electronics week 2
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2.0 Semiconductor materials
2.1 Elemental and compound semiconductors
---Periodic Table of some elements---
II III IV V VIB C (6) N O
Mg Al Si (14) P S
Zn Ga Ge (32) As Se
Cd In Sn Sb Te
Electron configuration of elemental semiconductors
1. C (diamond): (1s)2/(2s)2(2p)2,
inner orbital / outer orbital2. Si: (1s)2(2s)2(2p)6/(3s)2(3p)2
3. Ge: (1s)2(2s)2(2p)6/(3s)2(3p)6(3d)10/(4s)2(4p)2
Commom character of semiconductor
----outer orbital, (ns)2
(ns)2
------
Atomic number = Number of electrons
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Metal
Semi-
condu
ctor
Electronic
configuration of the
respective elements
Semi-
condu
ctor
Electron Energy of Na
Pauli Exclusion
principle (two
electrons of opposite
spin can occupy each
energy level)
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For optical devices like LED, LD, compound semiconductors
are very useful.
A. Elemental semiconductors CdiamondSi, Ge, Te,SnB. Compound Semi. III-V GaAs, GaPGaN, InSb, InAs, InP, AlP
II-VI ZnS, ZnSe, ZnO, CdS, CdSe, CdTe,
IV-IV SiGe, SiC, (V-VI Bi2Te3)C. Calcogen/Spinelmagnetic Semi.) CdCr2Se4, CdCrS4
D. Rare-earth,magnetic Semi.) EuO, EuS, EuSe
E. Amorphous Semi. Ge, Te, Se, GeTe, As2Te
F. Organic Semi. TCNQ
Compound Semiconductor (Man-made materials)Equivalent electron number (outer orbital) =4
Ga: (1s)2
(2s)2
(2p)6
/(3s)2
(3p)6
(3d)10
/(4s)2
(4p)1
As: (1s)2(2s)2(2p)6/(3s)2(3p)6(3d)10/(4s)2(4p)3
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2.2 Covalent bond and diamond structure
Covalent bond simplest case---Hydrogen molecule, H2,There are only three elements which form a crystal with a covalentbonddiamondCsilicon(Si)germanium(Ge)Covalent bond--one 3s orbital and three 3p (px, py, pz) orbital consist
of a new sp3
hybrid orbital
Electron distribution of sp3hybrid orbital
Tetrahedron structure
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Diamond structure
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Crystal structure of GaAs and GaN
Zinc-blend structure Wurzite structure
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Classification of Material structure
(a) Amorphous---no ordered atomic arrangement
(b) Polycrystallineshort range atomic order usually in small crystallinegrains (10Afew m)
(c) crystallinelong range, ordered, atomic arrangement, repeating unit
cell
All important semiconductor devices are based on crystalline materials (Siespecially) because of ---?
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Silicon ingot and wafer
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2.3 Electron Energy in the crystal
(The difference in the electrical characteristics among Metal,
Semiconductor and Insulator can be explained with the
Problems:
How does the electron energy change from atom to crystal?
New concept of energy band (Quantum theory of soild )
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2.3.1 Energy band by a qualitative model
---in case of electron Energy of Na crystal (Metal)
Energy level of outer electron (3s level)
sprits into N (number of Na atoms) levelswith very narrow distance-----called
Energy Band
While, energy levels of inner electron (2p,
2s and 1s) does not sprit and N levelsoverrapp.
Electron energy of Na atom
To form a crystal
Electron energy of Na crystal
Electronenergy
Electronen
ergy
Atom distance
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2.3.2 Energy band model (general model)
periodic potential
Vacuum level
Allowed
energy band
E, Electron Energy
K, wave number
Calculate the electron energy in the
crystal under periodic condition using
Schrodinger equation
Inside crystal
Outside
crystal
Forbidded
energy
band
A large number of energy levels = Number of atoms
Energy level
of innerorbit
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2.3.4 Band diagram of (a) metal, (b) semiconductor, and (c)
insulator.
Valence band
(completely full)Valence band
(almost full)
Valence band
Completely full)
Conduction bandCompletely empty)Conduction band(almost empty)Conduction band(half full)
Hole
Electron
EG: Energy Gap
Filled
band
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2.3.5 Energy band of Si and GaAs
Indirect semiconductor Direct semiconductor
Energy Band structure of Si Energy Band structure of GaAs
ElectronEnerg
y[eV]
ElectronEnergy[
eV]
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2.3.6 Electron effective mass, mn
Evs. krelation (E: electron energy, k:wave number)
-------parabolic--------- E=(k)2/2mn
Where1
=1
2(2
2)
called electron effective mass (the second derivative of E with respect to k)
For GaAs narrow conduction band, mn = 0.07m0, (m0:electron rest mass)
whereas for Si with a wider conduction band, mn = 0.19m0.
** Electron effective mass depends on crystal direction If we introduce the electron effective mass, electrons in the crystal under
electric field behave like as a single particle with effective mass.
(2.12)
(2.13)
(2.14)
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2.4 Extrinsic Semiconductors, n-type and p-type
Donor concentration :Nd[cm-3]
Electron concentration: n
Intrinsic carrier concentration: ni
n=Nd
p=ni2/Nd
(2.23)
(2.24)
Excess electron
submitted from
phosphorus atom
Positively ionized
phosphorus
atom
Conductionband
Valence
band
2.4.1 Donors
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2.4.2 acceptors
Acceptor concentration: Na[cm-3]
Hole concentration: p
p=Na
n=ni2/Na
(at room temperatures)
(2.25)
(2.26)
Negatively
ionized
boron atom
Breaking Si-Si bond, an
electron is emitted and it is
captured by boron atom,
completing covalent bond
An
missing
electron
leaves a
hole
hole
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2.4.3 intrinsic carrier concentration i
Ge: 2.40x1013cm -3at 300K
Si: 1.45x1010cm -3at 300K
GaAs: 1.79x106cm -3at 300K
Constancy of p product
p=ni2
ni={NcNv}1/2exp(-EG/2kT)
GaAs
Si
1.451010
1.79106
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
150
0100
0500 200 100 27 0 -50
T()
1000/T(K-1)
0.5106
107
108
10910
10
1011
1012
1013
1014
1015
1016
1017
10181019
ni
(cm-3)
(2.21)
(2.22)
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2.4.4 Temperature dependence of electron concentration
At high temperatures, for n-type semiconductors,
neutrality: n=p + Nd
np product constancy: np=ni2
Absolute Temperature [K]
At low temperatures
(
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Electric Field, Ex
In no electric field, free electrons and holes move through the crystal dueto random thermal motion ------ Thermal velocity : vth=10
7
cm/s
When the electric field, Exis applied, carriers move very slowly as compared
with thermal velocity. This situation seems to drift. Its velocity is called drift
velocity.
2.5 Carrier Transport in the electric field2.5.1 mobility
No Electric Field
Electron
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Electroncan be regarded as particle using effective mass. Ex: Electric field in x direction,
Vx: velocity of electron, mn: effective mass of electron
mn =qEx.
Then, vx=vxo (vxo: initial velocity of electron at t=0)
Above equation indicates the increase of electron velocity with time. However,real situation in the movement of many electrons differs. Electrons arescattered and collide with host atoms (Si) or other electrons. Average timebetween collision is called average relaxation time .
dt
dvx
n
x
m
tqE
This average velocity called drift velocity vd .
The proportional factor n is called mobility.
vd=n Ex, where n=nm
q
(2.30)
(2.31)
(2.32) (2.33) (2.34)
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Si GaAs
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2.5.2 Drift Current, Conductivity, and Ohms law
Electron drift curent Jnx=qnvx=qnnEx
Hole drift current Jpx=qpvx=qppEx
Total drift current J= Jnx +Jpx ,
=q(nn+ pp) Ex ,
where conductivity =q(nn+ pp)
Then, J= Ex, called Ohms law
In n-type semiconductor, n>>p, then =qnn
In p-type semiconductor, p>>n, then =qpp
Resistivity =1/
(2.35)
(2.36)
(2.37)
(2.38)
(2.39)
(2.40)
(2.41)
(2.42)
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2.5.3 Diffusion current----important in pn junction---
Flux F is proportional to the concentration gradient (dc/dx).
This is called Ficksfirst law.
F=D D: diffusion coefficient
c: concentration, x: distance
In semiconductor, diffusion current is generated due to the non-uniform distribution of carrier concentration .
Electron diffusion currentJdn=(q) (Dn )=q Dn
Hole diffusion currentJdp=(q) (Dp ) =q Dpdx
dn
dx
dn
dx
dpdx
dp
dx
dc(2.43)
(2.44)
(2.45)
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Total current
Electron current
Hole current
Total current J =Jn+Jp
Relationship between Mobility (Drift) and Diffusivity (Diffusion)
Einsteins Relation
(2.46)
(2.47)
(2.48)
(2.49)
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2.7 Carrier generation and recombination
In thermal equilibrium, electron-hole pairs are always generated and
recombine. In net, carrier concentrations are maintained at certain values
at temperatures.Consider that light is irradiated on a p-type semiconductor substrate
uniformly. We investigate the generation and recombination of the
minority carrier (here, electron) concentration.
During the irradiation of light, excess electron-hole pairs are generated.
GL: generation rate of electron-hole pairs: time constant for excess carrier to return to the thermal equilibrium
Time variation of electron concentration (minority carrier) in p-type
semiconductor is given by
At steady state(t
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If light is off (GL=0) at t=0, electron concentration returns to the thermal
concentration n0with time constant .
time
light
semiconductor
X: distance
(2.53)
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Summary of semiconductor materials--1
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Summary of semiconductor materials--2
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