Effective Masses in SiC

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. 

Dean et al [7] measured the Zeeman splitting of a luminescence line involving the 2p donor state, obtaining the electron effective mass m t=(0.24 0.01)mo and m /m, =0.36 0.01 for n-type cubic crystals. Measurements of infrared Faraday rotation due to free carriers were made by Ellis and Moss [8] at room temperature in a number of n-type hexagonal specimens belonging to the 6H and 15R polytypes of silicon carbide. One component of the total density-of-states effective mass was explicitly determined by this method. A value for the 

Electron effective mass Hole effective mass Method Ref 

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]. 

Chaudhry [18] investigated the electrical transport properties of 3C-SiC/Si heterojunctions using current-voltage (I-V) and capacitance-voltage (C-V) characteristics, and found the density-of-states effective mass of electrons in the conduction band of 3C-SiC to be 0.78 m0. This value is somewhat larger than Zeeman splitting, ECR and theoretical effective masses. 

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N Son WM Chen, O Kordina, AO Konstantinov, B Monemar, E Janzen. Electron effective masses in 4H SiC. Appl Phys Lett 66 1074, 1995. 

The changes in electronic structure of the various SiC polytypes have a corresponding effect on the electron and hole efieetive masses. Typical values are, for example, 1.1 mo in the 3C poly type and 1.75 mo and 0.66 mo in the 4H structure. The two latter values are for conduction in and perpendicular to the basal plane of the hexagonal strueture, respectively. [Egilsson et al. in Reference 15] The values for the 6H structure are similar to those of the 4H strueture but somewhat lower. Note that the effective mass in the 3C structure is roughly intermediate between the values... 

That the effective hole masses, or the density of states, is a complicated matter in SiC is well described in a review by Gardner et al. [118]. This article treats in some detail the valence band and estimates the contribution from the three top-most bands to the density of states, including the temperature dependence. Using the estimated effective mass the authors attempt to calculate the activation (i.e., the ratio of implanted and electrically active Al ions), and they achieve an activation of 37% of the implanted Al concentration of 10 cm after an anneal at 1,670°C for about 10 minutes. 

Population analysis and site-decomposed DOS indicate that, compared with GaN On, large numbers of extra electrons are introduced into the other sites in the vicinity of the Si-sites. This results in a small effective mass of the electrons introduced in the conduction band. From these findings, we can expect high-conductivity n-type GaN Sic crystals. 

Thermal diffusivity of oxidation-resistant SiC/C compositionally graded graphite materials has been measured by using the laser flash method. In order to study the effect of the SiC/C graded layer on the diffusivity, the thickness of the graded layer and the SiC content were changed. In addition, the specific surface areas of the SiC/C materials have been measured. It is shown that the effect of the SiC/C graded layer on thermal diffusivity was small within SiC contents (0.27-8.52 mass%) used in this study. 

Most wurtzite-type crystals are direct band-gap materials (2fP-SiC is an exception) and interband transitions can take place between these three Fils and the T7 CB minimum. These materials are anisotropic and this anisotropy reflects on the selection rules for the optical transitions and on the effective masses. The Tg (A) —> T7 (CB) transitions are only allowed for ETc while the two T7 (B. C) —> T7 (CB) transitions are allowed for both polarizations. However, the relative values of the transition matrix elements for the T7 (B, C) —> T7 (CB) transitions can vary with the material. For instance, in w-GaN, the T7 (B) —> T7 (CB) transition is predominantly allowed for ETc while the T7 (C) — I 7 (CB) transition is predominantly allowed for E//c [22]. Table 3.7 gives band structure parameters of representative materials with the wurtzite structure. 

A non-variational method has also been used by [25] to determine the donor energy levels in uniaxial crystals, with an application to 4 //-SiC. It considers first a constant-energy ellipsoid with three different electron effective masses mi, my and m-z along three mutually orthogonal axes, which... 

ODMR was first observed in SiC with the report of the acceptor resonance in 6H material containing A1 and N [3,7]. Three lines were reported which followed the simple cos0 law indicating an effective-mass acceptor (see TABLE 2). The lines were not assigned to specific sites. In subsequent work, hyperfine constants were inferred for Al acceptors from the linewidth of the ODMR [4,5]. The hyperfine constants imply a very small localization of the wavefunction on the Al nuclei. This is consistent with the p-like character of the hole wavefunction. 

Both 6H and 4H polytypes of SiC doped with B and N exhibit signals which were attributed to B [5,6,8]. The g-anisotropy is smaller than those for Al and Ga which is consistent with the greater depth of the B centres. Detailed resonance parameters were not quoted but the authors stated that the spectra were distinct from the B-centres observed in EPR. It is fair to conclude that these B-centres are not effective-mass acceptors. 

Theoretical calculations predict significant anisotropy in effective hole masses for the different valence bands of GaN, though the various calculations differ in the predicted magnitude of the anisotropy in each band [113-115]. Direct measurements of hole masses are, however, very difficult and most reported experimental values are indeed inferred from luminescence, magneto-optical studies of exciton luminescence, infrared reflectance and transmittance studies of polar materials, which are often isotropically averaged and thus not informative about the anisotropy. Directionally dependent Hall-effect measurements in m-plane GaN films grown on m-plane SiC substrates... 

The values of carrier mobility for n- and p- types and effective mass for electrons and holes in various SiC polytypes are tabulated in the literature (82). The electron mobility differs between... 

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In a previous study of cyclic SiCs, a residual inertial defect of only slightly smaller magnitude was found, despite the fact that an extremely high level of calculation (surpassing that in the present study) was used to determine the vibration-rotation interaction contributions to the rotational constants. This was subsequently traced to the so-called electronic contribution, which arises from a breakdown of the assumption that the atoms can be treated as point masses at the nuclear positions. Corrections for this somewhat exotic effect were carried out in that work and reduced the inertial defect from about 0.20 to less than 0.003 amu A. However, the associated change in the rotational constants had an entirely negligible effect on the inferred structural parameters. Hence, this issue is not considered further in this work. 

Further experimental evidence of shape effects in absorption spectra of SiC particles is found in the data of Pultz and Herd (1966), who investigated infrared absorption by SiC fibers with and without Si02 coatings. Although these measurements were not mass-normalized, they show a strong absorption band at 795 cm-1 and a weaker band at 941 cm-1. If the fibers are approximated as ellipsoids with L2 = L3 = and Lx = 0 (i.e., a cylinder), then the ellipsoid equation (12.27) predicts absorption peaks for particles in air at frequencies where c = -1 and c = — oo. This corresponds to absorption bands at 797 and 945 cm-1 for the dielectric function of isotropic SiC, in excellent agreement with the experimental peak positions for the fibers. 

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