E84 Lecture 3/26/14
K. Candler
Agenda
o Semiconductor Materials
o Crystal Growth
o Intrinsic Semiconductors
o Extrinsic Semiconductors
Introduction
– A semiconductor is a material that has electrical conductivity to a degree that is
between that of a conductor (such as copper, silver, gold) and an insulator (such as
glass).
–
Semiconductors are the foundation of modern electronics, e.g.,
o Transistors
o Solar cells
o Light-emitting diodes (LEDs)
o Photodiodes
o Digital and analog ICs
Semiconductor Materials
– Si, Ge, GaAs, SiC
– The bonding model:
(Figure from Pierret, Semiconductor Device Fundamentals, Addison Wesley)
o 4 valence electrons
o Covalent bonds
o Si is a very poor conductor at room temperature…no free electrons
–
Purity
o Purity of semiconductors needs to be very carefully controlled.
o Modern semiconductors are some of the purist solid materials that exist. In
silicon: Unintentional dopant atoms < 1 per 109 Si atoms (like finding 25
apple trees in a forest of pine trees planted coast to coast at 50 ft centers across
the U.S.)
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–
Structure
Amorphous
Polycrystalline
Crystalline
(Figure from Pierret, Semiconductor Device Fundamentals, Addison Wesley)
o Amorphous: No recognizable long-range order
o Polycrystalline: Completely ordered in segments
o Crystalline: Entire solid is made up of atoms in orderly array
Crystal Growth
– Obtaining Ultrapure Polycrystalline Si
(Figure from Pierret, Semiconductor Device Fundamentals, Addison Wesley)
–
Obtaining Single-Crystal Si
o Invented in 1916 by a Polish scientist, Jan Czochralski
o A seed crystal is dipped into a crucible of molten silicon and withdrawn
slowly, pulling a cylindrical single crystal as the silicon crystallizes on the
seed.
o Show video (up to 4 min mark):
http://www.youtube.com/watch?v=aWVywhzuHnQ
Intrinsic Semiconductors
– No impurities and lattice defects in its crystal structure
– If an electron gains enough energy (from thermal or optical excitation), it can break
the covalent bond and become a free carrier.
o E > Eg ; Eg = bandgap energy (the energy needed for an electron to break a
bond)
 Eg = 1.12 eV (Si)
 Eg = 1.42 eV (GaAs)
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

–
Eg = 0.66 eV (Ge)
Eg (metal) << Eg (semiconductor) << Eg (insulator)
When a bond is broken, two mobile charge carriers are created: electrons (negative
charge) and holes (positive charge)
(Figure from Howe & Sodini, Microelectronics, Prentice Hall)
–
–
–
–
no = po ≡ ni (at thermal equilibrium)
o no = electron concentration at thermal equilibrium [cm-3]
o po = hole concentration at thermal equilibrium [cm-3]
o ni = intrinsic carrier concentration (ni = 1.5 x 1010 cm-3 in Si at T = 300 K)
Exercise: How many bonds are broken in Si at room temperature? (Hint: silicon atom
density = 5 x 1022 Si atoms/cm3)
o Total possible bonds = 5 x 1022 Si atoms/cm-3 x 4 bonds/atom = 2 x 1023
bonds/cm-3
o # broken bonds at room temp = ni = 1.5 x 1010 cm-3
o # broken bonds/total possible bonds = 1.5 x 1010/2 x 1023 ~ 0.7 x 10-13  less
than one bond in 1013 is broken in Si at room temperature!
Main point: At room temperature, relatively few electrons gain enough energy to
become free electrons, the overall conductivity of semiconductors is low, thereby
their name semiconductors.
Increasing temperature leads to better or worse conductivity?
Extrinsic Semiconductors
– Contain impurity atoms, which contribute extra electrons and holes (improve
conductivity)
– Impurities are introduced through doping.
– Dopants are Group III (B, Ga, In, Al) or V (P, As, Sb).
– Doping with Group V Elements (Donors)
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(Figure from Pierret, Semiconductor Device Fundamentals, Addison Wesley)



–
Extra electrons: N-type semiconductor
Majority carrier: electron
Minority carrier: hole
Doping with Group III Elements (Acceptors):
(Figure from Pierret, Semiconductor Device Fundamentals, Addison Wesley)



–
Extra holes: P-type semiconductor
Majority carrier: hole
Minority carrier: electron
How to calculate # electrons and holes (mobile carriers) in doped Si?
o Mass Action Law:
n o ⋅ po = n i
2
o rate of electron-hole pair generation = rate of recombination  no
charge buildup inside Si in thermal equilibrium (no heat flow)
o N-type case
no ≅ N d
po =
ni2
no
(one electron per donor)
=
ni2
Nd
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o P-type case
(one hole per donor)
po ≅ N a
no =
ni2
po
=
ni2
Na
o Example: A silicon sample is doped with 1017 As atoms per cm3. What are
the carrier concentrations in the Si sample at 300 K?
As is n-type, Nd = 1017 cm-3
- no = Nd = 1017 cm-3
- po = ni2/ no = 1020/1017 = 103 cm-3
o Main point: The majority carriers outnumber the minority carriers by many
orders of magnitude!
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