EE143 Semiconductor Tutorial - EECS Instructional · PDF fileEE143 S06 Semiconductor Tutorial...
Transcript of EE143 Semiconductor Tutorial - EECS Instructional · PDF fileEE143 S06 Semiconductor Tutorial...
1Professor 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
2Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
Why bother knowing Electrons and Holes ?
Microfabrication controls dopant concentration distribution
ND(x) and NA(x)
Electron Concentration n(x)
Hole Concentration p(x)
Electrical resistivity
Sheet Resistance
Fermi level Ef (x)
PN Diode Characteristics
MOS Capacitor
MOS Transistor
Electric Field
E(x) EffectCarrier Mobility
3Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
Electron Potential Energy
Isolated atoms
Atoms ina solid
Available statesat discreet energy levels
Available statesas continuous energy levelsinside energy bands
Conduction Band and Valence Band
4Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
5Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
The Simplified Electron Energy Band Diagram
6Professor 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
ElectronEnergy
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
7Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
An unoccupied electronic state in the valence band is called a “hole”
Concept of a “hole”
ConductionBand
Valence Band
8Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
9Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
Electron and Hole Concentrationsfor homogeneous semiconductor at thermal equilibrium
n: electron concentration (cm-3)p : hole concentration (cm-3)ND: donor concentration (cm-3)NA: acceptor concentration (cm-3)
1) Charge neutrality condition: ND + p = NA + n
2) Law of Mass Action : n• p = ni2
Note: Carrier concentrations depend on NET dopant concentration (ND - NA) !
Assume completely ionized to form ND
+
and NA-
10Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
How to find n, p when Na and Nd are known
n- p = Nd - Na (1) pn = ni2 (2)
(i) If Nd -Na > 10 ni : n ≡ Nd -Na (ii) If Na - Nd > 10 ni : p ≡ Na- Nd
11Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
Mobile charge-carrier drift velocity v is proportional to applied E-field:
µn
µp
Carrier Mobility µ
| v | = µ E
Mobility depends on (ND + NA) ! (Unit: cm2/V•s)
12Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
R ≅ 2.6Rs
Electrical Resistance of Layout Patterns
(Unit of RS: ohms/square)
L=1µm
W = 1µm
R = Rs
R = Rs/2 R = 2Rs
R = 3Rs
1m
1mR = Rs
Metal contact Top View
13Professor N Cheung, U.C. Berkeley
Semiconductor TutorialEE143 S06
RIC resistor = Rpaper × RS
resistor
RSpaper
IC Resistor Pattern
Resistor Paper Pattern
micronscentimeters
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 RS
paper
Measure Rpaper
experimentally across the two terminals
You know RSresistor of
of a microfabricated
layer by 4-point
probe method.
Will this layout pattern
give the desired R value ?
You can deduce