optical properties of solids lecture 1 stefan zollner properties lecture 1 zollner.pdf · complex...
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Optical Properties of SolidsLecture 1
Stefan ZollnerNew Mexico State University, Las Cruces, NM, USA
and Institute of Physics, CAS, Prague, CZR (Room 335)[email protected] or [email protected]
NSF: DMR-1505172http://ellipsometry.nmsu.edu
http://www.bbc.co.uk/northernireland/yourplaceandmine/images/helpabout/keyboard_250x145.jpgmailto:[email protected]:[email protected]
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Acknowledgements
These lectures were supported by • European Union,
European Structural and Investment Funds (ESIF) • Czech Ministry of Education, Youth, and Sports (MEYS),
Project IOP Research Mobility – CZ.02.2.69/0.0/0.0/0008215
Thanks to Dr. Dejneka and his department at FZU.
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 2
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Contributions by Czech researchers
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 3
Jan TaucBrown University
a-Si:H (solar cells)
Karel KuncSorbonne (Paris)lattice dynamics
Josef HumlicekMasaryk Uellipsometry
Others:Frantisek Lukes, E. Schmidt (Masaryk University, Brno)Libuse Pajasova, A. Abraham, E. Antoncic, B. Velicky: Reflectance on Ge and GeO2E. Antoncic: Temperature dependence of band gaps
Czechoslovak Journal of Physics (1952-2006, Springer online)1960 ICPS-5 Conference held in Prague
Bedrich VelickyFZU
Ge, excitons, KK
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Optical Properties of Solids: Lecture 1• Introductions: Why are we here?• Lecture series overview• Spectroscopy: what is that?• Experimental spectroscopy techniques• Optical constants:
– Complex refractive index– Complex dielectric function– Absorption coefficient, extinction coefficient– Normal-incidence reflectance
• Solid-State Physics: What can we learn from optical properties?
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 4
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Where is Las Cruces, NM?
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 5
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New Mexico State UniversityNew Mexico State University
BiographyRegensburg/StuttgartGermany
Las Cruces, NMSince 2010
6
Motorola (Mesa, Tempe)Arizona, 1997-2005
Motorola, FreescaleTexas, 2005-2007Freescale, IBM
New York, 91-92;07-10
6
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New Mexico State University
SiGe:C Metrology: How thick is my film?
7
0.00
0.05
0.10
0.15
0.20
0.25
0 1 2 3 4 5Depth (a.u.)
Ge
atom
ic fr
actio
nSi cap(emitter)
SiGe:C base
Si substrate
theta (seconds)-2500 -2000 -1500 -1000 -500 0 500
Log
Inte
nsity
(a.u
.)
2
3
simulationdata
Si1-xGex alloys
Energy (eV)0 1 2 3 4 5 6 7
ε 2
0
10
20
30
40
50
Si9.06%14.93%21.10%26.86%
Si1-xGex alloys
Energy (eV)0 1 2 3 4 5 6 7
ε 1
-20
-10
0
10
20
30
40
50
Six=9.06%x=14.93%21.10%26.86%
High-resolution XRD
SpectroscopicEllipsometry
SZ, Hildreth, Liu, Zaumseil, Weidner, Tillack, J. Appl. Phys. 88, 4102 (2000)
Si1-xGex alloys
Si1-xGex 100 thickness measurementsNeed precise values of refractive index
Chart2
1.995
2
3
3.75
3.755
HBT1
Depth (a.u.)
Ge atomic fraction
0
0.07
0.2
0.2
0
Sheet1
depth (A)edgeR/2center blankHBT1 (a.u.)HBT1SE fit
0
12.7971.99539906030
25.59324000.078510.202
38.3936000.29940.202
51.1873.757500.29950
63.9833.7557510
76.78
89.577
102.37
115.17
127.97
140.76
153.56
166.36
179.15
191.95
204.75
217.54
230.340.0150730.019738
243.140.0250390.022393
255.930.0103170.016514
268.730.0269580.017159
281.530.0188730.018568
294.320.0366460.020069
307.120.0480370.024303
319.920.0720350.034608
332.710.0952750.036296
345.510.113340.055596
358.310.131850.074753
371.10.154050.093722
383.90.173360.10943
396.70.181810.11956
409.490.1960.13973
422.290.201920.16152
435.090.200340.17817
447.880.203830.19345
460.680.201730.19526
473.480.203540.19514
486.270.196820.19175
499.070.18260.19807
511.870.159330.19401
524.660.118970.19696
537.460.0670120.18729
550.260.0369390.17840.012898
563.050.021490.164070.009524
575.850.014120.133580.012981
588.650.0179510.0984980.013412
601.440.0531990.02513
614.240.0304850.017102
627.040.0316320.029739
639.830.0197340.035396
652.630.0188980.048201
665.430.062724
678.220.069877
691.020.087592
703.820.098341
716.610.099737
729.410.10657
742.210.11499
7550.12695
767.80.13892
780.60.15574
793.390.16963
806.190.18106
818.990.19029
831.780.19574
844.580.19317
857.380.1933
870.170.19367
882.970.19521
895.770.19705
908.560.19359
921.360.19644
934.160.19763
946.950.19815
959.750.19527
972.550.19231
985.340.18957
998.140.19342
1010.90.17796
1023.70.15841
1036.50.12804
1049.30.081886
1062.10.047244
1074.90.027949
0.020425
0.015073
0.017914
0.011093
0.010989
Sheet2
Sheet2
000399603
12.79712.79712.797400851
25.59325.59325.593600994
38.3938.3938.39750995
51.18751.18751.187751
63.98363.98363.983
76.7876.7876.78
89.57789.57789.577
102.37102.37102.37
115.17115.17115.17
127.97127.97127.97
140.76140.76140.76
153.56153.56153.56
166.36166.36166.36
179.15179.15179.15
191.95191.95191.95
204.75204.75204.75
217.54217.54217.54
230.34230.34230.34
243.14243.14243.14
255.93255.93255.93
268.73268.73268.73
281.53281.53281.53
294.32294.32294.32
307.12307.12307.12
319.92319.92319.92
332.71332.71332.71
345.51345.51345.51
358.31358.31358.31
371.1371.1371.1
383.9383.9383.9
396.7396.7396.7
409.49409.49409.49
422.29422.29422.29
435.09435.09435.09
447.88447.88447.88
460.68460.68460.68
473.48473.48473.48
486.27486.27486.27
499.07499.07499.07
511.87511.87511.87
524.66524.66524.66
537.46537.46537.46
550.26550.26550.26
563.05563.05563.05
575.85575.85575.85
588.65588.65588.65
601.44601.44601.44
614.24614.24614.24
627.04627.04627.04
639.83639.83639.83
652.63652.63652.63
665.43665.43665.43
678.22678.22678.22
691.02691.02691.02
703.82703.82703.82
716.61716.61716.61
729.41729.41729.41
742.21742.21742.21
755755755
767.8767.8767.8
780.6780.6780.6
793.39793.39793.39
806.19806.19806.19
818.99818.99818.99
831.78831.78831.78
844.58844.58844.58
857.38857.38857.38
870.17870.17870.17
882.97882.97882.97
895.77895.77895.77
908.56908.56908.56
921.36921.36921.36
934.16934.16934.16
946.95946.95946.95
959.75959.75959.75
972.55972.55972.55
985.34985.34985.34
998.14998.14998.14
1010.91010.91010.9
1023.71023.71023.7
1036.51036.51036.5
1049.31049.31049.3
1062.11062.11062.1
1074.91074.91074.9
0.020425
0.015073
0.017914
0.011093
0.010989
edge
R/2
center blank
HBT1
SE fit
Depth (A)
Ge atomic fraction
MB17652.1#14
0
0
0.07
0.202
0.2
0.202
0.2
0
0
0.015073
0.019738
0.025039
0.022393
0.010317
0.016514
0.026958
0.017159
0.018873
0.018568
0.036646
0.020069
0.048037
0.024303
0.072035
0.034608
0.095275
0.036296
0.11334
0.055596
0.13185
0.074753
0.15405
0.093722
0.17336
0.10943
0.18181
0.11956
0.196
0.13973
0.20192
0.16152
0.20034
0.17817
0.20383
0.19345
0.20173
0.19526
0.20354
0.19514
0.19682
0.19175
0.1826
0.19807
0.15933
0.19401
0.11897
0.19696
0.067012
0.18729
0.036939
0.1784
0.012898
0.02149
0.16407
0.009524
0.01412
0.13358
0.012981
0.017951
0.098498
0.013412
0.053199
0.02513
0.030485
0.017102
0.031632
0.029739
0.019734
0.035396
0.018898
0.048201
0.062724
0.069877
0.087592
0.098341
0.099737
0.10657
0.11499
0.12695
0.13892
0.15574
0.16963
0.18106
0.19029
0.19574
0.19317
0.1933
0.19367
0.19521
0.19705
0.19359
0.19644
0.19763
0.19815
0.19527
0.19231
0.18957
0.19342
0.17796
0.15841
0.12804
0.081886
0.047244
0.027949
Sheet3
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New Mexico State University
Key HW accomplishments for 3G smart phones
New Mexico State University
1. Power amplifier: InGaP Heterojunction bipolar transistor (HBT)
2. Low-noise amplifier:Silicon-germanium-carbon HBT
3. New CMOS materials:Advanced substrate materials (SOI)High-k (complex metal oxide) gate dielectricsMetal gateSi-Ge-C source-drain stressors Laser annealing (>100 citations)Nickel silicide Ohmic contactsCopper interconnectsLow-k interlayer dielectrics
4. Power, analog, passives
32nm CMOS on SOI
Double-poly capacitor
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 8
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Flat, clean, & uniform films, at least 5 by 5 mm2, 190 nm to 40 µm, 10-800 Klow 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]
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Introductions: Why are we here?
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 10
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Optical Properties of Solids: Overview1. Overview: spectroscopy, optical constants, and solid-state physics2. Crystal structures, Wyckoff positions, point and space groups,
classification of optical vibrations3. Maxwell’s equations in vacuum, plane waves, polarized light4. Maxwell’s equations in continuous media, dielectric function, Lorentz and
Drude model, Sellmeier, poles, Cauchy5. Analytical properties of the dielectric function, KK relations6. Application of Lorentz and Drude models to insulators and metals7. Electronic band structure, direct and indirect gap absorption8. Free electrons, effective masses in semiconductors, excitons9. Interband transitions, van Hove singularities, critical points10. Photoluminescence, Einstein coefficients, quantum confinement11. Applications: Anisotropic materials12. Applications: Thin films, stress/strain, deformation potentials
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 11
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Optical Properties of Solids: Text Book
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 12
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Optical Properties of Solids: Other Text Books
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 13
Part III:Optical Properties
M.L. Cohen & J. Chelikowsy: Electronic Structure & Optical Properties
Tanner (U FL): notes
C. Klingshirn: Semiconductor Optics
Ellipsometry:FujiwaraTompkins/HilfikerFujiwara/CollinsPalik I, II, IIIAzzam/Bashara
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Classification Schemes for Surface Spectroscopy I
Particles: Electron (e), ion (i), or photon (γ)The term spectroscopy implies that we prepare, vary, or measure the
energy (wavelength) and/or momentum of the primary and/or secondary particle.
For photons, we can also measure the polarization of the primary and/or secondary photon.
The interaction depth for thin films depends on the penetration depth of the primary particle and the escape depth of the secondary particle. (This can be nanometers to micrometers, depends on each technique.)
primary particlee, i, γ
secondary particlee, i, γ
φ ψ
surfacenormal
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 14
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Classification Schemes for Surface Spectroscopy II
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 15
1. Specular reflection: The angle of reflection is equal to the angle of incidence. For some spectroscopies, the angles are measured relative to the surface (XRR), for others relative to the surface normal (SE).
2. Diffuse reflection or scattering: There is no well-defined direction, in which the secondary particle exits. The scattering probability may depend on the angles.
3. Diffraction: Requires a periodic (crystalline) layer. There is a well-defined angular relationship between the spacing of the diffraction (Bragg) planes and the momentum of the incident/diffracted beams.
φ ψ2
Diffuse reflection/scattering:PL, Raman, SIMS, Auger
φ ψ3
Diffraction: XRD
φ φ1
Reflection:Ellipsometry, XRR
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Classification Schemes for Surface Spectroscopy III
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 16
• Elastic scattering: The energy of the incident particle equals that of the scattered particle.
• Inelastic scattering: The two energies are different, depending on the energy gained or lost by the interaction with the thin film.
• Both can yield information about the energy states in the film.
EgElastic: The intensity of the reflected (relative to the refracted beam) depends on the excited states of the system (band gaps).
Inelastic: The energy difference (gain or loss) provides information about vibrational (Raman) or electronic (Auger) energy states. The strength of the scattering process depends on the interaction with an intermediate state.Eg
Ei
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Classification Schemes for Surface Spectroscopy IV
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 17
− Spectroscopic Ellipsometry: Elastic, specular, γ → γThickness, Energy (band gap), refractive index, composition
− X-ray reflectivity: Elastic, specular, γ → γThickness, density, surface/interface roughness
− X-ray diffraction: Elastic, diffracted, γ → γLattice constant, stress/strain, composition
− UV Raman Spectroscopy: Inelastic, scattered, γ → γ Vibrational (phonon) energy, composition, stress/strain
− Secondary Ion Mass Spectrometry: Inelastic, scattered, i → iComposition, depth profile (sputtering), doping
− Auger Electron Spectrometry: Inelastic, scattered, e → eComposition, depth profile (sputtering)
− Rutherford backscattering: Inelastic, scattered, α → αComposition, some depth information, primary standard
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Bohr Model for the Hydrogen Atom
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 18
Quantum Numbers:n 1,2,3,…l 0,…,n-1m −l,…,ls +/− 1/2 Relativistic corrections:s electrons (l=0) close to the core
J=L+S total angular momentumSpin-orbit coupling L·SL=1, S=1/2 J=1/2 or 3/2
E(n)=−R/n2R=13.6 eV
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Bonding and Anti-Bonding Orbitals
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 19
s: Ψ=ψ1+ψ2 s∗: Ψ=ψ1−ψ2
px, py, pzp*
p
C electronic configuration: 1s2 2s2 2p2L shell forms sp3 hybrid: 1s2 2s1 2p3
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A simple band structure for Germanium
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 20
p
s
s*
p*
filled
empty
EF
Add
spin
-orb
it co
uplin
g: J
=L+S
Add
kine
tic e
nerg
ys
s*
j=1/2
j=3/2
j=1/2
j=3/2
∆0
∆0’
Ge electronic configuration: … 4s2 4p2N shell forms sp3 hybrid: … 4s1 4p3
K=mv2/2=p2/2m=2k2/2m
m: effective mass
CB (empty)e
so∆0
hhlh
4s VB
E
Momentum k
EF E0 band gap
filledfilled
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A simple band structure for Germanium
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 21
p
s
s*
p*
filled
empty
EF
Add
spin
-orb
it co
uplin
g: J
=L+S
Add
cubi
c sy
mm
etry
s
s*
j=1/2
j=3/2
j=1/2
j=3/2
∆0
∆0’FCC Brillouin zone
Band structure
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Carbon, Silicon, Germanium, Tin
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 22
The s* band moves down, as the elements get heavier.
In α-tin, the s* band moves into the p-band manifold, between the j=1/2 and j=3/2 states.This makes α-tin a zero-gap semiconductor.
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Classification Schemes for Surface Spectroscopy IV
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 23
− Spectroscopic Ellipsometry: Elastic, specular, γ → γThickness, Energy (band gap), refractive index, composition
− X-ray reflectivity: Elastic, specular, γ → γThickness, density, surface/interface roughness
− X-ray diffraction: Elastic, diffracted, γ → γLattice constant, stress/strain, composition
− UV Raman Spectroscopy: Inelastic, scattered, γ → γ Vibrational (phonon) energy, composition, stress/strain
− Secondary Ion Mass Spectrometry: Inelastic, scattered, i → iComposition, depth profile (sputtering), doping
− Auger Electron Spectrometry: Inelastic, scattered, e → eComposition, depth profile (sputtering)
− Rutherford backscattering: Inelastic, scattered, α → αComposition, some depth information, primary standard
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Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 24
Example: X-ray Photoelectron Spectroscopy: γ → e
Quantification using RBS standardsHigh depth resolution (small escape depth of photoelectrons)
K
L1L2
Vac
BindingEnergy
0EL2EL1
EK
Ekin = hω - EK - Φdet
incident(~1.5 keV)
γ scatterede-
Oxidation states
-
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 25
Example: Auger Electron Spectroscopy: e → e
K
L1L2
Vac
e-
ElectronImpact Ionization
BindingEnergy
0EL2EL1
EK
EAuger = (EK - EL1) - EL2
incident(5 – 20 keV)
scattered
0
0.2
0.4
0.6
0.8
1
0 1000 2000 3000 4000
Ato
mic
Fra
ctio
n
Depth (Å)
Ge
O
Si
Si
O
Xe+ Ion Beam70º Off Normal
5 keV Primary e- Beam5º Off Normal
Strained SiSiGe
Buried Oxide (SiO2)
Si Substrate
Xe+ Ion Beam70º Off Normal
5 keV Primary e- Beam5º Off Normal
Strained SiSiGe
Buried Oxide (SiO2)
Si Substrate
Quantification using RBS standardsHigh depth resolution (small escape depth of L electrons)
-
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 26
Fourier-Transform SpectrometerGrating Monochromator
Constructive interference: ∆x=NλDestructive interference: ∆x=(2N+1)λ/2
d(sinβ−sinα)=Nλ
Diffracted intensity depends on angle and polarization.
Common for mid-infrared spectroscopy (50-500 meV).
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Macroscopic Optical Constants
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 27
n: refractive index, n=c/vk: extinction coefficientn+ik: complex refractive index
R: reflectance at normal incidence (Irefl/I0)T: transmittance (Itrans/I0)R+T+A+S=1
α: absorption coefficientα=4πk/λ
ε: complex dielectric functionε=ε1+iε2=(n+ik)2
Why not n-ik?Wave goes like exp[i(kx-ωt)]
All are connected through Maxwell’s equations (Lectures 3/4).
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Reflection and Transmission
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 28
Law of reflection: αin=αoutSnell’s Law: n1sinαin=n2sinαoutn: Refractive Index
Beer’s Law: I(L)=I0exp(-αL)Also have diffuse scattering.
Absorption coefficient α (cm-1)Consider reflection losses
exp −𝛼𝛼𝛼𝛼 ≈𝑇𝑇
1 − 𝑅𝑅 2
𝑅𝑅 =𝑛𝑛 − 1𝑛𝑛 + 1
2
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Transmission: LSAT or (LaAlO3)0.3(SrAlTaO6)0.35
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 29
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Reflection from a rough surface
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 30
Debye-Waller correction:Assumes sinusoidal roughnessRrough=R0exp[-(4πσncosθ/λ)2]σ: rms surface roughness parameterD.K.G. de Boer, Phys. Rev. B 49, 5817 (1994).
Specular Specular+Diffuse
Also: I. Ohlidal, F. Lukes, and K. Navratil, Surf. Sci. 45, 91 (1974). 98 citations.
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Reflectance Spectroscopy Instrumentation
Spectroscopic Ellipsometer (VUV/UV/VIS-VASE)
Spectroscopic Ellipsometry:• Thickness (100 to 10000 Å)
• Absorption, band gap
• Refractive index
detectorMonochromator
polarizer
sample
analyzerΦ
X-ray diffraction & reflectance
XRD/XRR:• Crystal structure• Lattice spacings (strain)• Thickness (5 Å to 1000 Å)• Surface, roughness layer
thickness• Density
Spectroscopic Ellipsometer(IR-VASE)
FTIR ellipsometry:• Very thick films (> 5000 Å)
• Phonon absorption
• Optical Constants
detector
Rotating Compensator
polarizer
Source
PolarizerSpectral Range 1.25 to 40 μm(250 cm-1 to 8000 cm-1)
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 31
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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
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 32
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Thickness Measurements: InGaP HBT• How thick is my film?
New Mexico State University
Skyworks
Ellipsometry Spectrum
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 33
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X-ray Reflectance: SrTiO3 on Si
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 34
(Å)
LayerElectron Density
(eÅ-3)Bulk Electron density (eÅ-3)
Thickness(nm)
Roughness(nm)
SrTiO3 1.08 1.41 1.79 0.6152
SrTiO3 1.40 1.41 15.6 0.7396
SiO2 0.75 0.81 2.87 0.4202
Si 0.66 0.71 Substrate 0.4574
SiSiO2
SrTiO3
SrTiO3
Q=4𝜋𝜋 sin 𝜗𝜗𝜆𝜆
Small x-ray contrast between Si and SiO2.
Sheet1
LayerElectron Density (eÅ-3)Bulk Electron density (eÅ-3)Thickness(nm)Roughness(nm)
SrTiO31.081.411.790.6152
SrTiO31.401.4115.60.7396
SiO20.750.812.870.4202
Si0.660.71Substrate0.4574
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X-ray Diffraction: SrTiO3 on Si, Ge, and SrTiO3
ω-2θ scan (zoomed)
22 22.5 23 23.5 24 24.5 250
20
40
60
80
100
120
140
ω-2θ (°)
Inte
nsity
(cps
)
SrTiO3 on SiSTO (200)
FWHM=0.27°ω=23.27°
22 22.5 23 23.5 24 24.5 250
10
20
30
40
50
60
ω-2θ (°)
Inte
nsity
(cps
)
SrTiO3 on GeSTO (200)
FWHM=0.29°ω=23.28°
Grain Size = 168Å
Grain Size = 161Å
Vertical Strain= -0.15%
Vertical Strain = -0.18%
22 22.5 23 23.5 24 24.5 250
5
10
15
20
25
ω-2θ (°)
Inte
nsity
(cps
x10 6
)
SrTiO3 on SrTiO3STO (200)
FWHM=0.02°ω=23.24°
ω scan
21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 260
1000
2000
3000
4000
5000
6000
7000
ω (°)
Inte
nsity
(cps
)
SrTiO3 on SiSTO (200)
FWHM=0.80°
21 22 23 24 25 260
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
ω (°)
Inte
nsity
(cps
)
SrTiO3 on Ge
STO (200)
FWHM=0.94°
21 22 23 24 25 260
5
10
15
20
25
ω (°)
Inte
nsity
(cps
x 1
06)
SrTiO3 on SrTiO3STO (200)
FWHM=0.02°
FWHM=0.80º
FWHM=0.94º
FWHM=0.02º
ω-2θ scan
100
101
102
103
104
Inte
nsity
(cps
)
SrTiO3 on SiSi (400)
STO (200)
STO (300)
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 4010
2
103
104
105
106
107
108
ω-2θ (°)
Inte
nsity
(cps
)
SrTiO3 on SrTiO3STO (200)
STO (300)
Experimental DataModel
F
100
101
102
103
104
Inte
nsity
(cps
)
SrTiO3 on GeGe (400)
STO (200)
STO (300)
Bragg:2dsinθB=λ
Scherrer:λ=FWHM*t*cosθB
-
Raleigh scattering (elastic)
Why is the sky blue?
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 36
-
Elastic and Inelastic (Raman) Scattering
Raleigh(elastic)
Raman(Stokes)
Raman(Anti-Stokes)
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 37
CARS
-
Raman Spectroscopy
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 38
GaPLSAT Mg2AlO4 (spinel)
-
Photoluminescence
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 39
E0 band gap
electron
hole
γ
-
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
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 40
-
Materials properties accessible by optical spectroscopy
• 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).
Stefan Zollner, February 2019, Optical Properties of Solids Lecture 1 41
Optical Properties of Solids�Lecture 1Slide Number 2Contributions by Czech researchersOptical Properties of Solids: Lecture 1Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Introductions: Why are we here?Optical Properties of Solids: OverviewOptical Properties of Solids: Text BookOptical Properties of Solids: Other Text BooksSlide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Macroscopic Optical ConstantsReflection and TransmissionTransmission: LSAT or (LaAlO3)0.3(SrAlTaO6)0.35 Reflection from a rough surfaceSlide Number 31Crystalline CeO2 on sapphire (liquid deposition)Thickness Measurements: InGaP HBTX-ray Reflectance: SrTiO3 on SiX-ray Diffraction: SrTiO3 on Si, Ge, and SrTiO3Raleigh scattering (elastic)Elastic and Inelastic (Raman) ScatteringRaman SpectroscopyPhotoluminescenceSlide Number 40Materials properties accessible by �optical spectroscopy Backup SlidesSlide Number 43Slide Number 44Slide Number 45