PVMD Miro Zeman Delft University of Technology Derivation of light - - PowerPoint PPT Presentation

PVMD

Delft University of Technology

Illuminated P-N Junction - Illuminated JV Curve

Miro Zeman

Derivation of light I-V characteristic of P-N junction Assumptions:

▪ The Boltzmann approximation ▪ Abrupt depletion region ▪ Low level injection conditions ▪ No electric field and generation in quasi-neutral regions ▪ No recombination and thermal generation in depletion region ▪ Uniform generation-rate profile

Derivation of minority carrier in quasi-neutral regions

At steady state:

Δp=pn-pno (Δn=np-npo): concentration of excess minority carriers holes (electrons) Dp (Dn): diffusion coefficient for holes (electrons) τp (τn): lifetime of holes (electrons) G: generation rate

Holes in the n-type region:

 

2 2

     G p dx p d D

p n n p



 

2 2

     G n dx n d D

n p p n



Electrons in the p-type region:

Minority carrier concentration in quasi-neutral regions

PN-junction diode under illumination:

Electrons in p-type region: Holes in n-type region:

 

                                   

n n a p n p p

L x G kT qV n G n x n exp 1 exp  

 

                                 

p p a n p n n

L x G kT qV p G p x p exp 1 exp  

P-N junction under illumination: Carrier concentration

p = pn0 = n2

i/ND

p-type n-type Position

n = np0 = n2

i/NA

p = pp0 = NA n = nn0 = ND

ln(n) ln(p)

n = Gτn p = Gτp Ln Lp

Current density in a illuminated P-N junction diode

p-type region n-type region

   



  

x n p p

dx x dp qD x J

   

 

    

x p n n

dx x dn qD x J

 

n p a p n p n p n

L W L qG kT qV L p qD L n qD J                           1 exp

J-V characteristics of ideal illuminated P-N junction

Illuminated J-V characteristics

ph a

J kT qV J J                1 exp

         

p n p n p n

L p qD L n qD J

 

n p ph

L W L qG J   

External parameters of solar cell

External parameters: ▪ Short-circuit current Isc [A]

Standard test conditions

▪ AM1.5 spectrum ▪ Irradiance 1000W/m2 ▪ Temperature 25ºC I-V measurement External parameters: ▪ Short-circuit current Isc [A] ▪ Open-circuit voltage Voc [V] External parameters: ▪ Short-circuit current Isc [A] ▪ Open-circuit voltage Voc [V] ▪ Maximum (peak) power Pmax [Wp] External parameters: ▪ Short-circuit current Isc [A] ▪ Open-circuit voltage Voc [V] ▪ Maximum (peak) power Pmax [Wp] ▪ Fill factor FF External parameters: ▪ Short-circuit current Isc [A] ▪ Open-circuit voltage Voc [V] ▪ Maximum (peak) power Pmax [Wp] ▪ Fill factor FF ▪ Efficiency η

Isc Voc V I Peak Power Pmax [Wp] P=I×V P Pmax Imp Vmp

Standard test conditions

▪ AM1.5 spectrum ▪ Irradiance 1000W/m2 ▪ Temperature 25ºC I-V measurement

External parameters of solar cell

Isc Voc V I Peak Power Pmax [Wp] P=I×V P Pmax Imp Vmp

FF I V I V P

sc

• c

mp mp

 

max sc

• c

mp mp

I V I V FF 

I sc

• c

I

P FF I V P P  

max

