SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

156 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES

pn ppn n

Vf

EQUILIBRIUM FORWARD BIAS REVERSE BIAS

(a)

(b)

(c)

eVf

Vr

Vbi Vbi – Vf Vbi + Vr

Vp

Vn

EFn E

Fp

EFp EFn

EFp

EFn

eVr

Depletion region

}

EFn

EFp

EFp

EFn

Figure 4.5: A schematic showing (a) the biasing of ap-ndiode in the equilibrium, forward, and
reverse bias cases; (b) the energy band profiles. In forward bias, the potential across the junction
decreases, while in reverse bias it increases. The quasi-Fermi levels are shown in the depletion
region.

while for the reverse bias case it is (the applied potentialVis negative,V=−Vr,whereVrhas
a positive value)
VTot=Vbi−V=Vbi+Vr (4.3.2)

Undertheapproximationsgivenabove,theequationsforelectricfieldprofile,potentialprofile,
anddepletionwidthswecalculatedintheprevioussectionaredirectlyapplicableexceptthatVbi
isreplacedbyVTot.Thusthedepletionwidthandthepeakelectricfieldatthejunctiondecrease
underforwardbias,whiletheyincreaseunderreversebias,ascanbeseenfromequation 4.2.24
and4.2.25 ifVbiisreplacedbyVTot.