-Jan Smilde Martin Stark Julien Pascal Frederio Martin Charlène Alandi Emilie Dubard Florence Marchi Fabio Comin André Barski Joël Chevrier For the samples Denis Mariolle Nicolas Buffet Pierre Mur CEA Grenoble/LETI LEPES / LSP ESRF ESRF ESRF ESRF UJF / LEPES-CNRS ESRF CEA Grenoble / DRFMC ESRF / UJF / LEPES CNRS CEA Grenoble/LETI CEA Grenoble/LETI CEA Grenoble/LETI