Still Another Semiconductor Definition!
Clathrate Semiconductors
Not in the Texts!
• A research interest for me for about the last 12 years!
“New” crystalline phases of the
Group IV Elements:
Si, Ge, Sn (not C yet).
• Few pure elemental phases yet. Mostly compounds,
usually with Groups I & II elements (Na, K, Cs, Ba).
• Interesting properties (possible applications are for use
as a thermoelectric material).
Clathrate Crystal Structures
will be discussed briefly now & contrasted to the
diamond structure. More properties as class proceeds.
Group IV Elements


• The valence electron configurations of the free atoms are:
ns2 np2
[n = 2, C; n = 3, Si; n = 4, Ge; n = 5, Sn]
Group IV Crystals
• Si, Ge, Sn: Their ground state crystal structure is the
Diamond Structure
• Each atom tetrahedrally (4-fold) coordinated (4 nearestneighbors) with sp3 covalent bonding
• Bond angles: Perfect, tetrahedral = 109.5º
• Si, Ge: Semiconductors
• Sn: (α-tin or gray tin) - Semimetal
Carbon Crystals
• C: Graphite & Diamond Structures
Diamond 
An insulator or a wide
bandgap semiconductor
Graphite 
A planar structure
sp2 bonding
 a 2d metal (in plane)
The Ground State (lowest energy configuration) is
graphite at zero temperature & atmospheric pressure.
The graphite-diamond energy difference is VERY small!
Other Group IV Crystal Structures
(Higher Energy)
• C: “Buckyballs” (C60) 

“Buckytubes” (nanotubes),
other fullerenes

Graphene 
• Sn: (β-tin or white tin) - body centered
tetragonal lattice, 2 atoms per unit cell.
Metallic.
• Si, Ge, Sn: The Clathrates.
Clathrates
• Crystalline Phases of Group IV elements: Si,
Ge, Sn (not C yet!) “New” materials, but known (for
Si) since 1965!
– J. Kasper, P. Hagenmuller, M. Pouchard, C. Cros,
Science 150, 1713 (1965)
• As in the diamond structure, all Group IV atoms are 4fold coordinated in sp3 bonding configurations.
• Bond angles: Distorted tetrahedra  Distribution of
angles instead of the perfect tetrahedral 109.5º
• Lattice contains hexagonal & pentagonal rings, fused
together with sp3 bonds to form large “cages”.
• Pure materials: Metastable, expanded volume
phases of Si, Ge, Sn
• Few pure elemental phases yet. Compounds with
Group I & II atoms (Na, K, Cs, Ba).
• Potential applications: Thermoelectrics
• Open, cage-like structures, with large “cages” of
Si, Ge, or Sn atoms.
“Buckyball-like” cages of 20, 24, & 28 atoms.
• Many varieties. The two most common varieties are:
Type I (X46) & Type II (X136)
X = Si, Ge, or Sn
Meaning of “Clathrate” ?
• From Wikipedia, the free encyclopedia:
“A clathrate or clathrate compound or cage compound is a
chemical substance consisting of a lattice of one type of molecule
trapping and containing a second type of molecule. The word
comes from the Latin clathratus meaning furnished with a lattice.”
“For example, a clathrate-hydrate involves a special type of gas
hydrate consisting of water molecules enclosing a trapped gas.
A clathrate thus is a material which is a weak composite, with
molecules of suitable size captured in spaces which are left by
the other compounds. They are also called host-guest
complexes, inclusion compounds, and adducts.”
• Group IV clathrates have the same crystal
structure as clathrate-hydrates (ice).
Type I clathrate-hydrate crystal structure X8(H2O)46:
• Si46, Ge46, Sn46: ( Type I Clathrates)
20 atom (dodecahedron) cages &
24 atom (tetrakaidecahedron) cages,
fused together through 5 atom
rings. Crystal structure =
Simple Cubic, 46 atoms per cubic unit cell.
• Si136, Ge136, Sn136: ( Type II Clathrates)
20 atom (dodecahedron) cages &
28 atom (hexakaidecahedron) cages,
fused together through 5 atom
rings. Crystal structure =
Face Centered Cubic, 136 atoms per cubic unit cell.
Clathrate Building Blocks
24 atom cage:
Type I Clathrate

Si46, Ge46, Sn46
(C46?)
Simple Cubic
20 atom cage:

28 atom cage:
Type II Clathrate
Si136, Ge136, Sn136
(C136?)
Face Centered
Cubic
Clathrate Lattices
Type I Clathrate 
Si46, Ge46, Sn46
simple cubic
[100]
direction
Type II Clathrate 
Si136, Ge136, Sn136
face centered
[100]
cubic
direction
Group IV Clathrates
• Not found in nature. Synthesized in the lab.
• Not normally in pure form, but with impurities
(“guests”) encapsulated inside the cages.
Guests  “Rattlers”
• Guests: Group I (alkali) atoms (Li, Na, K, Cs, Rb) or
Group II (alkaline earth) atoms (Be, Mg, Ca, Sr, Ba)
• Synthesis: NaxSi46 (A theorists view!)
– Start with a Zintl phase NaSi compound.
– An ionic compound containing Na+ and (Si4)-4 ions
– Heat to thermally decompose. Some Na  vacuum.
Si atoms reform into a clathrate framework around Na.
– Cages contain Na guests
Type I Clathrate
(with guest “rattlers”)
20 atom cage
with a guest atom 
[100]
direction
+
24 atom cage
with a guest atom 
[010]
direction
Pure Materials: Semiconductors.
• Guest-containing materials:
– Some are superconducting materials (Ba8Si46) from
sp3 bonded, Group IV atoms!
– Guests are weakly bonded in cages:
 A minimal effect on electronic transport
– Host valence electrons taken up in sp3 bonds
– Guest valence electrons go to conduction band of
host ( heavy doping density).
– Guests vibrate with low frequency (“rattler”) modes
 A strong effect on vibrational properties =
Guest Modes  Rattler Modes
• Possible use as thermoelectric materials.
Good thermoelectrics should have
low thermal conductivity!
Guest Modes  Rattler Modes:
A focus of recent experiments.
• Heat transport theory says: The low frequency rattler
modes can scatter efficiently with the acoustic modes of the host.
The guest vibrations lower the thermal conductivity
 A good thermoelectric!
Clathrates of Interest:
Sn (mainly Type I). Si & Ge, (mainly Type II).
Recently, “Alloys” of Ge & Si (Type I ).