Excerpt
Comprehensive Study On Properties of Semiconductors
and p-n Junction
Umana Rafiq Ananna
Department of EEE, Ahsanullah University of Science and Technology, Dhaka,
Bangladesh.
Abstract: A comprehensive study of p-n junction is
necessary to design an electronic device as well as circuits.
An electronic device controls the movement of electrons. The
study of electronic devices requires a basic understanding of
the relationship between electrons and other components of
an atom. This leads to knowledge of the differences between
conductors, insulators and semiconductors and to an
understanding of p-type and n-type semiconductor material.
p-n junction is formed by joining p-type and n-type
semiconductor materials. So the concept of semiconductor,
majority and minority carrier of p-type and n-type
semiconductor, doping, depletion region of p-n junction,
mobility and conductivity, drift and diffusion current,
carrier concentration calculation and Fermi energy level is
actually the comprehensive study of p-n junction.
Introduction
Semiconductors as a separate class of materials were
known by the end of the 19th century. Not until the
development of quantum theory, however, could the
characteristics of dielectrics, semiconductors, and metals
be understood. But today Semiconductor elements are
widely used all over the world. Because of its unique
properties it has its popularity in the field of
manufacturing electronic devices over semiconductors.
However the summery can only describe a small portion
of the vast literature regarding semiconductors and the
most basic semiconductor device called "p-n junction". So
the study of the basic philosophy of a semiconductor
device naturally depends on the physics of
semiconductors. But at first we have to go through the
fundamentals of semiconductors.
I.
What is a semiconductor?
Semiconductor is a material that behaves in between a
conductor and an insulator. At ambient temperature, it
conducts electricity more easily than an insulator, but less
readily than a conductor. At very low temperatures, pure
or intrinsic semiconductors behave like insulators. At
higher temperatures though or under light, intrinsic
semiconductors can become conductive. The addition of
impurities to a pure semiconductor can also increase its
conductivity. Examples of semiconductors include
chemical elements and compounds such as silicon,
germanium, and gallium arsenide.
But before proceeding to the elaborate studies of
semiconductors we need to at first understand the
properties of solids and their types in which we will find
semiconductor. And it will tell us why semiconductors are
different from conductors and insulators.
II. Classification of conductor,
semiconductor and insulator
On the basis of relative values of electrical conductivity
() or resistivity (=1/), the solids are broadly classified
as Metals, Semiconductors and Insulators. They can also
be classified on the basis of band theory.
In the metallic conductors conduction band consists free
electrons which can be easily moved by the influence of
applied electric field. And each time and electrons leaves
a hole behind which is then filled up by the electrons from
valance band. Electrons from valance band thus move to
the conduction band and current flows. There is almost no
forbidden gap for the conductors.
Since the Forbidden gap for the insulators is so wide that
electrons in the valance band all remain bound and no
free electrons are available in the conduction band.
Since a semiconductor has narrow forbidden gap and the
valance band is completely full and conduction band is
empty. When an external energy is applied some excited
valance electrons move into conduction band and thus
creates a current flow.
*The orientation of the solid atoms also distinguishes the
conductor, semiconductor and insulator.
III. Conductivity in Semiconductors
Conductivity depends largely upon what happens to the
outer shell electrons when the atoms bond together to
form a solid. In the case of semiconductors, they usually
have four valance electrons (silicon) and four holes. So
when these atoms come close to each other to form a solid
piece, the valance electrons behave as if they are orbiting
between the valance shells of two atoms. In this way each
valance electrons fills one of the holes on the valance
shell of neighboring atom which is known as covalent
bonding. When semiconductor materials are prepared for
manufacturing devices, they are aligned into a three-
dimensional crystal lattice where each atom is covalently
bonded to 4 surrounding atoms.
The conductivity of semiconductor elements depends on
some
effects.
Semiconductors
possess
negative
temperature coefficient of resistance. Hence their
conducting nature increases with rise in temperature. At
absolute zero temperature (-273°C) it acts as an insulator.
As the temperature increases, and as the energy gap
between the conduction and valence bands is very small
(~1eV) so the thermal energy gained by the valence
electrons propels them to the conduction band. Because
when the temperature of a semiconductor rises above
absolute zero, there is more energy in the semiconductor
to spend on lattice vibration and on exciting electrons into
the conduction band.
When semiconductors are optically excited or excited by
the effects of light then it's conductivity increases.The
conductivity of an intrinsic semiconductor depends on its
temperature, but at room temperature its conductivity is
very low. When a small amount maybe few parts per
million (ppm), of a suitable impurity is added to the pure
semiconductor, the conductivity of the semiconductor is
increased manifold. Such materials are known as e
extrinsic semiconductors or impurity semiconductors. The
deliberate addition of a desirable impurity is called
doping and the impurity atoms are called dopant. Such a
material is also called a doped semiconductor. The dopant
has to be such that it does not distort the original pure
semiconductor lattice. It occupies only a very few of the
original semiconductor atom sites in the crystal. A
necessary condition to attain this is that the sizes of the
dopant and the semiconductor atoms should be nearly the
same.
Doping has a dependence on Dopant-Site binding
energies,
E
B
- m
n
X q
4
/[
2 (4 X X K
s
X X )
2
]
Where, E
B
= Binding energy
m
n
= effective mass of charge carrier
K
s
= Di-electric constant for silicon
IV.
Types Of semiconductors
Pure semiconductors are called intrinsic type material. It
is the condition of a semiconductor before the process of
doping. It cannot be used to make a device. It is free of
impurities and crystal Defect. When the temperature
increases more thermal energy is available to the
electrons and some of them may break away from the
valance shell and creates freed negative charges. This
ionizing process also creates holes or vacancies in the
structure with effective positive charge. But since these
charges are randomly distributed in the structure there is
no net current flowing through it and it remains in a
balanced condition. Apart from the process of generation
of conducting charges also occurs a process of
recombination in which electrons recombine with holes.
And the recombination happens because of the collision
of electrons and holes. Extrinsic type materials are
semiconductors which can conduct current unlike the
intrinsic material. Extrinsic type semiconductor must
contain impurity atoms that are added to them by the
process of doping. Due to adding impurity atoms (which
have their own crystal structure) and creating a spare
electron the extrinsic semiconductor has crystal defects.
This kind of semiconductors contains imbalance in the
carrier concentration. The net current flow is not zero.
On the basis of doping Extrinsic semiconductors are of
two types:
A. n-Type:
n-type semiconductors are made by donor doping. Donor
doping generates free electrons in the conduction band. It
is done by adding impurity atoms which have to be
pentavalent (five electrons and three holes in the valance
shell). The semiconductor (tetravalent) atoms have 4
electrons in the valance shell. So 4 of them make a
covalent bond with the 4 added impurity electrons. and
will produce a spare valance shell electron for each
addition. Then each of these spare electrons enters the
conduction band and thus improves the conductivity.
Since electrons are negative charge carriers so these
materials are referred to n-type materials. Here electrons
are majority carriers and holes are minority carriers.
For doping tetravalent Si or Ge atom typical donor
impurity atoms are: Arsenic (As), Antimony (Sb),
Phosphorous (P) etc.
P+
Si
Si
Si
Si
Si
Si
Si
Si
Free
electron
Figure 1: n-type semiconductor
B. p-Type:
p-type semiconductors are made by acceptor doping.
Acceptor doping produces holes or shortage of electrons
in valance band. In this case impurity atoms for doping
are trivalent (three electrons and five holes in the valance
shell). So during doping the three impurity electrons pair
with 3 electrons of semiconductor's valance shell. And
thus each of the additions leaves behind a vacancy or
holes. And now conduction may occur in the process of
hole transfer. These referred to as p-type materials.
Typical acceptor impurity atoms are: Gallium (Ga),
Boron (B), Aluminium (Al), Indium (In) etc. Here Holes
are majority carriers and electrons are minority carriers.
B-
Si
Si
Si
Si
Si
Si
Si
Si
Hole
Figure 2: p-type semiconductor
Neutrality : By doping of a semiconductor we can only
increase the no. of free electrons in the conduction band.
or no. of holes in the valance band. But Still it remains
electrically neutral. It happens because doping does not
change the atomic structure; rather it only changes the no.
of charge carriers. This is a kind of recombination which
causes the semiconductor to be electrically neutral before
applying any external potential.
There are also Semiconductors classified as Direct Band
gap and Indirect Band gap Semiconductors. Based On
Rated Compositions there are Elementary Semiconductors:
Si and Ge. Compound Semiconductors: combinations of
elements of Group (iii)-(iv), (iv)-(iv), (iv)-(v). Based On
Alloys there are semiconductors known as Binary: GaAs,
Tertiary: GeAsP
and
Quaternary: GaAsInP
V.
Carriers
Semiconductors alike conductors contain charge carrying
entities which can create a flow of current. But with
breaking the bond between the electron and atom no
current flow is possible. Equivalently if we consider the
Energy Band Theory then current flow is not possible if
the valance band is completely filled with electrons and
the conduction band is devoid of electrons. Though in
actual case the valance band electrons move about in the
crystal but no current arises. It is because The momentum
of electrons is quantized in addition to their energy. So
even if the valance band is full of electrons the net
momentum of the electrons is identically zero and thus no
current flow arises.
But when the bond (for example (Si-Si) is broken the
released electron can freely wander about the lattice and
acts as a negative charge carrier. In terms of the band
model, the excited electrons from valance band can move
into the conduction band and thus create charge carriers.
In addition, when a bond is broken and electron is
released a hole or vacancy is created. Which is
immediately replaced by the nearby electron creating
another hole and this goes on. In the band model it can be
visualized as if a hole that is created in the valance band
that is created while an excited electron jumped into the
conduction band; is filled by the nearby electron and
another hole is created. Thus no. of holes also moves
through the vast sea of valance electrons.
These holes are positive charge carriers which can also
create a flow of current.
VI.
Difference In Band Structure
The major difference based on which materials are
classified is not the nature of the energy band of their
band model, rather on the magnitude of the energy gap
between the bands. Insulators have wide band gap while
semiconductors have a narrow one. In metals the band
gap being so small due to the overlap of the conduction
and valance band; there is always abundance of charge
carriers.
C o n d u c t i o n
B a n d
F o r b i d d e n g a p
V a l e n c e B a n d
Figure 3: Band Structure
Semiconductors present the intermediate characteristics in
between the conductor and insulator. At room
temperature (T=300K), E
G
= 1.42 eV in GaAs, E
G
= 1.12
eV in Si and E
G
= .66 eV in Ge. In semiconductors the
increasing thermal energy can excite the electrons of the
valance band into the conduction band creating moderate
no. of charge carriers in these materials.
VII.
Carrier Properties
Charge carriers in the doped semiconductor materials
have the some unique properties which are very important
in the understanding of the characteristics of the
semiconductor after doping. The very first property is the
generation of Negative charges or electrons and positive
charges or holes. The magnitude of the charge of
electrons and holes is the same. To three place accuracy
in MKS units,
q=1.60X10
-19
Coulomb.
Mass, like charge , is another very basic property of
carriers. The apparent or effective mass of electrons
within a crystal is a function of the semiconductor
material (Si or Ge) and is significant from the mass of
electrons within a vacuum. It allows us to conceive of the
electrons and holes as Quasi-classical particles and to
employ classical particle relationships in most device
analysis. Effective masses can have multiple components.
It also varies with temperature. If electrons effective mass
is
m
n
,
the
force
on
the
charge
is,
F=-qX=m
n
X(dv/dt)
and for the holes,
F=qX=m
p
X(dv/dt)
Another significant property is the concentration of
carriers. Which is different in intrinsic and extrinsic
semiconductors.
VIII. State and Carrier Distribution
In the study of p-type and n-type semiconductors, it is
very important to calculate the precise numerical value of
the of the carrier concentrations in them. Another
property that is needed to be understood is the distribution
of carriers as a function of energy in the respective energy
bands and also te carrier concentration in the
semiconductors
under
equilibrium
conditions.
A. Density of States:
The state distribution is an important component to
determine carrier distributions and concentrations. To
determine the density of states, an analysis need to be
performed on the basis of quantum mechanical
considerations,
g
C
(E)=m
n
2m
n
X(EE
C
)
23 E>Ec
g
V
(E)=m
n
2m
p
X(E
V
E)
23 E<=Ev
Where, g
C
(E)=density of states at an energy E in
conduction band.
g
C
(E) = density of states at an energy E in valance band
m
n
= effective mass of electrons
m
p
= effective mass of holes.
B. The Fermi Function :
The Fermi Function (E) specifies, under equilibrium
conditions, the probability that an available state at an
energy E will be occupied by an electron.
Mathematically, the Fermi function is simply a
probability distribution function.
In mathematical symbols,
(E) = 1 / (1 + e
(E EF ) / kt
)
where,
E
F
= Fermi energy or Fermi level
k = Boltzmann constant (K = 8.617 )
T = temperature in Kelvin(K)
The Fermi function is universal in the sense that it
applies with equal validity to all materials insulators,
semiconductors and metals. Finally, the relative
positioning of the Fermi energy E
F
compared to E
c
(or
E
v
),an item of obvious concern, is treated in subsequent
subsections. It is a temperature dependent function.
C. Equilibrium Carrier Concentrations :
We have arrived at an important point in the carrier
modeling process, For the most part, this section simply
embodies the culmination of our modeling efforts, with
working relationships for the equilibrium carrier
concentration being established to complement the
qualitative carrier information presented in previous
sections.
D. Formulas for n and p :
Integration over the equilibrium distribution of electronics
in the conduction band yields
The equilibrium electron concentration. A similar
statement can be made relative to the hole concentration.
We therefore conclude
n = g
c
(E) (E)dE
p = g
v
(E)[1 (E)]dE
Identifying
F
1/2
() =
1/2
d / 1 +e
( c )
, the Fermi-
Direc integral of order ½ one obtains
n = N
c
X e
(EF
Ec
) / kT
p = N
v
X e
(Ev
EF
) / kT
E. The n
i
and np Relation:
The intrinsic carrier concentration can figure prominently
in the quantitative calculation of the carrier
concentrations. Continuing to establish pertinent carrier
concentration
relationships,
we
next
interject
considerations specifically involving this important
material parameter.
Firstly, one obtains
N
i
= (N
c.
N
v
) X e
-Eg/2kT
A second very important n
i
-based relationship is.
np = n
2
i
This relationship often proves to be extremely useful in
practical computations.
IX. Carrier Concentration of Electrons
The equation for the thermal equilibrium concentration of
electron can be found by integrating over the conduction
band energy or,
n
O
= g
C
(E) f
F
(E) dE
The lower limit of integration is E
C
and upper limit of
integration should be top of the conduction band energy.
Since the Fermi probability function rapidly approaches
zero with increasing energy we can take the upper limit
of the integration to be infinity.
We are assuming that the Fermi energy is within the
forbidden energy band-gap. For electrons in the
conduction band we have the Fermi probability function
reduced to Boltzmann approximation,
f
F
(E) = 1/ [1+ e
E-EF / kT
] e
E-EF / kT
So, the thermal equilibrium density of electrons in the
conduction band is found from,
n
O
= 4 (2mnkT/h
3
)
3/2
. e
^-EC-EF / kT
0
1/2
e
-
.d
The integral is the gamma function with a value of,
0
1/2
e
-
.d = ½
Then the value of n
O
will be after simplification,
n
O
= N
C
. e
-EC-EF / kT
X. Carrier Concentrations of Holes
Excerpt out of 8 pages
- Quote paper
- Umana Rafiq (Author), 2012, A comprehensive study on properties of Semiconductors and p-n Junction, Munich, GRIN Verlag, https://www.grin.com/document/278587
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