Still Another Semiconductor Definition!

Clathrate SemiconductorsNot in the Texts!

• A research interest for me for about the last 12 years!

“New” crystalline phases of theGroup 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 Structureswill 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 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

• 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.”

• 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 ClathrateSi46, Ge46, Sn46

(C46?)Simple Cubic

Type II ClathrateSi136, Ge136, Sn136

(C136?)Face Centered

Cubic

20 atom cage:

28 atom cage:

Clathrate Lattices

Type I Clathrate Si46, Ge46, Sn46

simple cubic

Type II Clathrate Si136, Ge136, Sn136

face centered cubic

[100]direction

[100]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

+

24 atom cagewith a guest atom

[100]direction

[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 havelow thermal conductivity!

Guest Modes Rattler Modes: A focus of recent experiments.

• Heat transport theory says: The low frequency rattlermodes 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 ).