[PDF]
http://dx.doi.org/10.3952/lithjphys.45106
Open access article / Atviros prieigos straipsnis
Lith. J. Phys. 45, 43–51 (2005)
HOLE SPIN SURFACES IN WURTZITE
SEMICONDUCTORS
A. Dargys
Semiconductor Physics Institute, A. Goštauto 11, LT-01108
Vilnius, Lithuania
E-mail: dargys@pfi.lt
Received 15 October 2004
Spin properties of holes in the wurtzite
semiconductors, when the hole with a given wave vector
ballistically propagates in either heavy-, light-mass or
crystal-field split-off band, are considered. Analytical solutions
for an averaged hole spin are found for two important cases, when
the hole wave vector is parallel and perpendicular to the
hexagonal axis. Shapes of the spin surfaces are presented for
these cases. It is shown that the surfaces, in general, are
spheroids. However, depending on the wave vector magnitude and
valence band parameters, the surfaces may also be spheres or
line-shaped. The properties of the spin surfaces are illustrated
for parameters of the wurtzite GaN, where the crystal field
dominates in the splitting of the valence band.
Keywords: wurtzites, spintronics, valence band, spin, GaN
PACS: 71.70.Ms, 72.20.Jv, 73.40.Gk, 78.55.–m, 79.90.+b
SKYLĖS SUKINIO PAVIRŠIAI
VIURCITO GARDELĖS PUSLAIDININKIUOSE
A. Dargys
Puslaidininkių fizikos institutas, Vilnius, Lietuva
Išnagrinėtos laisvosios skylės, kuri juda arba
sunkiosios, arba lengvosios masės energetinėje juostoje, arba
atskilusioje dėl kristalinio elektrinio lauko juostoje, sukinio
savybės nuo valentinės juostos parametrų ir skylės bangos
vektoriaus krypties bei dydžio. Rasti analiziniai sprendiniai,
kurie aprašo vidutinį sukinį dviem svarbiais atvejais: kai
balistinės skylės bangos vektorius nukreiptas arba lygiagrečiai,
arba statmenai kristalo heksagonalinei ašiai. Parodyta, kad abiem
atvejais sukinio paviršiai yra sferoidai. Priklausomai nuo skylės
bangos vektoriaus ilgio bei krypties, o taip pat nuo valentinės
juostos parametrų, sukinio paviršiai gali transformuotis į sferą
arba į tiesę. Skylės sukinių paviršių savybės pailiustruotos GaN –
puslaidininkio, kuriame vyrauja kristalinis laukas – atveju.
References / Nuorodos
[1] I. Žutić, Spintronics: Fundamentals and applications, Rev. Mod.
Phys. 76(2), 323–410 (2004),
http://dx.doi.org/10.1103/RevModPhys.76.323
[2] S.J. Pearton, C.R. Abernathy, M.E. Overberg, G.T. Thaler, D.P.
Norton, N. Theodoropoulos, A.F. Hebard, Y.D. Park, F. Ren, J. Kim,
and L.A. Boatner, Wide band gap ferromagnetic semiconductors and
oxides, J. Appl. Phys. 93(1), 1–13 (2003),
http://dx.doi.org/10.1063/1.1517164
[3] W. Prellier, A. Fouchet, and B. Mercey, Oxide-diluted magnetic
semiconductors: A review of the experimental status, J. Phys.:
Condens. Matter 15(37), R1583–R1601 (2003),
http://dx.doi.org/10.1088/0953-8984/15/37/R01
[4] A. Dargys, Coherent properties of hole spin, Lithuanian J. Phys.
43(2), 123–128 (2003)
[5] A. Dargys, Spin surfaces and trajectories in valence bands of
tetrahedral semiconductors, Phys. Status Solidi B 241(1),
145–154 (2004),
http://dx.doi.org/10.1002/pssb.200301909
[6] A. Dargys, Hole spin surfaces in A3B5
compounds, Phys. Status Solidi B 241(13), 2954–2961 (2004),
http://dx.doi.org/10.1002/pssb.200402078
[7] D.K. Young, E. Johnston-Halperin, D.D. Awschalom, Y. Ohno, and
H. Ohno, Anisotropic electrical spin injection in ferromagnetic
semiconductor heterostructures, Appl. Phys. Lett. 80(9),
1598–1600 (2002),
http://dx.doi.org/10.1063/1.1458535
[8] A. Dargys, Ultrafast control of hole spin by electric field in
semiconductors, IEEE J. Selected Topics Quantum Electron. 10(1),
155–158 (2004),
http://dx.doi.org/10.1109/JSTQE.2004.824078
[9] A. Dargys, Hole dynamics under π-pulse excitation, Phys.
Rev. B 70(12), 125207-1–11 (2004),
http://dx.doi.org/10.1103/PhysRevB.70.125207
[10] A. Dargys, Control of valence-band hole spin by electric field,
Acta Phys. Pol. A 105(3), 295–306 (2004).
http://dx.doi.org/10.12693/APhysPolA.105.295
[11] G.L. Bir and G.E. Pikus, Symmetry and Strain-Induced
Effects in Semiconductors (Wiley, New York, 1974) Chap. 5
[12] E.O. Kane, The k · p method, in: Semiconductors
and Semimetals, Vol. 1, eds. R.K. Willardson and A.C. Beer (Academic
Press, New York, 1966) p. 75–99
[13] S.L. Chuang and C.S. Chang, k · p method for
strained wurtzite semiconductors, Phys. Rev. B 54(4),
2491–2504 (1996),
http://dx.doi.org/10.1103/PhysRevB.54.2491
[14] G.B. Ren, Y.M. Liu, and P. Blood, Valence-band structure of
wurtzite GaN including the spin–orbit interaction, Appl. Phys. Lett.
74(8), 1117–1119 (1999),
http://dx.doi.org/10.1063/1.123461
[15] D. Fritsch, H. Schmidt, and M. Grundmann, Band-structure
pseudopotential calculation of zinc-blende and wurtzite AlN, GaN,
and InN, Phys. Rev. B 67(23), 235205-1–13 (2003),
http://dx.doi.org/10.1103/PhysRevB.67.235205
[16] M. Tiersten, Acoustic-mode scattering of holes, IBM J. Res.
Develop. 5(April), 122–131 (1961),
http://dx.doi.org/10.1147/rd.52.0122
[17] F. Szmulowicz and F.L. Madarasz, Angular dependence of
hole–acoustic-phonon transitions rates in silicon, Phys. Rev. B 26(4),
2101–2112 (1982),
http://dx.doi.org/10.1103/PhysRevB.26.2101