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