Electron-hole liquid in layered InSe: Comparison of two- and three-dimensional excitonic states

We have studied the photoluminescence (PL) spectra of the layered semiconductor indium selenide in a wide interval of optical excitation density using stationary and pulse pumping in the temperature range 5–100 K. Analysis of the results at the stationary excitation (SE) density $I_{\mathrm{ph}\mathrm{\le }{10}^{17}}$ photons/ ${\mathrm{cm}}^2$ sec allowed us to determine the binding energy of free and bound excitons in InSe. At 5 K we observed a rebuilding of the spontaneous emission spectrum at the SE density $I_{\mathrm{ph}\mathrm{\approxeq }{10}^{19}}$ photons/${\mathrm{cm}}^2$ sec. A new emission line (K) with a maximum at hν=1.32 eV appeared and dominated the spectrum. The K line which arose in a threshold ondensation of a gas of direct excitons to an EHL is not at all energetically favorable for 3D excitons. In practice the same is true also for 2D excitons where the difference between the binding energies of the EHL and the excitonic gas is 1.9 meV at T=0 K. It was established that an EHL can be formed only from indirect excitons in both cases. We have determined values for the binding energy of indirect excitons and the EHL as well as the equilibrium density of e-h pairs in the liquid phase at T=0 K. These values are $E_{\mathrm{ex}=24\mathrm{}}$ meV, $E_L$=33 meV, and $n_L$=4.7×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$ for 3D excitons and $E_{\mathrm{ex}=84\mathrm{}}$ meV, $E_L$=123 meV, and $n_L$=2.1×${10}^{13}$ ${\mathrm{cm}}^{\mathrm{-}2}$ for 2D excitons. Furthermore, we have calculated the shape of the emission line from the EHL in the 3D and 2D indirect excitonic transition cases. Comparing experimental results and computed parameters for layered InSe, we conclude that the K line is due to recombination of e-h pairs in an EHL which is formed by the condensation of 3D indirect excitons.