SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

168 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES

The generation-recombination current therefore has an exponential dependence on the voltage
as well, but the exponent is different. The generation-recombination current is

IGR = IR−IG=IR−IR(V=0)

= IGR◦

[

exp

(

eV

2 kBT

)

− 1

]

(4.4.12)

whereVis small so that the MRP is assumed constant.
The total device current now becomes

I = Io

[

exp

(

eV

kBT

)

− 1

]

+I◦GR

[

exp

(

eV

2 kBT

)

− 1

]

or

I ∼= IS

[

exp

(

eV

nkBT

)

− 1

]

(4.4.13)

= IS

[

exp

(

V

n

·

e

kBT

)

− 1

]

wherenis called thediodeidealityfactor or thevoltagepartitioningfactor because the factor of 2
in equation 4.4.12 is a consequence of recombination occurring at the maximum recombination
plane. The prefactorIGRo can be much larger thanIofor real devices. Thus at low applied
voltages the diode current is often dominated by the second term. However, as the applied bias
increases, the diffusion current starts to dominate. We thus have two regions in the forward I-V
characteristics of the diode, as shown in figure 4.14. One of the reasons it is experimentally
difficult to measure an IV curve with an ideality factor of 2 is because the MRP is actually
changing with applied bias.
In figure 4.15, we show the effects that material defects can have on the diode current char-
acteristics. We can see that defects such as threading dislocations can cause large undesirable
reverse leakage currents that are not predicted by the ideal diode characteristics calculated in this
section.

Example 4.2Consider thep-ndiodes examined in problem 4.12. In that example, the

diode prefactor was calculated assuming that there is no recombination in the depletion

region. Calculate the effect of the generation-recombination current assuming a lifetime of

10 −^6 s.

The prefactor of the generation-recombination current is

IGRo =

eAni

2 τ

πkBT

eE(0)

At zero applied bias, we know that the MRP occurs wherepp 0 e−

ψ(x)

kBT =ni. This allows