Download LECTURE-3 Electrons and Holes in semiconductors: Silicon crystal

LECTURE-3
Electrons and Holes in semiconductors: Silicon crystal structure, Donors and
acceptors in the band model
Electrons and holes in semiconductors
As pointed out before, semiconductors distinguish themselves 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 we
will introduce the concept of holes in a semiconductor. It is important for the
reader to understand that one could deal with only electrons (since these are the
only real particles available in a semiconductor) if one is willing to keep track of
all the electrons in the "almost-full" valence band.
The concepts of holes is introduced based on the notion that it is a whole lot easier
to keep track of the missing particles in an "almost-full" band, rather than keeping
track of the actual electrons in that band. We will now first explain the concept of a
hole and then point out how the hole concept simplifies the analysis.
Holes are missing electrons. They behave as particles with the same properties as
the electrons would have occupying the same states except that they carry a
positive charge. This definition is illustrated further with the figure below which
presents the simplified energy band diagram in the presence of an electric field.
Characteristics
Physical
Silicon crystallizes in a diamond cubic crystal structure
Silicon Crystal Structure
The above illustration shows the arrangement
after Kittel
of the silicon atoms in a unit cell, with the
numbers indicating the height of the atom
above the base of the cube as a fraction of the
cell dimension.
Silicon crystallizes in the same pattern as diamond, in a structure which Ashcroft
and Mermin call "two interpenetrating face-centered cubic" primitive lattices. The
lines between silicon atoms in the lattice illustration indicate nearest-neighbor
bonds. The cube side for silicon is 0.543 nm. Germanium has the same diamond
structure with a cell dimension of .566 nm.
Silicon is a solid at room temperature, with relatively high melting and boiling
points of 1414 and 3265 °C, respectively. It has a greater density in a liquid state
than a solid state. It does not contract when it freezes like most substances, but
expands, similar to how ice is less dense than water. With a relatively high thermal
conductivity of 149 W·m−1·K−1, silicon conducts heat well.
In its crystalline form, pure silicon has a gray color and a metallic luster.
Like germanium, silicon is rather strong, very brittle, and prone to chipping.
Silicon, like carbon and germanium, crystallizes in adiamond cubic crystal
structure, with a lattice spacing of 0.5430710 nm (5.430710 Å).[10]
The outer electron orbital of silicon, like that of carbon, has four valence electrons.
The 1s, 2s, 2p and 3s subshells are completely filled while the 3p subshell contains
two electrons out of a possible six.
Silicon is a semiconductor. It has a negative temperature coefficient of resistance,
since the number of free charge carriers increases with temperature. The electrical
resistance of single crystal silicon significantly changes under the application of
mechanical stress due to the piezoresistive effect.
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 number of charge carriers is therefore determined by the properties of
the material itself instead of the amount of impurities. In intrinsic semiconductors
the number of excited electrons and the number of holes are equal: n = p.
The electrical conductivity of intrinsic semiconductors can be due to
crystallographic defects or electron excitation. In an intrinsic semiconductor the
number of electrons in the conduction band is equal to the number of holes in the
valence band. An example is Hg
0.8Cd
0.2Te at room temperature.
An indirect band gap intrinsic semiconductor is one in which the maximum energy
of the valence band occurs at a different k (k-space wave vector) than the
minimum energy of the conduction band. Examples include silicon and
germanium. A direct band gap intrinsic semiconductor is one where the maximum
energy of the valence band occurs at the same k as the minimum energy of the
conduction band. Examples include gallium arsenide.
A silicon crystal is different from an insulator because at any temperature above
absolute zero, there is a finite probability that an electron in the lattice will be
knocked loose from its position, leaving behind an electron deficiency called a
"hole". If a voltage is applied, then both the electron and the hole can contribute to
a small current flow.
The conductivity of a semiconductor can be modeled in terms of the band theory of
solids. The band model of a semiconductor suggests that at ordinary temperatures
there is a finite possibility that electrons can reach the conduction band and
contribute to electrical conduction.
The term intrinsic here distinguishes between the properties of pure "intrinsic"
silicon and the dramatically different properties of doped n-type or p-type
semiconductors
To understand how diodes, transistors, and other semiconductor devices can do
what they do, it is first necessary to understand the basic structure of all
semiconductor devices. Early semiconductors were fabricated from the element
Germanium, but Silicon is preferred in most modern applications.
The crystal structure of pure silicon is of course 3-dimensional, but that is difficult
to display or to see, so the image to the left is often used to represent the crystal
structure of silicon. For you physics types, silicon (and germanium) falls in column
IVa of the Periodic Table. This is the carbon family of elements. The essential
characteristic of these elements is that each atom has four electrons to share with
adjacent atoms in forming bonds.
While this is an oversimplified description, the nature of a bond between two
silicon atoms is such that each atom provides one electron to share with the other.
The two electrons thus shared are in fact shared equally between the two atoms.
This type of sharing is known as a covalent bond. Such a bond is very stable, and
holds the two atoms together very tightly, so that it requires a lot of energy to break
this bond.
For those who are interested, the actual bonds in a 3-dimensional silicon crystal are
arranged at equal angles from each other. If you visualize a tetrahedron (a pyramid
with three points on the ground and a fourth point sticking straight up) with the
atom centered inside, the four bonds will be directed towards the points of the
tetrahedron.
Now we have our silicon crystal, but we still don't have a semiconductor. In the
crystal we saw above, all of the outer electrons of all silicon atoms are used to
make covalent bonds with other atoms. There are no electrons available to move
from place to place as an electrical current. Thus, a pure silicon crystal is quite a
good insulator. In fact, it is almost glass, which is silicon dioxide. A crystal of pure
silicon is said to be an intrinsic crystal.
Electrons and holes
In an intrinsic semiconductor such as silicon at temperatures above absolute zero,
there will be some electrons which are excited across the band gap into the
conduction band and which can support current flow. When the electron in pure
silicon crosses the gap, it leaves behind an electron vacancy or "hole" in the regular
silicon lattice. Under the influence of an external voltage, both the electron and the
hole can move across the material. In an n-type semiconductor, the dopant
contributes extra electrons, dramatically increasing the conductivity. In a p-type
semiconductor, the dopant produces extra vacancies or holes, which likewise
increase the conductivity. It is however the behavior of the p-n junction which is
the key to the enormous variety of solid-state electronic devices.
Donors and acceptors in the band model.
An extrinsic semiconductor is a semiconductor that has been doped, that is, into
which a doping agent has been introduced, giving it different electrical properties
than the intrinsic (pure) semiconductor.
Doping involves adding dopant atoms to an intrinsic semiconductor, which
changes the electron and hole carrier concentrations of the semiconductor at
thermal equilibrium. Dominant carrier concentrations in an extrinsic
semiconductor classify it as either an n-type or p-type semiconductor. The
electrical properties of extrinsic semiconductors make them essential components
of many electronic devices.
Semiconductor doping
Semiconductor doping is the process that changes an intrinsic semiconductor to an
extrinsic semiconductor. During doping, impurity atoms are introduced to an
intrinsic semiconductor. Impurity atoms are atoms of a different element than the
atoms of the intrinsic semiconductor. Impurity atoms act as either donors or
acceptors to the intrinsic semiconductor, changing the electron and hole
concentrations of the semiconductor. Impurity atoms are classified as donor or
acceptor atoms based on the effect they have on the intrinsic semiconductor.
Donor impurity atoms have more valence electrons than the atoms they replace in
the intrinsic semiconductor lattice. Donor impurities "donate" their extra valence
electrons to a semiconductor's conduction band, providing excess electrons to the
intrinsic semiconductor. Excess electrons increase the electron carrier
concentration (n0) of the semiconductor, making it n-type.
Acceptor impurity atoms have fewer valence electrons than the atoms they replace
in the intrinsic semiconductor lattice. They "accept" electrons from the
semiconductor's valence band. This provides excess holes to the intrinsic
semiconductor. Excess holes increase the hole carrier concentration (p0) of the
semiconductor, creating a p-type semiconductor.
Semiconductors and dopant atoms are defined by the column of the periodic table
in which they fall. The column definition of the semiconductor determines how
many valence electrons its atoms have and whether dopant atoms act as the
semiconductor's donors or acceptors.
Group IV semiconductors use group V atoms as donors and group III atoms as
acceptors.
Group III-V semiconductors, the compound semiconductors, use group VI atoms
as donors and group II atoms as acceptors. Group III-V semiconductors can also
use group IV atoms as either donors or acceptors. When a group IV atom replaces
the group III element in the semiconductor lattice, the group IV atom acts as a
donor. Conversely, when a group IV atom replaces the group V element, the group
IV atom acts as an acceptor. Group IV atoms can act as both donors and acceptors;
therefore, they are known as amphoteric impurities.
Group IV
semiconductors
Intrinsic semiconductor
Donor atoms
Acceptor atoms
Silicon, Germanium
Phosphorus,
Arsenic
Boron,
Aluminium
Selenium,
Tellurium,
Silicon,
Germanium
Beryllium, Zinc,
Cadmium,
Silicon,
Germanium
Aluminum phosphide,
Aluminum arsenide,
Group III-V
semiconductors Gallium arsenide, Gallium
nitride
The two types of extrinsic semiconductor
N-type semiconductors
Band structure of an n-type semiconductor. Dark circles in the conduction band are
electrons and light circles in the valence band are holes. The image shows that the
electrons are the majority charge carrier.
N-type semiconductors have a larger electron concentration than hole
concentration. The phrase 'n-type' comes from the negative charge of the electron.
In n-type semiconductors, electrons are the majority carriers and holes are the
minority carriers. N-type semiconductors are created by doping an intrinsic
semiconductor with donor impurities (or doping a p-type semiconductor as done in
the making of CMOS chips). A common dopant for n-type silicon is phosphorus.
In an n-type semiconductor, the Fermi level is greater than that of the intrinsic
semiconductor and lies closer to the conduction band than the valence band.
P-type semiconductors
Band structure of a p-type semiconductor. Dark circles in the conduction band are
electrons and light circles in the valence band are holes. The image shows that the
holes are the majority charge carrier
As opposed to n-type semiconductors, p-type semiconductors have a larger hole
concentration than electron concentration. The phrase 'p-type' refers to the positive
charge of the hole. In p-type semiconductors, holes are the majority carriers and
electrons are the minority carriers. P-type semiconductors are created by doping an
intrinsic semiconductor with acceptor impurities (or doping a n-type
semiconductor). A common p-type dopant for silicon is boron. For p-type
semiconductors the Fermi level is below the intrinsic Fermi level and lies closer to
the valence band than the conduction band.
Use of extrinsic semiconductors
Extrinsic semiconductors are components of many common electrical devices. A
semiconductor diode (devices that allow current in only one direction) consists of
p-type and n-type semiconductors placed in junction with one another. Currently,
most semiconductor diodes use doped silicon or germanium.
Transistors (devices that enable current switching) also make use of extrinsic
semiconductors. Bipolar junction transistors (BJT) are one type of transistor. The
most common BJTs are NPN and PNP type. NPN transistors have two layers of n-
type semiconductors sandwiching a p-type semiconductor. PNP transistors have
two layers of p-type semiconductors sandwiching an n-type semiconductor.
Field-effect transistors (FET) are another type of transistor implementing extrinsic
semiconductors. As opposed to BJTs, they are unipolar and considered either Nchannel or P-channel. FETs are broken into two families, junction gate FET
(JFET) and insulated gate FET (IGFET).
Other devices implementing the extrinsic semiconductor:
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Lasers
Solar cells
Photodetectors
Light-emitting diodes
Thyristors
To allow our silicon crystal to conduct electricity, we must find a way to allow
some electrons to move from place to place within the crystal, in spite of the
covalent bonds between atoms. One way to accomplish this is to introduce an
impurity such as Arsenic or Phosphorus into the crystal structure, as shown to the
right. These elements are from column Va of the Periodic Table, and have five
outer electrons to share with other atoms. In this application, four of these five
electrons bond with adjacent silicon atoms as before, but the fifth electron cannot
form a bond. This electron can easily be moved with only a small applied electrical
voltage. Because the resulting crystal has an excess of current-carrying electrons,
each with a negative charge, it is known as "N-type" silicon.
This construction does not conduct electricity as easily and readily as, say, copper
or silver. It does exhibit some resistance to the flow of electricity. It cannot
properly be called a conductor, but at the same time it is no longer an insulator.
Therefore, it is known as a semiconductor.
While this effect is interesting, it still isn't particularly useful by itself. A plain
carbon resistor is easier and cheaper to manufacture than a silicon semiconductor
one. We still don't have any way to actually control an electrical current.
But wait a moment! We obtained a semiconductor material by introducing a 5electron impurity into a matrix of 4-electron atoms. (For you physics types, we're
only looking at the outer electrons that are available for bonding -- electrons in
inner shells are not included in the process or in this discussion.) What happens if
we go the other way, and introduce a 3-electron impurity into such a crystal?
Suppose we introduce some Aluminum (from column IIIa in the Periodic Table)
into the crystal, as shown to the left? We could also try Gallium, which is also in
column IIIa right under aluminum. Now what?
These elements only have three electrons available to share with other atoms.
Those three electrons do indeed form covalent bonds with adjacent silicon atoms,
but the expected fourth bond cannot be formed. A complete connection is
impossible here, leaving a "hole" in the structure of the crystal.
Experimentation shows that there is an empty place where an electron should
logically go, and often an electron will try to move into that space to fill it.
However, the electron filling the hole had to leave a covalent bond behind to fill
this empty space, and therefore leaves another hole behind as it moves. Yet another
electron may move into that hole, leaving another hole behind, and so forth. In this
manner, holes appear to move as positive charges through the crystal. Therefore,
this type of semiconductor material is designated "P-type" silicon.
By themselves, P-type semiconductors are no more useful than N-type
semiconductors. The truly interesting effects begin when the two are combined in
various ways, in a single crystal of silicon. The most basic and obvious
combination is a single crystal with an N-type region at one end and a P-type
region at the other. A crystal with two regions as described is known as a
semiconductor diode, and is the topic of the next page.