Download Lecture 7: Optical Characterization of Inorganic - CDT-PV

Lecture 7
Optical Characterization of Inorganic Semiconductors
Dr Tim Veal, Stephenson Institute for Renewable Energy
and Department of Physics, University of Liverpool
Nov 3, 2016
L7
Lecture Outline
Lecture 7: 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
L7
Renewable Energy Mix
Max Birkett, PhD thesis, UoL (2016)
Note the complementary nature of wind and PV technologies
L7
Optical Spectroscopy in PV
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
Energy
cb
Eg
EF
vb
hn
Conversion efficiency
 One electron per photon
 Eg = energy available from each
cb
Eg
hn
EF
vb
hn
p-type
n-type
Power at ground level is about 1000 W/m2
L7
Solar spectrum
Max Birkett, PhD thesis, UoL (2016)
Shockley – Queisser efficiency limit
L M Peter
L7
Optical absorption
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:
1 d [ L(hv)]
  hn ) 
L(hn )
dx
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*
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
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
L7
Optical absorption
Therefore
 2 k 2  1
1 
hn  E g 
 *
*

2  me mh 
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)
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
L7
Optical absorption
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.)
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
L7
Optical absorption
For indirect absorption, a phonon is
required for momentum conservation.
For absorption of a phonon of energy,
Ep, the absorption coefficient is given by
 a (hn )  A(hn  Eg  E p ) 2
(hn  E g  E p )
and for phonon emission is:
 e (hn )  A(hn  Eg  E p ) 2
(hn  E g  E p )
Therefore plot of α1/2 versus hν for an indirect gap gives straight line
for absorption edge (see later)
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
L7
Optical absorption
Both phonon emission and absorption are possible for hv > Eg +Ep, so the absorption
coefficient is given by
 (hn )   a (hn )   e (hn )
(hn  Eg  E p )
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
L7
Optical absorption
L7
Absorption spectrometers
Two types of spectrometer are used for absorption: Fourier Transform infrared (FTIR)
UV-vis-near IR spectrophotometer
Max Birkett, PhD thesis, UoL (2016)
L7
How to measure absorption?
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...
L7
 from d, T and R?
reflection/transmission introduction
 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
Max Birkett, PhD thesis, UoL (2016)
reflection/transmission spectroscopy
Power reflection coefficient
Power transmission coefficient
Max Birkett, PhD thesis, UoL (2016)
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)
reflection/transmission spectroscopy
0
R=0
Self-consistent, iterative approach
Rtot =R0
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)
complexities in reflection/transmission spectroscopy
no unique solution may exist; noise further complicates.
solutions:
Rexpr-R(n)=0
Texpr-T(n)=0
T
R
Max Birkett, PhD thesis, UoL (2016)
complexities in reflection/transmission spectroscopy
no unique solution may exist; noise further complicates.
solutions:
Rexpr-R(n)=0
Texpr-T(n)=0
EXAMPLE: 1. consider a
material with some known
complex refractive index
Max Birkett, PhD thesis, UoL (2016)
complexities in reflection/transmission spectroscopy
no unique solution may exist; noise further complicates.
solutions:
2. calculate the reflectivity
Rsim
Rexpr
-R(n)=0
and transmission Tsim
which
Texpr-T(n)=0
will be found experimentally
Max Birkett, PhD thesis, UoL (2016)
complexities in reflection/transmission spectroscopy
no unique solution may exist; noise further complicates.
T
3. now explore solution
domain:
solutions:
separately eval. R andR T -R(n)=0
over
sim
complex refractive mesh,
plot
Tsim-T(n)=0
contours of residuals Rsim-R(n)
R
Max Birkett, PhD thesis, UoL (2016)
complexities in reflection/transmission spectroscopy
no unique solution may exist; noise further complicates.
solutions:
Rexpr-R(n)=0
Texpr-T(n)=0
T
R
4 solutions consistent with simulated R/T spectra
Max Birkett, PhD thesis, UoL (2016)
complexities in reflection/transmission spectroscopy
no unique solution may exist; noise further complicates.
solutions:
Rexpr-R(n)=0
Texpr-T(n)=0
T
R
simulated R/T spectra used this refractive index
Max Birkett, PhD thesis, UoL (2016)
vulnerabilities of typical absorption relations




typically used relations to evaluate optical absorption
use approximations which introduce inaccuracies
if we assume no internal reflections, then we can
solve the second equation for the absorption coefficient
(by ignoring the denominator and assuming R0=Rtot),
giving absorption spectra: α=1/d * log[(1-Rtot)²/Ttot]
the accuracy of such approximations may be evaluated
for a simulated system: by computing Rtot & Ttot, and
plotting the ratio of the evaluated to real absorption
Max Birkett, PhD thesis, UoL (2016)
vulnerabilities of typical absorption relations
typical relations find absorption strength inaccurately.
evaluated/actual absorption
Max Birkett, PhD thesis, UoL (2016)
vulnerabilities of typical absorption relations
typical relations find absorption strength inaccurately.
evaluated/actual absorption
very poor accuracy here
Max Birkett, PhD thesis, UoL (2016)
L7
SLME
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)
SLME efficiency versus minimum band gap for I-III-VI
materials for film thickness of 0.5 microns.
L7
SLME
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)
L7
SnS2 optical absorption
L. Burton, T. J. Whittles, T. D. Veal, V. R. Dhanak, A. Walsh, et al., J. Mater. Chem. A (2015)
L7
SnS2 optical absorption
L. Burton, T. J. Whittles, T. D. Veal, V. R. Dhanak, A. Walsh, et al., J. Mater. Chem. A (2015)
L7
SnS2 optical absorption
L. Burton, T. J. Whittles, T. D. Veal, V. R. Dhanak, A. Walsh, et al., J. Mater. Chem. A (2015)
L7
Temperature dependence
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.
T 2
E g (T )  E g (0) 
T 
where α and β are experimental determined parameters.
CuSbS2: T dependent absorption spectra
Absorption coefficient (cm-1)
1.0x105
8.0x104
4K
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
6.0x104
4
4.0x10
Eg(d) = 1.598 eV
2.0x104
Eg(d) = 1.687 eV
0.0
1.4
1.5
1.6
1.7
1.8
1.9
2.0
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.
2.1
Photon energy (eV)
Max Birkett, PhD thesis, UoL (2016)
CuSbS2: T dependent absorption spectra
Absorption coefficient (cm-1)
105
4K
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
104
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
Photon energy (eV)
Max Birkett, PhD thesis, UoL (2016)
CuSbS2: absorption indirect band gap
1.2x105
4K
Absorption coefficient (cm-1)
5
1.0x10
8.0x104
α=A(hν-Eg)2
6.0x104
Eg = 1.56 eV
4.0x104
2.0x104
0.0
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Photon energy (eV)
Max Birkett, PhD thesis, UoL (2016)
CuSbS2: absorption direct band gap
1.2x105
Absorption coefficient (cm-1)
4K
1.0x105
8.0x104
α=A(hν-Eg)1/2
6.0x104
Eg = 1.69 eV
4.0x104
2.0x104
0.0
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Photon energy (eV)
Max Birkett, PhD thesis, UoL (2016)
CuSbS2: T dependent direct band gap
Direct band gap (eV)
1.700
Direct band gap
Varshni T dependence
1.675
1.650
1.625
Eg(T) = Eg(0) - AT2/(B+T)
Eg(0) = 1.687 eV
1.600
1.575
A = 0.411meV/K
B = 106 K
0
50
100
150
200
250
300
Temperature (K)
Max Birkett, PhD thesis, UoL (2016)
L7
Temperature dependence
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
L7
Temp. effects on solar cells
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)
L7
T dependence of cell efficiency
Singh and Ravindra, Sol. Energy Mat. Sol. Cells 101 (2012) 36
0.4-7.8% absolute change in efficiency for 10K
temperature change, depending on material
L7
Low T absorption and DFT
First principles computational methods (density functional theory)
are increasingly being used to understand existing materials and
design ones for photovoltaics.
Density functional theory has
traditionally been really bad at
predicting band gaps. But now
with hybrid functional it is
generally reasonably good 
However, DFT calculated
properties at 0 K, so we need
experimental data at low temp
to compare with the calculations.
J. Furthmueller, F. Fuchs and F. Bechstedt, in
T. D. Veal (Ed.) Indium Nitride and Related Alloys
(CRC Press, 2009)
CuSbS2: DFT band structure (HSE06)
DFT HSE06
Indirect Eg = 1.67 eV
Direct
Eg = 1.82 eV
4 K exp values:
Indirect Eg = 1.56 eV
Direct
Eg = 1.69 eV
C. Savoury and
D. O. Scanlon, UCL
L7
FTIR
FTIR combined transmission and reflection for optical absorption
L7
FTIR
FTIR variable angle specular reflectivity for plasma and phonon measurements
L7
Photoluminescence
Photoluminescence can be powerful for investigating defect related transitions.
L7
PL
Photoluminescence of defect related transitions can be very complicated!.
L7
Absorption
L7
Absorption
L7
CdS
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
L7
CdS
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
L7
CdS
Martin Archibold, Durham PhD thesis (2007)
Reducing CdS layer thickness enables more high energy, short wavelength
photon to be harvested
L7
CdS
Martin Archibold, Durham PhD thesis (2007)
L7
Indium nitride
Common cation semiconductor band gaps
InN 1.89 eV
InP 1.35 eV
InAs 0.36 eV
InSb 0.18 eV
Common anion semiconductor band gaps
AlN 6.2 eV
GaN 3.4 eV
InN 1.89 eV
T. L. Tansley and C. P. Foley,
J. Appl. Phys. 59, 3241 (1986).
L7
Indium nitride
Low energy
PL
observed in
2001 at
Ioffe
Figures from T. D. Veal (Ed.) Indium Nitride and Related Alloys (CRC Press, 2009)
L7
Indium nitride
Low energy PL
also observed in
2002 at Berkeley
So is indium nitride
a high band gap semiconductor with below band gap defect related absorption and PL
Or a low band gap semiconductor with some other explanation for the previously
observed high energy absorption onset?
L7
Indium nitride
Common cation semiconductors
InN 0.65 eV
InP 1.35 eV
InAs 0.36 eV
InSb 0.18 eV
Common anion
semiconductors
AlN 6.2 eV
GaN 3.4 eV
InN 0.65 eV
J. Wu et al., Chapter 7 in T. D. Veal et al. (eds)
Indium Nitride and Related Alloys (CRC Press, 2009)
L7
Indium nitride
L7
Indium nitride
L7
Indium nitride
L7
Indium nitride
Main message from indium nitride is that it is not always
easy to determine the nature and magnitude of a band gap
of new (or sometimes long established) semiconductors!
Before 2000, DFT theory had the band gap of InN as 1.9 eV
Once experiment determined a different value, the theory
then got that value too! Theory can be useful but so can
healthy skepticism.
L7
Indium nitride
L7
Indium nitride
Low density of localized states dominate low temp PL
Absorption edge is determined by high density of band states
L7
Summary
• 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.