Under low level injection conditions, the concentration of minority carriers in a semiconductor increases greatly while the majority carrier concentration remains mostly unchanged. The low level injection equation, which describes this phenomenon, is derived from the current density, continuity, and diffusion equations. This low level injection equation can then be used to derive the diode equation, which models the current-voltage relationship of a PN junction diode under low level injection conditions.

1. Steady-State Low level injection
• Definition of low level injection.
• Derivation of low level injection eqn.
• Derivation of Diode-Equation from low level injection eqn

2. Definition of low level injection
• Low level injection conditions for a P-N junction refers to
the state where the number of minority carriers generated
are small compared to the majority carriers of the material.
Essentially, the semiconductor's majority carrier concentration
will remain (relatively) unchanged, while the minority carrier
concentration sees a large increase. In this condition minority
carrier recombination rates are linear.

3. Derivation of low level injection eqn
1. Low level injection equation is derived from diffusion eqn.
2. Diffusion equation is derived from continuity eqn.
3. Continuity equation is derived from current density eqn.
current density eqn > continuity eqn > diffusion eqn > low level injection eqn

4. Current density equation

5. Continuity equation

6. Diffusion equation
Current density Continuity eqn
Diffusion equation

7. Low level injection

9. Derivation of Diode-Equation from low level
injection eqn

10. Diode equation