程序代写 Semiconductor Fundamentals

Semiconductor Fundamentals
https://www.xjtlu.edu.cn/en/departments/academic-departments/electrical-and-electronic-engineering/staff/chun-zhao

Last Lecture: 3 key points

1. Moores’ Law
2. Technology Node Definition 3. Yield Definition
1. Moores’ Law:
The number of transistors on a chip doubled every 18 to 24 months.

2. Technology Node Definition
⚫ Images courtesy of . Used without permission.
“D” represents IC technology level. The names of “D”, nowadays:
“D technology”, or
“Generation D”, or “D node” 3

ITRS: http://www.itrs.net/home.html
⚫ The Roadmap for
International Semiconductors,
Technology
known throughout the world as the ITRS, is the fifteen-year assessment of the semiconductor industry’s future technology requirements.

ITRS Technology Node Definitions
Individual roadmaps are defined for high-performance, low-power, etc.
2D = 14nm For 7nm Technology
2D = 14nm For 7nm Technology

Y = Die yield =
No. of good chips per wafer 100% Total number of chips per wafer
Wafer cost
Dies per waferDie yield
Die cost =
⚫ in Fig.1, the yield is 50% and the die cost is £250 (If
this wafer costs £500).
Technology node
Die = Chip
this wafer costs £500).
⚫ In Fig.2, the yield is 87% and the chip cost is £36 (If
Fig.1 Fig.2

Chapter 2 Outline
Semiconductor Fundamentals-(I)
2.1 Atomic structures 2.2 Crystal structures
Semiconductor Fundamentals-(II)
2.3 Energy bands
2.4 The doping of semiconductors
Semiconductor Fundamentals-(III)
2.5 Boltzmann approximation & EF, n, p 2.6 Carrier drift and diffusion

Semiconductor Fundamentals – (I)
2.1 Atomic structures 2.2 Crystal structures

2.1 Atomic Structures
⚫ Elements
⚫ Bohr’stheory–orbits
⚫ Distributionofelectrons ➢ Valence electrons
➢ Ionised bond
➢ Covalent bond

Element Periodic Table

Semiconductor Materials
Gallium (Ga)
Phosphorus (P)
Antimony (Sb)

Semiconductor Materials
Elemental: Compound:

2.1 Atomic Structures
⚫ Elements
⚫ Bohr’stheory–orbits
⚫ Distributionofelectrons ➢ Valence electrons
➢ Ionised bond
➢ Covalent bond

Bohr’s Theory – Orbits
The electrons of an atom can only stay on a number of orbits. The radius of orbits changes discontinuously.
For example, hydrogen atom, 0.05nm
The orbit with smaller radius has lower energy.

• Electrons reside in stable configurations (orbits, orbitals)
• These orbitals are numbered (in order of increasing energy): 1s
2s 2p 3s 3p 3d 4s 4p 4d 4f …
• “s” levels: two electron states
• Each “p” level is 3 fold degenerate: six electron states
• Historical: “s” was chosen because the optical emission related
to transitions for these levels gives “sharp” lines (similarly: “principal”, “diffuse” etc.)
http://winter.group.shef.ac.uk/orbitron/
n=1: 1s n=2: 2s, 2p
n=3: 3s, 3p, 3d
n=4 n=4: 4s, 4p, 4d, 4f

2.1 Atomic Structures
⚫ Elements
⚫ Bohr’stheory–orbits
⚫ Distributionofelectrons ➢ Valence electrons
➢ Ionised bond
➢ Covalent bond

Distribution of electrons in atoms
Maximum number of electrons in an orbit is fixed
1st orbit: 2 (1s)
2nd orbit: 8 (2s, 2p) (3rd orbit: 3s, 3p, 3d)
Orbit with lowest energy is filled first, since the lower energy, the more stable.
The orbit with smaller radius has lower energy.
Electrons in the outmost orbit: ‘valence electrons’. Property of atoms depends on valence electrons
Valence Valence
-13.6eV -3.4eV -1.51eV

From Hydrogen to Silicon
# of Electrons
1s2 2s2 2p1
1s2 2s2 2p2
1s2 2s2 2p3
1s2 2s2 2p4
1s2 2s2 2p5
1s2 2s2 2p6
1s2 2s2 2p6 3s1
1s2 2s2 2p6 3s2
1s2 2s2 2p6 3s2 3p1
n=3: 3s, 3p, 3d
1s2 2s2 2p6 3s2 3p2
1s2 2s2 2p6 3s2 3p3
1s2 2s2 2p6 3s2 3p4
1s2 2s2 2p6 3s2 3p5
1s2 2s2 2p6 3s2 3p6

Valence Electrons of B, Si & Sb
⚫ The electrons in the outermost shell of an atom are called valence electrons; they dictate the nature of chemical reactions of atom and largely determine the electrical nature of solid matter.

Valence Electrons of Si & Ge
Solid state electronics arises from the unique properties of silicon and germanium, each of which has 4 valence electrons and which form crystal lattices.

2.1 Atomic Structures
⚫ Elements
⚫ Bohr’stheory–orbits
⚫ Distributionofelectrons ➢ Valence electrons
➢ Ionised bond
➢ Covalent bond

⚫ An unstable atom can achieve a quasi-stable
structure by bonding with other atoms.
⚫ Ionized bonds:
The atoms are ionized first and then bonded through electrostatic force.
Na1+Cl7 Na Cl8
outmost orbit 8 electrons: stable situation

Covalent bonds
⚫ Valence electrons are shared
⚫ Notation of a covalent bond (can’t be “seen”) Si Si Si Si Si Si
⚫ Si shares its 4 valence electrons with 4 other Si atoms by forming covalent bonds.
→Si Si Si →

Covalent bonds
⚫ The bonds are of equal length and angular separation to produce a crystal structure.

2.2 Crystal Structures
⚫ General material properties
⚫ Crystal structures
⚫ Crystallographic notation
⚫ Bohr’s theory – energy level & band 26

Material Properties
Generally crystalline in structure for IC devices
▪ In recent years, however, non-crystalline semiconductors have become commercially very important
polycrystalline amorphous crystalline

Material Properties: Example Transmission Electron Microscope
Amorphous Materials
Single-Crystal Material 28

2.2 Crystal Structures
⚫ General material properties
⚫ Crystal structures
⚫ Crystallographic notation
⚫ Bohr’s theory – energy level & band 29

Crystal : Atoms + Lattice
Si Crystal

Lattice and Crystal
A crystal can be thought of as being like wallpaper. The motif is analogous to the basis and the arrangement of the motif over the surface is like the lattice.

The Si Crystal: Unit Cell
Each Si atom has 4 nearest neighbors
Lattice Constant
= 5.431 Å
= 0.5431 nm
“diamond cubic” lattice

Silicon crystal structure
Silicon is a crystalline material: – long range atomic arrangement
Diamond lattice: – atoms tetrahedrally bonded by sharing valence electrons (covalent bonding)
Each atom shares 8 electrons: – low energy and stable situation Si atomic density: 5 ×1022 cm-3
#Atoms = 81/8+61/2+4 = 8 =51022cm−3 Volume a03 (5.4310−8 cm)3

Silicon crystal structure: Summary
⚫ Silicon atoms form covalent bonds and can
crystallize into a regular lattice.
⚫ Silicon atom has 4 electrons which it can
share in covalent bonds with its neighbors.
⚫ Silicon crystallizes in the same pattern as
⚫ Bold lines between silicon atoms in the lattice
illustration indicate nearest-neighbor bonds.

Compound Semiconductors
• “Zinc Blende” structure
Simply the diamond structure in which the species of atoms alternate
• III-V compound semiconductors: GaAs, GaP, GaN, etc. ✓ important for optoelectronics and high-speed ICs

2.2 Crystal Structures
⚫ General material properties
⚫ Crystal structures
⚫ Crystallographic notation
⚫ Bohr’s theory – energy level & band 36

Crystallographic Notation
⚫ Miller indices are a notation system in crystallography for
planes and directions in crystal lattices.
Miller Indices: (100)
Miller Indices: (110) Miller Indices: (111) 37

Crystallographic Notation: Directions Miller Indices:
Interpretation
crystal plane
equivalent planes
crystal direction
equivalent directions
h: inverse x-intercept of plane
k: inverse y-intercept of plane
l: inverse z-intercept of plane (Intercept values are in multiples of the lattice constant;
h, k and l are reduced to 3 integers having the same ratio.)

Crystallographic Notation: Planes Miller Indices:
Assignment:
Intercepts: 1⁄2 a , a , ∞ Fractional intercepts: 1⁄2 ,1,∞ Miller Indices: (210)
h: inverse x-intercept of plane k: inverse y-intercept of plane l: inverse z-intercept of plane
(Intercept values are in multiples of the lattice constant;
h, k and l are reduced/enlarged to 3 integers having the same ratio.)
Interpretation
crystal plane
equivalent planes
crystal direction
equivalent directions

Crystallographic Notation: Planes HW-2
Interpretation
crystal plane
equivalent planes
crystal direction
equivalent directions
h: inverse x-intercept of plane k: inverse y-intercept of plane l: inverse z-intercept of plane
Why the Miller indices of this plane is (010)?

2.2 Crystal Structures
⚫ General material properties ⚫ Crystal structures
⚫ Crystallographic notation
⚫ Bohr’s theory – energy level & band 41

Bohr’s Theory
⚫ The electrons of an atom can only stay on a number of orbits. The radius of orbits changes discontinuously.
⚫ For example, hydrogen atom,

The Bohr model
Energy levels and possible electronic transitions in a hydrogen atom. Shown are the first six energy levels, as well as three possible transitions involving the lowest energy level (n = 1)
Outmost Orbit

Energy Bands
⚫ Energy level of an isolated atom
⚫ In solids, atoms interact with each other
⚫ The orbits of electrons will be altered by interaction, which leads to splitting in energy level.
No splitting
2 isolated
If not close enough, no interacting 44

Si: From Atom to Crystal ..
N isolated
Interacting

Si: From Atom to Crystal 2 e for each Si
2 e for each Si
Energy levels in Si atom→energy bands in Si crystal
⚫ The highest nearly-filled band is the valence band
⚫ The lowest nearly-empty band is the conduction band

Formation of Energy Bands
Many atom interactions form energy bands.
Valence band: where valence electrons stay
Conduction band: where free electrons stay
Eg: The minimum energy required to free an electron from an atom.
Eg  0 for metals (Conductors)
Eg = 1.12eV for Si (Semiconductors) > 4eV for Insulators
Conduction band
Valence band
Allowed Bands
Forbidden gap

Energy Band Diagram
Simplified version of energy band model, indicating
⚫ bottom edge of the conduction band (Ec)
⚫ top edge of the valence band (Ev)
➢ Ec and Ev are separated by the band gap energy Eg 50
electron energy

Summary of Section 2.1 & 2.2 ⚫ CrystallineSi:
4 valence electrons per atom Diamond lattice
▪ each atom has 4 nearest neighbors 5 x 1022 atoms/cm3
⚫ Crystallographicnotation
➢ Miller indices are used to designate planes and directions within a crystalline lattice
⚫ Ec,EvandEg

Semiconductor Fundamentals-(I)
2.1 Atomic structures 2.2 Crystal structures
Semiconductor Fundamentals
2.3 Energy bands
2.4 The doping of semiconductors
Semiconductor Fundamentals-(III)
2.5 Boltzmann approximation & EF, n, p 2.6 Carrier drift and diffusion

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