SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

4.2.P-NJUNCTION IN EQUILIBRIUM 151

p n

–Wp 0

pp

Structure

Vp

Potential profile

Electron band

profile

pn

np nn

Wn

Hole density

Electron density

Vn

Ec

Ev

Ev

Ec

EF

eVbi

Vbi

Eg

Figure 4.3: A schematic showing thep-ndiode and the potential and band profiles. The voltage
Vbiis the built-in potential at equilibrium.

In this relationVbiis the built-in voltage in the absence of any external bias. Under the approxi-
mations discussed later, a similar relation holds when an external biasVis applied to alterVbito
Vbi−V, and will be used when we calculate the effect of external potentials on the current flow.
We need to solve the Poisson equation to calculate the width of the depletion region for the
diode under no applied bias. The calculation in the presence of a biasVwill follow the same
approach andVbiwill simply be replaced byVbi−V, the total potential across the junction. Note
that we have the equality
AWpNa=AWnNd (4.2.8)

whereAis the cross-section of thep-nstructure andNaandNdare the uniform doping densities
for the acceptors and donors.