-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
1/34
solid state electronic materialselectronic 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
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
2/34
Band Theory of Solids
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
3/34
Energy Levels
Valence bandelectrons are thefurthest from thenucleus and havehigher energy levelsthan electrons in
lower orbits. The region beyond
the valence band iscalled theconduction band.
Electrons in theconduction band areeasily made to befree electrons.
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
4/34
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
5/34
Semiconductor Crystals Tetravalent atoms such as silicon, gallium
arsenide, and germanium bond together to form a
crystalor crystal lattice. Because of the crystalline structure of
semiconductor materials, valence electrons aresharedbetween atoms.
This sharing of valence electrons is called covalent
bonding. Covalent bonding makes it more difficultfor materials to move their electrons into theconduction band.
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
6/34
2 major binding forces:
Binding forces coming from electron-pairbonds (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 andhalide insulators, and compoundsemiconductors
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
7/34
the motion of electrons (1023) in the solidsdetermines the electrical characteristics ofthe solid state electronic devices and
integrated circuit in vacuum, the motion of a few separately
objects Newton Law; F = ma classicallaw of mechanics
for solidsthere is particle densityclassical law must be extended
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
8/34
in a so l id high pack ing densi ty 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 condensedmatter
current or wave generated in solids resulted from averaged motion of electrons
statistical mechanics
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
9/34
Kristal (lattice of ions)
e- scatter in the periodic lattices
interacting particlesberlaku persamaan Schrodinger:H = E solved approximately
Band Diagram electron standing wavesallowed energies bands
forbidden energies band-gaps
Kristal fotonik (matriks danbola mempunyai sifatdielektrik yang berbeda)
photons scatter in the periodiclattices
non-interacting particlesberlaku persamaan Maxwell:
solved exactly
Band Diagram standing waves
allowed frequencies bandsforbidden frequencies band-gaps
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
10/34
1 e- atom quantized energy
uncertainties with small distances
large number of particles
Extrapolation on 1 crystal
allowed bands and forbidden bands
Wave mechanics applied (Schrodinger eqn.)
and statistic mechanics
Electronic energy levels are arranged inallowed and forbidden bands
multielectron system (~ 1023/cm3)
discrete energy
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 particlesin a gas (dilute matter)
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
11/34
Math solution to quantum
mechanic eqns model 1
electron
energy level of 1 electron
Applied :
Planck eqn. (EMR energy and
quantized particle wave)E = h
de Broglie eqn. (EMR
momentum and particle wave
~ 1/)
p = h/
ELECTRONIC SOLIDS
1 ELECTRON
band energyenergy level of 1 electron
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
12/34
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
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
13/34
r0 represents the equilibrium interatomic distance in the crystal
at r0 : allowed band consists of some discrete
energy level
Eg.: System co. 1019
atoms1e, the width of allowed band
energy at r0 = 1 eV
if assumed that each e-
occupies different energy level
and discrete energy levelequidistance allowed bands
will be separated by 10-19 eV
allowed band
The difference of 10-19 eV too small allowed bands to
be quasi-continueenergy distribution
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
14/34
Bands of atom 3e-
As 2 atoms get
closer, electron
interaction wasstarted from
valence electron,
n=3
At r0 :
3 allowed bands
separated by
forbidden were
formed
pita
energiterbole
hkan
pita
energiterlaran
g
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
15/34
Splitting energi pada atom 14Si
4 elektron valensi 3s2 3p2
3s2 : n=3 l=0
3p2 : n=3 l=1
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
Eg represents the width of forbidden band =
bandgap energy
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
16/34Pa e 16
Bonding In
Metals:
Lithium
according toMolecular
Orbital
Theory
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
17/34Pa e 17
Sodium According to Band Theory
Conduction band:
empty 3s antibonding
Valence band:
full 3s bonding
No gap
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
18/34Pa e 18
Magnesium
3s bonding and antibonding should be full
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
19/34Pa e 19
Magnesium
Conduction band:
empty
Valence band:
full
No gap: conductor
Conductor
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
20/34
Classification of solids into three types,
according to their band structure
insulators: gap = forbidden regionbetween highest filled band (valenceband) and lowest empty or partly filledband (conduction band) is very wide,about 3 to 6 eV;
semiconductors: gap is small - about0.1 to 1 eV;
conductors: valence band only
partially filled, or (if it is filled), thenext allowed empty band overlaps withit
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
21/34
Band structure and conductivity
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
22/34
Band gaps of some common
semiconductors relative to the optical
spectrum
0 1 2 3 4
InSb Ge Si
GaAs
CdSe
GaP
CdS SiC ZnS
Eg (eV)
7 3 25 1 0,5 0,35
(m)
Infrared UltravioletVisible
TiO2
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
23/34
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 wavelengthsin 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
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
24/34
Electron Distribution
Considering the distribution of electrons at two temperatures:
Absolute zero - atoms at their lowest energy level.
Room temperature - valence electrons have absorbed enoughenergy to move into the conduction band.
Atoms with broken covalent bonds (missing an electron) have a holepresent where the electron was. For every electron in theconduction band, there is a hole in the valence band. They arecalled electron-hole pairs (EPHs).
As more energy is applied to a semiconductor, more electrons willmove 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
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
25/34
At 0K, 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 aninsulator
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
C d S i d t bi ti f l t
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
26/34
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)
Compound Semiconductor: combination of elements
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
27/34
Impurities
strongly affects the electronic and optical
properties of semiconductor materials
used to vary conductivities from apoor
conductor into a good conductor of electriccurrent
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 re
lationship between energy gap and electronegativities of the
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
28/34Pa e 28Kimia Bahan Semikonduktor - Indriana
Empirical relationship between energy gap and electronegativities of the
elements
Metallic conductance (Sn)
Elemental semiconductors
(Si, Ge, etc)
Insulators:
-Elemental (diamond, C)
-Compound (NaCl)
Compound semiconductors
(GaAs, CdS, etc.)
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
29/34
Pa e 29Kimia Bahan Semikonduktor - Indriana
Impurity and Defect Semiconductor:
Creating band gap through electronegativity effect
P-typen-type
Semiconductor Doping
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
30/34
Pa e 30Kimia Bahan Semikonduktor - Indriana
Semiconductor Doping
Impurities are added to intrinsic semiconductor materials to improvethe electrical properties of the material.
This process is referred to as dopingand the resulting material iscalled extrinsic semiconductor.
There are two major classifications of doping materials.
Trivalent - aluminum, gallium, boron
Pentavalent - antimony, arsenic, phosphorous
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
31/34
Pa e 31Kimia Bahan Semikonduktor - Indriana
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
32/34
Pa e 32
Figure 13.29: Effect of doping silicon.
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
33/34
-
7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure
34/34
(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.
Energy bandmodel and
chemical bondmodel of
dopants in
semiconductors