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Semi

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EE143 S06

EE143 Semiconductor Tutorial

-Electrons and “Holes”

- Dopants in Semiconductors

- Electron Energy Band Diagram

- Mobility

- Resistivity and Sheet Resistance
Semiconductor Tutorial

Professor N Cheung, U.C. Berkeley

1 EE143 S06 Semiconductor Tutorial

Why bother knowing Electrons and Holes ?

Microfabrication controls dopant concentration distribution

ND(x) and NA(x)

Carrier Mobility

Electron Concentration n(x)

Hole Concentration p(x)

Electric Field Fermi level Ef(x)

Electrical resistivity

Sheet Resistance

Professor N Cheung, U.C. Berkeley E(x) Effect

PN Diode Characteristics

MOS Capacitor

MOS Transistor

2 EE143 S06

Electron Potential Energy Semiconductor Tutorial

Conduction Band and Valence Band

Available states Available states at discreet energy levels

Isolated atoms

Professor N Cheung, U.C. Berkeley as continuous energy levels inside energy bands

Atoms in a solid

3 EE143 S06

Professor N Cheung, U.C. Berkeley
Semiconductor Tutorial

4 EE143 S06 Semiconductor Tutorial

The Simplified Electron Energy Band Diagram

Professor N Cheung, U.C. Berkeley

5 EE143 S06

Density of States at Conduction Band: The Greek Theater Analogy
Semiconductor Tutorial Note that the number of available seats at same potential energy increases with higher electron energy

Energy Gap
(no available seats)

Electron Energy

Plan View of the amphitheatre at Epidarus

Professor N Cheung, U.C. Berkeley

Amphitheatre at Epidarus, Greece. Built c350 BC.

6 EE143 S06

Conduction Band

Valence Band

Concept of a “hole”

An unoccupied electronic state in the valence band is called a “hole”
Semiconductor Tutorial

Professor N Cheung, U.C. Berkeley

7 EE143 S06

Professor N Cheung, U.C. Berkeley
Semiconductor Tutorial

8 EE143 S06

Electron and Hole Concentrations for homogeneous semiconductor at thermal equilibrium
Semiconductor Tutorial

n: electron concentration (cm-3) p : hole concentration (cm-3) ND: donor concentration (cm-3) NA: acceptor concentration (cm-3)

1) Charge neutrality condition:

Assume completely ionized to form ND+ - and NA
ND+ p = NA+ n

2) Law of Mass Action : n• p = ni2

Note: Carrier concentrations depend on NET dopant concentration (ND- NA) !

Professor N Cheung, U.C. Berkeley

9 EE143 S06
Semiconductor Tutorial

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

Professor N Cheung, U.C. Berkeley

10 EE143 S06

Carrier Mobility ∝
Semiconductor Tutorial

Mobile charge-carrier drift velocity v is proportional to applied E-field:

| v | = ∝ E

∝n

Mobility depends on (ND+ NA) !

∝p

Professor N Cheung, U.C. Berkeley
(Unit: cm2/V•s)

11 EE143 S06

Electrical Resistance of Layout Patterns
Semiconductor Tutorial

(Unit of RS: ohms/square)

W = 1∝m

Metal contact

Top View

1m

R = Rs

L=1∝m

R = Rs

1m

R ≅ 2.6Rs

Professor N Cheung, U.C. Berkeley

R = Rs/2

R = 2Rs

R = 3Rs

12 EE143 S06

Resistance of Arbitrary Layout Patterns

Resistor Paper Pattern
Semiconductor Tutorial

IC Resistor Pattern

You know RSresistor of

Before you do the layout and fabricate the structure which is of a microfabricated

layer by 4-point probe method. Will this layout pattern

give the desired R value ? microns magnified centimeters

RSresistor expensive and time consuming. Cut out a similar pattern on a resistor paper with a known RSpaper
Measure Rpaper experimentally across the two terminals You can deduce

Professor N Cheung, U.C. Berkeley
RIC resistor = Rpaper ⋅
RSpaper

13…...

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