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