4 Bipolar Junction Diode II
4.1 Forward Bias Conditions
When an external electric field is applied to the p-n junction, which is
positive with respect to the p-type and negative with respect to the ntype, the device is said to be forward biased (see Fig. 4.1). In this case
the applied electric field tends to counteract the built-in field which
lowers the potential barrier between p-type and n-type materials by an
amount equal to the applied voltage. This lowers the barrier which
opposes current flow and allows an increased number of electrons to
cross the junction and diffuse into the p-region. Likewise an increased
number of holes can cross the junction and diffuse into the n-region.
This has the effect of raising the minority carrier concentration in both
regions above the equilibrium level. The increased levels of carrier
concentration are maintained as long as the external bias voltage is
applied. Carriers which recombine as they diffuse into the neutral
regions of the diode are replaced by the external supply to maintain
the increased carrier concentrations. This results in a continuous flow
of current in the forward direction from p-type to n-type through the
diode.
4.2 Reverse Bias Conditions
When an external electric field is applied to the p-n junction which is
negative with respect to the p-type and positive with respect to the ntype, the device is said to be reverse biased (see Fig. 4.1). In this case,
the applied field tends to enhance the built-in field, which increases
the potential barrier between p-type and n-type materials by an
amount equal to the applied voltage. In this case, charge carriers are
drawn further away from the junction, which lowers their
concentrations in this region from their unbiased equilibrium levels
towards zero. However, there is still a small amount of minority
carriers generated in each region, due to thermal agitation, which can
cross the junction and contribute to a small leakage current in the
reverse direction known as the reverse saturation current.
1
Physical Model
Equilibrium
V=0
Forward Bias
V = Vf
I
Reverse Bias
V = -Vr
I
+ + +
+++
+ p+
+ ++
+++
- - -- - n- - - - -
+
+
+
+
+
E
Barrier Potential
I
- - - - - - - -n
- - - -
+ +
+
p +
+ +
+ +
- - n
- - -
++
++
+p
++
++
E
E
Vn
Vo -Vf
Vo
Vo + Vr
Vp
Ecp
Ecp
Efp
Evn
q Vo
Ecn
Efn Evp
q(Vo - Vf) Ecp
Ecn
q(Vo + Vr)
q Vf
Evn
Evp
qVr
Ecn
Ev
n
Evn
Minority Carrier Concentration
npo
pno npo
xp
xn
pno
npo
Fig. 4.1 Bias Conditions of a p-n Junction with Na ≈ Nd
2
pno
4.3 Charge Transport Under Biased Conditions
The built-in electric field in the p-n junction is quite high, of the order
1000 kV/m (1MV/m). Hence, when an external electric field is applied
to bias the device, the applied field is developed almost entirely across
the junction or depletion region and only a very small field exists along
the main n-type and p-type regions of the diode as can be seen in Fig.
4.2. This means that carriers crossing the junction do so by a drift
mechanism while carriers passing through the main neutral regions do
so, primarily, by a diffusion mechanism. This means that at the
boundaries on either side of the junction, the situation is effectively
one where excess minority carriers are being injected into the nonionized doped regions and begin to diffuse into these regions,
recombining with majority carriers as they do so. Excess holes diffuse
into the n-type region while excess electrons diffuse into the p-region.
4.4 Carrier Injection Under Bias Conditions
As discussed in a previous lecture, excess minority carriers injected
through a boundary into a volume of semiconductor material rich in
majority carriers diffuse into the material, recombining with majority
carriers as they do so. This sets up an exponential minority carrier
concentration profile in the volume in question. Fig. 4.3 shows the
situation for the forward-biased p-n junction where there is an
exponential distribution of excess electrons into the p-region away
from the junction and a similar distribution of excess holes into the nregion away from the junction. Note that the exponential distribution
applies to excess carriers and, hence, sits on top of the unbiased,
normal equilibrium levels.
3
depletion
p-type
n-type
e-
eh+
eh+
h+
diffusion
diffusion
drift
_ internal electric +
field
I
Fig. 4.2
Current Flow Mechanisms in Forward Biased p-n Diode
n(x)
p (x)
p (x = 0)
n(x = 0)
p-type
n-type
Electron
concentration
Hole
concentration
p’(x = 0)
n ’(x = 0)
p0
n0
xp
0
0
xn
Direction of current flow
Fig. 4.3
Carrier Concentration Profiles in a Forward Biased p-n Diode
4
It can be shown that when a bias voltage, V, is applied to the junction,
the probability of a carrier crossing the junction is modified by a factor
of eqV/kT = eV/VT. Consequently, the concentration of minority carriers
on either side of the junction is also modified by the same factor from
the unbiased, equilibrium value. The profiles of the excess carrier
concentrations can, therefore, be related to the bias voltage, V, applied
to the p-n junction as follows…
I)
Concentrations at boundaries:
n(x = 0) = n0eV/VT
II)
;
p(x = 0) = p0eV/VT
Excess concentrations at boundaries:
n’(x = 0) = n(x = 0) - n0
;
p’(x = 0) = p(x = 0) - p0
n’(x = 0) = n0( eV/VT - 1)
;
p’(x = 0) = p0( eV/VT - 1)
III) Excess concentration as functions of distance:
n’(x) = n0( eV/VT - 1 ) e-x/Ln
4.5
;
p’(x) = p0( eV/VT – 1 ) e-x/Lp
The Ideal Diode Equation
It is desired to derive a current-voltage relationship for the p-n diode
so that it can be characterized as an electrical circuit element. Then,
an expression for the total terminal current through the device must
be obtained. If current flow in the neutral regions of the device is
taken to be by diffusion only, then the total current due to the applied
bias can be taken as the sum of the diffusion currents due to both
carrier types flowing at the boundaries of the junction with the neutral
regions (before recombination has taken place). It was shown
previously that the diffusion fluxes for electrons and holes are given
as:
J n diff
= qD
n
dn
dx
and
Jp
diff
= − qD
p
dp
dx
This is the case for electrons and holes traveling in the same xdirection. In the case of the forward biased diode, the electrons and
holes are traveling in opposite directions. If the positive x-direction is
taken as the direction of conventional current flow, i.e the direction of
flow for positive charge, then the total terminal current due to excess
charge carrier injection is given as:
5
I = − qAD
n
dn' (x)
|x = 0 − qAD
dx
dp' (x)
|x = 0
dx
p
Substituting for n’(x ) and p’(x ) gives:
d
d


I = −qA D n
n0 (e V/VT - 1)e − x/Ln + D p
p 0 (e V/VT - 1)e − x/Lp 
dx
 dx
x =0
[
]
[
]
 D

D
I = −qA − n n0 (e V/VT - 1)e − x/Ln − p p0 (e V/VT - 1)e − x/Lp 
Lp
 Ln
x =0
D

D
I = qA  n n0 + p p0  e V/VT − 1
Lp
 Ln

(
If V is large and negative, then e
conditions:
V/VT
)
→ 0 so that for reverse bias
D

D
IREV = −qA n n0 + p p 0  = −Is
Lp
 Ln

where, Is, is referred to as the reverse saturation current. Substituting
gives:
(
)
I = Is e V/VT − 1
This is called the Ideal Diode Equation and characterizes the currentvoltage relationship of the diode as an electrical circuit element.
6
The Ideal Diode relationship is shown plotted in Fig. 4.4. From the
curve it can be seen that when the diode is forward biased, the regular
exponential relationship can readily be recognized. The degree of
current conduction under this condition depends essentially on the
doping concentrations used in the semiconductor materials. When the
diode is reverse biased with the applied voltage V negative, the
exponential factor is negligible and the current levels off at the reverse
saturation value –IS. This value is small and it can be seen that once a
small value of reverse voltage is exceed the current becomes
independent of the voltage. This current is essentially a leakage
current present due to thermally generated carriers.
I
V
Fig. 4.4
Current-Voltage Relationship for Ideal Diode
7