SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

4.3. CURRENT FLOW: P-N DIODE UNDER BIAS 155

The built-in potential is given by

eVbi = Eg− 0. 06 − 0 .206 eV

=1. 1 − 0. 06 − 0. 206

=0.834 eV

The depletion width on thep-side is given by

Wp(Vbi)=

{

2 Vbi

e

[

Nd

Na(Na+Nd)

]} 1 / 2

∼=

{

2 ×(11. 9 × 8. 84 × 10 −^12 F/m)× 0 .834 (volts)

(1. 6 × 10 −^19 C)

×

1022 m−^3

1024 m−^3 ×(1. 01 × 1024 m−^3 )

} 1 / 2

=3. 2 × 10 −^9 m=32A ̊

The depletion width on then-side is 100 times longer:

Wn(Vo)=0. 32 μm

4.3 P-NDIODE UNDER BIAS ...........................

We have noted that in the absence of an applied bias, even though there is no current flowing
in the diode, there are drift and diffusion currents that flow and exactly cancel each other. In the
presence of the applied bias, the balance between the drift and diffusion currents is disturbed and
a net current will flow. Under the following simplifying assumptions, one can use the formalism
of the previous section to study the biased diode. These approximations are found to be valid
under usual diode operating conditions.

• We assume that the change in carrier densities is small so that we can use the concept of quasi-
  equilibrium. The diode is made up of quasi-neutral regions and the depletion region. In the
  depletion region, the electron and hole distributions are essentially described by a Boltzmann
  distribution and that the concept of a quasi-Fermi level (see section 3.7 and section 4.5.2) is
  valid for electrons and holes. The quasi-Fermi levels for the electrons and holes extend from the
  quasi-neutral regions as shown in figure 4.5.


• The external potential drops mainly across the depletion region because the major barrier to
  current flow is thep-njunction dipole.
  The key to thep-ndiode operation is that a bias applied across the diode can shrink or increase
  the barrier seen by electrons and holes. This is shown schematically in figure 4.5. When a
  forward biasVfis applied, thep-side is at a positive potential with respect to then-side. In the
  reverse bias case, thep-side is at a negative potential−Vrwith respect to then-side.
  In the forward bias case, the potential difference between then-andp-side is (applied bias
  V=Vf)
  VTot=Vbi−V=Vbi−Vf (4.3.1)