EE143 Semiconductor Tutorial

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6 Οκτ 2011 (πριν από 6 χρόνια και 1 μήνα)

1.315 εμφανίσεις

- Electrons and “Holes” - Dopants in Semiconductors - Electron Energy Band Diagram - Mobility - Resistivity and Sheet Resistance

1
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
EE143 Semiconductor Tutorial
-Electrons and “Holes”
- Dopants in Semiconductors
- Electron Energy Band Diagram
- Mobility
- Resistivity and Sheet Resistance
2
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
Why bother knowing Electrons and Holes ?
Microfabrication
controls dopant
concentration
distribution
N
D
(x) and N
A
(x)
Electron Concentration n(x)
Hole Concentration p(x)
Electrical resistivity
Sheet Resistance
Fermi level E
f
(x)
PN Diode Characteristics
MOS Capacitor
MOS Transistor
Electric Field
E(x) Effect
Carrier Mobility
3
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
Electron
Potential
Energy
Isolated
atoms
Atoms in
a solid
Available states
at discreet
energy levels
Available states
as continuous energy levels
inside energy bands
Conduction Band and Valence Band
4
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
5
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
The Simplified Electron Energy Band Diagram
6
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
Density of States at Conduction Band:
The Greek Theater Analogy
Plan View of the amphitheatre at Epidarus
Electron
Energy
Amphitheatre at Epidarus, Greece.
Built c350 BC.
Energy Gap
(no available seats)
Note that the number of available
seats at same potential energy
increases with higher electron energy
7
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
An unoccupied electronic state in
the valence band is called a “hole”
Concept of a “hole”
Conduction
Band
Valence
Band
8
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
9
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
Electron and Hole Concentrations
for homogeneous semiconductor at thermal equilibrium
n: electron concentration (cm
-3
)
p : hole concentration (cm
-3
)
N
D
: donor concentration (cm
-3
)
N
A
: acceptor concentration (cm
-3
)
1) Charge neutrality condition:N
D
+ p = N
A
+ n
2) Law of Mass Action : n p = n
i
2
Note
: Carrier concentrations depend on
NET dopant concentration (N
D
- N
A
) !
Assume completely
ionized to form N
D
+
and N
A
-
10
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06

How to find n, p when Na and Nd are known

n- p = N
d
- N
a
(1)
pn = n
i
2
(2)

(i) If N
d
-N
a
> 10 n
i
: n

N
d
-N
a

(ii) If N
a
- N
d
> 10 n
i
: p  N
a
- N
d

11
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
Mobile charge-carrier drift velocity v is proportional to applied E-field:

n

p
Carrier Mobility 
| v | =  E
Mobility depends
on (N
D
+ N
A
) !
(Unit:cm
2
/V•s)
12
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
R  2.6R
s
Electrical Resistance of Layout Patterns
(Unit of R
S
:ohms/square)
L=1m
W = 1m
R = R
s
R = R
s
/2
R = 2R
s
R = 3R
s
1m
1m
R = R
s
Metal contact
Top View
13
Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
R
IC resistor
= R
paper

R
S
resistor
R
S
paper

IC Resistor Pattern
Resistor Paper Pattern
microns
centimeters
magnified
Resistance of Arbitrary Layout Patterns
Before you do the
layout and
fabricate the
structure which is
expensive and time
consuming. Cut
out a similar
pattern on a
resistor paper with
a known R
S
paper
Measure R
paper
experimentally
across the two
terminals
You know R
S
resistor
of
of a microfabricated
layer by 4-point
probe method.
Will this layout pattern
give the desired R value ?
You can deduce