Energy Bands

Phillips, J. C.

doi:10.1016/b978-0-12-553350-8.50009-9

Cited by 112 publications

(174 citation statements)

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“…The ∆ in the second term represent the spill of the wave function from the quantum tube with the length l. Since the valence-band top has a character of the bonding sp 3 orbitals common to all the polytypes [2,5], the variation in (2) corresponds to that in the band gap in the polytypes expressed in (1). Our GGA calculation indeed provides ε 3C = 1.419 eV, showing agreement with the first term in (1). By further comparing the second terms in (1) and (2), we obtain the effective mass of m * = 0.326m 0 (m 0 : bare electron mass) which shows agreement with the experimental value of m * = 0.363m 0 [16].…”

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confidence: 74%

“…It is written in textbooks [1] that the resultant hybridized sp 3 bonding orbitals constitute valence bands, whereas the anti-bonding counter parts do conduction bands. This is not necessarily true, however: We have recently found that the wavefunctions of the conduction-band minima (CBM) of the semiconductors are distributed not near atomic sites but in the interstitial channels [2], as shown in Fig.…”

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confidence: 99%

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Interstitial Channels that Control Band Gaps and Effective Masses in Tetrahedrally Bonded Semiconductors

Matsushita

Oshiyama

2014

Phys. Rev. Lett.

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We find that electron states at the bottom of the conduction bands of covalent semiconductors are distributed mainly in the interstitial channels and that this floating nature leads to the band-gap variation and the anisotropic effective masses in various polytypes of SiC. We find that the channel length, rather than the hexagonality prevailed in the past, is the decisive factor for the band-gap variation in the polytypes. We also find that the floating nature causes two-dimensional electron and hole systems at the interface of different SiC polytypes and even one-dimensional channels near the inclined SiC surface.Most semiconductors, elemental or compound, have the four-fold coordinated tetrahedral structure caused by the hybridization of atomic orbitals. It is written in textbooks [1] that the resultant hybridized sp 3 bonding orbitals constitute valence bands, whereas the anti-bonding counter parts do conduction bands. This is not necessarily true, however: We have recently found that the wavefunctions of the conduction-band minima (CBM) of the semiconductors are distributed not near atomic sites but in the interstitial channels [2], as shown in Fig. 1. The wave-functions float in the internal space, i.e., the channels, inherent to the sp 3 -bonded materials.Another structural characteristic in the semiconductor is the stacking of atomic bilayers along the bond axis direction such as AB (wurtzite) or ABC (diamond or zincblende). The different stacking sequence leads to the different polytype [6] generally labeled by the periodicity of the sequence n and its symmetry, hexagonal (H) or cubic (C), as in 2H(AB), 3C(ABC), 4H(ABCB) and so on. These differences in the stacking sequence have been assumed to be minor in the electronic properties. However, the sequence determines the lengths and the directions of the interstitial channels, hereby affecting the shapes of the wave-functions of CBMs. The internal space overlooked in the past may be closely related to the electronic properties of the semiconductors, that we discuss in this Letter.Silicon carbide (SiC) is a promising material in power electronics due to its superior properties which are suitable to the operations under harsh environment [7]. From science viewpoints, SiC is a manifestation of the polytypes explained above: Dozens of polytypes of SiC are observed and the band gaps vary by 40 %, from 2.3 eV in 3C to 3.3 eV in 2H despite that the structures are locally identical to each other in the polytypes [8]. This mysterious band-gap variation has been discussed in terms of an empirical quantity, hexagonality [9], for a half century: A bilayer sandwiched by the two same stacking indexes, as in 2H structure, is called a hexagonal layer and the ratio of the hexagonal layers in whole stacking sequence is called hexagonality; the band-gap variation in the poly- [2,5] types is argued to be linear with respect to the hexagonality. Yet, the linearity is not satisfactory (see below) and moreover the underlying physics is totally lacking.In this Letter, we find, o...

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confidence: 74%

mentioning

confidence: 99%

Interstitial Channels that Control Band Gaps and Effective Masses in Tetrahedrally Bonded Semiconductors

Matsushita

Oshiyama

2014

Phys. Rev. Lett.

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“…The conduction c E and valence v E band edges, the spin-orbit splitting energy D, and the valence-conduction band parameters 1 γ , 2 γ , 3 γ , κ and F are functions of the coordinate z . It has been assumed that the band structure parameters change abruptly at the interface.…”

Section: Discussionmentioning

confidence: 99%

“…The crossing may be obtained if the full determinant that results from Eq. (7) is used, or the problem is solved numerically using the initial Hamiltonian (1). Figure 4 shows the dependence of 2D conduction and valence subband edges calculated with the exact Hamiltonian and parameter values in Table 1 as a function of composition x.…”

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confidence: 99%

“…Usually the former effect is much stronger than that of the spin-splitting of Kramers pairs. Typical values of the spin-orbit split-off energy D lie in the range of 0.1-1 eV [1], while the degenerate band spin-splitting energies are of the order of 0.01 eV for room temperature free charge-carriers [2,3]. The rearrangement of the energy bands and appearance of D is also reflected in carrier spin properties too: the average spin magnitude of the free carrier begins to depend on spin direction and magnitude of the wave vector [4].…”

Section: Introductionmentioning

confidence: 99%

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Spin properties of Hg_1–xCd_x Te/CdTe quantum wells

Dargys¹

2008

Physica Status Solidi (b)

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IntroductionThe effect of the spin-orbit (SO) interaction on a free charge carrier spin in semiconductors is twofold. First of all, it reorders the band structure at the center of the Brillouin zone, a typical example being the valence band rearrangement in elementary and compound semiconductors and appearance of new, SO split-off band. Secondly, the SO interaction lifts off the spin-splitting in otherwise degenerate energy bands, for example of the doubly degenerate Kramers pairs, if a semiconductor lattice or QW does not possess the inversion symmetry. This is a typical situation found in A 3 B 5 and A 2 B 6 compounds. Usually the former effect is much stronger than that of the spin-splitting of Kramers pairs. Typical values of the spin-orbit split-off energy D lie in the range of 0.1-1 eV [1], while the degenerate band spin-splitting energies are of the order of 0.01 eV for room temperature free charge-carriers [2,3]. The rearrangement of the energy bands and appearance of D is also reflected in carrier spin properties too: the average spin magnitude of the free carrier begins to depend on spin direction and magnitude of the wave vector [4].In the inverted band semiconductors represented by HgTe the energy gap g E has a negative value. The branches of conduction band dispersion in these semiconductors are directed downwards and merge with the valence band continuum. The role of the conduction band is

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Fundamental Coordination Chemistry, Environmental Chemistry, and Biochemistry of Lead(II)

Claudio

Godwin

Magyar

Progress in Inorganic Chemistry, Volume 51

110

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Energy Bands

Cited by 112 publications

References 4 publications

Interstitial Channels that Control Band Gaps and Effective Masses in Tetrahedrally Bonded Semiconductors

Interstitial Channels that Control Band Gaps and Effective Masses in Tetrahedrally Bonded Semiconductors

Spin properties of Hg_1–xCd_x Te/CdTe quantum wells

Fundamental Coordination Chemistry, Environmental Chemistry, and Biochemistry of Lead(II)

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Energy Bands

Cited by 112 publications

References 4 publications

Interstitial Channels that Control Band Gaps and Effective Masses in Tetrahedrally Bonded Semiconductors

Interstitial Channels that Control Band Gaps and Effective Masses in Tetrahedrally Bonded Semiconductors

Spin properties of Hg1–xCdx Te/CdTe quantum wells

Fundamental Coordination Chemistry, Environmental Chemistry, and Biochemistry of Lead(II)

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Spin properties of Hg_1–xCd_x Te/CdTe quantum wells