progress towards low vacuum critical dimension metrology

cnse.albany.edu

Progress towards Low Vacuum Critical Dimension Metrology

Brad Thiel & Vaso Tileli

College of Nanoscale Science & Engineering University at Albany

State University of New York

Frontiers of CharacterizationMay 14th, 2009 – Albany, NY

cnse.albany.edu

Acknowledgements

Thanks to:– Dr. Milos Toth, FEI Co.– Mr. W. Ralph Knowles, FEI Co.– Dr. András Vladár, NIST– Dr. Michael Postek, NIST

Funding from:

http://www.nist.gov/

cnse.albany.edu

Outline

• Introduction– Critical Dimension Metrology (CD SEM)– Necessity for Modeling

• Low Vacuum CD Metrology Approach– Charge Control– Contamination Control

• Principles of Low Vacuum SEM

• Analytical Modeling of Amplification and Noise Characteristics– ESD (Environmental Secondary Electron Detector)– Helix (Magnetic Immersion Lens Detector)

• Summary & Pending Work

cnse.albany.edu

• Scanning electron microscope methods are some of the most prevalent technologies for critical dimension (CD) measurement.

– High resolution imaging (spatial res. ~1nm, measurement res. ~1nm)– Acceptable throughput and speed (typically 1 wafer per ~5min, 17 points on wafer)– Site specific measurements– Well-established procedures for interpreting the results

• CD’s are rapidly approaching the limitations of conventional CD-SEM imposed by:

– Charging– Contamination– Specimen interaction volume– Secondary electron mean-free-path

• Low Vacuum SEM technology can address charging and contaminationwithout sacrificing performance

Critical Dimension (CD) Metrology

cnse.albany.edu

CD-SEM Measurement Process

• SEM information is distilled into an intensity profile• The peaks indicate the position of the edges• Simulation codes correlate peak position and shape with actual feature shape

– Edge “blooming” effect

chrome-on-quartz photolithographic mask MC simulation of electron trajectories near the edge of a line and corresponding line profile

edge of line

line profile

cnse.albany.edu

Edge Assignment Problem

Raw dataUseful & accurate info of device shape

w1

w2

ϕ

Modeling?ITRS – Need for standardization of CD process,

i.e. “robust conversion of massive quantities of raw data to information useful for enhancing the yield of the semiconductor manufacturing process”

ITRS (International Technology Roadmap for Semiconductors) 2008 update / Metrology section

cnse.albany.edu

Fit to poly-Si

line

Modeling for Accuracy: MONSEL

• Analytical descriptions are implemented for all physical processes– Electron beam/specimen interactions

• Instrumentation effects are included• Software that can reach, and if needed interpolate between a library of precomputed line

profiles for model geometries• Non-linear least squares algorithm solves for the particular set of parameters that produce

the best least squares match between measured and calculated images

217 nm

6.2° 6.0°

J.R. Lowrey et al., Proc. SPIE 2196 (1994) 85 M.T. Postek et al., J. Vac. Sci. Technol. B 23 (2005) 3015J.S. Villarrubia et al., Proc. SPIE 4689 (2000) 304 J.S. Villarrubia & Z.J. Ding, Proc. SPIE 7272 (2009)

Top down image intensity profile &Simulation fit

X-sectional image &X-sectional fittedshape

cnse.albany.edu

The Problem with Low Voltage CD SEM

• CD measurement of non-conductors is challenging because charging effectsdepend strongly on imaging conditions and cause:– Image distortion– Contrast inversion

E0=600eVI0=44pA Position along line

Scal

ed In

tens

ity

3μs

45μs

Position along lineSc

aled

Inte

nsity 12μs

24μs

Si3N4 contact holes

cnse.albany.edu

Low Vacuum CD-Related Advantages

• Good charge control independent of scan rate• Good SNR at even lower electron fluence• Contrast is preserved

E0=5keVI0=28pA

3μs

45μs

12μs

24μs


aled

Inte

nsity


aled

Inte

nsity

Si3N4 contact holes

cnse.albany.edu

• High resolution imaging with existing electron optics

M. Toth et al., Appl. Phys. Lett. 88 (2006) 023105

(a) & (b) chrome-on-quartz photolithographic mask(c) contact hole in Si3N4

(d) electrostatic discharge pit in SiO2


cnse.albany.edu

• Hydrocarbon contamination is reduced

M.T. Postek et al., J. Microlith. Microfab. Microsyst. 3 (2004) 224

3min e-beam irradiation (a) no contamination square(b) shrinkage of the residue

500nm 500nm200nm


cnse.albany.edu

Low Vacuum CD Metrology – Overview

• Surface charging stabilization

• High resolution imaging

• Contamination control

• Method for interpreting the results

ITRS challenges for both ≤ & ≥ 22nm

cnse.albany.edu

• Low Vacuum SEM technology can address charging and contaminationwithout sacrificing performance

• How are optimal conditions determined for alleviating charging artifacts?• How does the gas affect the incident beam?• How does the gas affect the secondary electron emission?• What are the sources of signal, background, and noise collected by the

detector?

Critical Dimension (CD) Metrology

cnse.albany.edu

Low Vacuum SEM

cnse.albany.edu

RP DP

IP

RP

RP DP

The Low Vacuum SEM

Specimen Chamber1-10 torr

e- gun

Pressure limiting aperture 1

Pressure limiting aperture 2

Water vapor/gas

Vent

10-8 torr

10-5 torr

10-1 torr

10-3 torr

cnse.albany.edu

Scattering of the Primary Beam

• Collisions of primary beam electrons with gas molecules result in a low current density “skirt” of scattered electrons surrounding the central beam

– It can extend over several hundred micrometers

– It does not degrade resolution– It contributes to the background

• The unscattered fraction of the beam is given by:

Q(E): total scattering cross-section, P : gas pressure, l : gas path length, R : gas constant, T : temperature

D.A. Moncrieff et al., J. Phys. D 12 (1979) 481 B.L. Thiel, Ultramicroscopy 99 (2004) 35

⎟⎠⎞

⎜⎝⎛−=

RTPlEQf )(exp

+ Va

low vacuumregion

high vacuumregion

cnse.albany.edu

Mean free path of Electrons in H2O Vapor

~2~2--5mm5mm

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30Electron Energy (keV)

Mea

n-fr

ee-p

ath

(mm

)

10 Pa100 Pa1000 PaLikely Low Vac

CD-SEM range

cnse.albany.edu

Gas Cascade Amplification

– Signal • Normally amplified SEs (gain

~103)

– Noise• SEs amplification is a

stochastic process

– Background• Inevitable multiplication of

BSEs and PEs

• The amplification of the emitted secondary electron (SE) signal takes place inside the chamber by ionizing collisions of the SEs with gas molecules

• A variety of electrodes and pole-pieces integrated into the final lens are used to create the electromagnetic field which drives the amplification cascade.

+ Va

low vacuumregion

high vacuumregion

cnse.albany.edu

Role of Ions

++

++++++

++++++++++

++ ++++

++

++

• Collisions of all emissions with gas molecules create positive gaseous ions

• Ions flow to regions of the specimen surface with a negative potential

• Ions recombine at surface, removing excess electronic charge

+ Va

low vacuumregion

cnse.albany.edu

Low Vacuum SEM: Challenges

• Operating parameter space is much larger to optimize

• Charge control is a strong function of operating conditions

• Signal, background, and noise production are strong functions of operating conditions– SE signal amplification via gas ionization cascade– Background due to elastic-scattering of the primary beam– Background due to inelastic high-energy electron scattering– Excess noise due to stochastic nature of cascade amplification

– High Vacuum• Beam energy• Beam current• Dwell time• Working distance

– Low Vacuum• Beam energy• Beam current• Dwell time• Working distance• Gas-path-lengh• Cascade distance• Gas type• Gas pressure• Detector bias

cnse.albany.edu

Cascade Amplification in a Constant Field

cnse.albany.edu

ESD

0

d

z

specimenstage

anode

Eur

primary beam

aV

ABC

D

0

d

z

specimenstage

anode

Eur

primary beam

aV

ABC

D

A: ionizing events caused by secondary electrons (SEs) emitted from the specimen;

B: multiplication process;

C: ionizing events caused by backscattered electrons (BSEs);

D: corresponding effect caused by primary electrons (PEs).

• Allows study of fundamental electron-gas interactions in a simple geometry– Uniform electric field– Ionization efficiency largely independent of position in cascade

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

aVBPdAPexpα

A,B : gas-specific parametersP : pressured : cascade distanceVa : detector bias

A. von Engel, Ionized gases (Clarendon Press, Oxford, 1955)

cnse.albany.edu

Flow Chart of the Signal Chain

Beam comes down the column

Beam enters into the chamber

Beam interacts with the

specimen

Emissions are

amplified in the gas

Cascade current is measured by the detector and converted into voltage at

the pre-amplifier

Image processing in the system and filtering

Display on screen

cnse.albany.edu

Amplified SE Signal

• The secondary electron cascade current Is arriving at the detector can be described by the following equation:

Io : primary electron beam currentδ : secondary electron yieldα : gas ionization efficiencyd : cascade distancef : fraction of primary electrons that do not scatter into the skirt

• However, this needs to be modified in order to include the total measured signal in our experimental set-up– Addition of all SEs (included those generated by the skirt, BSEs, & PEs

( )dfII os

D.A. Moncrieff et al., J. Phys. D 11 (1978) 2315

D.A. Moncrieff et al., J. Phys. D 12 (1979) 481

αδ exp =

( ) ( ) ( ) oPEBSE IdPSdPSdI ⎟

⎠⎞

⎜⎝⎛ −+−+= 1exp1expexp α

αα

αηαδ

cnse.albany.edu

Sources of Noise

• Beam or shot noise: Arising from Poisson distribution of emission of e-.

• Gas cascade noise:: Arising from the formation of plasma in the chamber.

– Contribution to noise from:• Secondary Electrons (SEs)• Primary Electrons (PEs)• Backscattered Electrons (BSEs)

• Amplifier or Johnson’s noise: Arising from thermal and electronic noise in the detection system.

beIN oBE 2=e : electron chargeIo: primary beam currentb : signal bandwidth

kTRbN AMP 4=k : Boltzmann’s constantT : temperatureR : resistor

W. Shockley and J. R. Pierce, Proc. IRE 26 (1938) 321 J. Johnson, Phys. Rev. 32 (1928) 97

cnse.albany.edu

Cascade Noise: Model

eFMN 2=

• The physical process of ionization of the gas in the presence of an electric field is similar to that of the production of e- - h+ pairs in an avalanche photodiode

• The contribution to noise from the cascade is:

M : amplification factor (gain)Fe : excess noise factor (gain uncertainty)

R.J. McIntyre, IEEE Trans. El. Dev. ED 13 (1966) 164R.J. McIntyre, IEEE Trans. El. Dev. 46 (1999) 1623

0 500 1000 15000

100

200

300

3Torr

num

ber o

f ele

ctro

ns

gain0 500 1000 1500

0

100

200

300

num

ber o

f ele

ctro

ns

gain

3.5Torr

0 500 1000 15000

100

200

300

num

ber o

f ele

ctro

nsgain

4Torr

V. Tileli et al., “Excess noise factor of the gas ionization cascade calculated by statistical analysis of Monte Carlo gain distributions”, in preparationCascade Monte Carlo Software

cnse.albany.edu

Cascade Noise: Model

eFMN 2=

• The physical process of ionization of the gas in the presence of an electric field is similar to that of the production of e- - h+ pairs in an avalanche photodiode

• The contribution to noise from the cascade is:

M : amplification factor (gain)Fe : excess noise factor (gain uncertainty)

R.J. McIntyre, IEEE Trans. El. Dev. ED 13 (1966) 164R.J. McIntyre, IEEE Trans. El. Dev. 46 (1999) 1623

• Application of the model for single carrier initiated/single carrier multiplication conditions (the lowest noise case for diodes) gives:

MFe

12 −=

• Therefore the multiplication noise can be described by the equation:

( )12 −= MMN

cnse.albany.edu

Cascade Contributions to Noise

• Secondary electrons

• Primary electrons

• Backscattered electrons

Io : primary beam current SPE & SBSE: PEs & BSEs ionization efficiencye : electron charge P : pressureb : bandwidth l : gas path lengthα: gas ionization efficiency d : cascade distanceδ: SE yield η : BSE yield

( ) ( )exp 1 exp 12 2 1PE o PE

d dN eI bS Pl

d dα αα α

− −⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠

( ) ( )exp 1 exp 12 2 1BSE o BSE

d dN eI b S Pl

d dα α

ηα α

− −⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠

V. Tileli et al., “Noise characteristics of the gas ionization cascade used in low vacuum scanning electron microscopy”, submitted to J. App. Phys.

( )( ) ( ) ( )( )1exp2exp12 −+= ddbeIN oSE ααδδ

cnse.albany.edu

Signal and Noise Contributions

• Total signal driven by the SE contribution• Total noise dominated by:

– Amplifier noise at low pressures– SE cascade component at high pressures

0 1 2 3 4

100

101

102

0 1 2 3 4

10-5

10-4

10-3

10-2

PE

SE

Total

Sig

nal (

nA)

Pressure (Torr)

BSE

NT NSE

NBSE

NPE

NDE

Noi

se (n

A/√

Hz)

Pressure (Torr)

NB

operating conditions: Eo=15keV, Io=300pA, Va=400V, d=5mm

cnse.albany.edu

Experimental Set-up

…..……………..

354.4anode

specimenstage

pre-amplifier

LCD monitor

DVM

spectrum analyzer

aV

…..……………..

354.4anode

specimenstage

pre-amplifier

LCD monitor

DVM

spectrum analyzer

aV

• SEM data– FEI Nova NanoSEM

• Signal data– Digital volt meter (DVM)

connected to the output of the pre-amplifier

• Noise data– Agilent E4401B Spectrum

Analyzer connected to the output of the pre-amplifier

• Noise marker function

cnse.albany.edu

• Total signal increases as the primary beam energy is lowered

• The pressure at which maximum gain occurs is proportional to the electric field strength

• Maximum gain is an exponential function of the anode bias

• Total signal is proportional to the incident current

0 1 2 3 40

10

20

30

40

0 1 2 3 40

2

4

6

15keV

30keV

Pressure (Torr)

Tota

l Sig

nal (

nA)

Tota

l Noi

se (p

A/√

Hz)

15keV Model 30keV Model

Pressure (Torr)0 1 2 3 4

0

10

20

30

40

0 1 2 3 40

2

4

6

Pressure (Torr)To

tal S

igna

l (nA

)

7mm Model 5mm Model 3mm Model

Tot

al N

oise

(pA

/√H

z)

7mm5mm

Pressure (Torr)

3mm

anode/specimen separation dbeam energy Eo

0 1 2 3 40

20

40

60

80

Signal and Noise

0 1 2 3 40

2

4

6

8

10

12

Tota

l Sig

nal (

nA)

Pressure (Torr)

450V Model 400V Model 350V Model 300V Model

Tot

al N

oise

(pA

/√H

z)

400V

Pressure (Torr)

300V

350V

450V

0 1 2 3 40

20

40

60

80

100

120

140

0 1 2 3 40

2

4

6

8

10

12

Pressure (Torr)

Tota

l Sig

nal (

nA)

406pA Model 100pA Model 27pA Model

Tota

l Noi

se (p

A/√

Hz)

406pA

100pA

Pressure (Torr)

27pA

beam current Io


detector bias Va

cnse.albany.edu

Signal-to-Noise Ratio (SNR)

• Total cascade current reaching the detector contains a significant background component

• Optimization through the master curve approach

0 2 4 6 8 100

2

4

6

8

10

12

0 2 4 6 8 1010-11

10-10

10-9

10-8

10-7

10-13

10-12

10-11

10-10

10-9

10-8

SNR of SE Amplified Signal

Total SNR

SNR

(a.u

.)

Pressure (Torr)

Sign

al (A

)

Pressure (Torr)

Noise

Effective SE Signal

Noi

se (A

/√H

z)

Total Signal

0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

SNR

(a.u

.)

Pd (Torr mm)

500V 400V 300V 200V

Eo=15keV, Io=200pA, Va=400V, d=5mm Eo=15keV, Io=100pA


cnse.albany.edu

Low Vacuum Immersion Lens Detector – Helix™

cnse.albany.edu

Helix™

sample

pole piece PLA

anode

anode

Monte Carlo simulation of a single SE trajectory inside the detector

• SEs are attracted by an electric field, confined by a magnetic field

• Most amplification takes place along the anode periphery

B.L. Thiel et al., Rev. Sci. Instr. 77 (2006) 033705M. Toth et al., Appl. Phys. Lett. 88 (2006) 023105

cnse.albany.edu

Helix™

Ions• Generated along the anode and the beam

axis• ~ ½ drift up to the PLA, and ½ down to

the sample• Excess ions charge up the sample

surface, reduce the detector field & give rise to imaging artifacts (gain 103)

• Ion trap helps in self-regulation of ion current reaching the sample

sample

pole piece PLA

anode

ion trap

B.L. Thiel et al., Rev. Sci. Instr. 77 (2006) 033705M. Toth et al., Appl. Phys. Lett. 88 (2006) 023105

cnse.albany.edu

Operating parameters: Eo=10kV, WD=5mm, Io=~100pA, Bf=200mT

Helix™ – Optimizing Imaging Conditions

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

1

10

100

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.1

1

10

Sign

al (n

A)

Pressure (Torr)

405V 400V 380V 360V 319.9 299.9

Noi

se (p

A/√

Hz)

Pressure (Torr)

200nm

(f) Va=480V(b) Va=315V(a) Va=300V (d) Va=400V(c) Va=350V (e) Va=430V

0.00 0.25 0.50 0.75 1.00 1.25 1.502

4

6

8

SNR

(a.u

)Pressure (Torr)

300V 320V 360V 380V 400V 405V

Operating parameters: Eo=5kV, WD=4mm, Io=~100pA, Bf=200mT, Pt

Good charge control and SNR achievable but not intuitive

cnse.albany.edu

Summary & Pending Work

• Low Vacuum SEM can be a viable approach for high resolution CD Metrology if appropriate modeling of the instrumental effects is developed

• Charge control and contamination reduction have been demonstrated

• Analytical signal and noise performance for the constant field cascade were modeled successfully

cnse.albany.edu

Remaining Work

• Identification of the optimal gas composition for CD measurements

• Generalize analytical expressions for the gain and noise processes for complex detector configurations

• Develop analytical expressions for non-linear cascade processes – Breakdown (secondary ionization effects)– Scavenging (recombination of SE’s with ions)

• Establish the limits of charge control under low vacuum conditions

• Evaluate the model for incorporation in the CD simulation code MONSEL for the realization of Low Vacuum Critical Dimension Metrology

cnse.albany.edu

Back-up slides

cnse.albany.edu

Low Voltage vs. Low Vacuum

Useful SEM imaging of dielectrics, i.e. no charging artifacts, is possible by:

Low voltage Low vacuum

But E2:• Is specimen dependent • Can vary within the imaged area• Is a function of electron fluence

Charging is stabilized by fine-tuning of the electron beam energy to a critical value E2

Charging is stabilized by a weakly ionized gas inside the specimen chamber

Effective because it does not rely on:• Landing energy modulation• SE recollection by the sample

Both suppress imaging artifacts but neither actually eliminates charging

cnse.albany.edu

Advantages of Low Vacuum SEM• It stabilizes the surface potential• It removes restriction on beam

energy allowing it to be chosen on the bases of different criteria

• It eliminates image distortion– Image fidelity on metrology

does not depend on imaging conditions

• It allows true SE imaging– Low voltage gives a signal

complimentary to the backscattered

• It is potentially useful for acquiring information on buried structures

– SE contrast reflects the local dielectric properties

cnse.albany.edu

Summing the Noise

Uncorrelated events add up in quadrature, correlated sum linearly

• All processes that take place in the cascade are correlated events– After ionization collisions, PEs and BSEs generate SE cascade

• Amplifier noise is independent of cascade processes

Therefore:

( ) 22AMPPEBSESET NNNNN +++=

cnse.albany.edu

Image Analysis – ESD

• Model predictions (plot) are in accordance with corresponding ESD images

• FFT image analysis is required to confirm the model predictions

200 250 300 350 400 450 5001.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.03 4 5 6 7 8

(f)

(e)(d)

(c)

(b)

P=4 Torr

SNR

(a.u

.)

anode bias (V) [d=5mm]

P=1 Torr

(a)

gap distance (mm) [Va=400V]

1μm

(a) (b) (c)

(d) (e) (f) 1μm

(a) (b) (c)

(d) (e) (f)

Images on Au on C taken at: 15keV, 100pA, 50kX, 1024x882, 0.4μs (no filters) x64frames

cnse.albany.edu

Helix – H2O vapor

• Signal and Noise exhibit the same characteristics

• Low pressure peak (LPP) centered at ~0.4Torr

• High gains introduce instability in the system

• LPP changes position– Positive bias moves the peak at lower

pressures– Negative bias moves the peak at

higher pressures • Grounded ion trap provides maximum gain

(for the conditions investigated)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

1

10

100

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.1

1

10

Sign

al (n

A)

Pressure (Torr)

410.3 404.7 399.9 390.3 379.9 370.3 359.9 350.3 339.9 319.9 299.9

Noi

se (p

A/√

Hz)

Pressure (Torr)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60

5

10

15

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.5

1.0

1.5

2.0

2.5

3.0

Sig

nal (

nA)

Pressure (Torr)

-100V 80V 60V 40V 20V 0V -20V -40V -60V -80V -100V

Noi

se (p

A/√

Hz)

Pressure (Torr)

anode bias effect [Vion trap = 0V]

ion trap bias effect [Vanode = 390.3V]

operating conditions: Eo=5keV, Io=94pA, WD=4mm, BF=4.0531355 sample: Pt aperture

cnse.albany.edu

Helix – Gases

• Noise follows signal behavior for all gases

• CO2 shows similar characteristics with H2O

• N2 and Ar do not exhibit LPP

• Pressure ranges are different for each gas due to lower column vacuum breakdown

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

1

10

operating conditions: Eo=5keV, Io=93pA, WD=3.5mm, Vion trap=0V, BF=4.467958 sample: Pt aperture

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

1

10

Sig

nal (

nA)

Pressure (Torr)

491.1V 475.9V 460.7V 445.5V 430.3V 415.1V 399.9V 384.7V 369.5V

CO2

Noi

se (p

A/√

Hz)

Pressure (Torr)0.0 0.2 0.4 0.6 0.8 1.0

0

5

10

15

20

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Sig

nal (

nA)

Pressure (Torr)

369.5V 384.7V 399.9V 415.1V 430.3V 445.5V

N2

Noi

se (p

A/√H

z)

Pressure (Torr)

0.0 0.2 0.4 0.60.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.2 0.4 0.60.1

0.2

0.3

0.4

0.5

Sig

nal (

nA)

Pressure (Torr)

270.3V 285.5V 300.7V 315.9V 331.1V

Ar

Noi

se (p

A/√

Hz)

Pressure (Torr)

progress towards low vacuum critical dimension metrology

Documents