ECE-305: Fall 2016

Ideal + Non-Ideal Solar Cells

Professor Peter BermelElectrical and Computer Engineering

Purdue University, West Lafayette, IN USApbermel@purdue.edu

Pierret, Semiconductor Device Fundamentals (SDF)pp. 260-281

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outline

2

1) Ideal Solar Cells

2) Non-ideal solar cells: reverse bias

3) Non-ideal solar cells: forward bias

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ideal IV characteristic

3PD = ITOTVD < 0

VD

ID

ITOT = I0 eqVD kBT -1( ) - ISC

-ISC

Pout = -ISCVD = 0

VOC

Pout = ITOTVOC = 0

Pout = ImpVmp = -ISCVOCFF

h =Pout

Pin

=ISCVOCFF

Pin

ID = I0 eqVD kBT -1( )

Superposition principle

Maximum power rectangle

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4

maximum short circuit current

Example: Silicon Eg = 1.1eV. Only photons with a wavelength < 1.12 mm will be absorbed.

solar spectrum (AM1.5G)

Pin = 100 mW cm2

l <hc

EG

JSC max= 44 mA cm2

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5

open-circuit voltage and efficiency

ITOT = I0 eqV /kBT -1( ) - ISC

I0 = 1´10-12 A

VOC =kBT

qln

ISC

I0

æ

èçö

ø÷

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VOC = 0.026 ln40 ´10-3

1´10-12

æ

èçö

ø÷= 0.63

ISC = 0.90´ 44 ´10-3 = 40 mA

h =Pout

Pin

=ISCVOCFF

Pin

h =Pout

Pin

=40 ´ 0.63´ 0.8

100= 0.20

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Example for silicon photovoltaics:

6

Increasing the efficiency

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h =Pout

Pin

=ISCVOCFF

Pin

VOC =kBT

qln

ISC

I0

æ

èçö

ø÷

I0 = qADn

WP

ni2

NA

æ

èçö

ø÷

1) Increase the short circuit current from 40 towards 44

2) Increase VOC (decrease I0)

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efficiency

Martin Green Group UNSW – Zhao et al., 1998 (25% at 1 sun)

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370 - 400 mm

FF = 0.81

JSC = 41.5 mA/cm2 94%( )VOC = 0.703 I0 = 0.075 ´10-12 A

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JSC – VOC trade-off

1) Smaller bandgaps give higher short circuit current

2) Larger bandgaps give higher open-circuit voltage

3) For the given solar spectrum, an optimum bandgap exists.

“Shockley-Queisser Limit”

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outline

9

1) Ideal Solar Cells

2) Non-ideal solar cells: reverse bias

3) Non-ideal solar cells: forward bias

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reverse bias breakdown

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VA

I

-VBR

0.6 - 0.7 V

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avalanche breakdown

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Fig. 6.12, Semiconductor Device Fundamentals, R.F. Pierret

Fp

Fn

Fp

Fn

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breakdown voltage and critical electric field

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ND >> NA ÞE 0( ) =2q Vbi +VR( )NA

Kse0

VBR µ1

NA xN Pxp-xn

E x( )

E 0( ) =E CR =2q Vbi +VBR( )NA

Kse0

VBR =Kse0

2qNA

E CR2 -Vbi

E 0( )

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breakdown vs. doping

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Fig. 6.11, Semiconductor Device Fundamentals, R.F. Pierret

VBR µ1

NA

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critical electric field

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E CR =2q Vbi +VBR( )NA

Kse0

E CR » 3´105 V/cm (Silicon)

E CR »1´105 V/cm (Germanium)

E CR » 5 ´106 V/cm (GaN)

E CR » 3´106 V/cm (air)

VBR µ1

NA

NA

SiO2

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tunneling

15

Fig. 6.13, Semiconductor Device Fundamentals, R.F. Pierret

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tunneling

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Fig. 6.14, Semiconductor Device Fundamentals, R.F. Pierret

W =2KSe0

q

NA + ND

NDNA

æ

èçö

ø÷Vbi

é

ëê

ù

ûú

1/2

»2KSe0

qNA

Vbi

é

ëê

ù

ûú

1/2

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outline

17

1) Ideal Solar Cells

2) Non-ideal solar cells: reverse bias

3) Non-ideal solar cells: forward bias

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non-idealities

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1) Breakdown

2) High forward bias

3) R-G current-forward-reverse

(SFD pp. 260-281)

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forward bias

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VA

I

-VBR

0.6 - 0.7 V

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FB current

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J = J0 eqVA /kBT -1( ) » J0eqVA /kBT

ln J( ) = ln J0( ) + qVA / kBT

ln J( ) m =q

nkBT

n =1

VA

ln J0( )

ln J( ) = ln J0( ) +mVA

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high bias

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I = I0 eq V-IRS( )/kBT -1( )

DnP =ni

2

NA

eqVA kBT -1( ) << NA

VA =V - IRS

1) series resistance

2) “high level injection”

RS-VA +

-V +

I

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real diodes in FB

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Fig. 6.10(a), Semiconductor Device Fundamentals, R.F. Pierret

IRS

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n =1

n = 2

FB diode current

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N P

transition region

xp-xn 0

Jn diffJ p diff “diffusion current”

Minority carrier recombination in quasi-neutral regions leads to diode current.

holes electrons

What about recombination

here?

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recombination in SCRs

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J VA( ) = qRTOT VA( )

FnFP

q Vbi -VA( ) Maximum recombination occurs when n(x) ≈ p(x)

qR VA( ) =qnie

qVA 2kBT

t eff

np = ni2eqVA kBT

Recombination in space-charge regions gives riseto n = 2 currents that go as ni not ni

2.

n̂ » p̂ µ nieqVA 2kBT

n x( ) p x( ) = ni2eqVA kBT

consider RB again (before breakdown)

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VA

I pA( )

I V( ) = -I0

FB

RB

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read diodes in RB

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IR µ VR

Fig. 6.10(b), Semiconductor Device Fundamentals, R.F. Pierret

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recombination-generation

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n0 p0 = ni2 R = 0 (equilibrium)

np = ni2eqVA kBT > ni

2 R > 0 (recombination, FB)

np = ni2e-qVR kBT < ni

2R < 0 (generation, RB)

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recombination-generation in the SCR

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ni2

ND

ni2

NA

Fp

Fn

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Fig. 6.15(a), Semiconductor Device Fundamentals, R.F. Pierret

recombination-generation in the SCR

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Fig. 6.15(a), Semiconductor Device Fundamentals, R.F. Pierret

np = ni2e-qVR kBT < ni

2

Fp

Fn

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RB diode current

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N P

xp-xn 0

e-h pairs generated here

give 1 electron in the external

circuit.

G = -R =ni

2t 0

I = -qni

2t 0

WA

W VA( )

W µ Vbi +VR

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read diodes in RB

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IR µ ni Vbi +VR

Fig. 6.10(b), Semiconductor Device Fundamentals, R.F. Pierret

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summary

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ID = I0 eqVA /nkBT -1( ) ID = I0 eq V-IDRS( )/nkBT -1( )

1) FB: recombination in quasi-neutral regions give n = 1 current (diffusion current).

2) FB: recombination in SCR gives n = 2 current

3) RB: constant when dominated by diffusion current

4) RB: increases as W for generation in SCR

5) RB: avalanche or Zener tunneling

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