Solar -...

Aug 2014

Solar ….

Clas Persson

Dept of Physics, University of Oslo, P.Box 1048 Blindern, NO-0316 Oslo, Norway

Dept of Materials Science and Engineering, Royal Inst of Technology, SE-100 44 Stockholm, Sweden

Why do we need solar energy ?

Different types of solar cells technologies

Materials for solar cells

Outline

Computational details

DFT LDA/GGA DFT/HSE GW BSE

CBM

VBM

Eg 0

exc

r-s

pace

k

-space

DFT ground state 2-particle excitation 1-particle excitation

electron

ħѡ ħѡ c;k c;k

c;k+q

exciton

ħѡ ħѡ

v;k-q v;k

c;k+q c;k

ħѡ ħѡ

v;k-q

v;k v;k

hole

Etot

ρ(r)




Outline

World Energy Consumption

~3 kW / person

2008 2050 .

People: 6-7 bil 12 bil

Energy: 15 TW 30 TW

What is Watt ? We will need ~30 TW in 2050

1 W 1 kW 1 MW 1 GW 1 TW

100 103 106 109 1012

Nuclear

reactor 20 hp ~15 kW e-car

1 kW array

~30 W

40 TW

Power of a human body

1 W 1 kW 1 MW 1 GW 1 TW

100 103 106 109 1012

100 - 800 W

30 W

10 x Boeing 747

.. each 0.1 GW

Nuclear

reactor

Can we use only nuclear power ??

We will need ~30 TW in 2050

1 nuclear

reactor

~1 GW I reactor ~1 GW

~30,000 nuclear reactors

(today ~450 reactors)

..... 2 new reactors every day over 40y !!

Different alternatives

Energy in TW

Year

Renewable wind, water, solar

ranium

CO2;

res: 50-150 y

Radioactive;

res: 50-100 y

We will need ~30 TW in 2050 E

nerg

y

(TW

)

today

2050, ~30TW

Different alternatives

Energy in TW

Year

Renewable wind, water, solar

ranium

CO2

50-150 y

radioactive

50-100 y

We will need ~30 TW in 2050 E

nerg

y

(TW

)

today (max) .

Hydro: 0.8 TW (3 TW)

Wind: 0.15 TW (5-70 TW)

Geo-ther: 0.03 TW (0.1-2 TW)

Solar: 0.1 TW (50,000 TW)

today

Solar power is ~100,000 TW

Over 100,000 TW incoming sun-light

Thus, we need 30/100,000 ≈ 0.03% of this sun-light

Required land area

Six power plants can cover our need:

500 x 500 km2 each

Problem is distribution, losses and storage

Average sunlight power:

~1 kW/m2

3 types of solar-energy technologies

1. Solar-thermal heat water

2. Solar-chemical

H2 from split of water

3. Solar-electricity

photovoltaics

or solar cells

Power tower in California: 10 MW Steam engine

mimic photo-catalyst reaction

~5 kW roof top system

http://lumbergusa.com/main/Bild/sp_pv_07/Brandis-Waldpolenz-Fotomont.jpg

Waldpolenz Solar Park in Germany ~52 MW

we have to build much

bigger power plants ~30 TW ~ 1 million of these

In operation 2008

€180 million

Advantage with solar cells

Much energy generation

will however be from

local recources

What we need

Sunlight power: ~1 kW/m2

Each person needs ~3 kW ~3 m2

In addition, we need

energy storage, ie, batteries !

Some slides about PV market today

3rd generation solar cells Martin Green, 3rd Generation PV,

Springer-Verlag, Berlin, (2003).

• Material cost

• Handling

• Processing

• Fabrication

• Packing

• Installation

• Efficiency

• Thinner (lower material costs)

• Crystal and device stability

=> better lifetime

(cost to replace)

With plenty of innovation still occurring in crystalline silicon PV manufacturing -- including new sawing techniques,

thinner wafers, conductive adhesives, and frameless modules -- companies are able to squeeze more pennies off the

cost of each panel. However, as the chart above shows, innovating "outside the module" to reduce the installed cost

of solar will be increasingly important as companies find it harder to realize cost reductions in manufacturing. Stephen Lacey, GreenTechMedia, Feb 3013, GTM Research's Global Intelligence PV Tracker:

Mainly due to

lower cost of Si

.. dumping prices

Now, installation

as is important

50 cent/W

We need 30 TW effect in 2050.

Thus 25 more PV installations/year

In 2013, capacity of ~140 GW

I

~40 GW/year

~25% in Europe (75% in 2011)

Evolution of global PV cumulative installed capacity 2000-2013

Solar cell, Basic physics

1839: French physicist A. E. Becquerel first recognized photovoltaic effect.

1883: First solar cell built, by Charles Fritts,

Au-coated semiconductor selenium.

1941: First silicon-based solar cell demonstrated, by Russell Ohl (>70y ago)

2014: Many solar-cell types, but crystalline Si is still dominating (80% market)

History PV = Photo+voltaic = convert light to electricity

sun

light

λ ~ 0.8 μm

E ~ 1.5 eV

λ ~ 0.5 μm

E ~ 2.5 eV

λ ~ 0.35 μm

E ~ 3.5 eV

Sun Light: Photon energies

Spectrum from sun

1.5 eV

3.5 eV

light particles = photons

Most photons have energy

1.0 < hv < 3.5 eV

Solar Cell: Absorption

Black-body concept

e

e

EinEout

e ee

e

Photon absorbed

Energy to electron

Black-body concept

e

e

EinEout

e ee

e

Photon absorbed

Energy to electron

HOMO

LUMO

VBM

CBM

VBs

CBs

Eg ~ 1.3 eV

k =

crystal momentum

E(k)

1.0 to 3.5 eV

sunlight spetrum

q ~ 0

e

e

Ein Eout

e e e

e

Photon absorbed

Energy to electron

e

How to transport out the electrons ??

1.3 eV bond

E

1) Internal electric field E(x)

2) Diffusion through electron density dn/dx

3) Diffusion through temperature (hot electrons) dT/dx

Solar Cell: Transport




Outline

AW Bett ,Fraunhofer Inst, Freiburg

1. crystalline Si (n 30%)

2. Thin-film solar cell (~20%)

3. Multi-junction solar cells (~40%)

4. Dye-sensitized solar cells (~10%)

Polymer solar cells

Nanocrystal solar cells

Man Solar, Petten

Nanostructure Materials &

Devices Laboratory, USC

SANYO, Amorton

CGS

S. Schuler, et al. 29th IEEE

PV Conf.(2002)

combinations of

#1 Crystalline Si

V

sun

light

200 μm

Si Eb ~ 1.1 eV

p-type Si

n-type Si

thick

device

Transport via pn-junctions

• Good efficiency (25 %)

• Expensive since thick device

~80% of solar cell market

Sun light λ~0.5 μm

Hair ~75 μm

Anti-reflecting &

Cover glass

Back

contact

http://upload.wikimedia.org/wikipedia/en/d/d7/Silicon_Solar_cell_structure_and_mechanism.svg

#1 Crystalline Si (pn-junction)

n-type p-type

EF

CBM

VBM

Eg

E

T >> 0

V = 0

n p

V= 0

i(hgen)

i(hrec)

i(egen)

i(erec)

i(egen) due to E-field

i(erec) due to entropy (dn/dx)

n-type p-type

EF,c

CBM

VBM

E

T >> 0

V > 0

illumination

n p

V> 0

i(hgen)

i(hrec)

i(egen)

i(erec)

i(egen) due to E-field

i(erec) due to entropy (dn/dx)

i(eph) from light absorption

P = V I, Vmp ~ 0.7Eg

qV

#1 Crystalline Si

Two main problemd with c-Si

1) 200 mm thick, much material. Si is costly to produce

2) Eg = 1.1 eV; large thermalization losses

#2 Thin-film Si

a-Si (or a-Si:Hi); amorphous silicon,

Low processing temperature (loser cost)

Eg = 1.7 eV, better absorber => thinner cell (~1 mm thick)

But much less efficiency compared to c-Si

nc-Si (microcrystalline Si)

Low processing temperature, Eg = 1.1 eV

Improved material quality over a-Si

1.8 mm thick, 10.7% efficiency (EPFL Inst of Microengin., Feb 2013)

a-Si + nc-Si; micromorphous

higher open-voltage

Eg = 1.1 and 1.7 eV

=> broader abs. spectrum

NorSun and Sunfilm; C: Rohr 2008

#1 Plasmonic solar cells (thin film)

a-Si, coated with metal nanoparticles

1-2 mm thick,

dissadvantage is low absorption

and heat generation

Light scatters through surface plasmon resonance, and get

trapped inside a-Si layer. >90% of light can be trapped.

Different NPs

anti-reflcting/coating

dielectric coating

thin-film a-Si:H

metal reflector

Metal NP

dielectric coating

(a) (b)

1-2 μm

#2 Other thin-film pn-junction

1 kW array

NREL, USA

a-Si Eg ~ 1.7 eV

CdTe (toxic) Eg ~ 1.5 eV

GaAs (expensive) Eg ~ 1.5 eV

CuIn1-xGaxSe2 Eg ~ 1.3 eV

Cu2ZnSn(S1-xSex)4 Eg ~ 1.3 eV

Ångström Solar Center, Uppsala Univ

0.5 mm

~0.5 mm

~1.5 mm

~0.3 mm ~50 nm

sun

light

V

n-type

p-type

Transport via pn-junction

• Good efficiency (20 %)

• Medium expensive

• Long life-time

Sun light λ~0.5 μm

One problem with one-band solar cells

Single-junction efficiency:

Theo. max ~31%

Thermalization losses

Below-Eg losses

V

sun

light

n-type

p-type

Eg =1.3 eV

Sunlight Spectra

~350 to 1000 nm

~3.5 to 1.0 eV

550 nm ~ 2.2 eV

Solar Cell: Efficiency, ideal PV cell

Black-body concept

e

e

EinEout

e ee

e

Photon absorbed

Energy to electron

Black-body concept

e

e

EinEout

e ee

e

Photon absorbed

Energy to electron

L. C. Hirst and N. J. Ekins-Daukes.

Dept of Physics, Imperial College

London

Single-junction,

single parabolic CB and VB.

n = 31 %

Eg(max) = 1.32 eV

Band gap Eg (eV)

Effic

iency

Single-junction efficiency:

Theo. max ~31%

With concentrators

Theo. max ~42%

V

sun

light

n-type

p-type

Solar cell

Lens

To concentrate

Extra cost

Does not address the

issue with thermal loss.

Increases Temperature

Use in TE, or

passive cooling heat sinc or TE

Concentrators

NREL home page

#3 Thin-film multi-junction (40%)

Ga-based 0.7< Eb < 2.0 eV

High efficiency, up to ~45%

but expensive

pn-junction #1: E > 2.0 eV



V

sun

light

Transport via pn-junctions

• High efficiency (40 %)

• Expensive

• Lattice matching

Multi-junction cell, GaAs-based

52% efficiency in 2013 for 3-junction cell

Marina S. Leite, et al. APL, 102, 033901 (2013)

Theoretical limit

31 % for single junction.

50% for 2-junction,

56% for 3-junction,

86% for infinite-junction

Nature Photonics 6, 146 (2012)

Thin-film intermediate band (future)

V

sun

light

• n ~ 47% (theo), instead of ~31% for single gap cell

• low absorption in QD,

• Extra non-radiative recomb

• difficult to realize a half-filled band wi no

tunneling, and ackummulation in IB

• Band (not defect level) to avoid SRH-recomb.

Luque and Martí, PRL 78, 5014 (1997)

Single-junction, but IB helps

absorbing different energies

Optimum: Eg = 0.7, 1.2, and 2.0 eV

qV

ZnTe:O 50% increase in power conversion efficiency Wang et. al, APL 95, 011103 (2009)

SEM: mesoporous anatase TiO2

M. Grätzel, Nature, 414, 338 (2001).

50 nm

#4. Dye-sensitized solar cell (O'Regan and Grätzel, 1991)

glass

V

back contact = cathode

sun

light

dye film (Ruthenium-based) good absorber

NP-TiO2

transparent and

good e– conductor,

through diffusion

electrolyte iodine ions

3 I– I– 3

Transport via electrolyte

• Inexpensive,

• slow diffusion in NP-TiO2

• Reasonable efficiency (15 %)

• Degradation and instability

e

sensitizing

dye

TiO2

NP/porous

EF

electrolyte

iodine/triiodide

I3–

Voc ~ 0.8 eV

3 I–

electrode cathode

redox

diffusion

-5.3

-4.9

-3.6

1.7 -4.1

Energy (eV)

w.r.t vacuum

3I– /

I3–

#4 Organic solar cells

Polymers (donor) Easy to vary gap 1-4 eV, good e-conductor;

Localizes e and h.

Absorb, confine, and transport e-h excitons

Fullerene (acceptor) Dissocioation, good e-conductor

SEM images of MDMO-PPV/PCBM

Mozer, CR Chimie, 9, 568 (2006).

Transport via diffusion

e-h diffusion lenght ~10nm

(needs 100nm for absorption)

• Inexpensive

• Low efficiency (8 %)

• Degradation and instability

InSnO

glass

V

back contact = cathode (Al)

sun

light ITO / TiO2

transparent and

good e– conductor

50 nm

Polymers p-type like

hole/polaron mediator

diffusion

Voc ~ 1.0 eV

ITO

InSnO

catode Fullerene n-type like

electron acceptor

exciton

-3.6

SnO2

Energy (eV)

w.r.t vacuum

-4.7 -4.9

-2.6

-6.1

-3.6 -3.7 (Mg)

2.3

Lab Results vs Module Efficiency

A. Saengprajak, Kasel Univ Press

also Wikepedia

Band engineering

1.3 eV



Materials for pn-junction solar cells

Outline

Material Properties

What properties do we want (for most solar cells)?

• High absorption in 1.0 < hv < 3.5 eV Eg > 1 eV

• High carrier mobility

• High crystal stability (long lifetime)

• No deep-level in-gap defects

• Dopability (n- and/or p-type)

Material Properties #2

… in addition,

• Earth abundant elements

• non-toxic elements

• inexpensive elements

• Inexpensive fabrication, handling, etc, etc,

VBs

CBs

k =

crystal momentum

E(k)

Radiative recombination is less

problem. It can be absorbed again.

But, yes, loss of energy.

Thermalization loss.

Electron kinetic loss.

Below Eg loss for photons

with hv < Eg

Material Properties: High absorption

Find mater with good Eg

Si: 1.1 eV

a-Si: 1.7 eV

GaAs: 1.5 eV

CdTe: 1.7 eV

CuInGaSe2: 1.0–1.7 eV

VBs

k

E(k)

Material Properties: High absorption

High joint DOS -2 < E < 3 eV

Many bands

Flat bands

Joint density of states

E

0.0

-2.0

2.0

1.0 d-states are normally

localized in energy

q ~ 0

* Direct band gaps (q ~ 0)

* Good having CBM/VBM a BZ edge

instead of at G-point, => higher JDOS

joint DOS describes

DOS for direct transitions

VBs

k

E(k)

Material Properties: High mobility ??

Flat band large mass

E

0.0

-2.0

2.0

1.0

m* ~ 1 / d2E/dk2

Joint DOS

VBs

k

E(k)

Material Properties: High absorp. & mobility

Small mass for minority carrier

That is, for n-type:

CB should have strong curvature (lower absorp)

But OK with flat VBs

E

0.0

-2.0

2.0

1.0

small effective mass:

m* ~ 1 / d2E/dk2

p-type: hole access

Less critical mobility

Joint DOS

flat 2nd band

VBs

k

E(k)

Material Properties: High absorp. & mobility

Maybe s-like state

E

0.0

2.0

1.0

G

Ec = CBM

Ev = VBM Eg~1.0

va

len

ce b

an

ds

con

du

ctio

n b

an

ds

CIGSe is actually close

to this picture

d-states form flat bands.

Cu-d in CIGSe (Ag, Au)

Cu(InGa)Se2

Cu(InGa)Se2 is today commercialized

1 kW array

NREL, USA

CISe = CuInSe2

CGSe = CuGaSe2

CIGSe = CuIn1-xGaxSe2

~ CIGSe ~ CIGS

iso-valent

elements

Cu

Se

In,Ga

Si

Si

Si

Zn

Se

Zn

diamond structure

e.g. group IV

Si, Ge, C

chalcopyrites

e.g. I-III-VI2

CuInSe2, AuAlO2

Ga

As

Ga

zinc-blende struct.

e.g. III-V and II-VI

GaAs, ZnSe

SiSi SiSi

4+4+4+4 =16

GaAs GaAs

3+5 +3+5 =16

ZnSe ZnSe

2+6 +2+6 =16

CuSe InSe

1+6 +3+6 =16

Ga

Mo

n-type

TCO

EF

K. Ottosson, Uppsala Univ 2006

p-type

CIGSe

pn-junction solar cell

absorber layer

pn junction

window layer

Mo

CdS n–

ZnO

CIGS p+ CIGSe

(220

)

Cross section SEM image

1mm

buffer layer

back contact

h+ e–

Mo

K. Ramanathan, et al. Prog. PV Res. Appl. 11, 225 (2003).

(1) Not better efficiency for high Ga content (x>0.30)

(2) Grain boundaries are harmless for the device !!!

(3) Best CIGSe material is Cu-poor ([VCu], [InCu] ~ 1%)

(4) polycrystalline, non-stoichiometric, ODP (eg CuIn3Se5)

(5) Extremely Cu-poor at surface/interfaces !!!

(6) CIGSe is typically p-type as grown !!!

(7) CISe can be n-type, but CGS cannot !!!

(8) Na at grain-boundaries is good for the device !!!

Puzzeling properties of CIGSe devices,

different from Si, GaAs and CdTe devices

Y. Yan, et.al, report,

NREL/CP-520-33615 (2003)

Defect phase

TEM image of

grain boundary

rockett.mse.uiuc.edu

X-SEM of grain boundary

Polycrystalline CIS

G

Eg ~1.7 eV

G

Ec = CBM

Ev = VBM Eg~1.0

va

len

ce b

an

ds

con

du

ctio

n b

an

ds

CISe and CGSe are direct band-gap semicond.

CISe = CuInSe2 CGSe = CuGaSe2

Solar cells need direct-gap materials because photons has q ~ 0

Why is not solar-cell efficiency increasing for x > 30% ???

CIGSe band gap fits sun-light spectrum

VBM

CBM

0 0.5 1.0

CuInSe2 CuGaSe2

1.0 eV

1.7 eV

Composition x

Today best

composition

~30% Ga

Best theoretical

composition

~50% Ga ??

CuIn1-xGaxSe2

sun-light spectrum

Eg

Gradient of band profile

Energyband diagram

M n-type p-type PV cell structure

z pn - junction z

E

pn - junction (open voltage)

EC

EV

EF

1.5 eV 1.0 eV

CuIn1-xGaxSe2

Electronic band-edge structure

CuInSe2

CuGaSe2

CIGSe =

CuIn0.5Ga0.5Se2

blue circles show fitted band structure

Persson, et al PRB 64, 033201 (2001)

Chen and Persson, Thin Solid Films 519, 7503 (2011).

Similar CB as GaAs

(but more VBs)

We are interested in details

near CBM and V BM

GaAs

mc1 = (0.08-0.09)m0 in CuInSe2 from

Faraday rotaion by Weinert et al. Phys.Stat.Sol.b 81, K59 (1977).

Shubnikov-Haas oscillation data Arushanov et at. APL 61, 958 (1992).

|| .

mc1 = 0.13 0.13

|| .

mc1 = 0.08 0.09

CuGaSe2

D2d

(001) (110)

6

7

7

6

Cs C2v

4

3

4

4

3

3

3 5

5

5

5

Eg = 1.7 eV

Ener

gy

[eV

] D2d

(110) (001)

6

6

7

7

3

4

Cs C2v

3

3

3

4

4

4

Eg = 1.0 eV

Persson, Appl. Phys. Lett. 93, 072106 (2008).

Electron masses are small and isotropic

Comparable to GaAs

mc1 = 0.07m0

CuInSe2

CB mass

Expt: 0.8-0.9 m0

Christensen, PRB 30, 5753 (1984); Persson et al, PRB. 64, 033201 (2001); ibid 54, 10257 (1996)

zb-AlN: mhh(GK) = –253.1m0 +3.1m0 J.Cryst Growth 231, 397 (2001)

GaAs without SOC

VBM

S = (110) D = (100)

G1

G5

(100) (110) (111)

mc1 = 0.07 0.07 0.07

mhh = 0.41 2.70 0.94

mlh = 0.41 0.41 0.94

mso = 0.07 0.06 0.06

(100) (110) (111)

mc1 = 0.07 0.07 0.07

mhh = 0.38 0.70 0.92

mlh = 0.09 0.08 0.08

mso = 0.18 0.18 0.18

S2

D2+4

D1

S1

S1

S1 D1

GaAs with SOC

S = (110) D = (100)

VBM

G6

G8

G7 D5

D5

D5

D5

S4

S3

S3

S4 S4

S3

Hole masses depends on spin-orbit coupling (SOC)

hh-mass

lh-mass

so-mass

CB mass

Christensen, PRB 30, 5753 (1984); Persson et al, PRB. 64, 033201 (2001); ibid 54, 10257 (1996)

zb-AlN: mhh(GK) = –253.1m0 +3.1m0 J.Cryst Growth 231, 397 (2001)

GaAs without SOC

VBM

S = (110) D = (100)

G1

G5

(100) (110) (111)

mc1 = 0.07 0.07 0.07

mhh = 0.41 2.70 0.94

mlh = 0.41 0.41 0.94

mso = 0.07 0.06 0.06

(100) (110) (111)

mc1 = 0.07 0.07 0.07

mhh = 0.38 0.70 0.92

mlh = 0.09 0.08 0.08

mso = 0.18 0.18 0.18

S2

D2+4

D1

S1

S1

S1 D1

GaAs with SOC

S = (110) D = (100)

VBM

G6

G8

G7 D5

D5

D5

D5

S4

S3

S3

S4 S4

S3

Hole masses depends on spin-orbit coupling (SOC)

hh-mass

lh-mass

so-mass

CB mass

NOT a question of SOC strength !!

It is due to change of symmetry

Test: HSO : HSO / 100

DSO : DSO / 100

…..but masses do not change

k.p-method for fcc:

mhh,lh = me /(A √B2 + C2/5)

which is independent of DSO

GaAs LDA

VBM

GaAs GGA+U

S = (110) S = (110) D = (100) D = (100)

VBM

G6

G8

G7

(100) (110) (111)

mc1 = 0.01 0.01 0.01

mhh = 0.32 0.56 0.77

mlh = 0.01 0.02 0.02

mso = 0.08 0.08 0.08

(100) (110) (111)

mc1 = 0.07 0.07 0.07

mhh = 0.38 0.70 0.92

mlh = 0.09 0.08 0.08

mso = 0.18 0.18 0.18

G7

G6

G8

EXPT (100) (110) (111)

mc1 = 0.07 0.07 0.07

mhh = 0.35 0.64 0.89

mlh = 0.09 0.08 0.08

mso = 0.17 0.17 0.17

K K X X

LDA error of masses

Persson et al. Phys.Rev B 64, 033201 (2001)

hh-mass

lh-mass

so-mass

CB mass

Expt data

(cyclotron resonance)

Cu

Se

In

Zn

Se

Zn

zinc-blende struct.

e.g. III-V and II-VI

GaAs, ZnSe

chalcopyrites

e.g. I-III-IV2

CuInSe2, AuAlO2

ZnSe ZnSe

2+6 +2+6 =16

CuSe In Se

1+6 +3+6 =16

Kesterite and stannite

e.g. I2-II-IV-IV4

Cu2ZnSnSe4 , Au2ZnGeSe4

CuSe (Zn,Sn)Se

1+6 +(2+4)/2 +6 =16

CuInSe2 Cu2ZnSnSe4

Similar absorption of CIGS, CZTS, and CZTSe

Energy w.r.t band gap

Cu3BiS3

Cu

Bi S

Kumar and Persson (2013)

DOS Band structure

flat

Cu3BiS3

Kumar and Persson, (2013)


Absorption Absorption

Cu3BiS3

Kumar and Persson, (2013)

CuSbS2 and CuBiS2

Fig. 1. Crystal structure of CuMS2 (where M = Sb or Bi)

Showing a unit cell containing

16 atoms and composed of distorted square pyramidal MS5 (red) unit,

tetrahedral CuS4 (grey) unit and S atoms (yellow).

Cu Sb or Bi

S


CuSbS2 and CuBiS2

Band structure CuSbS2 Band structure CuBiS2

flat

flat



CuSbS2 and CuBiS2

Absorption Absorption


M n-type p-type

z

E

e ? E

pn - junction

h ?

z

E

e

E E

pn - junction (open voltage)

h +

Eg ~ 1.3 eV

EV

e

EF Shallow acceptors

to pin EF

At open voltage we will not discuss

operation of solar cell

EC

High absorb in 1 < hv < 3.5 eV

High electron mobility Shallow acceptors

to pin EF

z

EF

EV

EC

SRH-defect

E

e−E

pn-junction

h−surface-defect

z

EF

EV

EC

SRH-defect

E

e−EE

pn-junction

h−surface-defect

Many types Recombinations

Auger,

avalanche multiplication

Zener breakdown

Scattering processes

charged defects

neutral defects

carrier-carrier

interfacial scatt

deformation pot

phonons, plasmons

M n-type p-type

Control of defects

Material Properties: Formation energy

We want to calculate the energy it requires to form a defect.

This formation energy shall be small for wanted dopants

but large for unwanted defects.

With this energy, we estimate concentration via statistics: N ~ e –E/kBT

VCu

CuInSe2


dHf(VCu) = E(VCu) – E(0)

CuInSe2

System 2

~ total energy of system with defect, minus

total energy for system without defect

Two big supercells:

one with VCu,

one without

VCu

System 1

CuInSe2

not the full expression


dHf(VCu) = [ E(VCu) – T∙S(VCu) – P∙V(VCu)] – [E(0) – T∙S(0) – P∙V(0)]

CuInSe2

System 2

VCu

System 1

CuInSe2

Gibbs free energy:

E = Ecohesive = total energy from ground-state DFT.

S = entropy

V = volume

Still not the full expression


dHf(VCu) = [ E(VCu) – T∙S(VCu) – P∙V(VCu)] – [E(0) – T∙S(0) – P∙V(0)]

CuInSe2

System 2

Gibbs free energy:

E = Ecohesive = energy from ground-state DFT.

For low defect concentrations:

S(VCu) ~ S(0) and V(VCu) ~ V(0)

VCu

System 1

CuInSe2

True for BIG supercells

Challenge: using HSE ….


dHf(VCu) = E(VCu) – E(0)

CuInSe2

System 2

.. but here you compare two systems with diff number of atoms !!

VCu

System 1

CuInSe2

not the full expression

Calculate total energies.

Calculate chemical potential for Cu.

Challenge: What is chemical potential for Cu


dHf(VCu) = [ E(VCu) + nCu mCu ] – E(0)

Reservoir

Cu mCu

CuInSe2

System 2

single Cu atom, solid Cu compound, gas CuCl, etc. ??

VCu

System 1

CuInSe2

nCu = +1 for

moving Cu

to reservoir

CISe and CGSe

VCu ~ 0.7 + DmCu [eV]

ZnTe

VZn ~ 3.0 + DmZn [eV]

Persson, et al. PRB 72, 035211 (2005)

Laks, et al. PRB 45, 10965 (1992)

Cheocg, et al. PRB 51, 10610 (1995)

DH(a,q) = E(a,q) – Ehost

+ S na(Dma+masolid)

+ q(EVBM + EF)

CIGS na, q

Reservoir

EF, ma

Cation vacancy formation energies

High quality CIGS is Cu-poor: 23.5 – 24.5 at.% (not 25%)

Material Properties: Dopability

Because V(Cu) has so low formation energy in CuInSe2,

the defect is a native acceptor in p-type CuInSe2.

What is the ionization energy (= transition energy) of

V(Cu) as acceptor.

How much energy does it cost to ionize it ??

Has to be < 0.1 eV. VCu

dHf(VCu;q) = [ E(VCu;q) + ncu mCu + qEF ] – E(0)

Reservoir

Cu mCu

EF ~ me

dHf(VCu) = [ E(VCu) + ncu mCu ] – E(0)

neutral

charged

CuInSe2

System 2

VCu

System 1

CuInSe2

Cu mCu

EF ~ me VCu

System 1

CuInSe2



neutral

charged

CuInSe2

System 2

Reservoir

The transition energy can be defined as

the Fermi energy for which dHf(VCu;q) = dHf(VCu)


Reservoir

Cu mCu

EF ~ me


neutral

charged

CuInSe2

System 2

VCu

System 1

CuInSe2

The transition energy can be defined as

the Fermi energy for which dHf(VCu;q) = dHf(VCu)

0 = E(VCu;q) – E(VCu) + qEF EF = Ea = [E(VCu) – E(VCu;q)] / q

Material Properties: Transition energy

LDA

VCu

Expt

Zhang et al,

PRB, 57 9642 (1998).

Ea ~ 30 meV:

References in

Prog.Photovolt Res.Appl.

18, 390 (2010).

CuInSe2


LDA

VCu

HSE 06

VCu

Expt

Zhang et al,

PRB, 57 9642 (1998).

Ea ~ 30 meV:

Oikkonen et al.,

J.Phys.:Cond Matter,

23, 422202 (2011)

Ea ~ 0

References in


18, 390 (2010).

CuInSe2 CuInSe2

always

ionized


Single acceptor

neutral

acceptor

and its hole

acceptor state

schematic !!

Pure material

VCu

How do we calculate transition energy:


How do we calculate transition energy:

Comparing two rather different systems

Single acceptor

neutral (N)

Single acceptor

Ionized (N+1)

acceptor

and its hole

acceptor state

schematic !!

add one electron

to ionize acceptor

add + charge

in background

to artificially

neutralize system

Ionized

acceptor states

not excited

from VBM

Pure material

VCu VCu


LDA

VCu

HSE 06

VCu

Expt

Zhang et al,

PRB, 57 9642 (1998).

Ea ~ 30 meV:

Oikkonen et al.,

J.Phys.:Cond Matter,

23, 422202 (2011)

Ea ~ 0

References in


18, 390 (2010).

CuInSe2 CuInSe2

always

ionized

Can we rearch accuracy of 25 meV ???

Can we reach accuracy of 25 meV ???

Single acceptor

neutral

Single acceptor

ionized add one electron

to ionize acceptor

add + charge

in background

to artificially

neutralize system

Ionized

acceptor states

not excited

from VBM

VCu VCu

Two rather different systems.

What approach?

* HSE+VBW (Scheffler)

* HSE+vdW (Gao)

* OT-RSH functional (Kronik)

* HSE: small cells, k-points

band filling: 0.1-0.5 eV

Neutral dopants shall be

ionized for concentr. >0.01%

Total energy or excitation ?

Ramprasad PRL 108, 066404 (2012).

Gao, PRL 111, 045501 (2013).


Ea

30 meV

Acceptor concentration

1017 cm3 1018

Single ?? acceptor

neutral

VCu

Expt findings:

for shallow dopants

HSE-calc: concentration is ~1020 cm3

Band-gap narrowing J.Appl.Phys. 86, 4419 (1999)

n-type Si p-type Si

For Ea ~ 30 meV, MNM concentration

is about 1017–1018 cm-3

Band gap narrowing ~ 0.1 eV

Green’s function calculation, using

the full-band LAPW band structure

DEg DEg

DEgopt

Researchers / Students

Thank you for your attention !

I thank organizers for inviting me!

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