Transcript KIMIA BAHAN SEMIKONDUKTOR (MKS 6212)

solid state electronic materials
electronic structure and band energy
to describe electrons and their
electrical properties in a solid
qualitative band model
quantitative bond model
Kimia Bahan Semikonduktor – 2010 – Dr. Indriana Kartini
Band Theory of Solids
Energy Levels



Valence band
electrons are the
furthest from the
nucleus and have
higher energy levels
than electrons in
lower orbits.
The region beyond
the valence band is
called the
conduction band.
Electrons in the
conduction band are
easily made to be
free electrons.
Isolated Semiconductor Atoms


Silicon and Germanium are electrically neutral;
that is, each has the same number of orbiting
electrons as protons.
Both silicon and germanium have four valence
band electrons, and so they are referred to as
tetravalent atoms. This is an important
characteristic of semiconductor atoms.
Semiconductor Crystals



Tetravalent atoms such as silicon, gallium
arsenide, and germanium bond together to form a
crystal or crystal lattice.
Because of the crystalline structure of
semiconductor materials, valence electrons are
shared between atoms.
This sharing of valence electrons is called covalent
bonding. Covalent bonding makes it more difficult
for materials to move their electrons into the
conduction band.
2 major binding forces:

Binding forces coming from electron-pair
bonds (covalent bonding)



For elemental semiconductors: C(diamond), Si
and Ge
typically around 4 eV in semiconductor device
Ionic bonding/heteropolar bonding

For ionic solids such as the nitride, oxide and
halide insulators, and compound
semiconductors
• the motion of electrons (1023) in the solids
determines the electrical characteristics of
the solid state electronic devices and
integrated circuit
• in vacuum, the motion of a few separately
objects  Newton Law; F = ma – classical
law of mechanics
• for solids there is particle density –
classical law must be extended
in a solid  high packing density
• in a volume of about 1 cm3, there are 1023 electrons
and ions packed
• in a vacuum tube, there are only 109-1010 electrons
• consequences in solids:
– very small interparticle distances ((1023)-1/3=2.108 cm)
– high interparticle forces (interacting particles)
– high interparticle collision (about 1013 per second)
• high particle density in solid system  condensed
matter
current or wave generated in solids resulted from averaged motion of electrons 
statistical mechanics
Kristal fotonik (matriks dan
bola mempunyai sifat
dielektrik yang berbeda)
Kristal (lattice of ions)
e- scatter in the periodic lattices
photons scatter in the periodic
lattices
non-interacting particles
berlaku persamaan Maxwell:
interacting particles
berlaku persamaan Schrodinger:
H = E 
solved approximately
Band Diagram – electron standing waves
allowed energies  bands
forbidden energies  band-gaps
solved exactly
Band Diagram – standing waves
allowed frequencies  bands
forbidden frequencies  band-gaps
1 e- atom
quantized energy
Extrapolation on 1 crystal
discrete energy
multielectron system (~ 1023/cm3)
• uncertainties with small distances
• large number of particles
allowed bands and forbidden bands
Wave mechanics applied (Schrodinger eqn.)
and statistic mechanics
Electronic energy levels are arranged in
allowed and forbidden bands
results of statistical mechanic analysis at thermodynamic equilibrium give the
Fermi-Dirac quantum distribution of the electron kinetic energy in a solid
(condensed matter) and Boltzmann classical distribution of electrons and particles
in a gas (dilute matter)
1 ELECTRON
Math solution to quantum
mechanic eqns model 1
electron
energy level of 1 electron
ELECTRONIC SOLIDS
energy level of 1 electron
band energy
Applied :
• Planck eqn. (EMR energy and
quantized particle wave)
E = h
• de Broglie eqn. (EMR
momentum and particle wave
~ 1/)
p = h/
Bands formation
As the two atoms interact  overlap  the two e- interact
interaction/perturbation in the discrete quantized energy level
splitting into two discrete energy levels
allowed band
• at r0 : allowed band consists of some discrete
energy level
• Eg.: System co. 1019 atoms
1e, the width of allowed band
energy at r0 = 1 eV
• if assumed that each eoccupies different energy level
and discrete energy level
equidistance  allowed bands
will be separated by 10-19 eV
r0 represents the equilibrium interatomic distance in the crystal
• The difference of 10-19 eV  too small  allowed bands to
be quasi-continue energy distribution
pita energi terlarang
pita energi terbolehkan
Bands of atom 3eAs 2 atoms get
closer, electron
interaction was
started from
valence electron,
n=3
At r0 :
3 allowed bands
separated by
forbidden were
formed
Splitting energi pada atom 14Si 
4 elektron valensi 3s2 3p2
Eg represents the width of forbidden band =
bandgap energy
3p2 : n=3 l=1
3s2 : n=3 l=0
At reduced distance : 3s and 3p interacted dan overlap  4 quantum state of upper bands (CB)
and 4 quantum state of lower bands (VB)  4 valence e- of Si will occupy lower band
Bonding In
Metals:
Lithium
according to
Molecular
Orbital
Theory
Page 16
Sodium According to Band Theory
Conduction band:
empty 3s antibonding
No gap
Valence band:
full 3s bonding
Page 17
Magnesium
3s bonding and antibonding should be full
Page 18
Magnesium
Conduction band:
empty
No gap: conductor
Valence band:
full
Conductor
Page 19
Classification of solids into three types,
according to their band structure



insulators: gap = forbidden region
between highest filled band (valence
band) and lowest empty or partly filled
band (conduction band) is very wide,
about 3 to 6 eV;
semiconductors: gap is small - about
0.1 to 1 eV;
conductors: valence band only
partially filled, or (if it is filled), the
next allowed empty band overlaps with
it
Band structure and conductivity
Band gaps of some common
semiconductors relative to the optical
spectrum
Visible
Infrared
Ultraviolet
GaAs
TiO2
GaP
CdSe CdS SiC
ZnS
InSb Ge Si
0
7 53 2
1
2
1
3
0,5
4
0,35
Eg (eV)
 (m)
Energy band gap
• determines among other things the wavelengths
of light that can be absorbed or emitted by the
semiconductors
– Eg GaAs = 1.43 eV corresponds to light wavelengths
in the near infrared (0.87 m)
– Eg GaP = 2.3 eV  green portion of the spectrum
• The wide variety of semiconductors band gap 
tunable wavelength electronic devices
– broad range of the IR and visible lights LEDs and
lasers
Electron Distribution
• Considering the distribution of electrons at two temperatures:
– Absolute zero - atoms at their lowest energy level.
– Room temperature - valence electrons have absorbed enough
energy to move into the conduction band.
• Atoms with broken covalent bonds (missing an electron) have a hole
present where the electron was. For every electron in the
conduction band, there is a hole in the valence band. They are
called electron-hole pairs (EPHs).
• As more energy is applied to a semiconductor, more electrons will
move into the conduction band and current will flow more easily
through the material.
• Therefore, the resistance of intrinsic semiconductor materials
decreases with increasing temperature.
• This is a negative temperature coefficient.
If the temperature increases, the valence
electrons will gain some thermal energy,
and breaks free from the covalent bond
→ It leaves a positively charged hole.
In order to break from the covalent bond,
a valence electron must gain a minimun
energy Eg: Bandgap energy
At 0°K, each electron is in its lowest
possible energy state, and each
covalent bounding position is filled.
If a small electric field is applied, the
electrons will not move → silicon is an
insulator
Compound Semiconductor: combination of elements
• For elemental/intrinsic semiconductor of Si and Ge: the
filled valence band of 4 + 4 = 8 electrons
• For non-intrinsic semiconductor: the filled valence band
of 8 electrons constructed by combination of elements
of group II-VI and III-V
• the E for the bandgap will differ from the elemental
semiconductors
• the bandgap will increase as the tendency for the e- to
become more localised in atom increases (a function of
constituent electronegativities)
Impurities
• strongly affects the electronic and optical
properties of semiconductor materials
– used to vary conductivities from apoor
conductor into a good conductor of electric
current
• may be added in precisely controlled
amounts  doping
Evaluation of both properties needs prior
understanding of the atomic arrangement of atoms
in the materials – various solids
Empirical relationship between energy gap and electronegativities of the
elements
Metallic conductance (Sn)
Elemental semiconductors
(Si, Ge, etc)
Compound semiconductors
(GaAs, CdS, etc.)
Insulators:
-Elemental (diamond, C)
-Compound (NaCl)
Kimia Bahan Semikonduktor - Indriana
Page 28
Impurity and Defect Semiconductor:
Creating band gap through electronegativity effect
P-type
Kimia Bahan Semikonduktor - Indriana
n-type
Page 29
Semiconductor Doping
• Impurities are added to intrinsic semiconductor materials to improve
the electrical properties of the material.
• This process is referred to as doping and the resulting material is
called extrinsic semiconductor.
• There are two major classifications of doping materials.
– Trivalent - aluminum, gallium, boron
– Pentavalent - antimony, arsenic, phosphorous
Kimia Bahan Semikonduktor - Indriana
Page 30
Kimia Bahan Semikonduktor - Indriana
Page 31
Figure 13.29: Effect of doping silicon.
Page 32
Energy band model and
chemical bond model of
dopants in
semiconductors
(a) donation of electrons
from donor level to
conduction band;
(b) acceptance of valence
band electrons by an
acceptor level, and the
resulting creation of holes;
(c) donor and acceptor
atoms in the covalent
bonding model of a Si
crystal.