Angular-dependent magnetoluminescence study of the layer compound2H-PbI2

Abstract

The near-band-gap recombination radiation of the layer compound $2H$-Pb${\mathrm{I}}_2$ is studied in magnetic fields up to 18 T from 1.7 to 40 K. The principal bound exciton (BE) splits anisotropically and shows a small diamagnetic shift in magnetic field. On the basis of these results the binding center of the BE is identified as being a neutral donor. According to the pseudoacceptor model for ($D^0, X$) bound excitons the isotropic $g$ value of the hole, $g_h=-0.4\mathrm{}$, is equal to the $g$ value of the valence band. The diamagnetic shift allows the determination of the free-hole mass to be $m_h=0.195\mathrm{}$ $m_0$. This is the first determination of these band-structure parameters for Pb${\mathrm{I}}_2$, and gives the effective-mass acceptor binding energy $E_A=71\mathrm{}$ meV, which is shown to be at the same time an upper limit for the excitonic binding energy. The anisotropic bound-electron $g$ values are deduced to be $g_{\parallel }=-1.4\mathrm{}$ and $g_{\perp }=-2.1\mathrm{}$. The sign and size of the parameters determined agree well with predictions of band-structure theory. The free exciton shows an angular-dependent shift to lower energy with increasing magnetic field. This is shown to be due to a linear Zeeman splitting of the $A_3^{-}$ exciton state, the upper split level becoming depopulated with magnetic field due to thermalization. Exciton $g$ values $g_{\mathrm{ex}}^{\parallel }=1.0\mathrm{}\pm 0.5$, $g_{\mathrm{ex}}^{\perp }=2.0\mathrm{}\pm 0.5$ are found. From this the free-electron $g$ values are deduced to be $g_{\mathrm{el}}^{\parallel }=1.4\mathrm{}\pm 0.6$, $g_{\mathrm{el}}^{\perp }=2.4\mathrm{}\pm 0.6$. By comparing the spectra obtained at zero magnetic field for $\overrightarrow{\mathrm{k}}$ parallel and perpendicular to $\overrightarrow{\mathrm{c}}$, the splitting of the $A_3^{-}$, $A_2^{-}$ exciton levels is derived to be ≤0.8 meV.