PN Junction
Diode
pn-juntion-Diode
Basics of p-n junction?
A p-n junction is the metallurgical boundary between the n
and p-regions of a semiconductor crystal.
P-n junctions consist of two semiconductor regions of opposite
type. Such junctions show a pronounced rectifying behavior.
They are also called p-n diodes in analogy with vacuum diodes.
The p-n junction is a versatile element, which can be used as a
rectifier, as an isolation structure and as a voltage-dependent
capacitor. In addition, they can be used as solar cells,
photodiodes, light emitting diodes and even laser diodes. They
are also an essential part of Metal-Oxide-Silicon Field-EffectsTransistors (MOSFETs) and Bipolar Junction Transistors (BJTs).
A p-n junction consists of two semiconductor regions with opposite
doping type as shown in Figure. The region on the left is p-type with
an acceptor density Na, while the region on the right is n-type with a
donor density Nd. The dopants are assumed to be shallow, so that
the electron (hole) density in the n-type (p-type) region is
approximately equal to the donor (acceptor) density.
Cross-section of a p-n junction
pn-juntion-Diode
We will assume, unless stated otherwise, that the doped
regions are uniformly doped and that the transition between
the two regions is abrupt. We will refer to this structure as
an abrupt p-n junction.
Frequently we will deal with p-n junctions in which one side is
distinctly higher-doped than the other. We will find that in
such a case only the low-doped region needs to be
considered, since it primarily determines the device
characteristics. We will refer to such a structure as a onesided abrupt p-n junction.
The junction is biased with a voltage Va as shown in Figure.
We will call the junction forward-biased if a positive voltage
is applied to the p-doped region and reversed-biased if a
negative voltage is applied to the p-doped region. The
contact to the p-type region is also called the anode, while
the contact to the n-type region is called the cathode, in
reference to the anions or positive carriers and cations or
negative carriers in each of these regions.
Flatband diagram
The principle of operation will be explained using a gedanken experiment, an
experiment, which is in principle possible but not necessarily executable in
practice. We imagine that one can bring both semiconductor regions together,
aligning both the conduction and valence band energies of each region. This
yields the so-called flatband diagram shown in Figure.
Energy band diagram of a p-n junction (a) before and (b) after merging the
n-type and p-type regions
Note that this does not automatically align the Fermi
energies, EF,n and EF,p. Also, note that this flatband diagram
is not an equilibrium diagram since both electrons and
holes can lower their energy by crossing the junction.
A motion of electrons and holes is therefore expected
before thermal equilibrium is obtained. The diagram shown
in Figure (b) is called a flatband diagram. This name refers
to the horizontal band edges. It also implies that there is no
field and no net charge in the semiconductor.
pn-juntion-Diode
At Thermal Equilibrium
A short time after the junction is
established and thermal equilibrium is
achieved, charge carriers in the vicinity of
the junction will neutralize each other
(electrons combining with holes), leaving
the unneutralized negatively ionized
acceptors, Na- , in the p-region and
unneutralized positively ionized donors,
Nd+ , in the n-region. This region of
ionized donors and acceptors creates a
space charge and its region is called the
depletion region.
The edge of the depletion region given by -xp on the p-side and +xn on the n-side.
the ionized donors and acceptors are located in substitutional lattice sites and
Cannot move in the electric field. The concentration of these donors and
acceptors are selected to give the p-n junction desired device properties
pn-juntion-Diode
Energy Band Diagram at Thermal Equilibrium
At thermal equilibrium
dE f
dx
=0
i.e. the Fermi level in the p- and n- type
semiconductors must be equal. This
requirement for constant Fermi level
pushes
the n-type semiconductor Fermi level
down to be constant with the p-type
semiconductor Fermi level, as shown in
the diagram. The amount the bands are
bent is the difference In work function.
The depletion width xd, where xd = xp + xn may
be calculated from
xd =
2e
q
æ 1
1 ö
çç + + - ÷÷Vbi
è N d N a ø While
Drift
Diffusio
n
Diffusio
n
Drift
Energy band diagram of a p-n junction in
thermal equilibrium
in thermal equilibrium no external voltage is applied
between the n-type and p-type material, there is an internal
potential, f, which is caused by the workfunction difference
between the n-type and p-type
pn-juntion-Diode
Junction Potential
Impurity distribution illustrating the space charge region
The build-in potential may
Electric field variation
be expressed as:
with distance, x
kT N a- N d+
Vbi =
ln
q
ni2
Potential variation
with distance, x
Where,
kT
= VT = 26mV
q
At T=300K
K – Boltzman constant
VT = Thermal voltage
pn-juntion-Diode
The built-in potential
The built-in potential in a semiconductor equals the potential across the
depletion region in thermal equilibrium. Since thermal equilibrium implies
that the Fermi energy is constant throughout the p-n diode, the built-in
potential equals the difference between the Fermi energies, EFn and EFp,
divided by the electronic charge.
It also equals the sum of the bulk potentials of each region, fn and fp,
since the bulk potential quantifies the distance between the Fermi energy
and the intrinsic energy. This yields the following expression for the builtin potential.
pn-juntion-Diode
Semiconductor Diode
No Applied Voltage
A semiconductor diode is created by joining the n-type semiconductor to a p-type
semiconductor.
In the absence of a
bias voltage across
the diode, the net
flow of charge is one
direction is zero. Bias is
the term used when an
external DC voltage
is applied
pn-juntion-Diode
Biasing the Junction Diode
Forward Bias
Reverse Bias
When an external voltage VD is applied as
shown, with - terminal to n-side and
+terminal to p-side, it forms a forward bias
configuration. In this setup, electrons and
holes will be pressured to recombined with
the ions near the boundary, effectively
reducing the width and causing a heavy
majority carrier flow across the junction.
As Vd increases, the depletion width
decrease until a flood of majority carriers
start
passing
through.
Is
remains
unchanged.
æ VD nVT ö
I D = I s çç e
- 1÷÷
è
ø
n~1
When an external voltage VD is applied as
shown, with + terminal to n-side and –
terminal to p-side, the free charge carriers
will be attracted away by the voltage
source. This will effectively increase the
depletion region within the diode. This
widening of the depletion region will create
too great a barrier for the majority carriers
to overcome, effectively reducing the
carrier flow to zero. The number of minority
carriers will not be affected. This
configuration is called reverse Bias. This
small current flow during reverse bias is
called the reverse saturation current, Is.
pn-juntion-Diode
We now consider a p-n diode with an applied bias voltage, Va. A forward bias
corresponds to applying a positive voltage to the anode (the p-type region)
relative to the cathode (the n-type region). A reverse bias corresponds to a
negative voltage applied to the cathode. Both bias modes are illustrated with
Figure. The applied voltage is proportional to the difference between the
Fermi energy in the n-type and p-type quasi-neutral regions.
As a negative voltage is applied,
the
potential
across
the
semiconductor increases and so
does the depletion layer width. As
a positive voltage is applied, the
potential
across
the
semiconductor decreases and
with it the depletion layer width.
The total potential across the
semiconductor equals the built-in
potential minus the applied
voltage, or:
Energy band diagram of a p-n junction under reverse and forward
bias
pn-juntion-Diode
Electrostatic analysis of a p-n diode
The electrostatic analysis of a p-n diode is of interest since it provides
knowledge about the charge density and the electric field in the depletion
region. It is also required to obtain the capacitance-voltage characteristics of
the diode. The analysis is very similar to that of a metal-semiconductor
junction. A key difference is that a p-n diode contains two depletion regions
of opposite type.
pn-juntion-Diode
What Are Diodes Made Out Of?
• Silicon (Si) and Germanium (Ge) are the two most
common single elements that are used to make Diodes.
A compound that is commonly used is Gallium
Arsenide (GaAs), especially in the case of LEDs
because of it’s large bandgap.
• Silicon and Germanium are both group 4 elements,
meaning they have
4 valence electrons.
Their
structure allows them to grow in a shape called the
diamond lattice.
• Gallium is a group 3 element while Arsenide is a group
5 element. When put together as a compound, GaAs
creates a zincblend lattice structure.
• In both the diamond lattice and zincblend lattice, each
atom shares its valence electrons with its four closest
neighbors. This sharing of electrons is what ultimately
allows diodes to be build. When dopants from groups
3 or 5 (in most cases) are added to Si, Ge or GaAs it
changes the properties of the material so we are able
to make the P- and N-type materials that become the
diode.
pn-juntion-Diode
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
The diagram above shows the
2D structure of the Si crystal.
The
light
green
lines
represent
the
electronic
bonds made when the valence
electrons are shared. Each Si
atom shares one electron with
each of its four closest
neighbors so that its valence
band will have a full 8
electrons.
N-Type Material:
+4
+4
+4
+4
+5
+4
+4
+4
+4
When extra valence electrons are introduced into
a material such as silicon an n-type material is
produced.
The extra valence electrons are
introduced by putting impurities or dopants into
the silicon. The dopants used to create an n-type
material are Group V elements.
The most
commonly used dopants from Group V are
arsenic, antimony and phosphorus.
The 2D diagram to the left shows the extra
electron that will be present when a Group V
dopant is introduced to a material such as silicon.
This extra electron is very mobile.
pn-juntion-Diode
P-Type Material:
+4
+4
+4
+4
+3
+4
+4
+4
+4
P-type material is produced when the dopant that
is introduced is from Group III.
Group III
elements have only 3 valence electrons and
therefore there is an electron missing. This
creates a hole (h+), or a positive charge that can
move around in the material. Commonly used
Group III dopants are aluminum, boron, and
gallium.
The 2D diagram to the left shows the hole that
will be present when a Group III dopant is
introduced to a material such as silicon. This
hole is quite mobile in the same way the extra
electron is mobile in a n-type material.
pn-juntion-Diode
The PN Junction
Steady State1
Na
P
Metallurgical
Junction
Nd
-
-
-
-
-
-
+
+
+
+
+
+
-
-
-
-
-
-
+
+
+
+
+
+
-
-
-
-
-
-
+
+
+
+
+
+
-
-
-
-
-
-
+
+
+
+
+
+
-
-
-
-
-
-
+
+
+
+
+
+
n
Space Charge
Region
ionized
acceptors
ionized
donors
E-Field
+
h+ drift =
_
+
h+ diffusion
e- diffusion =
pn-juntion-Diode
_
e- drift
The PN Junction
Metallurgical
Junction
Na
P
Steady State
Nd
-
-
-
-
-
+
+
+
+
+
-
-
-
-
-
+
+
+
+
+
-
-
-
-
-
+
+
+
+
+
-
-
-
-
-
+
+
+
+
+
n
Space Charge
Region
ionized
acceptors
ionized
donors
E-Field
+
h+ drift
_
+
=
h+ diffusion
e- diffusion
_
=
When no external source
is connected to the pn
junction, diffusion and
drift balance each other
out for both the holes
and electrons
e- drift
Space Charge Region: Also called the depletion region. This region includes
the net positively and negatively charged regions. The space charge region
does not have any free carriers. The width of the space charge region is
denoted by W in pn junction formula’s.
Metallurgical Junction: The interface where the p- and n-type materials meet.
Na & Nd: Represent the amount of negative and positive doping in number of
carriers per centimeter cubed. Usually in the range of 1015 to 1020.
pn-juntion-Diode
The Biased PN Junction
Metal
Contact
“Ohmic
Contact”
_
(Rs~0)
P
+
Applied
Electric Field
n
I
+
_
Vapplied
The pn junction is considered biased when an external voltage is applied.
There are two types of biasing: Forward bias and Reverse bias.
These are described
on then next slide.
pn-juntion-Diode
The Biased PN Junction
Forward Bias:
Vapplied > 0
Reverse Bias:
Vapplied < 0
In forward bias the depletion region shrinks slightly in width. With
this shrinking the energy required for charge carriers to cross the
depletion region decreases exponentially. Therefore, as the
applied voltage increases, current starts to flow across the
junction. The barrier potential of the diode is the voltage at which
appreciable current starts to flow through the diode. The barrier
potential varies for different materials.
Under reverse bias the depletion region widens. This causes the
electric field produced by the ions to cancel out the applied
reverse bias voltage.
A small leakage current, Is (saturation
current) flows under reverse bias conditions. This saturation
current is made up of electron-hole pairs being produced in the
depletion region. Saturation current is sometimes referred to as
scale current because of it’s relationship to junction temperature.
pn-juntion-Diode
Properties of Diodes
Figure 1.10 – The Diode Transconductance Curve2
ID
(mA)
• VD = Bias Voltage
• ID = Current through
Diode. ID is Negative
for Reverse Bias and
Positive for Forward
Bias
IS
VBR
~Vf
VD
• IS = Saturation
Current
• VBR = Breakdown
Voltage
• Vf = Barrier Potential
Voltage
(nA)
pn-juntion-Diode
Properties of Diodes
The Shockley Equation
• The transconductance curve on the previous slide is characterized by the
following equation:
ID = IS(eVD/hVT – 1)
• As described in the last slide, ID is the current through the diode, IS is the
saturation current and VD is the applied biasing voltage.
• VT is the thermal equivalent voltage and is approximately 26 mV at room
temperature. The equation to find VT at various temperatures is:
k = 1.38 x 10-23 J/K
VT = kT
q
T = temperature in Kelvin
q = 1.6 x 10-19 C
• h is the emission coefficient for the diode. It is determined by the way the diode
is constructed. It somewhat varies with diode current. For a silicon diode h is
around 2 for low currents and goes down to about 1 at higher currents
pn-juntion-Diode
Diode Circuit Models
The Ideal Diode
Model
The diode is designed to allow current to flow in
only one direction. The perfect diode would be a
perfect conductor in one direction (forward bias)
and a perfect insulator in the other direction
(reverse bias). In many situations, using the ideal
diode approximation is acceptable.
Example: Assume the diode in the circuit below is ideal. Determine the
value of ID if a) VA = 5 volts (forward bias) and b) VA = -5 volts (reverse
bias)
a) With VA > 0 the diode is in forward bias
and is acting like a perfect conductor so:
RS = 50 W
ID
VA
+
_
ID = VA/RS = 5 V / 50 W = 100 mA
b) With VA < 0 the diode is in reverse bias
and is acting like a perfect insulator,
therefore no current can flow and ID = 0.
pn-juntion-Diode
Diode Circuit Models
The Ideal Diode with This model is more accurate than the simple
ideal diode model because it includes the
Barrier Potential
approximate barrier potential voltage.
Remember the barrier potential voltage is the
+
Vf
voltage at which appreciable current starts to
flow.
Example: To be more accurate than just using the ideal diode model
include the barrier potential. Assume Vf = 0.3 volts (typical for a
germanium diode) Determine the value of ID if VA = 5 volts (forward bias).
RS = 50 W
ID
VA
+
_
With VA > 0 the diode is in forward bias
and is acting like a perfect conductor
so write a KVL equation to find ID:
0 = VA – IDRS - Vf
Vf
+
ID = VA - Vf = 4.7 V = 94 mA
RS
50 W
pn-juntion-Diode
Diode Circuit Models
The Ideal Diode
with Barrier
Potential and
Linear Forward
Resistance
+
Vf
RF =
RF
Δ VD
Δ ID
This model is the most accurate of the three. It includes a
linear forward resistance that is calculated from the slope of
the linear portion of the transconductance curve. However,
this is usually not necessary since the RF (forward
resistance) value is pretty constant. For low-power
germanium and silicon diodes the RF value is usually in the
2 to 5 ohms range, while higher power diodes have a RF
value closer to 1 ohm.
ID
Linear Portion of
transconductance
curve
Δ ID
VD
pn-juntion-Diode
ΔVD
Diode Circuit Models
The Ideal Diode
with Barrier
Potential and
Linear Forward
Resistance
Example: Assume the diode is a low-power diode
with a forward resistance value of 5 ohms. The
barrier potential voltage is still: Vf = 0.3 volts (typical
for a germanium diode) Determine the value of ID if
VA = 5 volts.
RS = 50 W
VA
ID
Once again, write a KVL equation
for the circuit:
+
0 = VA – IDRS - Vf - IDRF
+
_
Vf
RF
ID = VA - Vf = 5 – 0.3 = 85.5 mA
RS + RF
50 + 5
pn-juntion-Diode
Diode Circuit Models
Values of ID for the Three Different Diode Circuit Models
ID
Ideal Diode
Model
Ideal Diode
Model with
Barrier
Potential
Voltage
Ideal Diode
Model with
Barrier
Potential and
Linear Forward
Resistance
100 mA
94 mA
85.5 mA
These are the values found in the examples on previous slides
where the applied voltage was 5 volts, the barrier potential was
0.3 volts and the linear forward resistance value was assumed to
be 5 ohms.
pn-juntion-Diode
The Q Point
The operating point or Q point of the diode is the quiescent or nosignal condition. The Q point is obtained graphically and is really only
needed when the applied voltage is very close to the diode’s barrier
potential voltage. The example 3 below that is continued on the next
slide, shows how the Q point is determined using the
transconductance curve and the load line.
RS = 1000 W
ID
VA
First the load line is found by substituting in
different values of Vf into the equation for ID using
the ideal diode with barrier potential model for the
diode. With RS at 1000 ohms the value of RF
wouldn’t have much impact on the results.
ID = VA – V f
+
= 6V _
Vf
+
RS
Using V f values of 0 volts and 1.4 volts we obtain
ID values of 6 mA and 4.6 mA respectively. Next
we will draw the line connecting these two points
on the graph with the transconductance curve.
This line is the load line.
pn-juntion-Diode
The Q Point
ID (mA)
12
10
The
transconductance
curve below is for a
Silicon diode. The
Q point in this
example is located
at 0.7 V and 5.3 mA.
8
Q Point: The intersection of the
load line and the
transconductance curve.
6
5.3
4.6
4
2
VD (Volts)
0.2
0.4
0.6
0.8
pn-juntion-Diode
0.7
1.0
1.2
1.4
Dynamic Resistance
The dynamic resistance of the diode is mathematically determined
as the inverse of the slope of the transconductance curve.
Therefore, the equation for dynamic resistance is:
rF = hVT
ID
The dynamic resistance is used in determining the voltage drop
across the diode in the situation where a voltage source is
supplying a sinusoidal signal with a dc offset.
The ac component of the diode voltage is found using the
following equation:
vF = vac
rF
rF + RS
The voltage drop through the diode is a combination of the ac and
dc components and is equal to:
VDpn-juntion-Diode
= Vf + vF
Dynamic Resistance
Example: Use the same circuit used for the Q point example but change
the voltage source so it is an ac source with a dc offset. The source
voltage is now, vin = 6 + sin(wt) Volts. It is a silicon diode so the barrier
potential voltage is still 0.7 volts.
RS = 1000 W
ID
+
vin
vF = vac
Vf
+
The DC component of the circuit is the
same as the previous example and
therefore ID = 6V – 0.7 V = 5.2 mA
1000 W
rF = hVT = 1 * 26 mV = 4.9 W
ID
5.3 mA
h = 1 is a good approximation if the dc
current is greater than 1 mA as it is in this
example.
rF
= sin(wt) V
4.9 W
= 4.88 sin(wt) mV
rF + RS
4.9 W + 1000 W
Therefore, VD = 700 + 4.9 sin (wt)
mV (the voltage drop across the
pn-juntion-Diode
diode)
Types of Diodes and Their Uses
PN Junction
Diodes:
Are used to allow current to flow in one direction
while blocking current flow in the opposite
direction. The pn junction diode is the typical diode
that has been used in the previous circuits.
A
K
P
Schematic Symbol for a PN
Junction Diode
Zener Diodes:
n
Representative Structure for
a PN Junction Diode
Are specifically designed to operate under reverse
breakdown conditions. These diodes have a very
accurate and specific reverse breakdown voltage.
A
K
Schematic Symbol for a
Zener Diode
pn-juntion-Diode
Types of Diodes and Their Uses
Schottky
Diodes:
A
K
These diodes are designed to have a very fast
switching time which makes them a great diode for
digital circuit applications. They are very common
in computers because of their ability to be switched
on and off so quickly.
Schematic Symbol for a
Schottky Diode
Shockley
Diodes:
A
The Shockley diode is a four-layer diode while other
diodes are normally made with only two layers.
These types of diodes are generally used to control
the average power delivered to a load.
K
Schematic Symbol for a
four-layer Shockley Diode
pn-juntion-Diode
Types of Diodes and Their Uses
Light-Emitting
Diodes:
Light-emitting diodes are designed with a very large
bandgap so movement of carriers across their
depletion region emits photons of light energy.
Lower bandgap LEDs (Light-Emitting Diodes) emit
infrared radiation, while LEDs with higher bandgap
energy emit visible light. Many stop lights are now
starting to use LEDs because they are extremely
bright and last longer than regular bulbs for a
relatively low cost.
A
K
Schematic Symbol for a
Light-Emitting Diode
pn-juntion-Diode
The arrows in the LED
representation indicate
emitted light.
Types of Diodes and Their Uses
While LEDs emit light, Photodiodes are sensitive to
received light. They are constructed so their pn
junction can be exposed to the outside through a
clear window or lens.
Photodiodes:
A
A
K In Photoconductive mode the saturation current
l
Schematic Symbols for
Photodiodes
K
increases in proportion to the intensity of the
received light. This type of diode is used in CD
players.
In Photovoltaic mode, when the pn junction is
exposed to a certain wavelength of light, the diode
generates voltage and can be used as an energy
source. This type of diode is used in the
production of solar power.
pn-juntion-Diode
References
Dailey, Denton. Electronic Devices and Circuits, Discrete and Integrated. Prentice Hall, New
Jersey: 2001. (pp 2-37, 752-753)
2
Figure 1.10. The diode transconductance curve, pg. 7
Figure 1.15. Determination of the average forward resistance of a diode, pg 11
3
Example from pages 13-14
Liou, J.J. and Yuan, J.S. Semiconductor Device Physics and Simulation. Plenum Press,
New York: 1998.
Neamen, Donald. Semiconductor Physics & Devices. Basic Principles. McGraw-Hill,
Boston: 1997. (pp 1-15, 211-234)
1
Figure 6.2. The space charge region, the electric field, and the forces acting on
the charged carriers, pg 213.
pn-juntion-Diode