Lecture 6 Optical Characterization of Inorganic Semiconductors · 2018. 10. 30. · Optical absorption L6 J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc.,

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?


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


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



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)



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.)



)(

)()( 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)



)(

)()()(

pg

ea

EEh

hhh

n

nnn

Both phonon emission and absorption are possible for hv > Eg +Ep, so the absorption

coefficient is given by


Absorption spectrometersL6

Two types of spectrometer are used for absorption: Fourier Transform infrared (FTIR)

UV-vis-near IR spectrophotometer


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


from d, T and R?

reflection/transmission spectroscopy


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...


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.


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)





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


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.


CuSbS2: absorption indirect band gap


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


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


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


Reducing CdS layer thickness enables more high energy, short wavelength

photon to be harvested

CdSL6


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.

Documents

Lecture 6 Optical Characterization of Inorganic Semiconductors · 2018. 10. 30. · Optical absorption L6 J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc.,