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

Illuminated P-N Junction - Illuminated JV Curve PVMD Miro Zeman Delft University of Technology

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:     2 d n n    Electrons in the p- type region: p p D G 0  n 2 dx n     2 d p p    n n D G 0 Holes in the n- type region:  p 2 dx p Δ p=p n -p no ( Δ n=n p -n po ): concentration of excess minority carriers holes (electrons) D p (D n ): diffusion coefficient for holes (electrons) τ p ( τ n ): lifetime of holes (electrons) G: generation rate

Minority carrier concentration in quasi-neutral regions PN-junction diode under illumination:             Electrons in qV x                a  n x n G n  exp 1  G exp   p p 0 n p 0 n p - type region:         kT L n            qV x Holes in               a  p x p G p  exp 1  G exp   n n 0 p n 0 p     n- type region:   kT L   p

P-N junction under illumination: Carrier concentration p- type n- type n = n n0 = N D p = p p0 = N A ln(n) ln(p) L n L p n = G τ n p = G τ p n = n p0 = n 2 i /N A p = p n0 = n 2 i /N D Position

Current density in a illuminated P-N junction diode p- type region n- type region      dn x   dp x          p n J x qD 0 J x 0 qD p p n n dx dx    x 0 x 0         qD n qD p qV       n p 0 p n 0     a J exp 1 qG L W L   p n       L L kT   n p

J-V characteristics of ideal illuminated P-N junction Illuminated J-V characteristics     qV      a J J  exp 1  J 0 ph     kT   qD n qD p   n p 0 p n 0   J 0   L L   n p      J qG L W L ph p n

External parameters of solar cell I-V measurement Standard test conditions P max I ▪ AM1.5 spectrum P=I × V P ▪ Irradiance 1000W/m 2 ▪ Temperature 25ºC V mp V oc External parameters: External parameters: External parameters: External parameters: External parameters: V Peak Power ▪ Short-circuit current I sc [A] ▪ Short-circuit current I sc [A] ▪ Short-circuit current I sc [A] ▪ Short-circuit current I sc [A] ▪ Short-circuit current I sc [A] P max [ W p ] ▪ Open-circuit voltage V oc [V] ▪ Open-circuit voltage V oc [V] ▪ Open-circuit voltage V oc [V] ▪ Open-circuit voltage V oc [V] I mp ▪ Maximum (peak) power P max [W p ] ▪ Maximum (peak) power P max [W p ] ▪ Maximum (peak) power P max [W p ] I sc ▪ Fill factor FF ▪ Fill factor FF ▪ Efficiency η

External parameters of solar cell I-V measurement Standard test conditions P max I ▪ AM1.5 spectrum P=I × V P ▪ Irradiance 1000W/m 2 ▪ Temperature 25ºC V mp V oc V   Peak Power P V I V I FF max mp mp oc sc P max [ W p ] FF  V I V I I mp mp mp oc sc I sc P V I FF    max oc sc P P I I