Course outcome 1st
To understand the semiconductor
materials that are suitable for
To study the properties of materials
for electronic devices
To understand the biasing of diode
Able to design Diode circuit
Able to apply some types of diodes
3 Tests 15%
Text books: Electronic devices and
circuit theory by Robert L. Boylestad
and Louis Nashelsky
Semiconductors are a special class of
elements having a conductivity
between that of a good conductor and
that of an insulator.
They are fall into two classes : single
crystal and compound
Single crystal e.g Ge and Si
Compound e.g GaAs , CdS, GaN and
Ge-germanium; Si-silicon; Ga-gallium ;As –arsenide; Cd-cadmium; S-
sulfide; N-nitride; P-phosphide
Group → 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Diode , in 1939 was using Ge
Transistor, in 1947 was using Ge
In1954 Si was used in Transistor because Si is
less temperature sensitive and abundantly
High speed transistor was using GaAs in 1970
(which is 5 times faster compared to Si)
Si, Ge and GaAs are the semiconductor of
Each and every isolated electron has
a specific energy level associated with
shell and orbiting electron.
The farther an electron from the
nucleus, the higher is the energy
Electron left its parent atom has a
higher energy state than any electron
in the atomic structure.
Analogy to atoms
–From chemistry, we are familiar with the idea of
“electron clouds” orbiting the nucleus.
–The energy of the different clouds, or levels, is
discrete. Adding energy can cause an electron to “jump”
into a higher level. In the same way, an electron can
lose energy and emit a specific wavelength of light
when falling to a lower energy level. (Atomic spectra)
–Pauli Exclusion Principle: no two electrons can occupy
the same exact state at the same time. This is why
electrons fill the energy levels in the way they do.
–Valence electrons are the electrons bound farthest
from the nucleus
This bonding of atoms, strengthened by the sharing of electrons, is
called covalent bonding
Covalent bonding of Si crystal
Covalent bonding of GaAs
Name the materials that suitable for
What are the advantages and
disadvantages of each materials?
What is a covalent bonding? Describe
Energy from external natural cause the
valence electrons to absorb sufficient
kinetic energy and break the covalent bond.
This is assume to be free state.
Electron that has separated from the fixed
lattice structure is called free carriers.
At room temperature, approximately 1.5X
free carriers in 1 cm3
of intrinsic silicon
*intrinsic means material has been refined to
a very low level of impurities.
Table: Intrinsic carriers
Semiconductor Intrinsic carriers/cm3
GaAs 1.7 X 106
Si 1.5 X 1010
Ge 2.5 X 1013
Relative mobility µn
Relative mobility is the ability of free
carriers to move throughout the material.
Semiconductor µn (cm2
Effect on temperature
Conductor – increase resistance with
increase in heat ( number of carrier
do not increase)- is said to have a
positive temperature coefficient.
Semiconductor- increase conductivity
with increase in heat ( number of
carrier increase)- is said to have a
negative temperature coefficient.
What is a crystalline solid?
–A volume of atoms covalently bonded in a
periodic structure with well defined symmetries.
•Face-Centered Cubic (FCC) structure
•Group-IV elements (4 valence electrons)
Where are the electrons?
–Covalent bonds share electrons. The e-are
delocalized, they can move around the crystal,
orbit any atom, as long as there is an open state
(cannot violate Pauli Exclusion)
–This forms discrete energy bands. Solving
Schroedinger’s Equation in the specific periodic
structure reveals these bands.
In an atom, electrons orbit in their shell, at a given
•In a crystal, many electrons occupy a small energy
band. There is a width to the energy band, which is
why Pauli Exclusion is not violated.
•Within the band, electrons can move easily if there
are available states, because the difference in energy
•Between bands, electrons must get energy from
another source, because the band gap can be
Specifics of Crystals
The highest energy an electron reached if you were to
fill the solid with the intrinsic number of electrons at
absolute zero. (No added thermal energy)
•Meaningful! There is a sea of electrons sitting
beneath this energy.
–If you bring two solids together with different Fermi
energies, the electrons will move around to reach an
equilibrium. (Foreshadowing: PN junction)
–If you try to put a lower energy electron into a solid
(at absolute zero) with a higher Fermi energy, it won’t
fit. It cannot be done due to Pauli Exclusion.
•If the highest energy electron exactly fills a band,
the Fermi Energy is near the center of the bands.
The level of a single
quantum number n and
the energies are given as
Fermi energy for N particles and the spin is half , thus
h=plank’s constant; n =quantum no. , m mass ;
L =side length
Fermi level in three dimension
2 fnN π=
= Where is a vector quantum staten
Number of fermions is given by
Then the Fermi energy is given by
By replacing L2
Typical Fermi Energy of Nucleus
( ) 3/115
1025.1 AmR ××= −
( ) MeV30eV1030
A is a nucleons (proton and neutron)
Number density of nucleons in nucleus is
Fermi Energy of a Nucleus
Beyond 0 K: Fermi-Dirac Statistics
•Fermi Energy: The energy
state whose probability of being
occupied is exactly 1/2 .
•Electrons obey Fermi-Dirac-
statistics, which describe the
probability of an electron being
present in an allowed energy
•Note that if there are no
states at a given energy (i.e.,
in the band gap) there will be
no electrons, even if there is
finite probability.( )
k=Boltzmann’s constant, T=temp, E =energy , Ef=Fermi energy
Different Types of Solids
Fermi level falls
with a large band
gap. SiO2: 9 eV.
Fermi level falls
with a small band
gap.Si: 1.11 eV,
Ge:0.67 eV, GaAs:
Fermi level falls
inside the energy
band. Easy for
electrons to move
Transport in Semiconductors
Electrons that get excited into the conduction band carry current.
•The space left behind in the valence band is called a hole.
•Holes also conduct current. In reality, it’s the movement of all
the other electrons. The hole allows this motion. (Bubbles)
•Holes can easily travel “up” in energy.
•Holes have positive charge.
•Current flows in the same direction as the holes move.
•Holes have different mass (effective mass) and mobility
compared to electrons.
Fermi Level: All solids are characterized by an energy that
describes the highest energy electron at 0K, the level which
has1/2 probability of being occupied at finite temperature.
•Semiconductors: A solid with its Fermi level exactly between
bands, with a band gap small enough to be overcome at room
•Both electrons and holes carry current.
Silicon bond model: electrons
Si is in Column IV of periodic table:
Electronic structure of Si atom:
• 10 core electrons (tightly bound)
• 4 valence electrons (loosely bound, responsible for
• Ge, C (diamond form), SiGe
• GaAs, InP, InGaAs, InGaAsP, ZnSe, CdTe
(on average, 4 valence electrons per atom)
Silicon crystal structure
• Silicon is a crystalline material:
– long range atomic arrangement
• Diamond lattice:
– atoms tetrahedrally bonded by
sharing valence electrons
• Each atom shares 8 electrons:
– low energy and stable situation
• Si atomic density: 5 × 1022 cm−3
Controlling the properties of a
Silicon: 4 valence electrons.
Each Si atom bonds to four
•Replace some Si atoms with
atoms that do not have four
•These atoms will have an
extra electron (group IV), or
an extra hole (group III).
•Doping increases the
number of carriers and
changes the Fermi level.
A semiconductor material that has
been subjected to the doping process
is called an extrinsic material.
Type of materials
Phosphorus Doping (n-type)
Phosphorus has 5 valence electrons.
•P atoms will sit in the location of a Si atom in the
lattice, to avoid breaking symmetry, but each will
have an extra electron that does not bond in the same
•These electrons form their own band. Exactly where
depends on the amounts of the two materials.
•This new band is located closer to the conduction
band, because these extra electrons are easier to
excite (and can move around more easily)
Eg. Of n-type material doping
Doping with Sb
Sb - antimony
One electron loosely bound and
freely to move in the crystal
structure. The atoms (in this
case is antimony (Sb)) with five
valence electrons are called the
donor atoms. Similarly with
Phosphorus (P) which also a
Boron Doping (p-type)
Boron has 3 valence electrons.
•B will sit at a lattice site, but the adjacent
Si atoms lack an electron to fill its shell.
This creates a hole.
•These holes form their own energy band.
•This band is located closer to the valence
band, because these extra holes are easy
to “excite down” into the valence band.
Eg of p-type material
•In this case, an insufficient
number of electrons to
complete the covalent bonds.
•The impurities with three
valence electrons are called
acceptor atoms. E.g of
materials are Gallium (Ga),
•Void is called hole
• Doping involves in adding dopant atoms to
an intrinsic semiconductor.
• n-type materials: Doping Si with a Group V
element, providing extra electrons (n for
negative) and moving the Fermi level up.
• p-type materials: Doping Si with a Group
III element, providing extra holes (p for
positive) and moving the Fermi level down.
Group V (n-type) –usually
Group III (p-type)-usually Boron(B) ,
Gallium (Ga) and Indium (In)
Electron versus hole flow
•The valence electron
acquires sufficient kinetic
energy to break its
covalent bond and fills the
void created by hole
•When the electron move
to fill the hole therefore a
transfer of holes to the left
and electrons to the right
•This flow is known as
Majority and Minority Carriers
•N-type material, the electron is called majority carrier and hole the minority
•P-type material, the hole is called majority carrier and electron the minority
no=equilibrium electron carrier concentration
N(E)=density of states
( ) ( ) ( ) ( )
( ) kTEE
f(E) =fermi function k=Boltzmann’s const.
Equilibrium Concentrations: holes
po=equilibrium hole carrier concentration
N(E)=density of states
( )( ) ( ) ( )( ) ( )
( ) kTEE
f(E) =fermi function k=Boltzmann’s const.
• In intrinsic semiconductors (no doping) the electron and hole
concentrations are equal because carriers are created in pairs
( ) ( ) kTEE
( ) ( )
( ) kTEE
( ) kTEE
( ) 2//
C npneNNeNN gC
•This allows us to write
–As the Fermi level moves closer to the conduction
[valence] band, the n0[p0] increases exponentially
ni=no. of electrons (intrinsic) pi= no. of holes (intrinsic)
Temperature Dependence of
/105.1 cmni ×=
•The intrinsic concentration depends
exponentially on temperature. The
T3dependence is negligible.
•Ionization: only a few donors
[acceptors] are ionized.
•Extrinsic: All donors [acceptors] are
•Intrinsic: As the temperature increases
past the point where it is high enough to
excite carriers across the full band gap,
intrinsic carriers eventually contribute
•At room temp (300K), the intrinsic
carrier concentration of silicon is:
( ) ( ) kTEEkTE
Moving Carriers (i.e., current)
There are two mechanisms by which mobile carriers
move in semiconductors –resulting in current flow
•Carrier movement is induced by a force of some
•Carriers move (diffuse) from a place of higher
concentration to a place of lower concentration
Drude Model of Conductivity
The current is the charge*number of electrons*area*velocity in a unit
of time. For j = current density, divide by the area. The drift velocity
(vd) is a function of charge mobility (μn) and electric field (E).
•At equilibrium, there is no net motion of charge, vavg= 0.
•With an applied electric field, there is a net drift of electrons [holes]
against [with] the electric field resulting in an average velocity.
•This model allows us to apply Newton’s equations, but with an
effective mass. The effective mass takes the interactions with the rest
of the solid into account.
•Electrons are assumed to move in a direct path, free of interactions
with the lattice or other electrons, until it collides.
•This collision abruptly alters its velocity and momentum.
•The probability of a collision occurring in time dtis simply dt/τ,
where τ is the mean free time. τ is the average amount of time it
takes for an electron to collide.
εµυ υ nga qnqnJ ==
ato += υυ maqEF ==
( )EpnqJ pn µµ +=
•Consider an electron just after a collision. The velocity it acquires
before the next collision will be acceleration*time
•We want the average velocity of all the electrons, which can be
obtained by simply averaging the time, which we already know is τ
•We can also write this in terms of mobility:
•Taking both holes and electrons into account, we end up with the
following formula for current density due to drift.
( )BqF ×+= υε
Moving electrons experience a force
due to a perpendicular B field
An electric field develops in response
to this force.
•The sign of this field perpendicular
to the flow of current determines the
•Density and mobility can also be
•Diffusion results in a net flux of particles from the region of higher
concentration to the region of lower concentration
–This flux leads to current (movement of charged particles)
–Magnitude of current depends on the gradient of concentration
–Dnis the diffusivity coefficient
•Diffusivity is related to mobility by Einstein’s relationship
–Typical values for Si at room temp
•Dn= 34 cm2
/s and Dp= 13 cm2