Density-of-states effective mass

Ncv = 2Mc v (27rm v KT/ h2 )3/2 where Mc v — the number of equivalent minima or maxima in the conduction and valence bands, respectively, and m cv = the density of states effective masses of electrons and holes. 

TABLE 1 Electron effective masses (mo) of wurtzite GaN and AIN. The superscripts 1 and stand for parallel and perpendicular to the kz direction, respectively. m e denotes die density of states effective mass, which is evaluated according to m e = (m2j.m ),/3. 

Dean et al [7] measured the Zeeman splitting of a luminescence line involving the 2p donor state, obtaining the electron effective mass m t=(0.24 0.01)mo and m /m, =0.36 0.01 for n-type cubic crystals. Measurements of infrared Faraday rotation due to free carriers were made by Ellis and Moss [8] at room temperature in a number of n-type hexagonal specimens belonging to the 6H and 15R polytypes of silicon carbide. One component of the total density-of-states effective mass was explicitly determined by this method. A value for the... 

Chaudhry [18] investigated the electrical transport properties of 3C-SiC/Si heterojunctions using current-voltage (I-V) and capacitance-voltage (C-V) characteristics, and found the density-of-states effective mass of electrons in the conduction band of 3C-SiC to be 0.78 m0. This value is somewhat larger than Zeeman splitting, ECR and theoretical effective masses. 

TABLE 2 Electron effective masses (mo) of zincblende GaN and AIN. m e (0 denotes the density of states electron mass at the T point, and m e(X) and m e(X) denote the longitudinal and transverse electron masses at the X point, respectively. For ZB AIN, the conduction band minimum occurs at the X point. 

TABLE 5 Experimentally observed hole effective masses (mo) of wurtzite GaN. m h and m denote the density of states hole mass and its perpendicular component (hole mass in kx-ky plane). 

Remarkably, although band stmcture is a quantum mechanical property, once electrons and holes are introduced, theit behavior generally can be described classically even for deep submicrometer geometries. Some allowance for band stmcture may have to be made by choosing different values of effective mass for different appHcations. For example, different effective masses are used in the density of states and conductivity (26). 

That the effective hole masses, or the density of states, is a complicated matter in SiC is well described in a review by Gardner et al. [118]. This article treats in some detail the valence band and estimates the contribution from the three top-most bands to the density of states, including the temperature dependence. Using the estimated effective mass the authors attempt to calculate the activation (i.e., the ratio of implanted and electrically active Al ions), and they achieve an activation of 37% of the implanted Al concentration of 10 cm after an anneal at 1,670°C for about 10 minutes. 

The failure is not limited to metal-ammonia solutions nor to the linear Thomas-Fermi theory (19). The metals physicist has known for 30 years that the theory of electron interactions is unsatisfactory. E. Wigner showed in 1934 that a dilute electron gas (in the presence of a uniform positive charge density) would condense into an electron crystal wherein the electrons occupy the fixed positions of a lattice. Weaker correlations doubtless exist in the present case and have not been properly treated as yet. Studies on metal-ammonia solutions may help resolve this problem. But one or another form of this problem—the inadequate understanding of electron correlations—precludes any conclusive theoretical treatment of the conductivity in terms of, say, effective mass at present. The effective mass may be introduced to account for errors in the density of states—not in the electron correlations. 

The energy bands are no longer described by the -k dispersion relations, but instead by a density-of-states distribution N E), illustrated in Fig. 1.6. Also the electron and hole effective masses must be redefined as they are usually expressed as the ciu-vature of (k). 

---