Direct and indirect recombination

Recombination is the process in which a conduction band electron falls into an empty state (hole) in the valence band, so a free electron–hole pair disappears. It balances thermal generation in equilibrium.

1. Direct (band-to-band) recombination

The electron at the bottom of the CB falls straight into a hole at the top of the VB. Energy $\approx E_g$ is given out as a photon ($h\nu = E_g$).

• Possible only when CB minimum and VB maximum are at the same k (direct band gap: GaAs, InP).
• Rate is proportional to both concentrations: $R = Bnp$.
• Fast; used in LEDs and lasers.

 Ec ----- e ---------
          |
          |  photon hv = Eg  ~~>
          v
 Ev ----- h ---------

2. Indirect recombination (through recombination centres)

In indirect materials (Si, Ge) direct transition is very unlikely because momentum must also change. Instead recombination takes place through a recombination centre – an impurity (Au, Fe) or crystal defect – that creates a localised level $E_r$ deep in the gap.

Steps:

1. The centre captures a conduction electron; energy is given to lattice vibrations (phonons).
2. The trapped electron then drops into the valence band and fills a hole (or the centre captures a hole).
3. The centre is empty again and ready for the next event.

 Ec ----- e ---------
          | (phonons)
 Er  ...  * ......... recombination centre
          | (phonons)
 Ev ----- h ---------

The energy is released mainly as heat in small steps. Minority carrier lifetime is set by the centre density: $\tau = 1/(C_r N_r)$ approximately.

Comparison