# 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:

### 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