Delivered by T. Veal for CDT-PV Liverpool training module, 5 Nov 2015

1. Lecture 7
Optical Characterization of Inorganic Semiconductors
Dr Tim Veal, Stephenson Institute for Renewable Energy
and Department of Physics, University of Liverpool
Nov 5, 2015

2. Lecture Outline
L7
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

3. Optical Spectroscopy in PV
L7
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?

4. Conversion efficiency
Eg
cb
vb
EF
hn
Energy

5. Conversion efficiency
Eg
cb
vb
EF
hn
p-type n-type
hn
 One electron per photon
 Eg = energy available from each

6. Power at ground level is about 1000 W/m2

7. Shockley – Queisser efficiency limit
L M Peter

8. Optical absorption
L7
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
hL
h
)]([
)(
1
)
n
n 
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

9. Optical absorption
L7
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
Therefore








 **
22
11
2 he
g
mm
k
Eh

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)

10. Optical absorption
L7
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.)

11. Optical absorption
L7
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)

12. Optical absorption
L7
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.
)(
)()()(
pg
ea
EEh
hhh


n
nnn
Both phonon emission and absorption are possible for hv > Eg +Ep, so the absorption
coefficient is given by

13. Optical absorption
L7

14. Absorption spectrometers
L7
Two types of spectrometer are used for absorption: Fourier Transform infrared (FTIR)
UV-vis-near IR spectrophotometer

15. SnS2 optical absorption
L7
L. Burton, T. D. Veal, A. Walsh, et al., submitted to J. Mater. Chem. A

16. SnS2 optical absorption
L7

17. SnS2 optical absorption
L7

18. Temperature dependence
L7
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 experimental determined parameters.




T
T
ETE gg
2
)0()(

19. CuSbS2: T dependent absorption spectra
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1
0.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105
Eg(d)
= 1.598 eV
Absorptioncoefficient(cm-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.

20. CuSbS2: T dependent absorption spectra
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1
104
105
Absorptioncoefficient(cm-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

21. 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
0.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105
1.2x105
Absorptioncoefficient(cm-1
)
Photon energy (eV)
4 K
CuSbS2: absorption indirect band gap
α=A(hν-Eg)2
Eg = 1.56 eV

22. 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
0.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105
1.2x105
Absorptioncoefficient(cm-1
)
Photon energy (eV)
4 K
CuSbS2: absorption direct band gap
α=A(hν-Eg)1/2
Eg = 1.69 eV

23. 0 50 100 150 200 250 300
1.575
1.600
1.625
1.650
1.675
1.700
Direct band gap
Varshni T dependence
Directbandgap(eV)
Temperature (K)
Eg
(T) = Eg
(0) - AT2
/(B+T)
Eg
(0) = 1.687 eV
A = 0.411meV/K
B = 106 K
CuSbS2: T dependent direct band gap

24. Temperature dependence
L7
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

25. Temp. effects on solar cells
L7
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)

26. Low T absorption and DFT
L7
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)

27. 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

28. FTIR
L7
FTIR combined transmission and reflection for optical absorption

29. FTIR
L7
FTIR variable angle specular reflectivity for plasma and phonon measurements

30. Photoluminescence
L7
Photoluminescence can be powerful for investigating defect related transitions.

31. PL
L7
Photoluminescence of defect related transitions can be very complicated!.

32. Absorption
L7

33. Absorption
L7

34. CdS
L7
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

35. CdS
L7
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

36. CdS
L7
Martin Archibold, Durham PhD thesis (2007)
Reducing CdS layer thickness enables more high energy, short wavelength
photon to be harvested

37. CdS
L7
Martin Archibold, Durham PhD thesis (2007)

38. Indium nitride
L7
T. L. Tansley and C. P. Foley,
J. Appl. Phys. 59, 3241 (1986).
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

39. Indium nitride
L7
Figures from T. D. Veal (Ed.) Indium Nitride and Related Alloys (CRC Press, 2009)
Low energy
PL
observed in
2001 at
Ioffe

40. Indium nitride
L7
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?

41. Indium nitride
L7
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)

42. Indium nitride
L7

43. Indium nitride
L7

44. Indium nitride
L7

45. Indium nitride
L7
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.

46. Indium nitride
L7

47. Indium nitride
L7
Low density of localized states dominate low temp PL
Absorption edge is determined by high density of band states

48. Summary
L7
• 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
• 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.

49. L7