ln2 kimia bahan semikonduktor 2011-2 electronic structure

7/27/2019 LN2 Kimia Bahan Semikonduktor 2011-2 Electronic Structure

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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


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Band Theory of Solids


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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.


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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.


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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


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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


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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


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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


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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)


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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


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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


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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


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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


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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


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Bonding In

Metals:

Lithium

according toMolecular

Orbital

Theory


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Sodium According to Band Theory

Conduction band:

empty 3s antibonding

Valence band:

full 3s bonding

No gap


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Magnesium

3s bonding and antibonding should be full


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Magnesium

Conduction band:

empty

Valence band:

full

No gap: conductor

Conductor


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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


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Band structure and conductivity


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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


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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


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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


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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


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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


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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


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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.)


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Impurity and Defect Semiconductor:

Creating band gap through electronegativity effect

P-typen-type

Semiconductor Doping


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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


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Figure 13.29: Effect of doping silicon.


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(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

ln2 kimia bahan semikonduktor 2011-2 electronic structure

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