Transcript ELECTRONIC MATERIALS Lecture 10

ELECTRONIC MATERIALS
Lecture 10
SEMICONDUCTOR MATERIALS
Applied Electronics Department
Technical University of Cluj-Napoca
Cluj-Napoca, Cluj, 400027, Romania
Phone: +40-264-401412, E-mail: [email protected]
ELECTRONIC MATERIALS
Lecture 10
According to their electrical conductivity, materials are conventionally classified into
three groups: conductors, semiconductors and insulators. Conductors, which
include all metals, have high conductivities, semiconductors show intermediate
conductivities and insulators have low conductivities. The distinction between
semiconductors and insulators is only quantitative, whereas the distinction
between semiconductors and metals is more profound.
All characteristic properties of semiconductors are the consequence of a basic
physical phenomenon: the existence of certain energy bands in the energy
spectrum of electrons.
Semiconductor materials are insulators at absolute zero temperature that conduct
electricity in a limited way at room temperature. The defining property of a
semiconductor material is that it can be doped with impurities that alter its
electronic properties in a controllable way.
ELECTRONIC MATERIALS
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ELECTRONIC MATERIALS
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Once we know the bandstructure of a given material we still need to find out which
energy levels are occupied and whether specific bands are empty, partially filled or
completely filled.
Empty bands do not contain electrons. Therefore, they are not expected to
contribute to the electrical conductivity of the material. Partially filled bands do
contain electrons as well as available energy levels at slightly higher energies.
These unoccupied energy levels enable carriers to gain energy when moving in an
applied electric field. Electrons in a partially filled band therefore do contribute to
the electrical conductivity of the material.
Completely filled bands do contain plenty of electrons but do not contribute to the
conductivity of the material. This is because the electrons cannot gain energy
since all energy levels are already filled.
ELECTRONIC MATERIALS
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Semiconductors differ from metals and insulators by the fact that they contain an
"almost-empty" conduction band and an "almost-full" valence band. This also
means that we will have to deal with the transport of carriers in both bands.
To facilitate the discussion of the transport in the "almost-full" valence band of a
semiconductor, we will introduce the concept of holes. It is important to understand
that one could deal with only electrons if one is willing to keep track of all the
electrons in the "almost-full" valence band. After all, electrons are the only real
particles available in a semiconductor.
The concepts of holes is introduced in semiconductors since it is easier to keep
track of the missing electrons in an "almost-full" band, rather than keeping track of
the actual electrons in that band.
Holes are missing electrons. They behave as particles with the same properties as
the electrons would have when occupying the same states except that they carry a
positive charge.
ELECTRONIC MATERIALS
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ELECTRONIC MATERIALS
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CLASSIFICATION OF SEMICONDUCTORS
Group III elemental semiconductors
Boron (B)
Group IV elemental semiconductors
Diamond (C)
Silicon (Si)
Germanium (Ge)
Tin (Sn)
Group V elemental semiconductors
Phosphorus (P)
Arsenic (As)
Antimony (Sb)
Group VI elemental semiconductors
Sulfur (S)
Selenium (Se)
Tellurium (Te)
Group VII elemental semiconductors
Iodine (I)
Group IV compound
semiconductors
Silicon carbide (SiC)
Silicon germanide (SiGe)
III-V semiconductors
Aluminium antimonide (AlSb)
Aluminium arsenide (AlAs)
Aluminium nitride (AlN)
Aluminium phosphide (AlP)
Boron nitride (BN)
Boron arsenide (BAs)
Gallium antimonide (GaSb)
Gallium arsenide (GaAs)
Gallium nitride (GaN)
Gallium phosphide (GaP)
Indium antimonide (InSb)
Indium arsenide (InAs)
Indium nitride (InN)
Indium phosphide (InP)
ELECTRONIC MATERIALS
III-V ternary semiconductor alloys
Aluminium gallium arsenide (AlGaAs,
AlxGa1-xAs)
Indium gallium arsenide (InGaAs,
InxGa1-xAs)
Aluminium indium arsenide (AlInAs)
Aluminium indium antimonide (AlInSb)
Gallium arsenide nitride (GaAsN)
Gallium arsenide phosphide (GaAsP)
Aluminium gallium nitride (AlGaN)
Aluminium gallium phosphide (AlGaP)
Indium gallium nitride (InGaN)
Indium arsenide antimonide (InAsSb)
Indium gallium antimonide (InGaSb)
Lecture 10
III-V quaternary semiconductor alloys
Aluminium gallium indium phosphide
(AlGaInP, also InAlGaP, InGaAlP,
AlInGaP)
Aluminium gallium arsenide phosphide
(AlGaAsP)
Indium gallium arsenide phosphide
(InGaAsP)
Aluminium indium arsenide phosphide
(AlInAsP)
Aluminium gallium arsenide nitride
(AlGaAsN)
Indium gallium arsenide nitride
(InGaAsN)
Indium aluminium arsenide nitride
(InAlAsN)
III-V quinary semiconductor alloys
Gallium indium nitride arsenide
antimonide (GaInNAsSb)
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Lecture 10
II-VI semiconductors
Cadmium selenide (CdSe)
Cadmium sulfide (CdS)
Cadmium telluride (CdTe)
Zinc oxide (ZnO)
Zinc selenide (ZnSe)
Zinc sulfide (ZnS)
Zinc telluride (ZnTe)
I-VII semiconductors
Cuprous chloride (CuCl)
IV-VI semiconductors
Lead selenide (PbSe)
Lead sulfide (PbS)
Lead telluride (PbTe)
Tin sulfide (SnS)
Tin telluride (SnTe)
II-VI ternary alloy semiconductors
Cadmium zinc telluride (CdZnTe, CZT)
Mercury cadmium telluride (HgCdTe)
Mercury zinc telluride (HgZnTe)
Mercury zinc selenide (HgZnSe)
IV-VI ternary semiconductors
lead tin telluride (PbSnTe)
Thallium tin telluride (Tl2SnTe5)
Thallium germanium telluride
(Tl2GeTe5)
ELECTRONIC MATERIALS
Lecture 10
There are two main types of semiconductor materials:
•intrinsic - where the semiconducting properties of the material occur naturally i.e.
they are intrinsic to the material's nature.
•extrinsic - they semiconducting properties of the material are manufactured, by
us, to make the material behave in the manner which we require.
Nearly all the semiconductors used in modern electronics are extrinsic. This
means that they have been created by altering the electronic properties of the
material.
Several different semiconducting materials exist, but the most common
semiconductor material is Silicon and the two most common methods of modifying
the electronic properties are:
•Doping - the addition of 'foreign' atoms to the material.
•Junction effects - the things that happen when we join differing materials
together.
ELECTRONIC MATERIALS
Lecture 10
Semiconductors' intrinsic electrical properties are very often permanently modified
by introducing impurities, in a process known as doping. Usually it is reasonable to
approximate that each impurity atom adds one electron or one "hole" that may flow
freely. Upon the addition of a sufficiently large proportion of dopants,
semiconductors conduct electricity nearly as well as metals.
In addition to permanent modification through doping, the electrical properties of
semiconductors are often dynamically modified by applying electric fields. The
ability to control conductivity in small and well-defined regions of semiconductor
material, statically through doping and dynamically through the application of
electric fields (like transistors). Semiconductor devices with dynamically controlled
conductivity are the building blocks of integrated circuits.
In certain semiconductors, when electrons fall from the conduction band to the
valence band (the energy levels above and below the band gap), they often emit
light. This photoemission process underlies the light-emitting diode (LED) and the
semiconductor laser, both of which are tremendously important commercially.
Conversely, semiconductor absorption of light in photodetectors excites electrons
from the valence band to the conduction band, facilitating reception of fiber optic
communications, and providing the basis for energy from solar cells.
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Lecture 10
GROWTH OF SEMICONDUCTOR CRYSTALS
Like all crystals, semiconductor crystals can be obtained by cooling the molten
semiconductor material.
However, this procedure yields poly-crystalline material since crystals start growing
in different locations with a different orientation. Instead when growing singlecrystalline silicon one starts with a seed crystal and dips one end into the melt. By
controlling the temperature difference between the seed crystal and the molten
silicon, the seed crystal slowly grows. The result is a large single-crystal silicon
boule. Such boules have a cylindrical shape, in part because the seed crystal is
rotated during growth and in part because of the cylindrical shape of the crucible
containing the melt. The boule is then cut into wafers with a diamond saw and
further polished to yield the starting material for silicon device fabrication.
ELECTRONIC MATERIALS
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This pure silicon ingot is about six inches across
and a few feet long. When it's sliced, it will make
thousands of silicon wafers, ready for
processing.
These wafers have been sawed from a
solid ingot of silicon. Each wafer is six
inches in diameter. One side of each
wafer has already been polished
smooth. Note the slight flat spot on the
outside edge of each wafer to help hold
it still during the polishing process.
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Polishing the Wafer Smooth
Before the real work begins, one side of each wafer must be polished absolutely
smooth. These wafers will be so smooth after they're finished that you couldn't
detect any imperfections on the surface even with a microscope. The process is
called chemical-mechanical polishing (CMP). As the name implies, it involves
bathing the wafers in special abrasive chemicals and gently grinding any
imperfections away.
The wafers need to be smooth and flat because the features that will be projected
onto them in the chip "darkroom" are extremely small and close together. In
photography, it's important to keep the print lying flat as it develops because any
warping or bending will throw the picture out of focus. Each part of the print must
be the same distance from the projecting lens, and the principle is the same for
chip making. Any variations in the surface of the silicon wafer will make the chip
design out of focus, possibly causing shorts and other faults.
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Building the Layers
After a wafer is polished, it's time to start building up the layers of material that will
become the electronic components on the chip. A wafer is pure silicon, but it takes
more than silicon to make a chip work. There are the metal wires, but those will be
added later. At this stage, we need to build up a few layers of silicon (which
conducts electricity) alternating with a few layers of an insulator (which doesn't
conduct electricity). These two types of material will be stacked, like layers of
frosting between layers of cake. Later, we'll etch away some of this insulator (most
of it, actually), leaving a carefully planned-out three-dimensional pattern of silicon
and other materials that channel electricity in exactly the paths we want.
Engineers call this layering process deposition because chemicals are deposited
on the supersmooth surface of our wafer. Deposition can be done in a couple of
different ways. One way is to put the wafer in an oven along with pure oxygen gas
and let the oxygen seep into the top of the wafer. (Oxygen doesn't conduct
electricity; it is an insulator.) Another way is to spray the chemicals onto the wafer,
called chemical vapor deposition (CVD). After we've built up the first layer of our
chip, it will look like in figure.
ELECTRONIC MATERIALS
Lecture 10
Layers of material are sprayed or deposited on top of the base silicon wafer.
Alternating layers of conducting and insulating material are built up. The number
of layers depends on the complexity of the chip. After each pair of
conducting/insulating layers is put down, some of it is removed to make intricate
wires.
ELECTRONIC MATERIALS
Lecture 10
After we coat the wafer with insulating chemicals, there comes a second layer of
special chemicals, this one called photoresist. Photoresist is like the coating on
black-and-white print film before it's been developed. The stuff reacts to light,
which we're depending on to make our chips work.
Once the wafer is coated with photoresist, it's light sensitive and must be kept in
the dark so that it doesn't accidentally get "developed" before it's ready.
Fortunately for us, the photoresist is sensitive to light we can't see, so there's no
need to shut off the lights in the clean room. The wafer still needs to be handled
carefully, however, to avoid scratching its delicate and carefully prepared surface.
To develop the wafer, we put it into a machine called a stepper. Usually a robot
arm takes a wafer off the top of a stack and places it in the stepper automatically.
Mounted just a few inches above the wafer is a copy of the film negative that the
chip designers created (which was described in the previous chapter). Engineers
call this film the reticle, and it's usually made of quartz instead of normal camera
film. Just above the film is a lens and behind that is a bright light. Basically, we're
going to project an image of the film down onto our wafer, like projecting slides
onto a wall. The only real difference is the scale: The image we project will be tiny,
only a fraction of an inch on a side, just big enough to make one copy of our chip.
ELECTRONIC MATERIALS
Lecture 10
This wafer has been through several stages of the stepping and etching
processes. The chips inscribed on it are clearly visible, making a grid pattern on
the wafer's surface. Later, the wafer will be cut apart with a diamond-tipped saw,
separating each of the square chips.
ELECTRONIC MATERIALS
Lecture 10
These analog components, scattered across two silicon wafers, show the variety
of shapes and sizes these components can take.
ELECTRONIC MATERIALS
Lecture 10
ENERGY BAND DIAGRAMS OF SEMICONDUCTORS
The energy band diagrams of semiconductors are rather complex. The detailed
energy band diagrams of germanium, silicon and gallium arsenide are shown in
the next figure. The energy is plotted as a function of the wavenumber, k, along the
main crystallographic directions in the crystal, since the band diagram depends on
the direction in the crystal. The energy band diagrams contain multiple completelyfilled and completely-empty bands. In addition, there are multiple partially-filled
band.
Energy band diagram of (a) germanium, (b) silicon and (c) gallium arsenide.
ELECTRONIC MATERIALS
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The energy band diagrams are frequently simplified when analyzing
semiconductor devices. Since the electronic properties of a semiconductor are
dominated by the highest partially empty band and the lowest partially filled band,
it is often sufficient to only consider those bands. This leads to a simplified energy
band diagram for semiconductors as shown in the figure.
The diagram identifies the almost-empty conduction band by a horizontal line. This
line indicates the bottom edge of the conduction band and is labeled Ec. Similarly,
the top of the valence band is indicated by a horizontal line labeled Ev. The energy
band gap is located between the two lines, which are separated by the bandgap
energy Eg.
ELECTRONIC MATERIALS
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A simplified energy band diagram used to describe semiconductors. Shown are
the valence and conduction band as indicated by the valence band edge, Ev, and
the conduction band edge, Ec.
ELECTRONIC MATERIALS
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TEMPERATURE DEPENDENCE OF THE ENERGY BANDGAP
The energy bandgap of semiconductors tends to decrease as the temperature is
increased. This behavior can be better understood if one considers that the
interatomic spacing increases when the amplitude of the atomic vibrations
increases due to the increased thermal energy. This effect is quantified by the
linear expansion coefficient of a material. An increased interatomic spacing
decreases the average potential seen by the electrons in the material, which in
turn reduces the size of the energy bandgap. A direct modulation of the interatomic
distance - such as by applying compressive (tensile) stress - also causes an
increase (decrease) of the bandgap.
ELECTRONIC MATERIALS
Lecture 10
The temperature dependence of the energy bandgap, Eg, has been experimentally
determined yielding the following expression for Eg as a function of the
temperature, T:
T 2
Eg T   Eg 0 
T 
where Eg(0),  and  are the fitting parameters.
Parameters used to calculate the energy bandgap of germanium, silicon and
gallium arsenide (GaAs) as a function of temperature are listed in the next table.
ELECTRONIC MATERIALS
Lecture 10
Calculate the energy bandgap of germanium, silicon and gallium arsenide at
300, 400, 500 and 600 K.
ELECTRONIC MATERIALS
Lecture 10
Solution:
The bandgap of silicon at 300 K equals:
T 2
0.473  103  3002
Eg 300K   Eg 0 
 1.166 
 1.12eV
T 
300  636
Similarly one finds the energy bandgap for germanium and gallium arsenide, as
well as at different temperatures, yielding:
ELECTRONIC MATERIALS
Lecture 10
A plot of the resulting bandgap versus temperature is shown in the next figure for
germanium, silicon and gallium arsenide.
Temperature dependence of the energy bandgap of germanium (Ge), silicon (Si)
and gallium arsenide (GaAs).
ELECTRONIC MATERIALS
Lecture 10
INTRINSIC SEMICONDUCTOR
An intrinsic semiconductor, also called an undoped semiconductor or i-type
semiconductor, is a pure semiconductor without any significant dopant species
present. The presence and type of charge carriers is therefore determined by the
material itself instead of the impurities; the amount of electrons and holes is
roughly equal.
Intrinsic semiconductors conductivity can be due to crystal defects or to thermal
excitation. In an intrinsic semiconductor the number of electrons in the conduction
band is equal to the number of holes in the valence band.
ni=pi
A layer of i-type semiconductor is used in PIN diodes.
ELECTRONIC MATERIALS
Lecture 10
PIN diode
PIN diode (p-type, intrinsic, n-type diode) is a diode with a wide, undoped intrinsic
semiconductor region between p-type semiconductor and n-type semiconductor
regions.
PIN diodes act as near perfect resistors at RF and microwave frequencies. The
resistivity is dependent on the DC current applied to the diode.
A PIN diode exhibits an increase in its electrical conductivity as a function of the
intensity, wavelength, and modulation rate of the incident radiation.
The benefit of a PIN diode is that the depletion region exists almost completely
within the intrinsic region, which is a constant width (or almost constant) regardless
of the reverse bias applied to the diode. This intrinsic region can be made large,
increasing the area where electron-hole pairs can be generated. For these reasons
many photodetector devices include at least one PIN diode in their construction,
for example PIN photodiodes and phototransistors (in which the base-collector
junction is a PIN diode).
They are not limited in speed by the capacitance between n and p region anymore,
but by the time the electrons need to drift across the undoped region.
ELECTRONIC MATERIALS
Lecture 10
Conduction in Intrinsic Semiconductors
A solid with filled bands is an insulator, but at finite temperature, electrons can be
thermally excited from the valence band to the next highest, the conduction band.
The fraction of electrons excited in this way depends on the temperature and the
band gap, the energy difference between the two bands. Exciting these electrons
into the conduction band leaves behind positively charged holes in the valence
band, which can also conduct electricity.
An intrinsic (pure) semiconductor's conductivity is strongly dependent on the band
gap. The only available carriers for conduction are the electrons which have
enough thermal energy to be excited across the band gap, which is defined as the
energy level difference between the conduction band and the valence band.
ELECTRONIC MATERIALS
Lecture 10
E
CB
EC
Eg
EF
EV
VB
x
The band structure for intrinsic semiconductors.
In intrinsic semiconductors (like silicon and germanium), the Fermi level is
essentially halfway between the valence and conduction bands. Although no
conduction occurs at 0K, at higher temperatures a finite number of electrons can
reach the conduction band and provide some current.
ELECTRONIC MATERIALS
Lecture 10
Conduction in Intrinsic Semiconductors
Semiconductors are the class of elements which have four valence electrons. Two
important semiconductors are germanium (Ge) and silicon (Si). Early solid-state
electronic devices were fabricated almost exclusively from germanium, whereas
modern devices are fabricated almost exclusively from silicon. Gallium arsenide
(GaAs) is a semiconductor compound made up of gallium, which has three
valence electrons, and arsenic, which has five. This semiconductor is making
inroads in digital applications which require extremely high switching speeds and in
extremely high-frequency analog applications. However, silicon remains the most
useful semiconductor material and is expected to dominate for many years to
come.
Semiconductor materials are normally in crystalline form with each valence
electron shared by two atoms. The semiconductor is said to be intrinsic if it is not
contaminated with impurity atoms.
ELECTRONIC MATERIALS
Lecture 10
Si
Si
Si
Si
Si
Si
Si
Si
Si
Two-dimensional illustration of the crystal lattice of an intrinsic semiconductor at
T=0K.
ELECTRONIC MATERIALS
Lecture 10
The figure shows a two-dimensional view of an intrinsic semiconductor crystal.
Each circle represents both the nucleus of an atom and all electrons in that atom
except the valence electrons. The links between the circles represent the valence
electrons. Each valence electron can be assumed to spend half time with each of
two atoms so that each atom sees eight half-time electrons. Compared to a metal,
the valence electrons in a semiconductor are tightly bound.
The thermal energy stored in a semiconductor crystal lattice causes the atoms to
be in constant mechanical vibration. At room temperature, the vibrations shake
loose several valence electrons which then become free electrons. In intrinsic
silicon, the number of free electrons is approximately one in 1012 of the total
number of valence electrons. The free electrons behave similarly to those in a
metal. Under the influence of an applied electric field, they have a mobility and
exhibit a drift velocity which produces a conduction current. However, because of
the small number of free electrons, the conductivity of an intrinsic semiconductor is
much lower than that of a metal.
ELECTRONIC MATERIALS
Lecture 10
When an electron is shaken loose from an atom, an electron vacancy is left which
is called a hole. The parent atom then becomes an ion. The constant mechanical
vibration of the lattice can cause the ion to capture a valence electron from a
neighboring atom to replace the missing one. When such a transfer takes place,
the position of the hole moves from one atom to another. This is equivalent to a
positive charge +q moving about in the semiconductor. (The motion of a hole can
be likened to the motion of a bubble in water.) Like free electrons, holes have a
mobility and exhibit a drift velocity which produces a conduction current under the
influence of an applied electric field. Because of the opposite charge polarity of
electrons and holes, they drift in opposite directions under the influence of a field.
ELECTRONIC MATERIALS
Lecture 10
Si
Si
Si
Si
Si
Si
Si
Si
Si
Intrinsic semiconductor at T>0K.
ELECTRONIC MATERIALS
Lecture 10
Next figure illustrates the drift of free electrons and the drift of holes in an intrinsic
semiconductor under the application of an electric field that is directed from right to
left for free electrons. When an electron is shaken loose from its valence shell, an
electron-hole pair is formed. The force generated by the electric field causes the
free electrons to drift to the left. In effect, a hole drifts to the right when a bound
valence electron shifts to the left from one atom to another. The movement of
holes may be likened to the movement of bubbles of air in water, where the water
represents the bound electrons and the bubbles represent the holes. The
movement of a bubble in one direction is really the result of a movement of water
in the opposite direction.
In summary, the flow of current in the semiconductor is the result of the flow of two
components. One component is the flow of free electrons in one direction. The
other component is the flow of the absence of bound electrons in the other
direction. Because of the opposite charge polarities, the electron current and the
hole current add to produce the total conduction current.
ELECTRONIC MATERIALS
Lecture 10
Electric field
Si
Si
Si
Si
Si
Si
Si
Si
Si
Illustration of the drift of free electrons and the drift of holes under the
application of an external electric field.
ELECTRONIC MATERIALS
Lecture 10
Recombinations
Because hole-electron pairs are continually created by thermal agitation of a
semiconductor lattice, it might seem that the number of holes and free electrons
would continually increase with time. This does not happen because free electrons
are continually recombining with holes. At any temperature, a stable state is
reached when the creation rate of hole-electron pairs is equal to the recombination
rate. The mean lifetime τn(s) of a free electron is the average time that the electron
exists in the free state before recombination. The mean lifetime τp(s) for the hole is
defined similarly. In the intrinsic semiconductor, τn is equal to τp because the
number of free electrons must be equal to the number of holes. However, the
addition of an impurity to the semiconductor lattice can cause the mean lifetimes to
be unequal.
ELECTRONIC MATERIALS
Lecture 11
Conductivity
J  e  v e  h  v h  ni  e  h   q  E    E
This equation defines the conductivity σ of the intrinsic semiconductor. It is given
by:
  ni  e  h   q
ELECTRONIC MATERIALS
Lecture 11
Example 1
A rod of intrinsic silicon is 1 cm long and has a diameter of 1mm. At room
temperature, the intrinsic concentration in the silicon is ni = 1.5 × 1016 per m3. The
electron and hole mobilities are μe = 0.13m2 V−1 s−1 and μh = 0.05m2 V−1 s−1.
Calculate the conductivity σ of the silicon and the resistance R of the rod.
ELECTRONIC MATERIALS
Lecture 11
Solution.
The conductivity is calculated as follows:
The resistance is calculated as follows:
R
 l
S

l
0.01

  S 4.33  10 4    0.5  10 3


2
 29.4M
ELECTRONIC MATERIALS
Lecture 11
EXTRINSIC SEMICONDUCTORS
The preceding example illustrates how poor a conductor intrinsic silicon is at room
temperature. The conductivity can be increased by adding certain impurities in
carefully controlled minute quantities. When this is done, the semiconductor is
called a doped semiconductor. There are two classes of impurities that are used.
These are donor impurities and acceptor impurities. Typically one impurity atom is
added per 108 semiconductor atoms. A semiconductor that is doped with a donor
impurity is called an n-type semiconductor. One that is doped with an acceptor
impurity is called a p-type semiconductor.
ELECTRONIC MATERIALS
Lecture 11
n-Type Semiconductor
An n-type semiconductor is produced by adding a donor impurity such as arsenic,
antimony, or phosphorus to an intrinsic semiconductor. Each donor atom has five
valence electrons. When a donor atom replaces an atom in the crystal lattice, only
four valence electrons are shared with the surrounding atoms. The fifth valence
electron becomes a free electron as illustrated in figure. The number of free
electrons donated by the donor atoms is much greater than the number of free
electrons and holes in the intrinsic semiconductor. This makes the conductivity of
the n-type semiconductor much greater that of the intrinsic semiconductor.
Because the number of free electrons is far greater than the number of holes, the
free electrons are the majority carriers. The semiconductor is called n-type
because the majority carriers have a negative charge.
ELECTRONIC MATERIALS
Lecture 11
Si
Si
Si
Si
As
Si
Si
Si
Si
Two-dimensional illustration of the crystal lattice of an n-type semiconductor.
ELECTRONIC MATERIALS
Lecture 11
E
CB
EC
Eg
Ed
Ee
EV
VB
x
Structure of energy bands of extrinsic semiconductors, doped with donor
impurities.
ELECTRONIC MATERIALS
Lecture 11
Hole-electron pairs are continually formed by thermal agitation of the lattice in an
n-type semiconductor. Because of the large number of donor electrons, there are
many more free electrons available for recombination with the holes. This
decreases the mean lifetime for the holes which decreases the number of holes in
the n-type semiconductor compared to the intrinsic semiconductor. For this reason,
the current due to the flow of holes in an n-type semiconductor is often neglected
in calculations.
It is important to understand that a donor atom is electrically neutral if its fifth
valence electron does not become a free electron in the lattice. If the fifth electron
becomes a free electron, the number of protons in the atom is greater than the
number of electrons by one. In this case, the donor atom becomes a bound
positively charged ion.
ELECTRONIC MATERIALS
Lecture 11
p-Type Semiconductor
A p-type semiconductor is produced by adding an acceptor impurity such as
gallium, boron, or indium to an intrinsic semiconductor. Each acceptor atom has
three valence electrons. When an acceptor atom replaces an atom in the crystal
lattice, there are only three valence electrons shared with the surrounding atoms.
This leaves a hole as illustrated in next figure. The number of holes created by the
acceptor atoms is much greater than the number of free electrons and holes in the
intrinsic semiconductor. This makes the conductivity of the p-type semiconductor
much greater that of the intrinsic semiconductor. Because the number of holes is
far greater than the number of electrons, the holes are the majority carriers. The
semiconductor is called p-type because the majority carriers have a positive
charge.
ELECTRONIC MATERIALS
Lecture 11
Si
Si
Si
Si
B
Si
Si
Si
Si
Two-dimensional illustration of the crystal lattice of a p-type semiconductor.
ELECTRONIC MATERIALS
Lecture 11
E
CB
EC
Eg
Ea
VB
Eh
EV
x
Structure of energy bands and conduction of extrinsic semiconductors (doped with
acceptor impurities).
ELECTRONIC MATERIALS
Lecture 11
Hole-electron pairs are continually formed by thermal agitation of the lattice in a ptype semiconductor. Because of the large number of holes, there are many more
holes available for recombination with the free electrons. This decreases the mean
lifetime for the free electrons which decreases the number of electrons in the ptype semiconductor compared to the intrinsic semiconductor. For this reason, the
current due to the flow of free electrons in a p-type semiconductor is often
neglected in calculations.
It is important to understand that an acceptor atom is electrically neutral if the hole
created by the absence of its fourth valence electron is not filled by an electron
from an adjacent silicon atom.
Once an electron fills the hole, the number of electrons in that atom is greater than
the number of protons by one. In this case, the acceptor atom becomes a bound
negatively charged ion.
ELECTRONIC MATERIALS
Lecture 12
Mass-Action Law
In an intrinsic semiconductor, we have noted that the electron concentration and
the hole concentration are both equal to the intrinsic concentration, i.e. n = p = ni. If
this were not true, the material would not be electrically neutral. We have seen that
adding an n-type impurity to the semiconductor increases n and decreases p.
Similarly, adding a p-type impurity increases p and decreases n. It can be shown
that the product of n times p is a constant independent of the doping type and the
doping level. The product is given by:
n  p  ni2
This relation is called the mass-action law.
ELECTRONIC MATERIALS
Lecture 12
Electrical Neutrality
An intrinsic semiconductor is electrically neutral, i.e. there is no net charge stored.
The addition of n-type or p-type impurities does not change this. To state this
mathematically, let ND be the number of donor atoms per m3 and NA the number of
acceptor atoms per m3. We assume that all donor atoms and all acceptor atoms
are ionized so that there are ND bound positive charges per m3 and NA bound
negative charges per m3. Each donor ion has a charge +q and each acceptor ion
has a charge −q. The total number of negative charges per m3 is equal to the
number n of free electrons per m3 plus the number NA of bound acceptor atoms
per m3, i.e. n+NA. Similarly, the number of positive charges per m3 is equal to the
number p of holes per m3 plus the number ND of bound donor atoms per m3, i.e.
p+ND. Because the semiconductor is electrically neutral, the number of positive
charges must equal the number of negative charges. This gives the condition:
n + NA = p + N D
ELECTRONIC MATERIALS
Lecture 12
In an n-type semiconductor, NA=0 and p<<n so that the above equation can be
solved for n to obtain:
n = p + ND ≈ N D
The approximation in this equation and mass-action law can be used to solve for
the hole concentration p to obtain:
ni2
p
ND
Similarly, in a p-type semiconductor, we can write:
p  n  NA  NA
ni2
n
NA
ELECTRONIC MATERIALS
Lecture 12
Example 2
In the silicon rod of Example 1, the number of silicon atoms per m3 is 5×1028. A
donor impurity is added to the silicon in the concentration of one donor atom per
108 atoms of silicon. Calculate the new resistance of the rod. Assume that each
donor atom contributes one free electron.
ELECTRONIC MATERIALS
Lecture 12
Solution.
The donor concentration in the silicon is calculated as follows:
The free electron concentration is n ≈ND=5×1020 electrons per m3. The hole
concentration is


15 2
n
1.5  10
p

n
5  1020
2
i
 4.5  109
holes per m3
Because p << n, we can neglect p in calculating the conductivity. The conductivity
is:
  n  e  q  5  1020  0.13  1.602  1019  10.41S
m
The resistance is calculated as follows:
 l
l
0.01
R


S
  S 10.41   0.5  103


2
 1.22k
Compared to the intrinsic silicon rod of Example 1, this is smaller by a factor of
24,1.
ELECTRONIC MATERIALS
Lecture 12
PN junction
A pn junction is a merger of the semiconductor p- and n-type regions. In a
transition layer between the two regions the carrier densities are much lower than
in the neutral regions away from the junction. For this reason, this transition layer
is also called the depletion region. The simplest pn region is a junction where both
sides are homogeneously doped and the transition between the acceptor and
donor doping is abrupt. Such a junction is called an abrupt pn junction.
The width of the depletion region of an abrupt pn junction is given by
Here εs is the relative dielectric constant of the semiconductor, ε0 is the permittivity
of free space, NA and ND are the acceptor and donor concentrations at the p- and
n-side of the junction, respectively, Vbi(≤Eg/q) is the built-in potential, and V is the
externally applied bias voltage. V>0 if the p-side is positively biased.
ELECTRONIC MATERIALS
Lecture 12
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.
ELECTRONIC MATERIALS
Lecture 12
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 higherdoped 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 one-sided abrupt p-n junction.
The junction is biased with a voltage Va. 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.
ELECTRONIC MATERIALS
Lecture 12
Semiconductor materials
The most commonly used semiconductor material is Silicon. This is an element, it
has 14 electrons, and its pure solid form melts at 1420 °C. Used for thousands of
years to make ordinary glass, Silicon is a very common element. Silicon turns up in
lots of rocks and forms the sand on beaches.
The earliest commercial semiconductor devices mostly used Germanium. This
element has 32 electrons per atom and melts at 985 °C. It has now largely fallen
into disuse because it is much rarer and more expensive than Silicon and has no
real advantages for most purposes.
The second most common modern material is Gallium Arsenide, GaAs. This is a
combination of Gallium, an element with 31 electrons per atom, and Arsenic, with
33 electrons per atom. This is a crystalline compound, not an element. Hence we
can get an extra degree of control over its properties by varying the relative
amount of Gallium and Arsenic.
GaAs has the advantage of making semiconductor devices which respond very
quickly to electrical signals. This makes it better than Silicon for doing tasks like
amplifying the high frequency (1GHz to 10GHz) signals from TV satellites, etc. The
main disadvantage of GaAs is that it is more difficult to make and the chemicals
involved are quite often poisonous!
ELECTRONIC MATERIALS
Lecture 12
GaAs can be used with signal frequencies up to about 100 GHz. At even higher
frequencies more esoteric materials such as Indium Phosphide (InP) may be used.
At present, however, the MMWave region (frequencies above about 50 GHz) is
only used for special purposes, so most of the electronics in the world thends to be
based on Silicon, with some GaAs, and only a few InP devices.
Silicon carbide (SiC) is a ceramic compound of silicon and carbon.
Pure α-SiC is an intrinsic semiconductor with band gaps of 3.28 eV (4H) and 3.03
eV (6H) respectively.
Silicon carbide is used for blue LEDs, ultrafast Schottky diodes, MESFETs and
high temperature IGBTs and thyristors for high power switching. Due to its high
thermal conductivity, SiC is also used as substrate for other semiconductor
materials such as gallium nitride. Due to its wide band gap, SiC-based parts are
capable of operating at high temperature (over 350 °C), which together with good
thermal conductivity of SiC reduces problems with cooling of power parts. They
also possess increased tolerance to radiation damage, making it a material desired
for defense and aerospace applications. Its main competitor is gallium nitride.
Although diamond has an even higher band gap, SiC-based devices are easier to
manufacture due to the fact that it is more convenient to grow an insulating layer of
silicon dioxide on the surface of a silicon carbide wafer than it is with diamond.
ELECTRONIC MATERIALS
Lecture 12
Silicon
ELECTRONIC MATERIALS
Lecture 12
Germanium
ELECTRONIC MATERIALS
Lecture 12
Silicon Carbide
ELECTRONIC MATERIALS
Lecture 12
Silicon Carbide
ELECTRONIC MATERIALS
Lecture 12
THE HALL EFFECT
The Hall effect describes the behavior of the free carriers in a semiconductor when
applying an electric as well as a magnetic field. The experimental setup shown in
the figure, depicts a semiconductor bar with a rectangular cross section and length
L. A voltage Vx is applied between the two contacts, resulting in a field along the xdirection. The magnetic field is applied in the z-direction.
a)
b)
Hall setup and carrier motion for a) holes and b) electrons.
ELECTRONIC MATERIALS
Lecture 12
As shown in figure a), the holes move in the positive x-direction. The magnetic field
causes a force to act on the mobile particles in a direction dictated by the right
hand rule. As a result there is a force, Fy, along the positive y-direction, which
moves the holes to the right. In steady state this force is balanced by an electric
field, Ey, so that there is no net force on the holes. As a result there is a voltage
across the sample, which can be measured with a high-impedance voltmeter. This
voltage, VH, is called the Hall voltage. For the sign convention shown in 2.7.8, the
Hall voltage is positive for holes.
The behavior of electrons is shown in figure b). The electrons travel in the negative
x-direction. Therefore the force, Fy, is in the positive y-direction due to the negative
charge and the electrons move to the right, just like holes. The balancing electric
field, Ey, now has the opposite sign, which results in a negative Hall voltage.
To calculate the Hall field, we first calculate the Lorentz force acting on the free
carriers:
ELECTRONIC MATERIALS
Lecture 12
A measurement of the Hall voltage is often used to determine the type of
semiconductor (n-type or p-type) the free carrier density and the carrier mobility.
Repeating the measurement at different temperatures allows one to measure the
free carrier density as well as the mobility as a function of temperature. Since the
measurement can be done on a small piece of uniformly doped material it is by far
the easiest measurement to determine the carrier mobility. It should be noted that
the scattering mechanisms in the presence of a magnetic field are different and
that the measured Hall mobility can differ somewhat from the drift mobility. A
measurement of the carrier density versus temperature provides information
regarding the ionization energies of the donors and acceptor that are present in the
semiconductor. While the interpretation of the Hall measurement is straightforward
in the case of a single dopant, multiple types of impurities and the presence of
electrons and holes can make the interpretation non-trivial.
ELECTRONIC MATERIALS
Lecture 12
Exercise 1
A conducting line on an IC chip is 2.8 millimeters (mm) long and has a rectangular
cross section 1x4 micrometers (μm). A current of 5 mA produces a voltage drop of
100 mV across the line. Determine the electron concentration given that the
electron mobility is 500 cm2/Vs.
ELECTRONIC MATERIALS
Lecture 12
Solution.
The electron concentration can be obtain from conductivity. The conductivity is
determined by solving equation:
LI
2.8 10 3  5 10 3
7
S / m
 
 6

3
.
5

10
6
 A  U 10  4 10  0.1
1
R
L U

A I
Then, from equation:
  n  e  q
We obtain:

 
3.5 10 7
27
3
n


4
.
38

10
m
e  q 500 10  4 1.6 10 19
ELECTRONIC MATERIALS
Lecture 12
Exercise 2
An intrinsic silicon bar is 3 mm long and has a rectangular cross section 50x100
μm. At 300K, determine the electric field intensity in the bar and the voltage across
the bar when a steady current of 1 μA is measured. The resistivity of intrinsic
silicon at 300K is 2.30x105 [Ω·cm].
ELECTRONIC MATERIALS
Lecture 12
Solution
The field intensity can be obtained from the current density and conductivity as:
I
I   10 6  2.3 10 5 10 2
5
V / m
E 



4
.
6

10
6
6
 A 
A
50 10 100 10
J
The voltage across the bar is:
U bar  E  L  4.6 105  3 10 3  1380V 
The result obtained in this example indicates that an extremely large voltage is
needed to produce a very small current (1μA). This, however, is not surprising
since the intrinsic carrier concentration is much closer to that of an insulator than it
is to a conductor. Thus intrinsic semiconductor are not suitable for electron
devices. The carrier concentration must be increased.
ELECTRONIC MATERIALS
Lecture 12
Exercise 3
An n-type silicon sample is 3 mm long and has a rectangular cross section 50x100
μm. The donor concentration at 300K is 5x1014cm-3 and corresponds to 1 impurity
atom for 108 silicon atoms. A steady current of 1 μA exists in the bar. Determine the
electron and hole concentrations, the conductivity and the voltage across the bar.
(Note that this is an n-type sample that has the same dimensions and current as
does the intrinsic silicon in exercise 2.)
Intrinsic concentration at 300K is 1.45x1010 cm-3. The electron mobility at 300K is
1500 cm2/Vs.
ELECTRONIC MATERIALS
Lecture 12
Solution
The electron concentration is:

n  N D  5 1014 cm3

And the hole concentration is:
p
ni2
ND

1.45 10 

10 2
5 10
14

 4.2 10 5 cm 3

As n»p, only electron concentration need to be considered. So, that the
conductivity is:
  n  n  q  5 1014 1500 1.6 10 19  0.12  cm1
The voltage across the bar is:
Vbar
I L
10 6  0.3
 EL  L 

 0.05V 
3
2

S   5 10 10  0.12
J
ELECTRONIC MATERIALS
Lecture 12
The efficacy of using extrinsic semiconductors in electronic devices is readily
apparent when the results of exercises 2 and 3 are compared. To produce a small
current of 1μA, 1380V must be applied to the intrinsic sample, whereas only 50mV
is required for the n-type sample. This reduction of voltage by a factor of 28000
exactly equals the decrease in resistivity (from 2.3x105 to 8.33 Ω·cm). Yet the
dramatic increase in the number of free electrons (1.45x1010 to 5x1014 cm-3) occurs
when only 1 silicon atom in 100 million is replaced by an impurity atom!