7.5 Characteristics of a Practical Diode

The Shockley equation adequately predicts the current-voltage characteristics of germanium p-n junctions at low current densities. For Si and GaAs p-n junctions，however，the ideal equation can only give qualitative agreement. The departures from the ideal are mainly due to the following factors：

（1）The generation and recombination of carriers within the narrow depletion region

Based on the quantitative analysis，the current-voltage relation for a real pn junction is accurately modeled by an equation having two terms：

I=IS［exp（qVa/kT）-1］+Ir0［［exp（qVa/2kT）-1］ （7.2）

The first term，which is normally dominant in forward bias，is exactly as given in Eq.（7.1）. The second term，due to carrier generation and recombination in the depletion region，has an extra factor of 2 in the denominator of the exponent. Hence it varies roughly as the square root of the first term. Thus at small forward currents，and in reverse bias（i. e. Va＜0），the second term becomes an important factor ［Fig.7.5，curve（a）］. The pre-factor Ir0 is proportional to the volume in which this generation and recombination occurs，i. e. the volume of the depletion regions. Hence Ir0 increases with the increase in depletion-layer width，which occurs in reverse bias，and the reverse current is thus prevented from saturating in a real diode ［Fig.7.5，curve（e）］.

（2）The high-injectioncondition at high current densities（under the forward-bias condition）

Because of the high-injection the current then becomes roughly proportional to exp（qVa/2kT），as shown in Fig.7.5，curve（c）.

（3）Voltage drops across the series resistance

At high forward currents the diode current is limited more by the small series resistance Rs in the bulk semiconductor. As a result，the voltage across a junction carrying a high current is smaller by an amount IRs than the total applied voltage as shown in Fig.7.5，curve（d）. Thus Eq.（7.3）is a more accurate representation at high currents：

I=IS{exp［q（Va-IRs）/kT］-1} （7.3）

（4）The breakdownmechanism

Beyond a few volts of reverse bias，the diode current rises dramatically as shown in Fig.7.5，curve（f），a phenomenon termed breakdown discussed in next session.