Hybrid perovskites have emerged as a remarkable class of semiconducting materials due to their unique electronic and optoelectronic properties. Their band structure and optical characteristics are central to their performance in various applications, making a fundamental understanding of these properties essential. This article explores the electronic band structure, carrier dynamics, and optical behavior of hybrid perovskites, with a focus on how compositional tuning influences these properties.

The electronic band structure of hybrid perovskites is primarily determined by the arrangement of inorganic octahedra and the organic cations in their crystal lattice. The most studied hybrid perovskites, such as methylammonium lead iodide (MAPbI3), exhibit a direct bandgap at the gamma point in the Brillouin zone. This direct bandgap nature is advantageous for optoelectronic applications because it allows efficient radiative recombination of electrons and holes. The valence band maximum is composed of antibonding states from lead 6s and iodine 5p orbitals, while the conduction band minimum arises from lead 6p orbitals. The strong spin-orbit coupling in heavy elements like lead further splits the conduction band, reducing the bandgap compared to what would be expected without spin-orbit effects.

The bandgap of hybrid perovskites is highly tunable through compositional engineering. For instance, replacing iodine with bromine in MAPbI3-xBrx increases the bandgap due to the higher electronegativity and smaller atomic radius of bromine, which raises the conduction band minimum. Similarly, substituting lead with tin can reduce the bandgap, as seen in MASnI3, where the bandgap decreases to around 1.3 eV compared to 1.6 eV for MAPbI3. The bandgap can also be adjusted by varying the organic cation, such as switching from methylammonium to formamidinium, which stabilizes the perovskite structure and slightly reduces the bandgap.

Carrier effective masses in hybrid perovskites are relatively low, contributing to their excellent charge transport properties. The electron effective mass in MAPbI3 is approximately 0.2-0.3 times the free electron mass, while the hole effective mass is slightly higher, around 0.3-0.4 times the free electron mass. These low effective masses result from the dispersive nature of the conduction and valence bands, enabling high carrier mobilities. The balanced electron and hole effective masses also reduce the likelihood of charge carrier trapping, which is beneficial for optoelectronic applications.

Exciton binding energy is another critical parameter in hybrid perovskites. Due to their high dielectric constant and low effective masses, exciton binding energies are typically small, ranging from 2 to 50 meV, depending on the composition and temperature. This low binding energy means that excitons readily dissociate into free carriers at room temperature, which is advantageous for photovoltaic applications where efficient charge separation is required. The exciton binding energy can be further reduced by increasing the dielectric screening through compositional modifications, such as mixing halides or introducing larger organic cations.

The absorption characteristics of hybrid perovskites are dominated by their direct bandgap, leading to strong optical absorption near the band edge. MAPbI3 exhibits an absorption coefficient on the order of 10^5 cm^-1 at energies just above its bandgap, making it highly efficient at capturing light. The absorption edge can be shifted systematically by varying the halide composition. For example, MAPbBr3 has a higher bandgap than MAPbI3, resulting in a blue-shifted absorption edge, while MAPbCl3 shows an even larger blue shift. Mixed halide perovskites, such as MAPbI3-xBrx, allow for continuous tuning of the absorption edge across the visible spectrum.

Photoluminescence (PL) in hybrid perovskites is typically characterized by a narrow emission peak near the bandgap energy, reflecting their direct bandgap nature. The PL quantum yield can be very high, often exceeding 80% in high-quality single crystals and thin films, indicating minimal non-radiative recombination pathways. The emission wavelength can be precisely controlled through halide mixing, enabling color-tunable light emission. However, phase segregation in mixed halide perovskites under illumination can lead to spectral instability, where the PL peak shifts over time due to halide migration. This phenomenon is an active area of research to improve material stability.

Temperature and pressure also significantly influence the optoelectronic properties of hybrid perovskites. At low temperatures, the bandgap of MAPbI3 increases due to reduced lattice vibrations and electron-phonon interactions. Applying hydrostatic pressure can similarly modify the bandgap by altering the bond lengths and angles in the inorganic framework. These effects provide additional knobs for tuning the material properties but must be carefully controlled to avoid phase transitions or degradation.

The unique combination of tunable bandgap, low effective masses, and high absorption coefficients makes hybrid perovskites highly versatile for optoelectronic applications. Their electronic and optical properties can be systematically engineered through compositional adjustments, offering a powerful platform for designing materials with tailored characteristics. Future research will likely focus on further understanding and controlling the stability and defect physics of these materials to fully exploit their potential.