the opto-electronic physics that just broke the efficiency ... - … · solar energy mini-series...

Owen D. Miller & Eli Yablonovitch

UC Berkeley

Electrical Engineering & Computer Sciences Dept.

http://arxiv.org/abs/1106.1603

Solar Energy Mini-Series

Jen-Hsun Huang Engineering Center

Stanford, California

Sept. 26, 2011

The Opto-Electronic Physics That Just Broke

the Efficiency Record in Solar Cells

Cost per peak Watt for Solar Panels

Date

$10

$1

$0.30

X

X

1981 2011 2020

40GW installed cumulative

1TW installed

cumulative

subsidies will no

longer be needed

Year

From Allen Barnett

Univ. of Delaware

Value of High Photovoltaic Efficiency

Efficiency and Cost of Electricity (COE) inversely related:

OperatingFinanceEfficiencyInsolation

)Cost(CostCOE BOSmodule

Factors that impact COE:

Location: decides the available

input energy

Efficiency: decides the portion

that can be converted to

electricity

5% 8% 12%

18%

27%

40%

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800 900 1000

Cost of Photovoltaics ($/m2)

Co

st

of

Ele

tric

ity

(¢

/kW

h)

9

$

CdTe 11% Efficiency

$

c-Si 23% Efficiency

1. Why the pn junction is merely optional in solar

cells?

2. What determines the voltage of a solar cell?

3. What is the statistical mechanical approach to

optics that is needed in solar cells?

4. Are photonic crystals of any help toward solar

cells?

5. What are the top competing technologies?

6. What is the status of the industry today?

What is a Solar Cell?

A Solar Cell does not require a p-n junction!

E

EFn

EFp

V

h

e-

e-

e- e

-

e-

e-

h+

h+

h+

h+ h

+ h+ h

+ Wider Bandgap

top, bottom

and sides

double hetero-structure Selective

electron

contact

Selective

hole

contact

k

+ -

-

+

e-

e- e-

h+

h+

h+

e-

Diffusion potential to contacts is typically <1mVolt.

What is a Selective Contact?

It passes one type of carrier but not the other.

Most Ohmic electrical contacts barely work on even one type of carrier.

Therefore they are almost all selective.

The ideal type of selective contact is a hetero-contact:

e-

EC

EV

EFn

E

EF

semiconductor metal

EFp

EC

EV

EFn

E

EF

semiconductor metal

EFp

electron contact: hole contact:

Solar Cell as a Bucket feeding a Water Wheel

rainfall incident sunlight

sidewall leakage

surface recombination

bottom leakage

bulk recombination

pressure head voltage

water flow current

water wheel output solar cell power

sidewall leakage

surface recombination

power flow pressure

There are three things to know about Solar Cells:

1.Short Circuit Current

2.Open Circuit Voltage

3.Fill Factor

Open valve Low-pressure, high-flow

Closed valve High-pressure, low-flow

Partially restricted valve Optimal pressureflow

Three possible valve conditions

(Water wheel barely turns) (Max water wheel output) (Water wheel doesn’t turn)

Fill-Factor =

ratio of

these

two

rectangles

Fill-Factor is more a thermodynamic

property, rather than a circuit property.

Ideal Fill-Factor ~ 89%

What is the current to expect?

Absorb all the incoming light, in as thin a layer as

possible.

A direct bandgap uses less material than an indirect

bandgap

h

h

Solar Cell:

light trapping:

path length increased by 4n2=50

where n = refractive index

semi-

conductor

semiconductor

single pass only

h

h

Solar Cell:

light trapping:

path length increased by 4n2=50

where n = refractive index

semi-

conductor

semiconductor

single pass only

h

h

h

Light Emitting Diode:

semi-

conductor

semiconductor

only 1/4n2 = 1/50 = 2%

of the light escapes.

all the light eventually escapes.

Non-Ergodic Shapes:

h sphere

h

rectangle

h parallel ogram

Most of the internal light

can never escape

Ergodic Shapes:

h

h

ellipse

trapezoid

All the internal light

eventually escapes

3

2

c

8π

Density of

Optical Modes

per Unit Volume

in air

3

22

c

n8π

Density of

Optical Modes

per Unit Volume

in semiconductor

What is the ratio? …… n2

There is a factor 2 from double pass

and

There is a factor 2 from cos averaging

The net benefit is 4n2

Light Trapping Requirement:

1. Either the high index material has to be textured,

or the photon recycling should be very efficient.

The Benefit:

a. 4n2 ~50 times thinner layer can be sufficient to absorb the

sunlight saving semiconductor cost.

b. In a thinner cell, there is less series resistance, and a

higher Fill Factor

c. The operating point voltage, (not just Voc), increases by

kT ln{4n2} ~ 0.1Volts.

Total Internal Reflection is completely compatible

with an Anti-Reflection Coating.

semiconductor layer

A randomly rough surface does approach

the statistical mechanical limit,

regardless what angle the light is coming in on.

h h

h

h

h

Can a photonic crystal patterned surface do better

than a randomly rough surface?

What is the operating voltage?

e-

e-

e- e

-

e-

e-

h+

h+

h+

h+ h

+ h+ h

+

+ -

To extract current, voltage at contacts must be slightly lower than Voc

But, operating voltage linked directly to Voc

kT

qV

q

kTVV OC

OCOP ln

We only need to understand the open-circuit voltage

What is the ideal voltage Voc to expect, i.e. the Quasi-Fermi

Level separation, chemical potential, or Free Energy?

In molecules and quantum dots:

qVoc=Free energy = kT ln

In semiconductors with mobile electrons & holes:

Free energy = EFc-EFv=2kT ln

darktheinpopulationstateexcited

lighttheinpopulationstateexcited

darktheindensityelectron

lighttheindensityelectron

darktheinpopulationstateexcited

lighttheinpopulationstateexcited

kT

EnergyFreeexp

Boltzmann Factor

What is the voltage to expect, i.e. the Quasi-Fermi

Level separation, chemical potential, or Free Energy?

Shockley-Queisser Limit (1961):

qVoc = kT ln

But in quasi-equilibrium:

qVoc = kT ln

darktheinemissionbandtoband

sunlightincoming


emissionnt Luminesceexternal

qV =

Eg – kT{ln(/s) + ln(4n2) + ln(qVop/kT) –ln()-ln }

operating

point

Photon Free Energy = h - TS

Photon Free Energy = h - kT lnW

Yes photons have entropy, S

where s is the solid angle subtended by the sun

Entropy due

to loss of

directivity

information

Entropy

due to

incomplete

light

trapping

Free energy

loss due to

power-point

optimization

-0.28eV -0.1eV -0.1eV -0.0-0.3eV

Free energy

loss due to

poor

Quantum

Efficiency

nicest treatment:

R.T.Ross "Some Thermodynamics of PhotoChemical Systems", J. Chem. Phys. 46, 44590 (1967)

s

2

s

g

T

T

kT

E

+0.02eV

optical

mode

density

correction

qV =1.1eV – 0.8eV = 0.3eV operating

point

Small bandgaps are particularly vulnerable to entropy:

After you subtract off all the entropy terms, you don't

have much Free Energy left.

A lousy 0.3eV from all those big photons

In general we cannot afford to compromise with regard

to quantum efficiency.

no

rmal

so

lar

cel

ls

new

p

hys

ics

efficiency %

high performing cells

~25%

33.5% Shockley-Queisser limit (single-junction)

0%

Solar

radiation

Outgoing

luminescence

In an ideal solar cell, at open-circuit,

the outgoing luminescence will equal the incoming solar radiation

What did Shockley-Queisser say?

Any absorber also has to be an emitter!

At the open-circuit condition the electrons & holes

have no place to go.

They build up, and ideally they are lost only to luminescence.

h

h

semi-

conductor

only 1/4n2 = 1/50 = 2%


What if the material is not ideal, and the electrons and

holes are lost to heat before they can luminesce?

qVoc = qVoc-ideal – kT|ln{ext}|

The external

fluorescence yield ext is what matters!

Only external

Luminescence can balance

the incoming radiation.

no

rmal

so

lar

cel

ls

new

p

hys

ics

efficiency %

high performing cells

~25%

33.5% Shockley-Queisser limit (single-junction)

0%

(a)

e-

h+

h h h

(b) h h h hg hg

hg

e-

h+

h

h

semi-

conductor

only 1/4n2 = 1/50 = 2%


You may need an internal efficiency of int=99%

just to get an external efficiency of ext=50%

h

h

semi-

conductor

only 1/4n2 = 1/50 = 2%


Another way to look at this,

1. the recycled photons are not lost,

2. the carrier lifetime increases,

3. increasing carrier density

4. Increasing Voc

h

h

semi-

conductor

only 1/4n2 = 1/50 = 2%


But this is really hard to do:

You may need an internal efficiency of int=99%

just to get an external efficiency of ext=50%

0 0.2 0.4 0.6 0.8 1 24

27

33

Cel

l Eff

icie

ncy

(%

)

0 0.2 0.4 0.6 0.8 1

1.15

Vo

c (V

) 1.05

0.95

0.85

31.2%

33.2%

30.6%

1.061 1.081

1.145

Internal Fluorescence Yield


30

32.5mA/cm2

0 0.2 0.4 0.6 0.8 1


Jsc

( m

A/c

m2)

Efficiency vs. Internal Fluorescence Yield, GaAs 3m

90% Internal

Fluorescence Yield Is Not

Enough!

0 0.2 0.4 0.6 0.8 1 30.5

Reflectivity

Cel

l Eff

icie

ncy

(%

)

0 0.2 0.4 0.6 0.8 1

1.16

Reflectivity

Vo

c (V

olt

s)

1.14

1.12

1.10

1.08

1.06

Reflectivity 0 0.2 0.4 0.6 0.8 1

Jsc

(mA

/cm

2)

32

32.2

32.2%

33.2%

31.9%

1.104 1.115

1.145

32.43 32.46

32.50

31.5

32.5

33.5

32.4

32.6

Efficiency vs. Rear Reflectivity, GaAs 3m

90% Rear

Reflectivity Is Not

Enough!

Solar Cell Efficiency Limits for int < 1

Bandgap (eV) 0 0.5 1 1.5 2

5

10

15

20

25

30

35 So

lar

Cel

l Eff

icie

ncy

33.4% 31.0%

4%

int=100%

int=80% int=90%

Bandgap (eV)

0 0.5 1 1.5 2

Op

en-c

ircu

it V

olt

age

(V)

0.4

0.8

1.2

1.6 70 mV 20 mV

Textured good mirror Untextured good mirror Untextured bad mirror

Thickness 500nm 1 m 10m 500nm 1m 10m 500nm 1m 10m

Voc (volts) 1.14 1.13 1.12 1.16 1.15 1.14 1.08 1.08 1.07

Jsc (mA) 32.3 32.7 33.5 29.5 31.6 32.8 25.2 29.5 32.6

Fill Factor 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.89

efficiency % 32.8 33.1 33.4 30.6 32.6 33.3 24.3 28.3 30.9

Textured front

surface,

perfectly

reflecting mirror

Planar front

surface,

perfectly

reflecting mirror

Planar front

surface,

absorbing mirror

24

26

28

30

32

34

0.8 1 1.2 1.4 1.6

GaAs

33.5%

26.4%

Theory

Previous Record (2010) Voc=1.03V

GaAs, theory & expt.

25.1% record (1990- 2007)

~30%

Alta Devices 28.3% Voc=1.11V (2011)

32.1mA

Incoming light

External emission 0.04mA

Auger 710-6mA

Internal luminescence 5.40mA

Reabsorption 5.36mA Extracted

current 31.3mA

Planar, good mirror efficiency = 33.2%

efficiency = 30.6%

Planar, bad mirror

Mirror Loss 0.79mA

32.5mA

Incoming light

External emission 0.79mA

Auger 410-4mA

Extracted current 31.7mA

Mirror Loss 0mA

In both cases, you lose 0.76 mA. In the first case, that is luminescence out the top. In the second case, it is lost in the mirror. But the difference in external luminescence, and hence voltage, is significant.

Normalized for 1 cm2 area.

Internal luminescence 78.1mA

Reabsorption 77.3mA

For 3m thickness:

(a)

e-

h+

h h h

(b) h h h hg hg

hg

e-

h+

Internal Fluorescence Yield int >> 90%

Rear reflectivity >> 90%

Both

needed for

good ext

Counter-Intuitively, to approach the

Shockley-Queisser Limit, you need to have

good external fluorescence yield ext !!

What is the voltage to expect, i.e. the Quasi-Fermi Level

separation, chemical potential, or Free Energy?

Shockley-Queisser Limit (1961):

qVoc = kT ln

But in quasi-equilibrium:

qVoc = kT ln

The external Luminescence intensity is a “Volt-meter”

into the solar cell.


sunlightincoming


emissionnt Luminesceexternal

For solar cells at 25%,

good electron-hole transport is already a given.

Further improvements of efficiency above 25%

are all about the photon management!

A good solar cell has to be a good LED!

Counter-intuitively, the solar cell performs best

when there is

maximum external fluorescence yield ext.

http://arxiv.org/abs/1106.1603

p-Al0.2Ga0.8As

n-GaAs Eg=1.4eV

n-Al0.5In0.5P

n+-Al0.5In0.5P Eg~2.35eV

p+-Al0.5In0.5P Eg~2.35eV

p-Ga0.5In0.5P Eg~1.9eV

n-Al0.5In0.5P Eg~2.35eV

n-Ga0.5In0.5P Eg~1.9eV

Tunnel

Contact

GaAs

VOC=1.1V

Solar Cell p-GaAs Eg=1.4eV

Ga0.5In0.5P

VOC=1.5V

Solar Cell

Tunnel

Contact

GaAs

VOC=1.1V

Solar Cell

Ga0.5In0.5P

VOC=1.5V

Solar Cell

Dual Junction Series-Connected Tandem Solar Cell

h h

All Lattice-Matched ~34% efficiency should be possible.

p-Al0.2Ga0.8As

n-GaAs Eg=1.4eV

n-Al0.5In0.5P

n+-Al0.5In0.5P Eg~2.35eV

p+-Al0.5In0.5P Eg~2.35eV

n-Al0.5In0.5P Eg~2.35eV

Tunnel

Contact

p-GaAs Eg=1.4eV

Wide

Bandgap

VOC>1.5V

Tunnel

Contact

Wide

Bandgap

VOC>1.5V

There is much latitude for creativity in the higher

bandgap—nano-particles; nano-rods, etc.

h h

p-Al0.5In0.5P Eg~2.35eV

GaAs

VOC=1.1V

Solar Cell

GaAs

VOC=1.1V

Solar Cell

>35% efficiency

should be possible.

GaAs solar cells are the preferred technology,

where cost is no objection: Space

The Epitaxial Liftoff Process:

5. What are the top competing technologies?

a. c-Si ~ 15%-23% in production

90% market share

b. poly-CuInGaSe2 ~ 13% promised

~100 Start-Ups

c. poly-CdTe ~ 11% in production

First Solar Corp.

d. flat-plate GaAs ~ 28.3% in R&D

Alta Devices Inc.

e. Concentrators ~ 43.5% in R&D

triple-junction III-V Solar Junction Inc.

the opto-electronic physics that just broke the efficiency ... - … · solar energy mini-series...

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