**Branch :**Computer Science and Engineering

**Subject :**Fundamental of Electronic Devices

**Unit :**Junction Properties

## Effects of Contact Potential on Carrier Injection

If the forward-bias I-V characteristics of various semiconductor diodes are compared, it becomes clear that the band gap has an important influence on carrier injection.

**Effects of contact potential on carrier injection:**

The reason for the small current at low voltages for these devices can be understood from a simple rearrangement of the diode equation. If we rewrite Eq. for a forward-biased p^{ }-n diode (with V > kT/q) and include the exponential form for the minority carrier concentration pn, we obtain

This accounts for the dramatic increase in diode current near the band gap voltage in Fig. given below. Contributing to the small current at lower voltages is the fact that the minority carrier concentration p_{n} = n_{i}^{2}/N_{d} is very small at low temperature (n_{i} small) and with heavy doping (N_{d} large).

For high injection levels, however, Δp_{p} can be comparable to p_{p} and we must write

we get at either edge of the depletion region

For example at -x_{po} we then get

Keeping in mind that and in high level injection

Hence, the diode current in high-level injection scales as