Fundamentals of Modern VLSI Devices

Electron and hole generation and recombination processes play an important role in the operation of many silicon devices and in determining their current–voltage characteristics. Electron and hole generation and recombination can take place directly between the valence band and the conduction band, or indirectly via trap centers in the energy gap. Direct transitions involve energies larger than the bandgap energy Eg . Indirect transitions via trap centers involve energies smaller than Eg . As a result, indirect transitions are much more efficient than direct transitions. In this appendix, we derive the expressions for the generation and recombination rates due to indirect transitions via trap centers and examine the characteristics of generation and recombination currents.

Capture and Emission at a Trap Center

Consider a piece of silicon having in it a concentration of Nt trap centers per unit volume. For simplicity, we assume all of the trap centers to be identical and located at energy Et in the bandgap. Also, we assume that each trap center can exist in one of two charge states, namely neutral when it is not occupied by an electron and negatively charged when it is occupied by an electron. Each unoccupied center can capture an electron from the conduction band (electron capture). An electron in an occupied center can be emitted into the conduction band (electron emission). Similarly, each occupied center can capture a hole from the valence band (hole capture), and an unoccupied center can emit a hole into the valence band (hole emission). These four capture and emission processes are illustrated in Fig. A5.1. Note that in hole capture, the center turns from a negatively charged (occupied) state into a neutral (unoccupied) state. Hole capture from the valence band is equivalent to electron emission into the valence band. In hole emission, the center turns from a neutral (unoccupied) state into a negatively charged (occupied) state. Hole emission is equivalent to electron capture from the valence band.