DEPARTMENT OF

ELECTRICAL ENGINEERING

The PN junction diode

December 17, 2024

© Schultz, M. E., & Grob, B. (2015). Grob’s basic electronics.

Dubuque, IA: McGraw-Hill.
© Sedra, A. S., & Smith, K. C. (1998). Microelectronic circuits.
New York: Oxford University Press.
© Theraja, B. L., & Theraja, A. K. (2005). A textbook of
electrical technology: In S.I. system of units. New Delhi: S. Chand
and Co.
Ony
angoS
.Obur
a 1/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The pn-junction

An n-type or a p-type semiconductor isn’t very useful by itself,

its nearly just as useful as a resistor.

But when a crystal is doped so that half is p-type and half is

n-type, then a new thing, the pn-junction, comes into existence.

Ony
angoS
.Obur
a 2/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The pn-junction implements the diode,...

... and plays an important role in the structure and operation

of the BJT,...

...and in the understanding of all kinds of semiconductor

devices.

Ony
angoS
.Obur
a 3/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

In practice, both the p and n regions are formed within a

single silicon crystal by creating regions of p-type and n-type
dopings.

Figure 1: A simplified physical structure of the pn-junction.

Ony
angoS
.Obur
a 4/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The plane dividing the two zones is called junction. This plane is
assumed to lie where the density of donors and acceptors is
equal.

Because a pn-junction implements the junction diode, its

terminals are labelled anode and cathode.

The pn-junction diode is a unidirectional device; thus it only

allows current flow through it in one direction.

Ony
angoS
.Obur
a 5/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

(a) Basic construction of a diode

showing the separate p and n regions

(b) Schematic symbol for a semicon-

ductor diode showing the anode (A)
and cathode (K) terminals.

Figure 2: Simplified physical structure of the pn-junction.

Ony
angoS
.Obur
a 6/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The pn-junction with open-circuit terminals

(equilibrium)

Under open circuit (or equilibrium) condition, the external

terminals are left open.

The “+” signs in the p-type material denote the majority holes.

The charge of these holes is neutralised by an equal amount of

bound negative charge.

Ony
angoS
.Obur
a 7/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

In the n-type material the majority electrons are indicated by “−”

signs.

The charge of the majority electrons is neutralised by an equal

amount of bound positive charge.

Ony
angoS
.Obur
a 8/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The diffusion current ID

▶ There is greater concentration of holes in p-region than

in n-region and vice versa

▶ This concentration differences establishes density

gradient across the junction resulting in carrier diffusion

▶ Holes diffuse from p to n-region and electrons from n-to

p-region and terminate their existence by recombination

▶ These two current components add together to form the

diffusion current ID ,...

....whose direction is from the p to the n side, as indicated

in Figure 3

Ony
angoS
.Obur
a 9/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 3: (a) The pn-junction with no applied voltage (open-circuited

terminals). (b) The potential distribution along an axis perpendicular to
the junction.
Ony
angoS
.Obur
a 10/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The depletion region

The holes diffusing across the junction into the n region recombine
with the majority electrons present there and ∴ disappear.

Thus, some of the bound positive charge in the n-type material

will no longer be neutralised by the free majority electrons,
meaning that some positive charge is created.

This charge is said to have been uncovered (i.e., no longer

neutralised by the free majority electrons).

Ony
angoS
.Obur
a 11/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Since recombination takes place near the junction, there will be a

region close to the junction that is depleted of free electrons...

...and contains uncovered bound positive charge (or positively

ionised atoms), as indicated in Figures 3 and 4.

Figure 4: Formation of the depletion region.

Ony
angoS
.Obur
a 12/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Similarly, the electrons diffusing into p region recombine with some

of the majority holes there, and the holes there disappear.

This courses some of the bound negative charge in the p-type

material to be uncovered.

Thus, in the p material close to the junction, there will be a

region depleted of holes,...

Ony
angoS
.Obur
a 13/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

...and containing uncovered bound negative charge or

negatively ionised atoms, as indicated in Figures 3 and 4.

A carrier-depletion region ∴ exists on both sides of the junction,

with the n side being +vely charged and p side −vely charged.

This carrier-depletion region or, simply, depletion region is also

called the space-charge region.

Ony
angoS
.Obur
a 14/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The charges on both sides of the depletion region cause an

electric field E to be established across the region in the
direction indicated in Figures 3 and 4.

Thus, a p.d. results across the depletion region, with the n

side at a +ve voltage relative to the p side, as in Figure 3(b).

The resulting electric field opposes the diffusion of more

holes into the n region and more electrons into the p region.

Ony
angoS
.Obur
a 15/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Ony
angoS
.Obur
a 16/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The voltage drop across the depletion region is a barrier1

that has to be overcome for holes to diffuse into the n region
and electrons into the p region.

The larger the barrier voltage, the smaller the no. of carriers
that will be able to overcome the barrier and hence the lower
the magnitude of diffusion current.

Thus it is the formation of the barrier voltage, VB (sometimes

denoted as V0 ), that limits the carrier diffusion process.

1 Ony
A barrier because a
itngoS
has.Obu
to r
aovercome for holes to diffuse into the n region
be 17/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

It follows that the diffusion current ID depends strongly on VB .

Ony
angoS
.Obur
a 18/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The drift current IS and equilibrium

In addition to ID due to majority-carrier diffusion, a component

due to minority carrier drift exists across the junction.

Some of the thermally generated holes in the n material move

toward the junction and reach the edge of the depletion region.

There, they experience the electric field in the depletion

region, which sweeps them across that region into the p side.

Ony
angoS
.Obur
a 19/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Similarly, some of the minority thermally generated electrons in

the p material move to the edge of the depletion region.

There, they get swept by the electric field in the depletion

region and cross into the n side.

Ony
angoS
.Obur
a 20/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

These two current components, electrons from p to n and holes

from n to p, add together to form the drift current IS .

The direction of IS is from the n side to the p side of the

junction, as indicated in Figure 3.

Since IS is carried by thermally generated minority carriers, its

value is strongly dependent on temperature.

Ony
angoS
.Obur
a 21/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The value of IS is also strongly dependent on degree of doping,

and the physical size (cross-sectional area) of the junction.

Nonetheless, the value of IS is independent of VB .

This is ∵ the drift current is determined by the no. of minority

carriers that make it to the edge of the depletion region.

Ony
angoS
.Obur
a 22/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Minority carriers that get to the edge of the depletion region

will be swept across by E irrespective of the value of E or,
correspondingly, of VB .

Under open-circuit conditions (Figure 3) no external current exists,

and so the two opposite currents across the junction must be equal,

ID = IS
In equilibrium, under open-circuit conditions, the equality of drift
and diffusion currents applies not just to the total currents
but also to their individual components.

Ony
angoS
.Obur
a 23/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

That is, the hole drift current must equal the hole diffusion
current,...

...similarly, the electron drift current must equal the electron

diffusion current.

This equilibrium condition is maintained by the barrier voltage VB .

Ony
angoS
.Obur
a 24/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Thus, if for some reason ID exceeds IS , then more bound charge

will be uncovered (more atoms will be ionised) on both sides of
the junction,...

...the depletion layer will widen, and the voltage across it

(VB ) will increase.

This in turn causes ID to decrease until equilibrium is achieved

with ID = IS .

Ony
angoS
.Obur
a 25/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

On the other hand, if IS exceeds ID , then the amount of

uncovered charge will decrease,...

...the depletion layer will narrow, and the voltage across it

(VB ) will decrease.

This causes ID to increase until equilibrium is achieved with

ID = IS .

Ony
angoS
.Obur
a 26/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The junction built-in voltage

With no external voltage applied, the VB across a pn-junction is

given by,
 
NA ND
VB = VT ln (1)
ni2

where NA and ND are the doping concentrations of the p side

and n side of the junction, respectively, and VT is the thermal
voltage.

Thus, VB depends both on doping concentrations and on

temperature.

Ony
angoS
.Obur
a 27/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The VB is known as the junction built-in voltage.

Typically, at room temperature, the VB is approximately 0.7 V

for silicon, and approximately 0.3 V for germanium.

When the pn-junction terminals are left open-circuited, the voltage

measured between them will be zero.

Ony
angoS
.Obur
a 28/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

This is because, the contact voltages at the terminals, will

counter and exactly balance the barrier voltage.

If this were not the case, we would draw energy from the
isolated pn-junction, which would violate the principle of
conservation of energy.

Ony
angoS
.Obur
a 29/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Three phenomena at the junction

The following 3 phenomena take place at the junction:

1. A thin depletion layer or region is established on both

sides of the junction. Its thickness is about 10−6 m

2. A barrier potential or junction potential is developed

across the junction

3. The presence of depletion layer gives rise to junction and

diffusion capacitances

Ony
angoS
.Obur
a 30/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The pn-junction with an applied voltage

If a dc voltage is applied between the terminals of a pn-junction so

that the p side is more +ve than the n side, it is referred to as
a forward-bias2 voltage.

Conversely, if the dc voltage is applied such that it makes the n side

more −ve than the p side, it is said to be a reverse-bias voltage.

The pn-junction exhibits different conduction properties in its

forward and reverse directions.

2
Biasing is the application of fixed dc supply to a terminal of an electronic
component toO ny angoS
establish.Obura operating conditions for the component
proper 31/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Junction operation under reverse-bias condition

Figure 6 shows the pn-junction under reverse-bias condition. A

dc voltage VR is applied.

The applied VR is in the direction to add to VB , thus increasing

the effective barrier voltage to (VB + VR ).

Ony
angoS
.Obur
a 32/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 5: The pn-junction in the Figure 6: The pn-junction in the

reverse-bias condition. reverse-bias condition.

Ony
angoS
.Obur
a 33/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Holes are attracted by the −ve terminal and electrons by the +ve
terminal, increasing width of the depletion zone.

This reduces the no. of holes that diffuse into the n region
and the no. of electrons that diffuse into the p region.

The end result is that ID is dramatically reduced and the

junction offers high resistance.

Ony
angoS
.Obur
a 34/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

A reverse-bias voltage of ≈ 1 V is sufficient to cause ID ≃ 0, and

the current across the junction and thro’ the external circuit
will be equal to IS .

The current IS is expected be very small and strongly

dependent on temperature.

Ony
angoS
.Obur
a 35/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Thus in the reverse direction, the pn-junction conducts a very

small and almost-constant current equal to IS .

Ideally, the diode is considered to be in the non-conducting state

and acts like an open switch, with infinite resistance.

The reverse biasing condition is represented in the lower left

quadrant of the V -I characteristic curve in Figure 7.

Ony
angoS
.Obur
a 36/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 7: Volt-ampere characteristic curve of a silicon diode. The

Volt-Ampere characteristic curve is a graph of diode current vs voltage.

Ony
angoS
.Obur
a 37/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Junction operation under forward-bias condition

The forward-bias case is shown in Figures 8 and 9.

The upper right quadrant of the V -I characteristic curve in

Figure 7 represents the forward-bias condition.

The VF subtracts from VB resulting in a reduced barrier

voltage (VB − VF ) across the depletion region.

Ony
angoS
.Obur
a 38/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 9: The pn-junction in the

forward-bias condition.
Figure 8: The pn-junction in the
forward-bias condition.
Ony
angoS
.Obur
a 39/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The reduced barrier voltage results in reduced depletion-region

charge and narrower depletion-region width W .

This enables more holes to diffuse from p to n and more

electrons to diffuse from n to p, i.e permits easy flow of current.

The electron-hole recombination occurs. Thus ID increases

substantially and can become much larger than IS .

Ony
angoS
.Obur
a 40/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The current I in the external circuit is,

I = ID − IS

and it flows in the forward direction, from p to n.

Thus;
▶ a pn-junction can conduct a substantial current in the
forward-bias region and that,

▶ current is mostly ID and its value is determined by VF .

Ony
angoS
.Obur
a 41/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

For silicon diode, very little current I flows when the forward
voltage VF , is less than about 0.6 V .

Beyond 0.7 V , the diode current increases sharply. VF remains

relatively constant as I increases.

Ony
angoS
.Obur
a 42/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The V -I relationship of the junction

The V -I relationship of the pn-junction is described by,

 
I = IS e V /VT − 1 (2)

It considers a junction having a forward voltage V and derives I

that flows in the forward direction (from p to n).

The equation is general, giving a reverse current when V is

−ive.

Ony
angoS
.Obur
a 43/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 10 is the I -V characteristic of the pn-junction given by (2).

Figure 10: The pn-junction I -V characteristic.

Ony
angoS
.Obur
a 44/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Notice in the reverse direction that the current I saturates at a

value equal to −IS .

For this reason, IS is given the name saturation current.

Since, IS is directly proportional to the cross-sectional area,

A, of the junction, its other name is junction scale current.

Ony
angoS
.Obur
a 45/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Typical values for IS , for junctions of various areas, range from

10−18 A to 10−12 A.

Besides being proportional to A, IS is also proportional to ni2

which is a very strong function of temperature.

Ony
angoS
.Obur
a 46/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Reverse breakdown

At a reverse-bias voltage −V , with |V | ≫ VT , (2) indicates that

the reverse current is ≈ IS and is ∴ very small.

However, as the reverse-bias voltage V is increased, a value is

reached at which a very large reverse current flows as shown
in Figure 11.

As V reaches the value VBR , the dramatic increase in reverse

current is accompanied by a very small increase in the
reverse voltage...

Ony
angoS
.Obur
a 47/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

...that is, the reverse voltage remains very close to the value
VBR .

The phenomenon that occurs at V = VBR is known as junction

breakdown, thus denoted as VBR .

It is not a destructive phenomenon. That is, the diode can be

operated in the breakdown region repeatedly without a permanent
effect on its characteristics.

Ony
angoS
.Obur
a 48/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

However, this is based on the assumption that the magnitude of

the reverse-breakdown current is limited by the external
circuit to a “safe” value.

The “safe” value is one that results in the limitation of the

power dissipated in the junction to a safe, allowable level.

Ony
angoS
.Obur
a 49/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 11: The I -V characteristic of the pn-junction showing the rapid

increase in reverse current in the breakdown region.

Ony
angoS
.Obur
a 50/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

There are two possible mechanisms for pn-junction breakdown: the

zener effect3 and the avalanche effect.

If a pn-junction breaks down with a breakdown voltage VBR < 5 V ,

the breakdown mechanism is usually the zener effect.

Avalanche breakdown occurs when VBR is greater than

approximately 7V .

3
Note that the subscript Z in VZ denotes zener. VZ is sometimes used to
denote VBR whether the breakdown mechanism is the zener effect or the
Ony
avalanche effect.angoS.Obura 51/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

For junctions that break down between 5V and 7V , the

breakdown mechanism can be either the zener or the
avalanche effect or a combination of the two.

When a diode breaks down, both Zener and avalanche effects

are present.

One, or the other however, predominates based on the value of

VBR .

Ony
angoS
.Obur
a 52/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Zener effect

Zener effect occurs in a reverse biased pn-junction diode

when...

...the electric field enables tunnelling of electrons from the

valence to the conduction band of a semiconductor,...

...leading to a large no. of free minority carriers which

suddenly increase the reverse current

Ony
angoS
.Obur
a 53/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

When a diode is heavily doped, it’s depletion region will be

narrow

Under a reverse-bias voltage the depletion region widens,

leading to a strong electric field (≈ 108 V /m) across the junction

Ony
angoS
.Obur
a 54/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

This strong field ruptures the covalent bonds, generate the

electron-hole pairs,...

...and enables the tunnelling4 of electrons across the depletion

region, leading to a large no. of free charge carriers

This sudden generation of carriers rapidly increases the reverse

current and gives rise to the high slope conductance of the
Zener diode. This is known as zener effect

4
Tunnelling current occurs when electrons move thro’ a barrier that they clas-
sically shouldn’t be able to move thro’. That is, if they don’t have enough
energy to move On y
angoS
“over” a.
O bura they won’t
barrier, 55/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Avalanche effect

Avalanche effect occurs in a lightly-doped junction, where the

electric field is not strong enough to produce Zener effect

A small IR results due to surface leakage current from the many

holes on the edges of the crystal due to unfilled covalent bonds

These holes provide a path for few electrons. As they flow

(accelerated by this small field), these electrons collide with
valence electrons in other orbits

Ony
angoS
.Obur
a 56/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Upon collision, covalent bonds are broken and electron-hole

pairs are generated

The newly-generated charge carriers are also accelerated by

the electric field resulting in more collisions and further
production of charge carriers

This leads to an avalanche (or flood) of charge carriers and,

consequently, to a very low reverse resistance

Ony
angoS
.Obur
a 57/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Avalanche breakdown occurs when the reverse-bias voltage VR

becomes excessive and IR , increases sharply

Diodes should not be operated in the breakdown region

Ony
angoS
.Obur
a 58/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Diode approximations

First approximation of a diode

The first approximation:

▶ Treats a forward-biased diode like a closed switch with a
voltage drop of zero volts, see Figure 12(a)

▶ It also treats a reverse-biased diode like an open switch

with zero current, as shown in Figure 12(b)

Figure 12(c) indicates the ideal forward-bias and reverse-bias

characteristics
Ony
angoS
.Obur
a 59/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 12: First approximation of a diode. (a) Forward-biased diode

treated like a closed switch. (b) Reverse-biased diode treated like an
open switch. (c) Graph showing ideal forward and reverse
characteristics.
Ony
angoS
.Obur
a 60/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The first diode approximation is often used only if a rough idea

is needed of what the circuit voltages and currents should be.

The first approximation is sometimes called the ideal diode

approximation.

Ony
angoS
.Obur
a 61/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Second approximation of a diode

The second approximation:

▶ Treats a forward-biased diode like an ideal diode in series
with a battery, as shown in Figure 13(a)

For silicon diodes, the battery voltage (barrier potential,

VB ) is assumed to be 0.7V at the pn-junction

▶ It also treats a reverse-biased diode like an open switch.

See Figure 13(b)

Figure 13(c) shows the forward and reverse-bias characteristics of

the 2nd approximation.
Ony
angoS
.Obur
a 62/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 13: Second approximation of a diode. (a) Forward-biased

diode treated like an ideal diode in series with a battery. (b)
Reverse-biased diode treated like an open switch. (c) Graph showing
forward and reverse characteristics.
Ony
angoS
.Obur
a 63/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Notice that the diode is considered off until the forward

voltage, VF , reaches 0.7 V

Also, the diode is assumed to drop 0.7 V for all currents that
pass through it

The second approximation is used if more accurate answers are

needed for circuit calculations

Ony
angoS
.Obur
a 64/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Third approximation of a diode

The 3rd approximation includes a bulk resistance, designated rB .

The 3rd approximation of forward and reverse-biased diodes are

shown in Figures 14(a) and 14(b) respectively.

Notice the resistance across the open switch, it illustrates the

high leakage resistance for the reverse-bias condition.

Ony
angoS
.Obur
a 65/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 14: Third approximation of a diode. (a) Forward-biased diode

including the barrier potential, VB , and the bulk resistance, rB . (b)
Reverse-biased diode showing high resistance (not infinite) of the
reverse-bias condition. (c) Graph showing forward and reverse
characteristics.
Ony
angoS
.Obur
a 66/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

This high leakage resistance that exists when the diode is

reverse-biased...

...results in the small leakage current shown in Figure 14(c)

when the diode is reverse-biased.

Ony
angoS
.Obur
a 67/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING
r8 = 2.5 n o,
ov
+
+
RL = 100 0 \ljn = 10 V ~

IL=100mA

(a) (b)

V8 = 0.7 V r8 = 2.5 n

RL = 1000 RL = 100 0
~ \ljn = 10 V
VL = 9.3 V VL = 9 .07 v
IL = 93mA IL = 90.7mA

(c) (d)

Figure 15: Circuits used to illustrate the use of the first, second, and third
diode approximations in calculating the circuits’ voltage and current
values. (a) Original circuit. (b) First approximation of a diode. (c)
Second approximation of a diode. (d ) Third approximation of a diode.
Ony
angoS
.Obur
a 68/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Diode resistance
If an ideal diode is considered then it should offer zero resistance
in the forward bias and infinite resistance in the reverse bias.

An actual diode has some finite resistance in the forward bias

condition and very large resistance in the reversed biased
condition.

Unlike a resistor with a constant resistance regardless of the

operating condition,...

Ony
angoS
.Obur
a 69/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

...a diode has a non-linear relationship between the operating

voltage and current.

That is, the resistance of a diode will change with the operating
conditions.

The resistance of a diode can be classified in the following

categories;
1. Bulk resistance
2. dc or static resistance and
3. ac or dynamic resistance.

Ony
angoS
.Obur
a 70/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Ony
angoS
.Obur
a 71/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Bulk resistance
The bulk resistance, rB , is the resistance of the p and n
materials.

Its value is dependent on the doping level and the size of the
p and n materials.

The total diode voltage drop using the third approximation is

calculated as follows,

VF = VB + IF · rB (3)

rB , causes the forward voltage across a diode to increase

slightly with increases in the diode current.

Ony
angoS
.Obur
a 72/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

More on bulk resistance

Notice the slope of the diode curve in Figure 14(c) when
forward-biased.

The value of the bulk resistance, rB , can be determined by

using
∆V
rB = (4)
∆I
where ∆V represents the change in diode voltage produced by the
changes in diode current, ∆I

Ony
angoS
.Obur
a 73/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Example 1

A silicon diode has a forward voltage drop of 1.1 V for a forward

diode current, IF , of 1 A. Calculate the bulk resistance, rB .

ANSWER First, we can assume that the diode current, IF , is zero

when the forward voltage of the silicon diode is exactly 0.7 V. Then
∆V
rB =
∆I
1.1V − 0.7V
= = 0.4
1A − 0A

Ony
angoS
.Obur
a 74/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

dc or static resistance of a diode

The dc or static resistance of a diode is the resistance offered

by the diode when the applied input is dc voltage.

The dc resistance of a diode is calculated at a specific dc voltage

VF using the resulting dc current IF as follows,
Vdc
Rdc = (5)
Idc
where Vdc is the dc voltage drop and Idc is the dc current.

Ony
angoS
.Obur
a 75/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The dc operating condition of the diode is usually known as

Q-point5 of the diode.

Example 2

For the diode curve in Figure 7, calculate the dc resistance, RF , at

points A and B.

5
The Q-point or the operating point of a device, a.k.a a bias point, or quiescent
point is the steady-state dc voltage or current at a specified terminal of
Ony
an active device angoS.Obur a 76/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Solution: Using (5), the calculations are

VF 0.65 V
Point A: RF = = = 59.1 Ω (6)
IF 11 mA

VF 0.7 V
Point B: RF = = = 31.1 Ω (7)
IF 22.5 mA
Notice that as the diode conducts more heavily, the forward
resistance, RF , decreases.

Ony
angoS
.Obur
a 77/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

ac or dynamic resistance of a diode

The ac or dynamic resistance of a diode is the resistance
offered by the diode when the input is ac voltage.

It is assumed that before applying the ac signal, a finite dc

signal is being applied and the diode is already at some
Q-point.

Figure 16 a shows a dc source in series with an ac source.

Together, both sources supply current to the diode, D1 .

Ony
angoS
.Obur
a 78/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Figure 16: Combining ac and dc voltages in a diode circuit. (a) Vdc

provides a steady dc voltage that forward-biases the diode D1 . The ac
voltage source produces fluctuations in the amount of forward bias. (b)
Graph of VF versus IF showing ac variations.

Ony
angoS
.Obur
a 79/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The dc source provides the forward bias for D1 , while the ac

source produces fluctuations in the diode current.

The graph in Figure 16(b) illustrates how the diode current

varies with the ac voltage.

Ony
angoS
.Obur
a 80/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

For small ac signals, the diode acts like a resistance.

The term small signal is generally meant to be a signal that has a

peak-to-peak current ≤ 1/10 of the dc diode current.

The ac resistance for a diode is calculated using

∆VD
rac =
∆ID

Ony
angoS
.Obur
a 81/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

where VD is the diode voltage and ID is the diode current. But,

 
ID = IS e V /ηVT − 1

= IS e V /ηVT − IS thus

Finding the derivative of ID w.r.t. VD

∆ID IS
= × e VD /ηVT
∆VD ηVT

IS VD /ηVT
= e
ηVT

Ony
angoS
.Obur
a 82/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Note that IS e VD /ηVT = ID + IS

∆ID ID + IS
= but ID ≫ IS
∆VD ηVT

ID
=
ηVT
Thus
∆VD ηVT
rac = =
∆ID ID

Ony
angoS
.Obur
a 83/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Remember that
kT
VT =
q
where
▶ k is the Boltz Mann’s constant = 8.62 × 10−5 eV /K ,
▶ T is the temperature in Kelvin and
▶ q is the charge of electrons given as 1eV = 1.6 × 10−19 J.

Thus at T = 300 K ,

kT 8.62 × 10−5 × 1.6 × 10−19 × 300

VT = = ≈ 25.8 mV or
q 1.6 × 10−19

8.62 × 10−5 × 300

= = 25.8 mV
1

Ony
angoS
.Obur
a 84/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

and with η ≈ 1 for a diode,

25.8 mV
rac = (8)
ID
where
▶ rac represents the ac resistance of the diode to small ac
signals and
▶ ID represents the dc diode current.

Note that as the dc diode current, ID , increases, the ac resistance

decreases.

Ony
angoS
.Obur
a 85/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Average ac resistance of a diode

With ac (dynamic) resistance, we assumed small ac signals.

However,...

...if the applied ac signal has a large voltage swing, then the
resistance offered by the diode known as average ac resistance.

Ony
angoS
.Obur
a 86/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

The average ac resistance for a diode is calculated using

∆VD VDp−p
rav = =
∆ID IDp−p

where
▶ ∆VD or VDp−p is the voltage fluctuation and

▶ ∆ID or IIp−p is the current fluctuation across the diode.

Ony
angoS
.Obur
a 87/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

dc and ac/average resistance versus bulk resistance

The dc and ac/average resistance of a diode are different from the
bulk resistance.

The dc and ac/average resistance of a diode equals the bulk

resistance plus the effect of the barrier potential.

In other words, the dc and ac/average resistance of a diode

are its total resistance, whereas the bulk resistance is the
resistance of only the p and n regions.

Ony
angoS
.Obur
a 88/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Diode testing

The condition of a semiconductor diode can be determined using

either
▶ an ohmmeter or
▶ a digital multimeter (DMM).

Ony
angoS
.Obur
a 89/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Diode testing using an ohmmeter (analogue meter)

Check the resistance of the diode in one direction,...

...then reverse the meter leads and measure the resistance of

the diode in the other direction.

If the diode is good, it should measure

▶ a very high resistance in one direction and

▶ a low resistance in the other direction.

Ony
angoS
.Obur
a 90/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

For a silicon diode, the ratio of reverse resistance, RR , to forward

resistance, RF , should be very large, such as 1000 : 1 or more.

If the diode is faulty, then it can either be shorted or open.

▶ If the diode is shorted, it will measure a low resistance in
both directions.
▶ If the diode is open, it will measure a high resistance in both
directions.

Ony
angoS
.Obur
a 91/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

When using analogue ohmmeters to check a diode, do not use the

R × 1 range...

...because the current forced through the diode may exceed

the current rating of the diode.

The R × 100 range is usually the best range on which to check

a diode.

Ony
angoS
.Obur
a 92/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Diode testing using digital multimeters (DMMs)

Most DMMs cannot be used to measure the forward or reverse
resistance of the diode junction.

This is because the ohmmeter ranges in most DMMs do not

provide the proper forward bias to turn on the diode being
tested.

Thus, the resistance ranges on a DMM are often referred to as low

power ohm (LP) ranges.

Ony
angoS
.Obur
a 93/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Most DMMs provide a special range for testing diodes, called

the diode range.

Note that when the DMM forward-biases the diode being

tested,...

...the display will indicate the forward voltage dropped across

the diode rather than the forward resistance, RF .

Ony
angoS
.Obur
a 94/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

▶ A good silicon diode should show a voltage between 0.6 V

and 0.7 V for one connection of the meter leads and...
...an over-range condition for the opposite connection of
the leads.

▶ An open diode will show an over-range condition for both

connections of the meter leads

▶ A shorted diode will show a very low or zero reading for

both connections of the meter leads.

Ony
angoS
.Obur
a 95/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Diode ratings

Breakdown Voltage Rating, VBR this rating is very important, the

diode is usually destroyed if this rating is exceeded.

Average Forward-Current Rating, IO indicates the max. allowable

average current that the diode can handle safely.

Maximum Forward-Surge Current Rating, IFSM this is the max.

instantaneous current a diode can handle safely from
a single pulse

Ony
angoS
.Obur
a 96/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

Maximum Reverse Current, IR data sheets provide at least one

value of IR , for a specified amount of reverse-bias
voltage, from which the reverse resistance RR can be
computed.

The max. ratings of a diode should NEVER be exceeded. If any is

exceeded, it is likely that the diode will fail.

Ony
angoS
.Obur
a 97/98
 DEPARTMENT OF
ELECTRICAL ENGINEERING

98/98