Biasing pn Junctions - 2
• The forward bias will decrease the contact potential at the
junction so that the diffusion of majority carriers is enhanced.
qv D / kT
• The diffusion current is now: Id = I0 e
where q is the charge on an electron, vD is the voltage across the
pn junction, k is Boltzmann’s constant, and T is temperature.
Note: kT/q = constant at a given T ≅ 25 mV at room temperature.
• The net diode current under forward bias is given by the diode
equation:
iD = Id − I0 = I0 (e qv D / kT − 1)
• Because I0 is typically small
(10-9 to 10-15 A), if vD is larger than
a few tenths of a Volt, then this
can be approximated as:
diode
current
iD
iD ≅ I0 e qv D / kT
Diode
i-v
curve
diode voltage v D
PHY305F - Electronics Laboratory I, Fall Term 2003 (K. Strong)
Section 6, Page 9
Semiconductor Diodes - 1
• pn junctions are useful in circuits because they can conduct
current in only one direction, i.e., only when forward biased.
• A device having a single pn junction and ohmic contacts (metalsemiconductor) at its terminals is called a [semiconductor] diode.
• The behaviour of semiconductor
diodes is summarized in the i-v
curve.
iD
• This shows a reverse breakdown
region that exists when a very high
reverse bias is applied. If the
magnitude of the applied voltage is
> VZ, then the diode will conduct
current in the reverse direction.
PHY305F - Electronics Laboratory I, Fall Term (K. Strong)
vD
ohmic
contacts
pn junction
diode
circuit
symbol
p
n
Semiconductor Diodes - 2
Complete i-v characteristic of a semiconductor diode
iD
Diode behaves like an
open circuit, conducting
a small reverse current
Reverse
breakdown
region
_V
Diode behaves like a
short circuit, readily
conducting current
Reverse
bias
region
Forward
bias
region
Z
Diode behaves like a
short circuit, readily
conducting current,
now in the reverse
direction
Zener
voltage
V
Offset
voltage
vD
iD
+
vD
_
(from Rizzoni Figure 8.10)
PHY305F - Electronics Laboratory I, Fall Term (K. Strong)
Semiconductor Diodes - 3
• How does reverse conduction occur?
→ When a very large negative bias is applied to the pn junction, a reverse
current larger than the normal reverse saturation current can flow.
→ The large electric field also energizes electrons such that if they collide
with other charge carriers having lower energy, then they will transfer
some of their energy allowing more charge carriers to contribute to
conduction. This is called impact ionization.
→ The new carriers may have enough energy to repeat this process, so
that an avalanche occurs with one electron leading to the ionization of
several others. This is called avalanche breakdown.
• Zener breakdown is obtained by heavily doping regions near the
ohmic contacts. The high density of charge carriers can sustain a
large reverse breakdown current at a nearly constant reverse bias this is called the Zener voltage (VZ). Useful in voltage regulators...
PHY305F - Electronics Laboratory I, Fall Term 2003 (K. Strong)
Section 6, Page 12
6
Ideal Diodes - 1
• The i-v curve of an ideal diode can be represented by an open
circuit when vD < 0 and by a short circuit when vD ≥ 0.
diode
current
iD
Ideal
diode
i-v
curve
vD
ideal
diode
symbol
diode voltage v D
vD
circuit model
for v > 0 (short)
circuit model
for v < 0 (open)
• The model of an ideal diode can be useful when analyzing diode
circuits, for example, in determining whether a diode is
conducting or not. Let’s look at an example ...
PHY305F - Electronics Laboratory I, Fall Term (K. Strong)
Ideal Diodes - 2
vD
vD
1 kΩ
1.5 V
iD
Circuit containing
ideal diode
vD
1 kΩ
1.5 V
iD
Circuit assuming
ideal diode conducts
1.5 V
1 kΩ
iD
Circuit assuming
ideal diode does
not conduct
• Assume diode conducting (vD≥0). Substitute short circuit (vD=0). Diode current
is iD=1.5/1000=1.5 mA assumed positive (clockwise) because diode assumed
on. Because the direction of the current and the diode voltage are consistent
with the “on” assumption (vD≥0, iD>0), the diode must indeed be conducting.
• Assume diode not conducting (vD<0). Substitute open circuit. Apply KVL to show
that we must have vD=1.5 V since no current flows. Thus 1.5 = vD + 1000iD = vD.
But this contradicts the initial assumption that the diode is off and vD<0. So the
assumption must be wrong and the diode is conducting.
PHY305F - Electronics Laboratory I, Fall Term (K. Strong)
Methodology for Ideal Diodes
Methodology for determining the conduction state of an ideal diode:
(1) Assume a diode conduction state (on or off).
(2) Substitute the ideal circuit model into the circuit (short circuit if
on, open circuit if off).
(3) Solve for diode current and voltage using linear circuit analysis
techniques.
(4) If the solution is consistent with the assumption, then the initial
assumption was correct. If not, then the diode conduction state
is opposite to that initially assumed.
→ e.g., If the diode has been assumed to be off but the diode voltage
calculated after replacing it with an open circuit is a forward bias,
then it must be true that the actual state of the diode is on.
PHY305F - Electronics Laboratory I, Fall Term (K. Strong)
Rectification - 1
• A useful application of semiconductor diodes is in the rectification
of AC signals, i.e., the conversion of an AC signal with zero
average (DC) value to a signal with nonzero DC value.
→ e.g., can obtain a DC voltage supply from an AC line voltage
• Consider the circuit below with an AC voltage source connected
to a load through an ideal diode in series. The diode will only
conduct for the positive half-cycle of the sinusoidal voltage, i.e.,
vD ≥ 0 is only true when vi > 0.
_
+ vD
• The rectified waveform will have
nonzero DC voltage.
• Unknowns vL and iD can be
found using:
iD = v i RL
when v i > 0
v L = iDRL
PHY305F - Electronics Laboratory I, Fall Term (K. Strong)
+
+
_
v
i
t
= 155.56 sin
i
D
(from Rizzoni Figure 8.20)
R
L
v
L
_
60-Hz source voltage
Vi ( V )
Rectification - 2
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.06
0.07
0.08
0.09
0.1
Rectified voltage
VL ( V )
Time (s)
0
0
0.01
0.02
0.03
0.04
0.05
Time (s)
• The average load voltage is 1/T times the integral over one period:
π/ ω
ω
155.56
v load,DC =
155.56 sin ωt dt =
= 49.52 V
∫
2π 0
π
• This is a half-wave rectifier (preserves half the waveform).
Because it loses half the energy it is not efficient. Full-wave
rectifiers also recover the negative half of the AC waveform.
(from Rizzoni Figure 8.21)
PHY305F - Electronics Laboratory I, Fall Term (K. Strong)
Offset Diode Model
• The ideal diode model does not account for the presence of an
offset voltage, which is always present in semiconductor diodes.
• The offset diode model consists of an ideal diode in series with a
battery of strength equal to the offset voltage (typically Vγ = 0.6 V
for Si diodes). This battery shifts the i-v curve to the right.
• The offset diode model is an open circuit for vD < 0.6 V (Vγ) and
a 0.6 V battery for vD ≥ 0.6 V.
on
diode
current
iD
Offset
diode
i-v
curve
0.6
vD
0.6 V
0.6 V
offset
diode
PHY305F - Electronics Laboratory I, Fall Term (K. Strong)
off
circuit model
for v D > 0.6 V
(battery)
circuit model
for v D< 0.6 V
(open)