mesure à l'échelle nanométrique des propriétés électriques

CRISTECH Brice GAUTIEROctobre 2020

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Mesure à l'échelle nanométrique des propriétés électriques des matériaux par les techniques dérivées de la microscopie à force atomique

Brice GAUTIER

[email protected]

Institut des Nanotechnologies de LyonINSA de Lyon

David ALBERTINI, Alexander SYNGAEVSKI


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Sommaire

Atomic Force Microscopy modes● Contact● Non contact● Intermittent● Peak Force

Current measurements● Leakage currents in oxides● Dopants concentration in semiconductors

Capacitance measurements● Dopants concentration in semiconductors● Charges in oxides

Piezoelectric measurements● Dielectric polarisation in ferroelectrics and piezoelectrics

Electric field and potential measurements● Surface charges on ferroelectrics

p n


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Near field microscopies


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Scanning Tunneling Microscopy (STM) : tunneling current

Principle : measure the current flowing between the (metallic) tip and the (conducting) surface

The electrical circuit is not closed (gap of several nanometers)

=> only tunnel current can flow !

http://www.iap.tuwien.ac.at/www/surface/STM_Gallery/index.htmlxI varies exponentially

=> allows a precise adjustment of the distance

K : constant value : depends on the nature of the surface

dV

I ∼ V e−2Kd

1981 : Scanning Tunneling Microscope


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V

iThinned tungsten wire

Conducting surface

Feed-backV

piezo

Current I is kept constant at each point

Distance d is adjustedVoltage V applied on piezotube is used to adjust d

The STM signal is a voltage representing the local electronic density of states

STM has to be preferably implemented in Ultra-High Vacuum (pressure < 10-10 mbar) and with conducting samples

Scanning Tunneling Microscopy : principle

I ∼ V e−2Kd

V(x,y) represents the height map

(111) Silicon boron doped

F. Palmino et al., univ. Franche Comté

7X7 Silicon surface imaged by STM under UHV


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What happens with non conductive samples ?

Atomic force microscopy


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● Allows to image non conductive materials● Force microscopy : the force is at the origin of

the contrast● The force sensor is a tip attached to a

cantilever

Repulsive part : the tip touches the surface => contact mode

Attractive part : the surface is not touched => non contact mode

Operating mode is not the same for both

V LJ = Ar12

−Ar 6

F⃗ = −∇⃗ V LJ

AttractiveRepulsiveLennard Jones potential :

Atomic Force Microscopy

1986 : Atomic Force Microscope (AFM)


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Atomic Force Microscopy in contact mode

Piezoelectric tube

Laser focused on the cantilever back side

Surface

V

Cantilever supporting the AFM tip

FEED BACK LOOP

Constant deflection

Constant deflection=> constant force

F⃗ = k Δ z u⃗z

Photodiode : position of the laser

F⃗ = k Δ z u⃗z

=> Deflection

k : stiffness of the cantilever => Force

Tip sample

distance < 0,5 nm

<= repulsive part of the potential


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AFM in non contact mode

Tip does not touch the surface

● Attractive part of the LJ potential

● Distance > 0,5 nm

● The deflection is not measured

● The cantilever is set into motion by a piezoelectric bimorph

● The amplitude of vibration of the cantilever is measured


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AFM in non contact mode

ω=√ k−∂F∂ zm

frequency

amplitudephase

frequency

vacuum

air

Δ f

The lever is set in motion by a piezo-actuator

The amplitude of vibration is a function of the excitation frequency

Any interaction (force gradient) modifies the resonance frequency

Either the amplitude, the frequency or the phase can be tracked

High Q in vacuum


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Intermittent contact mode or tapping

A0

A

A>A0

FEED BACK LOOP

Photodiode : position of the laser

=> Amplitude A

VControl of the tip-sample distance

ASP

Constant amplitude

Less damage on soft surfaces

https://pubweb.eng.utah.edu/~lzang/images/Lecture_10_AFM.pdf

Tip touches sometimes the surface

FEED BACK LOOP

Deflexion


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« Peak Force » mode

The entire piezotube goes up and down

Tip is fixed, thousands of force curves are operated per second

The final value of the deflexion is fixed on the force curve. It can even be null.

Very soft / fragile samples can be imaged+ liquid media (no or little resonance)

Exemple d’imagerie de la double hélice

d’ADN : (site Bruker)

Bruker


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Electrical measurements with an AFM


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MOS structure : some caracterisation challenges

V

MOS : Metal Oxide Semiconductor

Leakage currents

Charged defects

Source Drain

Oxide

Substrate

Gate

Source / drain Dopants

concentration

Source Drain

Oxide

Substrate

Gate

Work function

Résistivity

Roughness

Gate and contactsSource / DrainGate oxide


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Mesures électriques en mode contact

AFM tip is used like an electrode of nanometric size displaced with a nanometric precision

Source : Bruker

Apply voltage, measure currentChoose range and linearity of the amplifier

=> resistance of the portion of sample located under the tip=> leakage currents in dielectrics

i>0i<0

TUNA (Tunneling AFM, linear amplifier) : 60 fA – 100 pA

C-AFM (Conductive AFM, linear amplifier) : 10 pA – 1 mA (Bruker)

SSRM : (Scanning Spreading Resistance Microscopy, logarithmic amplifier) => 1 mA

Resiscope : (logarithmic amplifier) : 100 fA – 1 mA


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TUNA : examples

épaisseur 50 nm

Current mapping and topography recorded at the very same time (fixed applied voltage)

Hot spots on the surface. TUNA signal is (fairly) independent of the topography)

Context : High k oxides

Thickness 20 nm

Thickness 50 nm

Influence of the layer’s thickness on leakage currents in SrTiO

3. (Couches de

SrTiO3, Guillan et al.)

Leakage current

gate oxide

LaAlO3, 3 nm, W. Hourani, INL


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Current spectroscopies

Oxide degradation by charge trapping

Fowler – Nordheim tunneling current

Evaluation of the equivalent oxide thickness (EOT) at the nanoscale

Satic tip : area probed : 100-20000 nm2

I=Aeff

αEEox2 exp [−

βE

ox ] A

0 1 2 3 4 5 6 7 8 9

1

10

I (p

A)

Vpointe (V)

SiO2 (5 nm)

tunnel FN (5 nm) SiO

2 (3.5 nm)

tunnel FN (3.5 nm)

Evaluation of the local area of contact


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SSRM principle

“Spreading resistance »= Maxwell resistance

Rmaxwell = C r / a

C : constant depending on the shape of the contactr : résistivitya = radius of contact (cylinder)

image NT-MDT, www.ntmdt.com

* Tip(1-10 kOhms)

* Contact(non linear with the applied voltage)

4 contributions of resistance

* Maxwell resistance (of interest)

* Back contact(ohmic contact needed here !)


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SSRM and carriers concentration

Resistivity versus carriers concentration n (or p) via mobility m

n ou (m

p)

=> High pressure of the tip required on silicon (> 10 Gpa !) => b-tin phase transformation of silicon (more conductive)=> Dedicated tip (tapping 40 N/m)=> Surface is scratched

High dynamic range for the measured current (from pA to mA to fit the 1015 – 1020 at/cm3 range)

TUNA/CAFM vs SSRM

Su

bstr

at

silic

ium

Cross section imaging

A. Syngaevski, INL

Calibration of carriers concentration in ZnO Gallium doped layers, A. Syngaevski, INL


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d-doped layers. Spacing 20 nm

SSRM : résolution

Examples :

SIMS profile :

Dark areas are the less doped

Depth (nm)

SIM

S in

tens

ity (

cps)


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Scanning Capacitance Microscopy (SCM)

ΔC doping level #1

depletionaccumulation

Capacitance

doping level #1

doping level #2

VDCΔV

Semiconductor

metal

MOS

oxide

ΔC doping level #2

VDC

C

n type

p type

The variation of CMOS

is inversely proportionnal to the doping level. Phase

Amplitude ΔC

Carrier concentration

Dopants type

Very weak capacitance variation : 10-18 F !Resonant circuit

+ Lock in amplifier


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VDC

C

type n VDC

C

type p

SCM measurements

p n

p and n zones appear with an opposite phase

contrast (180° difference)

Quand V increases, C decreases: C and V out of phase

When V increases, C increases: C and V in phase

Phase

Amplitude ΔC * Phase

SCM image of a sample containing pn junctions @ 0.125 Vdc

4.5 mmnp p n pp n p

450 nm thick layers, Si:B , different doping levels

Su

bstr

at

silic

ium

Cross section imaging


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SCM resolution

Beveled samples

Silicon substrate

a

Raw resolution : ~ 25 nmSample bevelling : resolution 12-13 nm, but modifications of carriers distribution

optical image of a beveled sample


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Scanning Microwave Microscopy (SMM)

High frequency electric wave f > GHz, Use of a vectorial network analyser (VNA)

Reflected wave measured : S11

Impedance of the system must be adapted

Variations of impedance detected => conductivity, dielectric constant, carriers concentration...

S11=ZS−Z ref

ZS+Z ref

Zref

: reference impedance (50 W)Z

s : sample impedance

VNAImpedance matching

S11

sample 50 W

Information in depth by

varying the frequency

Calibrated capacitances


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Caracterisation of ferroelectric and piezoelectric materials


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Ferroelectrics

Examples of ferroelectric materials when crystalline :

PbZrTiO3, LiNbO

3,

PbTiO3,

BIFeO3...

Order parameter : dielectric polarisation P

+

-

p

P = dp/dtDipole moment

p = qdPolarisation

d

+ + +++

- - - - -

P EP

Polarisation charge

Ep : depolarisation

field

PbZrxTi

1-xO

3


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Ferroelectric domains

Domains : areas where the parameter P is homogeneous

As grown domains : Spontaneous organisation of polarisation to decrease the depolarisation fieldEx : ErMnO

3 (sample : G. F. Nataf (Univ. Cambridge, UK), D. Meier

(Univ. Tronheim, Norway), image : INL), Domains are in the plane of the surface

Artificial domains : created by e.g. the application of an electric field Ex : periodically poled LiNbO

3 (PPLN, sample : S. Ballandras, T.

Baron, FEMTO-ST, Besançon, France, Image : INL)

P

P

50 mm x 50 mm

58 mm x 58 mm


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Use of piezoelectricity to detect polarisation

Piezo

Pyro

Ferro

20 classes

10 classes

Dielectric

D i = d ij σ j

Dielectric displacement Stress

Relative deformation (strain)

Electric field

Direct : Apply a mechanical stress => a charge appears

Inverse : Apply an electric field => a strain appears and deforms the crystal

Piezoelectric effect

Piezoelectric effect

Stress σ

Electric field

E

Dielectric displa-

cement D

Defor-mation

S

D⃗ = ϵ0 E⃗ +P⃗32 crystallines classes

ϵi = d ijk E jk


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Piezoelectric layer

Bottom electrode

Substrate

Photodiode

Topography + piezoelectric vibration

Laser

LOCK-IN amplifier

REF

AMPLITUDE x PHASE

180° 0°

f

P

P

Antiparallel domains vibrate with an opposite phase

Piezoresponse Force Microscopy

Strain Electric field

Converse Piezoelectric effectCONTACT

MODE

ϵi = d ij E j


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PFM on ferroelectric materials : general view

Strain Electric field

Converse Piezoelectric effect

Ferroelectric domains engineering (LiTaO3)

A. Brugère, PhD thesis, 2010

Domains mapping (LiNbO3)

B. Gautier, V. Bornand, Solid Films, 515(4-5):1592-1596, 2006

Local hysteresis loops on PZT

Amplitude Phase

ϵi = d ij E jϵi = d ij E j


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Thank you for your attention !

[email protected]

mesure à l'échelle nanométrique des propriétés électriques

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