Electron effective mass transverse

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. 

More direct determination of electron effective masses was first performed by Kaplan et al [16] using electron cyclotron resonance (ECR) in n-type 3C-SiC epitaxially grown onto a silicon substrate. They obtained transverse effective mass m t = (0.247 0.011) n, and longitudinal effective mass m, = (0.667 0.015) m0. The effective masses derived from cyclotron resonance agree, within experimental error, with the values obtained from Zeeman luminescence studies [7] of small bulk crystals. An average effective mass of an electron, given by the equation me = (m t2m, )l/3, is 0.344m0. Recently, similar ECR measurements were made by Kono et al [17]. 

In general, good agreement is found for the longitudinal and transverse effective masses, when measured by several techniques, within the various polytypes. There is a wider variability for the values of the overall electron effective mass. Theoretical studies yield values for electron effective masses which are in good agreement with measured values. Data on hole effective masses is scarce and much of what is available is from theoretical studies. 

Here k is the Fermi wave vector determined from the value of the hole concentration p assuming a spherical Fermi surface, m is the hole effective mass taken as 0.5/no (mo is the free electron mass), is the exchange integral between the holes and the Mn spins, and h is Planck s constant. The transverse and longitudinal magnetic susceptibilities are determined from the magnetotransport data according to x = 3M/dB and xh = M/B. 

The abbreviations mn and m L denote the longitudinal and transverse effective electron masses, respectively. m is the effective mass for isotropic conduction band minimum. 

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). 

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. 

The quadratic shift of the Zeeman components has been calculated for silicon and germanium by a perturbation method [117]8, [139] and by a full calculation [108], The physical interpretation of this second-order effect in terms of the ratio 7 of the transverse and longitudinal effective masses of the donor electron is far from simple. 

Expression (8.18) has been used to derive values of the transverse effective mass of donor electrons in silicon from experiments on the P donor for different orientations of the magnetic field [116]. The low-field data give mt = (0.195 0.002) me, a value slightly larger than the one derived for the free electrons from the CR experiments (see Table3.4). 

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