The electronic structure and optical properties of freestanding GaN wurtzite
quantum wires are studied in the framework of six-band effective-mass envelope
function theory. It is found that the electron states are either twofold
or fourfold degenerate. There is a dark exciton effect when the radius
R
of GaN wurtzite quantum wires is in the range of [0.7, 10.9] nm. The linear polarization factors
are calculated in three cases, the quantum confinement effect (finite long wire), the dielectric
effect and both effects (infinitely long wire). It is found that the linear polarization factor of a
finite long wire whose length is much less than the electromagnetic wavelength decreases as
R increases, is very close
to unity (0.979) at R = 1 nm, and changes from a positive value to a negative value around
R = 4.1 nm. The linear polarization factor of the dielectric effect is 0.934, independent of radius, as
long as the radius remains much less than the electromagnetic wavelength. The result for
the two effects shows that the quantum confinement effect gives a correction to the
dielectric effect result. It is found that the linear polarization factor of very long (treated
approximately as infinitely long) quantum wires is in the range of [0.8, 1]. The linear
polarization factors of the quantum confinement effect of CdSe wurtzite quantum wires are
calculated for comparison. In the CdSe case, the linear polarization factor of
R = 1 nm is 0.857, in agreement with the experimental results (Hu et al 2001
Science292 2060). This value is much smaller than unity, unlike 0.979
in the GaN case, mainly due to the big spin–orbit splitting energy
Δso
of CdSe material with wurtzite structure.