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Equations for Photovoltaics

Basic Equations

density of states in conduction and valence band


fermi function:

Carrier Concentration in Equilibrium

law of mass action:

carrier concentrations:

n-type material:

2元微信红包小扫雷群p-type material:

Carrier Concentration Under Bias


number of photons:

generation rate:

generation, homogeneous semiconductor: g = const:




2元微信红包小扫雷群general srh recombination rate:

under low injection conditions:

for electrons:

for holes:

basic pn junction equation set

1. poisson's equaion:

2. transport equations:

2元微信红包小扫雷群3. continuity equations:

2元微信红包小扫雷群general solution for no electric eifled, constant generation

Equations for PN Junctions

built-in voltage pn homojunction:

general ideal diode equation:

I02元微信红包小扫雷群 for wide base diode:

I02元微信红包小扫雷群 for narrow base diode:

2元微信红包小扫雷群full diode saturation currrent equation:

2元微信红包小扫雷群depletion region recombination:

Solar Cell Equations


for constant G, wide base

Material Constants and Commont Units

intrinsic carrier concentration:

2元微信红包小扫雷群effective density of states:

intrinsic energy level:


minority carrier diffusion length:

resistivity and conductivity:

resistance, homogeneous:


Radiant Energy

2元微信红包小扫雷群wavelength and energy of a photon:

2元微信红包小扫雷群if e is in ev and λ is in μm:

2元微信红包小扫雷群spectral irradiance for black body:

2元微信红包小扫雷群power density of a non-ideal black body:

photon flux and power density:


Material mn*/m0 mp*/m0 EG (eV) ni (cm-3) c (eV) eS
Si 1.18 0.81 1.12 1.0 × 1010 4.03 11.8
Ge 0.55 0.36 0.66 2.0 × 1013 4.13 16.0
GaAs 0.066 0.52 1.42 1.8 × 106 4.07 13.1
InP 0.08 0.6 1.34 1.3 × 107 4.38 12.5