Optical spectroscopy allows the study of light-matter interactions and provides information about electronic structures. It is a key technique used to probe various states of matter. Spectroscopy gives direct information about electronic structures through the absorption and emission of radiation. Measurement of absorption and photoluminescence emission spectra provides information about electronic band structures and transition rates in semiconductors.
2. Optical Spectroscopy
• Study of the interaction of matter and light (radiated energy).
• A key experimental technique use to probe all states of matter (atoms,
gas, plasma, solids, liquids etc).
• Gives direct information about electronic structure of a system.
• Can be used to explore relative composition of a material (i.e. relative
concentration of a known compound in solution).
• Widely used in industry and quality assurance.
• Key technique in semiconductor research.
3. Summary
Absorption and emission of radiation
Transition rates
Selection rules for optical transitions
Direct vs indirect semiconductors
Measurement of absorption
Measurement of emission and quantum yield
Fluorescence decay lifetime
For more information, see “Optical Properties of Solids” by
Prof. Mark Fox on which this lecture is loosely based.
4. • In quantum systems, we have interaction of a
stationary-state (e.g. an atom) with an oscillating
state – a photon.
• Coupling of the states is strongest when the energy
difference between the two states matches the
energy of the photon, e.g.
• Atoms can either absorb or emit this energy when
they jump between states.
E2 - E1 = hn
E1
E2
hn
E1
E2
hn
Absorption Emission
5. Transition rates
• Transition rates (W12) between two states can be calculated
using the wavefunction of the initial and final states through
Fermi’s golden rule.
• Here the M12 is the matrix element for the transition between
bands of levels. The matrix element can written as
where H is the perturbation that causes the transition (the
interaction between the atom and the photon). The strongest
interaction process is called the “Electric dipole interaction”.
• g(hn) is the photon density of states. This is defined as the
number of photon states per unit volume that fall into the energy
range E + dE, where E = hn
W12 =
2p
M12
2
g(hn)
M12 = y2
*
(r)H(r)ò y1 d3
r
6. • Here, the perturbation is expressed by
H = -p. e
where p is the dipole moment of the electron and e
is the electric field applied.
Because of this, such transitions are called ‘Electric
Dipole’, or ‘Dipole-Allowed’ transitions.
7. Selection rules for Electronic transitions.
Electric dipole transitions can only happen if a number of rules
about initial and final states are obeyed.
These are rules about the quantum numbers of the initial and final
states.
For an electron in a system with quantum numbers l, m, ms, the
selection rules are
(1)Parity of initial and final states must be different
(2) Dm = -1, 0 or +1
(3) Dl = +/- 1
(4) Dms = 0
The photon carries away one unit of angular momentum, so the
total angular momentum of the atom must change by one unit in
the transition.
8. From single emitters to electronic bands.
• Atoms in a solid are packed close-together, so outer orbitals
interact strongly together.
• This broadens discrete levels to bands. Electronic bands retain
of atomic character of states.
• Transitions between bands allowed if they are allowed by
selection rules.
• Absorption allowed over continuous range of wavelengths.
• Such materials have sizable optical effects, making them useful
for device technology.
GaAs
GaAs crystal structure Interatomic separation
E
9. Luminescence from a semiconductor
Excited states
Ground states
Inject electrons
Inject holes
tRtNR
Relaxation Rapid relaxation and thermalisation
Applies for electrons and holes.
Recombination of electrons and
holes can result in luminescence.
This often different from absorption.
Radiative and non-radiative processes
compete.
10. Quantifying luminescence efficiency
Luminescence quantum efficiency (F) can be calculated using
tR = radiative rate, tNR = non-radiative rate
Have,
where A = 1 / tR.
If tR << tNR, then F ~ 1.0 and all energy comes out as light.
If tR >> tNR, then F ~ 0 and the energy is lost internally as heat.
dN
dt
æ
è
ç
ö
ø
÷
total
= -
N
tR
-
N
tNR
F =
AN
N(1 tR +1 tNR )
=
1
1+tR tNR
11. Interband Semiconductor Luminescence
Direct-gap materials
Conduction
band
Valence band
electrons
holes
hn
Eg
Photons emitted when
electrons at the bottom
of the conduction band recombine
with holes at the top of the valence band.
Since momentum of the photon
is negligible compared to that
of the electron, e and h have same k-vector.
Energy of luminescence close
to energy-gap.
Examples: GaAs, GaN, GaInP
k
E
12. Generating Photoluminescence
• Excite a direct bandgap
semiconductor with a photon
whose energy is greater than the
energy-gap.
• Photons are absorbed, raising
electrons into the CB and holes
into the VB.
• Electrons loose energy very
quickly by emitting phonons.
Each step corresponds to the
emission of a phonon (~ 100 fs).
Energy and momentum is
conserved in this process.
• Relaxation process much faster
than radiative emission, so
electrons collect at bottom of CB
before recombining radiatively.
electrons
holes
hn
Eg
k = 0
E
13. Photoluminescence at low carrier density
holes
k = 0
E E
Density of states
electrons
At low carrier densities, the occupation of
electrons and holes have a Boltzmann distribution
f (E) µ exp -
E
kBT
æ
è
ç
ö
ø
÷
PL emission above energy-gap
falls off exponentially due to Boltzmann factor.
From “Optical Properties of Solids” by Mark Fox
15. GaN: Absorption and luminescence
Absorption and emission
are not the same!From “Optical Properties of Solids” by Mark Fox
16. Perovskites can be direct bandgap semiconductors
Saidaminov et al
Nature Communications 6, 7586 (2015)
Mott et al
Nature Communications
6 (2015) 7026
17. Indirect gap semiconductors
Conduction band
Valence
band
electrons
holes
hn
Eg
Phonon
Conduction band minimum
and valence band maximum
are at different point in Brillouin zone.
Conservation of momentum requires
that a phonon is either emitter or absorbed
when the photon is emitted.
This represents a ‘second-order’ process,
giving it a low probability.
Radiative lifetime is therefore slow, and
competition with non-radiative processes
makes luminescence weak.
Examples: Si, Ge
k
E
18. Quantifying absorbance
Sample
Io(l) I(l)
d
I = I0e-sdN
I0 and I are the power per
unit area of the radiation incident
and transmitted.
s is the attenuation cross-section of
the absorber
N is the number density of the absorbers
Absorbance is defined as A = -ln
I
I0
æ
è
ç
ö
ø
÷ = 2.302log10
I
I0
æ
è
ç
ö
ø
÷ =sdN
Very often, when measuring a thin film, we are actually
interested in S – the attenuation coefficient, where
Units for S are often expressed as cm-1.
A = Sd
19. Measurement of optical absorption
Basic principle - split white light into component wavelengths
using a dispersive element (e.g. a grating or prism). Measure how
efficiently the different wavelengths are absorbed.
20. Components inside an absorption
spectrometer
Light-source
Optical grating on
rotating turret
Entrance slit
Exit slit
Sample
Detector
Scan ‘probe’ wavelength
and measure transmitted
signal
21. Measuring optical absorption using a CCD
spectrometer.
Shine a white light through a sample
Determine the wavelengths transmitted
23. Emission dynamics
• Emission from an excited state comes via the process of
spontaneous emission
• If upper level has a population N at time t, the radiative emission
rate is given by
• This can be solved to show
where tR is the radiative lifetime of the transition.
The actual luminescence intensity I(hn) can be dependent on the
emission rate, and the relative probability that the upper level is
occupied and the lower level is unoccupied.
‘Allowed’ transitions often have radiative lifetimes of ~ 1 ns.
dN
dt
æ
è
ç
ö
ø
÷ = -AN
N(t) = N(0)exp(-At) = N(0)exp(-t /tR )
24. Measuring fluorescence decay lifetime
• Sample excited with a very short light-pulse.
• Emission recorded as a function of time.
• Lasers with pulses 100 fs to 1 ps now commonplace.
• Time-resolutions of 100 ps achievable with photomultiplier tubes. Resolutions of 1
ps possible with a ‘streak-camera’.
Pulsed laser
DetectorSample
Mirror
Lenses
25. Fluorescence dynamics
1
ttotal
=
1
trad
+
1
tNR
I(t) = Aexp(-t /t1)+
Bexp(-t /t2 )+...
Gives direct information about carrier relaxation, diffusion
and recombination mechanisms.
Often a series of processes going on, so practically need to
fit decay lifetimes to a series of exponential decay
functions.
26. Summary
• Absorption and PL spectra allow the
electronic states within a material to be
directly accessed.
• The properties of many semiconductor
materials have similarities, but also
distinct differences, depending on
atomic / molecular structure.
• Reviewed a number of key techniques
of use in routine spectroscopy labs.
