Optical Measurements

MSN506 notes

note: Most of the information in this presentation is collected off the web for educational purposes.

Overview

• Remember some relevant parts of EM theory

• Survey of some optical techniques– Large number of variants and different

techniques are present – It is not possible to cover all of them– Those that may be related to nanomaterial

characterization are highlighted

Why optical measurements

• Optical properties of materials can be naturally measured with optical measurements (i.e. measurements that involve light generation or scattering)

• Optical properties can be used to determine structural or other physical properties

• Generally non-destructive

Interaction of light with matter• Light is an electromagnetic wave and electric (or

magnetic fields) interact with charge• For light to interact with matter, generally

carriers must be present (which they generally are)

• Light can interact with bound or free carriers• Interaction can be non-resonant or resonant

(i.e. frequency or wavelength of light can coincide with a characteristic oscillation frequency of the sample)

The dipole moment• Emission (and absorption or scattering) of light

by the presence of a carrier is strongly affected by the dipole moment and its propertiesthe dipole moment and its properties

Oscillating dipole

Power radiated by a classical dipole

Proportional to the dipole moment

Dipole moment (Quantum Mech.)• The dipole moment can be calculated

for classical charge distributions repd =

1D potential well

Time dependent dipole during a transition between energy levels

• During a transition, dipole oscillates with a frequency

++ -

+-

EΔ=ω

Power radiated by a classical dipole

Light can be generated

Absorption can also be resonant (this can be understood via time reversal symmetry of electromagnetic waves)

A

B

A+B

A-B

Dipoles and refractive indicesDipoles and refractive indices

Refractive index as a function of frequencyis determined by the AC permitivity

Dipoles and refractive indicesDipoles and refractive indices

Refractive index as a function of frequencyis determined by the AC permitivitySometimes negative, depends on convention

Generally does not depend on frequency at optical frequencies

n2 =12

⎛⎜⎝

⎛⎝ ε' 2 + ε'' 2 ⎞

⎠ + ε' 2⎞⎟⎠

κ2 =12

⎛⎜⎝

⎛⎝ ε' 2 + ε'' 2 ⎞

⎠ – ε' 2⎞⎟⎠

n* = n + i · k

(n + ik)2 = ε' + i · ε''

Oscillator model

Classical charge oscillator

Solution(can be used to calculate polarization)

Absorbed EnergyOscillator strength

Damping factor

Lorentzian lineshape

Oscillator strength can be calculated through the transition matrix element for two given levels

Example

Silicon

Single oscillator

Density of oscillatorsStrength of oscillators

Multiple oscillators

Absorption due to an oscillatorSingle oscillator

Density of oscillators

Strength of oscillators

Absorption coefficient

Classical oscillator model is intuitive for absorption measurements

Example: Atomic spectra

Absorption lines characteristic for each atom

The Monochromator

Can be used to select a certain wavelength in a beam of white light

Diffraction grating

Blazed at an angle for higher efficiency

Multiple orders can be observed depending on the period and wavelength

Orders will repeat especially if the grating period is large

Summary of optical measurements• Thin films: absorption, reflection, transmission of

thin films, Ellisometry, refractive index models, applications, FTIR

• Atomic absorption measurements• Light scattering measurements: Raman

Scattering, Dynamic light scattering• Nonlinear property measurements• Photoluminescence• Pump/Probe experiments• Diffraction, X-ray Diffraction

Thin Films• A material is deposited (or coated) uniformly on

a substrate.• Measuring optical propeties of the film we can

learn a lot about the material• Semiconductors

• Band gap, absorption, refractive index, impurities, defects etc.

• Nanoparticles• Size distribution, crystallinity etc.

• Organic layers• Molecules

• Requires modelling of the measurement scheme

Thin film measurements

substrate

incident

reflected

absorbed

transmitted

Film of material to be characterized Support substrate of known optical properties

Incident Power = Reflected + Absorbed + Transmitted Powers

Fresnel Reflection

Normal incidence

Thin Film Reflection

TransmittanceIf the substrate is transparent to some degree in the wavelength range of interest, transmission measurements can be used to determine the optical constants. Simple formulas are available for restricted cases

1 T

Transmittance

Reflection at an angle

The Ellipsometer• Absolute quantities are always hard to measure,

and most of the time inaccurate• Making reflection measurements at two different

polarizations quickly one after another can yield better results

The Ellipsometer

Less sensitive to intensity fluctuations

The Ellipsometer

The Ellipsometer

Porosity as well

Modelling for Ellipsometry• Refractive index models (semiempirical or

empirical)• Surface and interface roughness• Composite material models, porosity• Layered materials and gradients

• A lot of complexity…• Multiple models can produce similar results

• One solution is Variable Angle Spec. Ellips.• Experience helps a lot in modelling

Refractive index models• Cauchy• Sellmeier• Other Models• Effective medium models (particularly

important for composite materials)

Example software: NKDGenGood illustration of thin film measurements

http://www.fen.bilkent.edu.tr/~aykutlu/elips.html

Example: Material Characterization using transmission data

Bulk Absorption MeasurementsExample: Atomic Absorption Spectrometer

Specialized elemental lamp for different atomsBurn the sample and analyze absorption of the flame!

Scattering Measurements• Light (generaly a laser) is incident upon

the sample• Interaction of sample and light generates

modulation of light frequency, spatial distribution and/or time

Raman Scattering

• observed by C.V. Raman 1928• Received Nobel price in 1930

Mechanical vibration excited by phonons

Electronic vibration excited by external monochromatic light

• If these are coupled by a nonlinear interaction, sum and difference frequencies of light can be generated• Light then carries information about the phonon density• Scattered light intensity is very weak compared to original

Energy Level Picture

• Selection Rules: Polariation• Raman Active modes• Requires a sharp clean light source and a high resolution monochromator

Example applications

Chemistry: Molecular vibrations

Example applications: Bulk Crystals

Different structures all at once!

300 350 400 450 5000

1

Type VII ta= 2 hours

SiOx: GeSiO 120 sccm Silicon

Inte

nsity

(a.u

)

Frequency shift (cm-1)

1000oC 900oC 800oC 700oC 600oC

1

2

5 SiGe alloy formation

Example:Low-resolution Raman Spectroscopy

• Still good for material recognition

Low resolution Raman spectrum of 1:1:1 mixture of ethanol, 2-

propanol, and 2-methyl.2-propanol.

• Surface Enhanced Raman Spec. – Plasmonic effects enhance the Raman signal– Single molecule sensitivity!

• Waveguide Raman– Multiple (large number) of interactions of laser

with sample film enhances the signal– Submonolayer sensitivity

• Micro Raman and Tip Enhanced Raman can be used for high spatial resolution

Variants

FTIR: Fourier Transform Infra Red Spectroscopy

• Interferometer has periodic resonance condition• This is used as an advantage in FTIR

FTIR principle

FTIR Operation

FTIR Operation

FTIR Operation

FTIR bands

FTIR summary• Characteristic Frequencies for certain

bonds• Dipole moment different for each bond

type, intensity varies• Density of bonds affect intensity• Frequency of vibration affected by film

stress• Overtones (harmonics) possible• … to get accurate quantitative information

meticulous analysis is needed

Dynamic Light Scattering• Theory of Operation1. A beam of monocromatic light is directed through a sample and the fluctuation of the intensity of

scattered light by the molecules is analyzed by an Avalanche Photo Diode.2. The Avalanche Photo Diode then sends electrical pulses to the Digital Signal Processor which

counts the number of photons detected in each successive time sample.3. The frequency spectrum of this signal is determined by the mathematical technique known as

autocorrelation. The similarity between the signal wave form and a slightly time delayed copy of itself is determined by multiplying the two wave forms together and then summing to give the autocorrelation function.

4. From this the Translation Diffusion Coefficient, DT can be calculated by performing a nonlinear least-squares fit of the autocorrelation coefficients to an exponential decay.

5. Under the assumption of Brownian Motion and that the molecules in solution are spheres, the Hydrodynamic Radius, RH can be calculated by using Stokes’ Equation.RH = kbT / 6πηDTkb = Boltzman’s ConstantT = Absolute Temperature in Kelvinη = Solvent Viscosity

6. Can also estimate the Molecular Weight from the RH and the sample temperature using a standard curve of Molecular Weight vs. RH of globular proteins.

7. The instruments assumes the sample fits a standard monomodal gaussian type distribution (monodisperse) and through a monomodal curve fit, determines the uniformity of the sizes of the species in solution.

8. If the sample is found to be polydisperse or nonmonomodal, the user can use the software to resolve a bimodal size distribution (bimodal analysis).

Dynamic Light Scattering

Measures size distributions of colloidal (nano) particles in a fluid medium

Dynamic Light Scattering

20 nm beads

64 nm beads

Nonlinear optical property measurements

• Z-Scan

Large spotsize means low energy density

Small spot size means large energy density

Photoluminescence• Measures radiative decay properties of

optically generated carriers

Photoluminescence

Photoluminescence• Temperature dependent• Time resolved• Resonant excitation• Pump power dependent• Polarization dependent

• By modelling carrier absorption, relaxation and emission we can estimate sample properties

Streak Camera for fast time-resolved measurements

Streak Camera

Pump-Probe experiments• Ultrafast or fast pulses are used to excite (pump) and

probe sample• Extremely fast carrier dynamics of samples can be

measured

Example setup

1 meter delay gives 3 nsec time delay

Pump-Probe experiments

X-Ray diffraction

• X-rays have extreme small wavelengths compared to visible light (angstroms)

• They can diffract off atomic planes!• X-Ray diffraction can be used to get

information about crystals, nano and micro structure of materials etc.

X-Rays• How are they produced?

High energy electrons knock out core electrons

XRD• Angle of diffraction • Width of peak gives information about

crystal domain size

XRD• Angle of diffraction tells lattice parameters • Width of peak gives information about

crystal domain size

• Molecular substances can be crystallized and analyzed by XRD