Magnetoluminescence and magnetoreflectance of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>exciton of CdS and CdSe

Abstract

Magnetoluminescence and magnetoreflectance have been measured on the $A$ exciton of CdS and CdSe in magnetic fields up to 12 T. In the case of CdS, we get the following results: For $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ the luminescence line at 2.553 eV, attributed to the ${\ensuremath{\Gamma}}_{6}$ triplet state splits into two components giving a $g$ factor $|{g}_{h\ensuremath{\parallel}}+{g}_{e\ensuremath{\parallel}}|=3.02\ifmmode\pm\else\textpm\fi{}0.10$. From the directly measured difference between ${\ensuremath{\sigma}}^{\ensuremath{-}}$ and ${\ensuremath{\sigma}}^{+}$ polarized light the $g$ factor of the ${\ensuremath{\Gamma}}_{5}$ singlet state is determined as ${g}_{h\ensuremath{\parallel}}\ensuremath{-}{g}_{e\ensuremath{\parallel}}=\ensuremath{-}0.56\ifmmode\pm\else\textpm\fi{}0.05$, and thus we derive the electron and hole $g$ values ${g}_{e\ensuremath{\parallel}}=+1.79\ifmmode\pm\else\textpm\fi{}0.10$ and ${g}_{h\ensuremath{\parallel}}=+1.23\ifmmode\pm\else\textpm\fi{}0.10$. In luminescence with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ polarization and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ a narrow line emerges with increasing magnetic field at energies below the ${\ensuremath{\Gamma}}_{5}$ luminescence peak. The additional line is attributed to the low-energy component of the ${\ensuremath{\Gamma}}_{6}$ triplet state. The most prominent feature of the magnetoreflectance spectra is the appearance of an additional reflectance structure below the main reflectance minimum for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$. This structure is attributed to the triplet state becoming observable due to magnetic-field-induced mixing between the ${\ensuremath{\Gamma}}_{5}$ and ${\ensuremath{\Gamma}}_{6}$ states of the $A$ exciton. From the diamagnetic shift of the ${\ensuremath{\Gamma}}_{6}$ state for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ we derive ${\ensuremath{\mu}}_{x}=0.16$, while ${\ensuremath{\mu}}_{z}={0.18}_{5}$ is obtained from the diamagnetic shift for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$. In the case of CdSe we derive from magnetoluminescence the $g$ value of the $A$ exciton $|{g}_{h\ensuremath{\parallel}}\ensuremath{-}{g}_{e\ensuremath{\parallel}}|=1.76\ifmmode\pm\else\textpm\fi{}0.20$. The magnetoreflectance spectra exhibit a corresponding splitting. The diamagnetic shift of the exciton structure yields reduced exciton masses ${\ensuremath{\mu}}_{x}=0.096\ifmmode\pm\else\textpm\fi{}0.01$ and ${\ensuremath{\mu}}_{z}=0.112\ifmmode\pm\else\textpm\fi{}0.010$. Mixing between the ${\ensuremath{\Gamma}}_{6}$ triplet and dipole allowed states is much less pronounced for CdSe than for CdS.