3
Bipolar Junction Diode I
3.1 Introduction
Consider a piece of doped n-type semiconductor and a piece of
intrinsic semiconductor. Both pieces of semiconductor are electrically
neutral i.e positive and negative charges are balanced. The doped, ntype material is, however, much richer in free electron carriers than
the intrinsic material in the conduction band, i.e. the concentration of
electrons in the conduction band is higher in the n-type material. (See
Figure 3.1 below.)
diffusion
EC
n_type
intrinsic
EV
Boundary
Fig. 3.1
Joining n-type and Intrinsic Material
If the two pieces of material are joined together perfectly so that the
crystalline structures of each meet exactly, the higher concentration of
free electrons in the n-type causes diffusion across the boundary
between the two materials. Electrons migrate from the n-type material
into the intrinsic material in an effort to equalize the electron
concentration throughout the material. Note, however, that as
electrons cross the boundary from n-type to intrinsic material,
positively charged, ionized atoms which donated these electrons
remain behind in n-type material.
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3.2 The p-n Junction
Consider the separate p-type and n-type materials shown in Fig. 3.2.
In isolation, both materials possess charge neutrality and the
conduction and valence band energies are at the same level in each
type. Note, however, that due to the doping involved, the Fermi levels
of the two materials are different, being close to the donor level in the
n-type and the acceptor level in the p-type.
When the two pieces of material are joined together, there is an
imbalance of free carrier concentrations in both conduction and
valence bands on each side of the junction. This gives rise to carrier
concentration gradients across the junction. Consequently, electrons
diffuse across the junction from n-type to p-type, while holes diffuse
from p-type to n-type material, setting up associated diffusion
currents. However, electrons entering the p-type material readily
recombine with the plentiful holes present here and likewise, holes
entering the n-type material readily recombine with the plentiful
electrons here. In fact, as this recombination takes place, the
concentration of free carriers in the vicinity of the junction drops
dramatically. Hence, the junction region is referred to as the depletion
region.
Furthermore, as the diffusion of carriers and the resulting
recombination progresses, there is a build-up of ionized dopant atoms
in the region of the junction, negatively charged acceptor atoms in the
p-type and positively charged donor atoms in the n-type material. This
results in the build-up of an electric field acting from n-type to p-type
material. This field, due to ionization, tends to oppose the diffusion of
electrons from n-type to p-type and also the diffusion of holes from ptype to n-type. In fact, the electric field sets up drift currents,
internally in the semiconductor, in the opposite direction to the
diffusion currents for both types of carrier. This electric field builds up
until an equilibrium is reached where the drift and diffusion currents
are equal and opposite in each case so that there is no longer any net
transfer of either type of carrier from one material to the other. The
internal built-up electric field then remains at this level giving rise to a
“barrier-potential” across the junction where the n-type material is
positive with respect to the p-type material.
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n-type
p-type
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-
-
-
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+
+
+
-
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-
+
+
+
+
+
-
+
+
+
+
+
-
p-type p-n junction n-type
+
+
+
+
+
+
+
+
+
+
+
+
+
+
-
-
-
- - -
+
E field
VN
VO
VP
EC
EFP
EV
EC ECP
EFN
qVO
ECN
EFN
EFP
EV
EVP
EVN
Carrier flow
Hole diffusion
Hole drift
Electron diffusion
Electron drift
Fig. 3.2




Changes in Energy Bands in the Formation of a p-n Junction
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The built-in field caused by the ionization of the junction gives rise to
an electrostatic potential difference between the two sides of the
junction. This is the potential or voltage measured with respect to
absolute ground or zero potential. This induces a shift in the energy
levels of both conduction and valence bands on each side of the
junction. The energy levels readjust so that they are higher in the ptype material relative to the n-type material (Note that this is
compatible with the electric field). In fact, equilibrium is reached when
the Fermi level in the p-type material becomes equal to the Fermi level
in the n-type material. In other words, the Fermi level is constant
across the entire p-n semiconductor and has a gradient of zero
throughout. If this were not the case, then the transfer of electrons on
the one hand and holes on the other, between the two types of
material would not be equal in both directions. Note that the
electrostatic potential is higher or more positive in the n-type material
than the p-type while the conduction and valence band energy levels
are lower in the n-type material than the p-type.
3.3 Barrier Potential
Under equilibrium conditions, the barrier potential exists entirely
across the junction as it is due to the ionization of fixed dopant atoms
as can be seen in Fig. 3.3. The carrier concentrations in the neutral
regions away from the junction can be closely approximated as those
in purely p-type and n-type materials, respectively.
p-type
p
Po
n Po
n-type
= Na
n no = Nd
2
ni

Na
pno
ni 2

Nd
VO
Fig. 3.3
Barrier Potential Developed across Ionised Depletion Region
4
Under equilibrium conditions, there is no net transfer of either type of
carrier from one material to the other i.e the combined diffusion and
drift currents are zero for both holes and electrons. Considering
electrons then:
Jn drift  Jn diff  0
nq nE  qDn
nnE  -Dn

From
the
Einstein
dn
0
dx
dn
dx
n
1 dn
E
Dn
n dx
relation
we
have,
n
q

Dn kT
so
that
after
substituting:

q
1 dn
E
kT
n dx
The electric field, E, exists across the junction and gives rise to the
potential barrier, VO. The field can be considered as the gradient of the
dV
electrostatic potential so that E  
where V can be taken as the
dx
electrostatic potential as a function of x. Note that the negative sign is
included to signify that the electric field is specified in the direction of
decreasing potential. Then:
q dV(x)
1 dn(x)

kT dx
n(x) dx
Integrating across the junction with respect to x from the p-type side
to the n-type side and applying the appropriate limits gives:
q
kT

Vn
Vp
1
dn
npo n
dV  
5
nno
Hence:
q
(Vn  Vp )  ln(n no )  ln(n po)
kT
The potential difference across the junction with voltages defined from
p-type to n-type material is Vp - Vn = V0, the barrier potential. In
addition, the electron concentrations in the p-type and n-type
materials are:
n-type
nno  Nd
p-type
ni2
npo 
Na
This gives…
n2i
q

VO  ln Nd  ln
kT
Na
so that…
VO  
NN
kT
ln a 2 d
q
ni
Note that the barrier potential is negative as measured in a positive xdirection from p-type to n-type material.
3.4
Junction Capacitance
The depletion region is greatly reduced in its concentration of free
charge carriers and is oppositely charged on either side due to the
presence of the ionized dopant atoms in each type of doped material.
This is analogous to the two charged plates of a capacitor and gives
rise to the property of junction capacitance. The capacitance is
dependent on the width of the junction and hence on the doping
concentrations of both p-type and n-type materials. It is also
dependent, however, on any electric field which may be applied
externally and is hence a bias voltage dependent property in
semiconductor devices.
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