Performance Evaluation in Conventional and Rectenna Solar Cells

Sachit GroverDevice Physicist, First Solar, Inc.

Santa Clara, CA, USA

2006-20112011-20132013-20142015-present

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http://investor.firstsolar.com/releasedetail.cfm?ReleaseID=917926

http://www.nrel.gov/ncpv/images/efficiency_chart.jpg

Record efficiency: 18.6% aperture area efficiency (18.2% full area)

"At one time, we might have been characterized as a low cost, low efficiency technology, but consistent with our technology projections we are now proving that CdTe thin film delivers both industry-leading performance AND sustainable thin-film cost structures.“

-Raffi Garabedian, First Solar CTO

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PV Module technology & manufacturing

• 98-99% reduction insemiconductor material

— Direct bandgap material

• Fully integrated, continuous process vs. batch processing

• Large 60 x 120cm (2' x 4')superstrate vs. 6" wafers

First Solar Fully Integrated, Automated and Continuous Thin Film (CdTe) Process

Polysilicon Ingot Wafer Solar ModuleSolar Cell

Conventional Crystalline Silicon Batch Technology

Glass In < 2.5 Hours Module Out

Semiconductor Deposition

CellDefinition

Final Assembly & Test

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Superior Temperature Coefficient of CdTe yields more energy

• Temperate Climate Example:

— Module Temps often reach 65°C; 40°C

above the STC rating

— The silicon module power output will be reduced by up to 20% at this temperature

— FSLR output will be reduced by only 10%

• Hot Climate:

— More hours at higher temps (Module

temps can reach 85°C)

— FS Advantage grows more pronouncedVirtuani, 25th EUPVSEC, 2010

Combining suns-VOC and VOC(T) to quantify recombination in solar cells

Outline

• Derive theoretical dependence of VOC on

• Light intensity

• Temperature

• Strength of recombination channels

• Apply formulation to

• Quantify recombination in different regions of the cell

• Extract material and interface quality

Grover et. al., APL, 103, 093502, 2013

9/17/2015 Grover @ UNSW 7

Express VOC in terms of SRH recombination in different regions

Quantitative estimate of (microscopic) recombination from conventional (macroscopic) measurements

9/17/2015 Grover @ UNSW 8

CIGS solar cellRau, Appl. Phys. A 69, 1999

Epitaxial silicon heterojunctionBranz, Thin Solid Films, 519, 2011

Recombination → Quasi-Fermi separation → VOC

9/17/2015 Grover @ UNSW 9

+

-

EFn

EFp

+

-

+

-

qVOC

+++

Heterojunction solar cell

Jo,total = Jo,Radiation + Jo,Auger + Jo,SRH + Jo,emitter + Jo,rear

Voc =kT

qln

Jsc

Jo,total

+1æ

èç

ö

ø÷

Not precise but workable!Loss of exact dependences on recombination mechanisms

Emitter

(p-type)

Absorber

(n-type)

Quasi-neutralSpace-charge

InterfaceFront surface

Rear surface

Majority of photogenerated carrier recombination at VOC

Relating VOC to carrier concentrations via β

For constant QFL separation, β is constant across cell

β2 = NDΔp/ni2 in quasi-neutral region

β can similarly be used to relate ne and ph at interface

emitter absorber

β

How to think of VOC in this analysis:

•Not a performance metric but a variable

•Depends on light intensity, temperature, and recombination

•Constant or near constant throughout the cell

•Breaks down for very strong recombination

9/17/2015 Grover @ UNSW 10

AFORS-HET

Recombination rate depends on limited availability of carriers

• Express recombination in terms of β

• Recombination

– Rate per unit volume: USRH

– Rate integrated over thickness: RSRH=USRH*thickness

• Equate generation and recombination G*W=ΣRSRH

– G*W=Jph

9/17/2015 Grover @ UNSW 11

Rate limiting carrier type:

Interface: electrons

Quasi-neutral: holes

Space-charge: both

Defining all recombination with common β

• Simplified SRH equation:

• Quasi-neutral/Bulk (n=1)

– ND >> Δp

– Activation: Eg

• Interface (n=1)

– p >> n

– Activation: Φnb,0

• Space charge (n=2)

– p ≈ n

– Activation: Eg

9/17/2015 Grover @ UNSW 12

Scheer, JAP, 105, 104505, 2009

SRH

p n

npU

n p

Recombination = Generation

R0

bb 2 + R0

Ib 2 + R0

db = Gx dxW

ò = GavgW

Solve quadratic to obtain β & VOC

+

-

EFn

EFp

+

-

+

-Quasi neutral

Space charge

Interface

Φnb,0

Eg

q VOC

p-type

(emitter)

n-type

(absorber)

+++

++ +

--Φnb,0-qVOC

light

WGdxGRRR avg

W

x

dIb

9/17/2015 Grover @ UNSW 13

Formula for VOC

VOC = 2kT

qln

k1 1+ k2Gavg -1éë

ùû

ni

é

ë

êê

ù

û

úú.

k1 =R0

d

2 R0

I + R0

b( ); k2 = 4W

R0

I + R0

b( )R0

d( )2

.

VOC dependence on:

• Operating conditions: light intensity, temperature

• Strength of SRH recombination in bulk, interface, and depletion

9/17/2015 Grover @ UNSW 14

Fitting the light intensity dependence of VOC

k1 =R0

d

2 R0

I + R0

b( ); k2 = 4W

R0

I + R0

b( )R0

d( )2

.VOC = 2kT

qln

k1 1+ k2Gavg -1éë

ùû

ni

é

ë

êê

ù

û

úú.

Measured light-intensity dependence of VOC

0.50.40.30.20.1

Gavg (suns)

0.58

0.56

0.54

0.52

0.50

0.48

VO

C (

V)

Voc ( fit)

Coefficients (values ± sigma)

k1=3.5E14 ± 4E12 cm-3

k2=20.8 ± 0.35 suns-1

a-Si/c-Si heterojunction solar cellusing heteroepitaxial silicon film

Convert light intensity generation rate

9/17/2015 Grover @ UNSW 15

Define and fit ideality factor (n)

n Gavg( ) =k2Gavg

1+ k2Gavg 1+ k2Gavg -1éë

ùû

n k2Gavg ® 0{ } = 2

n k2Gavg ®¥{ } = 1

2.0

1.8

1.6

1.4

1.2

Ideality

factor: n

0.50.40.30.20.1

Gavg (suns)

0.60

0.58

0.56

0.54

0.52

0.50

VO

C (

V)

n ( fit)

Voc ( fit)

k2 = 22.1 suns-1

k1=3.36x1014

cm-3

k2=22.1 suns-1

(fixed)

k1 & k2 are sufficient for quantifying recombination in absence of interface

n =kT

q

d lnGavg

dVOC

é

ëê

ù

ûú

-1

9/17/2015 Grover @ UNSW 16

Defining activation energy from VOC(T) extrapolation

VOC TR( ) =Ea

q+ TR

dVOC

dT TR

Ea =R0

bEg TR( ) + R0

Ifb,0

n TR( )R0

b + R0

I.

VOC = 2kT

qln

k1 1+ k2Gavg -1éë

ùû

ni

é

ë

êê

ù

û

úú.

Ea≠ Eg linked to interface recombinationAssuming k2Gavg >> 1 (negligible SCR, large fwd. bias):

Weighted mean of activation energiesWeights = strength of recombination

+

-

EFn

EFp

+

-

+

- Quasi neutral

Space charge

Interface

Φnb,0

Eg

q VOC

p-type (emitter)

n-type (absorber)

+ + +

+ + +

- - Φnb,0-qVOC

1.20

1.10

1.00

0.90

0.80

0.70

0.60

0.50

VO

C (

V)

4003002001000

Temperat ure (K)

EgEa

Extrapolated temperature dependence

VOC TR( ) =Ea

q+ TR

dVOC

dT TR

Linear extrapolation of VOC(T)

Substitute explicit dependence of VOC on T

9/17/2015 Grover @ UNSW 17

Quantifying recombination in different regions

1.20

1.10

1.00

0.90

0.80

0.70

0.60

0.50

VO

C (

V)

4003002001000

Temperat ure (K)

EgEa

+

-

EFn

EFp

+

-

+

- Quasi neutral

Space charge

Interface

Φnb,0

Eg

q VOC

p-type (emitter)

n-type (absorber)

+ + +

+ + +

- - Φnb,0-qVOC

2.0

1.8

1.6

1.4

1.2

Ideality factor: n

0.50.40.30.20.1

Gavg (suns)

0.60

0.58

0.56

0.54

0.52

0.50

VO

C (

V)

n ( fit)

Voc ( fit)

k2 = 22.1 suns-1

k1=3.36x1014

cm-3

k2=22.1 suns-1

(fixed)

Light-intensity variation Extrapolated temperature dependence

k1

k2

Ea

ì

íï

îïï

ü

ýï

þïï

VOC (T ,G )C (V )

¾ ®¾¾¾

Rb =16%

Rd = 46%

RI = 38%

ì

í

ïï

î

ïï

ü

ý

ïï

þ

ïïat 1 sun

9/17/2015 Grover @ UNSW 18

Recombination analysis in CIGS cells with varying [Ga]

0.80

0.76

0.72

VO

C (V

)

1.71.61.51.41.31.21.1

Bandgap Eg (eV)

10-1

100

101

RI 0

/Rb

0

(a)

(b)

M.A. Contreras, et.al., Prog. Photovolt: Res. Appl. (2012).

Grover et. al., APL, 103, 093502, 2013

•Agreement of lifetime obtained from VOC(T,I) and TRPL

•Successfully tracks nuances of recombination variations based on material properties

(a): VOC vs. bandgap (Eg) for CIGS solar cells. VOC saturates as Eg increases with increasing Ga content. (b): Ratio of interface (RI

0) and bulk (Rb0) recombination

strengths increases dramatically for the higher bandgap samples.

9/17/2015 Grover @ UNSW 19

Li et.al., A recombination analysis of CIGS solar cells with low and high Ga compositions,Sol. Energy Mat. and Sol. Cells, 124 (2014) 143-149

Procedure for calculation of recombination rates

9/17/2015 Grover @ UNSW 20

New equation for temperature coefficient of VOC

• n – ideality factor; combines all recombination channels

• n/m – experimental fitting parameter

9/17/2015 Grover @ UNSW 21

• VOC’ depends on interface recombination and Fermi-pinning

• Smaller VOC’ for larger interface recombination → not necessarily good

Green, PIP, 11(5), 333–340, 2003

Grover, 42nd PVSC, 2015

High [Ga] CIGS cells are interface limited

9/17/2015 Grover @ UNSW 22

Rearrange terms to calculate interface contribution:

Questions so far?

9/17/2015 Grover @ UNSW 23

Operating Principle of Rectennas

• Square-law rectification

– Signal strength smaller than diode switching voltage

1 mV for 1 sun incident over 1 μm2 and 100 Ω antenna

• Key diode parameters

– Resistance (RD), responsivity (βi)

9/17/2015 24

I

VVD

Diode I(V) curve

antenna

diode

Rectenna

EM wave

Grover @ UNSW

Operating range and industry impact

• Potential for high-efficiency low-cost

– 90% efficient microwave rectennas exist

Large-signal: diode operates as switch

• Current state

– IR detectors demonstrated (Q.E. ~ 0.01% @ 10.6 μm)*

– Solar cells proposed in 1972, no practical demonstration as yet

9/17/2015 25

Terahertz Infrared Visible

• Spectral range and applications

Detection• Active and passive imager

• Interconnect receiver

Energy harvesting• Solar

• Thermal

antenna

diode

load

*Phiar Corp., NRO report 2002Grover @ UNSW

Requirements for Efficient Rectennas

• Intrinsically fast diode

• Low RD to match to RA

• Low CD to prevent shunting RD

• High βi for rectification

• Large VA for high power-conversion efficiency

• Efficient antennas

9/17/2015 26

~

RA

VA CDβi, RD

DiodeAntenna

Small-signal circuit model of rectenna

Rdiode

Rload

+

Vload

-

Iload

+ Load

Antenna to diode coupling

Diode design

Field enhancement

Grover @ UNSW

Metal/Insulator/Metal Diode

• Mechanism

– Tunneling across thin insulator

Nonlinear I(V)

Femtosecond fast

• Summary of work done

– Fabrication

Sputtered metals and insulators

– Simulation

Transfer matrix method

– Modification

Field effect transistor

Double-insulator (MIIM) barrier design

9/17/2015 27

M1 M2I (nm scale)

VD

e-

E

x

VD

MIM diode energy-band profile

Grover @ UNSW

Grover, Ph.D. Thesis, CU Boulder, 2011

Semiclassical Theory of Rectification in MIM

Photon-assisted transport applies when ħω/e~ voltage-scale of diode nonlinearity

9/17/2015 28

Classical: low frequency Semiclassical: high frequency

2, ;illum D n dark D

n

eVI V V J I V n

e

Grover, et.al, J. Phys D., 46 (13), 135106, 2013; Tien, Gordon, Phys. Rev., 129(2), 1963

VD

Vω

E

x

VD

E

+ħω

x

-ħω

diode

DC I(V) under illumination:

Vωcos(ωt) ~

J1

J0

J-1

Grover @ UNSW

Efficiency limit for monochromatic response of rectenna

• Assume ideal diode – high fwd/rev asymmetry

• 1 μW input (low intensity regime) – 1 photon process

• |VO| < ћω/q, 1photon/1electron

9/17/2015 Grover @ UNSW 29

|VO| < ћω/q

|VO| = ћω/q

|VO| > ћω/q

(μA

)

Slide courtesy: Saumil Joshi, UC Boulder

Calculating broadband rectenna response for solar spectrum

9/17/2015 Grover @ UNSW 30

Frequency spectrum Time-domain signal

Slide courtesy: Saumil Joshi, UC Boulder

Efficiency limit for rectifying solar radiation (quantum regime)

• 5700 K blackbody

• 1000 W/m2

• Spatial coherence area ~19 μm

• Maximum power ~1.1 μW

• Quantum operation

• Peak efficiency ~ 44%

– Matches Shockley-Queisser’s ultimate efficiency limit

9/17/2015 Grover @ UNSW 31

I ill

um

Slide courtesy: Saumil Joshi, UC Boulder

Joshi, Moddel, Appl. Phys. Lett. 102, 083901 (2013)

Can we exceed the 44% limit?

• Microwave rectennas > 70%

• Use low energy photons?

• Three regimes

– Quantum (α < 1)

– Transition (α ~ 1)

– Classical (α >> 1)

• Increase diode voltage, relative to ћω/q

• Two ways to reach classical operating regime

– High input intensity

– High radiation resistance

9/17/2015 Grover @ UNSW 32

VD

α = qVD/ћω

Slide courtesy: Saumil Joshi, UC Boulder

Pin = 100 μW

Transition regime

Effect of input intensity on operating regime

9/17/2015 Grover @ UNSW 33

• Low intensity, high frequency

• Frequency-dependent

• Hump observed

Pin = 100 nW

Quantum regime

Slide courtesy: Saumil Joshi, UC Boulder

• Higher intensity, multiple photons

• Frequency-dependent

• Multiple steps

• Very high intensity

• Frequency independent

• Large number of photons

Pin = 10 mW

Classical regime

Joshi, Ph.D. Thesis, CU Boulder, 2015

Conclusion: efficiency limits of optical rectennas

• Quantum operation

– Low intensity, high frequency - single photon process

– Monochromatic efficiency 100%

– Broadband efficiency maximum = 44%

– Split-spectrum > 44%

• (Quantum) classical operation

– Possible at high frequencies through photon mixing → large voltage operation

– Broadband efficiency > 44%

• Rectenna solar cell efficiency can exceed Shockley-Queisser limit

– Through multi-photon process at high intensity

• Challenges

– Coherence limits power

– High diode resistance large RC time-constant

– Diode breakdown

9/17/2015 Grover @ UNSW 34

Slide courtesy: Saumil Joshi, UC Boulder

Thank you.

Email: Sachit.Grover@firstsolar.com