Chapter 1
ECE 4339-4119 - U Houston
Han Le - Copyrighted

1. Review of resistivity and conductivity

1.1 Resistance & conductance

Suppose we have a copper wire. We apply 1 V, and obtain 0.142 A.

1.1.1 Resistance

What is the wire resistance?

1.1.2 Conductance

What is the wire conductance? Conductance is: :

1.2 Scaling the wire dimensions

1.2.1 Scaling the length

Suppose we double the length of the wire, what will be the resistance?

1.2.2 Scaling the wire cross section

Suppose we obtain a new wire with diameter twice the diameter of the current wire, what will be the resistance?

1.3 Resistivity and conductivity

Current= number of charges passing per unit time. Analogy: traffic and the road size. What happens when 4-lane traffic is converted into 2-lane traffic? or vice versa?
   

Resistance inversely decreases as a function of cross section area
                                                  

If we double the length, each half has only 1/2 voltage, hence, 1/2 the current.
The total resistance is thus doubled.
Resistance increases linearly as a function of length:
                                                  
There is a coefficient to make the two side equal:
                                                
ρ is called the resistivity. It is a property of the material, and has nothing to do with the length or cross section area of any particular piece of a material.
A related definition is conductivity, defined as:
                                              

Discussion: fundamentally, what determines the conductivity of a material? (we’ll discuss more in Chapter 3).

From periodic table (example: http://www.ptable.com/)

Source code: Review of resistance and conductance

Demo: Review of resistance and conductance

Question: what do you think is the reason for semiconductors to have such a wide range of conductivity (but being neither good conductors nor good insulators)?

2. Crystal graphics

2.1 Basic crystallography

Demo

http://demonstrations.wolfram.com/SomeRepresentativeCrystalStructures/

http://demonstrations.wolfram.com/CubicCrystalLattices/  

http://demonstrations.wolfram.com/DiamondLattice/

http://demonstrations.wolfram.com/TheStructureOfDiamond/

http://demonstrations.wolfram.com/SpherePacking/

2.2 Crystallographic planes

http://demonstrations.wolfram.com/CrystallographicPlanesForCubicLattices/

http://demonstrations.wolfram.com/MillerIndicesForASimpleCubicLattice/

http://demonstrations.wolfram.com/ReciprocalLattice2D/

http://demonstrations.wolfram.com/GrapheneBrillouinZoneAndElectronicEnergyDispersion/

Homework

Source code: 2D crystal structure

Demo 2D crystal - HW graphene

3. Defect: edge dislocation

http://demonstrations.wolfram.com/MovementOfAnEdgeDislocation/

Created with Wolfram Mathematica 9.0