Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

a rapid growth at low fields, after which it rolls off at f20 T at a value of f0.6,well below complete saturation. At higher fields, the polarization degree doesnot remain constant, but rather continues to increase slowly, reaching f0.73at 60 T. Figure 1c also shows that the PL polarization degree for dark excitonsdrops quickly with increasing temperature, which is similar to the behaviorfor a thermal ensemble of optically active excitons distributed between twoZeeman-split sublevels.The polarization data can be understood in terms of a fine structure ofthe band-edge exciton in above-considered magnetic field. The PL at lowtemperature is due to the radiative recombination of the dark exciton from thetwo F = F2 sublevels that are activated by an external magnetic field [see Eq.(46)]. The polarization degree of PL depends on the relative population ofthese sublevels. The dark excitons with F = F2 obtain the polarizationproperties of the bright excitons with F = F1. In an ensemble of randomlyoriented NCs, all characteristics (Zeeman splitting of the exciton sublevels,the degree of the dark-exciton activation, and the degree of the PL circularpolarization) depend on the angle h H between the NC hexagonal axis andmagnetic field that coincides in this case with the light propagation direction(h = h H ) [see Eqs. (33), (34), (38), and (46)].Within the electric-dipole approximation, the relative probabilities ofdetecting r F light from the F = F2 excitons in NCs with axes oriented atangle h with respect to the field are P F = 2 (r F ) f(1 F cos h) 2 and P F = 2 (r F )f(1 b cos h) 2 . The relative population of the F = F2 exciton states isdetermined by the angular-dependent Zeeman splitting D = g ex,2 l B H cos h[see Eq. (38)]. Assuming the Boltzmann thermal distribution between thesetwo exciton states, we obtain the following expression for the intensity of thedetected PL with r + and r polarizations:I r FðxÞ ¼ ð1bxÞ2 e Db=2 þ ð1FxÞ 2 e Db=2e Db=2 þ e Db=2ð59Þwhere x = cos h and b = (k B T) 1 . Integrating over all orientations andcomputing the PL polarization degree, we obtainPðH; TÞ ¼ 2 m1 0 dx x tanhð0:5g ex;2l B HbxÞð60Þm 1 0dx ð1 þ xÞ2In the limiting case of low temperatures (or high fields) when g ex,2 l B Hb >>1,this polarization P(H, T ) ! 0.75. This is the maximum possible PL polarizationthat can be reached in a system of randomly oriented wurtzite NCs,and it should be noted that the data in Fig. 9c approach this limit at the lowesttemperatures and highest fields.Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.