Med Power Presentation

8/3/2019 Med Power Presentation

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MEDPOWER 2010 AYIA NAPA

Numerical Modeling of PhotovoltaicApplications

Assis. Prof. Antonis Papadakis


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OUTLINE OF PRESENTATION

INTRODUCTION

CONCLUSIONS

FUTURE WORK

MODEL DESCRIPTION

TRANSPORT PROPERTIES


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MODEL DESCRIPTION

Characterisation of thin film photovoltaics by solving :

Continuity equations of charged particles: (electrons, holes)

Poisson equation for the electric field

Coordinates :

2D Cylindrical Axisymmetric 2D Cartesian

Initial Conditions:

Photovoltaic cell dimensions

Doping electron and hole densities

Material Temperature

Conformal Finite Element Mesh


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MODEL DESCRIPTION

Poissons Equation :

Continuity Equations :

Poisson and Continuity model are coupled viaNe, Nh

)(. !ADeh

NNNNVI

eeeee

eSNDvN

t

N!

x

x)().( 2

hhhhh

hSNDvN

t

N!

x

x)().( 2


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Constitutive Equations :

MODEL DESCRIPTION

Simulation Limitations

VE !

Evee

Q!

Ev hh Q!

Q

I

eNtrd !

Ne

KTLD 2

I

!

Debye Length

Dielectric Relaxation

Electric Field

Electron Velocity

Hole Velocity


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Solution Procedure

MODEL DESCRIPTION

PO

Start of Time Step

POTPCON

TP CONV

n

)

n

86

n Vn+1/2

86n+1/2

)n+1/2

Vn+1

End of Time Step


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TRANSPORT PROPERTIES

Transport Properties of electrons and holes:

Velocities

Generation/Recombination

Mobilities

Diffusion

Generation and Recombination Processes:

Photon transition or optical generation and recombination

Phonon transition or Shockley-Read-Hall generation and recombination

Auger generation and recombination or three particle transitions

Impact ionization


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AUGER RECOMBINATION

+

- -

Auger Recombination

Electron Capture

+

-

+

E

Ec

Ev

Auger Recombination

Hole Capture

-

-+

Before After Before After

-+

DependencyonCarrierD

ensity +


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AUGER GENERATION

-

Auger Generation

Electron Emission

E

Ec

Ev

Auger Generation

Hole Emission

-

-+


-++

-

+

-

+ +

DependencyonCarrierD

ensity


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IMPACT IONIZATION

-

Impact Ionization

Electron Emission

E

Ec

Ev

Impact Ionization

Hole Emission

-

-+


-++

-

+

-

+ +

DependencyonCurrentDen

sity

and

T

emperature


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PHONON TRANSITION-RECOMBINATION

Phonon Transition

Electron Capture

E

Ec

Ev

Phonon Transition

Hole Capture

-


-++

- -


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PHONON TRANSITION-GENERATION

Phonon Transition

Electron Emission

E

Ec

Ev

Phonon Transition

Hole Emission


--

-+ +

-


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PHOTON TRANSITION

Photon Recombination

E

Ec

Ev

Photon Generation


--

-+ ++ -+


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GENERATION/RECOMBINATION FORMULAS

Impact Ionization: hhheeeion vNavNaS !bhe

heheE

B

AEa ))||(exp()(

,

,, !

Auger Recombination:

Band to Band Recombination:

Free Carrier Absorption:

)()( 2222 ihhehieeheaug NNNNCNNNNCS !

)( 2ieh

NNNBR !

b

p

a

eFC NKNKa PP 21 !

)()(

2

kT

E

ieh

kT

E

ihe

ieh

SHRtt

eNNeNN

NNNR

!

XX

Bulk Recombination Model:


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Fig. 1. Electron mobility with respect to the donor density at a

temperature of 300 K for silicon.

Electron Mobility


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Fig.2. Hole mobility versus the acceptor density at a temperature of

300 K for silicon.

Hole Mobility


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Fig. 3. Electron diffusion coefficient as a function of the electric field at a

temperature of 300 K in silicon.

Electron Diffusion


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Fig. 4. Hole diffusion coefficient against the electric field at a

temperature of 300 K in silicon.

Hole Diffusion


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Fig. 5. Intrinsic absorption coefficient as a function of temperature

in silicon.

Intrinsic Absorption Coefficient


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CONCLUSIONS/FUTURE WORK

Streamer Propagation Across Gap

Transport parameters are readily available for silicon

Differential equations identified

To simulate heating effects by solving conservation of mass,

momentum and energy for solids

FUTURE WORK:

Expand the model in 3-Dimensions

Exploit adaptive mesh techniques

CONCLUSIONS:

Perform thin film silicon simulations

Compare with commercial software PC1D

Mathematical model formulation identified

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