Scanning Electron Microscopy (SEM)

Short description Beam parameters

influence on image

e ^- gun components

filaments lenses

Beam-sample interaction

electron scattering

Image formation

Scanning Electron Microscopy (SEM)

Goldstein, Scanning Electron Microscopy and X-ray Microanalysis

Scanning Electron Microscope (SEM)

V-shaped Filament Extractor

Deflecting Plates

Backscattered Electrons

e

Detector Primary

e

Beam

Sample

Image Display

Electron Column

Field of view:

5x 5 mm

– 500 x 500 nm

Resolution: down to 1 nm

Scan quadrupole

Beam accelerator

Optical axis

How to sweep an electron beam

First coil deviate beam from optical axis

Second coil brings beam back at optical axis on the pivot point

Image formation point by point

collecting signal at each raster point

L = raster length on sample W = working distance

S = raster length on screen Magnification = S/L

L

S

L = 10 m, S = 10 cm X

m

x m

M x 10000

10 10

10 10

6

2





M depends on working distance

Effect of beam parameters on image

V

= beam voltage i

= beam current



= beam convergence angle

d

= beam diameter at sample

High resolution mode Noise on signal

Effect of beam parameters on image

i

= 1 pA, d

= 15 nm

i

= 320 pA, d

= 130 nm

High current mode Resolution too low

i

= 5 pA, d

= 20 nm Good compromise

i

= beam current d

= beam diameter

Resolution

Depth of focus

Effect of beam parameters on image

If 

is small, d

changes little with depth, so features at different heights can be in focus



= 15 mrad 

= 1 mrad

Effect of beam parameters on image

V

< 5 kV, beam interaction limited to region close to surface, info on surface details V

15 - 30 kV, beam penetrates into sample, info on interior of sample

V

= beam voltage

Electron energy

Electron column

e

are produced and accelerated

Beam is reduced to increase resolution

Beam is focused on sample

Filament

e

are accelerated to anode and the hole allows a fraction of this e

to reach the lenses

Wehnelt: focuses e

inside the gun Controls intensity of emitted e

Grid connected to filament with variable resistor

e

exit filament following + lines

The equipontential line shape

has focussing effect and

determines 

and d

Filament

Electron column

Filament head

The equipontential line shape

has focussing effect and

determines 

and d

Equipotential lines

Electron beam

Filament types

Tungsten hairpin (most common)

Lanthanum hexaboride (LaB

)

0.120 mm Tungsten wire

LaB6 crystal 0.20 mm

Operating principle: thermionic electron emission

Filament types

Tungsten hairpin Lanthanum hexaboride (LaB

)

E

= 4.5 eV

J

= 3.4 A/cm

at 2700 K Lifetime 50-150 hours

Energy width  0.7 eV Operating pressure 10

mbar

E

= 2.5 eV

J

= 40 A/cm

at 1800 °K Lifetime 200-1000 hours

Energy width  0.3 eV Operating pressure 10

mbar

T K

E c

c

e

T A

J ^{ 2 }

thermionic electron emission

A

= 120 A/cm

K

E

= work function

To reduce filament evaporation  operate the electron gun at the lowest possible temperature

Materials of low work function are desired.

Filament types

Thermal Field Emission

W-Zr crystal 0.20 mm I = 1 10

A/cm

at 1800 °C

Lifetime > 1000 hours Energy width  0.1 eV

Small source dimension (few nm) Operating pressure 10

mbar

Operating principle:

thermionic electron emission +

Tunnelling

E gun brightness

Tungsten hairpin Lanthanum hexaboride (LaB

) Thermal Field Emission

 = 10

A/sr cm

2 2 2 2 2

4 4

angle solid

area

current beam

p p

p

p p p

d i d

i



 

  

 







 



 

 

Brightness is conserved throughout the column

2 2

2

2

1

2 angle 4

solid

p p

p

d d

R

A 







 

 





 





 









R



d

 = 10

A/sr cm

 = 10

A/sr cm

Beam current changes throughout the column

d

: 30 – 100 m d

: 5 – 50 m d

: 5 nm

Electromagnetic Lenses

) ( v B F   e 

Demagnification of beam crossover image (d

) to get high resolution (small d

)

Beam focussing ^{High demag}

needed

d

: 5 – 100 m

for filaments d

: 5 nm for TFE Low demag

needed

coils Fringe field

radial

parallel

Electromagnetic Lenses

f = focal length

the distance from the point

where an electron first begins to change direction to the point where it crosses the axis.

Focusing process

e

interacts with B

and B

separately -e (v

x B

) produces a force into screen F

giving e

rotational velocity v

v

interacts with B

produces a force toward optical axis F

= -e (v

x B

)

The actual trajectory of the electron will be a spiral

The final image shows this spiraling action as a rotation of the image as the objective lens strength is changed.

Electromagnetic Lenses

I = lens coil current N = number of coils V

= accelerating voltage

Lens coil current and focal length

Increasing the strength (current) of the lens reduces the focal distance

 NI ⁰  ²

f ^ V

the focal length will become longer at higher accelerating voltages for the same lens current

Comparison to optical lenses

q p

f

1 1

1  

p M ^ q ion Magnificat

q m ^ p ation Demagnific

Beam crossover

d

= tungsten diameter = 50 m

Scaling from the figure, the demag factor is 3.4 so d

= d

/m = 14.7 m

CONDENSER LENSES: the aim is to reduce the beam diameter

Demagnification of beam crossover image (d

) = object

Objective Lenses

Scope: focus beam on sample

• Pinhole

• No B outside

• Large samples

• Long working distances (40 mm)

• High aberrations

They also provide

further demagnification

• Immersion

• Sample in B field

• Small samples

• Short working distances (3 mm)

• Highest resolution

• Low aberrations

• Separation of secondary from backscattered e

• Snorkel

• B outside lens

• Large samples

• Separation of secondary from backscattered e-

• Long working distances

• Low aberrations

They should contain:

Scanning coil Stigmator

Beam limiting aperture

Effect of aperture size

Aperture size: 50 – 500 m

Decrease 

for e

entering OL to 



determines the depth of focus

Determines the beam current

Reduces aberrations

Effect of working distance

Increase in WD  increase in q 

m smaller  larger d  lower resolution but longer depth of focus

q p

f ^{1  1  1}

q

m ^ p

Effect of condenser lens strenght

Increase in condenser strenght (current)  shorter q  larger m and smaller d

Also it brings a beam current reduction, so a compromise between current and resolution is needed

Weak Strong

q m ^ p

 NI



f ^ V

Higher I

Lower I

Lower d

Higher d

Decrease q

and increase p

 larger m

Gaussian probe diameter

2 2 2

4

p p

p

d i



  

Distribution of emission intensity from filament = gaussian with size d

d

= FWHM

2 2

4

p p G

d i



 

4

2 2 2

G p p

i  d 



With no aberrations, keeping d

constant would allow to increase i

by only increasing 

Understand how probe size varies with probe current

Calculate the minimum probe size and the maximum probe current

Knowing emitter source size, d

may be calculated from the total demagnification

Spherical aberrations

Origin: e- far from optical axis are deflected more strongly

2



s C s

d ^

So at the focal plane there is a disk and not a point

e

along PA gives rise to gaussian image plane No aberration

e

along PB cross the optical axis in d

Spherical aberration disk of least confusion



C

= Spherical aberration coefficient

 f

Immersion and snorkel C

~ 5 mm Pinholes C

~ 20-30 mm

So one need to put a physical aperture to limit aberrations x nm

d

x 0 . 16

2

10 64 10

5 2

) 10 4 ( 10

5 



 







x nm

d

x 2 . 5

2 10 10 5 2

) 10 10 ( 10

5 



 





Aperture diffraction

eV

 61  .

 0 d d

To estimate the contribution to beam diameter one takes half the diameter of the diffraction disk

E 24 .

 1

 nm rad

nm 10 24 . 1 10

@ KeV   

nm 89 . 10 1

4

10 24 . 1 61 . 0

3

2





 x



d

Origin: initial energy difference of accelerated electrons

For tungsten filament E = 3 eV

Chromatic aberrations

Chromatic aberration disk of least confusion

 

 



  

E

C E d _{C C} 

At 30 KeV E/E

= 10

At 3 KeV E/E

= 10

C

= Chromatic aberration coefficient  f

2 2

2

2

s d C

p d G d d d

d ^{   }

Origin: machining errors, asymmetry in coils, dirt

Astigmatism

Result: formation ow two differecnt focal points

Effect on image:

Stretching of points into lines

Can be compensated with octupole stigmator

Astigmatism

Beam-sample interaction

Backscattered e

Silicon V

= 20 KV

TFE,  = 1 10

A/sr cm

d

= 1 nm

I

= 60 pA Simulation of e

trajectories

Main reason of large interaction volume:

Elastic Scattering

Inelastic scattering

Beam-sample interaction

Elastic scattering cross section

  ^ _ ^

 

 



 



 



 







-2 0 2

20

tan 2 10

62 .

1 electron events atom/cm

E x Z

Q 

Z = atomic number;

E = e

energy (keV);

A = atomic number

N

= Avogadro’s number;

 = atomic density

Elastic Scattering

(cm)

0



 _ N A Q

Elastic mean free path =

distance between scattering events

Silicon

 = 2.33 g/cm

Z = 14

A = 28

N

= 6.022 10

 

nm Si

atom/cm electron events

x Si

Q

keV keV

2 . 1 )

(

10 66 . 1 )

(

1 5

2 15

1 5

0 0



















 

nm x

Si

atom/cm electron

events x

Si Q

keV keV

10 08 . 1 )

(

10 84 . 1 )

(

3 30 5

2 18

30 5

0 0

















Beam-sample interaction

Inelastic scattering energy loss rate

 

 



 

 J E

AE Z N

ds e

dE _i

i

166 .

ln 1 2 



Inelastic Scattering

Z = atomic number A= atomic number

N

= Avogadro’s number

 = atomic density

E

= e

energy in any point inside sample J = average energy loss per event

 9 . 76  58 . 5

 10

 Z Z x

J

E

= 20 KeV

The path of a 20 KeV e- is of the

order of microns, so the interaction volume

is about few microns cube

Beam-sample interaction

Simulation

Energy transferred to sample

Interaction volume 20 KeV beam incident on PMMA

with different time periods

Influence of beam parameters on beam-sample interaction

Beam energy

10 KeV 20 KeV

30 KeV Fe

E ds

dE E Q

1 1

2





Longer 

Lower loss rate

Elastic scattering cross section

Inelastic scattering energy loss rate

(cm)

0



 _ N A Q

Incidence angle

Influence of beam parameters on beam-sample interaction

45°

60°

Fe

Smaller and asymmetric interaction volume

Scattering of e

out of the sample

Reduced depth Same lateral dimensions

surface su rf

ac e

10% to 50% of the beam electrons are backscattered

They retain 60% to 80% of the initial energy of the beam

Atomic number

C (Z=6)

C, k shell

Fe (Z=26)

Influence of sample on beam-sample interaction

Fe, k shell

V

= 20 keV

Reduced linear dimensions of interaction volume

ds Z dE

Z Q





Elastic scattering cross section

Inelastic scattering

energy loss rate

Atomic number

Ag (Z=47)

Ag, k shell

U (Z=92)

Influence of sample on beam-sample interaction

U, k shell

V

= 20 keV

More spherical shape of interaction volume

Backscattered electrons

Signal from interaction volume (what do we see?)

Secondary electrons

Backscattered e

Backscattered electron coefficient

60°

B BSE i

BSE

i

 i

 

 

Relationship between

 and a sample property (Z)

This gives atomic number contrast

If different atomic species are present in the sample ^ 

i

C 



C

= weight concentration

BSE dependence

Monotonic increase

Incidence angle

60°







 _{( )} 

_cos

BSE dependence



= intensity at normal

Line length: relative intensity of BSE

Strong influence on BSE detector position

Energy distribution

BSE dependence

The energy of each BSE depends on the trajectory inside sample, hence different energy losses

Region I: E up to 50 %

Becomes peaked with increasing Z

Lateral spatial distribution

Region good for

high resolution Gives rise to loss in lateral resolution

At low Z the external region increases

Sampling depth

BSE dependence

Sampling depth is typically 100 -300 nm for beam energies above 10 keV

Fraction of maximum e

penetration

(microns) Percent of 

R

defines a circle on the surface (center in the beam) spanning the interaction volume

Energy distribution of electrons emitted by a solid

Signal from interaction volume (what do we see?)

Secondary electrons

Energy: 5 – 50 eV

Probability of e

escape from solid



e z

p ^{ }

 = e

mean free path

Origin: electron elastic and inelastic scattering

Secondary electrons

SURFACE SENSITIVE

SE

= secondary due directly to incident beam

SE

= secondary generated by backscattered electrons

Carbon: SE₂ /SE₁ = 0.18 Aluminum: SE₂ /SE₁ = 0.48 Copper: SE₂ /SE₁ = 0.9 Gold: SE₂ /SE₁ = 1.5

Low backscattering cross section

High backscattering cross section

Beam resolution

BSE resolution

SE Intensity angular distribution: cos

Image formation

Backscattered e

Secondary e

Volume sensitive Surface sensitive



e z

p ^

Sampling depth

~ 100 -300 nm

Image formation

Many different signals can be extracted from beam-sample interaction

So the information depends on the signal acquired, is not only topography

The beam is scanned along a single vector (line) and the same scan generator is used to drive the horizontal scan on a screen

A one to one correspondence is established between a single beam location and a single point of the display

For each point the detector collects a current and the intensity is plotted

or the intensity is associated with a grey scale at a single point

Signals to be recorded

Image formation

Magnification M = L

/L

But the best way is to calibrate the instrument

Image formation

Pixel = picture element

Pixel is the size of the area on the sample from which information is collected

Actually is a circle

PE SAMPLE

PE N

D ^ L Length of the scan on sample

number of steps along the scan line

The image is focused when the signal come only from a the location where the beam is addressed

At high magnification there will be overlap between two pixel Digital image: numerical array (x,y,Signal)

Signal: output of ADC Resolution = 2

8 bits = 2

= 256 gray levels 16 bits = 2

= 65536 gray levels

Considering the matrix defining the Dimension of Pixel Element

Image formation

For a given experiment (sample type) and experimental conditions (beam size, energy) the limiting magnification should obtained by calculating the area generating

signal taking into account beam-sample interactions and compare to pixel size 2

2 BSE

eff d B d

d ^{ }

beam Area producing BSe

V

= 10 keV, d

= 50 nm

on Al, d

= 1.3 m  d

= 1.3 m on Au d

= 0.13 m  d

= 0.14 m

There is overlapping of pixel signal intensity

10x 10 cm display

Different operation settings

for low and high magnification

Depth of field

Depth of field D = distance along the lens axis (z) in the object plane in which an image can be focused without a loss of clarity.

To calculate D, we need to know where from the focal plane the beam is broadened

2 tan /

D

 r



The vertical distance required to broaden a beam r

to a radius r (causing defocusing) is

For small angles    

2 tan /

D r

 D ^{ 2} r

Broadening means adjacent pixel overlapping

Depth of field

On a CRT defocusing is visible when two pixels are overlapped  r = 1 pixel (on screen 0.1 mm)

But 1 pixel size referred to sample depends on magnification

To increase D, we can either reduce M or reduce beam divergence

2 mm . 0 M  D ^

1 mm . 0 r ^ M



D ^{ 2} r How much is r?

Beam divergence is defined by the beam defining aperture

W

D

 R



Depth of field

W

D

 R



Optical SEM

Detector

Everhart-Thornley Secondary + BSE

Grid negative: only BSE

solid angle acceptance: 0.05 sr Geometric efficiency: 0.8 %

Grid Positive: BSE+SE

The bias attracts most of SE

Topographic contrast

Intensity of SE and BSE depends on beam/sample incidence angle () and on detector/sample angle ()

BSE coefficient increase with  BSE emission distribution ~ cos  SE emission distribution ~ sec 

Detector position and electron energy window are important

Topographic contrast

Negative bias cage to exclude secondary e

High contrast due to orientation of sample surfaces

- Detector is on one side of sample  anysotropic view - Small solid angle of acceptance  small signal

- High tilt angle

Analogy to eye view

Dierctional view

Topographic contrast

Positive bias cage to accept secondary e

Contributions:

Direct BSE+SE

SE distribution intensity I ~ sec 

Variation in SE signal between two surfaces with different  dI = sec  tan  d

So the contrast is given by dI/I = tan  d

The SE are collected from most emitting surfaces since the positive bias allows SE to reach the detector

Analogy to eye view

High resolution imaging

High resolution signal if selected in energy

High resolution signal generated by BSE

, SE

Separation of signal is necessary to obtain high resolution

SE

: e

directly generated by beam

BSE

: low energy loss (<2%) e

from beam SE

: e

generated by BSE into sample

BSE

: higher energy loss e

from beam

Silicon V

= 30 KV

TFE,  = 1 10

A/sr cm

d

= 1 nm

I

= 60 pA

SE

- BSE

width = about 2 nm Beam penetration depth = 9.5 m Emission area = 9.5 m

Scan width at 10000 X = 10x10 m

image 1024x1024, pixel width 10 nm

Low mag

Scanning at low M means field of view larger than SE

emission area

So there is large overlap between pixel

And the changes are due only to SE

variations

Scanning at high M means field of view smaller than SE

emission area

So as the beam is scanned, no changes in SE

but changes are due to SE

SE

gives large random noise

Scan width at 100000 X = 1x1 m

image 1024x1024, pixel width 1 nm

High mag

FWHM = 2 nm

Carbon nanotubes Ag NP on glass

TiO

on silicon

SEM in FOOD

Schematic representation of gaseous SED the role of imaging gas in VP-SEM

B. James / Trends in Food Science & Technology 20 (2009) 114

SEM in FOOD

50 μm

Blades of cocoa butter present on the surface Image taken with sample at 5 °C

using nitrous oxide at ~ 100 Pa (0.8 torr) as imaging gas

‘‘bloomed’’ chocolate.

SEM in FOOD

VP-SEM image of commercially produced mayonnaise.

Image taken with sample at 5.0 °C

using water vapor at around 670 Pa (5.0 torr) as imaging gas.

Light continuous phase is water mid grey discrete phase is oil.

Darkest grey areas are air bubbles

Disadvantages of conventional SEM techniques insulating specimens

impossibility of examining hydrated samples without altering their state (drying or freezing) Sample preparation treatments introduce artifacts

No studies of dynamic processes for such samples

20 μm

V-shaped Filament Extractor

Deflecting Plates

Backscattered Electrons

e

Detector

Primary e

Beam

Sample

Chemical Map Electron Energy Analyzer

Scanning Auger Microscopy (SAM)

Auger Spectrum

Two-Hole Final State One-Hole

Initial State

Ground State De-Excitation

Auger Process

Auger Spectroscopy

L

2s

e

e

K 1s L

2p

M

3s M

3p VB

E

E

E

E

(XYZ)= E

(X)-E

(Y)-E

(Z)-

XYZ Auger Process One-Particle Scheme Energy Conservation

E

(XYZ) = KE of Auger electron E

(X) = BE of X level

E

(Y) = BE of Y level

E

(Z) = BE of Z level

Usually additional terms must be included accounting for the two-hole final state

correlation interaction and the relaxation effects

F Two-Hole Final State Correlation Energy R Two-Hole Relaxation Energy

E

One electron binding energy

E _K (XYZ)= E _B (X)-E _B (Y)-E _B (Z)-F+R-

K L

M

VB

E

E

E

L

M

Auger Process Nomenclature

KL

M

Auger Process

L

L

M

Coster-Kronig Process

(the initial hole is filled by an electron of the same shell)

CCC Core-Core-Core Transition CCV Core-Core-Valence Transition CVV Core-Valence-Valence Transition

K L

M

VB

E

E

E

L

M

KL

M

K L

M

VB

E

E

E

L

M

L

L

M

3d M

3p M

Electron

Auger X-Ray

Fluorescence

3s M

2p L

1s K 2s L

2p L

E

Photon

Competitive processes

Relative Probabilities of Relaxation by Auger Emission and

by X-Ray Fluorescence Emission

For lines originating from shell L and M the Auger yield remains much

higher than X-ray emission

Principal Auger Lines while

Spanning the Periodic Table of the Elements

CHEMICAL SENSITIVITY

Electron distribution spectrum

Pulse Counting Mode Derivative Mode

Since Auger emission lines are often very broad and weak, their

detectability is enhanced by differentiating of the spectrum

Chemical environment sensitivity

Gas Solid

Auger Electron Spectroscopy Quantitative Analysis

In analogy to what developed for XPS,

one can determine the atomic concentration (C

) of the atomic species present

in the near-surface region of a solid sample



C _i 

I _i s _i

I _i s _i

 i C

Atomic Concentration of the i-th species

s

Orbital Sensitivity Factor of the i-th species

I

Spectral Intensity Related to the i-th species

Auger Spectra as Measured at Selected Points of the

Self-organized Agglomerated Au/Si(111) Interface

Flat region Island

Si L

VV

Au N

VV

Si L

VV Auger Line Shape as Measured at Selected Points of the Self-organized

Agglomerated Au/Si(111) Interface

Flat region

Island