ece 474: principles of electronic devices · ece 474: principles of electronic devices prof....

ECE 474:Principles of Electronic Devices

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State [email protected]

V.M. Ayres, ECE474, Spring 2011

Lecture 02:

Chapter 01

How to quantify physical structures of crystal systems that are important for devices:

Cubic systems: bcc, fcc, diamond, zinc-blendeNumber of atoms in unit cellLattice constant aPacking fractionNearest neighbor distancesDensity

Examples of each


.

The Nobel Prize in Physics 2010

Graphene

Carbon nanotubes

Why quantify:The physical structure is the environment through which current

travels in a deviceThe current interacts seriously with its environment


.


Graphene

Carbon nanotubes

Cubic systems: basic repeat pattern can be described within an imaginary cube of side a. Side a (in nm) is called the “lattice constant”.

a


.


Graphene

Carbon nanotubes

Cubic systems:


.


Graphene

Carbon nanotubes

Cubic systems: traditional semiconductors and many metals.

Copper,Aluminum

Silicon Gallium Arsenide


Repeat unit = “Unit Cell”.Stack many Unit Cells to make a crystalExample from book: bcc (chromium, cobalt)

Point: to stack Unit Cells sideways or up to make a crystal, you need to have the atoms in the box.


Correctly counting atoms in the imaginary box:

Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box


Correctly counting atoms in the box:


Example: Cr (bcc)

8 x 1/8 = 10 x ½ = 01 x 1 = 1Atoms in box = 2




Example: Cu (fcc)




Example: Cu (fcc)

8 x 1/8 = 16 x ½ = 30 x 1 = 0Atoms in box = 4




Example: Si (D)




Example: Si (D)

8 x 1/8 = 16 x ½ = 34 x 1 = 4Atoms in box = 8




Example: GaN (ZB)

8 x 1/8 = 16 x ½ = 34 x 1 = 4Atoms in box = 8




Example: GaN (ZB)Number of Ga :8 x 1/8 = 16 x ½ = 30 x 1 = 0Ga Atoms in box = 4




Example: GaN (ZB)Atoms in box = 8

Ga Atoms in box = 4N Atoms in box = 4

50:50% Ga and N

The proportions are called the Composition or Stoichiometry




Example: AlN (ZB)Atoms in box = 8

Al Atoms in box = 4N Atoms in box = 4

50:50% Al and NThe proportions are called the Composition or Stoichiometry


Example of Composition (or Stoichiometry):

Example: AlGaxN1-xAtoms in box = ?

Al Atoms in box = ? N Atoms in box = ?Ga Atoms in box = ?

Ternary and Quaternary structuresWhy: increased options for lattice matching

Composition: find x and fill in: AlGaxN1-x



Example 01: AlGaxN1-xAtoms in box = 8

Al Atoms in box = 8(1/8) + 6(1/2) =4 N Atoms in box = 3(1) = 3Ga Atoms in box = 1(1) =1


Composition: Al4Ga1N3 written as: AlGa0.25N0.75



Example 02: AlGaxN1-xAtoms in box = 8

Al Atoms in box = 8(1/8) + 6(1/2) =4 N Atoms in box = 2(1) = 3Ga Atoms in box = 2(1) =1


Composition: AlGa0.5N0.5


Cubic Systems:

1. Atomic arrangements

2. Sizes of the box “a”

“a” = “lattice constant”


Page 540

Also see Ashcroft & Mermin, Solid State Physics


SiO2

Si

Doped polySi

Cu Cu

n n


n nSi

Cu Cu

Cufcca =3.61 Ang

SiDiamonda = 5.43 Ang

Lattice mis-match at interface


Can get lattice matching between semiconductors by using a ternary or a quaternary:

ece 474: principles of electronic devices · ece 474: principles of electronic devices prof....

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