Conventional Semiconductor's Material Values

Material	Crystal Structure	Space Group	Point Group	Bandgap Type	Bandgap $E_g$ (eV, 300 K)	Electron affinity $\chi$ (eV)	Work function $\varphi$ (eV, intrinsic)	Relative permittivity ${\epsilon }_r$ (static)	Electron eff. mass $m_n^{\ast }/m_0$	Hole eff. mass $m_p^{\ast }/m_0$	Lattice constant $a$ (Å)
Si	Diamond cubic	$Fd\bar{3}m$ (No. 227)	$m\bar{3}m(O_h)$	Indirect	$1.12$	$4.05$	$\approx 4.6$	$11.7$	$1.08$	$0.81$	$5.431$
Ge	Diamond cubic	$Fd\bar{3}m$ (No. 227)	$m\bar{3}m(O_h)$	Indirect	$0.66$	$4.00$	$\approx 4.5$	$16.2$	$0.55$	$0.37$	$5.658$
C (diamond)	Diamond cubic	$Fd\bar{3}m$ (No. 227)	$m\bar{3}m(O_h)$	Indirect	$5.47$	$\approx 0.5$	$\approx 3.2$	$5.70$	$\approx 0.57$	$\approx 0.7$	$3.567$
GaAs	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Direct	$1.42$	$4.07$	$\approx 4.7$	$12.9$	$0.063$	$0.53$	$5.653$
GaP	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Indirect	$2.26$	$\approx 4.3$	$\approx 5.3$	$11.1$	$\approx 0.79$	$\approx 0.60$	$5.451$
GaSb	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Direct	$0.72$	$4.06$	$\approx 4.4$	$15.7$	$0.039$	$\approx 0.40$	$6.096$
InP	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Direct	$1.35$	$4.38$	$\approx 5.0$	$12.5$	$0.080$	$0.60$	$5.869$
InAs	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Direct	$0.36$	$4.90$	$\approx 5.1$	$15.15$	$0.023$	$\approx 0.41$	$6.058$
InSb	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Direct	$0.17$	$4.59$	$\approx 4.7$	$16.8$	$0.014$	$\approx 0.43$	$6.479$
AlAs	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Indirect	$2.16$	$\approx 3.5$	$\approx 4.6$	$10.06$	$\approx 0.5$	$\approx 0.51$	$5.661$
AlSb	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Indirect	$1.62$	$\approx 3.65$	$\approx 4.5$	$12.04$	$\approx 0.14$	$\approx 0.98$	$6.136$
GaN, wurtzite (direct)	Wurtzite	$P{6}_{3}mc$ (No. 186)	$6mm(C_{6v})$	Direct	$3.44$	$\approx 4.1$	$\approx 5.8$	$\approx 8.9$	$0.20$	$\approx 1.5$	$a=3.189,c=5.185$
AlN, wurtzite (direct)	Wurtzite	$P{6}_{3}mc$ (No. 186)	$6mm(C_{6v})$	Direct	$6.2$	$\approx 2.0$	$\approx 5.0$	$\approx 8.5$	$\approx 0.40$	$\approx 3\text{–}4$	$a=3.112,c=4.982$
InN	Wurtzite	$P{6}_{3}mc$ (No. 186)	$6mm(C_{6v})$	Direct	$0.7$	$\approx 5.8$	$\approx 6.2$	$\approx 15.3$	$\approx 0.07$	$\approx 1.63$	$a=3.545,c=5.703$
3C-SiC	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Indirect	$2.36$	$\approx 3.6$	$\approx 4.8$	$9.72$	$\approx 0.25$	$\approx 1.0$	$4.3596$
4H-SiC (indirect, $\perp c$)	Hexagonal (4H polytype)	$P{6}_{3}mc$ (No. 186)	$6mm(C_{6v})$	Indirect	$3.26$	$\approx 3.17$	$\approx 4.8$	$\approx 9.7$	$\approx 0.29$	$\approx 1.0$	$a=3.073,c=10.053$
ZnSe	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Direct	$2.70$	$\approx 4.09$	$\approx 5.4$	$9.1$	$\approx 0.17$	$\approx 0.6$	$5.668$
ZnS	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Direct	$3.68$	$\approx 3.9$	$\approx 5.7$	$8.9$	$\approx 0.28$	$\approx 0.58$	$5.410$
CdTe	Zinc blende	$F\bar{4}3m$ (No. 216)	$\bar{4}3m(T_d)$	Direct	$1.50$	$\approx 4.28$	$\approx 5.0$	$10.2$	$\approx 0.11$	$\approx 0.35\text{–}0.81$	$6.482$
CdS	Wurtzite	$P{6}_{3}mc$ (No. 186)	$6mm(C_{6v})$	Direct	$2.42$	$\approx 4.5$	$\approx 5.7$	$\approx 8.9$	$\approx 0.21$	$\approx 0.80$	$a=4.136,c=6.714$

Formula Reference

$\varphi =\chi +(E_C-E_F)$

${\varphi }_i\approx \chi +\frac{E_g}{2}+\frac{k_{B}T}{2}\ln \left(\frac{N_C}{N_V}\right)$

Variables: $\varphi$: work function; $\chi$: electron affinity; $E_C-E_F$: energy of the Fermi level below the conduction band edge; ${\varphi }_i$: work function of the intrinsic material, where $E_F$ sits near midgap; the second term is usually small compared to $E_g/2$ unless $N_C$ and $N_V$ differ greatly. For diamond, $\chi$ (and hence $\varphi$) depends strongly on surface termination and is negative for hydrogen-terminated surfaces. Approximate values: hydrogen-terminated $\chi \approx -1.3$ eV (negative electron affinity, ${\varphi }_i\approx 1.4$ eV); clean reconstructed surface $\chi \approx +0.4$ to $+0.5$ eV (${\varphi }_i\approx 3.1$ to $3.2$ eV); oxygen-terminated $\chi \approx +1.7$ eV, up to about $+2.6$ eV for some oxidised or fluorinated surfaces (${\varphi }_i\approx 4.4$ eV and above). The tabulated value is the clean-surface estimate $\chi +E_g/2$ with $\chi \approx 0.5$ eV. Reference: J. Ristein and L. Ley et al., Phys. Rev. Lett. 81, 429 (1998) and F. Maier et al., Phys. Rev. Lett. 85, 3472 (2000).

Important Questions

Ques: Why do the wurtzite materials (GaN, AlN, InN, CdS) and 4H-SiC share the same space group and point group?

$P{6}_{3}mc$ (point group $6mm$, $C_{6v}$) is the space group of the hexagonal wurtzite structure in general, so any compound that crystallizes in that structure type shares it regardless of chemical composition. GaN, AlN, InN, and CdS are all wurtzite compounds, and 4H-SiC is one of many possible close-packed stacking sequences (“polytypes”) of SiC that happens to also produce $P{6}_{3}mc$ symmetry; other SiC polytypes, such as 3C-SiC, crystallize instead as zinc blende ($F\bar{4}3m$). Sharing a space group does not imply the materials share electronic properties — bandgap, effective mass, and permittivity are still set by the specific atoms and bonding, not by symmetry alone. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007; Ioffe Institute NSM Archive, Physical Properties of Semiconductors.

Ques: Why do reported values of electron affinity and permittivity vary so much between sources for the wide-bandgap nitrides (GaN, AlN, InN)?

Unlike Si, Ge, and GaAs, which have been characterized for over 60 years with mature, high-purity bulk crystals, the III-nitrides are typically grown as heteroepitaxial thin films (usually on sapphire, SiC, or Si substrates), so measured properties such as electron affinity, work function, and permittivity are sensitive to strain, surface termination, polarity (Ga-face vs. N-face), and surface reconstruction/contamination in a way that bulk Si is not. InN in particular saw its accepted bandgap revised from roughly 1.9 eV to roughly 0.7 eV in the early 2000s once higher-quality single-crystal films became available, illustrating how much these values have moved as growth technology matured. As a result, the literature reports a real spread of values rather than a single settled number, and different research groups’ device models (e.g. the polarization-charge model used on this vault’s GaN HEMT page, which uses $\epsilon (x)=-0.3x+10.4$, giving $\epsilon (\mathrm{GaN})\approx 10.4$) may adopt values that differ from the “textbook” static permittivity given here ($\approx 8.9$). Per this vault’s convention, such conflicting conventions are noted explicitly rather than silently reconciled. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007; O. Ambacher et al., J. Appl. Phys. 85, 3222 (1999); I. Vurgaftman and J.R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94, 3675 (2003); Ioffe Institute NSM Archive.

Ques: Why is “work function” listed here as intrinsic, and how does it change with doping?

The work function $\varphi =\chi +(E_C-E_F)$ depends on where the Fermi level sits, which moves with doping: an n-type sample has $E_F$ closer to $E_C$ (lower $\varphi$), and a p-type sample has $E_F$ closer to $E_V$ (higher $\varphi$). The intrinsic values listed here place $E_F$ near midgap and are meant as reference points for band-diagram and Schottky-barrier calculations; for a specific doped device, $\varphi$ should be recalculated from the material’s actual $N_D$, $N_A$, $N_C$, and $N_V$ using the equilibrium carrier concentration equations on the Basic Semiconductor Equations page. Reference: D.A. Neamen, Semiconductor Physics and Devices, 4th ed., McGraw-Hill, 2012.