Effective mass table, electrons

The n-type conductivity is determined by the product of the reciprocal effective mass of electrons and the concentration of carriers in a semi-classical viewpoint. The effective mass is often calculated by fitting the dispersion curve near the bottom of the conduction band. The bottom is mainly composed of M-4s/5s orbitals in the oxides of the present interest, and the curvature is mainly determined by the M-M interactions. The situation is schematically shown in Fig. 4. The strong interaction among M-4s/5s orbitals should bring about wider M-4s/5s band-width and smaller effective mass. On the other hand, weaker M-4s/5s interactions result in narrower band-width and larger effective mass. With the increase of the atomic number in the same row of the periodic table, the M-4s/5s orbitals tend to be contracted. Assuming the M-M distance is the same, the M-4s/5s interactions should be weakened with the atomic number, in general. 

An electron in a solid behaves as if its mass [CGS units are used in this review the exception is for the tabulation of effective masses, which are scaled by the mass of an electron (m0), and lattice constants and radii associated with trapped charges, which are expressed in angstroms (1A = 10 8 cm)] were different from that of an electron in free space (m0). This effective mass is determined by the band structure. The concept of an effective mass comes from electrical transport measurements in solids. If an electron s motion is fast compared to the lattice vibrations or relaxation, then the important quantity is the band effective mass (mb[eff]). If the electron moves more slowly (most cases of interest) and carries with it lattice distortions, then the (Frohlich) polaron effective mass (tnp[eff]) is appropriate [11]. The known band effective and polaron effective masses for electrons in the silver halides are listed in Table 1. The polaron and band effective masses are related to a... 

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. 

Table Effective masses of electrons (in units of the electron mass mo) for Group IV semiconductors and IV-IV compounds...

Where b is Planck s constant and m and are the effective masses of the electron and hole which may be larger or smaller than the rest mass of the electron. The effective mass reflects the strength of the interaction between the electron or hole and the periodic lattice and potentials within the crystal stmcture. In an ideal covalent semiconductor, electrons in the conduction band and holes in the valence band may be considered as quasi-free particles. The carriers have high drift mobilities in the range of 10 to 10 cm /(V-s) at room temperature. As shown in Table 4, this is the case for both metallic oxides and covalent semiconductors at room temperature. 

The other semiconductor, apart from CdSe, that has been studied with deliberate emphasis on quantum size effects, is PbSe (see Table 10.3). There are several reasons for this. One is the long-known use of CD to deposit PbS and later PbSe. Second, and of particular importance, the electron/hole effective mass in PbSe is very... 

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). 

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. 

TABLE 3 Electron and hole effective masses in InN in units of mo. 

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. 

For analysis of the transition metals themselves, the use of free-electron bands and LCAO d states is preferable. The analysis based upon transition-metal pseudopotential theory has shown that the interatomic matrix elements between d states, the hybridization between the free-electron and d bands, and the resulting effective mass for the free-electron bands can all be written in terms of the d-state radius r, and values for have been listed in the Solid State Table. 

Molecular mass ligand-substitution effects. Steric and electronic effects can also be used to control the molecular mass of the PEs produced. Bis(phenoxy-imine)-based catalysts can yield polymers ranging from very low to extremely high molecular mass (Mv < 104 orMv > 106).1152 The MAO-activated prototype 135 system yields PEs with very low M v (about 7000-10000 see entries 19-22 in Table 18). As is typical for ct-olefin polymerizations, increasing the... 

The electron effective masses mn at the CB minimum at k = 0 are generally smaller than the ones for k /Z 0 CB minima, as can be judged from Table 3.6. The Luttinger VB parameters have been determined by many authors, though biased in some cases by the values used in the most recent calculations of the shallow-acceptor levels. The situation is complicated by the fact that for semiconductors like InSb, where there is an interaction between the valence and the conduction bands, effective Luttinger VB parameters 7j have been defined by [82] as ... 

With m in units of me, 7b = 4.2544 x 10 fi ( s/m )2 B(T). For shallow donors in multi-valley semiconductors, to is the electron transverse effective mass mnt of Table 3.4 and for QHDs in direct-band-gap semiconductors, it is the effective mass mn at the T minimum of the CB of Table 3.6. For the shallow acceptors where the effective Rydberg R oa is defined as Roo/li, Bo is equal to Rloa/jips- Values of Bo for shallow donors and acceptors in different semiconductors are given in Table 8.12. 

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