Optical study on intrinsic exciton states in high-quality ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$ single crystals

Organolead halide perovskites have emerged as potential building blocks for photovoltaic and optoelectronic devices. Yet the underlying fundamental physics is not well understood. There is lack of agreement on the electronic band structures and binding energies of coupled electron-hole pairs (excitons), which drive the photophysical processes. In this work, we conducted temperature-dependent reflectance and photoluminescence experiments on high-quality ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$ single crystals. Two direct optical transitions corresponding to intrinsic free-excitons are clearly resolved, showing excellent consistence between the low-temperature ($T=10$ K) reflectance and photoluminescence spectra. Remarkably, the excitons have different binding energies and behave oppositely with temperature, suggesting distinctive origins. Moreover, the asymmetric photoluminescence profile is counterintuitively dominated by the high-energy exciton that is explained by a long relaxation time between levels and by the favorable generation rate of electron-hole pairs at the high-energy band. Our study opens access to the intrinsic properties of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$ and sheds light to reconcile the large range of binding energies reported on these emergent direct band-gap semiconductors.

Figure 1

Reflectance and PL spectra taken at low temperature ($T=10$ K) on a high-quality ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbBr}}_3$ single crystal. Resonances $A$ ($\sim 2.244\mathrm{eV}$) and $B$ ($\sim 2.280\mathrm{eV}$) are clearly resolved in both reflectance (top black curve) and PL (bottom green curve) spectra. Inset: schematic energy diagram for direct optical transitions associated with intrinsic free excitons $A$ and $B$ given by red and blue arrows, respectively.

Figure 2

(a) Reflectance spectra (blue solid lines) at selected temperatures from 10 K (bottom) to 280 K (top). The green dashed lines are fitting curves using two Lorentz oscillators (see text). The red and blue dotted lines are guidelines. The phase transition occurs at 150 K. The spectra are vertically shifted for clarity. (b) Same as panel (a) for PL spectra.

Figure 3

(a) Resonance energies of free exciton $A$ (red circles) and $B$ (blue squares) versus temperature as extracted from the Lorentz model in Fig. 2. Error bars are comparable to the symbol sizes. (b) Reflectance amplitude of $X_B$ (blue squares) as a function of temperature along with the fitting curve (cyan solid line) by an Arrhenius-like equation (see text). The cartoon illustrates a free exciton, where the distance (black dashed line) between electron (green circle) and hole (pink circle) displays the coupling strength of the exciton at low-temperature (tightly bound electron-hole pair) and high-temperature (weakly bound electron-hole pair) ranges. (c) Reflectance amplitude of $X_A$ versus temperature with the same representation for excitons. The electron-hole pair is tightly bound at all temperatures, except at the phase-transition temperature $T\sim 150$ K. (d) Experimental reflectance at 10 K (blue solid line) along with the fitting curve (pink dotted line) derived from the combination of the Elliot theory and the Kramers-Kronig relationship (see text). (e) Total absorption coefficient as extracted from the model in panel (d) is shown by the pink dotted line. Different contributions include excitonic bands $X_A$ and $X_B$ (shaded area under the red and blue Lorentzian-shaped solid line, respectively) and the corresponding continuum bands $E_A^{\mathrm{b}-\mathrm{b}}$ and $E_B^{\mathrm{b}-\mathrm{b}}$ (areas under dark-orange and dark-blue solid lines, respectively).

Figure 4

(a) PL spectrum at 10 K (blue solid line) along with the fitting curve (green dashed line) using values from the reflectance modeling. The Lorentzian contributions from $X_A$ and $X_B$ to the total PL are represented by shaded red and blue areas, respectively. The intensity ratio is $I_B/I_A=3.2$. (b) Energy splitting ${\mathrm{\Delta }}_{BA}$ between excitonic levels $B$ and $A$ (green triangles) as a function of temperature. The orange solid line is a phenomenological linear fitting. (c) Schematic representation of free-exciton bands $A$ and $B$. The symbols are used in the kinetic three-level model (see text).