58 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS
CONDUCTION BAND VALENCE BAND INTRINSIC CARRIER
MATERIAL EFFECTIVE DENSITY (NC) EFFECTIVE DENSITY (NV) CONCENTRATION(ni = pi)Si (300 K) 2.78 x 1019 cm–3 9.84 x 1018 cm–3 1.5x 1010 cm–3Ge (300 K) 1.04 x 1019 cm–3 6.0 x 1018 cm–3 2.33x 1013 cm–3GaAs (300 K) 4.45 x 1017 cm–3 7.72 x 1018 cm–3 1.84x 106 cm–3Table 2.3: Effective densities and intrinsic carrier concentrations of Si, Ge, and GaAs. The
numbers for intrinsic carrier densities are the accepted values even though they are smaller than
the values obtained by using the equations derived in the text.
In electronic devices where current has to be modulated by some means, the concentration of
intrinsic carriers is fixed by the temperature and therefore is detrimental to device performance.
Once the intrinsic carrier concentration increases to∼ 1015 cm−^3 , the material becomes unsuit-
able for electronic devices, due to the high leakage current arising from the intrinsic carriers.
A growing interest in high-bandgap semiconductors, such as diamond (C), SiC, etc., is partly
due to the potential applications of these materials for high-temperature devices where, due to
their larger gap, the intrinsic carrier concentration remains low up to very high temperatures.
For GaN the background defect density usually does not allow one to reach theoretical intrinsic
carrier densities.
EXAMPLE 2.2Calculate the effective density of states for the conduction and valence bands of GaAs and
Si at 300 K. Let us start with the GaAs conduction-band case. The effective density of states is
Nc=2(
m∗ekBT
2 π^2) 3 / 2Note that at 300 K,kBT=26meV= 4 × 10 −^21 J.
Nc =2(
0. 067 × 0. 91 × 10 −^30 (kg)× 4. 16 × 10 −^21 (J)
2 × 3. 1416 ×(1. 05 × 10 −^34 (Js))^2) 3 / 2
m−^3=4. 45 × 1023 m−^3 =4. 45 × 1017 cm−^3In silicon, the density of states mass is to be used in the effective density of states. This is given by
m∗dos=6^2 /^3 (0. 98 × 0. 19 × 0 .19)^1 /^3 m 0 =1. 08 m 0