Experimental methods to investigate the optical properties ... 2010-11/mep jdg_intro... ·...

IPEQ - ICMP - SB - EPFLStation 3CH - 1015 LAUSANNE

J-D GaniereEPFL - SB - ICMP - IPEQCH - 1015 Lausanne

Credit: www.national.com

Experimental Methods in Physics

[2010-2011]

Experimental methods to investigate the optical properties of solids

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J-D Ganiere MEP/2010-2011

Outline ...

• Definition of "spectroscopy"

• "EM" spectrum - orders of magnitude

• Frequency or wavelength ?

linewidth

• Units

• Radiometry versus Photometry

• How to obtain the optical signature of a EM signal

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Spectroscopy

Spectroscopy is the study of the interaction between radiation (electromagnetic radiation, or light, as well as particle radiation) and matter.

excitationprobe

signal

energy filter

signaldetector

excitationsource

specimen

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Spectroscopy

The objective in spectroscopy is typically to measure the intensity of a signal as a function of the energy of a proposed event occuring in the sample

name probe signal

PL Photons Photons

CL Electrons Photons

EDS Electrons X-photons

AES X-rays Electrons

EELS Electrons Electrons

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An example : X-ray fluorescence

X-ray tube

sample

detector slit

Detector

crystal

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Spectroscopy

excitation(probe) sample

emission

reflection

electronsneutronsmolecules

atomsphotons

...

gasliquidsolid

biologicsemiconductor

...

absorption

transmission

scattering

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Optical Spectroscopy

• The optical spectroscopy of semiconductor is only a pretext to approach various important subjects in MEP.

• nothing too specific.

• Also useful in other domains (life science, chemistry, ...).

Raman map showing a horitzontal section of a carrot root. Based on miscoloured pictures the concentration profiles of betacarotin in plant tissue can be clearly illustrated.

Credit: IPA [Institute of Plant Analysis, www.bafz.de]

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Optical spectroscopy - motivation

Better understanding of the physics !

Important for the realization of efficient device (lasers,detectors, ..)

To study the dynamic processes in materials or chemical compounds

To obtain information on the electronic structure

ground state

excited

triplet state

excited

singulet state

S1

S2

T1

internal conversion

vibrational relaxation

10 fs - 100 ps

absorption - 10 fs

fluorescence

100 fs - 100 ns

phosphorescence

1 ms - 10 ms

intersystem

Crossing

non-radiative

relaxation

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Reminder

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kT

At room temperature

kT = 25 meV

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What you should know ...!

It is difficult to measure directly the frequency, that is why we use mostly the wavelength λ .

From the theoretical point of view, it is the frequency which plays a fundamental role, that is why we introduce a new unit, the wave number, σ, who expresses itself in

cm-1. The wave number is measured with the same precision as the wavelength !

v =m1= co

E = ho

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Some useful equivalences

Wavelength Wavenumber Frequency Photon energy

Symbol

Fact

or o

f co

nver

sion

Exam

ples

m [nm] v [cm-1] o [Hz] Ep [eV]

Ep

m

v

o

107 /m 3 $ 1017 /m 1224/m

107 /v 3 $ 1010 $ v 1.22 $ 10-4v

3 $ 1017 /o 3.33 $ 1011o 4.1 $ 10-15o

1224/Ep 8197 $ Ep 2.44 $ 1014Ep

200

500

1000

5 $ 104

2 $ 104

104

1.5 $ 1015

6 $ 1014

3 $ 1014

6.12

2.45

1.224

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cm-1, eV and/or nm ?

cm-1 (Vibrational and Rotational Transitions)

eV (semiconductors)

nm (photometry)

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Linewidth nm or eV ?

o=mc

do=-m2cdm

odo=-

mdm

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Units

Unit of length meter

Unit of mass kilogram

Unit of time second

Unit of electric current ampere

Unit of thermodynamic! temperature kelvin

Unit of amount of substance mole

Unit of luminous intensity candela

The candela was first defined as 1/60 the luminous intensity, in the perpendicular direction, of a1 cm2 blackbody radiator at the freezing temperature of platinum (about 2042 K) and a pressure of 1 atmosphereThe candela was first defined as 1/60 the luminous intensity, in the perpendicular direction, of a1 cm2 blackbody radiator at the freezing temperature of platinum (about 2042 K) and a pressure of 1 atmosphere

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

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Radiometry, Photometry

Radiometry the measurement of optical radiation over the entire spectrum from the ultra-violet to the infra-red.

Photometry the measurement of visible light as it appears to the human eye.

optical system

object image

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Radiometry, Photometry

Although describing fundamentally similar parameters,namely flux, energy, intensity, power per unit area a different system of units is used to distinguishbetween radiometric and photometric quantities.

incoherent radiation optical geometric laws apply no diffraction ...

The assumptions (radiometry and photometry)

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Data sheets ... photometric or radioemtric units ?

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A useful table ...

Radiant Energy Luminous Energy

Total amount of light emitted from source

Qe

Qv

JJ

Radiant Flux Luminous Flux

Rate of energy emitted or transferred from source

Φe

Φvϕ=dQ/dt

Wlm

Radiant IntensityLuminous Intensity

Flux emitted from a point source per unit solid angle

Ie

IvI=dϕ/dΩΩ W sr-1

lm sr-1 = cd

Radiant Emittance Luminous Emittance

Flux emitted per surface unit area of extended source

Me

MvM=dϕ/dA

W m-2

lm m-2 = lx

RadianceLuminance

Flux emitted per unit surface area of extended source, per unit solid angle at angle normal to surface n

Le

Lv

L=d2ϕ/

(dAdΩΩcosθ)W m-2 sr-1

lm m-2 sr-1 = cd m-2

IrradianceIlluminance

Flux arriving at a surface per unit surface area at an angle normal to the surface

Ee

EvE=dϕ/dA

W m-2

lm m-2 = lx

Radiant Energy DensityLuminous Energy Density

Energy emitted per unit volume of source w w= dQ/dV J m-3

J m-3

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Photometry

Photometric unitsPhotometric unitsPhotometric unitsPhotometric units

Photometry UnitsUnitsUnits

Photometry MKS CGS British

Luminous energy TalbotTalbotTalbot

Luminous power LumenLumenLumen

Illuminance Lux Phot Footcandle

Luminance NitApostilb, Blondel

StilbLambert Footlambert

Luminous intensity Candela (Candle, Candlepower, Carcel, Hefner)Candela (Candle, Candlepower, Carcel, Hefner)Candela (Candle, Candlepower, Carcel, Hefner)

Thus one nit is one lux per steradian is one candela per square meter is one lumen per square meter per steradian. Got it ? James Kajiya

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To be pragmatic

A particular algebraic symbol is used to describe the optical parameter, be it radiometric or photometric, the subscript "e" added to denote a radiometric quantity (e, like energetic) , the subscript "v" to denote a photometric quantity (v, like visual).

radiant flux is a radiometric quantity denoted by ϕe

luminous flux is a photometric quantity denoted by ϕv

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To be pragmatic

Note that radiometric and photometric parameters relate to the total amount of radiation emitted over all wavelengths (EM spectrum or visible). Sometimes need to define a parameter over a specific frequency or wavelength interval.

For example, spectral radiance is the flux per unit area per unit solid angle per unit frequency interval denoted as Lv(λ)

or Le(λ)

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An example

Characteristics of light sources

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Radiance

The radiance (luminance), L(x,ω), is the intensity

per unit area leaving a surface:

L(x,~) = dAdI(x,~)

= d~dAd2U(x,~)

Unit of radiance is: sr m2W; E

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Conservation of radiance

Conservation of radiance (formerely called “brightness theorem”)

In an optical system the radiance measured in the direction of propagation is an invariant (in fact, this is the quantity L/n2 which is an invariant)

In an optical system the radiance of the image is equal to the radiance of the source

optical system

object image

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Maximization of the radiant flux

In an optical system we will try to maximize the amount of radiant flux, ΩΩ, transferred from the source to the detector. If the system is aberration free and has no internal aperture, we verify the relation:

G= AsXs= AiXi= cste

The quantity, G, which is the same for the source and for the image is called the geometrical extent

Credit: http:www.newport.com

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Maximization of the radiant flux

If the optical system has a cylindrical symmetry, the 1D version of the optical extent ia applicable:

G= h1i1 = h2i2= cste

Credit: http:www.newport.com

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A practical case ...

excitation

sample

monochromator

the lowest geometrical extent of any component in an optical system limits system throughput. Generally the monochromator is the component with the lowest geometrical extent. The geometrical extent of the monochromator is the product of the entrance slit width and the angle of acceptance.

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The index of refraction

The index of refraction, n, of a material is a dimensionless number defined by the relationship:

where c and v are the speeds of the light in the vaccum and in the material respectively

n= vc

c=299'792'458 m $ s-15 ?

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The index of refraction

In the transparent materials, the index of refraction n, is equal or greater to 1 (réfringent material) :

n$1

http://ctd.grc.nasa.gov/organization/branches/eodb/metamateriallens.htmlmetamaterials: n ! 1

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Conventionnal spectroscopy

How to obtain the optical signature of a EM signal ?

Prism spectrometer Grating spectrometer Interferential spectrometer Fourier transform interferometer…

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Dispersive system

Dispersive SystemsPrism

Grating

Interferential

Spectrometer

Spectroscope

Spectrograph

Monochromator Image sensor, [CCD, CMOS, ...]

Flux detectors [PM, PD, ...

Optical filter

Light source

Spectral signature

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Time resolved spectroscopy

• Fermat principle still applies

• Heisenberg principle also ... !

DE $ Dt$'

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light sources sample

light analyzers

light detectors

crystallogenesis

epitaxy

cryogenic

magnetic field

sample

incoherent light sources- blackbody types- arc lamps- LED

coherent light sources - laser

synchrotron light

light source

monochromator (eg prism , grating type)

PF analyzer

light analyzer

quantum detectors (eg photographic plate, PM. PD, CCD, ...)

Thermal detectors (eg photoacoustic, ...)

light detector

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Imaging Spectroscopy - CL mapping

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Imaging Spectroscopy - CL mapping

SEM: Secondary electrons SEM: Cathodoluminescence mode

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Experimental methods to investigate the optical properties ... 2010-11/mep jdg_intro... ·...

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