solid state electronic materials

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29 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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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 (10
23
) 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 cm
3
, there are 10
23

electrons
and ions packed


in a vacuum tube, there are only 10
9
-
10
10

electrons


consequences in solids:


very small interparticle distances ((10
23
)
-
1/3
=2.10
8

cm)


high interparticle forces (interacting particles)


high interparticle collision (about 10
13

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 (lattice of ions)

e
-

scatter in the periodic lattices

interacting particles

berlaku persamaan Schrodinger:

H


= E


solved approximately

Band Diagram


electron standing waves

allowed energies


bands

forbidden energies


band
-
gaps

Kristal fotonik (matriks dan
bola mempunyai sifat
dielektrik yang berbeda)

photons scatter in the periodic
lattices

non
-
interacting particles

berlaku persamaan Maxwell:


solved exactly

Band Diagram


standing waves

allowed frequencies


bands

forbidden
frequencies



band
-
gaps

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 in
allowed and forbidden bands

multielectron

system

(~

10
23
/cm
3
)

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 particles
in a gas (dilute matter)

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 energy

energy level of 1 electron

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

r
0

represents the equilibrium interatomic distance in the crystal


at r
0 :
allowed band consists of some discrete
energy level


Eg.: System co. 10
19

atoms
1e, the width of allowed band
energy at r
0

= 1 eV


if assumed that each e
-

occupies different energy level
and discrete energy level
equidistance


allowed bands
will be separated by 10
-
19

eV

allowed band


The difference of 10
-
19

eV


too small


allowed bands to
be
quasi
-
continue

energy distribution

Bands of atom 3e
-

As 2 atoms get
closer, electron
interaction was
started from
valence electron,
n=3

At r
0

:

3 allowed bands
separated by
forbidden were
formed

pita energi terbolehkan

pita energi terlarang


Splitting energi pada atom
14
Si


4 elektron valensi 3s
2

3p
2

3s
2

: n=3

l
=0

3p
2

: 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

Page
16

Bonding In

Metals:

Lithium

according to

Molecular

Orbital

Theory

Page
17

Sodium According to Band Theory

Conduction band:

empty 3
s

antibonding

Valence band:

full 3
s

bonding

No gap

Page
18

Magnesium

3
s

bonding and antibonding should be full

Page
19

Magnesium

Conduction band:

empty

Valence band:

full

No gap: conductor

Conductor

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

0

1

2

3

4

InSb

Ge

Si

GaAs

CdSe

GaP

CdS

SiC

ZnS

Eg (eV)

7

3

2

5

1

0,5

0,35



(

m)

Infrared

Ultraviolet

Visible

TiO
2

Energy band gap


determines among other things the wavelengths
of light that can be absorbed or emitted by the
semiconductors


E
g

GaAs = 1.43 eV corresponds to light wavelengths
in the near infrared (0.87

m)


E
g

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.


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

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


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

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

Page
28

Kimia 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.)

Page
29

Kimia Bahan Semikonduktor
-

Indriana

Impurity and Defect Semiconductor:

Creating band gap through electronegativity effect

P
-
type

n
-
type

Page
30

Kimia Bahan Semikonduktor
-

Indriana

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

Page
31

Kimia Bahan Semikonduktor
-

Indriana


Page
32

Figure 13.29: Effect of doping silicon.


(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
band

model
and
chemical
bond

model

of
dopants

in
semiconductors