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: 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: 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