1. Still Another Semiconductor Definition!

2. Clathrate Semiconductors
A research interest for me for more than a decade!
“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 thermoelectric materials).
Clathrate Crystal Structures
will be discussed briefly now & contrasted to the diamond structure.

3. [n = 2, C; n = 3, Si; n = 4, Ge; n = 5, Sn]
Group IV Elements  
The valence electron configurations of the free atoms:
ns2 np2
[n = 2, C; n = 3, Si; n = 4, Ge; n = 5, Sn]

4. Group IV Crystals Diamond Structure
Si, Ge, Sn: Their ground state crystal structure is the
Diamond Structure
Each atom is tetrahedrally (4-fold) coordinated (4 nearest-neighbors) with sp3 covalent bonding
Bond angles: Perfect, tetrahedral = 109.5º
Si, Ge: Semiconductors
Sn: (α-tin or gray tin) - Semimetal

5. Carbon Crystals C: Graphite & Diamond Structures Diamond 
An insulator or a wide
bandgap semiconductor
Graphite 
A planar structure
sp2 bonding  a 2d
metal (in the plane)
The Ground State (lowest energy configuration) is graphite at zero temperature & atmospheric pressure. The first principles graphite-diamond energy difference VERY small!

6. Other Group IV Crystal Structures (Higher Energy)
C: “Buckyballs” (C60)  
“Buckytubes” (nanotubes)
& other Fullerenes
Graphene 

7. Si, Ge, Sn: The Clathrates.
Sn: (β-tin or white tin) - body centered tetragonal lattice, 2 atoms per unit cell.
Metallic.
Si, Ge, Sn: The Clathrates.

8. The 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 4-fold 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”.

9. “Buckyball-like” cages of 20, 24, & 28 atoms.
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

10. The 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.”

11. Type I clathrate-hydrate crystal structure X8(H2O)46:
Group IV clathrates have the same crystal structure as clathrate-hydrates (ice).
Type I clathrate-hydrate crystal structure X8(H2O)46:

12. 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)
28 atom (hexakaidecahedron) cages,
Face Centered Cubic, 136 atoms per cubic unit cell.

13. Clathrate Building Blocks
24 atom cage:
Type I Clathrate
Si46, Ge46, Sn46
(C46?)
Simple Cubic 
20 atom cage:
Type II Clathrate
Si136, Ge136, Sn136
(C136?)
Face Centered Cubic 
28 atom cage:

14. Clathrate Lattices Type I Clathrate  Si46, Ge46, Sn46 simple cubic
[100]
direction
Type II Clathrate 
Si136, Ge136, Sn136
face centered
cubic
[100]
direction

15. Synthesis: NaxSi46 (A theorists view!)
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

16. Type I Clathrate (with guest “rattlers”)
20 atom cage
with a guest atom 
[100]
direction +
24 atom cage
with a guest atom 
[010]
direction

17. Guest Modes  Rattler Modes
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

18. Good thermoelectrics should have Clathrates of Interest:
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 ).