Problem

For intrinsic semiconductors, the intrinsic carrier concentration ni depends on temperatur...

For intrinsic semiconductors, the intrinsic carrier concentration ni depends on temperature, as follows:

or, taking natural logarithms,

Thus, a plot of lnni versus 1/T (K)–1 should be linear and yield a slope of -Eg/2k. Using this information and the data presented in Figure 18.16, determine the band gap energies for silicon and germanium and compare these values with those given in Table 18.3.

Figure 18.16 Intrinsic carrier concentration (logarithmic scale) as a function of temperature for germanium and silicon.

(From C. D. Thurmond, “The Standard Thermodynamic Functions for the Formation of Electrons and Holes in Ge, Si, GaAs, and GaP,” Journal of the Electrochemical Society, 122, [8], 1139 (1975). Reprinted by permission of The Electrochemical Society, Inc.)

Table 18.3 Band Gap Energies, Electron and Hole Mobilities, and Intrinsic Electrical Conductivities at Room Temperature for Semiconducting Materials

Material	Band Gap (eV)	Electron Mobility (m2/V•s)	Hole Mobility (m2/V•s)	Electrical Conductivity (Intrinsic)(Ω•m)–1
		Elemental
Ge	0.67	0.39	0.19	2.2
Si	1.11	0.145	0.050	3.4 × 10–4
		III–V Compounds
AlP	2.42	0.006	0.045	—
AlSb	1.58	0.02	0.042	—
GaAs	1.42	0.80	0.04	3 × 10–7
GaP	2.26	0.011	0.0075	—
InP	1.35	0.460	0.015	2.5 × 10–6
InSb	0.17	8.00	0.125	2 × 104
		II–VI Compounds
CdS	2.40	0.040	0.005	—
CdTe	1.56	0.105	0.010	—
ZnS	3.66	0.060	—	—
ZnTe	2.4	0.053	0.010	—