Effective mass electron

Fig. 2. Electron drift velocities as a function of electric field for A, GaAs and B, Si The gradual saturation of curve B is characteristic of all indirect semiconductors. Curve A is characteristic of direct gap semiconductors and at low electric fields this curve has a steeper slope which reflects the larger electron mobiUty. The peak in curve A is the point at which a substantial fraction of the electrons have gained sufficient energy to populate the indirect L minimum which has a much larger electron-effective mass than the F minimum. Above 30 kV/cm (not shown) the drift velocity in Si exceeds that in...

Electron-donor end group, 20 504 Electron donors, in Ziegler-Natta polymerization, 26 518-521 Electron effective mass, in direct gap semiconductors, 22 143—144 Electronegativities, Pauling scale of,... 

InN is at the present time always grown n-type, and this has allowed experimental determinations of the electron effective mass from plasma reflectivity [4,8,24], Hole masses are generally obtained from band structure calculations. TABLE 3 lists some determinations of electron and hole masses of InN in units of mo. Most calculations agree with the experimental electron mass of 0.1 lmo, but the uncertainty regarding hole masses is still large at the present stage. 

Here are Luttinger parameters, and me is an electron effective mass, av, b, d and ac are Bir-Pikus deformation potentials. As0 is a spin-orbit splitting energy. L and a denote orbital and spin angular momentum operators, respectively. [Lf, LJ is defined as [Lf, LJ = (LjLj + LjLj)/2. The summation of i,j runs through x, y, z. 

Here Ai are inverse mass parameters in WZ structure, corresponding to Luttinger parameters in ZB structure, me11 and me1 are k-dependent electron effective masses. D , aic and a2c are Bir-Pikus deformation potentials. Ai and 3A2,3 correspond to the crystal-field and spin-orbit splitting energies, respectively. The definition of several operators is given as L+ = (U iLy)/V2, a+ = (ax iay)/2,... 

The calculated and measured electron effective mass m c and its k-dependency for WZ and ZB GaN and AIN are summarised in TABLES 1 and 2, respectively. Suzuki et al derived them with a full-potential linearised augmented plane wave (FLAPW) band calculation [4,5], Miwa et al used a pseudopotential mixed basis approach to calculate them [6]. Kim et al [7] determined values for WZ nitrides by the full-potential linear muffin-tin orbital (FP-LMTO) method. Majewski et al [8] and Chow et al [9,10] used the norm-conserving pseudo-potential plane-wave (PPPW) method. Chen et al [11] also used the FLAPW method to determine values for WZ GaN, and Fan et al obtained values for ZB nitrides by their empirical pseudo-potential (EPP) calculation [12],... 

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. 

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. 

The electron effective mass in GaN is now reasonably well established by cyclotron resonance measurements [14-16] asm, = (0.22 0.0 l)m, and the low frequency dielectric constant (appropriately averaged spatially) e(0) = 9.5 0.2, from infrared refractive index and optic phonon energy measurements [17]. We can therefore derive a reliable value for the hydrogenic donor ionisation energy of EDH = (33.0 1.5) meV which compares well with IR absorption measurements, giving Ed = (35 1) meV [18] (see below). The discrepancy is readily explained in terms of a small chemical shift. 

Of course, the details of the gain spectra depend on the dimensionality of the active material (bulk, quantum well, etc.) and on the details of the band structure. For such detailed calculations we refer to Chapter A6 of this volume. However, it is important to note that due to the specific band structure of the nitrides, the carrier densities needed to achieve inversion and optical gain are very large compared to other m-V semiconductors. In particular, both the electron effective mass (nw = 0.22 [7]) as well as the hole effective mass (mi, 2.0 [8-10]) are three- to four-fold larger than in GaAs. For the same reason, however, the maximum gain obtainable from nitride structures is also larger. 

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