1. SOLIDS AND SEMICONDUCTOR
DEVICES
Electrical conductivity
Energy bands in solids
Band structure and conductivity
Semiconductors
Intrinsic semiconductors
Doped semiconductors
n-type materials
p-type materials
Diodes and transistors
p-n junction
depletion region
forward biased p-n junction
reverse biased p-n junction diode

3. ELECTRICAL CONDUCTIVITY

R = ρL/A, R = resistance, L = length, A = cross section area; resistivity at 20 o
C in order of conductivity:
superconductors, conductors, semiconductors, insulators

superconductors: certain materials have zero resistivity at very low
temperature.

conductors: material capable of carrying electric current, i.e. material
which has “mobile charge carriers” (e.g. electrons, ions,..) e.g. metals,
liquids with ions (water, molten ionic compounds), plasma.

semiconductors: materials with conductivity between that of conductors
and insulators; e.g. germanium Ge, silicon Si, GaAs, GaP, InP.

insulators: materials with no or very few free charge carriers; e.g. quartz,
most covalent and ionic solids, plastics

4. ENERGY BANDS IN SOLIDS:
In solid materials, electron energy levels form bands of
allowed energies, separated by forbidden bands
valence band = outermost (highest) band filled with
electrons (“filled” = all states occupied)
conduction band = next highest band to valence band
(empty or partly filled)
“gap” = energy difference between valence and conduction
bands, = width of the forbidden band
Note:
electrons in a completely filled band cannot move, since
all states occupied (Pauli principle); only way to move
would be to “jump” into next higher band - needs energy;
electrons in partly filled band can move, since there are

5. Classification of solids into three
according to their band structure:
types,
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

6. Band structure and conductivity

7. What Is a Semiconductor?
•Many materials, such as most metals, allow electrical current
to flow through them
•These are known as conductors
•Materials that do not allow electrical current to flow through
them are called insulators
•Pure silicon, the base material of most transistors, is
considered a semiconductor because its conductivity can be
modulated by the introduction of impurities

8. Semiconductors


A material whose properties are such that it is not quite a
conductor, not quite an insulator
Some common semiconductors
 elemental
• Si - Silicon (most common)
• Ge - Germanium

compound
• GaAs - Gallium arsenide
• GaP - Gallium phosphide
• AlAs - Aluminum arsenide
• AlP - Aluminum phosphide
• InP - Indium Phosphide

9. Crystalline Solids

In a crystalline solid, the periodic
arrangement of atoms is repeated over the
entire crystal

Silicon crystal has a diamond lattice

10. Crystalline Nature of Silicon
 Silicon
as utilized in integrated circuits is
crystalline in nature
 As
with all crystalline material, silicon
consists of a repeating basic unit structure
called a unit cell
 For
silicon, the unit cell consists of an atom
surrounded by four equidistant nearest
neighbors which lie at the corners of the
tetrahedron

11. What’s so special about Silicon?
Cheap and abundant
Amazing mechanical,
chemical and electronic
properties
The material is very
well-known to mankind
SiO2: sand, glass
Si is column IV of the periodic table
Similar to the carbon (C) and the
germanium (Ge)
Has 3s² and 3p² valence electrons

12. Semiconductor Crystalline Structure

Silicon atoms have 4 electrons
in outer shell
 inner
electrons are very
closely bound to atom

These electrons are shared
with neighbor atoms on both
sides to “fill” the shell
resulting structure is very
stable
 electrons are fairly tightly
bound no “loose” electrons
 at
room temperature, if
battery applied, very little
electric current flows


13. Conduction in Crystal Lattices

Semiconductors (Si and Ge) have 4 electrons in their
outer shell
 2 in the s subshell
 2 in the p subshell

As the distance between atoms decreases the discrete
subshells spread out into bands

As the distance decreases further, the bands overlap and
then separate
 the subshell model doesn’t hold anymore, and the
electrons can be thought of as being part of the crystal,
not part of the atom
 4 possible electrons in the lower band ( valence band)
 4 possible electrons in the upper band ( conduction
band)

14. Energy Bands in
Semiconductors

The space
between the
bands is the
energy gap,
or forbidden
band

15. Nature of Intrinsic Silicon
 Silicon
that is free of doping impurities is
called intrinsic
 Silicon
has a valence of 4 and forms
covalent
bonds
with
neighboring silicon atoms
four
other

16. Insulators, Semiconductors, and Metals
The separation of the valence and conduction bands
determines the electrical properties of the material
 Insulators have a large energy gap
 electrons can’t jump from valence to conduction bands

no current flows
 Conductors (metals) have a very small (or nonexistent) energy
gap
 electrons easily jump to conduction bands due to thermal
excitation
 current flows easily
 Semiconductors have a moderate energy gap
 only a few electrons can jump to the conduction band
• leaving “holes”
 only a little current can flow


17. Insulators, Semiconductors, and
Metals (continued)
Conduction
Band
Valence
Band
Conductor
Semiconductor
Insulator

18. Hole - Electron Pairs


Sometimes thermal energy is enough to cause an electron to
jump from the valence band to the conduction band
 produces a hole - electron pair
Electrons also “fall” back out of the conduction band into the
valence band, combining with a hole
pair elimination
hole
pair creation
electron

19. Improving Conduction by Doping
 To
make semiconductors better conductors,
add impurities (dopants) to contribute extra
electrons or extra holes

elements with 5 outer electrons contribute an
extra electron to the lattice (donor dopant)

elements with 3 outer electrons accept an
electron from the silicon (acceptor dopant)

20. Improving Conduction by Doping (cont.)
Phosphorus and arsenic are
donor dopants
 if phosphorus is introduced
into the silicon lattice,
there is an extra electron
“free” to move around and
contribute
to
electric
current, very loosely bound
to atom and can easily
jump to conduction band
 produces n type silicon
 sometimes use + symbol
to indicate heavier doping,
so n+ silicon
 phosphorus
becomes
positive ion after giving up
electron

21. Improving Conduction by Doping (cont.)

Boron has 3 electrons
in its outer shell, so it
contributes a hole if it
displaces a silicon
atom

boron is an acceptor
dopant


yields p type silicon
Boronbecomes negative
ion after accepting an
electron

22. Diffusion of Dopants




It is also possible to
introduce dopants into
silicon by heating them so
they diffuse into the silicon

no new silicon is added
 high
heat
causes
diffusion
Can
be
done
with
constant concentration in
atmosphere
 close
to straight line
concentration gradient
Or with constant number
of atoms per unit area
 predeposition
 bell-shaped gradient
Diffusion
causes
spreading of doped areas
top
side

23. Hole and Electron Concentrations

To produce reasonable levels of conduction doesn’t require
much doping



silicon has about 5 x 1022 atoms/cm3
typical dopant levels are about 1015 atoms/cm3
In undoped (intrinsic) silicon, the number of holes and number
of free electrons is equal, and their product equals a constant

actually, ni increases with increasing temperature
np = ni2

This equation holds true for doped silicon as well, so increasing
the number of free electrons decreases the number of holes

24. INTRINSIC (PURE) SILICON
At 0 Kelvin Silicon density
is 5x10²³ particles/cm³
Silicon has 4 valence
electrons, it covalently bonds
with four adjacent atoms in
the crystal lattice
Higher temperatures
create free charge carriers.
A “hole” is created in the
absence of an electron.
At 23ºC there are 10¹º
particles/cm³ of free
carriers

25. DOPING
There are two types of doping
N-type and P-type.
The N in N-type stands for
negative.
A column V ion is inserted.
The extra valence electron is free
to move about the lattice
The P in P-type stands for
positive.
A column III ion is inserted.
Electrons from the surrounding
Silicon move to fill the “hole.”

26. Energy-band Diagram






A very important concept in the study of
semiconductors is the energy-band diagram
It is used to represent the range of energy a
valence electron can have
For semiconductors the electrons can have any
one value of a continuous range of energy levels
while they occupy the valence shell of the atom
That band of energy levels is called the valence
band
Within the same valence shell, but at a slightly
higher energy level, is yet another band of
continuously variable, allowed energy levels
This is the conduction band

27. Band Gap
 Between
the valence and the conduction
band is a range of energy levels where there
are no allowed states for an electron
 This is the band gap E G
 In silicon at room temperature [in electron
.
volts]: E G = 11 eV
 Electron volt is an atomic measurement
unit, 1 eV energy is necessary to decrease of
the potential of the electron with 1 V.
1eV = 1.602 × 10 −19 joule

28. Impurities

Silicon crystal in pure form is
good insulator - all electrons
are bonded to silicon atom

Replacement of Si atoms can
alter electrical properties of
semiconductor

Group number - indicates
number of electrons in
valence level (Si - Group IV)

29. Impurities


Replace Si atom in crystal with Group V atom

substitution of 5 electrons for 4 electrons in outer shell

extra electron not needed for crystal bonding structure
• can move to other areas of semiconductor
• current flows more easily - resistivity decreases
• many extra electrons --> “donor” or n-type material
Replace Si atom with Group III atom
 substitution of 3 electrons for 4 electrons
 extra electron now needed for crystal bonding structure
• “hole” created (missing electron)
• hole can move to other areas of semiconductor if
electrons continually fill holes
• again, current flows more easily - resistivity decreases
• electrons needed --> “acceptor” or p-type material

30. 
Intrinsic silicon:

DOPED SEMICONDUCTORS:

31. n-type material
Donor (n-type) impurities:
Dopant with 5 valence electrons (e.g. P, As, Sb)
4 electrons used for covalent bonds with surrounding Si
atoms, one electron “left over”; left over electron is only
loosely bound⇒ only small amount of energy needed
to lift it into conduction band (0.05 eV in Si)
⇒ “n-type semiconductor”, has conduction electrons, no
holes (apart from the few intrinsic holes)

32. p-type material
Acceptor (p-type) impurities:
dopant with 3 valence electrons (e.g. B, Al, Ga, In) ⇒ only 3 of the
4 covalent bonds filled ⇒ vacancy in the fourth covalent bond ⇒
hole.
“p-type semiconductor”, has mobile holes, very few mobile
electrons (only the intrinsic ones).

33. P-N Junction

Also known as a diode

One of the basics of semiconductor technology -

Created by placing n-type and p-type material in close
contact

Diffusion - mobile charges (holes) in p-type combine
with mobile charges (electrons) in n-type

34. P-N Junction

Region of charges left behind (dopants fixed in crystal lattice)



Group III in p-type (one less proton than Si- negative charge)
Group IV in n-type (one more proton than Si - positive charge)
Region is totally depleted of mobile charges - “depletion
region”

Electric field forms due to fixed charges in the depletion region

Depletion region has high resistance due to lack of mobile charges

36. p-n JUNCTION:
p-n junction = semiconductor in which impurity
changes abruptly from p-type to n-type ;
“diffusion” = movement due to difference in
concentration, from higher to lower concentration;
• in absence of electric field across the junction, holes
“diffuse” towards and across boundary into n-type and
capture electrons;
• electrons diffuse across boundary, fall into holes
(“recombination of majority carriers”); ⇒ formation of a
“depletion region”(= region without free charge carriers)
around the boundary;
• charged ions are left behind (cannot move):



negative ions left on p-side ⇒ net negative charge on p-side of
the junction;
positive ions left on n-side ⇒ net positive charge on n-side of the
junction
⇒ electric field across junction which prevents further diffusion.