Lecture 6
Optical Characterization of Inorganic Semiconductors Dr Tim Veal, Stephenson Institute for Renewable Energy
and Department of Physics, University of Liverpool
Lecture OutlineL6
Lecture 6: Optical properties of semiconductors
• Optical spectroscopy in PV research
• Optical spectroscopies, methods and proceses
Transmission, reflection, absorption, photoluminescence
• Phenomena/properties determined by optical spectroscopy
• Band gap type and energy determination: methods and pitfalls
• Some case studies
Renewable Energy MixL6
Max Birkett, PhD thesis, UoL (2016)
Note the complementary nature of wind and PV technologies
Optical Spectroscopy in PV L6
Need to measure optical properties of new and sustainable materials to determine
Suitability for PV applications
What band structure properties do we want from a PV absorber?
Band gap size, type?
Free carriers?
Max Birkett, PhD thesis, UoL (2016)
Conversion efficiency
Eg
cb
vbEF
hn
Ener
gy
Conversion efficiency
Eg
cb
vbEF
hn
p-type n-type
hn
One electron per photon Eg = energy available from each
Power at ground level is about 1000 W/m2
Solar spectrumL6
Max Birkett, PhD thesis, UoL (2016)
Shockley – Queisser efficiency limit
L M Peter
Optical absorptionL6
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
Absorption is expressed in terms of a coefficient, α(hν), which is defined as the
relative rate of decrease of light intensity L(hν) along its propagation path:
Every initial state Ei is associate with a final state Ef
such that:
Ef = hv – Ei
For parabolic bands, Ef – Eg = ℏ2k2/2me*
and Ei = ℏ2k2/2mh*
dx
hvLd
hLh
)]([
)(
1)
nn
Absorption coeff is proportional to the transition probability from Ei to Ef and also the
density of electrons in the initial state ni and the number of empty final states nf
Optical absorptionL6
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
Therefore
**
22 11
2he
gmm
kEh
n
It can be shown that the density of states is:
Therefore plot of α2 versus hν for a direct gap gives straight line for absorption edge (see later)
Optical absorptionL6
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
How thick does an absorber layer need to be so that the majority of photons are absorbed?
I(hv) = I0exp(-α(hv)z), z is the depth in the material, I0 is unattenuated light intensity
The higher the absorption coefficient, the thinner the layer can be.
(Si needs to be thick. CdTe can be thin.)
Optical absorptionL6
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
)(
)()( 2
pg
pga
EEh
EEhAh
n
nn
)(
)()( 2
pg
pge
EEh
EEhAh
n
nn
For indirect absorption, a phonon is
required for momentum conservation.
For absorption of a phonon of energy,
Ep, the absorption coefficient is given by
and for phonon emission is:
Therefore plot of α1/2 versus hν for an indirect gap gives straight line
for absorption edge (see later)
Optical absorptionL6
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
)(
)()()(
pg
ea
EEh
hhh
n
nnn
Both phonon emission and absorption are possible for hv > Eg +Ep, so the absorption
coefficient is given by
Optical absorptionL6
Absorption spectrometersL6
Two types of spectrometer are used for absorption: Fourier Transform infrared (FTIR)
UV-vis-near IR spectrophotometer
Max Birkett, PhD thesis, UoL (2016)
How to measure absorption?L6
But how do we measure light absorbed by a material?
We can only measure what is not absorbed.
We can measure what is transmitted, T
and what is reflected, R
Then, with knowledge of the film thickness, we convert T and R
to absorption coefficient, , somehow...
from d, T and R?L6
Assuming no reflections: T=transmissivity, d = film thickness
Assuming no internal reflections: R=reflectivity
And the reflection coefficient is approximately, 𝑅 =𝑛−1
𝑛+1
2where n is the refractive index.
=1
𝑑𝑙𝑜𝑔
1
𝑇
=1
𝑑𝑙𝑜𝑔
1−𝑅 2
𝑇
Usual approach taken to obtaining from d, T and R:
the reflectivity and transmissivity are respectively the ratios of reflected and transmitted to incident power
the Fresnel coefficients at each boundary are written in the refractive indexes of the materials, N=n+iK.
a simple approximation gives the reflectivity and transmissivity for a single incoherent optical layer
more complicated models consider oscillations in the spectra due to interference from internal reflections
generally, it may not be possible to solve R and T for N
reflection/transmission introduction
Max Birkett, PhD thesis, UoL (2016)
from d, T and R?
reflection/transmission spectroscopy
Max Birkett, PhD thesis, UoL (2016)
Power reflection coefficient
Power transmission coefficient
reflection/transmission spectroscopy
Phase shift average out for an incoherent system so can be ignored giving:
We are trying to find . We can do this by solving the quadratic in
exp(- d) given by the Ttot expression:
Except we don’t measure R0, we measure Rtot...
Max Birkett, PhD thesis, UoL (2016)
R=0
Rtot =R0
reflection/transmission spectroscopy0
Self-consistent, iterative approach
Ignoring internal reflections results in greater inaccuracies when the absorption coefficient is
low <104 cm-1, so exactly where we are most interested where the absorption edge begins.
Max Birkett, PhD thesis, UoL (2016)
SLMEL6
SLME efficiency versus minimum band gap for I-III-VI
materials for film thickness of 0.5 microns.
Shockley-Quiesser assumes
step function 100% absorption
for E>Eg and 0% for E<Eg
Spectrally limited maximum
efficiency (SLME) uses
absorptivity of
a(E) = 1-exp(-2(E)d)
with R = 0 for front surface and
R = 1 for back surface.
Better approx., but still far from
reality.
Yu and Zunger, Phys. Rev. Lett.
108, 068701 (2012)
SLMEL6
CuSbS2 and CuBiS2 have
stronger absorption onsets and
so will (just considering this
property) give greater efficiency
for thinner films.
They will get closer to the SQ
limit.
Kumar and Persson, J.
Renewable Sustainable Energy
5, 031616 (2013)
SnS2 optical absorptionL6
L. Burton, T. J. Whittles, T. D. Veal, V. R. Dhanak, A. Walsh, et al., J. Mater. Chem. A (2015)
SnS2 optical absorptionL6
L. Burton, T. J. Whittles, T. D. Veal, V. R. Dhanak, A. Walsh, et al., J. Mater. Chem. A (2015)
SnS2 optical absorptionL6
L. Burton, T. J. Whittles, T. D. Veal, V. R. Dhanak, A. Walsh, et al., J. Mater. Chem. A (2015)
Temperature dependenceL6
Temperature dependence of band gap of semiconductors is due to:
• Dilation of the lattice due to increasing temperature
• T-dependent electron phonon interactions
Most commonly used and simple parameterization of T
dependence of semiconductor band gaps is that of Varshni
(Physica 34 (1967) 149) but many more detailed treatments exist.
where α and β are experimentally determined parameters.
T
TETE
gg
2
)0()(
CuSbS2: temp-dependent T and R spectra
Max Birkett, PhD thesis, UoL (2016)
CuSbS2: T dependent absorption spectra
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.10.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105
Eg(d)
= 1.598 eV
Absorp
tion c
oeffic
ient (c
m-1)
Photon energy (eV)
4 K
10 K
20 K
30 K
40 K
50 K
60 K
70 K
80 K
90 K
100 K
125 K
150 K
175 K
200 K
250 K
300 K
Eg(d)
= 1.687 eV
Clear trend of
increasing
absorption edge as T
is reduced
Feature at 1.83 eV is
unidentified, but
reduces in intensity
as T is increased.
Max Birkett, PhD thesis, UoL (2016)
CuSbS2: absorption indirect band gap
Max Birkett, PhD thesis, UoL (2016)
T.J. Whittles, et al., ACS Appl. Mater. Int. (2017) in press.
0 50 100 150 200 250 3001.575
1.600
1.625
1.650
1.675
1.700
Direct band gap
Varshni T dependence
Direct band g
ap (
eV
)
Temperature (K)
Eg(T) = E
g(0) - AT
2/(B+T)
Eg(0) = 1.687 eV
A = 0.411meV/K
B = 106 K
CuSbS2: T dependent direct band gap
Max Birkett, PhD thesis, UoL (2016)
Temperature dependenceL6
Why does the temperature dependence of the band gap
matter for new and sustainable photovoltaic absorbers?
Solar cells operate over a significant range of
temperatures due to:
• range of ambient temperatures they are subjected to
• heating by solar radiation
Range of temperatures could be 0 to 60°C
Temp. effects on solar cellsL6
Temperature increase results in:
Short circuit current JSC slightly increasing due to increased
light absorption due to decrease in band gap
Open circuit voltage and fill factor decrease with increase temp.
due to decrease in band gap
Fall in VOC dominates T dependence
As an example, for Si, VOC falls by about 2.3 mV per °C temp.
increase*
So about 115 mV fall in VOC for 50°C temp. Increase, leading to
significant fall in device efficiency
*Martin Green, Solar Cells. Operating Principles, Technology and System Applications (Prentice Hall, 1982)
T dependence of cell efficiencyL6
0.4-7.8% absolute change in efficiency for 10K
temperature change, depending on material
Singh and Ravindra, Sol. Energy Mat. Sol. Cells 101 (2012) 36
FTIRL6
FTIR combined transmission and reflection for optical absorption
PhotoluminescenceL6
Photoluminescence can be powerful for investigating defect related transitions.
PLL6
Photoluminescence of defect related transitions can be very complicated!.
AbsorptionL6
AbsorptionL6
GaAs
CdSL6
Martin Archibold, Durham PhD thesis (2007)
CdS transmission as a function of film thickness on Pilkington FTO
Transmission cutoff at 2.4eV. Thin films transmit more 2.6 to 3.5 eV light
CdSL6
Martin Archibold, Durham PhD thesis (2007)
CdS transmission as a function of film thickness on Pilkington FTO
Transmission cutoff at 2.4eV. Thin films absorb less 2.6 to 3.5 eV light
CdSL6
Martin Archibold, Durham PhD thesis (2007)
Reducing CdS layer thickness enables more high energy, short wavelength
photon to be harvested
CdSL6
Martin Archibold, Durham PhD thesis (2007)
SummaryL6
• Optimum band gap for PV determined by solar spectrum and payoff
between absorption and thermal losses
• Thickness of absorber required is determined by absorption coefficient
• Absorption coefficient is not straightforward to obtain from T and R
• Direct band gap significantly better than indirect for PV absorber
• Temp. dependence of band gap influences efficiency mainly via VOC and
low temp. absorption measurements useful to compare with theory
• Optical properties are important, but electrical properties (such as carrier
lifetime) seem to dictate success, or otherwise, of PV materials:
Si is far from optimal in terms of optical properties 1.2 eV indirect band
gap, but it does pretty well.