### 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:

*I _{0}* for wide base diode:

*I _{0}* 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:

Material | mn*/m0 | mp*/m0 | EG (eV) | ni (cm-3) | c (eV) | eS |

Si | 1.18 | 0.81 | 1.12 | 1.0 × 10^{10} |
4.03 | 11.8 |

Ge | 0.55 | 0.36 | 0.66 | 2.0 × 10^{13} |
4.13 | 16.0 |

GaAs | 0.066 | 0.52 | 1.42 | 1.8 × 10^{6} |
4.07 | 13.1 |

InP | 0.08 | 0.6 | 1.34 | 1.3 × 10^{7} |
4.38 | 12.5 |