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:

p-type material:

Carrier Concentration Under Bias

Generation

Number of photons:

Generation rate:

Generation, homogeneous semiconductor: G = const:

P-type:

N-type:

Recombination

General SRH recombination rate:

Under low injection conditions:

For electrons:

For holes:

Basic PN Junction Equation Set

1. Poisson's equaion:

2. Transport equations:

3. Continuity equations:

General solution for no electric eifled, constant generation

Equations for PN Junctions

Built-in voltage pn homojunction:

General ideal diode equation:

I₀ for wide base diode:

I₀ for narrow base diode:

Full diode saturation currrent equation:

Depletion region recombination:

Solar Cell Equations

for constant G, wide base

Material Constants and Commont Units

Intrinsic carrier concentration:

Effective density of states:

Intrinsic energy level:

Diffusivity

Minority carrier diffusion length:

Resistivity and conductivity:

Resistance, homogeneous:

Permittivity:

Radiant Energy

Wavelength and energy of a photon:

If E is in eV and λ is in μm:

Spectral irradiance for black body:

Power density of a non-ideal black body:

Photon flux and power density: