Symmetry of Wurtzite

Casella, R. C.

doi:10.1103/physrev.114.1514

Cited by 57 publications

(27 citation statements)

References 15 publications

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“…1,2,35 The spin-orbit interaction removes what would otherwise be a degeneracy of spin-up and spindown states. Similarly, under inversion asymmetry no additional degeneracy appears at a general point of the BZ other than the Kramers degeneracy between ↑ (k) and T ↑ (k) ͓ϭ ↓ (Ϫk)͔, where T is the time-reversal operator: for kϭ0, one thus recovers a minimum double degeneracy.…”

Section: Linear-k Formalismmentioning

confidence: 99%

“…Without spin all states transform according to one of the single-group representations of C 6v , as given in Table I. In particular, s,p z ,d 3z 2 Ϫr 2ϳ ⌫ 1 , ͑ p x ,p y ͒,͑d zx ,d yz ͒ϳ⌫ 5 , ͑d x 2 Ϫy 2, d xy ͒ϳ⌫ 6 . ͑4͒…”

Section: A Symmetry Considerationsmentioning

confidence: 99%

“…1,2 The corresponding splittings of spin-degenerate states arise from the lack of inversion symmetry through the action of the spin-orbit coupling. At the ⌫ point of the BZ these energy splittings vanish.…”

Section: Introductionmentioning

confidence: 99%

“…13 The existence and influence of the linear-k terms for wurtzite has been vigorously investigated since the 1950s. 2,11,12,[14][15][16][17][18][19][20][21][22][23][24] Such a flurry of activity was initially mainly due to the simpler exciton structure, compared to the zinc-blende case, and the easy accessibility of the absorption edge of CdS (ϳ 2.5 eV͒ to spectroscopic sources. More recent interest was sparked by the proposal of Brenig, Zeyher, and Birman 25 that resonant Brillouin scattering could be used to decide among the various additional boundary conditions ͑the ABC problem 26 ͒ for light propagation across the interface of a crystal displaying spatial dispersion.…”

Section: Introductionmentioning

confidence: 99%

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Terms linear inkin the band structure of wurtzite-type semiconductors

et al. 1996

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Wurtzite has the space-group symmetry P6 3 mc. The absence of inversion symmetry allows linear-k terms in the electronic band structure when the spin-orbit interaction is included. Their existence has been confirmed in a number of experiments, but no microscopic calculations have been published. In the present paper, we discuss the origin of these linear-k terms using group theory and k•p arguments. The various contributions to these terms are identified through band-structure models. We present an ab initio calculation, performed with the linear-muffin-tin-orbital method, of these spin splittings in CdS, CdSe, and ZnO. A renormalization of the valence-band spin-splitting coefficients obtained in the linear-muffin-tin-orbital calculations was found necessary to correct for errors in the relative energies of the uppermost valence bands as compared with the experimental values. We point out that a similar procedure should be used when evaluating masses and other band parameters from calculated local-density-approximation band structures.

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Section: Linear-k Formalismmentioning

confidence: 99%

Section: A Symmetry Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Terms linear inkin the band structure of wurtzite-type semiconductors

et al. 1996

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“…This is consistent with the optical selection rules derived theoretically by Birman 10 and Casella. 11 Since the electrical and optical properties are related to the crystal symmetry, it is reasonable to measure the electrical properties with polarized light. This has been done for the photoconductivity of CdS 12 with externally applied fields.…”

mentioning

confidence: 99%

Effects of Polarized Light on Photocurrents and Photovoltages in ZnS

1959

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The anomalous short circuit photocurrents in ZnS have been measured using polarized light. In spite of the fact that for a given wavelength, light polarized perpendicular to the c axis is more strongly absorbed than light polarized parallel to the c axis, there are wavelength regions in which the absolute magnitude of the short circuit photocurrents are smaller for perpendicularly polarized light. The data are consistent with a double valence band model. P HOTOVOLTAGES larger than the energy gap have been reported for hexagonal ZnS. [1][2][3][4] In addition, the sign of the open circuit photovoltage (and the short circuit current) reverses with wavelength. 2,4 Similar reversals have been reported for CdS. 5 From measurements of the pyroelectric effect made in this laboratory and by Lempicki, 4 it has been definitely established that the sign of the photovoltage at a given wavelength is associated with the polarity of the c axis. These phenomena are related to general effects of the crystal symmetry on interactions with light.Another type of measurement falling into this category involves the polarization of light absorbed or emitted by the crystal. As an example we cite the work done on the dichroic optical absorption of ZnS and CdS 6-8 as well as the work on fluorescent measurements. 7,9 The results of the absorption measurements show that light polarized perpendicular to the c axis is more strongly absorbed than light polarized parallel. This is consistent with the optical selection rules derived theoretically by Birman 10 and Casella. 11 Since the electrical and optical properties are related to the crystal symmetry, it is reasonable to measure the electrical properties with polarized light. This has been done for the photoconductivity of CdS 12 with externally applied fields. We have measured the short circuit photocurrent as a function of the wavelength of incident light for the two directions of light polarization for ZnS. This communication presents the results. EXPERIMENTAL RESULTS AND DISCUSSIONThe measurements have been made by adding a polarizer to instrumentation which together with the sample preparation has been described in reference 2. It is important to discuss in some detail the nature of our crystal samples. Among workers in the field 2-4 there is some difference of opinion as to the role that crystalline disorder plays in the various properties of hexagonal ZnS. In an attempt to relate crystal disorder, such as inclusions of stacking faults and cubic phase, we have examined many samples for these inclusions. Sixty-five single crystals of hexagonal ZnS (40 unactivated and 25 activated with various combinations of Cu, Al, and Mn) were analyzed by x-ray diffraction techniques. (The x-ray radiation had no effect on the electrical properties.) Most of the crystals were about 4 mm long and exhibited uniform birefringent banding. With these, a one-mm spot in the middle of the crystal was chosen for x-ray examination. With crystals that exhibited heavy banding at one or more points, the one-mm spot in...

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