This slide set corresponds to the MaterialsConcepts YouTube video "Muddiest Point- Electronic Properties I. Here's the link: https://www.youtube.com/watch?v=BY8ZPobU8B0 To study the vocab used in this video, visit this site: http://quizlet.com/24383440/71-electronic-properties-i-conductors-insulators-semiconductors-flash-cards/ This work was supported by NSF Grants #0836041 and #1226325.

1. 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

2. 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

3. Band Structures
Conductors-Metals
ENERGY

4. Band Structures (Cont.)
Semiconductors Insulators
ENERGY

5. Electron and Hole Migration
ENERGY
- -+ +
Si4+
Si4+Si4+

6. 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

7. 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

8. 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))

9. 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))

10. Where does the charge carrier density
come from in a conductor?
𝒏 =
𝟏𝟎. 𝟒𝟗 𝒈
𝟏 𝒄𝒎 𝟑
∗
𝟏𝟎𝟎 𝟑
𝒄𝒎 𝟑
𝟏 𝒎 𝟑
∗
𝟏 𝒎𝒐𝒍
𝟏𝟎𝟕. 𝟗 𝒈
∗
𝟔. 𝟎𝟐 ∗ 𝟏𝟎 𝟐𝟑
𝑨𝒈 𝒂𝒕𝒐𝒎𝒔
𝟏 𝒎𝒐𝒍
∗
𝟏 𝒗𝒂𝒍𝒆𝒏𝒄𝒆 𝒆−
𝑨𝒈 𝒂𝒕𝒐𝒎
Ex: Charge Carrier Density of Silver (Ag)
𝒏 =
# 𝒂𝒕𝒐𝒎𝒔
𝟏 𝒎 𝟑
∗
# 𝒗𝒂𝒍𝒆𝒏𝒄𝒆 𝒆−
𝒂𝒕𝒐𝒎
𝐧 = 𝟓. 𝟗 ∗ 𝟏𝟎 𝟐𝟖
𝐯𝐚𝐥𝐞𝐧𝐜𝐞 𝐞−
/𝐦 𝟑

11. 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 𝟏𝟎 𝟕
(Ω-m)-1

12. Conductivity Equation (Cont.)
𝛔 = 𝐧𝐪𝛍 𝒆 + 𝐩𝐪𝛍 𝒉
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 = 𝒏𝒊 𝒒(𝛍 𝒆 + 𝛍 𝒉)

13. 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 = 𝒏𝒊 𝒒(𝛍 𝒆 + 𝛍 𝒉)𝛔 = 𝐧𝐪𝛍 𝒆 + 𝐩𝐪𝛍 𝒉

14. Conductivity Equation (Cont.)
𝛔 = 𝐧𝐪𝛍 𝒆 + 𝐩𝐪𝛍 𝒉
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 = 𝒏𝒊 𝒒(𝛍 𝒆 + 𝛍 𝒉)
*There will not be an insulator example calculation due to extremely low conductivity.

15. Conductivity Comparison
• Conductor-Silver
– 𝟓. 𝟑𝟖 𝐱 𝟏𝟎 𝟕
(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

16. 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

17. 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