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