Determination of the exciton binding energy and effective masses for the methylammonium and formamidinium lead tri-halide perovskite family (1511.06507v1)

Abstract: The family of organic-inorganic halide perovskite materials has generated tremendous interest in the field of photovoltaics due to their high power conversion efficiencies. There has been intensive development of cells based on the archetypal methylammonium (MA)and recently introduced formamidinium (FA) materials, however, there is still considerable controversy over their fundamental electronic properties. Two of the most important parameters are the binding energy of the exciton (R$^{*}$) and its reduced effective mass $\mu$. Here we present extensive magneto optical studies of Cl assisted grown MAPbI${3}$ as well as MAPbBr${3}$ and the FA based materials FAPbI${3}$ and FAPbBr${3}$. We fit the excitonic states as a hydrogenic atom in magnetic field and the Landau levels for free carriers to give R$^{*}$ and $\mu$. The values of the exciton binding energy are in the range 14 - 25 meV in the low temperature phase and fall considerably at higher temperatures for the tri-iodides, consistent with free carrier behaviour in all devices made from these materials. Both R$^{*}$ and $\mu$ increase approximately proportionally to the band gap, and the mass values, 0.09-0.117 m$_{0}$, are consistent with a simple \textbf{k.p} perturbation approach to the band structure which can be generalized to predict values for the effective mass and binding energy for other members of this perovskite family of materials.

• The paper determines exciton binding energies and effective masses in MA and FA perovskites using magneto-optical methods, revealing their key correlation with the band gap.
• The study finds binding energies between 14 and 25 meV and effective masses from 0.09 to 0.117 m₀, confirming predictions from hydrogenic and k.p models.
• The paper concludes that similar optoelectronic properties of MA and FA perovskites suggest potential material interchangeability to optimize photovoltaic device performance.

Overview of Exciton Binding Energy and Effective Mass Determination in Lead Tri-Halide Perovskites

The paper, authored by Galkowski and colleagues, provides a pivotal exploration into the exciton binding energy and effective masses characteristic of methylammonium (MA) and formamidinium (FA) lead tri-halide perovskite materials, with a focus on their implications for photovoltaic applications. The emergent family of organic-inorganic halide perovskites has seen significant advancements in solar cell efficiencies, primarily driven by materials such as MAPbI$_{3}$, achieving efficiencies over 20%. However, there remains ongoing debate over their fundamental optoelectronic properties, crucial for the optimization and innovation of photovoltaic technologies.

Research Methodology

To elucidate these properties, the authors conducted magneto-optical studies on a variety of perovskite samples, including MAPbI$_{3}$, MAPbBr$_{3}$, FAPbI$_{3}$, and FAPbBr$_{3}$. By modeling excitonic transitions using hydrogen-like models in the presence of a magnetic field, the researchers derived values for exciton binding energy ($R^{*}$) and reduced effective mass ($\mu$). Key results indicated that exciton binding energies are situated in the range of 14 - 25 meV at low temperatures, with a marked decrease at higher temperatures. Importantly, both $R^{*}$ and $\mu$ demonstrated a proportional increase with the band gap, with effective mass values ranging from 0.09-0.117 $m_0$, aligning with predictions from a k.p perturbation approach.

Key Findings

1. Exciton Binding Energy and Effective Mass: The research identified crucial correlations between these parameters and the bandgap, with reduced masses ($\mu$) of the order of 0.09 to 0.117 $m_0$, consistent with theoretical predictions derived from density functional theory and semi-empirical k.p models.
2. Band Gap Dependence: The paper highlights a clear dependence of both exciton binding energy and reduced mass on the band gap. The implications are that perovskites with larger band gaps maintain small exciton effective masses, essential for high-efficiency solar cells.
3. Material Interchangeability: A noteworthy conclusion is the similarity between materials using different cations (MA and FA), suggesting potential interchangeability without significant modifications to band structure, which is advantageous for device stability and performance.

Implications and Future Directions

The findings implicate a broader understanding of perovskite materials, facilitating the design and optimization of photovoltaic cells and potentially extending to other optoelectronic applications such as tandem PV cells, LEDs, and lasers. The suggested interchangeability between MA and FA materials could broaden the material palette for future device innovations. The results further propose that these materials, characterized by their small exciton binding energies relative to thermal energy at ambient conditions, will likely exhibit rapid excitonic ionization, pertinent for solar cell efficiencies.

Future research could expand on exploring temperature-dependent behaviors and extend the magneto-optical assessment to a more varied palette of perovskite compositions. Such studies would not only solidify the current understanding of charge carrier dynamics but also enhance predictive models that guide the synthesis of next-generation perovskite materials with tailored optoelectronic properties.