Lecture 3

Semiconductor

Nov 2, 2013 (4 years and 8 months ago)

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Lecture 3

Intrinsic Semiconductor

When a bond breaks, an electron and a hole are
produced:

n
0

=
p
0

(electron & hole concentration)

Also:

n
0
p
0
=
n
i

2

Then:

n
0

=
p
0
=
n
i

n
i

= intrinsic carrier concentration
[cm

-
3
]

In Si at 300K (room temperature):
n
i

= 1x 10
10
cm

-
3

Band Gap & Carrier Concentration

Eg

(
eV
)

n
i

[cm

-
3
]

Ge

0.67

2.4

x 10
13

Si

1.1

1.5 x 10
10

GaAs

1.43

5
x 10
7

Band gap and intrinsic carrier
concentration for germanium, silicon and
gallium arsenide at 300K

Extrinsic Semiconductor: Donor

N
d

= donor concentration [cm

-
3
]

If

N
d

<<
n
i

,
doping irrelevant

Intrinsic semiconductor

n
0

=
p
0
=
n
i

If

N
d

>>
n
i

,
doping controls carrier
concentrations

Extrinsic semiconductor

n
0

=
N
d

, p
0
=
n
i

2
/
N
d

Note:

n
0
>>
p
0

n
-
type semiconductor

Extrinsic Semiconductor: Acceptor

N
a

= acceptor concentration [cm

-
3
]

If

N
a
<<
n
i

,
doping irrelevant

Intrinsic semiconductor

n
0

=
p
0
=
n
i

If

N
a
>>
n
i

,
doping controls carrier concentrations

Extrinsic semiconductor

p
0

=
N
a

, n
0
=
n
i

2
/
N
a

Note:

p
0
>>
n
0

p
-
type semiconductor

Extrinsic Semiconductor:

Donor & Acceptor

Carrier concentration can be engineered by addition
of “
dopants
” (selected foreign atoms):

Pentavalent

impurities (P, As,
Sb
)

n
-
type semiconductor:

n
0

=
N
d

, p
0
=
n
i

2
/
N
d

Trivalent impurities (B, Al,
Ga
)

p
-
type semiconductor:

p
0

=
N
a

, n
0
=
n
i

2
/
N
a

Properties of Crystals

Two properties of crystals that are needed to
calculate the current in a semiconductor
:

First, we need to
know how many fixed and
mobile charges are present in the material
.

Second, we need to
understand the transport of
the mobile carriers through the semiconductor
.

Carrier Transport

Two carrier transport mechanisms
:

The
drift of carriers
in an electric field

The
diffusion of carriers
due to a carrier density

Electron

and

holes

will

move

under

the

influence

of

an

applied

electric

field

since

the

field

exert

a

force

on

charge

carriers

(electrons

and

holes)
.

These

movements

result

a

current

of

:

Carrier Drift

drift current

number of charge carriers per unit volume

charge of the electron

drift velocity of charge carrier

area of the semiconductor

Carrier Mobility ,

applied field

mobility of charge carrier

is a proportionality factor

So is
a measure how easily charge carriers move

under the influence of

an applied field or determines
how mobile

the

charge carriers

are.

n
-

type Si

+

-

V

n

type Si

e
-

Electric field

Electron movement

Current flow

Current

carriers are mostly electrons
.

+

-

V

p

type Si

hole

Electric field

Hole movement

Current flow

Current carriers are mostly holes
.

p
-

type Si

The PN Junction Diode

When a P
-
type semiconductor region and an
N
-
type semiconductor region are in contact, a
PN junction diode is formed.

V
D

I
D

+

Diode Operating Regions

In order to understand the operation of a
diode, it is necessary to study its behavior in
three operation regions: equilibrium, reverse
bias, and forward bias.

V
D

= 0

V
D

> 0

V
D

< 0

Carrier Diffusion across the Junction

Because of the difference in hole and electron
concentrations on each side of the junction,
carriers diffuse across the junction:

Notation
:

n
n

electron concentration on N
-
type side (cm
-
3
)

p
n

hole concentration on N
-
type side (cm
-
3
)

p
p

hole concentration on P
-
type side (cm
-
3
)

n
p

electron concentration on P
-
type side (cm
-
3
)

Depletion Region

A region in a semiconductor device, usually at
the juncture of P
-
type and N
-
type materials, in
which there is neither an excess of electrons
nor of holes.

Depletion Region

As conduction electrons and holes diffuse
across the junction, they leave behind ionized
dopants
. Thus, a region that is depleted of
mobile carriers is formed.

The charge density in the depletion region is not
zero.

The carriers which diffuse across the junction
recombine with majority carriers,
i.e.
they are
annihilated.

width=
W
dep

quasi
-
neutral
region

quasi
-
neutral
region

Carrier Drift across the Junction

Because charge density ≠ 0 in the depletion
region, an electric field exists, hence there is
drift current.

p
-
n
-
Juction
-
And
-
Diodes