Muddiest Points

Muddiest Points: • “What are band gaps and how do they relate to electronic

materials?”

• “Why is an insulator or semiconductor when heated, a better conductor?”

• “How does grain size/grain boundary area affect conductivity in metals and semiconductors?”

• “Calculations for number of charge carriers and what it means.”

• “Relation of electron and electron-hole mobility to conductivity.”

Electronic Properties I: Conductors, Insulators, & Semiconductors

Conductivity Classifications

METALS (Ω-m)-1 Silver 6.8 x 107

Copper 6.0 x 107

Iron 1.0 x 107

SEMICONDUCTORS (Ω-m)-1 Silicon 4 x 10-4

Germanium 2 x 100

GaAs 10-6

CERAMICS (Ω-m)-1

Soda-lime glass 10-10-10-11

Concrete 10-9

Aluminum oxide <10-13

POLYMERS (Ω-m)-1

Polystyrene <10-14

Polyethylene 10-15-10-17

*Values at Room Temperature

CONDUCTORS SEMICONDUCTORS INSULATORS

Band Structures Conductors-Metals

ENER

GY

Band Structures (Cont.)

Semiconductors Insulators

ENER

GY

Electron and Hole Migration EN

ERG

Y

- - + +

Si4+

Si4+ Si4+

What Affects Metal Conductivity?

Metals Resistivity decreases with or Conductivity increases with: • Fewer Imperfections

o Grain Boundaries o Impurity Atoms o Dislocations o Vacancies

• Decreasing temperature

Fewer imperfections reduces scattering of electrons

Smaller vibration amplitude reduces electron scattering

What Affects Semiconductor Conductivity?

Intrinsic Semiconductors Resistivity decreases with or Conductivity increases with: • Larger Size of Grains or Less

Grain Boundary Area o Only affects

polycrystalline semiconductors

• Increasing temperature

Lower Grain Boundary Area reduces electron scattering.

More Thermal Energy creates more electron-hole pairs

Conductivity Equation

𝛔 =𝟏

𝛒= 𝐧 𝐪 𝛍

General Form

σ = conductivity (ohm-m)-1 ρ = resistivity (ohm-m) n = carrier density (# of carriers/m3) q = electric charge 1.6x10-19 (C) μ = mobility (m2/(V-s))

Conductivity Equation (Cont.)

𝛔 = 𝐧 𝐪 𝛍 𝒆

Metals

σ = conductivity (ohm-m)-1

n = carrier density (# of carriers/m3)

q = electric charge 1.6x10-19 (C)

μe = electron mobility (m2/(V-s))

Where does the charge carrier density come from in a conductor?

𝒏 =𝟏𝟎. 𝟒𝟗 𝒈

𝟏 𝒄𝒎𝟑∗

𝟏𝟎𝟎 𝟑𝒄𝒎𝟑

𝟏 𝒎𝟑∗

𝟏 𝒎𝒐𝒍

𝟏𝟎𝟕. 𝟗 𝒈∗

𝟔. 𝟎𝟐 ∗ 𝟏𝟎𝟐𝟑 𝑨𝒈 𝒂𝒕𝒐𝒎𝒔

𝟏 𝒎𝒐𝒍∗

𝟏 𝒗𝒂𝒍𝒆𝒏𝒄𝒆 𝒆−

𝑨𝒈 𝒂𝒕𝒐𝒎

Ex: Charge Carrier Density of Silver (Ag)

𝒏 =# 𝒂𝒕𝒐𝒎𝒔

𝟏 𝒎𝟑∗

# 𝒗𝒂𝒍𝒆𝒏𝒄𝒆 𝒆−

𝒂𝒕𝒐𝒎

𝐧 = 𝟓. 𝟗 ∗ 𝟏𝟎𝟐𝟖 𝐯𝐚𝐥𝐞𝐧𝐜𝐞 𝐞−/𝐦𝟑

Example 1: Conductor

𝛔 = 𝐧 𝐪 𝛍 𝒆

Calculate the conductivity of the metal silver with an electron mobility of 0.0057 (m2/(V-s)) and a charge carrier density of 5.9 x 1028 per m3.

𝛍 𝒆= 0.0057 (m2/(V-s)) 𝒏 = 5.9 x 1028 m-3

𝛔 = (5.9 x 1028 m-3)(1.6x10-19 C)(0.0057 m2/(V-s))

𝛔 = 𝟓. 𝟑𝟖 𝐱 𝟏𝟎𝟕 (Ω-m)-1

Conductivity Equation (Cont.)

𝛔 = 𝐧𝐪𝛍𝒆 + 𝐩𝐪𝛍𝒉

Intrinsic Semiconductors (n=p)

σ = conductivity (ohm-m)-1

ni = intrinsic carrier density (# of carriers/m3)

q = electric charge 1.6x10-19 (C)

μe = electron mobility (m2/(V-s))

μh = electron hole mobility (m2/(V-s))

𝛔 = 𝒏𝒊𝒒(𝛍𝒆 + 𝛍𝒉)

Example 2: Semiconductor

Calculate the conductivity of intrinsic silicon with an electron mobility of 0.14 (m2/(V-s)), hole mobility of 0.05 (m2/(V-s)), and an intrinsic charge carrier density of 1.3 x 1016 per m3.

𝛍 𝒆= 0.14 (m2/(V-s)) 𝛍 𝒉= 0.05 (m2/(V-s)) 𝒏𝒊= 1.3 x 1016 m-3

𝛔 = (1.3 x 1016 m-3)(1.6x10-19 C)(0.14 + 0.05) m2/(V-s)

𝛔 = 𝟑. 𝟗𝟓𝐱 𝟏𝟎−𝟒 (Ω-m)-1

𝛔 = 𝒏𝒊𝒒(𝛍𝒆 + 𝛍𝒉) 𝛔 = 𝐧𝐪𝛍𝒆 + 𝐩𝐪𝛍𝒉

Conductivity Equation (Cont.)

𝛔 = 𝐧𝐪𝛍𝒆 + 𝐩𝐪𝛍𝒉

Insulators (n=p)

σ = conductivity (ohm-m)-1

ni = intrinsic carrier density (# of carriers/m3)

q = electric charge 1.6x10-19 (C)

μe = electron mobility (m2/(V-s))

μh = electron hole mobility (m2/(V-s))

𝛔 = 𝒏𝒊𝒒(𝛍𝒆 + 𝛍𝒉)

*There will not be an insulator example calculation due to extremely low conductivity.

Conductivity Comparison

• Conductor-Silver

– 𝟓. 𝟑𝟖 𝐱 𝟏𝟎𝟕 (Ω-m)-1

– (5.9 x 1028 m-3)(1.6x10-19 C)(0.0057 m2/(V-s))

• Semiconductor-Silicon

– 𝟑. 𝟗𝟓 𝐱 𝟏𝟎−𝟒 (Ω-m)-1

– (1.3 x 1016 m-3)(1.6x10-19 C)(0.14 + 0.05) m2/(V-s)

• Insulator-Concrete & Polyethylene

– Concrete= 𝟏𝟎−𝟗 (Ω-m)-1

– Polyethylene= 𝟏𝟎−𝟏𝟓 − 𝟏𝟎−𝟏𝟕 (Ω-m)-1

Conductivity Classifications

METALS (Ω-m)-1 Silver 6.8 x 107

Copper 6.0 x 107

Iron 1.0 x 107

SEMICONDUCTORS (Ω-m)-1 Silicon 4 x 10-4

Germanium 2 x 100

GaAs 10-6

CERAMICS (Ω-m)-1

Soda-lime glass 10-10-10-11

Concrete 10-9

Aluminum oxide <10-13

POLYMERS (Ω-m)-1

Polystyrene <10-14

Polyethylene 10-15-10-17

*Values at Room Temperature

CONDUCTORS SEMICONDUCTORS INSULATORS

Wrap-Up

• “What are band gaps and how do they relate to electronic materials?”

• “Why is an insulator or semiconductor when heated, a better conductor?”

• “How does grain size/grain boundary area affect conductivity in metals and semiconductors?”

• “Calculations for number of charge carriers and what it means.”

• “Relation of electron and electron-hole mobility to conductivity.”

Electronic Properties I: Conductors, Insulators, & Semiconductors