Electrons and Phonons: Precision Measurements of Optical … › files › 2019 › 05 › PIEZO-2019... · 2019-05-15 · • Ellipsometry allows us to study semiconductors, insulators,

Electrons and Phonons: Precision Measurements of Optical Constants with

Spectroscopic EllipsometryStefan Zollner

New Mexico State University, Las Cruces, NM, USAand Institute of Physics, CAS, Prague, CZR

NSF: DMR-1505172

http://ellipsometry.nmsu.edu [email protected]

http://www.bbc.co.uk/northernireland/yourplaceandmine/images/helpabout/keyboard_250x145.jpg

http://ellipsometry.nmsu.edu/

Spectroscopic Ellipsometry on Complex Oxides

• How Thick is My Oxide Layer?– Routine applications in semiconductor industry.– Automated tools with robot control.– Complicated for metal gate stack or SiGe S/D stressors.

• Infrared-Active Phonons– Compound Semiconductors (Si, Ge, GaP, GaAs, AlN, ZnO)– Cubic oxides (LiF, NiO, SrTiO3, spinels: MgAl2O4, Co3O4)– Complex oxides: LaAlO3, (LaAlO3)0.3(Sr2AlTaO6)0.35

• Electrons: Interband optical transitions– CeO2, SrTiO3, ZnO– MgAl2O4, Co3O4 (spinel)

Stefan Zollner, January 2019, Piezo 2019 Conference 2

Crystalline CeO2 on sapphire (liquid deposition)

• Insulating CeO2 film on sapphire, with band gap near 3.7 eV.• Determine film thickness from interference fringes in transparent region.• Fit optical constants with basis spline polynomials.

K. Mitchell, C.O. Rodriguez, Y. Li, 2013; X. Guo, Boston Applied Technologies, Inc.

transparent opaque

Fluorite (Oh5)

dielectricfunction

transparent


Crystal Structure (Point & Space Group)

Electrons Phonons

Solid State Physics (crystalline)

Defects

Magnetism Superconductivity

Transport

Phase Transitions

Surfaces Topological Insulators

CMOS RF Power Analog

Photovoltaics Energy Conversion

Magnetic Storage Catalysis

Lasers Sensors

10-80 meV0.3-10 eVFar-IR to mid-IRNear-IR, VIS, UV

Excitons


Polaritons

Infrared Lattice Vibrations in GaP

ReststrahlenBand

ε∞=9.14ε0=15.7

364.9 cm-1

402.5 cm-1


Td2

N.S. Samarasingha (unpublished)

lossfunction

dielectricfunction

Lattice Vibrations of Binary Compounds

Stefan Zollner, January 2019, Piezo 2019 Conference 6 JVST B 37, 012904 (2019)

Lattice Dynamics of NiO•Rocksalt crystal structure (FCC), Space group 225 (Fm-3m or Oh

5).•Single TO/LO phonon pair.•Antiferromagnetic ordering along (111), should cause phonon splitting (8-30 cm-1).

•Second-order phonon absorption.

TO TA+TO phonon

NiO Reststrahlen Band

Rooksby, Nature, 1943

ε0=11.3ε∞=5.0

Willett-Gies & Nelson, JVST A 33, 061202 (2015)

NiO cell


Bulk AlN: Anisotropic Phonon Absorption

Wurtzite structure (C6v4):

A1+E1 infrared-active phonons Biaxial model

• Ordinary and extraordinary dielectric function (TO/LO).


Compare J. Yang, J. Appl. Phys. 98, 043517 (2005)

Bulk ZnO: Anisotropic Phonon Absorption

Wurtzite structure (C6v4): A1+E1 IR active

Biaxial model• Ordinary and extraordinary dielectric

function (TO/LO).

-2 zno_ir 2 0.00 Å-1 zno_ir 1 0.00 Å0 biaxial 1 mm

Compare N. Ashkenov, J. Appl. Phys. 93, 126 (2003)

Stefan Zollner, January 2019, Piezo 2019 Conference 9 N.S. Samarasingha (unpublished)

New Mexico State University

ZnO Thin Films on Si (by ALD)

Real and imaginary parts of dielectric function of ZnO layers on Si decrease monotonically with decreasing thickness.

Small redshift and increasing broadening with decreasing thickness. Continuing to investigate.

Stefan Zollner, January 2019, Piezo 2019 Conference 10 N.S. Samarasingha (unpublished)

Bulk SrTiO3Lattice absorption


Perovskite structure (Pm-31 or Oh1)

3F1u(IR-active) + F2u(silent) modes

lossfunction:

LO phonons

dielectricfunction:

TO phonons

JVST B 18, 2242 (2001).

LO(Ti)

TO(O)

LO(O)

Sr mode at very low energy.

LO(Ti)

LO(O)

TO(O)

Stefan Zollner, January 2019, Piezo 2019 Conference 12Stefan Zollner, March 2014 12Stefan Zollner, March 2014 12

Phonons in more complex oxides


Space GroupWyckoff positions

( ) ( )φχ cos2det += RNR R

63 or 3dD R cLaAlO3

7 or 3hO Fd mMgAl2O4

FTIR Ellipsometry

Loss function:LO phonons

Dielectric function: TO phonons

Willett-Gies, Thin Solid Films, 2013Zollner, Thin Solid Films, 2013

LO LO

TO TO

LaAlO3

MgAl2O4

3.03.222TO,

2LO, ±== ∏∞

i i

is ω

ωεε

2.08.72TO,

2LO, ±== ∏∞

i i

is ω

ωεε


Phonons in LSAT (disordered double perovskite)

5 LO peaks:loss function

5-6 TO peaks:dielectric function

4 Raman peaks

T.N. Nunley, JVST A 34, 051507 (2016)

IR-active: 4F1uRaman-active: A1g+Eg+2F2g

Space group of Sr2AlTaO6 (SAT): F-43m or Td2

Extra peaks due to disorder.


Plasmon-phonon polaritons (doping effects)

JVST B 37, 012904 (2019)

Two reststrahlen bands:• Low energy: Drude plasmon• High energy: TO/LO phonon• Doping pushes LO phonon

higher (polariton effect).

Doped GaAs (n=7×1017 cm−3)

Undoped GaAs

Materials properties accessible by ellipsometry • Mid-infrared spectral range

– Insulator/semiconductor:Lattice vibrations (phonons)

– Metal: Free carrier properties (density, scattering rate)• Visible to UV range:

– Electronic excitations– Band gap, interband transitions

• Ellipsometry allows us to study semiconductors, insulators, and metals.

• Thin films and surfaces can be investigated with proper data analysis (curve fitting).


Bulk SrTiO3:Electronic Structure, Band Gap


Direct band gap: 3.36 eVOther transitions at higher energies.

JVST B 18, 2242 (2001).

Energy (eV)0 1 2 3 4 5 6 7 8

epsi

lon

0

2

4

6

8

10

12

2

1

this workJellison

derivative spectraline shape analysis band structure

Spinel (MgAl2O4) and LSAT (LaAlO₃)0.3(Sr₂TaAlO₆)0.7


C.J. Zollner, Thin Solid Films, 2013T.N. Nunley, JVST A 34, 051507 (2016)

Ozone surface cleaningSurface roughness correctionTauc-Lorentz+Gauss fitVery large band gap

LSAT

Another Oxide Example: Co3O4 on spinel (MBE)


Band gap: 0.75 eV

Co3O4(22 nm)

K.N. Mitchell, Kormondy, SZ, Demkov, JAP 115, 243708 (2014)

Cubic field splitting


SrTiO3 Thin Films on Si or Pt (MBE)

Epitaxial SrTiO3 layers have lower refractive index than bulk SrTiO3. It would be interesting to look at vibrational properties of SrTiO3 films on Si

(or other substrate) of different thicknesses.


JVST B 18, 2242 (2001)MRS Proc. 619, 167 (2000)

on Si

SrTiO3 Thin Films on Si (liquid deposition)

Epitaxial SrTiO3 layers have lower refractive index than bulk SrTiO3. Bulk-like low frequency dielectric response. Not sure how to explain the low/high frequency discrepancy: O vacancy ?

Stefan Zollner, January 2019, Piezo 2019 Conference 20J. Appl. Phys. 111, 054108 (2012)

on Si

Energy (eV)

750C anneal


ZnO thin film on Si (ALD)

Do the properties of ZnO layers on Si depend on the ZnO film thickness?

The excitonic enhancement disappears in thin films. Real and imaginary part of dielectric function of ZnO layers on Si decrease monotonically with

decreasing thickness. Small blueshift with decreasing thickness (confinement).

Kramers–Kronig consistent.

𝜺𝜺𝒁𝒁𝒁𝒁𝒁𝒁. 𝒕𝒕𝒆𝒆𝒆𝒆𝒆𝒆 − 𝟑𝟑𝟑𝟑𝑨𝑨𝒐𝒐

+ 𝜺𝜺𝑺𝑺𝑺𝑺𝒁𝒁𝟐𝟐.𝟑𝟑𝟑𝟑𝑨𝑨𝒐𝒐

= 𝜺𝜺𝒆𝒆𝒆𝒆𝒆𝒆. 𝒕𝒕𝒆𝒆𝒆𝒆𝒆𝒆



ZnO thin film on SiO2 (ALD)

The excitonic enhancement is reduced with decreasing thickness. Real and imaginary part of dielectric function of ZnO layers on SiO2 decrease

monotonically with decreasing thickness. Small blueshift with decreasing thickness (more apparent than for film on Si).

Do the properties of ZnO layers on SiO2 depend on the ZnO film thickness?

Kramers–Kronig consistent.



Materials properties accessible by ellipsometry • Mid-infrared spectral range:

– Insulator/semiconductor: Lattice vibrations (phonons)– Metal: Free carrier properties (density, scattering rate)

• Visible to UV range:– Electronic excitations, band gap, interband transitions

• Oxides are particularly interesting: complex vibrational & electronic structure.• Thin films and surfaces can be investigated with proper data analysis (curve

fitting).• Thin films often have different optical constants compared to bulk.

New Mexico State UniversityAPS conference in Socorro, NM

Hold the date: Next ICSE in Barcelona (2019).


http://ellipsometry.nmsu.edu

Send us your samples: Metals, insulators, semiconductors

Flat, clean & uniform films, at least 5 by 5 mm2, low surface roughness, films on single-side polished [email protected]

Grad Students (former):Nuwanjula Sandamali, Farzin Abadizaman, Carola Emminger, Rigo Carrasco, Nalin Fernando, Lina Abdallah (Ph.D), Nathan Nunley (MS), Cesar Rodriguez (MS), Travis Willett-Gies (MS)Undergrad Students (former):Pablo Paradis, Cesy Zamarripa, Zachary Yoder, Jackie Cooke, Alexandra Hartman, Dominik Martens, Jaime Moya, Troy Powell, Luis Barrera, Eric DeLong, Amber Medina, Khadijih Mitchell, Cayla Nelson, Laura Pineda, Ayana Ghosh, Chris ZollnerVisitors and Collaborators:Sudeshna Chattopadhyay, Alex Demkov, John Kouvetakis, Jose Menendez, Jim Kolodzey, Arnold Kiefer

http://ellipsometry.nmsu.edu


mailto:[email protected]

Backup Slides


New Mexico State UniversityNew Mexico State University

Flat, clean, & uniform films, at least 5 by 5 mm2, low surface roughness, layers on single-side polished [email protected] http://ellipsometry.nmsu.edu

Grad. Students: Nuwanjula Samarasingha, Farzin Abadizaman, Carola Emminger, Rigo CarrascoUndergraduate Students: Pablo Paradis,Cesy Zamarripa, Zachary YoderCollaborators: Jose Menendez (Arizona State), Sudeshna Chattopadhyay (IIT Indore)Samples: Arnold Kiefer (AFRL), Jim Kolodzey (Delaware), John Kouvetakis (Arizona State), Alex Demkov (UT Austin)

mailto:[email protected]

Thickness Measurements: InGaP HBT• How thick is my film?


Skyworks

Ellipsometry Spectrum

Instrumentation

Spectroscopic Ellipsometer (UV/VIS-VASE)

What spectroscopic ellipsometry (UV-VASE) reveals:• Thickness (100 Å to 10000 Å)

• Absorption, band gap

• Refractive indexdetector

Monochromatorpolarizer

sample

analyzerΦ

X-ray diffraction & reflectance

What x-ray diffraction reveals:• Crystal structure• Lattice spacings (strain)• Thickness (5 Å to 1000 Å)• Surface, roughness layer

thickness

Spectroscopic Ellipsometer(IR-VASE)

What spectroscopic ellipsometry (IR-VASE)reveals:• Phonon absorption

• Optical Constants

detector

Rotating Compensator

polarizer

Source

PolarizerSpectral Range 1.7 μm to 40 μm(250 cm-1 to 5900 cm-1)


Ellipsometry: How does it work ?

21

222

~

11tan1sin~

tan

εεε

ρρφφε

ρ

i

eEE

EE

RR i

rs

is

ip

rp

s

p

+=

+−

⋅+=

Ψ=⋅== ∆

Angle of incidence

Optical constants versus photon energy

P plane P plane E

S plane

Splane

Bulk sample

Monochromator orInterferometer (λ)

polarizer analyzer

detector

Φ

We measure the change in the polarization state of light, when it is reflected by a flat surface (bulk).

Result:

Reflectance ratio


Ellipsometry: Maxwell’s equations in solid


– Gauss’ law (electric field):ε0 permittivity of vacuum

– Gauss’ law (magnetic field):

– Faraday’s law:

– Ampere’s law:µ0 permeability of vacuum

– Dielectric displacement

0=•∇ D

0=•∇ B

tBE∂∂

−=×∇

tDB∂∂

=×∇

0µ

densityflux magnetic

strength field electric

B

E

( ) ( ) ( )ωωεεω ED

0=


Lorentz Model: Frequency dependence of ε

( ) ( )tiEtE ωexp0=

( ) ( )tikibm

qEtx

makxbvqEmaF

ωωω

−−+

−=

=−−=

exp20

( )

mkmnq

i

P

P

=

=

−−+=

20

0

22

220

2

1

ω

εω

γωωωωωε

Charge density

Resonance frequency

q

𝐷𝐷 = 𝜀𝜀0𝐸𝐸 + 𝑃𝑃 = 𝜀𝜀𝜀𝜀0𝐸𝐸

Absorption peaks


Absorption and dispersion: Frequency dependence of ε

• Causality (Kramers-Kronig transform): The polarization cannot precede the external electric field: ε1 can be calculated from ε2 by complex residual integration (and vice versa).

• Dispersion and absorption are related!

( ) ( )

( ) ( )22

1

02

022

21

2

2

ξωξεξ

πωωε

ωξξξεξ

πεωε

−=

−+=

−

∫

∫∞

∞

∞

dP

dP

relations KronigKramers

phonons

electronicstates

ε

∞εlfε

ε1: Energy storedε2: Energy dissipated


Infrared Lattice Absorption

• Si-Si bonds are non-polar.• Bonds: no dipole moment.• No infrared absorption.

• Ni2+-O2- bonds are polar.• Ni-O vibration has dipole moment.


Silicon:Diamond lattice

NiO or NaCl or LiF:Rocksalt lattice

Silicon dielectric function (IR)

Wave Number (cm -1)200 400 600 800 1000

<ε1>

11.688

11.690

11.692

11.694

11.696

11.698

11.700

ε2=0

FTIR ellipsometry

NiO

Typical Lorentz oscillator

Documents

Electrons and Phonons: Precision Measurements of Optical … › files › 2019 › 05 › PIEZO-2019... · 2019-05-15 · • Ellipsometry allows us to study semiconductors, insulators,