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8/3/2019 Med Power Presentation
1/20
MEDPOWER 2010 AYIA NAPA
Numerical Modeling of PhotovoltaicApplications
Assis. Prof. Antonis Papadakis
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MEDPOWER 2010 AYIA NAPA
OUTLINE OF PRESENTATION
INTRODUCTION
CONCLUSIONS
FUTURE WORK
MODEL DESCRIPTION
TRANSPORT PROPERTIES
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MEDPOWER 2010 AYIA NAPA
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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MEDPOWER 2010 AYIA NAPA
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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MEDPOWER 2010 AYIA NAPA
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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MEDPOWER 2010 AYIA NAPA
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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MEDPOWER 2010 AYIA NAPA
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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MEDPOWER 2010 AYIA NAPA
AUGER RECOMBINATION
+
- -
Auger Recombination
Electron Capture
+
-
+
E
Ec
Ev
Auger Recombination
Hole Capture
-
-+
Before After Before After
-+
DependencyonCarrierD
ensity +
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MEDPOWER 2010 AYIA NAPA
AUGER GENERATION
-
Auger Generation
Electron Emission
E
Ec
Ev
Auger Generation
Hole Emission
-
-+
Before After Before After
-++
-
+
-
+ +
DependencyonCarrierD
ensity
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MEDPOWER 2010 AYIA NAPA
IMPACT IONIZATION
-
Impact Ionization
Electron Emission
E
Ec
Ev
Impact Ionization
Hole Emission
-
-+
Before After Before After
-++
-
+
-
+ +
DependencyonCurrentDen
sity
and
T
emperature
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MEDPOWER 2010 AYIA NAPA
PHONON TRANSITION-RECOMBINATION
Phonon Transition
Electron Capture
E
Ec
Ev
Phonon Transition
Hole Capture
-
Before After Before After
-++
- -
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MEDPOWER 2010 AYIA NAPA
PHONON TRANSITION-GENERATION
Phonon Transition
Electron Emission
E
Ec
Ev
Phonon Transition
Hole Emission
Before After Before After
--
-+ +
-
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MEDPOWER 2010 AYIA NAPA
PHOTON TRANSITION
Photon Recombination
E
Ec
Ev
Photon Generation
Before After Before After
--
-+ ++ -+
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MEDPOWER 2010 AYIA NAPA
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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MEDPOWER 2010 AYIA NAPA
Fig. 1. Electron mobility with respect to the donor density at a
temperature of 300 K for silicon.
Electron Mobility
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MEDPOWER 2010 AYIA NAPA
Fig.2. Hole mobility versus the acceptor density at a temperature of
300 K for silicon.
Hole Mobility
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MEDPOWER 2010 AYIA NAPA
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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MEDPOWER 2010 AYIA NAPA
Fig. 4. Hole diffusion coefficient against the electric field at a
temperature of 300 K in silicon.
Hole Diffusion
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MEDPOWER 2010 AYIA NAPA
Fig. 5. Intrinsic absorption coefficient as a function of temperature
in silicon.
Intrinsic Absorption Coefficient
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MEDPOWER 2010 AYIA NAPA
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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