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Engineering Sciences
Sinai University Faculty of Engineering Science
Department of Basic sciences
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
4/7/2015
1
Course name: Electrical materials
Code: ELE163
Text references
1- Principles of Electronic Materials and Devices, 3rd edition
2- Kittel, Introduction to Solid State Physics
3-College Physics , Serway, 7th edition
4-Lecture notes (power points)
5- Internet sites
Prepared by
Pr Ahmed Mohamed El-lawindy
[email protected]
4/7/2015
Faculty site: www.engineering.su.edu.eg
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
2
These PowerPoint color
diagrams can only be used by
instructors if the 3rd Edition
has been adopted for his/her
course. Permission is given to
individuals who have
purchased a copy of the third
edition with CD-ROM
Electronic Materials and
Devices to use these slides in
seminar, symposium and
conference presentations
provided that the book title,
author and © McGraw-Hill are
displayed under each diagram.
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
4.3 Semiconductors, Si, Ge, GaAs
The electronic structure of 14Si
Need explanation
n=3
n=2
n=1
Very close to the nucleus
Full and stable orbits
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (© McGrawHill, 2005)
Fig 4.15
Explanation
(b) When Si is about to bond, the one 3s
orbital and the three 3p orbitals become
perturbed and mixed to form four
hybridized orbitals, hyb, called sp3
orbitals, which are directed toward the
corners of a tetrahedron.
The hyb orbital has a large major lobe
and a small back lobe. Each hyb orbital
takes one of the four valence electrons.
sp3 hybridization
The 3s and 3p energy levels are quite close, and when five Si atoms
approach each other, the interaction results in the four orbitals  (3s), 
(3px),  (3py) and  (3pz) mixing together to form four new hybrid orbitals,
which are directed in tetrahedral directions; that is, each one is aimed as
far away from the others as possible.
Other
examples:
From Principles
of Electronic Ge, Silane- SiH4, methane-CH4, InP, GaAS
Materials and Devices, Third
Edition, S.O. Kasap (© McGrawHill, 2005)
Fig 4.16
Si- Solid
(a) Formation of energy bands in the Si crystal first involves hybridization of 3s and 3p orbitals to four
o
identical hyb orbitals which make 109.5 with each other as shown in (b). (c) hyb orbitals on two
neighboring Si atoms can overlap to form B or A. The first is a bonding orbital (full) and the second is an
antibonding orbital (empty). In the crystal yB overlap to give the valence band (full) and A overlap to give
From Principlesband
of Electronic
the conduction
(empty).
Materials and Devices, Third
Edition, S.O. Kasap (© McGrawHill, 2005)
Fig 4.17
Energy band diagram of a semiconductor. CB is the conduction band and VB is the valence
band. At T =0 0K, the VB is full with all the valence electrons.
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Fig 4.18
4.4 Electron Effective mass
(a) An external force Fext applied to an
Electron in a vacuum results in an
acceleration avac = Fext / me.
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (© McGrawHill, 2005)
(b) An external force Fext applied to an
Electron in a crystal results in an acceleration
acryst = Fcryst / me*
Fig 4.19
Ch 5: Objectives
• 1-Develop a basic understanding of the properties of intrinsic
and extrinsic semiconductors
• 2- Understand the conduction mechanisms for both p- and ntype semiconductors
• 3- Illustration of the importance of Fermi level
• 4- Calculate the concentration of donors and acceptors via
solved examples and problems
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Chapter 5: Semiconductors
• Intrinsic semiconductors
The crystal consists of Si atoms perfectly bonded to each other in the diamond
structure,
number of free electrons equals the number of free holes
• Extrinsic Semiconductors
Contains impurities or crystal defects, such as dislocations and grain
boundaries
• number of free electrons not equals the number of free holes,
• extra acceptors, p-type or donors, n-type semiconductors+ .
• At T> T0
• Si vibrates in its lattice, with an average energy, 3kT, not enough to break SiSi bond.
• In some region, this energy is sufficient to break a bond, creating an electron
and a hole in its bond site.
• Free electrons and holes are created, wonder in the lattice, so that both
From
Principles of Electronic
contribute
to electrical conduction.
Materials and Devices, Third
Edition, S.O. Kasap (©
5.1 Intrinsic semiconductor
5.1.1 Silicon crystal and energy band diagram
The width of
conduction band
is called electron
affinity,
(d)
(a) A simplified two-dimensional illustration of a Si atom with four hybrid orbitals
hyb. Each orbital has one electron.
(b) A simplified two-dimensional view of a region of the Si crystal showing
covalent bonds.
(c) The energy band diagram at absolute zero of temperature.
(d) A two-dimensional pictorial view of the Si crystal showing covalent bonds as
two lines where each line is a valence electron.
Fig 5.1
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
5.1.2 Electrons and holes
(a) A photon with an energy greater than Eg can
excite an electron from the VB to the CB.
(b) When a photon breaks a Si-Si bond, a free
electron and a hole in the Si-Si bond is
created.
Fig 5.3
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Thermal vibrations of atoms
can break bonds and
thereby
create electron-hole pairs.
Explanation
A pictorial illustration of a hole in the valence band wandering around the crystal due to
the tunneling of electrons from neighboring bonds.
Fig 5.5
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
5.1.3 Conduction in semiconductors
Total energy, E
In case of no electric field, Ex , E=KE + PE
In case of electric Field, E=KE+PE+PE(x)
(dV/dx)=-Ex, V(x)=-Ax+B, PE(x)= -eV(x)
So as x increases, PE(x) increases
When an electric field is applied, electrons in the CB and holes in the VB can drift and contribute to the conductivity.
(a) A simplified illustration of drift in Ex.
(b) Applied field bends the energy bands since the electrostatic PE of the electron is –eV(x) and V(x) decreases in the
direction of Ex, whereas PE increases.
Fig 5.6
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Electron and Hole Drift Velocities
Current density: J=envde + epvdh
vde = eEx and vdh = hEx
vde = drift velocity of the electrons, e = electron drift mobility, Ex = applied
electric field, vdh = drift velocity of the holes, h = hole drift mobility
Conductivity of a Semiconductor
e 
e e
*
me
h 
e h
*
mh
 = ene + eph
 = conductivity, e = electronic charge, n = electron concentration in the CB, e =
electron
drift
mobility, p = hole concentration in the VB, h = hole drift mobility
From Principles
of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
5.1.4 Electron and hole concentration
(a) Energy band diagram.
(b) Density of states (number of states per unit energy per unit volume).
(c) Fermi-Dirac probability function (probability of occupancy of a state).
(d) The product of g(E) and f (E) is the energy density of electrons in the CB (number of electrons per unit energy
per unit volume). The area under nE(E) versus E is the electron concentration.
Fig 5.7
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Electron Concentration in CB
 ( E c  E F ) 
n  N c exp 



kT
5.6
n = electron concentration in the CB, Nc = effective density of states at the CB
edge, Ec = conduction band edge, EF = Fermi energy, k = Boltzmann constant, T =
temperature
Effective Density of States at CB Edge
 2  m * kT
e
N c  2 

2
 h
3 / 2



5.7
Nc = effective density of states at the CB edge, me* = effective mass of the electron
in the CB, k = Boltzmann constant, T = temperature, h = Planck’s constant
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Hole Concentration in VB
 ( E F  E v ) 
p  N v exp 



kT
5.8
p = hole concentration in the VB, Nv = effective density of states at the VB edge, EF
= Fermi energy, Ev = valence band edge, k = Boltzmann constant, T = temperature
Effective Density of States at VB Edge
 2  m kT
h
N v  2 

2
 h
*
3/2




5.9
Nv = effective density of states at the VB edge, mh* = effective mass of a hole in the
VB, k = Boltzmann constant, T = temperature, h = Planck’s constant
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Mass Action Law
 Eg 

np  n  N c N v exp  

 kT 
2
i
5.11
ni = intrinsic concentration
The np product is a constant, ni2, that depends on the material properties Nc, Nv,
Eg, and the temperature. If somehow n is increased (e.g. by doping), p must
decrease to keep np constant.
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Fermi Energy in Intrinsic Semiconductors
E Fi
 Nc 

 E v  E g  kT ln 

2
2
 Nv 
1
1
5.12
EFi = Fermi energy in the intrinsic semiconductor, Ev = valence band edge, Eg = Ec - Ev
is the bandgap energy, k = Boltzmann constant, T = temperature, Nc = effective
density of states at the CB edge, Nv = effective density of states at the VB edge
E Fi
* 

1
3
me

 E v  E g  kT ln 
 * 
2
4
 m h 
me* = electron effective mass (CB), mh* = hole effective mass (VB)
From equations 5.6, 5.7, 5.8, 5.9, 5.10, 5.11
FromProof
Principles of Electronic
equations 5.12 and 5.13
Materials and Devices, Third
Edition, S.O. Kasap (©
5.13
Since ni2=np=constant
decreases
means that if n increases p
If intrinsic semiconductor, n=p
Nc=Nv, or m*e=m*h
Then EFi=Ev + ½ Eg
If n-type semiconductor,
Then Ec-EF<EF-Ev
n>p
If p-type semiconductor,
Then Ec-EF<EF-Ev
p>n
EF in the middle
Then EF is closer to Ec than Ev
Then EF is closer to Ev than Ec
Energy band diagrams for
(a) Intrinsic,
(b) n-type, and
(d) p-type semiconductors.
In all cases, np = ni2
Fig 5.8
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Average Electron Energy in CB
E
CB
 Ec 
3
kT
2
E CB= average energy of electrons in the CB, Ec = conduction band edge, k = Boltzmann
constant, T = temperature
(3/2)kT is also the average kinetic energy per atom in a monatomic gas (kinetic molecular
theory) in which the gas atoms move around freely and randomly inside a container.
The electron in the CB behaves as if it were “free” with a mean kinetic energy that is
(3/2)kT and an effective mass me*.
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Important notes for examination
Don’t memorize equations but know the
physical meaning for each physical parameter
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
5.2 Extrinsic semiconductors
1
B
2p
5
2 3p2
Si
3s
14
23p3
p
3s
15
24p1
Ga
4s
31
24p2
Ge
4s
32
24p3
As
4s
33
1As: 106Si
Arsenic-doped Si crystal.
The four valence electrons of As allow it to bond just like Si, but the fifth electron is left
orbiting the As site. The energy required to release the free fifth electron into the CB is
very small.
Fig 5.9
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Binding
energy
for an electron
*
Eb 
Si
notice
mee
that
around
As

4
8 h
2
o
in
2
 2 . 18  10
Si
 18
J  13.6
environmen t ,
r,
eV,
for
and
4
8  h
2
o
Eb   E I 
me
2
r
2
 0 . 032
eV
3kT  0.07 eV
Energy band diagram for an n-type Si doped with 1 ppm As. There are donor
energy levels just below Ec around As+ sites.
Fig 5.10
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
n 1
m  me
*
n-Type Conductivity
 ni
  eN d  e  e 
N
 d
2

  h  eN d  e


 = electrical conductivity
e = electronic charge
Nd = donor atom concentration in the crystal
e = electron drift mobility, ni = intrinsic concentration,
h = hole drift mobility
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
5.2.2 p-type doping
22p1
B
2s
5
2 3p2
Si
3s
14
23p3
p
3s
15
24p1
Ga
4s
31
24p2
Ge
4s
32
24p3
As
4s
33
Boron-doped Si crystal.
B has only three valence electrons. When it substitutes for a Si atom, one of its bonds has an
electron missing and therefore a hole, as shown in (a). The hole orbits around the B- site by
the tunneling of electrons from neighboring bonds, as shown in (b). Eventually, thermally
vibrating Si atoms provide enough energy to free the hole from the B- site into the VB, as
shown.
Fig 5.11
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
  eN a  h
Energy band diagram for a p-type Si doped with 1 ppm B.
There are acceptor energy levels Ea just above Ev around B- sites. These acceptor levels
accept electrons from the VB and therefore create holes in the VB.
Fig 5.12
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Compensation Doping
If both donors or acceptors are doped to an intrinsic semiconductor
More donors than acceptors
n  Nd  Na
More acceptors than donors
p  Na  Nd
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
N d  N a  n i
p
n
2
i
n

2
i
Nd  Na
n
N a  N d  n i
n
n
2
i
p

n
2
i
Na  Nd
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