20 Semiconductor Nanoparticle
Prof. Subhasis Ghosh
In semiconductors we are interested in the valence band and conduction band. Moreover, for most applications we are interested in what happens near the top of the valence band and the bottom of the conduction band. These states originate from the atomic levels of the valence shell in the elements making up the semiconductor.
IV Semiconductors
C 1s2 2s2 2p2
Si 1s2 2s2 2p6 3s2 3p2
Ge 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p2
III-V Semiconductors
Ga 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p1
In 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 5p1
As 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p3
P 1s2 2s2 2p6 3s2 3p3
II-VI Semiconductors
Cd 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2
Zn 1s2 2s2 2p6 3s2 3p6 3d10 4s2
S 1s2 2s2 2p6 3s2 3p4
Se 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p4
Te 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 5p4
Band structure: CdSe
The dash line represents the Fermi level (EF) at – 4.0427 eV, LCB and HVB are the lowest conduction and the highest valence bands, respectively. The band structure of hexagonal CdSe (c), Z(001), M(110) are the Brillouin-zone boundary points.
CdSe band structure along major direction (ΓZ lines in Brillouin zone) is corresponding band dispersion (along ΓM and ΓZ direction).
(a) The Brillouin zone for 3D zinc-blende structure and its 2D projection. (b) Comparison of the band structures of CdSe NP (black lines) and bulk CdSe (red lines).
Parameter | CdSe |
Spin orbit splitting (eV) | 0.39 |
Lattice constant (nm) | 0.61 |
me (m0) | 0.18 |
mhh (m0) | 0.89 |
Band Structure: Silicon
Although the band structure of Si is far from ideal, having an indirect band gap, hig hole masses, and small spin-orbit splitting, processing related advantages make Si the premier semiconductor for consumer electronics. On the right we show constant energy ellipsoids for Si conduction band. There are six equivalent valleys in Si at the band edge.
Indirect gap material weak optical transitions, can’t be used to produce lasers.
Band Structure: GaAs
The bandgap at 0K is 1.51 eV and at 300 K it is 1.43 eV. The bottom of the conduction band is at k = (0, 0, 0), i.e., the G-point. The upper conduction band valleys are at the L-point.
Conduction band:
– Electron mass is light. m* = 0.067 m0
– Upper valley mass is large. m* = 0.25 m0 results in negative differential resistance at higher fields.
– Material is direct bandgap and has strong optical transitions can be used for light emission
Valence band:
- Heavy hole mass: 0.45 m0; light hole mass = 0.08 m0.
- Intrinsic carrier concentration at 300 = 1.84 x 106 cm-3.
Band Structure: Ge, AlAs, InAs, InP
Bandstructure of Ge. Bandstructure of AlAs. Bandstructure of InAs. Since no adequate substitute matches InAs directly, it is often used as an alloy (InGaAs, InAlAs, etc.,) for devices. Bandstructure of InP. InP is a very important material for high speed devices as well as a substrate and barrier layer material for semiconductor lasers.
Electronic properties of some semiconductors
Material | Band gap (eV) | Relative dielectric constant ( r) |
C | 5.5, I | 5.57 |
Si | 1.124, I | 11.9 |
Ge | 0.664, I | 16.2 |
SiC | 2.416, I | 9.72 |
GaAs | 1.424, D | 13.18 |
AlAs | 2.153, I | 10.06 |
InAs | 0.354, D | 15.15 |
GaP | 2.272, I | 11.11 |
InP | 1.344, D | 12.56 |
InSb | 0.230, D | 16.8 |
CdTe | 1.475, D | 10.2 |
AlN | 6.2 D | 9.14 |
GaN | 3.44, D | 10.0 |
ZnSe | 2.822, D | 9.1 |
ZnTe | 2.394, D | 8.7 |
Material | Electron mass (m0) | Hole mass (m0) |
AlAs | 0.1 | |
InSb | 0.12 | ∗ = 0.98 |
GaN | 0.19 | ∗ = 0.60 |
GaP | 0.82 | ∗ = 0.60 |
GaAs | 0.067 | ℎ∗ = 0.082, ℎℎ∗ = 0.45 |
GaSb | 0.042 | ∗ = 0.40 |
Ge | = 1.64, = 0.08,= 0.56 | ℎ∗ = 0.044, ℎℎ∗ = 0.28 |
InP | 0.073 | ∗ = 0.64 |
InAs | 0.027 | ∗ = 0.4 |
InSb | 0.13 | ∗ = 0.4 |
Si | = 0.98, = 0.19,= 1.08 | ℎ∗ = 0.98, ℎℎ∗ = 0.98 |
Properties of some semiconductors are illustrated above. D and I stand for direct and indirect gap, respectively. The data are at 300 K. Note that ‘Si’ has six conduction band valleys, while ‘Ge’ has four.
Some Important properties of Si and GaAs
Zinc Blende and Wurtzite
Bandgap (in eV) of some semiconductors
Tetrahedrally bonded materials
NonTetrahedral bonded materials
Symbol stands for
i: Indirect gap, D: Diamond Z: Zinc Blende W: Wurtzite R: Rocksalt O: Orthorhombic Rh: Rhombohedral T:
Trigonal OR: Orthorhombic distorted rocksalt M: Monoclinic
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