# Semiconductor Devices and Models I

Semiconductor

Nov 1, 2013 (4 years and 8 months ago)

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November 2, 2013

sawyes@rpi.edu
www.rpi.edu/~sawyes/courses.html

1

ECSE
-
6230

Semiconductor Devices and Models I

Lecture 11

Prof. Shayla Sawyer

Bldg. CII, Rooms 8225

Rensselaer Polytechnic Institute

Troy, NY 12180
-
3590

Tel. (518)276
-
2164

Fax. (518)276
-
2990

e
-
mail: sawyes@rpi.edu

1

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November 2, 2013

Lecture Outline

PN Junction Models

Small Signal Model

SPICE Model

MOS Capacitors

Energy Bands

Accumulation, Depletion and Inversion

Surface Charges

Surface Potential

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Diffusion Capacitance

When
forward biased
, a significant
contribution to
junction
capacitance

come from the
rearrangement of the minority
carriers density

Diffusion capacitance is the
dominant capacitance component
for pn junctions under
moderate to
large forward biases.

Typically,

the

pn

junction

is

biased

with

a

large

(
0
.
7
V)

dc

bias

voltage

V
0

and

a

small

(
20
-
40
mV)

ac

voltage

V
1
.

V(t)

=

V
0

+

V
1

exp

(

j

t

)

J(t)

=

J
0

+

J
1

exp

(

j

t

)

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Small
-
Signal Model

Electron and hole densities at the depletion region can be
obtained from our previous equations (deriving Shockley
equation where:

Becomes

1st term
-

dc component

2nd term
-

small
-
signal ac component at depletion boundary

Similar expression for electron density, n
p
, on the p
-
side.

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Small
-
Signal Model

Substituting p
n1

into the continuity equation,

we have

Eq. (*) is analogous to the dc Diffusion Eq. if the
carrier lifetime is express as

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Small
-
Signal Model

AC Component

Y = J
1

/ V
1

= G
d

+ j

C
d

Where G
d

is the diffusion conductance and

C
d

is the diffusion capacitance.

Both can be found and they are frequency dependent

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Small
-
Signal Model

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Small
-
Signal Model

Also,

C
d

decreases with
increasing frequency and for
large

, C
d

-
1/2
.

C
d

increases with increasing J
0

( or exp( qV
0
/kT )) and hence
is especially
important at low
-
frequency and under forward
biased conditions
.

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AIM
-
SPICE Model

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Introduction to MOS (or MIS)

Basic structure

Thermal Equilibrium

Band Alignment

Applied Bias

Accumulation

Depletion

Weak Inversion

Strong Inversion

Surface Charge

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MOS (or MIS), CCD

Metal
-
Oxide
-
Semiconductor (MOS) or

Metal
-
Insulator
-
Semiconductor (MIS),

The convention is that V is positive when the plate is
positively biased with respect to the semiconductor body

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MOS Capacitors

Vacuum level is a
continuous function of
position

Know electron affinity
of the insulator and
semiconductor

Know work function of
semiconductor and
metal

Separated materials

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MOS under Thermal Equilibrium

D
ox

=

ox

ox

= D
Si

=

Si

Si

ox

=

Si

(

Si

/

ox

)

3

Si

We can assume there is
some path
for transfer

so in thermal
equilibrium the fermi level can
align.

Voltage drop across insulator

A charge imbalance occurs because
of negative charges for equilibrium:
Work functions in metal is 0.8V less
than work function of silicon.

Leaves a sheet of positive charge at
the metal surface near the oxide.

An equal quantity of negative
charge is stored on the silicon side.

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MOS Capacitors

MOS capacitors with an applied bias:

(a)

Accumulation,

(b)

Depletion,

(c)

Inversion.

Ideal MOS capacitors are assumed:

(1)

V = 0, flatband condition.

V
FB

= 0.

ms

=

m

-

s

= 0.

M

= f(which metal),

s

= f( N
A

or N
D

).

For p
-
type semicond.,

ms

=

m

-

(

+ (E
g

/ 2) +

B

) = 0

(2)

No oxide charge.

(3)

No carrier transport across the insulator,

R
insulator

=

.

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Flatband Condition

N
-
type

P
-
type

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Accumulation

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Depletion

Inversion

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Surface Potential

Potential is defined as the
potential E
i
(x)/q with
respect to the bulk of the
semiconductor (band
bending)

ψ
p

=
ψ

P
-
type semiconductor

Electron and hole conc. as
a function of
ψ
p

Relate surface potential to
the width of the depletion
layer

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Q
s

vs.

s

Variation of surface
charge density as a
function of the surface
potential

Negative
ψ
s
, Q
s
positive,
accumulation, dominated
by first term in F

Ψ
s
= 0, Q
s

= 0 flat band

Positive
ψ
s
, Q
s
negative
,
depletion and weak
inversion, dominated by
2
nd

term in F

Strong inversion, function
F is dominated by fourth
term