Still Another Semiconductor Definition!

1. Still Another Semiconductor Definition!

2. Clathrate SemiconductorsNot in the Texts! • A research interestfor me for about the last 12 years! “New” crystalline phasesof the Group IV Elements: Si, Ge, Sn(not Cyet). • 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 & contrastedto the diamond structure. More properties as class proceeds.

3. 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] 

4. Group IV Crystals • Si, Ge, Sn:Their ground state crystal structure is the Diamond Structure • Each atom tetrahedrally (4-fold) coordinated (4 nearest-neighbors) withsp3 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 plane) The Ground State(lowest energy configuration) is graphiteat zero temperature & atmospheric pressure. The graphite-diamond energy difference is VERY small!

6. OtherGroup IV Crystal Structures(Higher Energy) • C:“Buckyballs” (C60)   “Buckytubes”(nanotubes), other fullerenes  Graphene 

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

8. 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 insp3 bonding configurations. • Bond angles:Distorted tetrahedra Distribution of angles instead of the perfect tetrahedral 109.5º • Lattice contains hexagonal & pentagonal rings, fused together with sp3bonds to form large “cages”.

9. 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. 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 clathratusmeaning 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. 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 IClathrates) 20atom (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 IIClathrates) 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.

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. 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 NaSicompound. • An ionic compound containing Na+ and (Si4)-4 ions • Heat to thermally decompose. Some Na vacuum. Siatoms reform into a clathrate framework around Na. • Cages contain Naguests

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

17. 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 sp3bonds • 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. 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 ).