Optical Characterization of Inorganic Semiconductors

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

Lecture OutlineL7

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

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?

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

Shockley – Queisser efficiency limit

L M Peter

Optical absorptionL7

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 absorptionL7

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 absorptionL7

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 absorptionL7

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 absorptionL7

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 absorptionL7

Absorption spectrometersL7

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

UV-vis-near IR spectrophotometer

SnS2 optical absorptionL7

L. Burton, T. D. Veal, A. Walsh, et al., submitted to J. Mater. Chem. A

SnS2 optical absorptionL7

SnS2 optical absorptionL7

Temperature dependenceL7

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

TETE

gg

2

)0()(

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

Ab

so

rptio

n c

oe

ffic

ien

t (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: T dependent absorption spectra

1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1

104

105

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

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.90.0

2.0x104

4.0x104

6.0x104

8.0x104

1.0x105

1.2x105

Absorp

tion c

oeffic

ient (c

m-1)

Photon energy (eV)

4 K

CuSbS2: absorption indirect band gap

α=A(hν-Eg)2

Eg = 1.56 eV

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.90.0

2.0x104

4.0x104

6.0x104

8.0x104

1.0x105

1.2x105

Ab

so

rption

coe

ffic

ien

t (c

m-1)

Photon energy (eV)

4 K

CuSbS2: absorption direct band gap

α=A(hν-Eg)1/2

Eg = 1.69 eV

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 dependenceL7

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 cellsL7

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)

Low T absorption and DFTL7

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

FTIRL7

FTIR combined transmission and reflection for optical absorption

FTIRL7

FTIR variable angle specular reflectivity for plasma and phonon measurements

PhotoluminescenceL7

Photoluminescence can be powerful for investigating defect related transitions.

PLL7

Photoluminescence of defect related transitions can be very complicated!.

AbsorptionL7

AbsorptionL7

CdSL7

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

CdSL7

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

CdSL7

Martin Archibold, Durham PhD thesis (2007)

Reducing CdS layer thickness enables more high energy, short wavelength

photon to be harvested

CdSL7

Martin Archibold, Durham PhD thesis (2007)

Indium nitrideL7

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

Indium nitrideL7

Figures from T. D. Veal (Ed.) Indium Nitride and Related Alloys (CRC Press, 2009)

Low energy

PL

observed in

2001 at

Ioffe

Indium nitrideL7

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?

Indium nitrideL7

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)

Indium nitrideL7

Indium nitrideL7

Indium nitrideL7

Indium nitrideL7

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.

Indium nitrideL7

Indium nitrideL7

Low density of localized states dominate low temp PL

Absorption edge is determined by high density of band states

SummaryL7

• 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.

L7