lecture 1 crystal lattice eee 313 summer 2015
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What is a Semiconductor?Low resistivity => “conductor”High resistivity => “insulator”
Intermediate resistivity => “semiconductor”conductivity lies between that of conductors and
insulatorsgenerally crystalline in structure for IC devices
In recent years, however, non-crystalline semiconductors have become commercially very important
polycrystalline amorphous crystalline
From Hydrogen to Silicon
11s 2s 2p 3s 3p 3d
1 H 1 1s1
2 He 2 1s2
3 Li 2 1 1s2 2s1
4 Be 2 2 1s2 2s2
5 B 2 2 1 1s2 2s2 2p1
6 C 2 2 2 1s2 2s2 2p2
7 N 2 2 3 1s2 2s2 2p3
8 O 2 2 4 1s2 2s2 2p4
9 F 2 2 5 1s2 2s2 2p5
10 Ne 2 2 6 1s2 2s2 2p6
11 Na 2 2 6 1 1s2 2s2 2p6 3s1
12 Mg 2 2 6 2 1s2 2s2 2p6 3s2
13 Al 2 2 6 2 1 1s2 2s2 2p6 3s2 3p1
14 Si 2 2 6 2 2 1s2 2s2 2p6 3s2 3p2
15 P 2 2 6 2 3 1s2 2s2 2p6 3s2 3p3
16 S 2 2 6 2 4 1s2 2s2 2p6 3s2 3p4
17 Cl 2 2 6 2 5 1s2 2s2 2p6 3s2 3p5
18 Ar 2 2 6 2 6 1s2 2s2 2p6 3s2 3p6
Z Name Notation2 3
# of Electrons
The Silicon Atom14 electrons occupying the 1st 3 energy levels:
1s, 2s, 2p orbitals filled by 10 electrons3s, 3p orbitals filled by 4 electrons
To minimize the overall energy, the 3s and 3p orbitals hybridize to form 4 tetrahedral 3sp orbitals
Each has one electron and is capable of forming a bond
with a neighboring atom
Unit cell concept
The unit cell is a small portion of any given crystal that could be used to reproduce a crystal.
Two different ways of representing a unit cell
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Simple 3D unit cells
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• 2 FCC lattices displaced by ((1/4) a, (1/4) a, (1/4) a) along body diagonal*
• 8 atoms per unit cell• Diamond lattice (also called “zincblende” if interpenetrating
FCC lattices are made of different elements like in GaAs)• Each atom is bonded to 4 other atoms (tetrahedral bonding
structure)
Crystal structure of Si and Ge and other common semiconductors
* The lattice constant or cubic edge is “a”. Generally a is expressed in Angstroms. 1 Å = 10–8 cm = 10–10 m
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Diamond and zincblende lattice unit cells
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Diamond lattice (detail)
The Si Crystal
• Each Si atom has 4 nearest neighbors
• lattice constant = 5.431Å
“diamond cubic” lattice
How Many Silicon Atoms per cm-3?• Number of atoms in a unit cell:
• 4 atoms completely inside cell• Each of the 8 atoms on corners are shared among cells count as 1 atom inside cell• Each of the 6 atoms on the faces are shared among 2 cells count as 3 atoms inside cell Total number inside the cell = 4 + 1 + 3 = 8
• Cell volume:(.543 nm)3 = 1.6 x 10-22 cm3
• Density of silicon atoms = (8 atoms) / (cell volume) = 5 x 1022 atoms/cm3
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What is the density of Si?
Atomic weight of Si = 28.1 i.e. 1 mole (NA = 6.023 x 1023 atoms) of Si has a mass of 28.1 g
323
322
cmg2.33
moleatoms106.02
molegm28.1
cmatoms105
Density
Example
Compound Semiconductors
G a
A s
• “zincblende” structure• III-V compound semiconductors: GaAs, GaP, GaN, etc.
important for optoelectronics and high-speed ICs
Crystallographic NotationMiller Indices: Notation Interpretation
( h k l ) crystal plane{ h k l } equivalent planes[ h k l ] crystal direction< h k l > equivalent directions
h: inverse x-intercept of planek: inverse y-intercept of planel: 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 Planes and Si Wafers
Silicon wafers are usually cut along a {100} plane with a flat or notch to orient the wafer during IC fabrication:
Crystallographic Planes in SiUnit cell:
View in <100> direction View in <110> direction
View in <111> direction
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