Hole effective mass heavy

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. 

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. 

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. 

According to Fig. 1.5, the conduction as well as the valence band consists of several bands. Some valence bands are degenerated around k = 0 (the F point). Since the curvature differs from one band to another, each band is associated with a different effective mass (see also Appendix D). Rather flat energy profiles correspond to heavy holes... 

Ideally, the specific heat of conduction electrons (or holes) in a metal is a linear function of temperature C = yT, where y, known as the Sommerfeld constant, is in the range 0.001 to 0.01 J/(molK ) for normal materials. In HF compounds, y reaches values up to 10 times larger (see tables 9, 10 and 11). In the basic theory of the specific heat of itinerant electrons (free Fermi gas), y is proportional to the effective mass m of the charge carriers, and so the name heavy fermions has come to be attached to these high-y materials (see Stewart 1984). The linear relation between C and T is strictly fulfilled only in the limit of a free degenerate electron gas. In real materials, weak non-linearities show up that can be encompassed by, for example, allowing y to be temperature dependent, y T). The Sommerfeld constant of interest is then the extrapolation of y for... 

One important aspect of the impurity-related states is the effective mass of charge carriers (extra electrons or holes) due to band-structure effects, these can have an effective mass which is smaller or larger than the electron mass, described as light or heavy electrons or holes. We recall from our earlier discussion of the behavior of electrons in a periodic potential (chapter 3) that an electron in a crystal has an inverse effective mass which is a tensor, written as [(/n) ]o . The inverse effective mass depends on matrix elements of the momentum operator at the point of the BZ where it is calculated. At a given point in the BZ we can always identify the principal axes which make the inverse effective mass a diagonal tensor, i.e. [(m) ]a = as discussed in chapter 3. The energy of electronic... 

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