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ECE 474:Principles of Electronic Devices
Prof. Virginia AyresElectrical & Computer EngineeringMichigan State Universityayresv@msu.edu
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
V.M. Ayres, ECE474, Spring 2011
.
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
V.M. Ayres, ECE474, Spring 2011
.
The Nobel Prize in Physics 2010
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
V.M. Ayres, ECE474, Spring 2011
.
The Nobel Prize in Physics 2010
Graphene
Carbon nanotubes
Cubic systems:
V.M. Ayres, ECE474, Spring 2011
.
The Nobel Prize in Physics 2010
Graphene
Carbon nanotubes
Cubic systems: traditional semiconductors and many metals.
Copper,Aluminum
Silicon Gallium Arsenide
V.M. Ayres, ECE474, Spring 2011
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.
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the imaginary box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
Example: Cr (bcc)
8 x 1/8 = 10 x ½ = 01 x 1 = 1Atoms in box = 2
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
Example: Cu (fcc)
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
Example: Cu (fcc)
8 x 1/8 = 16 x ½ = 30 x 1 = 0Atoms in box = 4
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
Example: Si (D)
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
Example: Si (D)
8 x 1/8 = 16 x ½ = 34 x 1 = 4Atoms in box = 8
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
Example: GaN (ZB)
8 x 1/8 = 16 x ½ = 34 x 1 = 4Atoms in box = 8
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
Example: GaN (ZB)Number of Ga :8 x 1/8 = 16 x ½ = 30 x 1 = 0Ga Atoms in box = 4
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
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
V.M. Ayres, ECE474, Spring 2011
Correctly counting atoms in the box:
Corner atom: 1/8 atom IN boxFace atom: ½ atom IN boxInside atom: 1 atom IN box
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
V.M. Ayres, ECE474, Spring 2011
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
V.M. Ayres, ECE474, Spring 2011
Example of Composition (or Stoichiometry):
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
Ternary and Quaternary structuresWhy: increased options for lattice matching
Composition: Al4Ga1N3 written as: AlGa0.25N0.75
V.M. Ayres, ECE474, Spring 2011
Example of Composition (or Stoichiometry):
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
Ternary and Quaternary structuresWhy: increased options for lattice matching
Composition: AlGa0.5N0.5
V.M. Ayres, ECE474, Spring 2011
Cubic Systems:
1. Atomic arrangements
2. Sizes of the box “a”
“a” = “lattice constant”
V.M. Ayres, ECE474, Spring 2011
Page 540
Also see Ashcroft & Mermin, Solid State Physics
V.M. Ayres, ECE474, Spring 2011
SiO2
Si
Doped polySi
Cu Cu
n n
V.M. Ayres, ECE474, Spring 2011
n nSi
Cu Cu
Cufcca =3.61 Ang
SiDiamonda = 5.43 Ang
Lattice mis-match at interface
V.M. Ayres, ECE474, Spring 2011
Can get lattice matching between semiconductors by using a ternary or a quaternary:
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