photo-voltaicsand solar cells - cornell university · pn diodes as photo-voltaic cells x-xp xn...

1

ECE 407 – Spring 2009 – Farhan Rana – Cornell University

Photo-Voltaics and Solar Cells

In this lecture you will learn:

• Photo-Voltaic Cells• Carrier Transport, Current, and Efficiency • Solar Cells• Practical Photo-Voltaics and Solar Cells


Photo-Voltaic Cells

IL = Short circuit current due to light

Photovoltaic Cell

Light power = Energy per sec= Pinc

EQE = (Output current) / q

(Incident light power) / inc

L

P

qI

External Quantum Efficiency:

A device that produces a current when exposed to light ….!!(e.g. a solar cell)

Short Circuit Output Current:

IL = Short circuit current due to light

External quantum efficiency compares the number of electrons produced in the external circuit per second (under a short circuit connection) to the number of photons incident on the device per second

2


I = Current when a load resistor is present

Photovoltaic Cell

Light power = Energy per sec= Pinc

How much electrical power can be delivered to a load resistor?

It will not be just IL R

Because I will change (i.e. will not equal IL) when a load resistor is present

Photo-Voltaic Cells Connected to a Load

R

E = Power delivered to the load

Incident light power

2

inc

I R

P

Power Conversion Efficiency:

2


PN Diodes as Photo-Voltaic Cells

x-xpxn

P-doped N-doped+ ++ ++ +

- -- -- -

V+ -

I

1KT

qV

o eII

Consider the standard pn diode:

The pn diode can be used as a photo cell that generates electrical power when exposed to light ….!!

Such a device is a called a photo-voltaic cell (e.g. a solar cell)

Wn + xn-Wp - xp

3


PN Junction Photo-Voltaic Cells: Some Intuition

x-xpxn


- -- -- -

Wn + xn-Wp - xp

1) Suppose a photon creates one electron-hole pair:

2) Quasi neutrality implies that electron and hole stay together3) If they recombine – end of story!

4) If they diffuse and reach the metal contact, they recombine – end of story!

x-xpxn


- -- -- -

Wn + xn-Wp - xp

x-xpxn


- -- -- -

Wn + xn-Wp - xp

IL = 0

IL = 0

Short circuit operation


x-xpxn


- -- -- -

Wn + xn-Wp - xp

5) If they diffuse and reach the junction, they separate (because of the E-field in the junction):

x-xpxn


- -- -- -

Wn + xn-Wp - xp

6) They contribute one unit of charge to the external current

x-xpxn


- -- -- -

Wn + xn-Wp - xp

PN Junction Photo-Voltaic Cells: Some Intuition

4


Boundary Conditions

x-xpxn


- -- -- -

Wn + xn-Wp - xp

IL

Light

Short the device outputShine light uniformly on the P-sideHow much current IL flows in the external circuit?

01'2

KT

qV

a

ip

D

eNn

xn 01'2

KT

Vq

d

in

D

eNn

xp

No excess carrier densities at the edges of the depletion region

0' nn xWp 0' pp xWn


Carrier Transport

x-xpxn


- -- -- -

Wn + xn-Wp - xp

Light

Electron and hole generation rate on the P-side: (units: per unit volume per sec)LG

Start from the steady state equation:

2

210

x

xnDRG

xxJ

qRG n

n

xnnxn po '

Equilibrium electron density Excess electron densitya

ipo N

nn

2

•Then the generation-recombination term becomes: n

Lxn

GRG'

•And we get:

n

L

nn DG

Dxn

x

xn

''2

2 Diffusion equation for the excess electron density

IL

5


Carrier Transport

x-xpxn


- -- -- -

Wn + xn-Wp - xp

Light

01'2

KT

Vq

a

ip

D

eNn

xn

0' pp xWn

We need to solve:

Assume the short-base limit (no recombination):

n

L

DG

x

xn

2

2 ' 01'2

KT

Vq

a

ip

D

eNn

xn

0' pp xWn

Solution is:

pppn

L xxxWxD

Gxn

2'

n

L

nn DG

Dxn

x

xn

''2

2

IL


Carrier Transport

x-xpxn


- -- -- -

Wn + xn-Wp - xp

Light

Solution is:

Quasi-neutrality

-xp-Wp - xp

xn'

IL

pppn

L xxxWxD

Gxn

2'

pppn

L xxxWxD

Gxnxp

2''

6


Carrier Transport

x-xpxn


- -- -- -

Wn + xn-Wp - xp

Light

-xp-Wp - xp

xpxn ''

2

2' ppLnn

xWxqG

xxn

qDxJ

-xp-Wp - xp

xJn

x

xn Wn + xn

Minority carriers flow by diffusion only

IL


Carrier Transport

x-xpxn


- -- -- -

Wn + xn-Wp - xp

Light

2

2' ppLnn

xWxqG

xxn

qDxJ

-xp-Wp - xp

xJn

xn Wn + xn

xJpTJ

2 p

L

pnT

WqG

xJJ

IL

7


External Current

x-xpxn


- -- -- -

Wn + xn-Wp - xp

Light

-xp-Wp - xp

xJn

xn Wn + xn

xJp xJT

pLTL AWGq

AJI2

IL

Total number of electron-hole pairs generated in the entire P-side per second


External Quantum Efficiency

x-xpxn


- -- -- -

Wn + xn-Wp - xp

Light

IL

EQE = (Output current) / q

(Incident light power) / inc

L

P

qI

Suppose every incident photon generates one electron-hole pair, then:

pLinc WAG

P

Then:

21

pL

L

WAG

qIEQE Why just one-half?

Every incident photon generates one electron-hole pair but only half of the generated electron-hole pairs contribute to the external current!

8


x-xpxn

+ ++ ++ +

- -- -- -

P-doped N-doped

Wn + xn-Wp - xp

Suppose light is now shown on the junction depletion region

1) A photon creates an electron-hole pair

2) They are separated by the large E-field in the junction

3) They contribute one unit of charge to the external circuit

Photo-Excitation in the Depletion Region

x-xpxn

+ ++ ++ +

- -- -- -

P-doped N-doped

Wn + xn-Wp - xp

x-xpxn


- -- -- -

Wn + xn-Wp - xp



x-xpxn

+ ++ ++ +

- -- -- -

Light

IL

Electron Current (assuming no recombination inside the depletion region):

pnLxx Lnnpn

x

xL

x

x

n

LoLon

xxqGdxGqxJxJ

dxGdxx

xJq

GRGGRGx

xJqt

xn

np

n

p

n

p

1

1'

Hole Current (assuming no recombination inside the depletion region):

P-doped N-doped

Wn + xn-Wp - xp

Suppose light is now shown on the junction region

0

pnLxx Lppnp

LoLop

xxqGdxGqxJxJ

GRGGRGx

xJ

q

np

1

Integrate over the depletion region

9



x-xpxn

+ ++ ++ +

- -- -- -

Light

IL

P-doped N-doped

Wn + xn-Wp - xp

Electron and Hole Current:The electric field inside the depletion region sweeps the electrons towards the n-side and the holes towards the p-side. Consequently, it must be that:

0

0

np

pn

xJ

xJ

Total Current:

pnL

pppnnpnnT

xxqG

xJxJxJxJJ

pnLxx Lnnpn xxqGdxGqxJxJ n

p

0

pnLxx Lppnp xxqGdxGqxJxJ n

p

0

0 0



x-xpxn

+ ++ ++ +

- -- -- -

Light

IL

P-doped N-doped

Wn + xn-Wp - xp

-xp-Wp - xp

xJn

xn Wn + xn

xJp

xJT pnL

TL

xxAqG

AJI

1

pnL

L

xxAG

qIEQE

External Quantum Efficiency:

L

n Gx

xJq

1

L

p Gx

xJ

q

1

10


n doped substrate

p+ doped

Light

x

0

AR coatingPassivation

Metal contacts

Common Photo-Voltaic Structures

n doped substrate

p+ doped

Light

x

0

AR coating

intrinsic

Passivation

Metal contacts

A PN Junction Photodetector

The depletion region is not thick enough

A PIN Junction Photodetector

The depletion region can be very thick!


Solar Cells

11


PN Photo-Voltaic Cells as Solar Cells

x-xpxn

+ ++ ++ +

- -- -- -I

+ -VD

R

The circuit current I has two components:

i) The current due to the biased pn junction given as:

ii) The current IL due to photogeneration

These two components can be added together (why?) to give the total current:

1KTqVo

DeI

LKTqV

o IeII D 1

-+

P-doped N-doped

Wn + xn-Wp - xp

VD

Light Pinc

pnLL xxAqGI


x-xpxn

+ ++ ++ +

- -- -- -I

+ -VD

R

- +

P-doped N-doped

Wn + xn-Wp - xp

IR

Light Pinc

LKT

qV

o IeIID

1

0 DVIR

VD

I

Isc = -|IL|Increasing R

Voc

LKT

qV

o IeIID

1

RV

I D

We also have the load-line equation:

Solution of these two equations gives the operating point

Graphical solution:

We have:

PN Photo-Voltaic Cells as Solar Cells

12


Electrical Power Output

DLKTqV

o

Dout

VIeI

IVRIP

D

1

2

x-xpxn

+ ++ ++ +

- -- -- -I

+ -VD

R

P-doped N-doped

Wn + xn-Wp - xp

Light Pinc

VD

I

Voc

LKT

qV

o IeIID

1

RV

I D

Power delivered to the load resistor:

Power delivered to the load is given by the area of the lightly shaded region

There is an optimal value of the load resistor that allows maximum power delivery to the load

Isc = -|IL|

- +IR


Energy Conversion Efficiency

x-xpxn

+ ++ ++ +

- -- -- -I

+ -VD

R

-+

P-doped N-doped

Wn + xn-Wp - xp

VD

Light Pinc

VD

I

Voc

LKT

qV

o IeIID

1

RV

I D

DLKT

qV

o

Dout

VIeI

IVP

D

1

Power delivered to the load resistor:

External Power Conversion Efficiency:

inc

D

inc

out

PIV

P

PE

Fill Factor = FF =

Area of lightly shaded region

Area of dark shaded region

Isc = -|IL|

ocsc

D

VIIV

13


Design of Silicon Solar Cells

The PERL Si solar cell (Green et al., 1994)Efficiency ~25%

Material Voc (V) Jsc (Amp/cm2) FF (%) Efficiency (%)Crystalline Si 0.705 42.7 82.8 25.0Crystalline GaAs 1.045 29.7 84.7 26.1Poly-Si 0.664 38.0 80.9 20.4a-Si 0.859 17.5 63.0 9.5CuInGaSe2 (CIGS) 0.716 33.7 80.3 19.4CdTe 0.845 26.1 75.5 16.7

Typical Performances of Semiconductor Photocells (Green at al., Prog. Photovolt: Res. Appl., 17, 85 (2009))

Energy Conversion Efficiencies of Some Common Solar Cells

+


Design of Solar Cell Modules

The IV characteristics of pn junctions connected in series must identical (or nearly so)

photo-voltaicsand solar cells - cornell university · pn diodes as photo-voltaic cells x-xp xn...

Documents