# L08_5340_Sp11x

Semiconductor

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EE 5340

Semiconductor Device Theory

Lecture 08

Spring 2011

Professor Ronald L. Carter

ronc@uta.edu

http://www.uta.edu/ronc

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15Feb2011

2

Second Assignment

Submit a signed copy of the document
posted at

www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf

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15Feb2011

3

Test 1

Tuesday 22Feb11

11 AM Room 129 ERB

Covering Lectures 1 through 9

Open book
-

1 legal text or ref., only.

You may write notes in your book.

Calculator allowed

A cover sheet will be included with
full instructions. For examples see
http://www.uta.edu/ronc/5340/tests/.

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15Feb2011

4

Diffused or Implanted

IC Resistor (Fig 2.45
1
)

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15Feb2011

5

An IC Resistor with

L = 8W

(M&K)
1

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6

Typical IC doping

profile (M&K Fig. 2.44
1
)

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15Feb2011

7

Mobilities**

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8

IC Resistor

Conductance

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15Feb2011

9

An IC Resistor with

N
s

= 8, R = 8R
s
(M&K)
1

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10

The effect of lateral

diffusion (M&K
1
)

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15Feb2011

11

A serpentine pattern

IC Resistor (M&K
1
)

R = N
S
R
S

+ 0.65

N
C
R
S

note: R
C

= 0.65

R
S

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15Feb2011

12

The equilibrium carrier concentration
ahd the Fermi energy are related as

The potential

f

= E
f
-
E
fi
)/q

If not in equilibrium,

a quasi
-
Fermi level

(imref) is used

Fermi Energy

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13

Electron quasi
-
Fermi

Energy (n = n
o

+

n)

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14

Hole quasi
-
Fermi

Energy (p = p
o

+

p)

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15

E
x
-
field when

E
f

-

E
fi

not constant

Since
f

㴠(E
f
-

E
fi
)/q = V
t
ln(n
o
/n
i
)

When E
f

-

E
fi

= is position dependent,

E
x
=
-
d
f
/d‽
-
[d(E
f
-
E
fi
)/dx]

=
-

V
t

d[ln(n
o
/n
i
)]/dx

If non
-
equilibrium

f
n

= (E
fn
-
E
fi
)/q = V
t
ln(n/n
i
), etc

E
xn
=
-
[d
f
n
/dx] =
-
V
t
d[ln(n/n
i
)]/dx

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15Feb2011

16

Si and Al and model

(approx. to scale)

q
f
m,Al
~
4.1 eV

E
o

E
Fm

E
Fp

E
Fn

E
o

E
c

E
v

E
Fi

q
f
s,n

q
c
si
~
4.05

eV

E
o

E
c

E
v

E
Fi

q
f
s,p

metal

n
-
type s/c

p
-
type s/c

q
c
si
~
4.05

eV

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15Feb2011

17

Making contact be
-

tween metal & s/c

Equate the E
F

in
the metal and s/c
materials far from
the junction

E
o
(the free level),
must be continuous
across the jctn.

N.B.: q
c

=4⸰5敖e(Si),

and q
f

=ⁱ
c

E
c

-

E
F

E
o

E
c

E
F

E
Fi

E
v

q
c

(electron
affinity)

q
f
F

q
f

(work function)

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15Feb2011

18

Equilibrium Boundary
Conditions w/ contact

No discontinuity in the free level, E
o

at
the metal/semiconductor interface.

E
F,metal

= E
F,semiconductor

to bring the
electron populations in the metal and
semiconductor to thermal equilibrium.

E
o

-

E
C

= q
c
semiconductor

in all of the s/c.

E
o

-

E
F,metal

= q
f
metal

throughout metal.

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15Feb2011

19

Ideal metal to n
-
type

barrier diode
(
f
m
>
f
s
,V
a
=0)

E
Fn

E
o

E
c

E
v

E
Fi

q
f
s,n

q
c
s

n
-
type s/c

q
f
m

E
Fm

metal

q
f
Bn

q
f
i

q
f

n

No disc in
E
o

E
x
=0 in metal
==>
E
o
flat

f
Bn
=
f
m
-

c
s

=
elec

mtl

to
s/c
barr

f
i
=
f
Bn
-
f
n
=
f
m
-
f
s

elect s/c to
mtl

barr

Depl reg

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15Feb2011

20

Metal to n
-
type

non
-
rect cont (
f
m
<
f
s
)

E
Fn

E
o

E
c

E
v

E
Fi

q
f
s,n

q
c
s

n
-
type s/c

q
f
m

E
Fm

metal

q
f
B,n

q
f
n

No disc in E
o

E
x
=0 in metal
==> E
o

flat

f
B,n
=
f
m
-

c
s
= elec mtl to
s/c barr

f
i
=
f
Bn
-
f
n
< 0

Accumulation
region

Acc reg

q
f
i

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15Feb2011

21

Ideal metal to p
-
type

barrier diode (
f
m
<
f
s
)

No disc in
E
o

E
x
=0 in metal ==>
E
o
flat

f
Bn
=
f
m
-

c
s

=
elec

mtl

to s/c
barr
.

f
Bp
=
f
m
-

(
c
s

+
E
g
)
=
hole m to
s
barr
.

f
i

=
f
m
-
f
s,p

= hole
s/c to
mtl

barr
.

E
Fp

E
o

E
c

E
v

E
Fi

q
f
s,p

q
c
s

p
-
type s/c

q
f
m

E
Fm

metal

q
f
Bn

q
f
i

q
f
p
<0

Depl reg

q
f
Bp

q
f
i

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15Feb2011

22

Metal to p
-
type

non
-
rect cont (
f
m
>
f
s
)

No disc in
E
o

E
x
=0 in metal ==>
E
o

flat

f
B,n

=
f
m

-

c
s

=
elec

mtl

to s/c
barr

f
Bp
=
f
m
-

(
c
s

+
E
g
)
=
hole m to s

f
i

=
f
m
-
f
s,n

= s/c
to
mtl

barr
.

E
Fi

E
o

E
c

E
v

E
fP

q
f
s,n

q
c
s

n
-
type s/c

q
f
m

E
Fm

metal

q
f
Bn

q(
f
i
)

q
f
p

Accum reg

q
f
Bp

q
f
i

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15Feb2011

23

Metal/semiconductor

system types

n
-
type semiconductor

Schottky diode
-

blocking for
f
m

>
f
s

contact
-

conducting for
f
m

<
f
s

p
-
type semiconductor

contact
-

conducting for
f
m

>
f
s

Schottky diode
-

blocking for
f
m

<
f
s

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15Feb2011

24

References

1 and
M&K
Device

Electronics for Integrated
Circuits
, 2 ed., by Muller and
Kamins
, Wiley,
New York, 1986. See
Semiconductor Device
Fundamentals
, by
Pierret
-
Wesley,
1996, for another treatment of the

model.

2
Physics of Semiconductor Devices
, by S. M.
Sze
,
Wiley, New York, 1981.

3 and **
Semiconductor Physics & Devices
, 2nd ed.,
by
Neamen
, Irwin, Chicago, 1997.

Fundamentals of Semiconductor Theory and
Device Physics
, by
Shyh

Wang, Prentice Hall,
1989.