2. Outline
Introduction
Formation of the p–n Junction
Energy Band Diagrams
Concepts of Junction Potential
Modes of the p–n Junction
Derivation of the I–V Characteristics of a p–n Junction
Diode
Linear Piecewise Models
Breakdown Diode
Special Types of p–n Junction Semiconductor Diodes
Applications of Diode
3. INTRODUCTION
The origin of a wide range of electronic devices being used can be
traced back to a simple device, the p–n junction diode.
The p–n junction diode is formed when a p-type semiconductor
impurity is doped on one side and an n-type impurity is doped on the
other side of a single crystal.
All the macro effects of electronic devices, i.e., wave shaping,
amplifying or regenerative effects, are based on the events occurring at
the junction of the p–n device.
Most modern devices are a modification or amalgamation of p–n
devices in various forms.
Prior to the era of semiconductor diodes, vacuum tubes were being
extensively used. These were bulky, costly and took more time to start
conducting because of the thermo-ionic emission.
The semiconductor diodes and the allied junction devices solved all
these problems.
4. FORMATION OF THE p–n
JUNCTION
When donor impurities are introduced into one side and acceptors into the
other side of a single crystal semiconductor through various sophisticated
microelectronic device-fabricating techniques, a p–n junction is formed.
The presence of a concentration gradient between two materials in such
intimate contact results in a diffusion of carriers that tends to neutralize this
gradient. This process is known as the diffusion process.
The nature of the p–n junction so formed may, in general, be of two types:
A step-graded junction:- In a step-graded semiconductor junction, the
impurity density in the semiconductor is constant.
A linearly-graded junction:- In a linearly-graded junction, the impurity
density varies linearly with distance away from the junction.
A semiconductor p–n junction
5. ENERGY BAND DIAGRAMS
The discussion in this section is based on the realistic assumption that a
junction is made up of uniformly doped p-type and n-type crystals forming
a step-graded junction.
The p–n Junction at Thermal Equilibrium
p-type and n-type semiconductors just before
contact
From the discussion of the law of mass action, the carrier concentrations on
either side away from the junction are given by:
(where pn is the hole concentration in n-type semiconductors, np is the
electron concentration in p-type semiconductors; nn and pp are the electron
and hole concentrations in n- and p-type semiconductors respectively.)
6. The energy band diagram of a p–n junction under the
condition of thermal equilibrium
Band structure of p–n junction
ENERGY BAND DIAGRAMS
7. CONCEPTS OF JUNCTION
POTENTIAL
Space-charge Region
The non-uniform concentration of holes and electrons at the junction
gives rise to a diffusive flow of carriers.
Since the electron density is higher in the n-type crystal than in the p-
type crystal, electrons flow from the n-type to the p-type and
simultaneously, due to reversibility, the holes flow from the p-type to the
n-type.
The result of this migration of carriers is that the region near the
junction of the n-type is left with a net positive charge (only ionized
donor atoms) while that of the p-type is left with a net negative charge
(only ionized acceptor atoms).
This diffusive mechanism of migration of the carriers across the
junction creates a region devoid of free carriers, and this region is called
the space-charge region, the depletion region or the transition region.
8. The junction, as noted above, has three major properties:
1. There is a space charge and an electric field across the
junction, which in turn indicates that the junction is pre-biased
(i.e., there exists a built-in potential, a very important concept,
which will be discussed shortly);
2. The impure atoms maintaining the space charge are immobile
in the temperature range of interest (at very high
temperatures, the impurities become mobile). The pre-biased
condition can be maintained indefinitely;
3. The presence of any free electron or hole is strictly forbidden.
Built-in and Contact Potentials
This diffusive flow process results in a space-charge region and
an electric field.
The resulting diffusion current cannot build up indefinitely
because an opposing electric field is created at the junction.
The homogeneous mixing of the two types of carriers cannot
occur in the case of charged particles in a p–n junction because
of the development of space charge and the associated electric
field E0.
CONCEPTS OF JUNCTION
POTENTIAL
9. The electrons diffusing from the n-type to the p-type leave behind
uncompensated donor ions in the n-type semiconductor, and the
holes leave behind uncompensated acceptors in the p-type
semiconductors.
This causes the development of a region of positive space charge
near the n-side of the junction and negative space charge near the
p-side. The resulting electric field is directed from positive charge
towards negative charge.
Thus, E0 is in the direction opposite to that of the diffusion current for
each type of carrier.
Therefore, the field creates a drift component of current from n to p,
opposing the diffusion component of the current.
Since no net current can flow across the junction at equilibrium, the
current density due to the drift of carriers in the E0 field must exactly
cancel the current density due to diffusion of carriers.
Moreover, since there can be no net build-up of electrons or holes
on either side as a function of time, the drift and diffusion current
densities must cancel for each type of carrier.
CONCEPTS OF JUNCTION
POTENTIAL
10. CONCEPTS OF JUNCTION
POTENTIAL
Therefore, the electric field E0 builds up to the point where the
net current density is zero at equilibrium.
The electric field appears in the transition region of length L
about the junction, and there is an equilibrium potential
difference V0 across L (known as contact potential).
In the electrostatic potential diagram, there is a gradient in
potential in the direction opposite to E0. In accordance with the
following fundamental relation:
The contact potential appearing across L under condition of zero
external bias is a built-in potential barrier, in that it is necessary
for the maintenance of equilibrium at the junction.
It does not imply any external potential. V0 is an equilibrium
quantity, and no net current can result from it. In general, the
contact potential is the algebraic sum of the built-in potential and
the applied voltage. The variations in the contact potential under
the condition of applied bias are given in the subsequent
sections.
11. Assuming that the field is confined within the space-charge
region L, the potential barrier Vd and the field E0 are related by:
It should be noted that a voltmeter cannot measure this
electrostatic potential since the internal field is set up to oppose
the diffusion current and also since the built-in potential is
cancelled exactly by the potential drop across the contact.
The barrier energy corresponding to barrier potential Vd is
expressed as EB = eVd. The value of EB can be changed by
doping change. The value of EB is different for different
semiconductors.
CONCEPTS OF JUNCTION
POTENTIAL
12. Effect of Doping on Barrier Field
The width of the depletion region is inversely proportional to the
doping strength, as a larger carrier concentration enables the
same charge to be achieved over a smaller dimension.
It should be noted that the depletion charge for different doping
is not constant.
The barrier field is normally independent of the doping
concentration except under conditions of heavy doping, which
may alter the band-gap itself, thereby modifying the barrier field.
The value of Vd in terms of the hole and electron concentrations
can be derived in the following manner.
CONCEPTS OF JUNCTION
POTENTIAL
13. CONCEPTS OF JUNCTION
POTENTIAL
At thermal equilibrium, the non-degenerate electron
concentrations for the n-type and p-type can be written as:
where Ecn, Ecp, Efn, and Efp are the conduction and Fermi level
energies of the n-type and p-type semiconductors, respectively,
and Nc is the effective density-of-states.
The Fermi levels are given by:
At equilibrium condition, the Fermi level must be constant
throughout the entire crystal.
Otherwise, because of the availability of lower energy levels, a
flow of carriers would result. The Fermi levels, therefore, must line
up at the equilibrium.
14. MODES OF THE p–n JUNCTION
There are two modes of switching of a p–n junction diode.
Forward-biased p–n
junction
When the positive
terminal of a battery is
connected to the p-type
side and the negative
terminals to the n-type side
of a p–n junction, the
junction allows a large
current to flow through it
due to the low resistance
level offered by the
junction. In this case the
junction is said to be
forward biased. Energy band diagram of
Forward-biased p–n junction
15. Reverse-biased p–n
junction
When the terminals of
the battery are reversed
i.e., when the positive
terminal is connected to
the n-type side and the
negative terminal is
connected to the p-type
side, the junction allows a
very little current to flow
through it due to the high
resistance level offered by
the junction. Under this
condition, the p–n junction
is said to be reverse-
biased.
Energy band diagram of
Reverse-biased p–n junction
MODES OF THE p–n JUNCTION
16. MODES OF THE p–n JUNCTION
The p–n Junction with External Applied Voltage
If an external voltage Va is applied across the p–n junction, the
height of the potential barrier is either increased or diminished as
compared to Va, depending upon the polarity of the applied voltage.
The energy band distribution, with applied external voltage, is
shown in below figure. For these non-equilibrium conditions, the
Fermi level can no longer be identified. In order to describe the
behaviour of the p–n junction, quasi- Fermi levels are introduced.
17. MODES OF THE p–n JUNCTION
Rectifying Voltage–Current Characteristics of a p–n Junction
If the polarity of the applied voltage is such that the p-type region is
made negative with respect to the n-type, the height of the potential-
barrier is increased.
Under this reverse-biased condition, it is relatively harder for the
majority of the carriers to surmount the potential-barrier.
The increase in the potential barrier height is essentially equal to
the applied voltage.
Under an external applied voltage, the carrier concentrations near
the junction are:
(where, the plus and minus signs are for the reverse-biased and the
forward-biased conditions.)
18. MODES OF THE p–n JUNCTION
The injected or extracted minority-carrier concentrations near the
junction can be written as:
The plus sign is for the forward-biased case where minority carriers
are injected. The minus sign is for the reverse-biased case where
minority carriers are extracted.
Electron and hole carriers at the boundaries of a
p–n junction under an externally applied voltage
The concentration
of the carriers on the
boundaries, for the
usual cases, Na >> ni
and under an external
applied voltage V is
shown in right side
figure.
19. MODES OF THE p–n JUNCTION
The Junction
Capacitance
Two types of idealized
junctions, which are
approximated closely in
practice. These are:
1. The abrupt or
step junction,
which results
from the alloying
technique.
2. The graded
junction, which
results from the
crystal-growing
technique.
The profiles of charge density, potential, and
electric field in an abrupt junction
20. The Varactor Diode
“Varactor” is actually an abbreviated form of “variable reactor”.
One property of a p–n junction is that the width of the junction
depletion region (and hence the depletion capacitance) is a function
of the applied voltage, which is utilized in this application.
MODES OF THE p–n JUNCTION
The schematic diagram of the
varactor diode
The doping profiles used in
varactor diode
21. DERIVATION OF THE I–V
CHARACTERISTICS OF A p–n
JUNCTION DIODE
Let us consider the fact that the drift component of the current is
negligible. Then from continuity equation, we can write:
where, Lp = √Dpτp is the diffusion length and pn is the equilibrium density of
holes in the n-region far away from the junction.
The solution of the ordinary differential is:
where, C1 and C2 are two arbitrary constants.
The boundary conditions in this case are:
From above two equation we get C2 = 0 and
22. DERIVATION OF THE I–V
CHARACTERISTICS OF A p–n
JUNCTION DIODE
Substituting the values of constants C1 and C2 we get:
The current density of holes in n-type semiconductors along the x
direction by diffusion is given by:
From above two equation we get :
The hole current density at the edge of the transition region i.e, at x =
xn, from above equation is given as:
23. The hole current density at the edge of the transition region i.e, at x = xp, from
above equation is given as:
DERIVATION OF THE I–V
CHARACTERISTICS OF A p–n
JUNCTION DIODE
The total diode-current density is given by:
The total direct current of the diode, with a cross-sectional junction area A, is:
where
24. DERIVATION OF THE I–V
CHARACTERISTICS OF A p–n
JUNCTION DIODE
Actual and theoretical I–V characteristics of a
typical semiconductor diode
The plot of the
voltage–current
characteristics of the
diode, for forward-
bias and reverse-
bias, is shown
below.
It should be noted
that because of the
higher concentration
of holes in the p-
region the hole
current is much
larger than the
electron current.
25. LINEAR PIECEWISE MODELS
The p–n junctions are unilateral in nature, i.e., they conduct current in only one
direction. Thus, we can consider an ideal diode as a short circuit when forward-
biased and as an open circuit when reverse-biased.
Forward biased diodes exhibit an offset voltage (Vy) that can be approximated
by the simple equivalent circuit with a battery in series with an ideal diode.
The series battery in the model keeps the ideal diode turned off for applied
voltage less than V; the actual diode characteristic is improved by adding a series
resistance (r) to the equivalent circuit. The equivalent diode model, is called the
piecewise linear equivalent model.
Linear piecewise models of a diode for
different order of approximations
I–V Characteristics of p–n
junction diode
26. BREAKDOWN DIODE
Breakdown diodes are p–n junction diodes operated in the reverse-bias
mode.
This breakdown occurs at a critical reverse-bias voltage (Vbr). At this
critical voltage the reverse current through the diode increases sharply, and
relatively large currents flow with little increase in voltage.
These diodes are designed with sufficient power-dissipation capabilities to
work in the breakdown region. The following two mechanisms can cause
reverse breakdown in a junction diode.
Reverse-biased p–n junction
Reverse breakdown in a p–n junction
27. BREAKDOWN DIODE
Zener Breakdown
Zener breakdown occurs when a sufficiently large reverse-bias is applied
across a p–n junction diode. The resulting electric field at the junction
imparts a very large force on a bound electron, enough to dislodge it from its
covalent bond.
The breaking of the covalent bonds produces a large number of EHP
(electron–hole pairs). Consequently the reverse current becomes very large.
This type of breakdown phenomena is known as Zener breakdown.
Energy band
diagram of a Zener
diode
Reverse bias with electron
tunnelling from p to n
leads to Zener breakdown I–V characteristics
28. BREAKDOWN DIODE
Avalanche Breakdown
In a reverse-biased junction, the minority-carriers drift across the depletion
region. On their way across this region, they occasionally have collisions with
atoms in the lattice.
With a large enough field, a carrier drifting across the depletion region is
accelerated to the point where it has enough energy to knock a valance
electron free from its host atom during a collision.
The field then separates the electron and hole of this newly created EHP
and we now have three mobile carriers instead of one. This process is called
avalanche multiplication.
The multiplication can become quite large if the carriers generated by this
collision also acquire to create more carriers, thereby initiating a chain
reaction.
Once the process starts, the number of multiplication that can occur from a
single collision increases rapidly with further increase in the reverse-bias, so
the terminal current grows rapidly, and we say that the junction breaks down.
This is called avalanche breakdown.
29. BREAKDOWN DIODE
Avalanche breakdown in
low doped semiconductor
A single such event results in multiplication of carriers; the original electron as
well as the secondary electron are swept to the n-type semiconductor, while, the
generated hole is swept to the p-type semiconductors.
Carrier multiplications in the depletion
region due to impact ionization
30. BREAKDOWN DIODE
Comparison between Zener and avalanche breakdown
The I–V characteristics comparison
between Zener and avalanche breakdown
Comparison of Zener breakdown of Ge
and Si semiconductor diodes with respect
to I–V curve
31. SPECIAL TYPES OF p–n JUNCTION
SEMICONDUCTOR DIODES
Tunnel Diode
The tunnel diode is a negative-resistance semiconductor p–n junction
diode. The negative resistance is created by the tunnel effect of the electrons
in the p–n junction as already discussed in the section of Zener diode.
Tunnel diode under zero bias equilibrium Small reverse bias
32. The doping of both the p- and n-type regions of the tunnel diode is very
high—impurity concentration of 1019 to 1020 atoms/cm3 are used (which
means both n-type and p-type semiconductors having parabolic energy
bands are highly degenerate)—and the depletion layer barrier at the
junction is very thin, in the order of 10-6cm.
SPECIAL TYPES OF p–n JUNCTION
SEMICONDUCTOR DIODES
Small forward bias
Increased forward bias
Increased forward bias
condition where the
current begins to increase
again
33. SPECIAL TYPES OF p–n JUNCTION
SEMICONDUCTOR DIODES
Small-signal model of the tunnel diode.
(Typical values for these parameters for
a tunnel diode of peak current IP 10 mA
are –Rn – 30 Ω, Rs 1 Ω, Ls 5 nH and
capacitance C 20 pF respectively)
I–V characteristics of a
tunnel diode
Symbol of tunnel diode
34. SPECIAL TYPES OF p–n JUNCTION
SEMICONDUCTOR DIODES
Light-emitting Diode
Charge carriers recombination takes place at the p–n junction as
electron crosses from the n-side and recombines with holes on the p-
side.
When the junction is forward-biased the free electron is in the
conduction band and is at a higher energy level than the hole located
at valence band.
The recombination process involves radiation of energy in the form
of photons. If the semiconductor material is translucent, the light will be
emitted and the junction becomes a light source, i.e., a light-emitting
diode (LED). LEDs are p–n junctions that can emit spontaneous
radiation in ultraviolet, visible, or infrared regions.
Advantages of LEDs
1. Low operating voltage, current and power consumption make LEDs
compatible with electronic drive circuits.
2. LEDs exhibit high resistance to mechanical shock and vibration
and allow them to be used in severe environment conditions.
3. LEDs ensure a longer operating life line, thereby improving the
overall reliability and lowering the maintenance costs of equipment.
35. SPECIAL TYPES OF p–n JUNCTION
SEMICONDUCTOR DIODES
4. LEDs have low inherent noise levels and also high immunity to
externally generated noise.
5. LEDs exhibit linearity of radiant power output with forward current
over a wide range.
Limitations of LEDs
1. Temperature dependence of radiant output power and wavelength.
2. Sensitivity to damages by over voltage or over current.
3. Theoretical overall efficiency is not achieved except in special
cooled or pulsed conditions.
(a) Schematic showing the basic process of
absorption (b) emission The symbol of an LED
36. SPECIAL TYPES OF p–n JUNCTION
SEMICONDUCTOR DIODES
Photovoltaic Diode
The photovoltaic diode or solar cell is an important technological device
for overcoming energy problems.
It is also known as solar energy converter; it is basically a p–n junction
diode which converts solar energy into electrical energy.
The energy reaching the earth’s surface from the sun is primarily
electromagnetic radiation, which covers a spectral range of 0.2 to 0.3
micrometre.
The conversion of this energy into electrical energy is called
photoelectric effect.
Construction and working principle
A photovoltaic diode essentially consists of a silicon p–n junction
diode usually packaged with a glass window on the top.
Surface layer of the p-material is made extremely thin so that the
incident light (photons) can penetrate and reach the p–n junction
easily.
37. SPECIAL TYPES OF p–n JUNCTION
SEMICONDUCTOR DIODES
When these photons collide with the valence electrons, they impart in
them sufficient energy so that they gain enough energy to leave the
parent atoms. In this way, free electrons and holes are generated on
both sides of the junction. Consequently, their flow constitutes a current
(minority current).
This current is directly
proportional to the illumination
(lumen/m2 or mW/m2).
This, in general depends on the
size of the surface being
illuminated. The open circuit voltage
Voc is a function of illumination.
Consequently, power output of a
solar cell depends on the level of
sunlight illumination. Power cells
are also available in the form of a
flat strip so as to cover sufficiently
large surface areas.
Structure of a solar cell
38. SPECIAL TYPES OF p–n JUNCTION
SEMICONDUCTOR DIODES
I–V characteristics of an illuminated solar cell
showing the point of maximum power
Top finger contact with anti-
reflecting coating
Current–voltage characteristics
It is seen that the curve passes through the fourth quadrant and hence
the device can deliver power from the curve.
The power delivered by the device can be maximized by maximizing the
area under the curve or by maximizing the product (Isc Voc). By properly
choosing the load resistor, output power can be achieved. In the absence of
light, thermally generated minority carriers across the junction constitute the
reverse saturation current.
39. APPLICATIONS OF DIODE
Radio Demodulation:- In demodulation of amplitude modulated (AM)
radio broadcasts diodes are used. The crystal diodes rectify the AM signal,
leaving a signal whose average amplitude is the desired audio signal. The
average value is obtained by using a simple filter and the signal is fed into
an audio transducer, which generates sound.
Power Conversion:- In the Cockcroft–Walton voltage multiplier, which
converts ac into very high dc voltages, diodes are used. Full-wave rectifiers
are made using diodes, to convert alternating current electricity into direct
current .
Over-voltage Protection:- Diodes are used to conduct damaging high
voltages away from sensitive electronic devices by putting them in reverse-
biased condition under normal circumstances. When the voltage rises from
normal range, the diodes become forward-biased (conducting). In stepper
motor, H-bridge motor controller and relay circuit’s diodes are used to de-
energize coils rapidly without damaging voltage spikes that would otherwise
occur. These are called a fly-back diodes.
Logic Gates:- AND and OR logic gates are constructed using diodes in
combination with other components. This is called diode logic.
40. Ionizing Radiation Detectors
In addition to light, energetic radiation also excites semiconductor
diodes.
A single particle of radiation, having very high electron volts of
energy, generates many charge carrier pairs, as its energy is
transmitted in the semiconductor material.
If the depletion layer is large enough to catch the whole energy or to
stop a heavy particle, an accurate measurement of the particle’s energy
is possible.
These semiconductor radiation detectors require efficient charge
collection and low leakage current. They are cooled by liquid nitrogen.
Common materials are Ge and Si.
Temperature Measuring:- The forward voltage drop across the diode
depends on temperature. A diode can be used as a temperature measuring
device. This temperature dependence follows from the Shockley ideal diode
equation and is typically around -2.2 mV per degree Celsius.
Charge-coupled Devices:- Arrays of photodiode, integrated with readout
circuitry are used in digital cameras and similar units.
APPLICATIONS OF DIODE
