Semiconductor Diode - Basic of Electronics Engineering

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Nov 1, 2013 (4 years and 11 days ago)

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CSE 177/EEE 177 : Electronics I

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Semiconductor Diode

Prof. Dr. Md. Nurunnabi

Dean

Faculty of E & T

Eastern University

CSE 177/EEE 177 : Electronics I

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Physical Operation of Diodes


Lecture


1 & 2

CSE 177/EEE 177 : Electronics I

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Basic Semiconductor Concepts


Pn junction:






Semiconductor diode is basically a pn junction.


Pn junction consists of p
-
type semiconductor material
(such as Si) & n
-
type semiconductor material (such as
Si).


In actual practice, both p & n regions are the part of the
same Si crystal by creating regions of different doping (p
& n).

CSE 177/EEE 177 : Electronics I

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Silicon Types

Silicon

Intrinsic Si

(pure Si)

Extrinsic Si

p
-
type (B, Al, etc)

n
-
type (P, N, etc)

CSE 177/EEE 177 : Electronics I

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Intrinsic Silicon


Silicon has 4
valence electrons


Forms covalent
bonds with other
atoms.


At low
temperatures, all
electrons are in a
covalent bond and
thus no electrons
are free to conduct
electricity.

CSE 177/EEE 177 : Electronics I

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Thermal Ionization

Thermal Ionization in Intrinsic
Silicon:


At room temperature, some
electrons break free from
their bonds (free electron)


This process leaves a
positively charged “hole” at
the atom.


Note that the overall
charge of the crystal is
still neutral


Both electrons and holes
are considered to be
“charge”
carriers.


Hole motion is a
movement of charge
just as electron motion.

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Recombination


Recombination


As the free electrons move randomly around the
silicon, some will fill in some of the holes.


This process is called recombination.


Recombination is proportional to the number of free
electrons and holes, which is, in turn, determined by
the ionization rate.


The ionization rate is a strong function of
temperature.


At thermal equilibrium, the recombination rate is equal
to the ionization rate.

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Equilibrium


At equilibrium, the ionization rate is equal to the recombination rate,
and there is a concentration of free electrons and an equal
concentration of holes.


n = p = n
i
; where n
i

= intrinsic concentration

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Summary of Intrinsic Silicon


Summary of Intrinsic Silicon


Intrinsic Silicon is a crystal with four valence
electrons


At room temperature, a number of these
break free (ionize).


Some of these recombine with the holes that
are left behind


The silicon reaches equilibrium when the
recombination rate is the same as the
ionization rate.


CSE 177/EEE 177 : Electronics I

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Current in Crystals


Two mechanisms for motion (current) in
crystals


Diffusion


Random motion of particles (electrons or holes)
due to thermal excitation. Like all other diffusion,
elements move from an area of
higher
concentration to an area of lower
concentration
.


Drift


Movement of electrons and holes in response to
an electric field.

CSE 177/EEE 177 : Electronics I

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Diffusion mechanism


Associated with random motion due to thermal
agitation.


In a Si crystal with uniform concentrations of free
electrons and holes, this random motion does
not result in a net flow of current.


So, if by some mechanism, the concentration of
free electrons is made higher in one part of
piece of Si than in other, then
electrons will
diffuse from the high concentration region to the
low concentration region
. This process gives rise
to a Diffusion current.

CSE 177/EEE 177 : Electronics I

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Diffusion mechanism
-
cont
.


Consider the bar of Si in figure in
which the hole concentration
profile has been created along the
x
-
axis by some unspecified
mechanism.


+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + +

+ + + +

x

0

Slope = dP
/dx

Hole concentration, P

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Diffusion mechanism
-
cont


Hole concentration profile results a hole diffusion current in x
direction, magnitude of current at any point is proportional to
the slope of the curve at that point


J
P

=
-
q D
P

dP/dx

( hole diffusion)

Where J
P

= hole current density ( i.e. current per unit area of the plane


perpendicular to x axis) in A/cm
2


q = magnitude of electron charge = 1.6
×
10
-
19
C


D
P

= Diffusion constant or diffusivity of holes

CSE 177/EEE 177 : Electronics I

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Diffusion mechanism
-
cont

And for current diffusion

J
n

= q D
n

dn/dx

(electron current
diffusion)

Where J
n

= electron current density ( i.e. current per unit area of the plane


perpendicular to x axis) in A/cm
2


q = magnitude of electron charge = 1.6
×
10
-
19
C


D
n

= Diffusion constant or diffusivity of electrons


For holes and electrons diffusing in intrinsic Si, typical values for diffusion


constants



D
p

= 12 cm
2
/s and D
n

= 34 cm
2
/s

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Drift


Assume that an electric field is applied across a
piece of silicon.


Free electrons and holes are accelerated by the
electric field and acquire a velocity component
(superimposed on the velocity of their thermal
motion) called
drift velocity
.


If the field strength is denoted E (in V/cm), the
positively charged holes will drift in the direction
of E and acquire a velocity given by:

CSE 177/EEE 177 : Electronics I

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Mobility


Mobility

CSE 177/EEE 177 : Electronics I

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Drift Current Density


Drift Current Density

CSE 177/EEE 177 : Electronics I

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Summary of Current


Diffusion Current


Based on concentration differences, particles
move from higher to lower concentrations


Drift Current


In the presence of an electric field, free
electrons move opposite the field, holes move
in the direction of the field.

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Question: Consider a Si crystal having a hole density P and a
free electron density n. An electric field E is applied to the
crystal. Find the expression of resistivity for that material.

Solution:

Electric field = E

Hole density = P

Electron density = n

Holes will drift in same direction as E and drift velocity for holes =
μ
P

E

Thus, for positive charge density ( qP C/cm
3
) moving in x
direction with velocity (
μ
P

E), in 1s amount of charge flow
across a plane A perpendicular to x
-
axis is I
P

= qP
μ
P
EA (
current flows for holes)


so, J
P
-
drift

= I
P
/A = qP
μ
P
E
----------

(1)


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For electrons, negative charge density (
-
qn) moving
in

x direction with drift velocity (
-
μ
n
E), so I
n

=
qn
μ
n
EA


and J
n
-
drift

= qn
μ
n
E
---------------

(2)

So, total drift current density, J
drift

= J
p
-
drift

+ J
n
-
drift







= q(p
μ
p
+ n
μ
n
)E

Using Ohm’s law, E = IR = I(
ρ
l/A)

For unit length (l=1cm), E = I
ρ
/A = J
drift
ρ


so,
ρ

=E/J
drift






ρ

= 1 /q(p
μ
p
+ n
μ
n
)

ρ

= 1 /q(p
μ
p

+ n
μ
n

)

CSE 177/EEE 177 : Electronics I

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Einstein Relationship


Relation between carrier diffusivity and mobility is
known as Einstein relationship. The relation is as
follow



Where V
T

= thermal voltage = 25 mV at room
temperature for intrinsic Si

CSE 177/EEE 177 : Electronics I

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Doping Semiconductors


Doped Semiconductors


By adding an impurity, one kind of carrier
predominates


Doped silicon where the majority of charge
carriers are the
negatively

charged electrons
is called
n
-
type


Doped silicon where the majority of charge
carriers are the
positively

charged holes is
called
p
-
type

CSE 177/EEE 177 : Electronics I

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N
-
type


n
-
type


Doped with a

pentavalent

element such as
phosphorus
.


Five valence electrons


four form covalent bonds


one becomes a free
electron


This is called a
donor
.


No holes are created by this
doping, thus there are free
electrons without associated
holes


There are still holes created
due to thermal excitation.
These are called
minority
carriers
.

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The concentration of free electrons in n
-
type silicon, or
majority carriers

is
determined almost completely by the
dopant rather than thermal properties.


the concentration of majority carriers is
generally independent of temperature.


The overall charge is still neutral due to
the
bound charge

associated with the
nucleus of the penta
-
valent atom


CSE 177/EEE 177 : Electronics I

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N type (contd.)


If N
D

= concentration of donor atoms


n
no

= concentration of free electrons in N
-
type Si in
thermal equlibrium


then, n
n0

= N
D

So, product of hole & electron concentration remains
constant i.e,

n
no

×

p
n0

= n
i
2

Or, p
n0

= n
i
2
/ N
D

Here, n
i

is a function of temperature


p
n0

is a function of temperature


n
n0

is independent of temperature.

CSE 177/EEE 177 : Electronics I

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P
-
type


p
-
type


Doped with a
trivalent

element
such as
boron
.


Three valence electrons


three form covalent
bonds


other bond has a hole.


This is called an
acceptor
.


No electrons are freed by this
doping, thus there are holes
without associated free
electrons.


There are still electrons freed
due to thermal excitation.
These are called
minority
carriers
.

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The concentration of holes in p
-
type
silicon, or
majority carriers

is determined
almost completely by the dopant rather
than thermal properties.


the concentration of majority carriers is
generally independent of temperature.


The overall charge is still neutral due to
the
bound charge

associated with the
nucleus of the trivalent atom


CSE 177/EEE 177 : Electronics I

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P type (contd.)


If N
A

= concentration of acceptor atoms


P
p0

= concentration of holes in P
-
type Si in thermal
equilibrium


then p
po

= N
A

So, product of hole & electron concentration remains
constant i.e,

p
p0

×

n
p0

= n
i
2

Or, n
p0

= n
i
2
/ N
A

Here, n
i

is a function of temperature


n
p0

is a function of temperature


p
p0

is independent of temperature.

CSE 177/EEE 177 : Electronics I

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Thank You