Hole effective mass light

TABLE 3 Hole effective masses (mo) of wurtzite GaN and AIN. The superscripts L and stand for the perpendicular and parallel to the kz direction, respectively. m h denotes the density of states effective mass, which is evaluated according to m h = (nrjmn)13. HH, LH and CH denote heavy, light and crystal-field split-off hole masses, respectively. 

Electron and hole effective masses of various SiC polytypes have been determined by various methods, such as Hall measurements, Faraday rotation, Zeeman splitting of a photoluminescence line, electron cyclotron resonance, and infrared light reflection. There have also been several theoretical studies of the effective masses of 3C-SiC. The effective masses of electrons and holes thus obtained are listed in TABLE 1. 

An additional complication is seen in the valence band structures in Fig. 2.13. Here, two different E k valence bands have the same minima. Since their curvatures are different, the two bands correspond to different masses, one corresponding to heavy holes with mass mn and the other to light holes with mass m/. The effective scalar mass in this case is m = (m]j + Such light and heavy holes occur in several... 

In equation 3, ran is the effective mass of the electron, h is the Planck constant divided by 2/rr, and Eg is the band gap. Unlike the free electron mass, the effective mass takes into account the interaction of electrons with the periodic potential of the crystal lattice thus, the effective mass reflects the curvature of the conduction band (5). This curvature of the conduction band with momentum is apparent in Figure 7. Values of effective masses for selected semiconductors are listed in Table I. The different values for the longitudinal and transverse effective masses for the electrons reflect the variation in the curvature of the conduction band minimum with crystal direction. Similarly, the light- and heavy-hole mobilities are due to the different curvatures of the valence band maximum (5, 7). 

Here mu, mu, and mch denote effective masses of heavy hole (HH), light hole (LH) and crystal-field split-off hole (CH) bands, respectively. In ZB structure, the hole masses along [kOO], [kkO] and [kkk] directions are given as follows ... 

We do this by using the k p method, (called k-dol-p), which is based upon the perturbation theory of Eq. (1-14). In this method, energy is calculated near a band maximum or minimum by considering the wave number (measured from the extremum) as a perturbation. (The method is described in many solid state texts, such as Kittel, 1963, p. 186, or Harrison, 1970, p. 140.) The method was used for a study of effective masses by Cardona (1963, 1965). It was also usetl in the more extensive study by Lawaetz (1971) referred to in the discussion of heavy-hole bands. We shall discuss here only the conduction band and the light-hole band where the effects of interaction are great. 

Wc have written the state at the conduction-band minimum as c> and that of the light hole as a). In just the same way we can compute the effective mass of the light hole ... 

The effective masses of electrons and holes are estimated by parabolic approximation a large curvature corresponds to a small effective mass and a small curvature corresponds to a large mass. With this band concept, light absorption and luminescence are interpreted as follows Light is absorbed by the transition from valence band to conduction band. Therefore, the broadening of the absorption spectrum originates basically from the one dimensionality of the joint density of states, which is described by (E - g) . Excited electrons and holes relax to the bottom of the bands and then recombine radiatively. Therefore, the photoluminescence of the spectrum is very sharp. The energy difference between two peaks is called the Stokes shift. 

Effective light hole mass (mip) 0.14mo 0.3mo O.lOmo 3.53mo 0.150mo... 

The calculation of the hole levels is much more complicated since the band structure of many important semiconductors has hole bands with fourfold degeneracy at k = 0. This leads to heavy and light holes with different effective masses. Consequendy, a double set of hole energy levels is formed in the QW with different spacings between levels—one set for the light holes, the second set for the heavy holes, as shown in Fig. 3.3. Solutions to the problem have been reported for both infinite (Bastard, 1981 Altarelli, 1985) and finite (Bastard and Brum, 1986) potential barriers. 

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