Prof David Lidzey
University of Sheffield
• 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.
Absorption and emission of radiation
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.
• 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
• 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
M12 = y2
(r)H(r)ò y1 d3
• 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.
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
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
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
• Absorption allowed over continuous range of wavelengths.
• Such materials have sizable optical effects, making them useful
for device technology.
GaAs crystal structure Interatomic separation
Luminescence from a semiconductor
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
Quantifying luminescence efficiency
Luminescence quantum efficiency (F) can be calculated using
tR = radiative rate, tNR = non-radiative rate
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.
N(1 tR +1 tNR )
Interband Semiconductor Luminescence
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
Examples: GaAs, GaN, GaInP
• Excite a direct bandgap
semiconductor with a photon
whose energy is greater than the
• 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.
k = 0
Photoluminescence at low carrier density
k = 0
Density of states
At low carrier densities, the occupation of
electrons and holes have a Boltzmann distribution
f (E) µ exp -
PL emission above energy-gap
falls off exponentially due to Boltzmann factor.
From “Optical Properties of Solids” by Mark Fox
Interband Semiconductor absorption
Transitions are possible at a
Wide range of energy (wavelengths)
from the Valence band to the
GaN: Absorption and luminescence
Absorption and emission
are not the same!From “Optical Properties of Solids” by Mark Fox
Perovskites can be direct bandgap semiconductors
Saidaminov et al
Nature Communications 6, 7586 (2015)
Mott et al
6 (2015) 7026
Indirect gap semiconductors
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
I = I0e-sdN
I0 and I are the power per
unit area of the radiation incident
s is the attenuation cross-section of
N is the number density of the absorbers
Absorbance is defined as A = -ln
÷ = 2.302log10
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
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.
Components inside an absorption
Optical grating on
Scan ‘probe’ wavelength
and measure transmitted
Measuring optical absorption using a CCD
Shine a white light through a sample
Determine the wavelengths transmitted
Measuring photoluminescence emission
This is considerably easier if the sample under test is
an efficient emitter (i.e. F ~ 1.0)
• Emission from an excited state comes via the process of
• 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.
÷ = -AN
N(t) = N(0)exp(-At) = N(0)exp(-t /tR )
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’.
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
• Absorption and PL spectra allow the
electronic states within a material to be
• 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.