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.

[n = 2, C; n = 3, Si; n = 4, Ge; n = 5, Sn] 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 Diamond Structure Si, Ge, Sn: Their ground state crystal structure is the Diamond Structure Each atom 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

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 

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.

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”.

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.”

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:

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.

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:

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

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

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

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

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 ).